ISSN:0308-6003    

DOI:10.1039/PR97471FX001

出版商:RSC    

年代:1974

数据来源: RSC

ISSN:0308-6003    

DOI:10.1039/PR97471BX003

出版商:RSC    

年代:1974

数据来源: RSC

摘要:

2 Ab initio Calculations on Small Molecules and Potential Energy Surfaces By C. THOMSON Department of Chemistry University of St. Andrews St. Andrews KY16 9ST Glossary of Abbreviations CGTO contracted gaussian- type orbitals DZ(+P) double zeta (+polarization) FSGO floating spherical gaussian orbitals GTO gaussian type orbitals GVB generalized valence bond H-F Hartree-Fock HFPD Hartree-Fock with proper dissociation ICSCF internally consistent self-consistent field IEPA independent electron pair approximation MCSCF multi-configuration self-consistent field ovc optimized valence configuration RHF restricted Hartree-Fock SCF self-consistent field S(T)O Slater (type) orbital UHF unrestricted Hartree-Fock 1 Introduction Recent developments in quantum chemistry with particular emphasis on the theoretical methods which are currently in use were reported by Duke in 1971,’ but there has not been a detailed report of recent work on small molecules for several years although some work was reported in 1970.2 The present review is restricted to a discussion of ab initio calculations on small molecules and the ab initio investigation of potential energy (P.E.)surfaces involving such species.It should be emphasized that this review deals primarily with investigations which seem to the author to be particularly interesting to the non-specialist in theoretical chemistry. A more detailed review of the recent work in theoretical chemistry is to be found in two recent Specialist Periodical report^.^,^ B.J. Duke Ann. Reports (A) 1971 68 3. E. Steiner Ann. Reports (A) 1970 67 5. ‘Theoretical Chemistry’ ed. R. N. Dixon (Specialist Periodical Reports) The Chemical Society London 1974 Vol. 1. ‘Theoretical Chemistry’ ed. R. N. Dixon and C. Thomson (Specialist Periodical Reports) The Chemical Society London 1975 Vol. 2. 5 C. Thomson Results of calculations are quoted in atomic units which are used by the majority of theoretical chemists and also in the Specialist Periodical report^.^?^ In these units energy values (E) are in hartree (1 hartree = 27.210 eV = 4.36 x lo'* J) and distances are in bohr (1 bohr = 0.529 A = 5.2918 x lo-'' m). A number of recent books and review articles have dealt with various aspects of ab initio calculations and the books by Schaefer5 and Cook6 provide excellent introductions for the non-specialist.A comprehensive bibliography by Richards et al.' has recently been updated. Reviews of recent work on diatomic species are provided by Wahl' and Goodisman.' Browne and Matsen" have reviewed recent work on three- and four-electron molecules and the proceedings of two recent conferences which have appeared in book forrn"*l2 deal with many different aspects of ab initio work. Other general reviews are cited in Ref. 4. Section 2 deals with ab initio investigations of small molecules containing up to four atoms and Section 3 with ab initio investigations of P.E. surfaces. Cal- culations on large organic molecules were reviewed last year by Clark l and are also reviewed in ref.4 by Duke. The ab initio calculations discussed here involve the solution of the non- relativistic Schrodinger equation assuming the Born-Oppenheimer approxima- tion. Calculations on a few molecules removing this approximation have been reviewed el~ewhere.~ The various methods used to obtain approximate solu- tions to Schrodinger's equation have been discussed by Duke' and no radically new methods have appeared since that report. The total energy the orbital energy and the wavefunction and properties computed from it are the main molecular quantities discussed here. 2 Ab initio Calculations on Diatomic Molecules Investigations on diatomic species AH A, and AB have involved two main areas firstly the testing of new computational methods and secondly the exten- sion of calculations on several familiar molecules to their excited states H,.-There have been several investigations on H, and one of particular interest is the direct calculation of the Brueckner orbitals.' A single-determinant wave- function constructed from these orbitals has maximum overlap with the exact H.F. Schaefer tert. 'Electronic Structure of Atoms and Molecules' Addison Wesley Boston 1972. D. B. Cook 'Ab-Initio Valence Calculations in Chemistry' Wiley London 1974. ' W. G. Richards T. E. H. Walker and R. Hinkley 'Bibliography of ab-initio molecular wave functions' O.U.P. 197 1 Supplement 1974. A. C. Wahl in 'Theoretical Chemistry' ed. W. Byers Brown MTP International Review of Science Physical Chemistry Series 1 1972 Vol.1. J. Goodisman 'Diatomic Interaction Potential Theory Vol. l' Academic Press New York 1972. lo J. C. Browne and F. A. Matsen Adu. Chem. Phys. 1973 23 161. l1 'Energy Structure and Reactivity' ed. D. W. Smith and W. B. McRae John Wiley New York 1973. 'Computational methods for large molecules and localized states in solids' ed. F. Herman A. D. McLean and R. K. Nesbet Plenum Press New York 1973. D. T. Clark Ann. Reports (B) 1972 69 40. l4 V. Staemmler and M. Jungen Theor. Chim. Acta 1972 24 152. Calculations on Small Molecules 7 wavefunctions. Such a function is particularly suitable for the study of correla- tion effects in molecules. For the H ground state this wavefunction gave more reliable values for one-electron properties than the SCF wavefunction and also gave reliable P.E.curves. Recent work on H using Boys' transcorrelated wavefunction meth~d'~,'~ has been reported by Handy.I7 In this method a single-configuration Slater deter- minant @ is multiplied by a specific correlation factor C of the form for n electrons and sincefcan depend on rij,Boys showed that using the operator C-'HC very accurate wavefunctions can be obtained without the n4 integral problem which occurs in conventional methods. The early calculations on He Be Ne and LiH'5*16 gave the most accurate wavefunctions to date for these species but the integrals were evaluated numerically. Handy' has recently shown how these can be evaluated analytically in terms of a gaussian basis set. Even with a small basis set the correlation energy (E,) obtained was impres- sive; for LiH 92% of E was obtained; for H,O 70%.The extension of this method to larger molecules may not be easy but if possible it promises reliable values of E with less computational effort than for example conventional con- figuration interaction (CI) calculations. One problem with this method is the difficulty compared with conventional variational methods of evaluating expectation values a point emphasized by Armour.'8i1 Although nuclear spin-spin coupling constants JAB are readily obtained from n.m.r. spectra their evaluation theoretically has proved difficult because of the necessity of including the excited states which are involved in the equation for JAB. A recent calculation2' of JHD in HD has shown that if the zeroth order wavefunction is correlated (via a large CI calculation) and all singly- or doubly- excited triplets included in the first-order correction the computed value of JHD of 43.48 Hz is in good agreement with the experimental value of 42.94 & 0.1 Hz.It should be possible to extend the method to larger systems and further applications should be most interesting. A variety of excited states of H have been studied using various methods and these are discussed in ref. 4. Among these,21 the use of the generalized valence bond (GVB) method by Goddard and co-workers (which has been reviewed is of particular interest. We return to this method later. The thermodynamic properties of H2 have been computed by Kosloff et al.from ab initio wavef~nctions.~~ Is S. F. Boys and N. C. Handy Proc. Roy. SOC. 1969 A309,209; A310,43,63. l6 S. F. Boys and N. C. Handy Proc. Roy. SOC. 1969 A311 309. N. C. Handy Mol. Phys. 1972 23 1. E. A. G. Armour Mol. Phys. 1973 25 993. l9 E. A. G. Armour Mol. Phys. 1973 26 1093. *O J. Kowalewski B. Roos P. Siegbahn and R. Vestin Chem. Phys. 1974 3 70. " D. L. Huestis and W. A. Goddard tert. Chem. Phys. Letters 1972 16 157. '' W. A. Goddard tert. T. H. Dunning jun. W. J. Hunt and P. J. Hay Accounts Chem. Res. 1973 6 383. 23 R.Kosloff R.D. Levine and R. B. Bernstein Mof. Phys. 1974 27 981. 8 C. Thomson Diatomic Hydrides.-Recent calculations have focused attention on various excited states with the wavefunctions being evaluated in extensive CI calculations.Docken and in two important papers have examined the P.E. curves for five valence excited states of LiH by the MCSCF method. Using a large STO basis set the computed dissociation energy of the ground state was only 0.003 hartree less than experiment. Computed P.E. curves and one-electron proper- ties are in reasonable agreement with experimental data where these are available. LiH has also been extensively studied by the GVB method developed by Goddard and co-workers.22 This method employs a single-determinant wave- function with singly occupied orbitals i.e. different spatial orbitals for different spins and can correctly describe molecular dissociation. A number of variants have been described26 which differ primarily in the spin-coupling schemes.Very interesting discussions of the bonding in various small molecules using this method have been described and reviewed,22726 and applications to both ground and excited states of LiH reported. Its relation to other methods has been discussed.26d The original VB method has also been applied recently to several first-row hydrides by Gallup and co-worker~.~~ The IEPA method is based on Sinan6glu's many-electron theory2* and has been used with some success recently to study electron correlation in a variety of first-row hydrides including LiH.29*30 Calculations beyond H-F on LiH and other hydrides are neither easy nor inexpensive and are thus not readily applicable to larger molecules. Therefore attempts to obtain the correlation energy semi-empirically are of considerable interest and two recent papers by Lie and Clementi are of particular impor- tan~e.~~,~~ The authors compute E in terms of a functional of the Hartree-Fock density E = 0.0209q1.2 + pi)-'p;dv + jO.02096 In(1 + 2.39pi)pmdv (2) I where p = Cnip; iii = n,exp [-042 -r~,)~] (3) I n is the orbital occupation number.This form ensures that the computed and experimental atomic correlation energies agree for first-row atoms and is 24 K. K. Docken and J. Hinze J. Chem. Phys. 1972,57,4928. " K. K. Docken and J. Hinze J. Chem. Phys. 1972 57 4936. 26 (a)W. A. Goddard tert. Phys. Rev. 1967 157,81; (b)W. E. Palke and W. A. Goddard tert. J. Chem. Phys. 1969 50 4524; (c) W. A. Goddard tert.and R. C. Ladner J. Amer. Chem. SOC.,1971 93 6750; (d) W. J. Hunt P. J. Hay and W. A. Goddard tert. J. Chem. Phys. 1972,57 738; (e)R. C. Ladner and W.A. Goddard tert. J. Chem. Phys. 1969 51 1073. 27 G. A. Gallup Internat. J. Quantum Chem. 1972,6 899; G. A. Gallup Adu. Quantum Chem. 1973 7 I1 3; J. M. Norbeck and G. A. Gallup Internat. J. Quantum Chem. 1973 IS 161. 0.Sinandglu Adv. Chem. Phys. 1964 6 315; 1969 14 237. *' R. Ahlrichs and W. Kutzelnigg J. Chem. Phys. 1968,48 1819. 30 M. Jungen and R. Ahlrichs Theor. Chim. Acta 1970 17 339. 31 G. C. Lie and E. Clementi J. Chem. Phys. 1974,60 1275. 32 G. C. Lie and E. Clementi J. Chem. Phys. 1974,60 1288. Calculations on Small Molecules 9 subsequently used to calculate E in hydrides from H-F values of p or from MCSCF calculations in which enough Slater determinants were included to ensure the correct dissociation behaviour for the wavefunction.The latter wave- functions are referred to as HFPD (Hartree-Fock with proper dissociation). The computed value of the binding energy was much improved together with the varia- tion along the series and spectroscopic constants were also significantly better. Extensions to large molecules should be much easier than direct calculations of E ,since H-F calculations on large molecules are becoming increasingly reliable.4 Calculations on other hydrides using conventional CI have also been reported of particular note being a very extensive study of the P.E. curves of BeH (A2nand X2C+)by Bagus et Agreement with experiment was excellent but it was pointed out that with less than complete CI there can be spurious maxima in the curves.BH has been extensively studied by Csizmadia’s group,34*35 both the ground and five excited singlet states using average natural orbitals and extensive CI. Results were in good agreement with experiment. (Table 1 compares the Table 1 Calculated energies and spectroscopic constants of BH/a.u. Method E D re we(x lo2) Re& H-F -25.13 15 0.102 2.268 1.140 a VB -25.1454 0.110 2.527 1.258 b -VB -25.1453 0.107 2.536 C -SO-GVB -25.1664 0.121 2.360 d bet he-Goldstone -25.1723 0.169 2.331 1.139 e CI -25.1797 0.120 2.412 0.984 b Separated pair -25.2054 0.142 2.343 1.324 f CI -25.2150 0.131 2.357 1.259 g Experimental -25.289 0.131 2.336 1.078 h (a)P.E. Cade and W. M. Huo J. Chem. Phys. 1967 47,614. (6)J. C. Browne and E. M. Greenwalt Chem. Phys. Letters 1970 7 363. (c)J. F. Harrison and L. C. Suen J. Mol. Spectroscopy 1969 29 432. (d)R. J. Blint W. A. Goddard tert. R. C. Ladner and W. E. Palke Chem. Phys. Letters 1970,5 302. (e)G. A. Van der Velde and W. C. Nieuw- poort Chem. Phvs. Letters 1972 13 409. (f)E. L. Mehler K. Ruedenberg and D. M. Silver J. Chem. Phys. 1970 52 1181. (g) S. A. Houlden and I. G. Csizmadia Theor. Chim. Acta 1974 35 173. (h)J. W. C. Johns F. A. Grimm and R. F. Porter J. Mol. Spectroscopy 1967 22 435. results of recent work on BH.) Mehler has also used a new method similar to IEPA to study correlation effects in BH and BH+.36 Goddard and co-workers have discussed in considerable detail GVB calculations on LiH26 and BH3’ and 33 P.S. Bagus C. M. Moser P. Goethals and G. Verhaegen J. Chem. Phys. 1973 58 1886. 34 S. A. Houlden and I. G. Csizmadia Theor. Chim. Acta 1973 30,209. 35 S. A. Houlden and I. G. Csizmadia Theor. Chim. Acta 1974 35 173. 36 E. L. Mehler Theor. Chim. Acta 1974 35 17. 37 C. F. Melius and W. A. Goddard tert. J. Chem. Phys. 1972,56 3348; R. J. Blint and W. A. Goddard tert. J. Chem. Phys. 1972,57,5296; W. J. Hunt P. J. Hay and W. A. Goddard tert. J. Chem. Phys. 1972 57 738; W. A. Goddard tert and R. J. Blint Chem. Phys. Letters 1972 14 616; R. J. Blint and W. A. Goddard tert. Chem. Phys. 1974 3 297. 10 C. Thomson their various excited states with particular emphasis on the electron distribution.Rydberg states have been studied by M~lliken.~~ Schaefer’s first-order wave- function method’*39 has also been applied to this species.40 The important molecules CH41 and CH’ 42 have been studied using large basis sets and exten- sive CI. The GVB orbital description of the CH molecule is ill~minating.~~ In contrast to most workers Tantardini and Sim~netta~~ have reported minimal basis conventional VB calculations with surprisingly good results. The FSGO method has been applied to a variety of diatomic specie^.^' The species NH NH+ and OH have all been studied in detail especially NH for which various CI wavefunctions were reported,46 and also MCSCF calcula- tion~:~ the latter giving impressive agreement with the experimental values of the spectroscopic constants.The P.E. curves of the OH radical were investi- gated by Bondybey et al.48 with first-order wavefunctions whilst MCSCF calculations were reported by Karo et Goddard and co-workers have also investigated OH by the GVB procedure.” The problem of the accurate calculation ofdipole moments has been thoroughly reviewed by Green who investigated OH and OD5 among other diatomics and concluded that an accuracy of kO.06 D is currently feasible. OH-has been studied by the IEPA method by Lishka.” Both the theoretical P.E. curves4’ and the theoretical dipole moment function have been computed for HF the latter from MCSCF calculation^.^^ A comparison of minimal basis MO and perfect pairing wavefunctions for HF has appeareds4 and also a careful eight-con- figuration MCSCF study.55 Various calculations on hydrides containing elements below the first row have appeared.SiH has been studied using CI by Wir~am,~~ NeH and NeH’ by Bondybey et al.?* and TiH by Scott and Richardss7 who obtained approximate SCF wavefunctions and predict a ‘@ ground state. A very detailed study of MnH 3* R. S. Mulliken Internat. J. Quantum Chem. 1971 3 83. 39 H. F. Schaefer tert. J. Chem. Phys. 1971 54 2207. 40 P. K. Pearson C. F. Bender and H. F. Schaefer tert. J. Chem. Phys. 1971,554235. 41 G. C. Lie J. Hinze and B. Liu J. Chem. Phys. 1972 57 625 (this paper contains extensive references to earlier work); 1973 59 1872 1887. 42 S. Green P. S. Bagus B. Liu A.D. McLean and M. Yoshimine Phys. Rev. 1972 AS 1614; M. Yoshimine S. Green and P. Thadeus Astrophys. J. 1973. 183 899. 43 P. J. Hay W. J. Hunt and W. A. Goddard tert. J. Amer. Chem. Soc. 1972 94 8293. 44 G. F. Tantardini and M. Simonetta Chem. Phys. Letters 1972 14 170. 45 P. H. Blustin and J. W. Linnett J.C.S. Faraday If 1974 70 327 826. 46 S. V. O’Neil and H. F. Schaefer tert. J. Chem. Phys. 1971 55 394. 47 W. J. Stevens J. Chem. Phys. 1973,58 1264; G. Das and A. C. Wahl J. Chem. Phys. 1972,56 1769; G. Das A. C. Wahl and W. J. Stevens J. Chem. Phys. 1974 61,433. 48 V. Bondybey P. K. Pearson and H. F. Schaefer tert. J. Chem. Phys. 1972 72 1123. 49 A. M. Karo M. Krauss and A. C. Wahl Internaf.J. Quantum Chem. 1973 7S 143. S. L. Guberman and W. A.Goddard tert. J. Chem. Phys. 1970 53 1803. 51 S. Green J. Chem. Phys. 1973,58 4327; S. Green Adv. Chem. Phys. 1974 25 179. 52 H. Lishka Theor. Chim. Acta 1973 31 39. 53 G. C. Lie J. Chem. Phys. 1974 60 2991. 54 R. E. Bruce K. A. R. Mitchell and M. L. Williams Chern. Phys. Letters 1973 23 504. 55 M. Krauss and D. Neumann Mol. Phys. 1974 27 917. s6 B. Wirsam Chem. Phys. Letters 1971 10 180. ’’ P. R. Scott and W. G. Richards J. Phys. (B) 1974 7 500. Calculations on Smll Molecules 11 by Bagus et al.shows the utility of SCF calculations for these species.58 Bausch- licher and Schaefer5’ have examined the basis orbitals to be used in such calcula- tions and concluded that the use of fully contracted gaussian orbitals (CGTO) for inner shells is permissible.Extensive CI calculations on HCl with different basis sets have been reported by Petke and Whitten.60 However even a 206 configuration wavefunction only recovered ca. 4% of E,. The inclusion of C13d functions improved E and also the molecular properties. Homonuclear Diatomic Species.-These molecules continue to be studied at various levels of approximation. Possibly the most significant new paper is the extension by Clementi and Lie of their semi-empirical calculations of E referred to above to these molecules.32 The same density functional was used and HFPD wavefunctions were evaluated followed by E,. In this case however rather more care has to be taken in the choice of the reference function if the same degree of accuracy is to be achieved as for AH.However the success in these papers for this approach suggests that extensions to larger molecules will be fruitful. Goddard and co-workers61 have studied Li and Li,’ using GVB wave- functions and a near H-F calculation on Li,’ has also been reported.62 C and C -have been studied by Barsuhn using a GTO lobe basis set and CI.63 Predic- tions as to hitherto unobserved states of the latter were made. Mulliken has reported an interesting investigation of the correlation diagram of N using optimized SCF wavefunctions over a large range of internuclear distances.64 There are several interesting features of these diagrams which are not expected from purely qualitative discussions. A number of other more specialized calculations on N are discussed in ref.4. The most extensive calcula- tion yet published on N is that by Langhoff and Da~idson~~ who in an extensive CI calculation obtained ca. 63% of E, carrying out the calculation in terms of both ICSCF66 and canonical orbitals. Schaefer has studied 0 using first-order wavefunctions with 128 configura-tion~.~~ The computed dissociation energy was 4.27 eV (experiment = 5.21 eV). The GVB method both with and without CI has also been applied to 0,.68 A recent calculation of the Rydberg states6’ has used a modified Hamiltonian” which improves the virtual orbitals so that they are better approximations to excited-state orbitals with results in good agreement with experiment. Various ’* P. S. Bagus and H. F. Schaefer tert. J. Chem. Phys. 1973 58 1844.59 C. W. Baushlicher jun. and H. F. Schaefer tert. Chem. Phys. Letters 1974 24 412. 6o J. D. Petke and J. L. Whitten J. Chem. Phys. 1972 56 830. 61 W. A. Goddard tert. J. Chem. Phys. 1968 48 1008 5337. 62 G. A. Henderson W. T. Zemke and A. C. Wahl J. Chem. Phys. 1973 58 2654. 63 J. Barsuhn 2. Naturforsch. 1972 27a 1031; J. Phys. (B) 1974 7 155. 64 R. S. Mulliken Chem. Phys. Letters 1972 14 137. 65 S. R.Langhoff and E R. Davidson Internat. J. Quantum Chem. 1974 8 61. 66 E. R. Davidson J. Chem. Phys. 1972,57 1999. 67 H. F. Schaefer tert. J. Chem. Phys. 1971 54 2207. 6a W. J. Hunt P. J. Hay and W. A. Goddard tert. J. Chem. Phys. 1972 57 538. 69 D. C. Cartwright W. J. Hunt W. Williams S. Trajmar and W. A. Goddard tert. Phys. Rev. 1973,8A 2436.70 W. J. Hunt and W. A. Goddard tert. Chem. Phys. Letters 1969 6 414. 12 C. Thomson excited states of 0,have been studied by Mor~kuma,~’ and a detailed study of the fine structure has appeared,72 using CI wavefunctions and a variety of basis sets. About two-thirds of the observed splitting is ascribed to spin-orbit effects. Photoelectron spectral measurements have prompted near H-F calculations on the 1s hole states of 02+.73 Agreement with experiment was found only if the restriction of the MO symmetry to g or u was lifted corresponding to the singly occupied 1s orbital being localized on one of the two 0 atoms. The electron affinity of 0 has been estimated from OVC calculations on 02-,with the computed value close to e~periment.~~ The MCSCF (OVC) method has been much used for the study of F, and recent work has been re~iewed.~.~’ The ground and excited states have been studied including CI by both VB and MO rnethod~.’~ Studies on molecules containing second-row atoms of this type have been few in number but several calculations on Ne have been published.77 Na has been studied at the MCSCF and also the P.E.curve of C1 ,using a VB-CI wavefun~tion.’~ The calculated D was however only ca. 29% of the experi- mental value and very little improved over the H-F value. An interesting and detailed comparison of the bonding in P and N has been reported by Mulliken and Liu who found near H-F wavefunctions and examined the influence of 3d orbitals on the bonding.80 Heteronuclear Diatomic Species-There have been several calculations on diatomics containing rare-gas atoms.Details of calculations of interaction energies for relatively unstable species can be found in ref. 4. A particularly interesting recent calculation is a near H-F study of KrF and KrF+.8’ Only the latter gave a non-repulsive P.E. curve with D,= 0.07 hartree and Re = 3.3 bohr. More recently the P.E. curves for XeF (’C’ and ,lI)were com- puted,82 and only a weak Van der Waals interaction was predicted. This result is not consistent with interpretations of several experimental studies. 71 K. Morukuma and H. Kohnishi J. Chem. Phys. 1971,55 402. ’* S. R. Langhoff J. Chem. Phys. 1974,61 1708. 73 P. S. Bagus and H. F. Schaefer tert. J. Chem. Phys. 1972 56 224. 74 W.T. Zemke G. Das and A. C. Wahl Chem. Phys. Letters 1972 14 310; M. Krauss D. Neumann A. C. Wahl G. Das and W. Zemke Phys. Reu. 1973 7A 69. 75 G. Das and A. C. Wahl J. Chem. Phys. 1972 56 1769. ’6 E. Kasseckert Z. Naturforsch. 1973 28a 704. 77 A. Conway and J. N. Murrell Mol. Phys. 1974 27 873; G. Starkschall and R. G. Gordon J. Chem. Phys. 1971,56,2801; E. Kochanski Chem. Phys. Letters 1974 25 380; W. J. Stevens A. C. Wahl M. A. Gardner and A. M. Karo J. Chem. Phys. 1974,60 2195. 78 A. M. Karo M. Krauss and A. C. Wahl Internat. J. Quantum Chem. 1973 7S 143. 79 T. G. Heil S. V. O’Neil and H. F. Schaefer tert. Chem. Phys. Letters 1970 5 253. 8o R. S. Mulliken and B. Liu J. Amer. Chem. Soc. 1971 93 6738. 81 B. Liu and H. F. Schaefer tert. J. Chem. Phys.1971 55 2369; P. S. Bagus B. Liu and H. F. Schaefer tert. J. Amer. Chem. Soc. 1972 94 6635. 82 D. H. Liskow H. F. Schaefer tert. P. S. Bagus and B. Liu J. Amer. Chem. SOC.,1973 95,4056. Calculationson Small Molecules 13 There have been several calculations on the alkali oxides. An extensive study of Li0,83 both SCF and CI gave results in good agreement with experiment. A later papers4 reported results on A10 and reviewed the computation of spectro- scopic band intensities. Several excited states of A10 and A10' were also studied by Schampss5 and by Wahl and co-workers,86 who also investigated NaO and its ions.87 Experimental uncertainty as to the ground-state configuration of alkaline-earth oxides has resulted in several calculations on these species.Several papers on various states of Be0 have appeared the ground state being X'C+.88 H-F calculations on MgO predict a 311ground state; however since the order of the 311and 'Z' states of Be0 is interchanged when CI is included the MgO ground- state question is still not completely resol~ed.~~~~~ Most ab initio calculations neglect relativistic effects but for high atomic numbers relativistic energies are large. A minimal basis calculation on the 90-electron Pb0,9 'and comparison of the valence-shell electronic structure with that of CO have been carried out. The errors in D,and in spectroscopic constants at this level are comparable hence relativistic effects may be neglected without sizeable errors in chemically interesting properties.A near H-F calculation of the low-lying states of FeO has appeared,92 and also the results of a limited CI treatment on various states. The lowest 'C+ state was subjected to extensive CI but it was concluded that this state is not the ground state. Recent calculations on CO have focused attention on the excited states but a very large CI study of the ground state obtained ca. 70% of Ec.93 MCSCF calculations have been reported of the quadruple moments of CO N, and NO+ with reasonable agreement with e~periment.~~ It was emphasized that correla- tion must be included in order to obtain reliable values. The accurate calcula- tion of dipole moments for CO and CS has been reviewed by Green9' who describes his extensive studies on this subject.96 The P.E.curves for 72 excited states of SiO have been reported by Heil and S~haefer,~' who used a full CI and a minimal basis set. Such calculations have been reviewed by S~haefer,~ and they seem to give reliable results for this type 83 M. Yoshimine J. Chem. Phys. 1972 57 1108. 84 M. Yoshimine A. D. McLean and B. Liu J. Chem. Phys. 1973,58 4412. 85 J. Schamps Chem. Phys. 1973 2 352. 86 G. Das T. Janis and A. C. Wahl J. Chem. Phys. 1974 61 1274. '' P. A. G. O'Hare and A. C. Wahl J. Chem. Phys. 1972,56,4516. H. F. Schaefer tert. J. Chem. Phys. 1971 55 176; S. V. O'Neil P. K. Pearson and H. F. Schaefer tert. Chem. Phys. Lerters 1971 10 404; P. K. Pearson S. V. O'Neil and H. F. Schaefer tert. J. Chem. Phys. 1972 56 3938. 89 J. Schamps and H. Lefebvre-Brion J.Chem. Phys. 1972 56 573. 90 N. J. Staggand W. G. Richards Mol. Phys. 1974 27 787. 91 G. M. Schwenzer D. H. Liskow H. F. Schaefer tert. P. S. Bagus B. Liu A. D. McLean and M. Yoshimine J. Chem. Phys. 1973 58 3181. yL P. S. Bagus and H. J. T. Preston J. Chem. Phys. 1973,59 2986. 93 A. K. Q. Siu and E. R. Davidson Internat. J. Quantum Chem. 1970 4 223. 94 F. P. Billingsley and M. Krauss J. Chem. Phys. 1974 6Q,2767. 95 S. Green Ado. Chem. Phys. 1974,25 179. 96 S. Green J. Chem. Phys. 1970,52 3100; 1971,54 827; 1972,56 729; 1972 57 2830. 97 T. G. Heil and H. F. Schaefer tert. J. Chem. Phys. 1972 56 958. C. Thomson of problem. The predictions as to the order of the states should be useful for interpreting spectroscopic data. Several papers have dealt with NO NO+ and NO-(see ref.4 for details). The most recent CI study by Thulstrup et aLg8has compared theoretical values with a variety of experimental results. Green has computed CI wavefunctions and spin densities for the 'C' state.99 Mulliken and LiuB0 have obtained SCF wavefunctions for PO and more extensive CI calculations of the P.E. curves for a variety of excited states have been reported by Tseng and Grein,' O0 and also by Roche and Lefebvre-Brion.' O' Calculations on C10 and FO and their ions at the near H-F'''*lo3 level gave results in good agreement with the relatively sparse experimental data. Diatomic metal halide molecules have been studied by various experimental techniques and there have been several theoretical studies of these.One interest- ing paper dealt with the study of the effect of the basis set on the charge distribu- tion for LiF.lo4 It is again noted that minimal basis sets tend to give unrealistic charge distributions. In recent years some of the computational problems which have hampered VB calculations have been solved and among recent work with this method we note in particular an investigation of TiF3 +.'05 However a pseudo-potential ap- proach to the core-electrons was adopted. CF and its ions have been studied in detail with the dipole moment predicted in the sense C-F+.lo6 It is thought unlikely that the sign is incorrect but MCSCF calculations are needed. Calculations on several excited states were reported with a different basis set,'" and these authors also obtained the same sign for the dipole moment of the ground state.SiF and its ions have also been studied by Wahl et a1.,'06.'08and also NF and PF and their ions.'" Beyond H-F calculations (minimal basis -full CI) on NF and NF+ by Anderson et a!. gave significantly different results from the SCF calculation.' ' Other fluorides studied by Wahl et al. were SF SeF and AsF.' ' '-' ' A large number of states of CN have been studied by O'Neil and Schaefer1l4 and also by Das et aLB6 98 P. W. Thulstrup E. W. Thulstrup A. Anderson and Y. Ohrn J. Chem. Phys. 1974 60 3975. 99 S. Green Chem. Phys. Letters 1972 13 552; 1973 23 115. loo T. J. Tseng and F. Grein J. Chem. Phys. 1973,59 6563. lol A. L. Roche and H. Lefebvre-Brion J. Chem. Phys.1973,59 1914. lo2 P. A. G. O'Hare and A. C. Wahl J. Chem. Phys. 1970 53 2469. lo3 P. A. G. O'Hare and A. C. Wahl J. Chem. Phys. 1971 54 3770. lo4 J. E. Williams and A. Streitweiser jun. Chem. Phys. Letters 1974 25 507. lo5 P. J. Carrington and P. G. Walton Mol. Phys. 1973 26 705. Io6 P. A. G. O'Hare and A. C. Wahl J. Chem. Phys. 1971 55 666. lo' J. A. Hall and W. G. Richards Mol. Phys. 1972 23 331. Io8 P. A. G. O'Hare J. Chem. Phys. 1973.59 3842. lo9 P. A. G. O'Hare and A. C. Wahl J Chem. Phys. 1971,54,4563. lo A. Anderson and Y.Ohrm J. Mol. Spectroscopy 1973 45 358. ''I P. A. G. O'Hare and A. C. Wahl J. Chem. Phys. 1970,53 2834. IL2 P. A. G. O'Hare J. Chem. Phys. 1974 60 4084. P. A. G. O'Hare A. Batana and A. C. Wahl J. Chem. Phys. 1973 59 6495.l4 T. G. O'Neil and H. F. Schaefer tert. J. Chem. Phys. 1971 54 2573. Calculations on Small Molecules 15 Agreement between the two sets of calculations was good although many more configurations are needed in the case of the conventional CI calculation. NS and BC are other diatomic open-shell species which have been studied recently."5."6 A number of calculations on interhalogens such as ClF have been discussed elsewhere the most extensive work being a DZ + P study of many of these species including a DZ basis set calculation on IBr.' ' 3 Ab initio Calculations on Triatomic Molecules The past two years have seen a large increase in the number of ab initio calcula-tions on triatomic molecules particularly potential energy surface calculations (see below).As in Section 2 we will discuss only a few representative examples of such calculations. Hydrides AH .-Calculations on linear BeH including correlation by the IEPA method have been reported by Ahlrichs and Kutzelnigg.' '' There have also been several VB calculations"g~'20 and a comparison of both MO and VB Calculations.' The most extensive study to date is the large CI calculation of Hosteny and Hagstrom'22 who obtained ca. 55 % of E, using an STO basis set. LiH has been investigated by Goddard et al. using the GVB method. Several authors have investigated the stability of species containing rare-gas atoms. KrF has been extensively studied,'23.' 24 the most accurate wave-function being obtained by Bagus et ul.' 24 from a CI calculation.Only if CI is included is the molecule predicted to be found but the computed D is only ca. 1/3 of the experimental value. Electron correlation effects were shown to be very important. XeF has also been studied at the SCF The dihalide ions HX,-(X = halogen) have been studied extensively experi- mentally and Almlof'25 has performed near H-F calculations on HF,- which is predicted to be symmetrical. This species was also studied by Noble and Kortzeborn.' 26 Both Janoschek'" and Thomson et u1.12* have investigated CIHCI- the latter paper showing that this species should be bound but the P. A. G. O'Hare J. Chem. Phys. 1971,54,4124. l6 J. E. Kouba and Y. ohrn J. Chem. Phys. 1970,53 3923. l" P. A. Straub and A. D. McLean Theor. Chim. Acta 1972 32 227.11' R. Ahlrichs and W. Kutzelnigg Theor. Chim. Acra 1968 10 377. l9 R. G. A. R.Maclagan and G. W. Schnuelle J. Chem. Phys. 1971,55 5431. lZo G. A. Gallup and J. M. Norbeck Chem. Phys. Lerrers 1973 21 495. lZ1 K. A. R. Mitchell and T. Thirunamachandran Mol. Phys. 1972 23 947. '*' R. P. Hosteny and S. A. Hagstrom J. Chem. Phys. 1973,58,4396. l2 G. A. D. Collins D. W. J. Cruickshank and A. Breeze Chem. Comm. 1970,884; J.C.S. Faraday II 1974 70 393. 124 P. S. Bagus B. Liu and H. F.Schaefer tert. J. Amer. Chem. Soc. 1972 94 6635. 12' J. Almlof Chem. Phys. Letters 1972 17 49. P. N. Noble and R. N. Kortzeborn J. Chem. Phys. 1970 52 5375. R. Janoschek Theor. Chim. Acta 1973 29 57. C. Thomson D. A. Clark and T. Waddington to be published. 16 C.Thomson radical HC1 is probably not bound. An SCF study of OH03- has also been reported.' 29 An interesting recent study of HCN and HNC including extensive CI was carried out in order to see if HNC could be responsible for a radio frequency galactic emi~sion.'~' Computation of the known geometry of HCN enabled the authors to predict confidently the geometry and B of HNC. The authors conclude that the emitter could be HNC. An extensive study of a large number of excited states of HCN has given useful criteria for describing these excited states in MO terms and examination of 12 low-lying states showed that the experimental assignment of the B'A" state is probably incorrect.' 31 The isoelectronic molecules HBS'32 and HCP' 33,134 have been the subject of near H-F calculations.A large number of one-electron proper tie^'^^ were computed and compared with recent experimental data. HCC' 35 and HBO' 36 are two other examples of unstable species recently investigated by SCF calcula- tions. It should be emphasized that accurate SCF calculations on unstable intermediates can yield reliable information on geometry and one-electron properties which is not readily accessible experimentally. CO has been studied many times in the but only recently have exten- sive calculations on the excited states appeared. Using a DZ + P GTO basis set open-shell SCF calculations on 13 excited states were reported by Winter et ~1.'~'and used in interpreting experimental spectra. The molecules Li,O and A1,O are both predicted to be linear in SCF calculation^,'^^ a result in disagree- ment with semi-empirical work.Li20 has been the subject of separated-electron pair type calculations.' 39 OCC and TiCO are both unstable species and Thomson and Wishart have studied the former,' 40 predicting the equilibrium geometry in near H-F calcula- tions. Goddard and M~rtola'~' obtained GVB wavefunctions for TiCO and TiCO+ and gave a useful discussion of carbonyl bonding in the light of their calculations. H. Blum R. Frey H. S. H. Gunthard and T.-K. Ha. Chem. Phys. 1973 2 262. 130 P. K. Pearson G. L. Blackman H. F. Schaefer tert. B. Rees and U. Wahlgren Astrophys. J. 1973 184 L19. 131 G. M. Schwenzer S. V. O'Neil H. F. Schaefer tert. C. P. Baskin and C. F. Bender J.Chem. Phys. 1974,60 2787. 13' C. Thomson Theor. Chim. Acta 1974 35 237. 133 J. B. Robert H. Marsmann I. Absar and J. R. Van Wazer J. Amer. Chem. SOC.,1971 93 3320. 134 C. Thomson Chem. Phys. Letters 1974 25 59. 13' J. Barsuhn Astruphys. Letters 1972 12 169. 136 C. Thomson and B. J. Wishart Theor. Chim. Acta 1974 35 267. 13' N. W. Winter C. F. Bender and W. A. Goddard tert. Chem. Phys. Letters 1973 20 489. 13* E. L. Wagner Theor. Chim. Acta 1974 32 296. 139 T. K. Liu and D. D. Ebbing Internat. J. Quantum Chem. 1972 6 297. I4O C. Thomson and B. J. Wishart Theor. Chim. Acta 1973 31 347. 141 A. P. Mortola and W. A. Goddard tert. J. Amer. Chem. SOC. 1974 96,1. Calculations on Small Molecules 17 A very extensive set of calculations on various linear molecules containing B N and C has been reported by Th~mson'~~ which show that BNC BCC and BCB are predicted to be more stable than their isomers The results on BCC are consistent with the e.s.r.description as a a-radical. A similar study of NCN NNC CNC and CCN14' gave results in reasonable agreement with experimental data. One important conclusion from these calcula- tions carried out with various STO basis sets was that discussions of the bonding and charge distribution using the Mulliken population analyses can lead to quite wrong conclusions unless basis sets of at least DZ + P quality are used for the calculations. The spin-spin interaction in NCN CNN and OCC has been computed by Williams,'44 with results which were not in particularly good agreement with experiment.There have been many interesting studies of non-linear species. H3+ has been extensively studied and most recently the excited states have been investigated using a large CI.'45 Handy has suggested a new form for the correlation factor and studied H3+ with this method.'46 Although Walsh's rules predict BeH2+ to be linear both SCF and VB-CI calculations'47 show the ground state to be an electrostatically bound complex with 2Al symmetry and LHBeH = 20". BH has been thoroughly studied by Bender and S~haefer,'~~ and by Goddard et and most recently by Staemmler and Jungen' 50 who in IEPA calculations computed a large number of properties for both the 2Al and 2B states. Jungen has also studied BH +.l5 ' Walsh's rules have been reviewed by Buenker et and further studied by Stenkamp and Davidson.' 53 The power of ab initio calculations is well illustrated by several calculations on CH ,where theory firmly predicts a bond angle of CQ.134",and this has led to a revision of the earlier experimental value.'54 Details of earlier work are to be found in the recent papers by Bender et a1.l 55 There have also been several VB 142 C. Thomson J. Chem. Phys. 1973,58 216. 143 C. Thomson J. Chem. Phys.. 1973 58 841. 144 G. R. Williams Chem. Phys. Letters 1974 25 602. 14' L. J. Schaad and W. V. Hicks J. Chem. Phys. 1974,61 1934. 146 N. C. Handy Mol. Phys. 1973 26 169. 14' R. D. Poshusta D. W. Klint and A. Liberles J. Chem. Phys. 1971 55 252. 14* C. F. Bender and H.F. Schaefer tert. J. Mol. Spectroscopy 1971 37 423. 149 W. A. Goddard tert. and R. J. Blint Chem. Phys. Letters 1972 14 616. "O V. Staemmler and M. Jungen Chem. Phys. Letters 1972 16 187. M. Jungen Chem. Phys. Letters 1970 5 241. R. J. Buenker and S. D. Peyerimhoff Chem. Reo. 1974,74 127. L. Z. Stenkamp and E. R. Davidson Theor. Chim. Acta 1973,30 283. Is* W. A. Lathan W. Hehre and J. A. Pople J. Amer. Chem. SOC.,1971 93 808; W. A. Lathan W. Hehre L. A. Curtis and J. A. Pople J. Amer. Chem. SOC.,1971.93 6377; J. del Bene Chem. Phys. Letters 1971 9 68; S. V. O'Neil H. F. Schaefer tert. and C. F. Bender J. Chem. Phys. 1971,55 162. Is' D. R. McLaughlin C. F. Bender and H. F. Schaefer tert. Theor. Chim. Acra 1972 25 362; C. F. Bender H. F. Schaefer tert.D. R. Franceschetti and L. C. Allen J. Amer. Chem. SOC.,1972 94 6888; J. F. Harrison and L. C. Allen J. Amer. Chem. Soc. 1969 91 807; J. F. Harrison J. Amer. Chem. Soc. 1971 93 4112; G. F. Tantar-dini M. Raimondi and M. Simonetta Internat. J. Quantum Chem. 1973 7 893; P. J. Hay W. J. Hunt and W. A. Goddard tert. Chem. Phys. Letters 1972 13 30. 18 C.Thomson calculations on this molecule and also GVB calculations.' '' Calculations on the excited and in particular the magnitude of AE('A -3B,) have shown that inclusion of electron correlation is of crucial importance. The most extensive calculations give AE = 0.014 & 0.004hartree. A large number of molecular properties were computed by Staemmler'" and the most extensive CI calculation was used to obtain the spin-spin splitting parameters.' 58 The most recent calculations on NH including CI oia first-order wavefunc- tions gave useful information on various states of this m~lecule.''~ NH2+ has also been carefully studied recently.156,160 Of particular note is the predicted AE( 'A -3B1),which is about twice as large as in CH2. Brown and Williams'6'9'62 have used the unrestricted Hartree-Fock (UHF) method to study a large number of triatomic radicals including NH . The 2B2 state was predicted to have LHNH = 26.6",and Thomson and Br~tchie'~~ in near H-F calculations confirm this. However this state is unbound and seems to correspond to H + N*. Some analogous states of BF are bound (see below). Brown et a/.16'have also computed spin-dependent properties from their wave- functions.Minimal basis sets were used throughout. The water molecule is of paramount importance and a very near H-F calcula- tion investigated a large number of ground-state properties. 164 An alternative method has been used by Thomsen and Swanstr~m.'~' VB calculations have also been reported and most recently electron correlation has been included in some detail for details we refer the reader to ref. 4. The most accurate wave- function currently available is due to Meyer'66 and the results were discussed by Schaefer.' About 85% of E was obtained. A large number of papers have dealt with the excited states and ref. 167 cites other recent work. H20+ and H2S+ have also been studied re~ent1y.l~~ H,F+ has only recently been observed and the optimum geometry has been computed by Diercksen et Lishka' and Leib~vici'~' have also studied S.Y. Chu A. K. Q. Siu and E. F. Hayes J. Amer. Chem. SOC.,1972 94 2969. 57 V. Staemmler Theor. Chim. Acta 1973 31,49. J. F. Harrison J. Chem. Phys. 1971 54 5413; S. R. Langhoff and E. R. Davidson Internat. J. Quantum Chem. 1973 7 759; J. F. Harrison and R. C. Liedtke J. Chem. Phys. 1973,58 3106. 159 C. F. Bender and H. F. Schaefer tert. J. Chem. Phys. 1971 55 4798. 160 J. F. Harrison and C. W. Eakers J. Amer. Chem. SOC.,1973 95 3467. 16' R. D. Brown and G. R. Williams Chem. Phys. 1974,3 19. 162 R. D. Brown and G. R. Williams Mof. Phys. 1973 25 673. C. Thomson and D. A. Brotchie Mof. Phys. 1974 28 301. 164 T. H. Dunning jun. R.M. Pitzer and S. Aung J. Chem. Phys. 1972 57 5044. 16' K. Thomsen and P. Swanstrom Mof.Phys. 1973 26 735 751. 166 W. Meyer Internat. J. Quantum Chem. 1971 55 341. 16' W. A. Goddard tert. and W. J. Hunt Chem. Phys. Letters 1974 24 464. 16' H. Sakai S. Yanabe T. Yanabe K. Fukui and N. Kato Chem. Phys. Letters 1974 25 541. 169 G. H. F. Diercksen W. von Niessen and W. P. Kraemer Theor. Chim. Acta 1973 31 205. ''lo C. Leibovici Internat. J. Quantum Chem. 1974 8 193. Calculations on Small Molecules 19 this species. There have also been recent calculations on H2S17' and H2Si," the latter calculations including the excited states. Hydrides HAB.-The HO radical has for many years been postulated as an important intermediate but only recently has its geometry been definitely estab- lished via accurate cal~ulations,'~~ which show R(0-H) = 1.84 bohr R(0-0) = 2.70bohr LHOO = 104.6".Gole and Hayes also studied the excited 'A" and ,A' HCO has been investigated recently using near H-F wavefunctions'75 and also by the UHF method.' 76 Thomson and Brotchie' 75 computed isotropic hyper- fine coupling constants and Botschwima' 76 force constants for this molecule. HCO' has also been studied using extensive CI (6343 configurations) how-ever although this molecule has been suggested as the species responsible for an observed astrophysical emission line this has also been attributed to HCC.'35 Clearly more work is needed on this problem. HNF and HBF are related to NH and NF and BH and BF and have been studied by Brotchie and Th~mson'~' and by Brown,16' using different methods.Some low-lying excited states were also investigated. Calculations on HNO and on HON using small GTO basis sets enabled Peslak et al. to compute electron density maps.'79 CHF CHF+ and NHF+ are related molecules studied by Harrison.'60 HCF' 79~180and HOCl' 81 have been investigated with rather small basis sets. AB Molecules.-This type of molecule with many more electrons presents a greater computational problem and most studies have been of SCF wavefunc- tions relatively few however being close to the H-F limit. Ozone 0,,is described rather poorly at the SCF level and extensive CI calcula-tions have been reported by Heaton et UI.''~ and by Goddard (GVB-CI).'83 Various other excited-state calculations have been reported and more extensive discussion is to be found elsewhere (ref.4). 171 S. Rothenberg R. H. Young and H. F. Schaefer tert. J. Amer. Chem. SOC.,1970 92 3243; B. Roos and P. Siegbahn Theor. Chim. Acta 1971 21 368. 172 B. Wirsam Chem. Phys. Letters 1972 14 214. 173 D. H. Liskow H. F. Schaefer tert. and C. F. Bender J. Amer. Chem. SOC.,1971 93 6734. J. L. Gole and E. F. Hayes J. Chem. Phys. 1972,57 360. 175 C. Thomson and D. A. Brotchie Internat. J. Quantum Chem. 1974 SS,277. 176 P. Botschwina Chem. Phys. Letters 1974 29 98. 177 U. Wahlgren B. Liu P. K. Pearson and H. F. Schaefer tert. Nature Phys. Sci. 1973 246,4. 17' D. A. Brotchie and C. Thomson Chem. Phys. Letters 1973 22 338. J. Peslak jun. D. S.Klett and C. W. David J. Amer. Chem. Soc. 1971 93 5001. *' H. Kim and J. R. Sabin Chem. Phys. Letters 1973,20,215; T.-K. Ha J. Mol. Structure 1973 18 486; D. P. Chong F. G. Herring and D. McWilliams Chem. Phys. Letters 1974 25 568. G. L. Bendazzoli D. G. Lister and P. Palmieri J.C.S. Faraday ZZ 1973 69 791. M. H. Heaton A. Pipano and J. J. Kaufman Internat. J. Quantum Chem. 1972 6S 181. ln3P. J. Hay and W. A. Goddard tert. Chem. Phys. Letters 1972 14 46; P. J. Hay T. H. Dunning jun. and W. A. Goddard tert. Chem. Phys. Letters 1973 23 457. W. R.Wadt and W. A. Goddard tert. J. Amer. Chem. SOC.,1974 96 1689. 20 C. Thomson LiO has an isosceles triangle ground state (,A,) but a similar shape (,B,) is close in energy.'84 A mixed basis set method has been tested on Li02.'85 The excited states of NO have been studied by Hay,'86 and the NO,' ground state in SCF calculations by Cremashi et ~1.~~' McCain and Palke investigated a large number of triatomic radicals and their isotropic and anisotropic hyperfine coupling constants in a minimal basis STO-SCF study.'88 SO and SiF are isoelectronic but near H-F calculations on both species show that d-orbital participation in the bonding is substantially less in SiF,' 89 than in SO .190 Unless large basis sets are used for this type of species too large d-orbital populations are often obtained.Wirsam has also studied SiF, includ- ing CI in the cal~ulations.'~' The series BeF ,BF ,CF ,NF ,and OF are all known and a comparison of similar quality (DZ + P basis) SCF calculations and computed properties has appeared.192 Thomson and Brotchie have also carefully studied BF par-ticularly the equilibrium geometry of X2A (LFBF = 120°) and the A2Bl ,A, and ,B1 excited states the latter with minimal GTO basis sets.Hyperfine coupling constants for B are reasonably well reproduced for the RHF wave- functions but those for F are a factor of two too small. The ,B state also has an acute angle but is predicted to be bound.194 NF was also studied by the same authors and by Brown and Williams.'95 Better agreement was obtained for the coupling constants when d-orbital opti- mization was carried out by Hinchcliffe and C~bb.'~~ There have been several calculations on difluorides of Group IIA elements and Coulson has reviewed the bond angles in these molecules.197 BeF and MgF are linear in the ground state but the energy required to deform the molecules is The excited states of EkF and MgF have also been studied.'99 The Walsh energy diagram for ZnF has been investigated theoreti- cally by Yarkony and Schaefer.'" S.V. O'Neil H. F. Schaefer tert. and C. F. Bender J. Chem. Phys. 1973 59 3608. la' F. P. Billingsley and C. Trindle J. Phys. Chem. 1972 76 2995. lS6 P. J. Hay J. Chem. Phys. 1973,58 4706. P. Cremaschi and M. Simonetta Theor. Chim. Acta 1974 34 175. D. C. McCain and W. E. Palke J. Chem. Phys. 1972,56 4957. C. Thomson Theo?. Chim. Acta 1973 32 93. 190 B. Roos and P. Siegbahn Theor. Chim. Acta 1971 21 368; P. D. Dacre and M. Elder ibid. 1972 25 254.19' B. Wirsam Chem. Phys. Letters 1973 22 360. 19' S. Rothenberg and H. F. Schaefer tert. J. Amer. Chem. SOC.,1973 95 2095. 193 C. Thomson and D. A. Brotchie Chem. Phys. Letters 1972 16 573; Theor. Chim. Acta 1973 32 101. 194 C. Thomson and D. A. Brotchie Mol. Phys. 1974,28 301. 19' R. D. Brown F. R.Burden B. T. Hart and G. R. Williams Theor. Chim. Acta 1973 28 399. 196 A. Hinchcliffe and J. C. Cobb Chem. Phys. 1974 3 271. 19' C. A. Coulson Israel J. Chem. 1973 11 683. 19' J. L. Gole A. K. Q. Siu and E. F. Hayes J. Chem. Phys. 1973 58 857. 199 J. L. Gole J. Chem. Phys, 1973 58 869. D. R.Yarkony and H. F. Schaefer tert. Chem. Phys. Letters 1973 15 514. Calculations on Small Molecules 21 Reference 4 gives more examples of this type of molecule and we mention finally calculations on PF ,20' and a large calculation on SC1 ,where d-functions were shown to be more important on S than on C1.202 ABC Molecules.-We have already mentioned the TiCO calculations.141 LiON and LiNO and FNO and FON were studied with a small basis set by Peslak et ~1."~ Minimal basis calculations on NSF have been reported,,' and more recently a large DZ basis calculation on NSF and SS0,204with particular refer- ence to the interpretation of photoelectron spectroscopy measurements. A series of more extensive calculations on FNO by Pulay and co-workers showed that force constants can be reliably obtained using even a (5s2p)Gaussian basis set.205 4 Ab initiu Investigationson Tetra-atomic Molecules The past two years have seen a considerable number of increasingly accurate calculations on these molecules especially including correlation.Hydrides AH,.-The question of the stability of HeH,+ is not yet resolved despite fairly extensive CI calculations by Benson and McLaughlin?O6 since the more accurate calculations predict it to be unbound whereas VB-C1207 predicts a weakly bound species. The dimerization energy of BH3 has been extensively investigated by IEPA calculations and predicted to be 0.057 hartree.," The equilibrium geometry and force constants have also been computed.209 Other work on BH has appeared.21 There have been several recent studies on CH, culminating in a very large basis set calculation of the optimum geometry.21 ' Kohnishi and Morukuma'" have thoroughly investigated the hyperfine coupling constants in CH using various CI wavefunctions and IEPA calculations have also been rep~rted.~' The ions CH,- and CH,' have also been studied the former which is pyramidal being investigated with respect to the inversion barrier.The origin of the barrier has been ascribed to polarization function influence and correlation effects by different authors." ,v2l4 201 J. C. Cobb and A. Hinchcliffe Chem. Phys. Letters 1974 24 75. 202 B. Solouki. P. Rosmus and H. Bock Chem. Phys. Letters 1974 26 20. 203 R. L. Dekock D. Lloyd A. Breeze G. A. D. Collins D. W. J. Cruickshank and H. J. Lempka Chem. Phys. Letters 1972 14 525. 204 P. Rosmus P. D. Dacre B. Solouki and H. Bock Theor. Chim. Acta 1974 35 129.205 W. Sawodny and P. Pulay J. Mol. Spectroscopy 1974 51 135. 206 M. J. Benson and D. R. McLaughlin J. Chem. Phys. 1973.56 1322. 20' R. D. Poshusta and V. P. Agrawal J. Chem. Phys. 1973,59,2477. M. Gelus A. Ahlrichs and W. Kutzelnigg Chem. Phys. Letters 1971 7 503. *09 M. Gelus and W. Kutzelnigg Theor. Chim. Acta 1973 28 103. M. E. Schwartz and L. C. Allen J. Amer. Chem. SOC.,1970,92 1466; J. Paldus J. Cizek and I. Shavitt Phys. Rev. 1972 SA,. 50. l R. E. Kari and I. G. Csizmadia Internat. J. Quantum Chem. 1972,6 401. 212 H. Kohnishi and K. Morukuma J. Amer. Chem. SOC.,1972 94 5603. '13 F. Driessler R. Ahlrichs V. Staemmler and W. Kutzelnigg Theor. Chim. Acta 1973 30,315. 214 A. J. Duke Chem. Phys. Letters 1973 21 275. 22 C. Thomson Several investigations of NH and PH have appeared.A large STO basis near H-F calculation reproduced the barrier and Laws et al. have computed a large number of one-electron Pulay and Meyer2I7 have evaluated the force constants for a variety of basis sets. An alternative set of d-functions has been used by Gerloff et ~1.~'~ Dejardin and co-workers have carried out MCSCF calculations including 51configurations and have analysed the resulting wavefunctions.2'9~220 Localized orbitals have been obtained by Wilhite and Whitten from both SCF and CI wavefunctions and these authors have also compared NH and PH3.221*222 The influence of &orbitals on the angle is much less in NH, although they are important in the a-bonding. Lehn and Munschz2 have investigated PH using a variety of basis sets.Bond functions have been shown to be an efficient means of introducing polarization into the basis set by calculations on H20 NH, H202 and N2H4 .224 There have been various investigations on H30+ and once again it was shown that polarization functions have to be included in the basis set to obtain a pyramidal structure.225 The inversion barrier was predicted to be only ca. 0.003hartree. Lishka and Dyczmons226 in an IEPA calculation however obtained a barrier substantially larger (ca.0.005 hartree). Among second-row hydrides some calculations on PH have already been mentioned and SiH and its ions have been investigated in both ground and Aarons et al. have studied a variety of similar excited states by Wir~am.~~' open-shell species including SiH .228 AB Molecules.-BF and BCl have been further studied,229 as has CF3,212 which like CCl is For ACl molecules relatively small basis sets have to be used but SiF and SiCl both turn out to be pyramidal.230 Several other calculations are discussed in ref.4. Finally we note a rather large calcula- tion on FeF in which the deficiencies of small basis set calculations are pointed out.231 It should thus be emphasized that ab initio calculations on large molecules must employ reasonably sized basis sets and the usefulness of isolated minimal basis set calculations is questionable. 2*J R. M. Stevens J. Chem. Phys. 1971 55 1725. 216 E. A. Laws R. M. Stevens and W. N. Lipscomb J. Chem. Phys. 1972 56 2029. 217 P.Pulay and W. Meyer J. Chem. Phys. 1972,57 3337. 218 M. Gerloff E. Ady and J. Brickmann Mol. Phys. 1973 26 561. 219 P. Dejardin E. Kochanski and A. Veillard Chem. Phys. Letters 1972 15 248. 220 P. Dejardin E. Kochanski A. Veillard B. Roos,and P. Siegbahn J. Chem. Phys. 1973,59 5546. 221 D. L. Wilhite and J. L. Whitten J. Chem. Phys. 1973 58 948. 222 J. D. Petke and J. L. Whitten J. Chem. Phys. 1973 59 4855. 223 J. M. Lehn and B. Munsch Mol. Phys. 1972 23 91. 224 J. 0.Jarvie A. Rauk and C. Edmiston Canad. J. Chem. 1974,52 2778. 225 P. A. Kollman and C. F. Bender Chem. Phys. Letters 1973 21 271. 226 H. Lishka and V. Dyczmons Chem. Phys. Letters 1973 23 167. 227 B. Wirsam Chem. Phys. Letters 1973 18 578. 22* L. J. Aarons I. H. Hillier and M. F. Guest J.C.S.Furaday II 1974 70 167. 229 D. Goutier and L. A. Burnelle Chem. Phys. Letters 1973 18 460. 230 M.F. Guest I. H. Hillier and V. R. Saunders J.C.S. Faraday II 1972 68 867. z3' R. W. Land J. W. Hunt and H. F. Schaefer tert. J. Amer. Chem. SOC.,1973 95 4517. Calculations on Small Molecules 23 MiscellaneousTetra-atomicMol~ule~.-H4 is dealt with below. Both N4and P4 have been investigated by Hillier’s and P by Brundle et al.233 As expected N is not stable although P is predicted to be. An extensive investigation of basis set dependence has been reported in the case of H202234and the results have been compared with Veillard’s earlier calculations.235 H,S has also been N,H is usually assumed to have a ‘A ground state. However Wagniere found the A state to be lower in energy,237 but the geometry was not optimized in this work.The correlation energy in C,H has been investigated by Duben et al.,238and SCF calculations on Si,H2 have been reported by Wir~am.~~’ Among the relatively few A,B molecules studied we may note a study of the possible forms of F2C2,240 where the acetylene was shown to be more stable. Both C20 and C202+ are bound C,O having a 3C.-ground state.241 Various AB-AB dimers have been discussed el~ewhere.~ Formaldehyde continues to receive much attention from theoreticians. A good account of the electronic spectrum is given by SCF-CI calculations,242 but the ‘A m* state energy has been in dispute. A recent calculation using the MCSCF procedure puts the state 0.41 hartree above the ground state.243 H,CS has also been recently in~estigated.~, Space does not permit mention of other work on tetra-atomic species and we refer the reader to ref.4 for a more ex- tensive discussion. 5 Ab ikitio Calculations of Potential Energy Surfaces Several of the papers referred to above have dealt with this problem and a very thorough and comprehensive review by Bader and Gangi in ref. 4 contains a detailed discussion of work up to mid-1974. In this section discussion is restricted to a few representative calculations which represent the state of the art in this field. Calculations of the total energy of a polyatomic molecule or molecules as 32 M. F. Guest I. H. Hillier and V. R. Saunders J.C.S. Furuday 11 1972 68 2070. 233 C. R. Brundle N.A. Kuebler M. B. Robin and H. Basch Znorg. Chem. 1972 11 20. 234 J. P. Ranck and H. Johansen Theor. Chim. Acta 1972 24 334. 235 A. Veillard Theor. Chim. Acta 1970 18 21; A. Veillard and H. Demuynck Chem. Phys. Letters 1970 4 476. 236 M.Schwartz J. Chem. Phys. 1969 51,4182. 23’ G. Wagniere Theor. Chim. Acta 1973 31 269. 238 A. 1Duben L. Goodman H. 0. Pamuk and 0.Sinanaglu Theor. Chim. Actu 1973 30,177; S. Y. Chu I. Ozkan and L. Goodman J. Chem. Phys. 1974 60,1268. 239 B. Wirsam Theor. Chim. Acta 1972 25 169. 240 0.P. Strausz R.Norstrom A. C. Hopkinson M. Schoenborn and I. G. Csizmadia Theor. Chim. Acta 1973 29 183. 241 N. F. Beebe and J. R. Sabin Chem. Phys. Letters 1973 24 389. 242 R. J. Buenker and S. D. Peyerimhoff J. Chem. Phys. 1970,53,1368; S.D. Peyerimhoff, R. J. Buenker W. F. Kammer and H. Hsu Chem. Phys. Letters 1971 8 129; J. L. Whitten J. Chem. Phys. 1972 56 5458; W. H. Fink J. Amer. Chem. Soc. 1972 94 1073 1078; D. M.Hayes and K. Morukuma Chem. Phys. Letters 1972 12 539. 243 S. R.Langhoff S. T. Elbert C. F. Jackels and E. R. Davidson Chem. Phys. Letters 1974 29,247; N. C. Baird and J. R. Swenson J. Phys. Chem. 1973 77 277. 244 P. J. Bruna S. D. Peyerimhoff R. J. Buenker and P. Rosmus Chem. Phys. 1974 3 35. 24 C. Thomson a function of the positions of the nuclei in order to obtain a P.E. surface are expensive computationally but much useful information is obtainable from suitable systems. Calculations at the SCF Level.-It is now well established that near Hartree-Fock calculations can give reliable geometry predictions and even for basis sets of DZ quality the same holds true provided polarization functions are included.How- ever the incorrect dissociation behaviour leads to a correlation energy error which is not constant over a wide range of intermediate distances in general. However if a molecule dissociates to closed-shell products i.e.there is no change in the number of electron pairs during the dissociation process the asymptotic behaviour of the wavefunction is correct ;E does not vary much with R and the H-F and true P.E. curves are approximately parallel. In these cases the H-F method is capable of yielding semi-quantitative P.E. curves with geometrical parameters characterizing minima in the surface accurate to ca.1-2 % energy barriers accurate to ca. 0.001-0.003 hartree (1-2 kcal mol -l) and energies of reaction within 0.008-0.016 hartree (5-10 kcal mol- ’). Bader and Gangi give details of many earlier studies on such systems the first of these being Clementi’s calculation on NH + HCl,245 which surprisingly has not been re-investigated with polarization functions in the basis set. The reaction of H with HeH’ gives He and H3+ and the work of Benson and McLa~ghlin’~~ on this system showed the minimum energy pathway to exhibit C, symmetry and predicted an exothermicity of 0.096 hartree with no barrier or local minima along the path. The corresponding CI calculations con- firmed that the H-F and correlated surfaces were probably closely parallel.Calculations by Kutzelnigg and co-workers provided further evidence for the close parallelism of the surfaces in the case of LiH2+.247 Lester248 has also studied this system. A second class of systems A + B where A possesses a closed shell and B a half-filled shell also have the proper dissociation behaviour for diatomic species. When A and/or B is diatomic or polyatomic the H-F method cannot yield a surface parallel to the true P.E.surface. A reaction of this type studied by Schaefer et dZ4’ was H2 + C1-+ H + HC1. The calculated SCF barrier for the linear pathway of 0.042 hartree (26.2 kcal mol-’) was far too large. A similar calcula- tion on H2 + F -+ H + HF showed the same general overestimation of the barrier height250 (see below). Several SN2reactions have been studied in order to find the minimum energy pathway between reactants and products.Full details are to be found in ref. 4 and as an example we consider F-+ CH,F -+ [F-CH,-F]--+ CH,F + F-(4) 245 E. Clementi J. Chem. Phys. 1967 46 3851. 246 M. J. Benson and D. R. McLaughlin J. Chem. Phys. 1972,56 1322. 247 W. Kutzelnigg V. Staemmler and C. Hoheisel Chem. Phys. 1973 1 27. 248 W. A. Lester J. Chem. Phys. 1970,53 1511; 1971 54 3171. 249 S. Rothenberg and H. F. Schaefer tert. Chem. Phys. Letters 1971 10 565. 250 S. V. O’Neil P. K. Pearson and H. F. Schaefer tert. J. Chem. Phys. 1973 58 1126. Calculations on Small Molecules 25 studied by Veillard et and Duke and Bader,," both groups using large basis sets and polarization functions.Both predicted an intermediate rather than a transition state without polarization functions and found the linear pCH,F]-complex of D, symmetry and a reaction barrier of -0.0114.12hartree (7-8 kcal mol-') with polarization functions. One feature found in this and other S,2 reactions is the delayed departure of the leaving group. Schaefer et ~1.~'~ have studied the isomerization CH,NCe CH,CN (5) which is believed to exhibit slow intramolecular vibrational relaxation. They did not find a minimum in the potential path when the P.E. surface was computed as a function of both the CH rotational angle and the CNC angle. Various other interaction potentials have been reviewed by Yarkony et There are however two frequently used techniques which enable one to correct for the wrong dissociation behaviour of the H-F wavefunction without involving large CI.These are (1) the UHF method in which the single deter- minant is built up of spin orbitals with different spatial parts for different spins and (2) correcting the RHF single determinant by adding enough determinants usually only a few to give the correct asymptotic behaviour. This type of calcula- tion is reviewed in detail for O(,P or 'D)+ H by Bader4 and we refer the reader to this review for details of the reaction 0+ H -+ H,O (6) The contributions of the additional configurations are usually only really impor- tant for large internuclear distances. The symmetrical insertion of O(,P)into H gives a barrier of ca. 0.127 hartree (80kcal mol- ') and predicts a linear stable intermediate and the energy minimum on this path is a saddle point which does not represent a stable nuclear configuration of triplet H,O.Murrell and co-~orkers~~~ have examined the P.E. surface for the symmetrical insertion of CH (singlet and triplet) into H ('Zg+),with similar results to those quoted above. Baskin et ~1.~'~ have studied the abstraction reaction CH + H -+ CH + H (7) and among other studies. of this type we mention CH3++ H +CH5+,Z57 CH + H -+CH ,,'* and the dissociation pathways for H,O -+H,O + HZs9 2s1 G. Berthier D. J. David and A. Veillard Theor. Chim. Actu 1969 14 369; A. Dedieu and A. Veillard Chem. Phys. Letters 1970 5 328; J. Amer. Chem. SOC. 1972 94 6730. 252 A. J. Duke and R. F. W.Bader Chem. Phys. Letters 1971 10,631. 253 D. H. Liskow C. F. Bender and H. F. Schaefer tert. J. Amer. Chem. SOC. 1972 94 5178; J. Chem. Phys. 1972,57,4509. *" D. R. Yarkony S. V. O'Neil and H. F. Schaefer tert. J. Chem. Phys. 1974 60 855. 2s5 J. N. Murrell J. B. Pedley and S. Durmaz J.C.S. Furuduy 11,1973 69 1370. 256 C.P. Baskin C. F. Bender C. W. Bauschlicher jun. and H. F. Schaefer tert. J. Amer. Chem. SOC.,1974 96,2709. 257 M. F. Guest J. N. Murrell and J. B. Pedley Mol. Phys. 1971 20 81. 258 S. Ehrenson and M. D. Newton Chem. Phys. Letters 1972 13 24. 259 R. A. Gangi and R. F. W. Bader Chem. Phys. Letters 1971 11 216. 26 C. Thomson and NH -+ NH + H.260 One interesting conclusion is that of the species CH, H30 and NH, only the last-named requires more than 0.032 hartree (20 kcal mol-') for its decomposition.Additions of atoms to double bonds such as S(,P 'D) to ethylene has been studied by Csizmadia's group,261 and Buenker 262 and co-workers have carried out very detailed studies of the electrocyclic transformations between cyclic and .~~~ open-chain hydrocarbons. Horsley et ~1have also studied the full 21-dimen- sional hypersurface of the isomerization of cyclopropane. Before we consider explicit calculations designed to include as large a fraction of the correlation as possible we should mention an important series of papers dealing with the solvation process with particular reference to the hydration of simple ions. P.E. surfaces for H,O in the field of Li' Na' and K' and F- and C1-were studied using a large GTO basis set and a single-determinant wave- function.264 Later papers dealt with an extensive investigation of the HzO dimer.265 Other workers have also investigated solvation notably Pullman's group,266 using however rather smaller basis sets.Calculations including Extensive Electron Correlation.-We consider in this section those calculations designed to include enough C1 to ensure that the reaction surface is similarly described along the whole path. In principle full CI calculations can achieve this but in practice various lesser CI calculations have to be carried out. Minimal CI ensures the inclusion of those configurations necessary to ensure proper dissociation as exemplified above and we now turn to the intermediate or truncated CI results.The problem of selection of configurations is a difficult one and is dealt with elsewhere. Transformation to natural orbitals is now commonly used or alternative procedures such as those proposed by KraussZ6' or Bender and Davidson.268 The alternative to conventional CI is the MCSCF procedure as given in detail by Wahl and co-workers.8 The IEPA method which is referred to several times above is also a useful method for small systems. The simplest exchange reaction H+H,+H,+H (8) has been thoroughly reviewed el~ewhere,~ and the most recent work on this system culminates in Liu's surface which is probably very close to the true surface. The 260 J. Pelletier and R. F. W. Bader unpublished results cited in ref. 4. 261 0.P.Strausz H. E. Gunning A. S. Denes and I. G. Csizmadia,J. Amer. Chem. SOC. 1972 94,83 17. 262 K. Hsu R. J. Buenker and S. D. Peyerimhoff J. Amer. Chem. SOC.,1971 93 21 17; 1972 94 5639; R. J. Buenker S. D. Peyerimhoff and K. Hsu ibid. 1971 93 5005. 263 J. A. Horsley Y.Jean C. Moser L. Salem R. M. Stevens and J. S. Wright J. Amer. Chem. SOC.,1972 94 279. "* H. Kistenmacher H. Popkie and E. Clementi J. Chem. Phys. 1973 58 5627 and earlier papers in this series. 265 H. Kistenmacher H. Popkie E. Clementi and R. 0. Watts J. Chem. Phys. 1974,60 4455. 266 M. Dreyfus B. Maigret and A. Pullman Theor. Chim. Actu 1970 17 109. 267 C. Edmiston and M. Krauss J. Chem. Phys. 1966,45 1833. 268 C. F. Bender and E. R. Davidson J. Phys. Chern. 1966 70 2675.Calculations on Small Molecules 27 surface for the H2 + D -+ 2HD (9) problem is still not completely understood despite a large amount of effort. The problem is that the experimental results from shock-tube experiments suggest a barrier height which is low compared to any yet computed from various possible transition states. The most extensive recent work of Silver and Stevens270 still has not resolved this question. The more complicated system HeH+ + H -*He + H3+ has been studied where the best calculations indicate no barrier to reaction.246 The extensive series of calculations of Schaefer and co-workers on the reactions and H+F,-+HF+H (1 1) probably indicate accurately the current state of the art in this field. A large (DZ + P) basis set was contracted and a large CI calculation carried out a geometry search carried out over a large number of points (ca.300) with the result that the linear path was found to be of lowest energy and d and p polariza-tion basis functions are necessary to obtain a reasonable barrier height for the first reaction. The 19-electron problem H + F +HF + F was then studied,250 using a DZ-GTO contracted basis the results on the above reaction indicating this basis should be capable of yielding qualitatively accurate results. 555 configura-tions were included and once again the linear approach was favoured. It is expected that DZ + P calculations will improve the computed barrier height which is less than the experimental value. Further calculations on Li + F -P LiF + F (12) have been reported.272i273 Pearson et al.carried out an SCF calculation and also a two-configuration calculation. The minimum energy path was found for the collinear reaction. A deep well (ca. 0.05 hartree) was found for a C, sym-metry LiFLi species. 269 B. Liu J. Chem. Phys. 1973,58 1925. 270 D. M. Silver and R. M. Stevens J. Chem. Phys. 1973,59 3378. C. F. Bender P. K. Pearson S. V. O’Neil and H. F. Schaefer tert. J. Chem. Phys. 1972 56 4626; C. F. Bender S. V. O’Neil P. K. Pearson and H. F. Schaefer tert. Science 1972 176 1412. 272 G. G. Balint-Kurti Mol. Phys. 1973 25. 393; G. G. Balint-Kurti and M. Karplus, Chem. Phys. Letters 1971 11 203. 273 P. K. Pearson W. J. Hunt C. F. Bender and H. F. Schaefer tert. J.Chem. Phys. 1973,58 5358. C.Thornson Although most workers in this field have used SCF-CI calculations Bas~h~’~ has examined the use of MCSCF in studying the reaction 2CH2-+C2H4 and a few authors have used VB-CI wavefunctions (see ref. 4). To summarize we can see that the past two years have seen an impressive gain in accuracy in P.E. surface studies and it is clear that more chemically interesting results will be forthcoming in this area during the next few years. 274 H. Basch J. Chem. Phys. 1971,55 1700.

ISSN:0308-6003    

DOI:10.1039/PR9747100005

出版商:RSC    

年代:1974

数据来源: RSC

摘要:

3 Atomic and Molecular Photoassociation By B. STEVENS Department of Chemistry University of South Florida Tampa Florida 33620 U.S.A. 1 Introduction The tragic death of Professor Th. Forster in 1974 coincided with the twentieth anniversity of his publication of an article’ entitled ‘A Concentration Reversal of Fluorescence’ in which the origin of a blue structureless fluorescence band observed in concentrated solutions of pyrene in benzene was attributed to ‘an excited double molecule. ..formed from one excited and one unexcited pyrene molecule (which) decomposes after deactivation.’ A key observation was the concentration independence of the absorption spectrum indicating that molecular association follows the act of light absorption and the term ‘excimer’ has been adopted to distinguish this product of photoassociation from an excited dimer produced by excitation of a relatively stable dimeric ground state.’ As with the development of triplet-state spectroscopy the phenomenon of photo- association was recognized in atomic systems many years earlier3 and emission from the mercury ‘excimer’ Hg,* was undoubtedly present in the light source used by Forster to excite pyrene.Since 1954 it has been recognized that photoassociation is a general property of aromatic hydrocarbons (unless sterically hindered) and has been extended largely due to the work of Weller and of Mataga to include exciplexes formed by non-identical molecules as distinct from excited electron donor-acceptor (EDA) complexes stable in the ground state.The quantum-mechanical description of excimer and exciplex binding forces in terms of exciton and charge-resonance contributions is parametrized by donor ionization potentials and acceptor electron affinities much as the ionic character of covalent bonds is related to atomic elect ronegat ivities. The development of this field is marked by the appearance of excimer and exciplex as index keywords and the organization of an International Exciplex Conference at the University of Western Ontario in May 1974. A detailed account of the field is presented by Birks in his monumental treatise4 and by Th. Forster and K. Kasper 2.phys. Chem. 1954 1 275. E.g. T. Kajiwara R. W. Chambers and D. R. Kearns Chem. Phys. Letters 1973,22,37. ’ S. Mrozowski Z.Physik 1937 106 458. J. B. Birks ‘Photophysics of Aromatic Molecules’ Wiley London and New York 1970. 29 B. Stevens 'M* + M +'Q* &:I +Q-12 3M* + M +3Q* M +Q +hVp Figure 1 Photoassociation and exciplex relaxation scheme Mataga and Kubota,' while reviews by Forster6 and have appeared in recent years. The complexity and consequences of photoassociation are illustrated by the scheme in Figure 1 where evidence exists for each of the pro- cesses involved (although not usually in the same system) and this is presented as a basis for reporting some novel processes and different systems. These include atomic photoassociation excimer and exciplex triplet states photo- dimerization and photoaddition exciplexes of molecular oxygen excited dimers and complexes and practical applications.2 Atomic Systems Despite the expectations that atomic photoassociation will be termolecular in the gas phase and that non-radiative relaxation of the diatomic product will be of less importance than it is in molecular complexes the study of atomic systems may continue to provide precedent for the interpretation of molecular phenomena. The emission spectrum of mercury vapour contains at least two broad structure- less bands assigned to transitions (1) and (2) which decay exponentially following Hgf(31,) +2Hg('Z:) +hv(Lax =335nm) (1) HSZ(~O;) +2Hg('C;) +hv(l,, =480nm) (2) pulsed electron excitation with a common lifetime of 14~s; however as the mercury vapour pressure is increased to several atmospheres the 480nm peak shifts to 457nm and the decay becomes non-exponential.Eckstrom et a1.' N. Mataga and T. Kubota 'Molecular Interactions and Electronic Spectra' Marcel Dekker New York 1970. Th. Forster Angew. Chem. Internat. Edn. 1969 8 333. B. Stevens Adv. Photchem. 1971 8 161. M. Ottolenghi Accounts Chem. Res. 1973 6 153. D. J. Eckstrom R. M. Hill D. C. Lorents and H. H. Nakarno Chem. Phys. Letters 1973 23 112. Atomic and Molecular Photoassociation attribute the blue shift to effective vibrational relaxation of the emitter and inter- pret the hyperbolic decay component in terms of the (triplet-triplet?) excimer annihilation process (3) with a rate constant of the order of 10-'' cm3 s-' (the Hgt + Hgt + Hgt* + 2Hg (3) collision frequency is of the order 10- lo cm3 s-').However since vibrational stabilization of Hgl should lead to a red-shift of the associated emission band the high-pressure band at 457 nm may originate from the annihilation product Hg:* which by analogy with the same process in molecular systems could be the excimer singlet state [see process (10)below]. Jortner and co-workers" have reported that the excimer spectra of argon (A,, N-128 nm) and of xenon (A,, 1 172 nm) are virtually identical in the gas liquid and solid phases (at similar temperatures) and show that the increase in band width with temperature (in the gas phase) is consistent with harmonic vibrational frequencies of 140cm-' (Xez) and 310 cm- (Ar;). The emitting state is predominantly "Cf formed from the long-lived 3P2atomic state which has been monitored in absorption in the region 810-995 nm by Oka et al.' for Ne; Art and Kr;.In the absence of any pressure effects over the range 2- 1400 Torr these authors conclude that the respective decay constants of 0.15 0.31 and 2.83 ps-describe the purely radiative relaxation. Spectroscopic evidence has been reported12 for KrXe* (A,, N 158 nm) and KrAr* (A,, 1 135nm) in the liquid phase and for NeHe* in ab~orption,'~ whereas XeAr* XeNe* KrNe* and ArNe* do not appear to be stable with respect to dissociative processes 3kMc or 3kQCof Figure 1. A broad structureless emission band with a maximum at 275 nm ~bserved'~ from mercury vapour excited at 254 nm in the presence of xenon has been assigned to 3HgXe* whereas no comparable bands were observed in the presence of He Ne Ar or Kr; since these have higher ionization potentials than Xe it appears that Hgti3PO acts as electron acceptor in 3HgXe*.From an extensive examination of the emission characteristics of charge- transfer complexes (exciplexes) of Hg63P0 with such molecular electron donors as H20 NH3 alcohols and primary amines in the gas phase Phillips and his group' found that the wavelength maximum of the structureless emission band (in the region 285-360nm) undergoes a red shift with reduction in ionization potential of the donor. The emission quantum efficiencies are high for the simple lo 0. Chesnovsky B. Raz and J. Jortner Chem. Phys. Letters 1972 15 475. T. Oka K. V. S.Rama Rao J. L. Redpath and R. F. Firestone J. Chem. Phys. 1974 61 4740. l2 0.Cheshnovsky A. Gedanken B. Raz and J. Jortner Chem. Phys. Letters 1973,22,23. l3 Y. Tanaka and K. Yoshino J. Chem. Phys. 1972,57,2964. l4 C. G. Freeman M.J. McEwan R. F. C. Claridge and L. F. Phillips Chem. Phys. Letters 1970 6 482. ' C. G. Freeman M. J. McEwan R. F. C. Claridge and L. F. Phillips Trans. Furaduy SOC. 1971 67 67 2004; R. H. Newman C. G. Freeman M. J. McEwan R. F. C. Claridge and L. F. Phillips ibid. p. 1360. B. Stevens donors (0.70 for HgNHf and 0.19 for HgH20*) but generally decrease rapidly with donor complexity due largely to donor reactions with Hg6,Pl the precursor of Hg6,Po. An interesting feature of Hg63Po exciplex emission is the red shift of the maximum intensity wavelength with increasing donor pressure which these authors ascribe to vibrational relaxation through well-defined levels of the complex.In the case of NH this shift amounts to ca. 1700cm-' as the NH3 pressure is increased to 760 Torr which providesa lower limit of 5 kcal mol-for the exciplex dissociation energy ; the binding energy limits for Hg-amine complexes are somewhat lower than this. At relatively low pressures of NH, the phase-shift difference between the Hg63P1 and HgNH; emission is pressure dependent reflecting the rate of exciplex formation in processes (4) and (5) and Hg6,Po + NH -+HgNH (4) Hg6,P0 + 2NH + HgNH + NH (5) providing rate-constant values of k = 3.2 x 10-'3cm3molecule-'s-1 k = 2.3 x cm6 molecule-* s-l The constant residual phase shift at high pressures indicates that NH does not quench the exciplex and is consistent with an exciplex radiative lifetime of 1.86 ps.A different interpretation of the HgNH; emission red shift has been presented by Callear and ConnorI6 who note that this reaches a maximum value in the presence of added N2 or CF4(due to vibrational relaxation) which is considerably less than that produced by an increase in NH3 pressure alone. The latter is attributed to the successive formation of a series of complexes Hg(NH3),* with n = 1-4 (and possibly 5 and 6) and by an iterative procedure these authors deconvolute the emission profiles to obtain dissociation constants for the equilibrium (6) of the order of 10'' molecules cm-,.A mean binding energy Hg(NH,) Hg(NH,):- + NH of cu. 9 kcal mol- ' for each NH3 molecule in Hg(NH,)f is estimated from the high-energy threshold emission frequencies of the separated emission profiles. An interesting feature of this work which may be of relevance to molecular systems is the appearance of a green structureless emission band (A,, LZ 520 nm) which increases in intensity with pressure of Hg vapour and which is attributed" to emission from Hg; formed in process (7). Emission from the Cd3P0 exciplex HgNHj + Hg6'S + Hg + NH (7) with NH has been reported18 with Amax 'v 430nm (red-shifted by 7400cm-' from the Cd3P1 line) and a radiative lifetime of 0.49 ps. l6 A. B. Callear and J. H. Connor Chem. Phys. Letters 1972 13 245. " See however L.F. Phillips Chem. Phys. Letters 1973 21 28. l8 P. D. Morten C. G. Freeman M. J. McEwan R. F. C. Claridge and L. F. Phillips Chem. Phys. Letters 1972 16 148. Atomic and Molecular Photoassociation 33 3 Photoassociation of Singlet States Excimer-Exciplex Fluorescence.-Unambiguous evidewe of photoassociation (Process kCMof Figure 1) is provided by the appearance of a broad structureless red-shifted fluorescence band as the concentration of Q (or M in the case of an excimer) is increased ;this is accompanied by a reduction in fluorescence intensity of the directly excited molecule in the absence of any concentration dependence of the absorption spectrum. The radiative lifetime is considerably longer than that of the excited molecular precursor since the associated transition is symmetry forbidden and additional criteria are provided by a negative temperature coeffi- cient of intensity at higher temperatures due to an increase in rate constant k, of the dissociative feedback process and in the case of the exciplex a reduction in intensity with increase in solvent dielectric constant which promotes ionic dissociation (rate constant k:).The overall quantum yield of exciplex fluorescence reflects both the intrinsic yield given by equation (8) where k is the rate constant of the ith non-radiative 1 exciplex relaxation process and the photoassociation efficiency which if k, = 0 is given by equation (9). Thus if the lifetime T of the molecular precursor 'M* ~CM = ~cMTM[QI/(~ -4-~CMTM[QI) (9) is short and [Q] (or [MIfor an excimer formation) is limited by solubility photo- association will be restricted particularly in viscous solvents at low temperatures where the diffusional process (rate constant kcM)is slow.Various ingenious techniques have been exploited to increase the photo- association efficiency. Johnson and Offen' have used the negative activation volume of photoassociation to record the elusive orange excimer fluorescence of perylene in cyclohexane at high pressures and reported an associated lifetime of 72 ns at 77 K (T = 6.6 ns) which is reduced to 13.4 ns at 296 K by a competing non-radiative process with an activation energy of 670 cm-' and a frequency factor of 1.7 x lo9s-' characteristic of kz. The very short fluorescence lifetime T~, and low emission yields of hetero- cyclic compounds are usually attributed to efficient intersystem crossing from the lowest nn* singlet state.In the case of quinoline and isoquinoline the energy of this state is raised above that of the singlet nn* state in hydrogen-bonding solvents with the result that T is increased and at higher concentrations in ethanol at 160 K excimer fluorescence bands are observed2' red-shifted by 6500 and 6700 cm-',respectively from the molecular 0-0bands ;no correspond- ing changes in the absorption spectra with concentration were noted. An increase in local concentration (and photoassociation efficiency) may be effected in several ways the simplest of which conceptually is use of the pure l9 P. C.Johnson and H.W. Offen Chem. Phys. Letters 1973 18 258. R. P. Blaunstein and K. S. Gant Photochem. and Photobiol. 1973 18 347. 34 B. Steuens solid phase where 'sandwich' pairs of molecules may be present as the structural unit of the crystal or as defect sites induced by pressure or rapid sublimation. In this way Muller et aL2' have excited a broad structureless emission band (V,, = 15500 cm-') in a sublimed tetracene film at 110 K characteristic of excimer fluorescence with a lifetime of 65 ns (z = 6.4 ns). Although this lifetime is independent of temperature the emission intensity is thermally quenched with an activation energy of 0.12 eV corresponding to the energy deficiency for singlet (molecular) exciton fission into two triplet excitons.The estimated value of 2 x 10" s-' for the rate constant of excited-pair formation is believed to describe the frequency of energy transfer from initially excited molecules to dimer site traps. An effective increase in local concentration is also achieved by 1,3-distribution of aryl groups in a hydrocarbon (or other polymer) chain. From a study of the time-resolved intramolecular excimer fluorescence of 1,3-bis(a-naphthyI)propane in ethanol-glycerol mixtures El-Bayoumi et ~1.~~ obtained a radiative lifetime of 720 ns which is significantly longer than the value of 500 ns reported for the excimer of 1-methylnaphthalene in ethanol. The suggestion that the methylene chain locks the molecule in a perfect sandwich excimer configuration restricting the torsional oscillations necessary to induce the symmetry-forbidden transition is consistent with an apparent red shift of 1:lo00 cm-' in Lax relative to the 1-methylanthracene excimer band peak.The relatively low values of the viscosity-dependent rate constants k, and k, indicate that rotation about the methylene chain limits the rates of photoassociation and dissociation in this intramolecular system. Chandross et al.23have also observed the intramolecular excimer fluorescence of 1,3-bis(a-naphthyI)propaneproduced by photochemical cleavage of the photoadduct in a rigid glass at 77 K and noted that the excimer band is removed by thermal recycling which presumably allows rotation about the methylene chain. The generation of isolated sandwich pairs by photolysis of solutions of the photodimer or photoadduct in a rigid low-temperature glass has also been used by Chandros~,~~ who developed this technique to record the naphthalene- anthracene exciplex emission from the photochemically cleaved adduct of 1-(9-anthry1)-3( 1-naphthy1)propane ; the exciplex fluorescence peak is red-shifted by 3200 cm- 'from the 0band of9-methylanthracene (or by 10 OOO cm-' from the 0band of 1-methylnaphthalene) and is characterized by a quantum yield of 0.37 and a lifetime of 33 ns at 77 K.A similar emission band is exhibited by single crystals2 of this cyclo-adduct following photochemical cleavage where however the lifetime is increased to 80 ns (at 60 K) indicating that some relaxation of the sandwich pair along the repulsive ground-state potential is accommodated '' H.Muller H. Bassler and G. Vaubel Chem. Phys. Letters 1974 29 102. '' P. Avouris J. Kordas and M. A. El-Bayoumi Chem. Phys. Letters 1974 26 373. 23 E. A. Chandross and C. J. Dempster J. Amer. Chern. SOC.,1970 92 704. 24 E. A. Chandross and A. H. Schiebel J. Amer. Chem. Soc. 1973,95 1671. 25 J. Ferguson A. W.-H. Mau and M. Puza Mol. Phys. 1974 27 377; 28 1457 1467 Atomic and Molecular Photoassociation 35 by a hydrocarbon glass. Other aspects of this work are reported in appropriate sections below. Triplet-triplet annihilation [process (lo)] generates excited singlet and ground-state molecules in close proximity which may subsequently photoasso- 3M* + 3M* -+ 'M* + M (10) ciate in a re-encounter ;this accounts for the increased ratio DEF/DF of excimer/ molecular fluorescence intensities in the delayed emission spectrum relative to this ratio in the prompt fluorescence spectrum and for the reduction in this ratio as the solvent viscosity is increased at lower temperature.Alternatively triplet- triplet annihilation may produce the excimer directly in the competitive process (1 1). Tachikawa and Bard26 have shown that the DEF/DF ratio of pyrene and 3M* + 3M* -b 'MM* (11) of 1,Zbenzanthracene in cyclohexane at room temperature is essentially independent of applied magnetic field up to 8 kG consistent with a common origin of both emitting species. Since excimer dissociation is thermally restricted at low temperatures where DF >> DEF these findings which contradict the results of a previous study of magnetic field effects by Wyrsch and Labhart," support the exclusive operation of process (10) as the primary annihilation event.Indirect evidence for process (10) as the primary annihilation event is provided by the interesting report by Nickel28 that this leads to emission from higher singlet states S of benzanthracene (n = 1 2 or 3) and fluoranthene (n = 1 2 3 or 4) in liquid paraffin ;the absence of corresponding excimer bands may be attributed to the very rapid radiative decay of S (n > 1) which effectively competes with re-encounter association. Excited and unexcited molecules may also be generated in close proximity by the doublet-doublet annihilation process (12) (rate constant k' of Figure 1) 2M-+ 2Q+ -+ 1*3M*+ Q (12) 2M-+2Q+ 1,3MQ* (13) j where M* may be a triplet state if electron transfer enthalpy is insufficient to produce 'M* in which case process (12) may be followed by (10) or (1 1).Again direct association [process (1 3)] must also be considered and the resulting emission is described as chemiluminescence (CL) if the radical ions are prepared chemically or electrogenerated chemiluminescence (ECL) if they are produced electrochemically. Following a study of the CL of 9-methylanthracene (M) and tri-p-tolylamine (Q)Weller and Zacharia~se~~ concluded that the primary process (13) is followed by singlet exciplex emission which competes with thermal 26 H. Tachikawa and A. J. Bard Chem. Phys. Letters 1974 26 568.*' D. Wyrsch and H. Labhart Chem. Phys. Letters 1971 8 217. B. Nickel Chem. Phys. Letters 1974 27 84. 29 A. Weller and K. Zachariasse Chem. Phys. Letters 1971 10 590. 36 B. Stevens dissociation (process k, of Figure 1) responsible for the observed fluorescence of M. However Tachikawa and Bardz6 find that the reaction enthalpy computed from electrochemical data for this system is insufficient to produce 'MQ* in process (1 3) whereas magnetic field effects implicate intermediary triplet-triplet annihilation in the formation ofboth 'M* and 'MQ*. These authorsz6 suggested that 3M* is formed in process (12) and subsequently undergoes process (lo) as in the pyrene-tetramethylenephenylenediaminesystem but the origin of 'MQ* if this is indeed responsible for the broad emission band at 520nm is less certain.Balzani's group3* have reported the appearance of a well-characterized structureless emission band (A,, = 650 nm) as naphthalene is added to solutions of the cis-dichlorobis-( 1,lO-phenanthroline)iridium(IIr) cation ; this is attributed to the first 'inorganic' exciplex in which naphthalene adopts a sandwich con- figuration with a phenanthroline ligand with an estimated binding energy of 4 kcal mol-' ; however the exciplex spectrum is not exhibited by 1,lO-phen- anthroline in the presence of naphthalene. The first report of molecular excimer fluorescence in the vapour phase concerns l-azabicyclo[2,2,2]octane,which exhibits a structureless emission band (A,, = 375 nm) red-shifted by 12 400 cm- ' from the molecular 0-0fluorescence band.Halpern3' found that this low-energy band is enhanced by the addition of n-hexane and analysed the data in terms of a photoassociation mechanism to obtain an associated lifetime of 44011s and an equilibrium constant (k&kMc) of 2.4 x 10' dm-3 mol-'. Excimer-Exciplex Absorption.-The observation of excited singlet states in absorption facilitated by the development of excitation pulses and detection techniques with resolution in the nanosecond region has been extended to excimers and exciplexes. Assignments are usually based on intensity variations with temperature and concentration and may be confirmed by the coincidence of relaxation times in absorption and emission although this is not always possible.Thus Thomas and co-w~rkers,~ using pulsed radiolysis find transient absorption bands in the xylenes mesitylene and pseudocumene at 600nm which are enhanced on cooling and are attributed to singlet excimer absorption; the exponential decay is characterized by lifetimes of ca. 20 ns and molar extinction coefficients of the order lo4dm3 mol-' cm-' are calculated from the total singlet G-values and the photoassociation equilibrium constants. An absorption band at 1100 nm in the transient spectrum of anthracene in benzene following pulsed radiolysis has been assigned by Rodger~~~ to the anthracene excimer with a lifetime of <3 ns. 30 R. Ballardini G. Varani L. Moggi and V. Balzani J. Amer. Chem. SOC., 1974,96 7123. 31 A. M. Halpern J. Amer.Chem. SOC.,1974 96 4392. 32 R. V. Bensasson J. T. Richards T. Gangwer and J. K. Thomas Chem. Phys. Letters 1972 14 430. 33 M. A. J. Rodgers Chem. Phys. Letters 1972 12 612. Atomic and Molecular Photoassociation 37 A pyrene excimer absorption band (A,, = 490nm) has been reported by Ottolenghi's using nitrogen laser excitation ;the associated lifetime is reduced by an increase in excitation intensity due to excimer-excimer annihilation analogous to process (3). The assignment has been confirmed by Slifkin et ~1.~~ using modulation excitation spectroscopy. The assignments of more complex exciplex absorption spectra are facilitated by the recognition that certain bands are due to localized excitation of donor and acceptor radical ions [processes (14) and (15)] exhibited by ground-state '(M'Q-) + hv + '(M+*Q-) (14) '(MfQ-) + hv -+ '(M+Q-*) (15) EDA complexes.Thus peaks at 540 580 and 620nm in the biphenyl(BP)- tetramethylphenylenediamine(TMPD) exciplex spectrum are assigned36 to TMPD+ whereas those at 410 and 650 nm are attributed to BP-. Additional bands originate in reverse CT transitions (16) and (17) whereas others may be '(M'Q-) + hv -+ '(M*Q) (16) '(M'Q-) + hv -P '(MQ*) (17) associated with states of donor or acceptor which are inaccessible by one-photon absorption. The reader is referred to the excellent review by Ottolenghi' for further details of this important area of molecular spectroscopy. An interesting consequence of exciplex absorption is ionic dissociation leading to transient photoconductivity in a biphotonic process as exemplified by the naphthalene(N)-TMPD system excited by a nitrogen laser (A = 337.1 nm) in non-polar solvents.36 The second-power dependence of photoconductivity on TMPD %'TMPD* -% '(TMPD+N-) hv,_ TMPD+ + N-(18) light intensity is consistent with the sequence (1 8) where the energy of the dis- sociated ion pair exceeds that of the laser quantum.In solvents of higher dielectric constant the energy of the ion pair is reduced and the photoconductivity varies linearly with laser excitation intensity.37 Kinetic Consequences of Photoassociation.-In the absence of direct spectroscopic evidence photoassociation may be inferred from the negative temperature coefficient of the yield- of a bimolecular photochemical or photophysical process due to the energy dependence of the competing feedback process (kMcof Figure 1).An example is provided by the photochemical addition of trans-stilbene to olefins described by Saltiel et aL3' Lewis and Ware3' have shown at some length how the feedback process may introduce discrepancies between steady-state and 34 C. R. Goldschmidt and M. Ottolenghi J. Phys. Chem. 1970 74 2041. '' M. A. Slifkin and A. 0.Al-Chalabi Chem. Phys. Letters 1973 20 21 1. 36 A. Alchalal M. Tamir and M. Ottolenghi J. Phys. Chem. 1972 76 2229. 37 Y. Taniguchi Y.Nishima and N. Mataga Bull. Chem. SOC. Japan 1972,45 764. 38 J. Saltiel J. T. D'Agostino 0.L. Chapman and R. D. Lura J. Amer. Chem. SOC.,1971 93 2804. 39 C. Lewis and W. R. Ware Mol.Photochem. 1973 5 261. 38 B. Stevens time-dependent quenching constants which can be analysed to obtain lifetimes and binding energies of excimers-exciplexes even when these are non-fluorescent and two papers4' have recently appeared from Ware's laboratory describing the application of these methods to real systems. Seliger et aL4' have pointed out that exciplex binding energies can only be obtained from the temperature dependence of fluorescence intensity quotients if the photoassociation and feedback frequencies greatly exceed the relaxation constants of the emitting species and suggested that the independence of this quotient on concentration of added quencher (e.g.0,)be adopted as a criterion for this condition. These authors question the findings of Mataga et that the photoassociation enthalpy of the pyrene-dimethylaniline exciplex is reduced from 6.9 kcal mol-' in hexane (E = 1.9) to 2.3 kcal mol-' in pyridine (E = 12.3) on the grounds that equilibrium is not established.An increase in association .~~ enthalpy with dielectric constant reported by Koizumi et ~1 is to be expected. If it is accepted that the exchange transfer of electronic excitation energy is accommodated by processes k, and k (Figure 1)' then any radiative or non- radiative exciplex relaxation process will reduce the sensitization efficiency of Q*below the quenching efficiency of M* and may provide indirect evidence of photoassociation. However discrepancies of this type do not seem to have been reported for energy transfer in the singlet manifold.4 Excimer-Exciplex Triplet States Spectroscopic Evidence.-Since exciton interactions are not expected to con- tribute significantly to binding energies of the excimer triplet state these will be considerably smaller than the singlet-state binding energy and excimer phosphor- escence should only be observed at low temperatures under conditions where diffusional processes permit photoassociation. The question then arises as to whether the triplet excimer is produced by intersystem crossing from the excimer singlet state (process kk) or directly by photoassociation in the triplet manifold (process 3kCQ);in either case the effects of trace amounts of quenching or luminescent impurities cannot be overlooked and several authors have preferred to eliminate these by examining rigid systems containing molecular pairs of the appropriate geometry.Following a useful summary of the evidence for excimer triplet states Averis and El-Bay~umi~~ reported the phosphorescence of 1,3-diphenylpropane in isopentane which shifts from a toluene-like (molecular) spectrum at 77 K to a broader band (A,, = 420 nm) at 115 K and is replaced by the excimer fluores- cence at higher temperatures. These authors ascribe the 420 nm emission band to excimer phosphorescence red-shifted by ca. 5000 cm -from the molecular 40 W. R. Ware D. Watt and J. D. Holmes J. Amer. Chem. Soc. 1974 96 7853; W. R. Ware J. D. Holmes and D. R. Arnold ibid. p. 7861. 41 R. J. McDonald and B. K. Selinger Mol.Photochem. 1971 3 99. 42 T. Okada H. Matsui H. Oohari H. Matsumoto and N. Mataga J. Chem. Phys. 1968 49 4717. 43 S. Murata H. Kokubun and M. Koizumi Z. phys. Chem. (Frankfurt),1970,70 47. 44 P. Averis and M. A. El-Bayoumi Chem. Phys. Letters 1973 20 59. Atomic and Molecular Photoassociation 39 0-0 phosphorescence band and ascribe its formation to photoassociation of the ~ molecular triplet state. Yokoyama et uE.~ report the presence of a broad band (A,, = 459 nm) in the phosphorescence spectrum (T = 32 ms) of poly-(3,6- dibromo-N-vinylcarbazole) in rigid 2-methyltetrahydrofuran at 77 K. This ex- hibits a linear dependence on light intensity and in the absence of photochemical decomposition is assigned to the (intramolecular) excimer phosphorescence which is red-shifted by 2200cm-' from the 0-0 phosphorescence band of the 3,6-dibromo-N-ethylcarbazolemolecule chosen as a model monomer ; this red shift may be compared with the value of 3000 cm- ' observed for the correspond- ing excimer fluorescence.Rigid low-temperature solutions of the photochemically cleaved photodimer of 1,3-bis(a-naphthyl)propaneexhibit excimer fluorescence and a structured phosphorescence shifted to the red of naphthalene phosphorescence by 250 nm. After thermal recycling only molecular fluorescence and phosphorescence is observed leading Chandross and Demp~ter~~ to the conclusion that the naph- thalene triplet-state photoassociation is prevented by steric requirements or thermal instability. Ferguson and co-w~rkers~~ concluded that the phosphor- escence quantum yield of anthracene sandwich pair produced by dimer cleavage must be < 1% of the molecular phosphorescence yield.The structureless phosphorescence emission band at 13 800 cm-exhibited by single crystals of pyrene at room temperature has also been observed from powdered pyrene after the sample was subjected to high pressures (15 ton cm-2) to create lattice defects and is attributed by Langelaar et to defect excimers lying 2000 cm- ' below the triplet exciton energy in the crystal. Perhaps the most conclusive evidence for triplet excimers has been reported by El-Sayed's group,48 who used the phosphorescence microwave double-resonance technique to determine the principal magnetic axes of the triplet state responsible for excimer emission in a hexachlorobenzene crystal at 1.6 K ; the zero-field transition frequencies are 101+ JEJ= 4.665 GHz 101-14 = 3.692 GHz and 214 = 0.972 GHz.Using the modulation excitation technique Slifkin et a1.49 observed broad new structureless absorption bands in very concentrated solutions of pyrene benzanthracene and dibenzanthracene attributed to the products of triplet- state photoassociation. In this respect it is of interest to note the thesis of Hoytink et which ascribes the short concentration-dependent lifetimes of aromatic hydrocarbon triplet states in solution to self-quenching uia photoassociation rather than to impurity quenching. Following a detailed treatment of the concentration and temperature dependence of these lifetimes these authors 45 M.Yokoyama M. Funaki and H. Mikawa J.C.S. Chem. Comm. 1974 372. 46 J. Ferguson A. W.-H. Mau and J. M. Morris Austral. J. Chem. 1973 26 91. 4' 0.L. Gijzeman J. Langelaar and J. D. W. VanVoorst Chem. Phys. Letters 1970,5,269; 1971 11 526. 48 M. A. El-Sayed C. T. Lin and R. Leyerle Chem. Phys. Letters 1974 25 457. 49 M. A. Slifkin and A. 0.Al-Chalabi Chem. Phys. Letters 1973 20 21 1 ; 1974 29 1 10. 50 J. Langelaar G. Jansen R. P. H. Rettschnick and G. J. Hoytink Chem. Phys. Letters 1971 12 86. 40 B. Stevens found that the triplet excimer formation efficiency is of the order for four different fluor molecules and is attended by an energy barrier of ca. 400 cm-' which excludes triplet-state photoassociation at 77 K.Lindquist et have attributed the concentration quenching of the pentacene triplet state to the formation of a dimeric species which undergoes ground-state dissociation with an activation energy of 4600 cm-' and frequency factor of 10' 's-',consistent with a lifetime of 36 ms at 298 K. Ottolenghi et aLS2 found that the decay of the '(TMPD+N-)* exciplex absorption in non-polar solvents generates the naphthalene triplet state at the same rate. The overall process may be regarded as an intersystem crossing to the exciplex triplet state (kz) which rapidly dissociates (3k,,). This 'slow' inter- system crossing from the thermalized exciplex is distinguished from a 'fast' process which leads to the absorption of aromatic triplet states in the presence of NN-diethylaniline immediately after the laser flash and prior to any significant decay of the singlet exciplex; this is attributed to intersystem crossing from the vibrationally unrelaxed exciplex.Since both 'slow' and 'fast' intersystem crossing populate the acceptor triplet state the yield of the latter is temperature dependent as in the case of isolated molecules where intersystem crossing to different triplet states above and below the singlet state is believed to take place. Whitten and co-~orkers~~ have assigned new transient absorption spectra from anthracene and metalloporphyrin triplet states in the presence of nitro- and chloro-aromatic quenchers at high concentration to triplet exciplexes of 1 1 and 1 :2 stoicheiometry. These may result from exciplexes of different geometry described by Chandross et al.54as sandwich pair and localized pair the latter being responsible for non-linear Stern-Volmer quenching at high quencher concentrations due to the formation of 1 2 exciplexes which shift A,, (of exciplex fluorescence) to longer wavelengths.Kinetic Evidence.-In support of an intersystem crossing (process kk) in the excimer various workers have reported non-radiative relaxation of singlet excimers with rate constants of the order expected for spin-prohibitive transitions i.e. ca. lo9s-'. Thus Offen et found that the temperature dependence of the perylene excimer fluorescence decay constant is characterized by a frequency factor of 1.7 x lo9s-' whereas Cundall's group55 reported a temperature dependence of the non-radiative relaxation of the 1-methylnaphthalene excimer in the form k,,/s-' = 5 x lo6 + 3.2 x 10" exp(-3400K/T) with the reasonable suggestion that these numerical terms describe intersystem crossing and internal conversion respectively.This same group reported an C. Hellner L. Lindquist and P. C. Roberge J.C.S. Furuduy 11 1972 68 1928. '* N. Orbach J. Novros and M. Ottolenghi J. Phys. Chem. 1973 77 2831; C. R. Goldschmidt R. Potashnik and M. Ottolenghi ibid. 1971 75 1025. 53 J. K. Roy F. A. Carroll and D. G. Whitten J. Amer. Chem. SOC.,1974 96 6349. 54 G. N. Taylor E. A. Chandross and A. H. Schiebel J. Amer. Chem. SOC.,1974,% 2693. 55 R. B. Cundall and L. C. Pereira Chem. Phys. Letters 1972 15 383; R. B. Cundall L.C. Pereira and D. A. Robinson ibid. 1972 13 253. Atomic and Molecular Photoassociation 41 increase in benzene triplet yield with benzene concentration to 0.56 in pure benzene from which an analysis based on the increased intersystem-crossing yield in the excimer provides an intrinsic value of 20.71 for this parameter. If the transfer of triplet energy involves photoassociation (processes 3k, and 3k of Figure 1) any competing relaxation of the exciplex triplet state will reduce the rate (and yield) of excited acceptor formation below the rate of donor quenching. To the Reporter's knowledge this has only been observed56 for the energy donor-acceptor system of biacetyl-benzil where the donor quenching constant and acceptor sensitization constants are 900 and 390 dm3 mol- ' s-' respectively.This energy transfer deficiency provides indirect evidence for an intermediate exciplex triplet state which may undergo chemical or physical relaxation and it may be operating in other systems where an energy-transfer efficiency of unity is assumed to compute either triplet acceptor absorption coefficient^^^ or donor intersystem crossing yield^.^ * 5 Oxygen Exciplexes The interpretation of bimolecular quenching of electronically excited molecules in terms of primary photoassociation with the quenching species followed by exciplex relaxation should logically apply to oxygen as an effective quenching molecule. However the photoassociation scheme in this case is more complex than that shown in Figure 1 owing to the triplet nature of the 02(3Xg-) ground state the existence of several low-lying singlet states (0,'Ag at 8000cm-' and 0,'Z; at 13 OOO cm-' above 023Xg-) and the relatively high electron affinity of 023Zg-;thus the lowest state of the oxygen exciplex (or oxciplex) is a singlet and of the (dissociated) ground state is a triplet.The evidence for oxygen exciplexes with aromatic molecules is largely mech- anistic although the excited complexes produced by absorption at high oxygen pressures in the classic work of Evans59 are almost certainly those which result from photoassociation ;moreover Ottolenghi and co-workers6' have observed the radical cation of pyrene following oxygen quenching of the triplet state in solvents of high dielectric constant and the new low-energy emission bands observed by Kasha et aL61 from air-saturated dye solutions may originate from an oxygen exciplex state.Mechanistically the evidence is largely based on kinetic studies62 of the sensitized photoaddition of molecular oxygen to an aromatic hydrocarbon M such as anthracene which can act as its own sensitizer. A wealth of evidence supports the intermediary role of 021Ag which appears to be formed solely by oxygen quenching of the sensitizer triplet state and the kinetic observations are " H. H.Richtol and A. Belorit J. Chem. Phys. 1966,45 35. " R. Bensasson and E. J. Land Trans. Faruday SOC.,1971,67 1904. R. B. Cundall and W. Tippett Trans. Furuduy SOC.,1970 66 350. '' E.g. D. F. Evans J. Chem. Soc. 1961 2566.6o R. Potashnik C. R. Goldschmidt and M. Ottolenghi Chem. Phys. Letters 1971,9,424. '' D. E. Brabham and M. Kasha Chem. Phys. Letters 1974 29 159. 62 B. Stevens Accounts Chem. Res. 1973,6,90. B. Stevens + t I I 9 + I I I 2 I I Figure 2 The suggested role of oxciplex states in the self-sensitized photoperoxidation of an aromatic hydrocarbon M (Reproduced by permission from Chem. Phys. Letters 1974,27 157) consistent with the sequential operation of processes 1-3 of Figure 2 rather than direct addition of 0,(31=) to either the excited singlet or triplet states of the aromatic hydrocarbon M. This has been rati~nalized~~ in terms of electronic relaxation of the intervening states Tiof the oxciplex indicated in Figure 2 by solid arrows which may involve dissociation and recombination to overcome the spin barrier 'rj -+'rj(processes a and b) or symmetry restriction attending the internal conversion 'rk-+'rm (processes c and d).A complete photoassociation scheme should include the state 3rh( T,'Z) which may lie above or below rj,together with 'rj(TI3C)and the ground state 3T0(S031=) but as yet even less is known of the behaviour of the first two of these. 6 Photoaddition From the purely photochemical standpoint process ki leading to the formation of photoadduct (or photodimer) is the important exciplex (excimer) relaxation route. The intermediary role of the exciplex in photoaddition is confirmed experimentally in at least one case but is more often a conceptual convenience in systems where exciplex fluorescence is not observed.A novel system has been reported by Chandross and S~hiebel,~~ who found that 1-(9-anthryl)-3-( 1-naphthy1)propane undergoes an intramolecular photo- addition at low concentrations (2 x lo-' mol dm-3) in methylcyclohexane but at higher concentrations (> mol dm-3) forms an intermolecular photo- dimer of two anthracene moieties. Chandross and DempsterZ3 also report that the intramolecular photodimerization of a-naphthyl substituents at the 1 and 3 positions of an alkane chain competes with excimer emission and is reversible 63 B. Stevens J. Photochem. 1974 3 393. 64 E. A. Chandross and A. H. Schiebel J. Amer. Chem. Soc. 1973,95 61 1 1671. A tomic and Molecular Photoassociat ion whereas the same substituents at 1,2-and 1,4-positions are photochemically unreactive and exhibit no spectroscopic evidence of intramolecular photoassocia- tion.Ferguson and co-workers2’ found that the thermal quenching of the low- temperature intramolecular exciplex emission of 1-(9-anthryl)-3-(1-naphthyl)-propane is due to photoaddition since both processes are characterized by the same frequency factor and an activation energy of 600cm-’; this must be regarded as conclusive evidence for the role of the exciplex intermediate in this case and it may be instructive to examine the orbital correlations for the excimer- photodimer system using anthracene A in which the excimer is believed to be of ‘Laorigin as a model. The correlation diagram shown in Figure 3 is restricted to the HOMO (Y7)and LUMO (y8)orbitals of two anthracene molecules which transform as b, and b3 under symmetry operations of the D, point group.In the symmetrical sandwich excimer configuration of the same symmetry these split into dimer orbitals Y7+ Y7 (b2,),Y7 -Y7 (big) y/8 + y8 (alg),and v8 -y8 (b3,)as shown. Correlation of these with the photodimer orbitals is facilitated by the correlation of Y,-Y,and y8 -Y14 ll-orbitals of each anthracene molecule with symmetry-adapted linear combinations YifYi (i = 1,2 or 3) and YjfYj(j= 4,5 or 6) of the benzene ring H-orbitals in the photodimer ; this restricts further examination to symmetry-adapted linear combinations of a-orbitals located at the 9,9’-and lO,lO’-positions in the photo- dimer which transform as ulg (a + a=),b, (a -ac) b, (a + a,*) and bl (a -o,*),under the same symmetry operations.As is evident from the orbital occupancies shown in Figure 3 the excimer correlates with a singly-excited state I I I i \ \ \ A* + A AA* At Figure 3 Orbital correlation diagram for the photodimerization of anthracene A via the excimer intermediate AA* 44 B. Stevens of the photodimer which unless subject to electronic relaxation along the reaction profile must undergo internal conversion or bimolecular quenching in the product configuration. In this respect it is interesting to note that Saltiel and T~wnsend~~ have reported an increase in the quantum yield of anthracene photodimerization in the presence of conjugated dienes which also quench the anthracene fluorescence.Of the a1 terna tive processes 'MM* + Q -+M + Q (19) 'MQ*+M -+ M,+Q (20) these authors found that the latter is quantitatively consistent with their data ; however the dependence of yield on anthracene concentration was not examined and exciplex emission was not observed although the exciplex lifetime must exceed that of the anthracene singlet state (ca. 5 ns) if process (20)is to offset the quenching of this state by the diene. Campbell and Lid6 have reported the general diene catalysis of 9-phenyl- anthracene photodimerization which was previously believed to be sterically hindered and following a detailed analysis of mechanisms involving either process (19) or process (20),they have shown that only the former is consistent with the observed linear dependence of reciprocal quantum yield on reciprocal concentration of 9-phenylanthracene.A possible implication of these results is re-formation of the excimer from the excited dimer in the absence of diene quenching facilitated by the small energy barrier to photochemical addition reported by Ferguson et ~1.;~' in this case symbolic differentiation of excimer and excited dimer in the sequence (21) may be desirable. 'M* + M * 'MM* 'MT -+ M (21) Compelling evidence for the intermediary role of the exciplex in the photo- addition of phenanthrene to dimethyl fumarate and maleate is provided by the work of Creed and Cald~e11,~~ who found that quenching of the exciplex fluor- escence by electron donors quantitatively parallels the reduction in yield of the photoproducts ;these authors suggest the term 'exterplex' to describe the excited termolecular intermediate for which precedent is reported in atomic systems [process (6),n = 21.Sasaki et ~1.~~ have found that the photochemical addition of cycloheptatriene to anthracene competes with anthracene photodimerization and that the adduct/dimer yield quotient is reduced in heavy-atom solvents ; these authors assume the formation of a singlet exciplex intermediate but the results may be consistent with photodimerization (of anthracene) in the triplet manifold. This is accommodated by the orbital correlation scheme in Figure 3 where it also appears that triplet-triplet annihilation could lead directly to the photodimer ground state.65 J. Saltiel and D. E. Townsend J. Amer. Chem. SOC.,1973,95 6140. 66 R. 0.Campbell and R. S. H. Liu Mol. Photochem. 1974,6 207. 67 D. Creed and R. A. Caldwell J. Amer. Chem. SOC.,1974,96 7369. 68 T. Sasaki K. Kanematsu and K. Hayakawa J. Amer. Chem. Soc. 1973,95 5632. Atomic and Molecular Photoassociation 45 Suggested chemical reactions of the exciplex are not restricted to addition Thus Gutierrez and Whitten6’ find that the quantum yield of trans-cis isomeriza-tion of 1,2-bis-(4-pyridyl)ethylene(BPE) in acetonitrile is reduced by the addition of bromoethane which also quenches the PBE fluorescence to a different extent ; this is attributed to the formation of a relatively long-lived BPE-solvent exciplex which interacts with bromoethane to release the cis-BPE isomer.Proton transfer in the exciplex is proposed by Bowman et ~1.~’ in connection with the photo- addition of acrylonitrile to indene and by Yang and Libman7 ’in their mechanism for the 9,lO-addition of secondary amines to anthracene in benzene the quantum yield of which is reduced by deuteriation of the amine. The reverse of photoaddition (process kt of Figure 1) may be expected to generate molecular excited states and is the basis of mechanisms proposed for chemiluminescence in certain systems. Thus Turro and Lechtken7’ have demon- strated that tetramethyl-l,2-dioxetan thermally decomposes to tRo molecules of acetone one of which is in the lowest triplet state whereas in the oxalate- hydrogen peroxide system an energetic dioxetandione (a CO dimer) has been suggested as a key intermediate73 which can sensitize emission from fluorescent acceptors with simultaneous self-dissociation.7 Excited Dimers and Complexes The absence both of vibrational structure in the excimer fluorescence spectrum and of a corresponding band in the absorption spectrum is consistent with a repulsive interaction potential between the unexcited molecular components in the excimer configuration. However the introduction of energy barriers to molecular separation as in the crystalline state or in rigid glass solutions of photochemically cleaved photodimers may produce an interaction potential minimum leading to characteristic dimer absorption bands which by definition are associated with an excited dimer as the upper state although the resulting emission is usually indistinguishable from excimer fluorescence if the dimer pair has a sandwich configuration.In this case the topochemical requirements for photodimerization are satisfied and the red excimer fluorescence of crystalline sandwich pairs of anthracene is thermally quenched.” Since the ‘exact’ sandwich pair configuration is probably the least stable in the ground state a partial relaxation of the energy barriers to rotation and dissociation by softening the glass or photochemical disruption of the crystal lattice will lead to more stable pair configurations with different absorption and emission characteristics and photochemical properties.These have been 69 A. R. Gutierrez and D. G. Whitten J. Amer. Chem. SOC.,1974 96 7129. 70 R. M. Bowman T. R. Chamberlain C. W. Huang and J. J. McCullough J. Amer. Chem. SOC.,1974,96,692. 71 N. C. Yang and J. Libman J. Amer. Chem. SOC.,1973,95 5783. 72 N. J. Turro P. Lechtken N. E. Schore G. Schuster H. C. Steinmetzer and A. Yekta Accounts Chem. Res. 1974 7 97; N. J. Turro and P. Lechtken J. Amer. Chem. SOC. 1972 94 2886; Mol. Photochem. 1974 6 95. 73 H. Gusten and E. F. Ullman Chem. Comm. 1970,28. 46 B. Stevens studied by Ferguson and ~o-workers,~ who prepared molecular pairs by photo- chemical cleavage of photodimers in the crystalline state and in rigid glass solutions or by the controlled softening of glassy solutions of anthracene and derivatives at low temperatures.In the latter case74 the appearance of new absorption spectra with isosbestic points is attributed to the successive formation of thermally unstable dimers and tetramers with well-defined spectral properties and short (ca. 5 ns) fluorescence lifetimes ; the existence of in-phase and out-of- phase dimer components is established from the polarized fluorescence excita- tion spectrum in the 26000cm-' region indicating an angle of ca. 60" between the short in-plane molecular axes. The behaviour of sandwich dimer pairs formed by dianthracene photocleavage in a rigid matrix at 77 K is marked by discontinuities in their fluorescence char- acteristics with progressive softening of the glass.46 Thus the characteristic excimer emission maximum first shifts slightly to the blue and the lifetime changes from 200 to 100 ns following which the lifetime is reduced to 5 ns and broad structure appears in the emission band ;if the latter is associated with an excited dimer as these authors suggest then this must be distinguished from the excimer not only in the association-excitation sequence.Conceivably the 100ns com- ponent could originate from an unrelaxed excited state of the photodimer (Figure 3) which may be in photochemical equilibrium with the excimer if the activation energy is low (cf:600 cm- ' for anthracene-naphthalene photoaddition) since the radiative transition from this correlated state should also be forbidden. The spectroscopic identity of the exciplex and excited (EDA) complex has been proposed by Itoh7 following an examination of the emission characteristics of both species for a series of 9,lO-dicyanoanthracene-alkylnaphthalenesystems.The exciplex was formed following acceptor excitation in 3-methylpentane at room temperature whereas absorption in the CT band at 77 K was used to excite the EDA complex. A similar conclusion was reached by Shirota et al.76 for arene-fumaronitrile complexes in non-polar solvents. However depending on the donor-acceptor properties of other systems the exciplex may be identifi-able as the unexcited EDA complex. 8 Applications Studies of photoassociation in aromatic polymer chains have been used to estimate the distribution of 'excimer-forming sites' and the rate of interconversion of chain conformations resulting from C-C bond rotation.An excellent sum- mary of the extensive work in this area is given in a recent paper by Frank and Harrah.77 74 J. Ferguson A. W.-H. Man and J. M. Morris Austral. J. Chem. 1973 26 103. 75 M. Itoh Chem. Phys. Letters 1974 24 551 ;26 505. 76 Y.Shirota I. Tsuhui and H. Mikawa Bull. Chem. SOC.Japan 1974,47 991. " C. W. Frank and L. A. Harrah J. Chem. Phys. 1974,61 1526. Atomic and Molecular Photoassociation Recent work concerning the role of excimers and exciplexes in biochemical systems is included in recent reviews by Song.78 Of interest here is the use of pyrene excimer fluorescence as an optical probe to determine coefficients of lateral diffusion in the hydrophobic regions of membranes.79 Since by definition photoassociation leads to population inversion and excimer-exciplex emission is significantly red-shifted from the molecular absorption spectrum the feasibility of stimulated emission from these systems has been recognized for some time.Unfortunately radiative transition prob- abilities from the sandwich configuration are relatively small and success appears to have been achieved only when the molecular components adopt a coplanar configuration due to hydrogen or other intramolecular bonding and the transition becomes allowed. Thus Srinavasan et ~1.~’ reported laser emission from con- centrated solutions of alkylaminocoumarins in the presence of an acid and suggested that the emitting state is a protonated coplanar excited dimer of these dipolar molecules.Mataga et have summarized the possibilities of exciplex laser systems and reported laser action from the intramolecular exciplex emission of p-(9’-anthryl)-NN-dimethylaniline in non-polar solvents ; however the structure and absorption spectrum of this molecule do not seem to warrant use of the term ‘intramolecular exciplex’. An analysiss2 of the laser capabilities of molecular mercury has been referred to recently.’ ” P.4. Song Photochem. andPhotobiol. 1.973,18,531; P.-S. Song and H. Baba ibid. 1974 20 527. 79 H.-J. Galla and E. Sackman Biochem. Biophys. Acta 1974 339 103. R. Srinivasan R. J. von Gutfeld C. S. Angadiyavar and R. W. Dreyfus Chem. Phys. Letters 1974 25 537.N. Bakashima N. Mataga C. Yamanaka R. Ide and S. Misumi Chem. Phys. Letters. 1973 18 386. 82 D. C. Lorents R. M. Hill and D. J. Eckstrom ‘Molecular Metal Lasers’ Semiannual Technical Report No. 1 Contract Nooo-14-72-C-0478 Stanford Research.

ISSN:0308-6003    

DOI:10.1039/PR9747100029

出版商:RSC    

年代:1974

数据来源: RSC

摘要:

4 Interactions between Molecules and Electrons of Low Energy By I. C. WALKER Department of Chemistry University of Stirling 1 Introduction High-energy electrons have long been used by chemists to explore molecular structure ; witness mass spectroscopy and electron diffraction. Recent years have seen the development of techniques for handling electrons of low energy and it is now apparent that they also can reveal a wealth of information on molecular structure not readily accessible by other means. It will be the aim of this Report to introduce to chemists this relatively novel field of study through those recent results and developments which impinge on areas of chemical interest. In keeping with the philosophy of the Annual Reports the hope is to provide an article palatable to the general reader.Only seiected references are given. This has meant the omission of some very fine detailed work on simple systems where these are judged primarily of interest to physicists. Also a brief outline of fundamental concepts is included although these are in general available in textbooks.' ,2 Different aspects of electron-molecule interactions have been reviewed in recent years; reference will be made to these as appropriate in the text. 2 Basic Concepts A. Definitions.-Electron-impact studies are concerned with sorting out what happens when an electron of low energy meets a molecule. To begin with one can attempt to classify the interactions into resonant and non-resonant processes. In the former the electron is directly scattered by the target molecule with or without excitation of molecular energy states.In this latter scattering proceeds via formation and decay of a short-lived negative ion ;this is a resonant process because apart from any other requirements in order to be captured the electron must have just the right energy to be accommodated in an orbital of the target molecule. Not surprisingly such a classification is not clear-cut ; in practice ' H. S. W. Massey 'Electronic and Ionic Impact Phenomena' Vols. I and 11. 2nd edn. Oxford University Press 1969. J. 9. Hasted 'Physics of Atomic Collisions' 2nd edn. Butterworths London 1972. 49 I. C. Walker the negative ion resulting from electron capture may be too short-lived to be distinguished from direct potential scattering.The language of electron-impact experiments is that of scattering theory and events are described in terms of collision cross-sections rather than rate constants or extinction coefficients. Figure 1 is a schematic diagram of a typical experimental set-up. A beam of electrons of energy Ei and intensity I, is directed through the target gas. The attenuation of the electron beam is given by equation (l),where n is the molecule number density 1 the path length and Q I = I exp ( -nQ/) (1) which may be seen to have the dimensions of area is a collision cross-section. It is proportional to the probability that an electron be scattered in travelling unit distance through the gas at unit number density and is the sum of the cross- sections for all contributing scattering processes [equation (2)] where Qe is Q + C Qi = Qel 1 the elastic scattering cross-section ; the summation includes all inelastic pro- cesses -those in which the electron transfers energy to (or from) internal degrees of freedom of the molecule.These may be identified by collection and energy analysis of the scattered electrons. The scattering angle 8 is an important experimental parameter ;a knowledge of the angular distribution of the scattered electrons helps one to deduce details of the electron-molecule interaction. So a differential cross-section I(8)is defined [equation (3)] giving the probability of scattering into the solid angle d0 = sin 8 d8 d$ where $ is the azimuthal scattering angle.B. Theoretical.-It has been suggested that electron-scattering processes can be treated theoretically using only classical mechanics and indeed some remarkable results have been claimed using classical concept^.^ However conventional approaches use quantum theory which recognizes that the electron wavelength (A = where E is in eV) cannot be neglected for energies in the eV ,/mA, region. Firstly any electron will have an angular momentum J about the scattering centre and this must be quantized as shown in equation (4). A wave J = Jl(1 + 1)h (4) for which 1 = 0 is an s-wave one for which 1 = 1 is a p-wave and so on. Equation (3) implies also that the electron-impact parameter b is quantized as shown in equation (9, where meis the electron mass and u its velocity.An exact description J = meveb (5) M. Gryzinski Phys. Rev. Letters 1970 24 45. Interactions between Molecules and Electrons of Low Energy of the scattering process requires of course solution of the appropriate wave equation. The resulting eigenfunction Y must have the asymptotic form of equation (6),where k the electron wavenumber is 241. The first term here '4' = exp (ikz) + r-exp (ikr)f(0) (6) represents the incoming electron wave the second term the outgoing scattered wave. The problem is to evaluate f(O) the amplitude of the scattered wave; equation (7) shows how it is related to the differential cross-section Z(0). It turns 40) = If(0)12 (7) out that I(0)= ,@ + B2 where A and B are defined by equation (S) PI are the A = +J(21 + l)[cos 2VI -l]P,(cos0) (84 B = $,z(21 + 1) sin ~~,P,(cos (8b) 0) Legendre polynomials and qI are phase shifts introduced by the scattering molecule into the incident electron wave-trains.An observer detects scattering through these phase shifts. It follows [cJ equation (3)] that Q can be defined by equation (9). The summations are over all the partial waves that 'see' the molecule. 4n Q = -X(21 + 1) sin2q (9) k2 If the electron velocity is very low so that b = J/rn,u is large even for a p-wave (I = l) then only the s-wave will be scattered (in a head-on collision) and the cross-section will be given by equation (10). Equations (8)illustrate that scattering 4n Qo = 2sin2qo (10) need not be isotropic ;the angular distribution of the scattered electrons depends on which waves are scattered.There is a class of experiments electron swarm experiments in which cross- sections are not measured directly but deduced from the behaviour of a swarm or pulse ofelectrons pushed through the gas by a d.c. electric field. The measurable parameters depend on the momentum transfer cross-section QD a cross-section weighted according to the anisotropy of collisions and defined by equation (11). In terms of phase shifts QD may be expressed as equation (12). These equations may be generalized to include inelastic effects. The task confronting the theoretician is to calculate the phase shifts. For electrons of low energy no one theory is universally applicable. Several different approaches are currently applied and then only to the simplest systems.Discus- sion of these is outside the scope of this article but reference to them will be made in the text as appropriate. At high electron energies the cross-sections are I. C. Walker calculable using the Born approximation. Briefly then the electron-molecule interaction is taken simply as the Coulomb interaction between incident and bound electrons and it is assumed that the electron wave is negligibly disturbed by the molecule. For inelastic scattering this approximation demonstrates that at high incident energies the molecule does not distinguish between the electron and a passing photon so that scattering is predominately in the forward direction and any molecular transitions excited are optically allowed.As the electron energy is reduced and one looks at large scattering angles optically forbidden transitions gain over those that are electric-dipole-allowed. Spin-forbidden electronic transitions excited through electron exchange are particularly enhanced at low energy. Happily these conclusions of the Born approximation confirmed experimentally may be extrapolated to low energies where the theory is no longer valid. An electron energy-loss spectrum recorded at low incident energies and large scattering angles may be dominated by optically forbidden transitions. One other result of the Born approximation appears to be generally applicable ; the relative differential cross-sections for excitation of different vibrational levels of a molecular transition are invariant with incident electron energy Eiand angle 8 and equal the Franck-Condon factors.This last point is an important one; if in a transition departures from the Franck-Condon factors appear as either Eior 8 is varied then one must suspect contributions from an underlying tran~ition.~ It is the practice to describe inelastic processes in terms off the generalized oscillator strength. For a transition of energy loss W,f is defined by equation (13) where K is defined by equation (14) and kiand k are initial and final wave- numbers respectively. Equation (13) allows one to define f by equation (15) f = 2Wz*/K2 (15) where E is a transition matrix element. In the limit of high impact energy and zero scattering angle the generalized oscillator strength reduces to the optical oscillator strength.This allows a direct comparison of electron-scattering results with those from optical spectroscopy. Lassettre has reviewed this aspect of electron-scattering spectro~copy.~ The generalized oscillator strength appears in a useful equation [equation (16)] recently derived relating the energy of a triplet state E, to that of the corresponding singlet state E,.6 Wis the excitation E -E = (ngW)-' /om K2f dK energy of the singlet state g its degeneracy and fits generalized oscillator strength. This equation applicable where the Born approximation is valid has been tested for several states in helium and carbon monoxide for which both (E -ET) S. Trajrnar J. K. Rice and A.Kuppermann Adu. Chem. Phys. 1970 18 15. E. N. Lassettre Cunud. J. Chem. 1969 47 1733. ' E. N. Lassettre and M. A. Dillon J. Chem. Phys. 1973 59 4778. Interactions bet ween Molecules and Electrons of’Low Energy and f are known. It offers the interesting prospect of positioning a triplet state from experimental measurements on the corresponding singlet at high electron energies. C. Experimental Considerations.-Common to all electron spectroscopy experiments is the need to know the energy of the incident electrons. This is most frequently achieved by passing the electrons usually from a thermionic source through electrostatic and/or magnetic fields tuned to transmit electrons of a single energy. Favourite monochromators are the 127” electrostatic selector and the spherical electrostatic selector.These have been fully described in the literature.’ With such instruments workable electron beams of 30-50 meV energy spread are relatively easily obtained (1 eV = 1.60199 x J mole-cule-’). ‘Workable’ is an important qualification in describing electron beams. Beams of low energy are very sensitive to space-charge effects surface imperfec- tions and various ‘relaxation’ processes not yet understood all of which serve to broaden the energy distribution. So although a nice beam may emerge from the monochromator one cannot assume that it will survive into the collision region particularly in the presence of molecular gases which have pronounced effects on surface potentials and hence on the electron beam.One somewhat novel and essentially simple monochromator has been developed which avoids some of these problems. In this the trochoidal electron monochromator electron energy selection results from passage of the electrons through mutually perpendicular electrostatic and magnetic fields.’ The latter is in the direction of the incident electron beam and ‘contains’ the low-energy electrons so that the Molecules Electron energv selector I Incident electron beam. Electron energy \ analyser Figure 1 Schematic diagram of an electric scattering experiment. An electron beam of energy Ei intensity I, crosses a molecular beam or passes through a chamber contain- ing the sample gas at low pressure. The scattered electrons of intensity I,, have energy E,; 0 is the scattering angle.I is the intensity of the transmitted electron current J. B. Hasted Confernporary Phys. 1973 14 357. A. Stamatovic and G. J. Schulz Rev. Sri. Insrr. 1970 41 423. I.C. Walker monochromator can be used from zero energy upwards with a resolution of about 20 meV at best. The magnetic field which must penetrate through to the collision region does however mean that the scattering angle 6 (Figure l) is not measurable. High-resolution spectra at low energies have been obtained without mono- chromation of the electron beam by time-of-flight analy~is.~ Single electrons which have drifted through a long path-length L are detected and registered according to their respective times of flight t. For any electron velocity = L/t.Electron energy is thus determined from two accurately measurable parameters L and t. Measurements are made without and with gas (under single-collisions conditions) in the flight path and thus cross-sections are determined simultane- ously for a range of electron energies. Another technique which avoids the use of monochromators produces electrons through photoionization. ' A recently described source generates electrons by photoionization of a metastable ('D2) barium beam with a He-Cd laser. The resulting photoelectrons have 17 meV kinetic energy and a calculated energy spread of less than 1meV. It is not easy to verify such an energy spread experimentally but it seems that in the final beam it is about 6 meV and most of this is ascribable to Doppler broadening in the target beam and to potential gradients across the collision volume.This is something of a breakthrough in electron-beam technology. The electrostatic and magnetic monochromators can of course be used to analyse the energy of the scattered electrons if this is desired. In practice the analyser end of an electron-scattering system is simpler to design than the input end because inter-electron interactions are less troublesome after scattering. (Hence photoelectron spectrometers in which the energies of photo-ejected electrons are analysed are much more easily designed and operated than electron- scattering spectrometers.) Many measurements on molecular excitation by electrons have been made in systems designed to collect only those electrons which lose all their energy in the collision.Frequently in such threshold excitation spectra optically forbidden transitions are prominent (Section 2B). In the trapped-well method initiated like so many electron-scattering techniques by Schulz the electron-molecule interaction region is a potential 'well' such that the scattered electrons having zero energy are trapped in the collision region and eventually migrate to a surrounding scattered-electron collector.' This experiment does have disadvantages ; for example negative ions as well as electrons are retained in the well and it is not easy to separate negative-ion current from electron current. However a modification to the system has been described in which the potential barrier defining the exit to the well can be modulated.' ' This overcomes the negative-ion problem as well as improving the effective resolution of the trap.' G. C. Baldwin and S. I. Friedman Rev. Sci. Instr. 1967 38 519. lo A. C. Gallagher and G. York Rev. Sci. Instr. 1974,'45 662. " F. W. E. Knoop. H. H. Brongersma and A. J. H. Boerboom Gem. Phys. Letters 1970 5 450. Interactions between Molecules and Electrons of Low Energy 55 A completely new technique for obtaining high-resolution threshold excitation spectra has been developed by CvejanoviC and Read.12 A weak electric field penetrates into the collision chamber producing a potential distribution which has the effect of extracting from the collision region only those electrons whose energy is within about 16meV of zero.It would be nice to see some molecules studied in this system. 3 'Direct' Scattering A. Elastic and Total Collision Cross-sections.-The equations of Section 2B indicate that total molecular collision cross-sections might be expected to vary markedly with electron energy even for simple potential scattering. While it is too much to hope that molecular electron distributions be established from electron-scattering data one can begin to try by correlation of experiment and theory to identify the dominant electron-molecule interactions. The most direct measurement of total collision cross-sections is in a single- collision experiment where I is measured at different gas pressures (Figure 1). Log I [cf.equation (l)] as a function of molecule number density n gives Q. This kind of experiment has disadvantages particularly if absolute cross-sections are demanded. Firstly n must be measured accurately and this is not a trivial exercise in the relevant pressure region 10-3-10-4Torr (760Torr = 101 325 N m-2). Most usually capacitance manometers are used but such instruments must be calibrated indi~idually.'~ Further the path length I is not easily defined. Finally electrons scattered through small angles may enter the trans- mitted-current collector. However if carefully done this kind of experiment is still useful at least for measuring relative cross-sections. An alternative and completely different technique is the molecular-beam recoil experiment.In this scattering is detected by recoil of the target molecule not of the electron. One obvious advantage of this is that instead of the molecule number density the electron number density is required and this is easily measured as electron current. A possible disadvatage is that because of the great difference between molecule and electron momenta the 180"centre-of-mass scattering angle is compressed into a few degrees of apparatus angle. (Contrast the electron-scattering situation where centre-of-mass and laboratory scattering angles are effectively the same). This means that in some cases the transformation from apparatus to centre-of-mass angle is not simple. Recent workers describe a fairly sophisticated kinematic analysis of beam recoil data.I4 This is one of a series of papers on scattering of electrons by alkali-metal halides.' These molecules are well chosen.They have very large dipole moments (-10 D FZ 3.33 x C m). The long-range electron-dipole interaction gives cross-sections which are very high and should be amenable to theoretical treatment. I S. CvejanoviC and F. H. Read J. Phys. (B),1974 7 1180. l3 G. C. Baldwin and M. R. Gaerttner J. Vacuum Sci. Technol. 1973 10 215. '4 M. G. Fickes and R. C. Stern J. Chem. Phys. 1974 60,4710. Is R. C. Slater M. G. Fickes W. G. Becker and R. C. Stern J. Chem. Phys. 1974 61 2290. I. C. Walker In fact the first Born approximation has been applied to the scattering of very low-energy electrons from polar molecules the justification being that most of the cross-section comes in small contributions from distant and thus only slightly perturbed electrons.The Born approximation gives a cross-section that is purely inelastic involving rotational motion [equation (17)] where rn is the electron-molecule reduced mass ,u is the molecular dipole moment (assumed to be a point dipole) J is the molecular rotational quantum number and J is either J (for the transition J-+ J -1) or J + 1 (for J-J + 1). Other transitions contribute nothing to Z(0). In the beam recoil experiments cross- sections are extracted from measurements using model 'Born-type' cross-sections with adjustable parameters which may be chosen to fit the measured data ; that is they are model-dependent. Total cross-sections so obtained are about a factor of two smaller than those calculated from equation (17) while associated momentum transfer cross-sections differ from calculated values by as much as a factor of ten below 1 eV.A modification to the simple Born approach produces better agreement with experiment. This gives the molecule a core of finite size arising out of the repulsive forces between incident and molecular electrons which are assumed to be so great that the electron can never penetrate the molecule.' Cross-sections for Na and K have also been obtained in molecular beam recoil experiments.' ' Very low-energy total collision cross-sections have been estimated from time-of-flight measurements (Section 2C). An early paper describing the time-of- flight spectrometer in detail reported cross-sections for helium and argon.' A recent one examines electron-nitrogen scattering for 0.3-1.6 eV.' At 0.9-1.5 eV the total collision cross-section equals numerically the momentum transfer cross-section obtained from analysis of swarm experiments.This means that within this energy range the scattering is isotropic; at lower energies Q is less than QD,indicating predominance of back-scattering [equation (1 l)]. These results vindicate the electron-swarm work. In the swarm experiments a pulse of electrons is pushed through the gas at high number density N by a d.c. electric field E. The swarm very quickly establishes its velocity distribution which depends only on E/N. Transport coefficients (diffusion coefficients drift velocity) are measurable as functions of E/N.These of course depend on the nature of the collisions between the electrons and the gas molecules. However the evaluation of cross-sections consistent with the measured parameters is not easy. The most satisfactory analytical technique was pioneered by Phelps et al. In this the Boltzmann transport equation appropriate to the particular system l6 M. R. H. Rudge J. Phys. (B) 1974 7 1323. " T. M. Miller and A. Kasdan J. Chem. Phys. 1973 59 3913 G. C. Baldwin Phys. Rea. (A) 1974 9 1225. Interactions between Molecules and Electrons of Low Energy 10-15 N .E 6 C .-* V x UY 0 I.V L 2 C *L. 10-l4 $ C E, z 10-IS 10-16 Electron enerpy/eV Figure 2 Momentum transfer cross-sections QD,as a function of electron energy for some hydrocarbons.(a) Saturated molecules (C,,H2,,+2); (I) methane CH," (2)ethane C,H,b (3)propane C,H 8b (4)butane C,H ob (5)neopentane C(CH,),' (b) (I) acetylene C2HZd (2)ethylene C2H,d (3)propylene C3H6b (4)cyclopropane C3H6' (5)but-I-ene C,H,' " Ref. 19; ref. 20; I. C. Walker unpublished results; C. W. Duncan and I. C. Walker J.C.S. Faraday ZZ 1972,68 1800 58 I. C. Walker is solved numerically using assumed cross-sections to give the electron energy distribution. Then transport coefficients are evaluated by suitably averaging over the distribution function. Comparison of these calculated values with experimental ones allows tailoring of the input cross-sections until calculated and experimental quantities agree.A method has been developed which allows the lengthy refinement process to be carried through automatically.’ This approach to cross-section determinations involving as it does the evaluation of microscopic cross-sections from a small number of measured average parameters suffers from the fundamental disadvantage that the derived cross-sections need not be unique. However experience suggests that it does provide meaningful cross- sections in fairly complicated species at low energies and indeed it is the only route to cross-sections at close to thermal energies (0.028 eV at 300 K). Some momentum transfer cross-sections derived in this way are illustrated in Figure 2.In all of these gases large inelastic cross-sections had to be included at vibrational threshold in order to force a fit between measured and calculated data.20 A recent book is devoted to electron-swarm behaviour,” and a bibliography of momentum transfer cross-sections has been compiled.’’ Chang has obtained an analytic expression [equation (18)Jfor the diffusion cross-sections of non-polar molecules in any rotational state J.23 This is pro- duced using the postulates of modified effective range theory originally developed for electron-atom scattering. In this the partial wave phase-shifts [equations (8)] are expressed as power series in k and In k for the long-range electron-molecule potentials. In equation (18) q is the molecular quadrupole moment a and a2 are the isotropic and anisotropic parts respectively of the polarizability tensor and a is the so-called scattering length ;it contains all the short-range potentials.When J is zero this expression reduces to equation (19) which is the more familiar equation for electron-atom scattering. For para-hydrogen 99.5 of which is in the J = 0 level equation (19)applies. A good fit to measured momentum transfer cross-sections is obtained for a = 5.5 a,. This compares with 5.44 a measured independently and 5.41 a calculated. The scattering length is 1.26a,; the cross- section extrapolates to 4na2 at zero energy. (Atomic units are used; rn = e = li = a = 1.) Analysis for other gases is less straightforward because of the ’’ C. W. Duncan and I. C. Walker J.C.S.Furuduy II 1972,68 1514. 2o C. W. Duncan and I. C. Walker J.C.S. Furuduy II 1974 70,577. z’ L. G. H. Huxley and R. W. Crompton ‘The Diffusion and Drift of Electrons in Gases’ John Wiley New York 1974. Y.Itikawa Argonne National Laboratory Report ANL-7939 1972. 23 E. S. Chang Phys. Rev. (A),1974 9 1644. Interactions between Molecules and Electrons of Low Energy 59 rotational dependence of the cross-sections but it seems clear that the term in 9,/a2 is correct and that QDdoes depend on the rotational population. Differential cross-sections contain more information than total collision cross-sections but few such measurements have been made at low energies. Truhlar et al. have studied simple diatomic species at intermediate energies.They attempt to reproduce experimental differential cross-sections using a Born-type approximation with different model interaction potentials. The energy region they scan is too low for the Born approximation to be strictly valid but in carbon monoxide for example one potential (the sum of dipole quad- rupole and polarization interactions) chosen by Crawford and Dalgarno to give correct momentum transfer cross-sections at 0.03 eV produces good differential cross-sections at 10-80 eV ; i.e. a model potential 'calibrated' at thermal energies can account for intermediate energy results.24 That theory and experiment are closely interdependent in this field of study is illustrated by He. Momentum transfer cross-sections believed good to 204 have been evaluated for helium from swarm data.The calculated value is still 5% lower than that measured. The discrepancy still has to be sorted out and this for the second most simple scattering system.25 B. Electronic and Vibrational Excitation.-One aspect of electron scattering which has obvious implications for our understanding of chemical processes is inelastic scattering with electronic excitation. As indicated above when the energy of the incident electron is low optically forbidden transitions may be excited. In particular spin-forbidden transitions are accessible through excitation with electron exchange and this affords a reliable means of positioning triplet states of molecules. Excitation with exchange requires the electron to associate fairly intimately with the molecule so that scattering tends to be isotropic; in a spin-allowed transition scattering is predominately about 8 = 0".This means that a spin-forbidden transition is recognizable because its differential cross-section relative to that of a spin-allowed transition increases with scattering angle. Also the cross-sections for excitation of spin-forbidden transitions tend to peak close to threshold energy while those for spin-allowed transitions are maximal at higher energie~.~ In Table 1 some low-lying triplet levels of unsaturated molecules recorded in electron scattering are listed. Most of the assignments are supported by calcula- tions. In some cases (notably acetylene) information on the triplet manifold comes solely from electron scattering.Where triplets have been located optically in general the 0 enhancement technique pioneered by Evans has been used. In this a spectrum is recorded in the presence of several atmospheres of 0 -this is hazardous to say the least. An alternative technique simply uses very long path lengths to ensure detectable absorption but this is very sensitive to impurities. In contrast an electron energy-loss spectrum is recorded at low gas pressures so is not sensitive to impurities and close to threshold a spectrum may be dominated by triplets. 24 D. G. Truhlar W. Williams and S. Trajmar J. Chem. fhys. 1972 10 4307. 25 D. K. Gibson R. W. Crompton and G. Cavelleri J. fhys. (B),1973 6 11 18. I. C. Walker Table 1 Triplet states in some unsaturated molecules.The energy/eV refers to the position of maximum intensity T stateslev Molecule TI T T3 Method and reference CH,=CH 4.3(jBlU) -7 -MeC H =CH 4.35 -EtCH=CH 4.25 -cis-MeCH =CH Me 4.3 -trans-MeCH =CH Me 4.3 -Me,C=CHMe 4.2 -Me C =C Me 4.1 -CHF=CH 4.4 -CF,=CH 4.63 cis-CHF=CHF 4.28 -electron energy- trans-CHFZCHF 4.18 -loss c CHF=CF 4.43 CF =CF 4.68 =i s-trans-butadiene 3.22 (3B2u) 4.91 (' Ag) -electron energy- loss d trans-hexa- 1,3,5-triene 2.66 ('B,) 4.2 ('A,) -modulated trap e HCcCH 5.3 (3ZU+) 6.0 ('Aa,) 8.01 (3n,)) MeC-CH 5.2 5.8 EtCrCH 5.3 5.8 -MeCECMe 5.0 5.8 J acetone 4.16 5.3-6.1 -electron energy- loss g a D. F. Dance and I. C. Walker Proc. Roy. Soc. 1973 A334. 259; 'D.F. Dance and I. C. Walker unpublished results; M. J. Coggiola 0. A. Mosher W. M. Flicker and A. Kuppermann Chem. Phys. Letters 1974 27 14; * 0.A. Mosher W. M. Flicker and A. Kupperrnann J. Chem. Phys. 1973 59 6502; F. W. E. Knoop and L. J. Oosterhoff Chem. Phys. Letters 1973 22 247; D. F. Dance and 1. C. Walker J.C.S. Faraday 11 1974 70 1426; W. M. St. John R. C. Estler and J. P. Doering J. Chem. Phys. 1974 61 763. Simpler species which have been studied are carbon dioxide26 and nitrous In the former an energy-loss spectrum recorded for incident energies very close to threshold and over a range of scattering angles has been unravelled with the aid of theoretical calculations on excited states to give transitions assigned to excitation of 3CU+,1*3Zu-,1*313g and 'q3AUstates between 7 and 10eV; likewise for N,O where a number of new low-lying states are claimed starting jlt about 5 eV.No electronic levels below 5 eV are apparent. This contradicts earlier threshold work which positions triplet states at 3.8 and 4.4 eV.28 The spectrum of water has been explored extensively. An explanation for one controversial '' R. I. Hall A. Chutjian and S. Trajrnar J. Phys. (B) 1973 6 L264. " R. I. Hall A. Chutjian and S. Trajrnar J. Ph-vs. (B) 1973 6 L365. M.-J. Hubin-Franskin and J. E. Collin. Bull. SOC.roy. Sci. Liege 1971 5-8. 361. Interactions between Molecules and Electrons of Low Energy 61 aspect of its spectrum has been offered by Lassettre and Huo.~~ Most of the recorded spectra for H,O show a weak feature corresponding to an energy loss of about 4.5 eV which experimentalists liked to assign to the lowest triplet state is 3B,.This would imply a bound state; the dissociation limits are 5.11 eV for OH(%) + H(2S) and 5.03 eV for O(3P)+ H2('Zg+). However repeated com- putations have not been able to produce a suitably attractive potential for this triplet level. Lassettre and Huo have now pointed out that in each of the experiments H -could have been transmitted to the scattered electron collector to give a signal at about 4.5 eV.29 The ii 3B state probably lies at 7.2 eV. This is near the calculated position. Also measurements on the optical oscillator strength of the corresponding singlet at 7.4 eV for 300,400 and 500 eV incident energies lead through equation (16) to3' equation (20).A position of 7.2eV E -E = 0.58 0.42 (20) for the 38,state is just within this range. Another H20 triplet has been located at 9.81 eV.31 Results for triplet states in a number of other molecules are cited in a recent review of electron-scattering spectroscopy. 32 At the other end of the spectrum electron energy-loss is useful for sorting out high-energy transitions. These include excitation of Rydberg states. A Rydberg-excited state is one where the excited electron finds itself in an orbital sufficiently far from the positive ion core to see it as atom-like. The energies of Rydberg states are then given by the formulae (21) where A is an ionization energy R is w= A -[R/(n -6)7 (21) the Rydberg constant and 6 the Rydberg correction or quantum defect.For molecules built up from atoms of the first Period 6 < 0.1 for states derived from nd electrons 0.34.5 for np electrons and 0.9-1.2 for ns electrons. The study of these excited states in molecules has been somewhat neglected because they frequently correspond to the vacuum-u.v. region of the spectrum and also because as the ionization limit is approached transitions to Rydberg- excited states become weaker and are difficult to sort out from strong valence transitions in the same spectral region. In electron scattering Rydberg states are frequently strongly excited. The interpretation of electron-scattering results is helped by photoelectron spectroscopy. Firstly photoelectron spectroscopy gives accurate values for ionization energies.Secondly because Rydberg orbitals do not contribute to bonding the vibrational structure associated with a Rydberg transition is similar to the vibrational spacing of the positive ion core and this is also observed in photoionization. Thus it is likely that photoelectron and electron-scattering spectroscopy will combine to give useful results in this area. l9 E. N. Lassettre and W. M. Huo J. Chem. fhys. 1974 61 1703. '' E. N. Lassettre and A. Skerbele J. Chem. Phys. 1974. 60,2466. -jl S. Trajmar W. Williams and A. Kuppermann J. Chem. fhys. 1973 58 2521. 32 1. C. Walker Chem. SOC.Rev. 1974. 3 467. 62 I. C. Walker Oxygen is a case in point; only a small number of Rydberg states are easily studied in photoabsorption.Electron-impact work aided by ab initio calculations and photon absorption measurements has located the first members (n = 3) of the Rydberg series which converge to the 02+(8211g)state (removal of a n* electron).33 The lowest of these is the 311gRydberg state which is the result of excitation of the n (n*)electron to the 3s0 level ; it appears in electron impact as structure on top of the Schumann-Runge continuum (B 3X=,-+8 3Eg-). The spacing and relative intensities of this vibrational structure indicate that the internuclear distance of this 311g(R)state is greater than that of the positive ion to which it is converging. Further the spacing between the vibrational levels 1 and 2 in this R state is anomalously large compared to that between levels 0 and 1.This is taken as evidence that the R state is crossed by a repulsive potential-curve between u’ = 1 and 2. This same anomalous spacing has been observed for the negative ion 02*-, in which two electrons are accommodated in the 3sa orbital34 (see Section 4). The assignment of the electronic spectrum of acetone is still a matter of some debate. The lowest singlet transition seen as the A band of vertical transition energy 4.4eV is no +n* but there has been considerable speculation as to the origin of all higher transitions. An electron-energy-loss spectrum has identified higher members of three Rydberg series with quantum defects of 1.03,0.81 and 0.315.35 The lower members of these extend into the spectral regions of the B c,and d bands which explains why they could not be classified in terms of valence transitions.Work on naphthalene likewise emphasizes the need to include Rydberg configurations for any theoretical analysis of its spectrum.36 Rydberg series have been assigned in alkyl derivatives of water and aliphatic carbonyl compounds and substituent effects on Rydberg orbital energies have been discussed using Taft (T* value^.^' Electron-impact and photoelectron spectra of cyclopropenone have been interpreted with the aid of SCF MO calculation^.^^ Removal of either an oxygen lone-pair electron or an olefinic electron causes significant change in the structure of the ion relative to the ground-state molecule indicating that these electrons are delocalized in the molecule.A number of Rydberg states are observed. Peart and Dolder claim to have prepared in its ground electronic state H3+ e-+ H3+ -* H+ + 2H + e-(22) the simplest polyatomic species.39 In the reaction (22) the threshold for H+ production is -15 eV which can be equated with the energy of the first excited 33 D. C. Cartwright W. J. Hunt W. Williams S. Trajmar. and W. A. Goddard. Phys. Rev. (A) 1973 8 2436. 34 L. Sanche and G.J. Schulz Phys. Rev. (A),1972 6 69. 35 R. H. Huebner R. J. Celotta S. R. Mielczarek andC. E. Kuyatt J. Chem. Phys. 1973 59. 5434. 36 R. H. Huebner S. R. Mielczarek and C. E. Kuyatt Chern. Phys. Letters 1972 16 464. 37 W.-C. Tam and C. E. Brion J. EIectron Spectroscopy 1974. 3 467. 38 W. R. Harshbarger N. A. Kuebler and M.B. Robin J. Chern. Phys. 1974. 60 345. 39 B. Peart and K. T. Dolder. J. Phys. (B),1974. 7 1567. Interactions between Molecules and Electrons of Low Energy 63 electronic state of H3+,3E while further enhancement of H+ production places the 'E level at about 19.25eV. Calculations of cross-sections for electronic excitation of molecules by electrons of low energy are few. Chung and Lin report calculated excitation functions for eleven electronic states of carbon monoxide (singlet and triplet) from threshold to lo00 eV.40 For the molecular wavefunctions Gaussian-type orbitals are used and a Born-type approximation is employed. This is of course a high- energy approximation and so good results are not to be expected at low energies. It also turns out that the experimental data are inadequate for an assessment of the accuracy of the calculations.Electrons can excite almost all vibrational modes of molecules. Swarm results are consistent with large inelastic cross-sections for i.r.-active vibrations close to threshold ;*O this could happen through interaction of the electron with the instantaneous molecular dipole. A variety of other interactions (electron- quadrupole electron-induced dipole etc.) can cause excitation of i.r.-inactive vibrational modes.4' 4 Resonance Scattering The negative ions familiar to chemists are those formed by attachment of an electron to a ground-state molecule having a positive electron affinity. Being bound they survive for sufficiently long to be detected in a negative-ion mass spectrometer.A study of electron scattering reveals negative ions where the electron is associated with excited molecular states. It is not unusual for a molecule which has a negative electron affinity in the ground state to have excited states with positive electron affinities. Also negative ions lying above the parent molecular state are detectable in scattering work.. Not surprisingly these negative ions have relatively short lifetimes and are frequently referred to as electron-molecule resonances. The discovery of these resonances (the first firmly identified by Schulz in 1963 in helium) caused a flurry of activity among physicists and in fact is probably directly responsible for much of the current popularity of atomic and molecular physics.Resonance phenomena were familiar to physicists ;they are widespread in sub-nuclear particles. The mathe- matical and physical properties of resonances have therefore been developed within the framework of nuclear physics. Schulz has summarized our present understanding of resonances in atoms and diatomic molecules.42 Briefly a resonance which lies above its parent state is a shape resonance so-called because the trapping is the result of the shape of the effective interaction potential ;the electron is held within a potential barrier generated by a combination of attractive forces and repulsive (centrifugal) forces. The repulsive potential which requires the electron to have angular momentum is lacking for s-waves and this places 40 S.Chung and C. C. Lin Phys. Rev. (A) 1974 9 1954. 41 H. T. Davis and L. D. Schmidt Chem. Phys. Letters 1972; 16 260. 42 G. J. Schulz Rev. Mod. Phys. 1973 45 423. I. C. Walker a symmetry restriction on the molecular orbitals which can trap the electron. The other kind of resonance is described as Feshbach resonance. A Feshbach resonance results when the electron enters an orbital of an excited molecule to give a bound negative ion. Usually a Feshbach resonance lies within 1 eV of its parent molecular state. These resonances are of course not stationary states; they decay exponentially with time as shown in equation (23) where 111/n12 ~XP (-rnt/h) (231 $, is the resonance wavefunction and r,,its linewidth. Its lifetime T equals h/r,,. In general Feshbach resonances are the longer-lived and may survive for suffi- ciently long to have well-developed vibrational structure.The lifetimes of shape resonances vary considerably. At the one extreme they may be so short-lived as to be barely detectable; at the other for a system with a sufficiently attractive potential within a high barrier a shape resonance may merge into a bound conventional negative ion. In the presence of resonance scattering the phase shift has two components a potential one qIp,and a resonance one qlr,which are related by equation (24). VI = Vlp + Vl (24) So a resonance may produce structure in the total cross-section at the resonance energy. Also a resonance may decay into lower-lying excited states [equation (25)] M + e -+ (M*-) + M* + e2 (25) and so be detectable as enhancement of particular inelastic cross-sections at the resonance energy.For short-lived resonances (10-14-10-s) any associated structure in the total collision cross-section is broad and may not be distinguish- able from any broad structure that is due to potential scattering. It may then be profitable to study the resonances in inelastic scattering. The different fates of a resonance are summarized in equations (26). ~ AB + e- elastic scattering (264 AB* + e- inelastic scattering (26b) AB + e- + (AB-*) T A + B- dissociative attachment (264 AB- attachment (requires removal of energy) (264 Table 2 gives properties of some molecular resonances seen as fine structure in the electron current transmitted through the sample gas; electron energy was selected in a trochoidal electron rnono~hromator.~~ Each of these resonances (except perhaps that for SO2)is a shape resonance in which the electron enters the 43 L.Sanche and G. J. Schulz J. Chem. Phys. 1973 58 479. Interactions bet ween Molecules and Electrons of Low Energy Table 2 Some properties of shape resonances in polyatomic molecules" Vibrational Molecule E nergy/eV Vibrational mod2 spacing (0-1 )/eV Symmetry co2 NO2 so2 N2O H2S C2H4 C6H6 3.14 (onset) 0.14 (onset) 2.87 (onset) 2.34 (max.) 2.30 (max.) 1.76 (max.) 1.14(onset) 100 100 010 100 --C-C 0.138 0.13W0.065 0.093' or 0.128 0.123 -- 2n. lA1 -2c B," 2E2" :A 1 sym. str. L. Sanche and G. J. Schulz J. Chem.Phys. 1973,58,479; The three numbers represent the quantum numbers for symmetrical stretching bending and unsymmetrical stretching respectively ; 'These values were obtained by extrapolating the spacing of the vibrational progressions to below zero energy stopping at the known electron affinity 2.38 eV; dThi value depends on the identity of the resonance. If the observed structure corresponds to highly excited levels of a ground-state shape resonance then the spacing is 0.128 eV. If the resonance is associated with an excited molecule 0.093 eV applies; see text. lowest available molecular orbital in the ground-state molecule. SO is anom- alous. It has a positive electron affinity (E.A. -1.1 eV) ie. the negative ion formed when an electron goes into the lowest available orbital is stable with respect to the neutral ground-state molecule.One then expects to see resonance structure corresponding to formation of vibrationally excited SO - starting for electrons of energy close to zero volts. The structure in fact does not start until -2.8 eV. Perhaps SO,-in its lower vibrational levels is so long-lived (sharp) that it is not detectable in this experiment while at higher energies the lifetime decreases making the resonance visible. Alternatively the resonance may be associated with an excited electronic level of SO,. Benzene appears to have a second shape resonance at 4-6 eV in addition to the one tabulated; this is interpreted in terms of a negative ion in which the electron enters the highest vacant x* molecular orbital.Substitution in the benzene ring removes the degeneracy of the lowest n* orbitals so that substituted benzenes have two shape resonances below 2 eV;44 the same is true of N-heterocyclic molecules.45 At higher energies each of the molecules in Table 2 (except benzene) shows sharp structure arising from Feshbach resonances associated with Rydberg-excited molecular states. Only one such resonance is apparent in ethylene lying about 0.5 eV below the first Rydberg excited state (the R state). This same resonance was independently identified in a threshold excitation e~periment.~~ The lowest Rydberg excited state of acetylene likewise has an electron affinity of ca. 0.5 eV.47 44 L. G. Christophorou D. L. McCorkle and J. G. Carter J. Chem. Phys.1974.60 3779. 45 M. N. Pisanias L. G. Christophorou J. G. Carter and D. L. McCorkle J. Chem. Phys. 1973.58 2 I 10. '' D. F. Dance and I. C. Walker Proc. Roy. SOC.,1973 A334 259. 47 D. F. Dance and I. C. Walker. J.C.S. Furuduv II 1974 70 1426. 66 I. C. Walker Bound negative ions are not apparent in the alkyl-substituted ethylenes and ace t y1enes. Of the polyatomic shape resonances in Table 2 that in CO has been most intensively studied.48 At 3.8 eV vibrational excitation of CO is possible both directly and via the resonance ;in the former case scattering is predominantly in the forward direction. The resonance can thus be nicely examined through large-angle scattering with vibrational excitation. Energy-loss spectra recorded at 90” scattering angle and around 3.8 eV incident energy show resonance excita- tion of no0 (symmetric stretch) and n10(symmetric stretch plus bend) vibrational modes.For any particular energy-loss the cross-section as a function of energy shows structure whose position and spacing depend on incident energy and also the particular vibrational modes excited. This irregularity in the structure has also been seen in the N shape resonance (-2.3 eV) and there successfully interpreted in terms of a resonance of ‘intermediate’ lifetime the ‘boomerang’ model. (Were the negative ion long-lived the structure would correspond to its vibrational levels.) The lowest lying C0,-ion is bent in its equilibrium configuration and also has a longer equilibrium C-0 bond length than the neutral ground-state molecule.Therefore at the instant of attachment the CO,- in order to attain its equilibrium configuration begins to stretch rapidly and more slowly to bend. If the ion survives for about s then it has time to complete about one complete stretching vibration but only part of a bending cycle. The stretching motion will therefore encompass many highly vibrationally excited stretching levels of the ground-state molecule but only a few low-lying bending vibrations as is observed. Angular-distribution measurements support the notion of two distinct energy-loss processes (in addition to direct e~citation).~’ Symmetry considerations show that the angular distributions of electrons resonantly scattered by molecules depend on the vibronic symmetry of the molecular states involved and for CO,-the theoretically predicted distributions conform to those measured.” This same negative-ion state of CO has been detected in a mass spectrometer with a lifetime of some microsecond^.^^ In this case it was produced by bombardment of succinic anhydride or maleic anhydride with electrons.In these organic species the CO entity is ‘bent’ and the long lifetime against detachment is explicable if there is an unfavourable Franck- Condon overlap between the bent ion and the linear neutral parent and if the potential-energy curve of the negative ion lies below that of the ground-state neutral species at 134”. It is of course about 3.8eV above at 180”. Shape resonances in more complicated molecules are discussed in a recent review article.32 Detailed measurements on resonances in diatomics and atoms continue.A high-resolution study on oxygen using a time-of-flight spectrometer has resolved the doublet structure of the 211g02-ion.52 This experiment confirms 48 M. J. W. Boness and G. J. Schulz Phys. Rev. (A) 1974 9 1969. 49 D. Danner thesis Physikalisches lnstitut der Universitat Freiberg 1970. 5” D. Andrick and F. H. Read J. Phys. (B) 1971 4 389. ’*C. D. Cooper and R. N. Compton Chem. Phys. Lefters 1972 14 29. 52 J. E. Land and W. Raith Phys. Rev. (A),1974. 9 1592. Interactions between Molecules and Electrons of Low Energy 67 an accidental coincidence between the u = 3 level of O2 (% 3Xg-) and the u = 8 level of 02-.Vibrational excitation of 0 at energies between 4 and 15 eV is resonance-enhan~ed.~ Two low-lying resonances 4Zu-(shape) and *Xu(valence Feshbach) appear to be accessible in this region.54 It has been established that any molecule or radical whose dipole moment exceeds 1.625 D (1 D = 3.33 x C m) has a positive vertical electron affinity; the additional electron is bound by the molecular dipole.55 Sharp structure has been observed in the elastic and vibrational cross-sections of the ground electronic state of carbon monoxide at energies coincident with the u = 0.1 and 2 levels of the d 311 state a valence excited state (m-+ x*).~~ No comparable structure is detectable in the energy range of the equivalent fi 3rIgstate of isoelectronic nitrogen. The explanation offered is that the electric dipole moment of the excited CO state (1.38 D) temporarily binds the incoming electron.The fi 31Tgstate of nitrogen does not have a permanent dipole moment. A common energy-calibration point in electron-impact work is the helium resonance (He- ls,2s2). Two recent measurements place this resonance at 19.367 f0.009 eVS7 and 19.361 f0.009eV.12 The first ofthese also evaluates the s-wave phase shift at the resonance energy from measurements on the elastic differential cross-section at 90" scattering angle where there is no contribution from p-wave scattering [equations (8)] ;this gives qo = 106" 3". The resonance width is given as 9 & 1 meV which is in good agreement with previous estimates. Incidentally as suggested by Gibson and D~lder,~~ this helium resonance offers a means of making measurements absolute independent of a knowledge of gas pressures (see Section 3A).Differential measurements give access to the phase shifts at the resonance energy [equations (8)]. These can then be used to calculate absolute cross-sections. This calibration technique may be applied to other simple systems where differential measurements are feasible. 5 Stable Negative Ions A. Experimental Methods for Measuring Electron Affinities.-Electron scattering does give some information on the structure of stable negative ions where these appear as nuclear excited resonances but a complete description of these negative ions including perhaps the most important fundamental property -the electron affinity-requires measurements on the ground-state negative ion.That this is not easy is manifest in the fact that accurate electron affinities are at present available for only a handful of species. Most of these have been obtained within the past three or so years the result of the development of beam techniques in particular those based on photodetachment processes (27). The measured 53 S. F. Wong M. J. W. Boness and G. J. Schulz Phys. Rev. Letters 1973 31 969. 54 M. Krauss D. Neumann A. C. Wahl G. Das and W. Zemke Phys. Rev. (A) 1973 7 69. 55 0. H. Crawford Mol. Phys. 1973 26 139. 56 S. F. Wong and G. J. Schulz Phys. Rev. Letters 1974 33 134. 57 S. CvejanoviC. J. Comer and F. H. Read J. Phys. (B) 1974 7 468. 58 J. R. Gibson and K. T. Dolder J.Phys. (B),1969 2 1180. I. C.Wslker AB x M Q) w Internuclear Distance Figurn 3 Energy terms associated with negative ions. E.A. is the electron aflnity VA.E. is the vertical attachment energy and KD.A. is the vertical detachment energy. Recent electron-afinity determinations concentrate on measurement of detachment-energy spectra AB-+ hv -+ AB + e-(27) quantity is the photon energy needed to detach the electron from the negative ion For a molecule the electron affinity is the detachment energy between the rotational ground state of the negative ion in its zeroth vibrational state and the corresponding rotational ground state of the neutral molecule in its zeroth vibrational state. This and other measurable parameters are illustrated in Figure 3.A good description of photodetachment experiments is given in a review article.” Now particularly with laser sources they are producing unambiguous electron affinities for atoms and simple molecules. Three somewhat different experiments are currently employed. In the first a linearly polarized laser beam of fixed frequency crosses the negative-ion beam prepared in a discharge.60 The ejected electrons are directed ihto a hemispherical electrostatic analyser where they are analysed for energy E,. Then E.A. = hv -E,. In this experiment a current maximum is recorded at energy E,; the maximum can be precisely located with reference to the electron signal from a species of known s9 B. Stejner ‘Case Studies in Atomic Collision Physics II’ ed.E. W. McDaniel and M.R. C. McDowell North-Holland Publishing Company Amsterdam 1972 p. 483. 6o M. W. Siegel R. J. Celotta J. L. Hall J. Levine and R. A. Bennett Phys. Rev. (A) 1972 6 607. Interactions between Molecules and Electrons of Low Energy 69 electron affinity say 0-(E.A. = 1.462+:::: eV). A molecular ion will usually give a detachment spectrum corresponding to transitions between different vibrational levels of ionic and neutral species (Figure 3). The different vibrational levels must be identified of course to give the electron affinity as defined. This same experiment has the useful facility of giving the anguIar distributions of ejected electrons by rotation of the laser polarization rather than by changing the geometry of the collision region.In a second experiment a fast negative-ion beam is crossed by a beam from a continuously tuneable laser.b1 Detachment is detected by directing the resulting fast neutral species at the cathode of a multiplier and monitoring the secondary electron current. The signal proportional to the cross-section for neutral atom production is a step function of the energy. This particular experiment allows exploration of the cross-section near threshold. This is expected to be a function of the forces between the product particles.62 For atoms Q cc I?'" ')I2 where I is the orbital angular momentum of the detached electron and E is its energy. Experiment has shown that this threshold law applies only very close to threshold within 5 meV in Se6' and 50meV in heavier species.This emphasizes the errors inherent in extrapolating cross-section data to threshold over wide energy ranges. In molecules the threshold behaviour will be modified by additional long-range electron-molecule interactions and this is not yet fully understood. Detachment using a tuneable laser has provided evidence for excited electronic states of Cz-.63The electron affinity of C is ca. 3.5 eV one of the highest known electron affinities. Irradiation of C,-with a laser over the wavelength range 5300-5450 A (2.5-2.2 eV) detaches an electron. The results are consistent with a two-photon process in which electronic excitation to a bound electronically excited state is followed by electron detachment from this intermediate state.These measurements establish that the ground state of C,-is 'Xg+. Bound electronic excited states are not known in the gas phase for any other molecular negative ion. A third photodetachment experiment using a laser source can be carried out in an ion-cyclotron mass ~pectrometer.~~ Negative ions are generated in the resonance cell in which a tuneable laser is directed along the cell axis. Photo- detachment is detected by monitoring the negative-ion concentration in the mass spectrometer ;the signal is a step function of the laser frequency. All of these experiments can of course be performed with conventional sources. However it seems likely that the best electron-affinity measurements will continue to be obtained using such photodetachment procedures with laser beams.The experimental procedures are fully described in the cited papers. Two other beam techniques are aIso being applied to the determination of electron affinities. Both are based on the measurement of energy-threshold 6' H. Hotop T. A. Patterson and W. C. Lineberger Phys. Rev. (A) 1973 8 762. 62 T. F. O'Malley fhys. Rev. (A) 1965 137 1668. 63 W. C. Lineberger and T. A. Patterson Chem. fhys. Letters 1972 13 40. b4 K. Smythe and J. I. Brauman J. Chem. Phys. 1972,56 1 132. 70 I. C. Walker processes producing the negative ion in question. In endothermic negative-ion charge-transfer the reaction is :65 X-+AB-+ X+AB-(28) A negative-ion beam whose energy can be varied is directed through the sample gas AB and the threshold energy Eth,for production of AB-is measured.Then equation (29)is valid. This experiment requires a knowledge of the electron E.A.(AB) = E.A.(X) -Eth (29) affinity of X as well as a means of establishing the threshold energy. This last requirement is not easy. Experimentally the cross-section as a function of energy displays tailing and curvature which can obscure the true onset. This tailing depends on the thermal velocity distribution of the neutral gas molecules (Doppler broadening) and the shape of the true threshold function. This can be arrived at by substituting a calculated energy distribution into an assumed threshold function and adjusting the threshold function to get a match with the experimental curve. In addition any one value of electron affinity should be deduced from several different charge-transfer reactions and using negative-ion reactants produced in different sources.Considering the difficulties associated in evaluating the data the results achieved for small molecules in this experiment seem good and stand up to comparison with those from photodetachment work. The other charge-transfer reaction is collisional ionization :66 X+AB+ X++AB-(30) where X is commonly caesium. A Cs beam of variable energy passes through the sample gas and as before the threshold energy for reaction (30) is identified. If AB and AB-are in their ground energy levels equation (31) holds. Cs is a E.A.(AB) = I.P.(Cs)-Eth (31) popular component in molecular beams and so the physics of the interaction leading to the electron transfer is fairly well understood.In this experiment again the energy threshold is obscured by the essential lack of resolution and unfolding techniques must be used to produce a true cross-section curve from that observed. Details of the data-handling procedures have been described.64 Calculations suggest that the Cs' acts as a very efficient third body removing excess vibrational energy from the negative ion so that equation (31) applies. However absolute values appear less good than those from endothermic charge- transfer reactions ;where comparison with reliable values is possible collisional ionization values appear somewhat high (Table 3). B. Measured Electron Affinities.-The electron-affinity values in Tables 3 and 4 are limited mainly to those recently measured using tested techniques.For some b5 B. M. Hughes C. Lifshitz and T. 0.Tiernan J. Chem. Phys. 1973 59 3162. 66 S. J. Malley R. N. Compton H. C. Schwanter and V. E. Anderson J. Chem. fhys. 1973,59,4125. Interactions between Molecules und Electrons of Low Energy Table 3 Selected molecular electron afinities Ion E.A./eV Method Ref Comments 0.440 f0.008 Pa a see text 02 --2.0 CT b 03-1.663 f0.040 Pa c see text s2-F2 -3.08 f0.1 CT d c1,-2.32 f0.1 CT e 2.38 f0.1 CT d Br,-2.62 f0.2 CT e 2.51 f0.1 CT d 2.42 f0.2 CT e I2 -2.58 f0.1 CT d IBr-2.7 f0.2 CT d NH-0.38 f0.03 Pa c + 0.010 c OH-0.014 Pa 1.825 f0.002 Pb f see text OD-1.823 k0.002 Pb f SH-2.301 f0.001 Pc g SeH-2.21 f0.03 Pc h + 0.01 1 NO-0.024 -0.005 Pa 0.015 f0.1 CT e 0.1 f0.1 CI j 0.025 ES k N20-0.15 f0.1 CI j NO -2.36 f0.10 Pb 1 see text 2.5 f0.1 CI j 2.28 f0.1 CT e 2.38 f0.06 CT m NH -0.779 f0.037 Pa e 0.744 f0.022 Pc n PH -1.25 f0.03 Pc 0 ASH,-1.27 f0.03 Pc n C2H-2.21 & 0.4 CT e SiH,-< 1-44 0.03 Pc P GeH3-< 1.74 f0.04 Pc P so 1.097 f0.036 Pa C see text 0.99 f0.1 CT e cs -0.5 & 0.2 CT e SF -22.8 f0.1 CT 4 22.8 f0.2 CI r SF6-20.6 f0.1 CT 4 + 0.1 0.54 -0.17 CI r TeF6-3.34 ::;7 CI r (hexafluorobenzene)-(octafluorotoluene) -(perfluorocyclohexene) (nitrobenzene)-(tetracyanoethylene)-(ethyl nitrene) 21,8 f0.3 CT 4 2 1.7 & 0.3 CT 4 21.4 f0.3 CT 4 20.7 f0.2 CT 4 2.03 f0.07 Pd S <1.87 f0.16 Pc t 72 I.C. Walker Table kontinued Ion E.A./eV Method Ref Comments (maleic anhydride)- (cyclopen tadienide) -(methylcyclo-pentadienide)-(tetrafluorosuccinic 1.4 f0.2 < 1.84 f 0.03 < 1.67 &-0.04 CI Pd Pc U U V anhydride)-(hexafluoroglu taric 0.5 f 0.2 CI W anhydride)- 1.5 &-0.2 CI W Abbreviations Pa photodetachment with a fixed frequency laser Pb photodetachment with a tuneable laser Pc photodetachment in an ion-cyclotron resonance mass spectrometer Pd photodetachment with conventional optical sources CT charge transfer [equation (28)] CI collisional ionization [equation (30)] ES electron scattering; R. J. Celotta R. A. Bennett J. L. Hall M. W. Siegel and J.Levine Phys. Rev. (A) 1972,6 631 ; J. A. Ruther- ford B. R. Turner and D. A. Vroom J. Chem. Phys. 1973 58 5267; R. J. Celotta R. A. Bennett and J. L. Hall J. Chem. Phys. 1974,60,1740; W. A. Chupka J. Berkowitz and D. Gutman J. Chem. Phys. 1971,55 2724; ref. 65; H. Hotop and T. A. Patterson J. Chem. Phys. 1974 60 1806; J. R. Eyler and G. H. Atkinson Chem. Phys. Letters 1974 28 217; K. C. Smyth and J. 1. Brauman J. Chem. Phys. 1972 56 5993; ' ref. 60; ref. 66; Ir P. Burrow Chem. Phys. Lerrers 1974 26 265; ' E. Herbst T. A. Patterson and W. C. Lineberger J. Chem. Phys. 1974 61 1300; D. B. Dunkin F. C. Fehsenfeld; and E. E. Ferguson Chem. Phys. Letters 1972,15,257; " K. Smyth and J. I. Brauman J. Chem. Phys. 1972 56 4620; 'ref. 64; K. J. Reed and J.I. Brauman J. Chem. Phys. 1974 61 4830; 4C. Lifshitz T. 0. Tiernan and B. M. Hughes J. Chem. Phys. 1973 59 3182; 'R. N. Compton and C. D. Cooper J. Chem. Phys. 1973 59 4140; 'L. E. Lyons and L. D. Palmer Chem. Phys. Lerrers 1973 21 442; ' J. H. Richardson L. M. Stephenson and J. I. Brauman Chem. Phys. Lerters 1974 25 321 ;" R. v. Compton and P. W. Rein-hardt J. Chem. Phys. 1974 60 2953; "J. H. Richardson L. M. Stephenson and J. I. Brauman J. Chem. Phys. 1973 59 5068; C. D. Cooper and R. N. Compton J. Chem. Phys. 1974 60 2424. diatomic species the measured data allow construction of a potential-energy curve for the negative ion giving access to structural parameters for the ion. For 0,- re = 134.1 k 1 pm and o,= 1089 cm-' (corresponding values for the 0 ground state are 120.74 pm and 1580.36 cm-').For NO- re = 125.8 5 1 pm and a,= 1470 cm- (corresponding values for NO are 115.08 pm and 1904 cm- '). A number of experiments on the hydroxyl radical confirm that the internuclear distance and vibration frequency of the negative ion are very close to those of the neutral parent radical r,(OH-) = r,(OH) k 0.1 pm and o,(OH-) = o,(OH) -(51 74)cm-'. This is consistent with placement of the extra electron in a non-bonding orbital. The vibration frequency of S2-is 725.68 cm- ' (hvvi = 0.065 eV) and the symmetric stretch frequency of SO,-is 988.37 cm-' (hvvi = 0.122eV). The difference in electron affinities between OH and OD is believed to be real and almost entirely due to differences in position of the rota- tional states in OH ('n,) and OD ('n,).The electron affinities of the halogens are not known precisely but do increase in the order C1 < Br x I < F,. The electron affinity of NO, long disputed is at last established as -2.36 eV. Further the photodetachment experiments have indicated an isomer of NO - perhaps a peroxy isomer with an electron affinity of ca. 1.8eV. Calculations seem to support the existence of such a species. The contrasting behaviour of Interactions between Molecules and Electrons of Low Energy Table 4 Selected atomic electron ufinities Ion E.A./eV Method Ref Comments Li- 0.620 Pa a 0.61 k 0.05 Pd b Na- 0.548 Pa a 0.543 Pb a 0.53 f0.05 Pd b K- 0.5012 Pa a 0.50 f0.05 Pd b Rb- 0.486 Pa a see text 0.4859 Pb a 0.48 f0.05 Pd b cs- 0.470 Pa a 0.472 Pb a 0.47 f0.05 Pd b Ge- 1.20 f0.1 Pd b Sn - 1.25 +_ 0.1 Pd b P- 0.77 t 0.05 Pd b As- 0.80 t 0.05 Pd b Sb- 1.05 & 0.05 Pd b Bi- 0.9-1.2 Pd b 0- Pa see ref.c S- 2.0772 0.0005 Pb d Se- 2.0206 f0.003 Pb e Te- 1.9 & 0.15 Pd b Cr- 0.66 t 0.05 Pd b cu - 1.226 0.01 Pa C Ag- i-0.007 1.303 -0.01 1 Pa C Au - 2.3086 f0.0007 Pb f Pt- 2.128 & 0.002 Pb f Abbreviations are as for Table 3; J. A. Patterson H. Hotop A. Kasdan D. W. Norcross and W. C. Lineberger Phys. Rev. Letters 1974 32 189; bD. Feldmann R. Rackwitz E. Heinicke and H. J. Kaiser Phys. Letters 1973 45A,404; H. Hotop R. A. Bennett and W. C. Lineberger J. Chem. Phys. 1973,58,2373;* W. C. Lineberger and B. Woodward Phys.Rev. Letters 1970 25 424; H. Hotop and T. A. Patterson Phys. Rev. (A) 1973 8 762; H. Hotop and W. C. Lineberger J. Chem. Phys. 1973 58 2379. SF and TeF towards low-energy electrons is interesting. As indicated in Table 3 TeF has a very large electron affinity and yet it has a very small attach- ment rate constant. The converse holds for SF,. The photodetachment experiments of Patterson et al. on the alkali metals have revealed in addition to reliable electron-affinity values strong resonances just below the first excited electronic states 'P+ and 'Pt. In Rb the lower resonance has an estimated width of about 150 peV by far the narrowest resonance yet detected. Comparison of the electron-affinity data of Table 4 with those in a recent compilations9 shows that until now the best estimates of many of these electron affinities were calculated values.In particular some of the empirical methods 74 I. C. Walker where electron affinities are extrapolated from known ionization energies have given remarkably good results.59 The exact quantum calculation of electron affinities is a challenging problem. Any electron affinity is the small difference between two large quantities the energy of neutral species and ion respectively. So for example correlation effects which are sometimes negligible in Hartree- Fock computations cannot be ignored in electron-affinity calculations. A review of the theoretical methods that have been adopted is contained in a paper which also details a new approach to the problem.67 In this ionization energies (which include electron affinities) are determined directly without recourse to separate evaluation of energies and wavefunctions of the neutral and ionic species.For OH it gives an electron affinity within 0.1 eV of the measured value.68 An alter- native direct calculation using the one-particle Green-function method has also been applied to the evaluation of molecular electron affinities. It gives -0.24 eV9 for the electron affinity of the methyl radical; this has not yet been measured. Uncertainties associated with experimental electron affinities are frequent 1y due to uncertainty about the energy state of the ion under study. Negative-ion formation through electron attachment [equations (26c) and (26d)l is an active area of study not treated here.A chapter of a recent book covers this topic.” 6 Conclusion This article has concentrated exclusively on electron-molecule systems in the gas-phase. In this area there are now available experimental techniques which could be almost routinely applied to the exploration of molecules of chemical interest. It is hoped that this Report has indicated the usefulness of such work. At the other extreme the study of electrons in condensed phases is attracting increasing attention. It would seem appropriate to look also at the changing behaviour of electrons from dilute gases through high-pressure gases to liquids in which a good deal is already known about the physical and chemical behaviour of solvated electron^.^' Some work in this area has been done in the measurement of electron drift velocities in gases at up to 50atm.pressure when the drift velocity becomes a function of gas pressure. Two not necessarily mutually exclusive explanations have been offered. Firstly at moderate pressures electron trapping through resonance formation could impede the electron’s progress through the gas ;at such pressures the cumulative effect of the very many delaying encounters would be measurable.’* At very high pressures a more plausible explanation is that the electron sees a homogeneous scattering medium approaching the condensed-phase situation. This could account for observed 67 J. Simons and W. D. Smith J. Chem. Phys. 1973,58,4899. 68 W. D. Smith T.-T. Chen and J. Simons Chem.Phys. Letters 1974 21 499. 69 L. S. Cederbaum and W. von Messen Phys. Letfers 1974 47A,199. 70 L. G. Christophorou ‘Atomic and Molecular Radiation Physics’ Wiley-Interscience New York 1971 Ch. 6. 71 See e.g. D. C. Walker Quarr. Rev. 1967 21 79; M. Anbar ibid. 1968 22 578. 72 R. W. Crompton and A. G. Robertson Austral. J. Phys. 1971 24 543. Interactions between Molecules and Electrons of Low Energy effects.’ Of course under these conditions resonances arising from electron trappings by aggregates of molecules might be feasible. More recently Christophorou et al. have looked at electron attachment to sample gases in the presence of very high pressures of inert molecules. They conclude from measure- ments on benzene that it must have a small positive electron affinity;74 other electron-scattering experiments have not indicated this (see for example Table 2).In any event it seems likely that the free electron will find increasing applications as a ‘reactant’ in chemistry laboratories. ” W. Legler Phys. Letters 1970 31A 129. L. G. Christophorou and R.E. Goans J. Chem. Phys. 1974,60 4244.

ISSN:0308-6003    

DOI:10.1039/PR9747100049

出版商:RSC    

年代:1974

数据来源: RSC

摘要:

5 Heavy-atom Kinetic Isotope Effects By A. MACCOLL Department of Chemistry University College London WC 7 H OAJ 1 Introduction To the best knowledge of the reporter this subject has not as such been previously reported on although specific results of the application of the techniques have been referred to from time to time. For this reason it is proposed to give a general account of the theory and practice of the technique so that the reader interested in applying it or assessing the results obtained will have key references. A useful starting point is the indexed bibliography produced by Stern and Wolfsberg and published by the National Bureau of Standards.' This lists papers published since the earliest entry until 1965 in the case of experimental work and 1968 in the case of reviews and theoretical papers.The plan of the present article is to summarize first the terms used and the theoretical treatment. This is then followed by a section on experimental methods and on the interpretation of the experimental results. Finally an account is given of applications of the method in the cases of carbon nitrogen oxygen sul- phur and chlorine. One of the challenging problems of chemical kinetics is the specification of the properties of the transition state of a chemical reaction. The problem may be approached at either a topological or a metrical level; in the latter case one requires as well as the geometrical structure the mechanical properties. By topological level is meant the discussion of whether for example a transition state is cyclic or acyclic or which end of a bidentate group attacks a molecule.Such is the province of physical organic chemistry although the metrical aspects can be hinted at when the degree of bond breaking or bond forming is discussed. The requirement of knowing the geometry and the mechanical properties must be met if an attempt is to be made at predicting quantitatively the rate of reaction. Thus in the case of unimolecular gas-phase reactions (of molecules radicals or ions) the rate constant as a function of internal energy is given by ' M. J. Stern and M. Wolfsberg 'Heavy Atom Kinetic Isotope Effects. An Indexed Bibliography' N.B.S. Special Publication 349 U.S. Dept. of Commerce Washington D.C. 1972. 77 A.Maccoll where e is the critical energy e the internal energy CT the reaction path de- generacy W(e -e,) the number of states of the activated complex with energy less than or equal to e -e, and p(e)the density of states for the normal molecule at energy e. ZAIBIC and (IAIBIc)* are the products of the principal moments of inertia for the ground and transition states respectively. To evaluate both the density and the number of states a knowledge of the vibrational frequencies in both the ground and transition states is required. For a reaction of a molecule the ground-state frequencies are usually known ; those for the transition state have to be estimated. On the other hand for the reaction of a radical (e.g.decom-position) or of an ion (e.g.electron impact fragmentation) the frequencies for the ground state are usually unknown as are those of the transition state so the problem really becomes difficult.Any evidence pertaining to the properties of the transition state must per se be valuable. In the case of ground-state molecules spectroscopic techniques including isotopic substitution can lead to a complete structural definition together with an identification of the vibrational frequencies. This suggests that the effects of isotopic substitution upon reaction rates can in principle do the same for transition states which is the underlying reason for the studies described herein. The term 'heavy-atom kinetic isotope effect' refers to the effect for atoms other than hydrogen mainly carbon nitrogen oxygen sulphur and chlorine.The atomic weights and percentage abundances are shown in Table 1. The important Table 1 Isotopic masses and percentage abundances Element 12C Atomic mass (C = 12.000 00) 12.00000 Percentage abundance 98.892 'jC I4N 13.003 36 14.003 07 1.108 99.645 I5N 15.000 11 0.355 6O 15.994 9 1 99.759 170 16.999 13 0.037 *O32sjsj4S36s 17.999 16 3 1.972 07 32.971 46 33.967 86 35.967 09 0.204 95.01 8 0.750 4.215 0.017 3 5c1 34.968 85 75.529 37c1 36.96590 24.471 approximation that can be made in this case is m* m << m,m* and v -v* << v v* where the asterisk refers to the heavy isotope. The first person to realize the importance of and to formalize the treatment of kinetic isotope effects was Bigeleisen2 following upon the formalization of isotopic equilibria by Bigeleisen and G~eppert-Mayer.~ The theory will be dealt with * J.Bigeleisen J. Chem. Phys. 1949 17 675. J. Bigeleisen and M. Goeppert-Mayer J. Chem. Phys. 1947,15 261. Heavy-atom Kinetic Isotope Eflects in a subsequent section. Experimentally most workers have used isotopic species of natural abundance and made precise measurements of the isotopic ratio as a function of percentage reaction. To do this a double-collector mass spectrom- eter is necessary which enables a comparison of the ion beam from the minor isotopic species to be backed off against a fraction of the ion beam from the major isotopic species e.g. [' 3C02'I/[' 2C02'3. For technical reasons such as dis- crimination in the mass spectrometer absolute ratio measurements are not attempted ;rather the ratio for the unknown is compared with that for a standard.This is quite suitable for kinetic studies since the ratio for the reactant (or product) at time t can be compared with that of the reactant at zero time or a product (provided it contains all the isotopic species) at infinite time. Because of the experimental skills required and because twin-collector mass spectrometers have only recently become available commercially work in this field has in the past been restricted to a relatively small number of schools. Since it is a method of considerable power it can be anticipated that increasing efforts will be made in this field. This is especially true in the area of gas-phase kinetics where the behaviour of an isolated molecule can be examined without the complicating co-operative effects of the solvent inherent in studies of reactions in solution.2 Some Terms and Definitions The isotope effect is measured as k/k* where the asterisk refers to the heavier species. If k/k* > 1 the effect is said to be direct or normal; if k/k* < 1 it is said to be inverse. If the heavy atom is directly concerned in bond breaking or bond making in the transition state the effect is said to be primary ;if not the effect is secondary. Consider a species such as malonic acid for which there are four possible decarboxylation reactions (Scheme 1). k3/k2measures the intramolecular CO,H / CH -% CH,CO,H + CO \ CO,H / 13C02~9CH,13C0,H + CO CH2 \ COZH %A CH,C02H + 13C0 CO,H k4 VH -13CH,C0,H + CO \ CO2H Scheme 1 A.Maccoll kinetic isotope effect and k,/k2 the primary intermolecular kinetic isotope effect. k,/k4 measures the secondary intermolecular kinetic isotope effect. 3 Theoretical Treatment Bigeleisen2 started with the absolute rate theory equation (;)+ where the symbols have their usual significance. The ratio of the rate constants is then given by -k -~c Q*(M**)* (3) k* K*Q** M* This equation finally reduces to 3n-6 3n-6 S -1 -exp (-ui) exp C (ui -u:)/2 k~ -S* 1 -exp(-u*) I 3n4 -7 k* K* S* 3, -7 1 -exp(-u') S* * -exp(-ut*) exp C (u? -ut+)/2 _--"1 1 (4) by substituting the usual expressions for the partition functions.In equation (4),the M's are the molecular weights the Z's the moments of inertia and the u's are given by ui= hvi/kT where the vi's are the vibration frequencies. The s's are the symmetry numbers. For isotopically substituted molecules the Teller- Redlich product rule4 holds namely where the m's are the masses of the atom or atoms which are isotopically sub- stituted. Introducing (5) into (4)gives where the v *'s represent the imaginary frequencies corresponding to motion along the reaction co-ordinate. The symmetry numbers can be removed by multiplying both sides of equations (4)and (6)by (s*/s**)/(s/s*) to yield ks*S*K* ~~ = HRR k*s* 0.Redlich Z. Phys. Chem. 1935 B28,371. Heavy-atom Kinetic Isotope-Eflects where HRR is the rate constant ratio on the harmonic oscillator rigid rotator approximation.? Equations (4)and (6)can also be written HRR = MMI x EXC x ZPE (44 V* ~ HRR = ,1* * x VP x EXC x ZPE (64 In these expressions MMI is the mass-moment of inertia factor EXC the vi-brational excitation factor ZPEthe zero point energy factor and VP the vibrational frequency product factor.$ In the case of heavy atom kinetic isotope effects Bigeleisen introduced the quantity Aui = ui -u and using the fact that Aui << ui,expanded equation (6) to yield 3n-6 3nt -7 G(u,)Au -C G(u’)Au’ (7) I where G(u)= (1/2) -(l/u) + [l/(eu-l)] and had previously been tabulated by Bigeleisen and G~eppert-Mayer.~ An alternative form of equation (4),appro-priate to the case of unimolecular gas-phase reactions has been suggested by Chri~tie.~ It is r 3n-6 HRR = MI 1 + $ C (coth uJ2) Aui -33,-C7 (coth u’/~)Au+ 1 li i where MI = In order to apply these formulae it is necessary to know the geometry of the ground and transition states and also the vibrational frequencies.In the cases of equations (4),(6),and (8) the expression for HRR can be factored into a tem- perature-independent factor (TIF) and a temperature-dependent factor (TDF). The above formula can be simplified at low and high temperatures. For as T +0 u+co and EXC +1 equations (4)and (6)become HRR = MMI x ZPE (9) t This seems a better use of the letters than “harmonic rate ratio” used by Van Hook.’ $ This nomenclature was introduced by Wolfsberg and Stern.’ W. A. Van Hook,in ‘Isotope Effects in Chemical Reactions’ ed. C. J. Collins and N. S. Bowman ACS monograph No 167 Von Nostrand Rheinhold New York 1970 p. 11. M. Wolfsberg and M. J. Stern Pure Appl. Chem. 1964 8 225. ’ Private communication. See also J. R. Christie W. D. Johnson A. G. Loudon A. Maccoll and L. M. N. Machacek J.C.S. Furuduy I submitted for publication A. Maccoll Because of the approximations made in deducing equation (8) it is not amenable to proceeding to the limit T -P 0. Again at high temperatures u 0 ZPE + 1 and EXC +(VP)-and equations (4)and (6)become MMI HRR = ~ VP The high-temperature limit of equation (8) is HHR = MI (13) A further form of the high-temperature approximation is given by expanding equation (7) in powers of T-‘.This yields where aii -a is the difference in the diagonal element of the Cartesian force constant between the ground and the transition state. Alternatively where the fij and gijare the elements of the Wilson F and G matrices.* To extend the range of application of equations (14) and (15) to lower temperatures Bigeleisen and Wolfsberg’ defined a parameter 7= 12G(ui)/ui,and replaced the factor 1/24 by 7/24 and 7*/24 where 7 is an average value for the given molecule 7’ being that for the activated complex. This approximation depends upon the fact that yi is a slowly varying function of ui. Wolfsberg and Stern6 examined the validity of this approximation concluding that it is only useful for making qualitative predictions of isotope effects.The question arises as to the calculation of v*/v** and two approaches have been used. The first derives from the Slater theory,” in which bond rupture occurs when a bond reaches a critical extension. In this case V* (;) v*+ = f where p = M,MB/(M + MB),A and B being the two atoms concerned in the bond. Alternatively Bigeleisen and Wolfsbergg consider the two fragments produced by bond rupture in which case the atomic masses in equation (16) become replaced by the fragment masses. More realistically the vibrational prob- lem can be solved on the basis of an assumed patential-energy surface for the E. B. Wilson jun. J. C. Decius and P. C. Cross ‘Molecular Vibrations’ McGraw-Hill New York,1955.J. Bigeleisen and M. Wolfsberg Ado. Chem. Phys. 1958 1 15. ’ O J. C. Slater ‘Theory of Unimolecular Reactions’ Methuen London 1959. Heavy-atom Kinetic Isotope Eflects transition states and the ratio of the imaginary frequencies for crossing the col calculated. It has already been noted that in order to treat any specific case the geometry of both the ground state and the transition state must be known as must the vibration frequencies for each of the states. The moments of inertia of the ground state can readily be obtained from structural data; those for the transition state will contain parameters which can be varied according to the model. It should be noted that using equation (4) or (8) the terms MMI and MI are temperature- independent and so in principle should enable transition-state geometry to be decided.Unfortunately the correspondence will not be one to one in that a range of parameters will give rise to the same value of MMI or MI. The frequencies for the two species in the ground state can be determined experimentally or calculated by the Wilson method from a knowledge of the force constants. It will be found that only a limited number of these will change significantly upon isotopic sub- stitution. For the transition state the frequencies or force constants have to be assumed. This part of the model will be reflected in the temperature-dependent factor of the rate constant ratio. Williams and Taylor,'' in their studies of t-butyl chloride have synthesized t-C4H,35C1 and t-C4H937C1 and measured their spectra.They have also used Wilson's FG method to calculate the frequencies. Frequencies for t-C,H 5C1 Table 2 Vibrational frequencies and shifts in t-C,H,Cl Obseri,ed/cm-' Calculated/cm-' Degeneracy1 v(t-C.,H 35Cl) Av v(t-C,H9 35Cl) Av 2 30 1 d 1.5 301.0 1.48 1 312 3.8 f0.5 372.2 4.16 2 408 - 408.0 0.10 1 585 2.6 & 0.1 585.0 2.7 1 1 818 0.5 f0.3 818.1 0.72 2 1210 d 0.2 1210.1 0.20 and the corresponding shifts are shown in Table 2. By these methods a complete treatment of the calculation of the rate constant ratio can be made. Stern and Wolfsberg6*12 have described a 'cut-off technique that simplifies the calculation. They point out that the computer time required for the solution of the vibrational problem varies roughly as the third power of the number of atoms.Thus for a molecule of any degree of complexity the computer time required may be prohibitive. According to equation (15) it is permissible 'to omit (cut off) portions of the molecule that do not include the atoms necessary to specify all the internal co-ordinates which both involve the isotopic position and have associated with them force constant or geometry changes between reactant and transition state'. The results of calculations of these authors on the decomposition of malonic acid (vide infra) are shown in Table 3.12 'I R. C. Williams and J. W. Taylor J. Amer. Chem. Soc. 1973 95 1710. I' M. J. Stern and M. Wolfsberg J. Chem. Phys. 1966,45 4105. 84 A. Maccoll Table 3 Cut-ofScalculutionsforHOOCCH,L3COOH-+[HOOCCH,..3COOH]* k1/2k3 ___ Individual factors at GLIGL 300 K" Model reaction 300K VP EXC ZPE v:/vz HOOCCH,"COOH -+[HOOCCH,...' 3COOH]b 1.0245 0.9946 1.OOO4 1.0296 1.0054 C-CH~'3COOH-+[C-CH~**~'3COOH] 1.0244 0.9962 0.9994 1.0290 1.0038 45Y-CH2'3COOH-)[45Y-CH2~~~13COOH]C 1.0244 0.9944 1.OOO4 1.0298 1.0056 C-' 3COOH +[COO'3COOH] 1.0241 0.9977 0.9991 1.0273 1.0023 s9y-13COOH~[s9y...13COOH]d 1.0265 0.9938 0.9992 1.0338 1.0063 C-CH,-l3C -+ [C-CH,. *.13C] 1.0340 0.9740 1.0027 1.0587 1.0267 c-'3c+[C...-'3C] 1.0334 0.9806 1.0005 1.0533 1.0198 (a)MMI in all cases is unity since reactant and transition-state geometries are identical. (b) Complete cal- culation. Geometry and force constants given in footnote a of Table 8 of ref.12. (c) 4sY is an atom with mass of 45 a.m.u. representing COOH. (d) 59Yis an atom with mass of 59 a.m.u. representing HOOCCH,. A further example of cut-off calculations comes from Fry et al.' These authors investigated 14C and 37Cl isotope effects for the reaction Y + R*CH,X + [Y*.*R*CH,*-.X]*+ R*CH2Y+ X The models used were (1) the complete molecule (2) inclusion of three ring- carbon atoms and (3) inclusion of only one ring-carbon atom. HH HH HH \/ \/ \/ y...c...c1 y.. .c.. .c1 y...c.. .c1 I I C C c'/\ ....-1 'c v (1) (2) (3) The calculations were performed for various bond orders of the Y-C (nl) and C-Cl (nJ bonds. The corresponding force constants were taken to be Table 4 Culculated 14C(upper)and 37Cl(lower) isotope eflects at 30 "C Complete model Cut-off models n1 0.9 (1)1.03764 1.03894(2) 1.04531(3) 1 .OO348 1.00208 1.00048 0.7 1.05 576 1.05750 1.06907 1.01077 1 .OO924 1.00607 0.5 1.05473 1.05619 1.06788 1.01 702 1.01582 1.01265 0.3 1.03922 1.04022 1.04939 1.02123 1.02064 1.01784 0.1 1.01090 1.01158 1.01 689 1.02451 1.02386 1.02493 l3 L.B. Sims A. Fry L.T. Netherton J. C. Wilson K. D. Reppond and S. W. Crook J. Amer. Chem. SOC.,1972 94 1364. Heauy-atom Kinetic Isotope Eflects 85 Fob = and Fobc = nobnbcF:bbc for a typical stretch and bend frequency. The nijare the bond orders. Constant total bonding was assumed in the reaction i.e. n + n2 = 1. The results are shown in Table 4 where Y is taken to be 0 as in hydrolysis.An interesting difference is found between the effects for I4C and 37Cl. The latter effect increases monotonically as the bond order of the C-Cl bond in- creases whereas the former effect goes through a maximum. This behaviour has not as yet been reported experimentally. The reaction A + BC -+ AB + C has been discussed in some detail by Bigeleisen. ’ The anomalous temperature dependence of carbon kinetic isotope effects has been examined theoretically by Yankwich and his collaborators. Crossover refers to a change-over from a situation in which k/k* > 1 to one in which k/k* < 1 or vice versa as the temperature is changed. They used a modification of the Wilson FG matrix method to solve the vibrational problem and explore the effects of cross-terms in the potential function.They concluded that cross- over does not occur ‘when the reaction co-ordinate contains but a single element’ but can occur if more than one element is involved. Such crossover has been reported for small-molecule isotopic exchange reactions by Stern et al.’ Following a series of papers on the calculation of the Bigeleisen-Mayer function by use of a finite orthogonal polynomial expansion,’ ’-” Bigeleisen and Ishida2 ’ have developed simple expressions for the calculation of isotope effects consequent upon end-atom substitution. The effects can be calculated from a knowledge of the atomic masses and the stretching and bending force constants. The solution of the vibrational secular equations is not necessary. Further calculations by this method are promised.Kidd and Yankwich22 have considered the effect of curvature of the potential- energy surface along the reaction co-ordinate at the transition state upon heavy- atom kinetic isotope effects. The results are analysed in terms of the TIF and TDF. The work so far described regards the reacting molecule as being in the gas phase. Medium effects have been investigated by Keller and Yankwich23 using a cell model developed by Stern Van Hook and W~lfsberg~~ for the study of vapour pressure isotope effects. The model predicts that medium-induced l4 J. Bigeleisen Pure Appl. Chem. 1964 8 217. l5 T. T. S. Huang W. J. Kass W. E. Buddenbaum and P. E. Yankwich. J. Phys. Chem. 1968 72 4431. M. J. Stern W. Spindel and E.U. Monse J. Chem. Phys. 1968,48 2908. ’’ J. Bigeleisen and T. Ishida J. Chem. Phys. 1968 48 131 1. I* J. Bigeleisen and T. Ishida Ado. Chem. Ser. 1969 89 192. l9 J. Bigeleisen T. Ishida and W. Spindel Proc. Nut. Acad. Sci. U.S.A. 1970 67 113. 2o J. Bigeleisen T. Ishida and W. Spindel J. Chem. Phys. 1971 55 5021. 21 J. Bigeleisen and T. Ishida J. Amer. Chem. SOC.,1973 94 6155. 22 R. W. Kidd and P. E. Yankwich J. Chem. Phys. 1973,59 2723. ” J. H. Keller and P. E. Yankwich J. Amer. Chem. SOC.,1973 95 481 1 7968. 24 M. J. Stern W. A. Van Hook,and M. Wolfsberg J. Chem. Phys. 1963 39 3179. A. Maccoll isotope effects will be negligible unless medium-reactant interactions are so strong that gross rate effects would be observable. Keller and YankwichZ5 subsequently introduced a structured medium model as distinct from the cell or continuous medium model.A non-linear triatomic molecule is taken as the re- actant but it is influenced by the attachment and coupling of one or two mass points representing the effects of the medium. The effects on the TDF calculated in this fashion are greater than those calculated on thecell model. Also substantial effects are produced on the TIF which have no counterparts on the cell model. The authors suggest that a comparison of related inter- and intra-molecular kinetic isotope effects would be useful in discovering the conditions for which a given model should be used. 4 Experimental Methods The magnitude of the heavy-atom kinetic isotope effect can be gauged from model calculations26 based on a diatomic molecule (Table 5).It is seen that the effects Table 5 Estimates of heauy-atom kinetic isotope eflects (k/k*) TemperaturerC System 25 100 200 '2C'2C/'2C' 3C 1.0548 1.0444 1.0363 12C'4N/'2c'5N 1.0436 1.0354 1.0290 12C160/'2C'80 1.0675 1.0547 1.0447 12c32s~12c34s 1.0184 1.0152 1.0128 '2C35C1/'2C37C1 1.0141 1.0118 1.0101 are very small. It is possible in principle to prepare isotopically pure specimens of A and A* and by using conventional kinetic techniques determine k and k*. However the observed effect is not greatly different from the experimental error and so it is much better to use a comparative technique. To this end a twin- collector mass spectrometer is e~sential.~' Those commercially available are usually small-radius permanent magnetic analysers with electrostatic scanning.Two types of twin collector are possible the first consisting of a slit and a collector (Figure la) the main beam being collected on the slit and the minor beam on the (a) Figure 1 (b) 25 J. H. Keller and P. E. Yankwich J. Amer. Chem. SOC.,1974 96 2303. 26 V. J. Shiner and W. E. Buddenbaum in M.T.P. International Review of Science Physical Chemistry Series Two Volume 5 ed. A. Maccoll Butterworths London 1975. '' J. H. Beynon 'Mass Spectrometry and its Applications to Organic Chemistry' Elsevier Amsterdam 1960. Heavy-atom Kinetic Isotope Eflects 87 collector ;the second (Figure lb) has a pair of slits and collectors which have to be positioned for a given isotopic species.The disadvantage of the first system is that beams other than the main beam will also be collected on the slit and ofthe second that the collector system must be repositioned when the isotopic species is charged. In either case a double inlet system is used preferably with time- controlled magnetic valves so that the ratio can be determined alternately for the unknown sample and the standard. If the ratio for the reactant is determined at various degrees of reaction the obvious standard is the reactant itself. If on the other hand the ratio for the product is determined provided all the isotopic species goes into the product investigated then the product at completion of reaction is the appropriate standard. Thus either r = (A*/A)/(A3/Ao)or r' = (P*/P)/(Pz/P,)are the observed quantities.In order to test the mass spectrometer measurements should be made on zero enrichment. To this end 10 sets of 10 differences of ratios with the same sample admitted to each inlet system are measured. The mean and the standard deviation can then be calculated. Reproducibility should be within 0.01 % or better depend- ing on the instrument. The results of such a test on a GEC-AEI MS20 are shown in Table 6. In all cases the observed values are within the permitted limits. Table 6 The zero enrichment test Atom Ratio (zero enrichment) '3C/'2C(C02) +0.0014 f 0.0079 '5N/14N(N2) +0.0016 f 0.0089 7C1/3 'CI(CH,CI) +0.0062 f 0.013 (C*H,Cl) -0.0079 0.010 It is usually desirable to convert the compound to be analysed into a small gaseous molecule before analysis.Great care must be taken to ensure that isotopic fractionation does not occur during the preparation of the sample. Also if the compound under investigation contains more than one atom of the type that is isotopically substituted care must be taken to ensure that the compound analysed contains only the atom of interest and none of the other atoms of the same type. Alternatively the assumption of isotopic homogeneity can be made namely that the isotopic label has an equal probability of occurrence at each possible position. Thus in the case of malonic acid (Scheme 1 p. 79) the labelled carbon can occur either at one of the carbonyl positions or in the methylene group. In phenyldiazonium compounds the labelled nitrogen can occur either adjacent to or remote from the ring.Beyn~n~~ has discussed the determination of isotopic ratios in some detail. For I3C conversion into carbon dioxide is the accepted method:28 for "N conversion into nitr~gen.~' In the case of '*O,oxygen gas can be used,30 but 28 D. D. Van Slyke and J. Folch J. Biof. Chem. 1940 136 509; F. Pregl and J. Grant 'Quantitative Organic Analysis' Churchill London 195 1. 29 D. Rittenberg and L. Ponticorvo J. Appl. Radiation and Isotopes 1956 1 208. 'O C. C. Sweeley W. H. Elliot I. Fries and R. Ryhage Analyt. Chem. 1966,38 1549. 88 A. Maccoll more conveniently the oxygen can be converted into water and equilibrated with carbon dioxide which is then measured.31 In the case of sulphur the compound can conveniently be converted into sulphur dioxide and measured as For the halogens the elemental substances or the hydrides have the disadvantage of producing corrosion and long-lived memory effects and so the compound is usually converted into methyl chloride.33 A recent paper recommends the use of negative ion mass spectrometry for determining 37C1/3sC1 ratios.34 5 Interpretation of Experimental Results This subject has been fully treated by Bigeleisen and Wolfsberg’ and by Melander3’ and will be summarized here since the results obtained are fundamen- tal to the method.Considering the kinetics of a system undergoing a thermal A~P+Q A* % p* + Q Scheme 2 unimolecular isotopic competitive reaction (Scheme 2) the rates of decomposition of isotopically substituted reactants are -dA -dA* = kA -~= k*A dt dt Thus dA k A -dA* k* A* or lnA/A ~ k -~--k* In A*/Ao* In this form equation (18) is of little use; since the observed quantities are (A*/A)/(A,*/A,)or (P*/P)/(P&/P,)depending upon whether the isotopic ratio is determined on the remaining reactant or on the products.Solution of the differential equations (17a,b) gives In A/Ao = -kt In A*/Ao = -k*t. For the fraction undecomposed (1 -f) (1 -f)=-A* + A* -A*Ro(l + R,-) A + A,* A,*R,-(l + R,) 31 C. R. McKinney J. M. McCrea S. Epstein H. A. Allen and H. C. Urey Rev. Sci. Instr. 1950 21 724; L. Freedman and J. Bigeleisen J. Chem. Phys. 1950 18 1325. 32 A. G. Harrison and H.G. Thode Trans. Faraday SOC.,1957,53,1648;V. Agarwala E. E. Rees and H. G. Thode Canad. J. Chem. 1965,43 2802. 33 J. W. Hill and A. Fry J. Amer. Chem. Soc. 1962,84 2763. 34 J. W. Taylor and E. P. Grimsrud Analyt. Chem. 1969 41 805. 35 L. Melander ‘Isotope Effects on Reaction Rates’ The Ronald Press New York 1960. Heavy-atom Kinetic Isotope Eflects Then equation (18) can be written where Rf = A*/A Ro = A,*/Ao r = R,/Ro and S = (1 + Ro)/(I + Rf). The factor S is essentially a correction term and can be estimated with sufficient accuracy by using the literature value for A,*/A, or it can be measured from which R = rRo can be substituted into equation (20). The latter is the relevant equation for calculating k/k* where isotopic analysis is made on the substrate.In the other case of interest namely where isotopic analysis is made on the product of reaction the set of differential equations for product formation can be written dP dP* -= k(P -P) __ = k*(P* -P*) (1 7cd) dt dt or by division dP k (P -P) -dP* k* (P* -P)* which on solution gives The fraction which has undergone reaction can be defined as where R; = P*/P Rb = P*,/P,and r’ =Rj/R’ . Then since k lOg[1 -f(1 + RL)/(l +R;)] - ______ k* log [l -r;(l + RL)/(l + R;)] or k lOg[l -fs’] ---k* log [l -r’js’] where S’ = (1 + R&)/(l+ R>) and the value of Rb = R is taken from the literature. S‘ can be calculated by the substitution R; = r‘Rb or measured. For reactions involving elements such as carbon,oxygen,nitrogen and sulphur for which one isotopic species is present to the extent of only a few percent A.Maccoll equations (20) and (24) reduce to k/k* = log (1 -f)/log [r(l -f)] k/k* = log (1 -r'f)/log (1 -f) Even for molecules containing heavy isotopes for which Ro or R' 2 1 equations (17a) and (17b) can be employed without appreciable loss of accuracy. For if Rf = (1 -6)R then Iff is small then equation (25b) reduces further to k -= r' k* as can be seen by expanding the logarithms. This implies making measurements on the initial product. Bigeleisen and Allen36 and Jones37 have made estimates of the accuracy with which k/k* can be derived from equations (25a) and (25b). Carbon Isotope Effects.-These are of very great importance in the investigation of organic reaction mechanisms since organic reactions of necessity involve change of bonding at a carbon atom.By far the most widely investigated reaction is the decarboxylation of diacids such as malonic acid. Bigeleisen and Friedman3* first reported results on this system using the molten phase; k,/k = 1.0204 and k,/2k3 = 1.037 at 138 "C,the rate constants being defined on p. 79. Results obtained by other authors are shown in Table 7. In addition some measurements Table 7 3CIsotope eflects in the decarboxylation of rnalonic acid k,/k 3 1.020 1.021 1.028 1.030 1.027 1.027 kl/2k3 1.037 1.036 -1.040 k,/k --1.017 Temp./"C 138 138-199 140 140 150 Ref. 38 39,40 41 42,43 44 36 J. Bigeleisen and T. L. Allen J.Chem. Phys. 1951 19 760. 37 W. M. Jones J. Chem. Phys. 1951,19 78. 38 J. Bigeleisen and L. Friedman J. Chem. Phys. 1949 17 998. 39 J. G. Lindsay A. N. Bourns and H. G. Thode Cunud. J. Chem. 1951 29 192. 40 J. G. Lindsay A. N. Bourns and H. G. Thode Cunud. J. Chem. 1952,30 163. 41 P. E. Yankwich and E. C. Stivers J. Chem. Phys. 1953 21 61. " P. E. Yankwich and A. L. Promislow J. Amer. Chem. SOC.,1954,76 4648. Heavy-atom Kinetic Isotope Eflects 91 were done with '"C. The early measurements by different workers were incon- sistent but Yankwich et ~1."~ finally reported for k4/k3 1.0285 (13C) and 1.0545 ('"C) the difference being in agreement with that expected from theory. One value for kl/k2 ('"C) 1.076 (154 0C)45is not in agreement with the 13Cvalue for this ratio reported in Table 7.Bigeleisen and Wolfsberg' have made cal-culations assuming that a carbon-stretching frequency is lost in the transition state using equations (7) and (16) together with the fragment mass approximation for the calculation of v*/v**. The results were k1/2k3 = 1.029 and k4/k3 = 1.025 in reasonable agreement with the experimental results. However a concerted six-centre mechanism (Scheme 3) yielding the enol form of acetic acid is also a 0 II K.3 CH;-o* I j -,co,+ tH2 C C 10/\ 0 1 HO Scheme 3 possibility. The interpretation is rendered less certain by a lack of knowledge of the molecularity of the reaction and the extent of cooperative interaction between the molecules in the liquid phase.An elegant series of papers arose out of a study of 13Cisotope effects in the solvolysis of 1-bromo-1-phenylethane. Stothers and Bourns46 investigated nucleophilic substitution at the saturated carbon atom on the assumption that kinetic isotope effects might provide a useful criterion of mechanism since on a simplistic view the main change in the SN1 mechanism is bond cleavage whereas in the SN2 mechanism both bond cleavage and bond formation are of importance suggesting that the kinetic isotope effect might be greater for the SN1 reaction than for the S,2. However while their work was in progress Bender et al. had shown47 that in the SN2 reaction of methyl iodide with several tertiary amines gave 12k/13k= 1.09-1.14 whereas hydrolysis of t-butyl chloride in dioxan a classic SN1 reaction gave ' k/' 3k = 1.03.Bender et al. in consequence concluded that 13Ckinetic isotope effects were of little use in differentiating between the SNland SN2 mechanisms. Stothers and Bourns developed an ingenious method for determining ['3C]/['2C] at the carbon atom being substituted and found 12k/13k= 1.0065 for methanolysis at 25 "C and 1.0064 for methanolysis at 45 "C. These rather 43 P. E. Yankwich A. L. Promislow and R. F. Nystrom J. Amer. Chem. SOC., 1954 76 5893. 44 A. G. Loudon A. Maccoll and D. Smith J.C.S. Faraday I 1973 69 894. 45 G. A. Ropp and V. F. Raaen J. Amer. Chem. SOC.,1952,74,4992. 46 J. B. Stothers and A. N. Bourns Canad. J. Chem. 1960 38,923. 47 M. L. Bender and D. F. Hoeg Chem.and Ind. 1957,463; J. Amer. Chem. SOC.,1957 79 5649; G. J. Buist and M. L. Bender J. Amer. Chem. SOC.,1958,80,4308. 92 A. Maccoll surprising results were interpreted as indicating a strengthening of the bonding of the isotopic carbon with the ring in the transition state. This view received support from subsequent by Kresge et relating to strengthening of the Ar-C+ bond in the triphenylmethyl carbonium ion. Stothers and Bourns also claimed that their results supported the fragment model of Bigeleisen for calculating heavy-atom kinetic isotope effects. In a subsequent paper these two authors in~estigated~~ the '3Ceffect for the bimolecular reaction of 1-bromo-1-phenylethane and benzyl bromide with alkoxide ions in alcoholic solution. The former compound gave 2k/' 3k = 1.0032 for ethoxide ion in ethanol and the latter 1.0531 for reaction with methoxide ion in methanol.The former value was later corrected to 1.0321. The authors con- cluded that the kinetic isotope effect provides a very sensitive means of obtaining information about the transition state. A recent paper5' by Bron reports cal- culations on the benzyl bromide system which rationalize the observed differences in '3C and D isotope effects and their temperature dependences in SN1 and sN2 and borderline mechanisms. Bron and Stotherssl then took up the matter of the temperature dependence of '2k/' 3k for the alcoholysis of 1-bromo-1 -phenylethane. They found mean values of 1.0018 1.0044 and 1.0064 at 0,25 and 45 "C respectively.Of consider-able interest is the increasing isotope effect with increasing temperature. They calculated the *k/' 3k ratio on the basis of equation (7) calculating the Avi on the diatomic approximation (vi/vT) = @:/pi)* a method which may overestimate the effect. The results suggested "k/' 3k = 0.9924 (0 "C) and = 0.9931 (45 "C). Thus an inverse effect was predicted as against the direct effect observed. This may also be due to the solvolysis proceeding through an intimate ion-pair transition state. For the bimolecular displacements of benzyl bromide and 1 -bromo-1-phenyl- ethane relatively large temperature effects were found namely for the former compound 1.0578 (-23 "C)and 1.0531 (0"C) and for the latter 1.0359 (0"C) and 1.0321 (25 0C).52These compounds show the expected temperature depen- dence i.e.'2k/13k decreasing as the temperature is increased. This contrasts with the behaviour of 1 -bromo-1-phenylethane in alcoholysis where the opposite effect is reported. A further paper53 describes the effect of p-substitution on the alcoholysis of 1-bromo-1-(p-substituted phenyl) ethanes. The results are shown in Table 8. The general conclusion to be drawn from this work is that low 13Cisotope effects are to be predicted for SN1 reactions as compared with sN2. Also electron-donating groups at the reaction centre tend to stabilize the activated complex (more bond formation) leading to lower isotope effects. In fact as Table 8 shows the effect for Me is inverse. 4x A. J. Kresge N. N. Lichtin K. N. Rao and R.E. Weston J. Amer. Chem. SOC.,1965 87 437. 49 J. B. Stothers and A. N.Bourns Canad.J. Chem. 1962,40 2007. J. Bron Canad.J. Chem. 1974,52 903. s1 J. Bron and J. B. Stothers Canad.J. Chem. 1968,46 1435. 52 J. Bron and J. B. Stothers Canad.J. Chem. 1968,46 1825. 53 J. Bron and J. B. Stothers Canad.J. Chem. 1969,47 2506. Heauy -atom Kinetic Is0tope Egec ts Table 8 '2k/'3kfor the alcoholysis of 1-bromo-1 -(p-substituted pheny1)-ethanes MeOH EtOH p-Substiruenr Me 0 "C 0.9995 25 "C - 0 "C 1.0005 25 "C - H 1.0005 1.0065 1.0018 1.0044 Br 1.0127 1.0113 - - Another means of studying nucleophilic displacement reactions is by labelling the nucleophile as was first done by Nair,54 who reported 12k/13k= 1.005. Lynn and Yank~ich~~ studied the effect in the attack of cyanide ions upon methyl iodide reporting "k/' 3k = 1.0149 (1 1.4 "C) thus confirming the SN2 character of this reaction.Little work has been done on 13C isotope effects in gas-phase reactions. The structural isomerization of cyclopropane to propylene probably the most widely investigated unimolecular reaction was studied by Sims and Yank~ich,~~ over a pressure range 1-760mmHg and a temperature range 450-519°C. At 760 mmHg '*k/13k = 0.995 exp (19.1IRT) values being 1.012 (513.8 "C) and 1.014 (450.3 "C). The pressure dependence of the isotope effect was explained at least qualitatively on the basis of the transition state proposed by Simons and Rabin~vitch,~' involving ring relaxation with hindered rotation of the enol methylene groups.Wettaw and Sim~~~ have reported an investigation of the isomerization of methyl isocyanide to acetonitrile from 10-760 mmHg at 226°C. Values of 12k/13kof 1.018 at 760mmHg falling to 1.011 at lOmmHg were reported. The average value of the effects for 13CH3NC and CH3N13C was related to the individual isotope effects which were calculated on the basis of Rice-Ramsperger-Kassel-Marcus theory. Good agreement was obtained with a cyclic transition state suggested by Rabin~vitch.~~ An interesting gas-phase application of I4C was carried out by Bigley and Thurman6' in their investigation of the pyrolysis of 2,2-dimethyl-4-phenylbut-3-enoic acid (Scheme 4). At 278 "C k/k* = 1.035 ('"C) and at 286 "C kH/kD was CH CH CH CH, \/ \/ C,H,-CH ' C,H,-CHD /O D Scheme 4 54 P.M. Nair Diss. Abs. 1957 17 1469. 55 K. R. Lynn and P. E. Yankwich Chem. and Ind. 1960 117; J. Amer. Chem. SOC.,1961 83 53. 56 L. B. Sims and P. E. Yankwich J. Phys. Chem. 1967 71 3459. 57 J. W. Simons and B. S. Rabinovitch J. Phys. Chem. 1964 68 1322. sn J. F. Wettaw and L. B. Sims J. Phys. Chem. 1968 72 3440. 59 F. W. Schneider and B. S. Rabinovitch J. Amer. Chem. SOC.,1962 84 4215; F. J. Fletcher B. S. Rabinovitch K. W. Watkins and D. J. Locker J. Phys. Chem. 1966 79.2823. 60 D. B. Bigley and J. C. Thurman J. Chem. SOC.(B) 1967 941; Tetrahedron Letters 1967 2377. 94 A. Maccoll 2.87 the deuterium being substituted in the OH group. The results were taken to support the six-centre mechanism.Nitrogen Isotope Effects.-Decomposition of substituted phenyldiazonium salts has been the subject of a number of studies. Early work by Lewis and Insole61 compared the rates of decomposition of CH3C6H414N2+BF4- and CH,C6H4'5N'4N+BF4-(>99 %) and found I4k/' 5k= 1.019. Brown and Drury62 measured the rate ratios for a number of substituted compounds using two different nucleophiles at two low temperatures. Values ranged from 1.043 to 1.047. Later work by Lewis et al.63 suggested that the decomposition in aqueous solution was essentially a bimolecular attack of water on the diazonium cation. Loudon et have presented evidence to the effect that the reaction is essentially unimolecular. This is consistent with the observed values of 14k/15k.Ayrey Bourns and VyaP5 investigated the nitrogen isotope effect in the reac- tion of the 2-phenyltrimethylammonium ion with ethoxide ion in ethanol. A value of 1.017 was found for 14k/'Sk at 60°C. For the reaction of the same substrate with hydroxide ions in water Bourns and Smith66 reported 14k/' 5k = 1.009 at 97 "C. These values are relatively large and indicate a con- siderable amount of C-N weakening in the transition state. Values of 1.014 1.015 and 1.01 1 for p-CH30 p-H,and p-C1 substituted substrates were reported.66 Bourns et al. have continued work in this field the latest paper6' reporting values of 1.0137 1.0133 1.0114 aTd 1.0088 for p-OCH3 p-H p-C1 and p-CF3 in the reactions of XC6H4(CH2),N(CH3) with sodium ethoxide in ethanol. A striking result of the effect of the stereochemistry of the substrate upon the kinetic isotope effect has been reported.68 For the decomposition of trimethyl- cis-2-phenylcyclohexylammonium iodide the isotope effect was 1.012 whereas that for the trans compound was only 1.002.These values are correlated with the fact that the former compound can undergo trans-elimination whereas the latter can react only by cis-elimination. Seltzer and his co-~orkers~~ have investigated 14k/' 5k ratios for the decom- position of some azo-compounds PhCH(CH,)N=NR. For R = methyl isopropyl and a-phenylethyl the values were 1.013,1.015 and 1.023. Two possible routes are [PhCH(CH,)-.N'=N-R] PhCHCH + N =NR L [PhCH(CH,)-.N'=N.-R]-+ PhCH(CH,)R + N 6' E. S. Lewis and J.M. Insole J. Amer. Chem. SOC. 1964 86 34. 62 L. L. Brown and J. S. Drury J. Chem. Phys. 1965 43 1688. 63 E. S. Lewis L. D. Hartung and B. M. McKay J. Amer. Chem. SOC. 1969 91 419. 64 A. G. Loudon A. Maccoll and D. Smith J.C.S. Faraday I 1973 69 899. 65 G. Ayrey A. N. Bourns and V. A. Vyas Canad. J. Chem. 1963 41 1759. Ob A. N. Bourns and P. J. Smith Proc. Chem. SOC. 1964 366. 67 P. J. Smith and A. N. Bourns Canad. J. Chem. 1974,52 749. 68 G. Ayrey E. Buncel and A. N. Bourns Proc. Chem. Soc. 1961 458. 69 S. Seltzer and F. T. Dunne J. Amer. Chem. SOC.,1965 87 2628; S. Seltzer and S. G. Mylonakis J. Amer. Chem. SOC. 1967 89,6584. Heavy-atom Kinetic Isotope Eflects On the basis of the above evidence and from a study of the [13C]methyl and [2H3]methyl compounds it was concluded that whereas the methyl compound decomposed by the two-step process and the a-phenylethyl compound by the one-step process the isopropyl compound decomposed by a mixture of the two.A nitrogen isotope effect study of an aromatic nucleophilic substitution re- action has been rep~rted.~' Hydrolysis of p-nitroaniline in aqueous sodium hydroxide was shown to be second order and Arrhenius parameters were repor- ted. No nitrogen isotope effect was found (14N'4N/'4N15N) = 136.09 0.015 at 10%reaction and 136.14 & 0.11 at 100%reaction. It was concluded that C-N stretching was unimportant in the transition state. Oxygen Isotope Effects.-Hart and Bourns 71 investigated the 16k/18kratio in the displacement of phenoxide ion by piperidine in pheny12,6dinitrophenyl ether -0 N /o-+ + H2C "OPh Scheme 5 (Scheme5).When the concentration of base is high the first step is rate-controlling and as the bonding at 0 is not appreciably altered the isotope effect would be expected to be small. At low base concentrations however the second step should be rate-controlling and a normal isotope effect for bond rupture should be observed. With increasing concentrations of base from 0.005 to 0.149 the observed values of 16k/18k were 1.0109 1.0070 and 1.0024 confirming the proposed mechanism. Oxygen kinetic isotope effects have also been used in the study of the methan- olysis of aryl benzoates. Mitton and S~howen~~ found 16k/18k = 1.018 and 1.024 for X = Brand H in Scheme 6.The effect is very large despite the fact that It Ph-C-OCH + XC6H4l8O-Scheme 6 70 G. Ayrey and W. A. Wylie J. Chem. SOC.(B) 1970 738. 71 C. R. Hart and A. N. Bourns Tetrahedron Letters 1966 2995. l2 C. G. Mitton and R. L. Schowen Tetrahedron Letters 1968 5803. 96 A. Maccoll it is essentially a secondary effect. However the transition state suggested does imply a considerable change in bonding to 0,and so it could be considered as a primary effect. Mention has been made already of the use of 16k/18kmeasurements in a study of gas-phase decarboxylation. Ropp and G~illory~~ have investigated the '8O isotope effect on the rate of photochemical oxidation of formic acid by chlorine in the gas phase. The ratio obtained 1.002 caused the authors to conclude that the abstraction of the hydroxyl hydrogen by chlorine atoms makes no appreciable contribution to the reaction mechanism.A large l8O isotope effect has been reported by Gold~tein~~ in the thermal dissociation of acetyl peroxide. The value was 1.023 at 45 "C. He suggested that C-C cleavage must accompany 0-0 cleavage to a large extent on the basis of model calculations. Not surprisingly l80isotope effects have been investigated in the field of inorganic mechanisms. Thus Taube and co-workers7 have studied the replace- ment ofX in [CO(NH,),X]~' (X = C1 Br or I) by H20. The results are discussed in terms of SN1and SN2 mechanisms. Taylor76 has measured 16k/18k for the attack of phenoxide upon substituted beniyldimethylsulphoniumtoluenesulphonates.The values were 1.0074 1.OO82 and 1.0095 for p-Me H and m-Cl. These values are all very small and since the error ranges overlap no definite conclusions can be drawn. Sawyer and Kirs~h'~ have investigated the l80 kinetic isotope effect for re- actions of methyl formate([' 80]methoxyl). Their results are shown in Table 9. Table 9 "0 Kinetic isotope effects for methoxy-labelled methyl formate Reaction ' 6k/' *k Acid-catalysed hydrolysis 1.0009 & O.OOO4 Alkaline hydrolysis 1.0091 fO.OOO4 General base-catalysed hydrolysis 1.01 15 f0.0002 H ydrazinolysis 1.0048 f 0.0006 Hydrazinol ysis 1.0621 0.O008 In the case of hydrazinolysis the two values refer to conditions under which the formation of the tetrahedral intermediate and its breakdown are rate-controlling.1.r. studies yielded methyl rocking and formyl-C-methoxyl-0 stretching frequen- cies of 1162.3 1144.8 and 1208.3 1187.4 cm-' respectively. From these the maximum effect was calculated as 1.052. The very small effect observed for acid catalysis was taken to confirm a mechanism in which equilibrium protonation of the ester is counterbalanced by the normal kinetic isotope effect for attack of water on the oxocarbonium ion. For the remaining four reactions it was 73 G. A. Ropp and W. A. Guillory J. Phys. Chem. 1961,65 1496. 74 M. J. Goldstein Tetrahedron Letters 1964 1601. l5 F. A. Posey and H. Taube J. Amer. Chem. SOC.,1357 79,252; M. Green and H. Taube Inorg. Chem. 1963 2 948. l6 L. H. Taylor PhD Thesis Massachusetts Institute of Technology 1963.77 C. B. Sawyer and J. F. Kirsch J. Amer. Chern. SOC.,1973 95 7375. Heavy -a tom Kinetic Is0 tope Eflec ts 97 concluded that the order of the acyl carbon-methoxyl oxygen bond is only slightly reduced in the transition state. A very careful study has been made by Margolin and of the 13C and l80 kinetic isotope effects in the decarbonylation of benzylformic acid in concentrated sulphuric acid. The original Hammett mechanism79 is shown in Scheme 7. Roppeo measured the 13C isotope effect and found 12k/13k= 1.039 +0-H OH II /.-PhCOC02H 5 Ph-C-C I H*SO Y -I PhCOzH CO + PhCO+ 3 [PhCOCO]' + H,O Scheme 7 a value inconsistent with the Hammettscheme. A mechanism which makes C-C rupture rate-controlling is shown in Scheme 8.k 1slow No PhC02H + PhCO' + HC \+ OH2 No k, HC % HCO++H,O \+ k-b fast OH2 k 1 CO + Ht Scheme 8 Margolin and Samuel calculated the oxygen isotope effects on the basis of the 180/160 ratio in the product carbon monoxide. There are three '*Oeffects intermolecular (2k3/k = 0.981) primary intramolecular (k3/k2 = 0.986) and secondary intramolecular (2k2/k1= 0.995). For carbon the effect may be on the carboxyl carbon (I 3k/12k = 0.947) or on the carbonyl carbon (' 3k/12k = 1.OOO). By a kinetic analysis of the two schemes including the reversible exchange of oxygen between the carbonyl group and solvent water (1 -1) (Scheme 7) or (4 -4) (Scheme 8) the authors deduced the following rate equations Scheme 7 kexp = k,k2/(k-,[H2OI + k2) x Kphg Scheme 8 kexp = k,K& Z.Margolin and D. Samuel Chem. Comm. 1970 802. 79 L. P. Hammett 'Physical Organic Chemistry' McGraw-Hill New York,1940 p. 253. G. A. Ropp J. Amer. Chem. SOC.,1960,82 842. 98 A. Maccoll where ho is the Hammett acidity function. The equations indicate that when C-0 bond rupture is rate-limiting (Scheme 7) an isotope effect of the carbonyl carbon can only be expected when there is oxygen exchange with the solvent. However when C-C rupture is rate-limiting (Scheme 8) there should be a carbon isotope effect of the carbonyl carbon. In 99.5-100 %sulphuric acid at 0 "C no exchange was observed during decarbonylation. The observed results show conclusively that the Hammett mechanism is correct.Many studies have been made of the role of the monophosphate ion inter- mediate in the unimolecular decomposition of monophosphate esters. Goren- stein" has reported a direct kinetic isotope study of the hydrolysis of the dianion of 2,4dinitrophenyl phosphate by comparing the rate of decomposition of the l60 ester with that of the l80 ester. It was found that 16k/18k=1.0204 f0.0044 in the temperature range 39-55 "Cand the pH range 4.4-8.0. Bunton et and Kirby and VarvoglisP3 have shown that the hydrolysis probably proceeds through P-0 cleavage. The present observation of a large l8Oeffect is taken by the author to indicate substantial P-0 bond breaking in the transition state. Preliminary results reported suggest that no isotope effect has been found for dibenzyl-2,4-dinitrophenyl phosphate a compound which must hydrolyse through addition-elimination or by a direct S,2(P) mechanism a result in marked contrast to that observed for the unimolecular process.Sulphur Isotope Effects.-Bader and Bournss4 were able to distinguish between two suggested mechanisms for the Tschugaeff reaction (Scheme 9). For "S and \" /C.. .S-Me -H-* I \/+cos C II C +MeSH /\ I1 Scheme 9 bS the effects were 1.0086 and 1.0021 respectively while for 'C "k/' 3k =1.OOO4. Thus it would appear that there is a large bonding change at "S a small one at 81 D. G. Gorenstein J. Amer. Chem. SOC.,1972 94 2523. 82 C. A. Bunton D. R. Llewellyn K. G. Oldham and C. A. Vernon J. Chem. SOC.,1958 3574.83 A. J. Kirby and A. G. Varvoglis J. Amer. Chem. SOC.,1967,89,415. 84 R. F. W. Bader and A. N. Bourns Canada J. Chern. 1961,39 348. Heavy-atom Kinetic Isotope Efects % and almost none at ‘C. On this basis I was ruled out and I1 confirmed as the structure of the transition state. An interesting effect of solvent upon a sulphur isotope effect has been reported by Cockerill and Saunders” in the reaction of hydroxide ion with 2-phenyl- ethyldimethylsulphonium bromide. In pure water 32k/34k = 1.0074 decreasing to 1.001 1 in an aqueous solution containing 7 moll- of Me,SO. These authors also studied the /?-deuterium effect and found this to pass through a maximum as the Me,SO content increased. They interpreted these results as indicating a reagent-like transition state with less weakening of both the C-S and a-C-H bonds as the Me2S0 increased.The bromodesulphonation of sodium p-methoxybenzenesulphonate(Scheme 10) (and of potassium 1 -methylnaphthalene-4-sulphonate)has been investigated by Baliga and Bourns.86 For low concentrations of bromide ion the first step ‘OMe Br-+ SO3 6+ Br [o] -$+ S03-Br SO3-Scheme 10 is rate-controlling the species in the bracket is an intermediate and 32k/34k = 1.0032. In the presence of added bromide ion the first step becomes reversible the rate falls and the second step becomes rate-controlling. The isotope effect increases to 1.0127 at 0.03 M bromide and 1.0173 at 0.5 M bromide. -I Chlorine Isotope Effects.-As chlorine is a well-established leaving group in nucleophilic substitution 3sk/37k values have proved useful in determining mechanism.Following on the original investigation of Bartholemew Brown and Lo~nsbury,’~ Hill and Fry’’ investigated the effect in reactions of benzyl and substituted benzyl chlorides with various nucleophiles. These authors observed that for those reactions following first-order kinetics 35k/37k2 1.008 whilst for those following second-order kinetics the value was 1.006. They suggested that the value of 35k/37kmight be used to differentiate between SN1 and SN2reactions. Grimsrud and Taylor” investigated nucleophilic displace- ments at a saturated carbon atom by varying both the nucleophilic power of the attacking group and the electron-donating power of the p-substituent in a series of benzyl chlorides with a view to testing the predictions of Thornton.” In the 85 A.F. Cockerill and W. H. Saunders J. Amer. Chem. SOC.,1967,89,4985. 86 B. T. Baliga and A. N. Bourns Canad. J. Chem. 1966,44 363. ” R. M. Bartholemew F. Brown and M. Lounsbury Canad. J. Chern. 1954 32 979; Nature 1954 174 133. J. W. Hill and A. Fry J. Amer. Chem. SOC.,1962,84,2763. E. P. Grimsrud and J. W. Taylor J. Ampr. Chem. SOC.,1970 92 739. 90 E. R. Thornton ‘Solvolysis Mechanisms’ Ronald Press New York 1964. 100 A. Maccoll case of attack by C,H,S- and CH30- 35k/37k decreased in the order CH30 > H > NO2 these being the p-substituents. Again for the variation of the nucleophile in the case of p-nitrobenzyl chloride and t-butyl chloride the isotope effect was smaller for n-C,H,S- than for C6H,S-.Finally for the reac- tions of the same substrates the isotope effect was greater for n-C,H,S- than for CH30- and greater for C6H,S- than for C,H,O-. The fact that the oxide nucleophiles show consistently smaller effects than the sulphur analogues suggests that the oxides are the stronger nucleophiles a view not consistent with the rate data kRs->> kRo-. This contradiction was discussed in terms of the basicity polarizability and solvation effects on the nucleophile. A very careful study of temperature effects on 35k/37kin the solvolysis of n- and t-butyl chlorides was made by Taylor and co-worker~.~' The results are shown in Table 10. In each case log 35k/37kis inversely proportional to tem- Table 10 35k/37k for solvolysis of the butyl chlorides Substrate 0°C 20°C 40°C 60°C n-Butyl chloride 1 .OO96 1.WO 1.OO84 1.0079 t-Butyl chloride 1.0109 1.0106 1.0099 1.0095 perature as predicted by simple theory.The authors also reported theoretical calculations based upon equation (7). In fact it was assumed that only the ground- state C-Cl stretch was lost in the transition state. so that TDF = 1 + G(u,)Au where ui= hvi/kT vi being the C-Cl stretching frequency. They concluded that 'the temperature dependence of the kinetic isotope effect is best evaluated from consideration of the ground-state configuration plus information on the number of isotopically important ground-state vibrational frequencies for a given reactant'.In a later series of papers Williams and Taylor' ',92 have initiated a thorough study of models for use in calculating chlorine kinetic isotope effects. They in- vestigated" the isotopic shifts of the C-Cl frequencies for a series of alkyl chlorides and compared them (in the case of t-butyl chloride) with values cal- culated by the Wilson FG matrix method (see p. 82). These authors also applied92 equation (4)to the calculation of the kinetic isotope effect for t-butyl chloride solvolysis. The ground-state geometry and the ground-state force field (leading to vibration frequencies) are known ; the corresponding data for the transition state were assumed for a series of models and 35k/37kwas calculated. The most probable transition state for methanolysis was C-Cl = 1.89& C-CH3 = 1.508, and z(CH3) = -0.16 8 relative to the central carbon atom.These values together with an assumed force field gave values of 35k/37kof 1.010 87 and 1.009 51 at 10 and 60 "C respectively. The experimental values were 1.01097 and 1.00953. 9' C. R. Turnquist J. W. Taylor E. P. Grimsrud and R. C. Williams J. Amer. Chem. Soc. 1973,95 4133. q2 R. C. Williams and J. W. Taylor J. Amer. Chem. Soc. 1974 96 3721. Heavy -a tom Kinetic Is0tope Efec ts Graczyk and Taylorg3 have used kinetic isotope effects to investigate the participation of ion-pairs in the reactions of p-methoxybenzyl chloride in aqueous acetone. This was done by competition between water and sodium azide. It was found that the observed effect increases by >30% as the azide concentration is varied from 0.25moll-'.This observation is shown to be consistent with the ion-pair theory but not with simultaneous SN1and SN2 processes.Raaen et al. have discussed isotope criteria in relation to the problem of ion-pair par- ti~ipation.~~ Sims et ~1.'~ have made model calculations for S,2 reactions assuming variable degrees of bond breaking and bond forming in the transition state. They found that while the 12C/14Ceffect goes through a maximum at ca. 50% breaking the 35C1/37CIeffect increases monotonically. So far no experiments have been reported which confirm this prediction. Up to the present no chlorine kinetic isotope effects have been reported in gas-phase reactions.However current experiments by Maccoll and Machacek' are designed to determine the variation of 35k/37kover the series ethyl iso- propyl and t-butyl chlorides. Results to date show that the effect is very much larger for t-butyl chloride than for ethyl chloride. 93 D. G. Graczyk and J. W. Taylor J. Amer. Chem. SOC.,1974,96 3255. 94 V. F. Raaen T. Juhlke F. J. Brown and C. J. Collins J. Amer. Chem. Soc. 1974 96 5928. 95 A. Maccoll and L. M. N. Machacek unpublished work.

ISSN:0308-6003    

DOI:10.1039/PR9747100077

出版商:RSC    

年代:1974

数据来源: RSC

摘要:

6 The Thermochemistry of Organometallic Compounds By W. V. STEELE Department of Chemistry University of Stirling Stirling FK9 4LA Scotland 1 Introduction The thermochemistry of organometallic compounds is still a field which is sparse in accurate data ;therefore reliable information on the strength of carbon- metal bonds is still meagre. This sorry state of affairs has been caused by a number of difficulties not usually encountered in the thermochemical investiga- tion of organic compounds. The standard enthalpy of formation of an organic compound containing C H 0 and N is usually obtained by conventional oxygen bomb calorimetry in a static-bomb calorimeter. The standard enthalpies of formation of the products of equation (l) AH; (CO, g) = -393.51 0.13 kJ mol-' and AH (H20,1) = -285.830 & 0.042 kJ mol-' are both accurately known so the standard enthalpy of formation of the organic compound can be calculated by a simple Hess's cycle.However when a metallic atom is present e.g. M(CH,) in the tetra-alkyls of Group IVB organo-metallic compounds the products are usually found to contain not only C02(g) H,O (l) and MO ,the standard oxide of the metal but also a number of other inorganic compounds in varying amounts. These are usually other oxides free metal carbonates nitrates and unburnt carbon admixed with the metal. Such mixtures would need to be analysed accurately before the final state for the combustion calorimetry could be defined. This if possible would be time- consuming and would need to be repeated for each combustion since every combustion gives a different ratio of products.An example quoted by Good and Scott,' is the study of the combustion of tetraethyl-lead carried out by Knowlton in a static-bomb calorimeter. Here the products were found to contain PbO PbO, PbCO, and Pb(NO,) admixed with unburnt Pb. The inter- pretation of the measured energy of combustion with respect to these products led to a value for the enthalpy of formation of tetraethyl-lead which was in error by no less than 170 kJ mol-'. ' W. D. Good D. W. Scott and G. Waddington J. Phys. Chem. 1956.60 1090. 103 104 W. V. Steele 2 Rotating-bomb Calorimetry During the past two decades the introduction by Sunner2 of rotating-bomb combustion calorimetry has helped to overcome some of the difficulties en- countered in static-bomb calorimetry.The rotating-bomb combustion calorimeter combines the functions of a combustion calorimeter and a solution calorimeter in the same instrument. By introducing a suitable solvent the products of combustion can be dissolved immediately after formation to give a well-defined final solution of uniform composition in the bomb. The choice of solvent is restricted somewhat since it must not react with the interior of the bomb and it is advantageous not to produce any gaseous products on dissolving the solids produced. Similarly if an alkali is used as solvent it should be of sufficient strength to dissolve completely the carbon dioxide produced. The experimentalist must exercise considerable artifice exploring such variables as sample size container material auxiliary substance used to promote combustion oxygen pressure amount and nature of liquid reagent and crucible size shape and mass in order to find the conditions which ensure a thermodynamically definable state after combustion.In conventional bomb calorimetry of compounds containing C H 0,and N Washburn3 devised a series of standard corrections to convert the measured energy released in the combustion reaction to that which would be released under idealized isothermal conditions. To set up such a correction procedure for each solvent used in the rotating-bomb calorimetry of organometallic compounds is a massive task so some sort of comparison experiment is required.The normal type of comparison experiment is set out below. In it an oxide of the metal whose enthalpy of formation is well defined is dissolved in the solvent after combustion of a standard organic compound to produce as accurately as possible the same amount of carbon dioxide and the same evolution of energy as in the combustion of the organometallic compound. Within limits combina- tions of benzoic acid with a hydrocarbon oil usually give the desired amounts of energy and carbon dioxide. If both the evolution of energy and the production of carbon dioxide cannot be made to match the latter at least should be made to do so. After correction for the energy of combustion of the organic sample the results of the comparison experiments yield a value of the enthalpy of solution of the oxide (plus water from combustion of the organic sample) in the initial bomb solution to form the final solution.By combining the result with that found in the main experiments it is possible to obtain an enthalpy of combustion of the organometallic compound which depends only on the enthalpies of formation of water and carbon dioxide and on the enthalpy of formation of the oxide actually used in the comparison experiments. A comparison experiment of this type makes a separate standard-state correction unnecessary and so eliminates errors which would arise through inadequate information on the quantities (e.g.the solubility and enthalpy of solution of C02in the final solution) S. Sunner Svensk. kern. Tidskr.1950 58 71. E. M. Washburn J. Res. Nar. Bur. Stand. 1933 10 525 The Thermochemistry of Organometallic Compounds that would have to be used in reducing the bomb contents to standard states. It also removes uncertainties about the enthalpies of formation of the combustion products under the conditions in which they are produced in the bomb. The most troublesome problem in the combustion calorimetry of organo- metallic compounds by rotating-bomb calorimetry is that of incomplete com- bustion. Incomplete combustion can either mean that not all of the sample has burned or that the carbon is not oxidized completely. The attainment of complete combustion is an art and may be obtained by either higher or in some cases lower oxygen pressures or a change of crucible size and shape.Some organo- metallic compounds detonate on combustion e.g. tetramethyl-lead while others e.g. lead oxalate do not sustain combustion. In both cases the addition of an auxiliary substance of known energy of combustion in a suitable amount sustains smooth complete combustion. Where solid unburnt residue is produced a correction for incomplete combustion has to be applied. The mass of the residue must be determined with an accuracy of f0.05mg or even better in careful work. The energy of combustion of the deposit will depend on the composition and physical state of the residue and may be greater or less than that of carbon in its standard state. If sufficient sample is present for analysis its composition can be found and a suitable correction made but if not the experi- mentalist must select the value he considers appropriate.Usually an equimolar amount of compound and carbon is selected. Sometimes complete combustion has to be sacrificed in order to obtain the desired form of solid products that can dissolve in the solvent in the bomb. A fuller account of the methods and problems attached to the combustion calorimetry of organometallic compounds by rotating-bomb calorimetry can be found in ref. 4. Details of the methods used in specific cases are given below in the discussion of the standard enthalpies of formation of metal alkyls. 3 Reaction Calorimetry Other methods used for the determination of the standard enthalpies of formation of organometallic compounds lack the specificity of the combustion reaction.Enthalpies of reaction can be determined directIy by calorimetry or indirectly from the temperature dependence of the equilibrium constant or from a know- ledge of the equilibrium constant and the entropy change at one temperature. The application of non-combustion thermochemistry to organometallic compounds has been widespread. The determination of the enthalpies of forma- tion of transition-metal complexes has become a massive field of its own and will not be covered at all in this Report. During the past decade considerable effort has gone into the development of calorimetric techniques suited to the study of complex formation and the output of new thermochemical data on these compounds has been considerable.The whole field until 1970 has been extensively reviewed by Ashcroft and Mortimer in their 'Experimental Thermochemistry' ed. H. A. Skinner Wiley-Interscience New Y ork 1962 Vol. 11. S. J. Ashcroft and C. T. Mortimer 'Thermochemistry of Transition Metal Complexes' Academic Press London 1970. 106 W. V.Steele The most common types of reactions studied calorimetrically are usually classified as ‘hydrogenation’ ‘halogenation’ and ‘hydrolysis’. The design and operation of a calorimeter suitable for any one of the above types of reaction depends on many variables such as the nature of the compounds to be studied e.g. whether they are gaseous or solid and on the energy output in the reaction. The general principles involved in such constructions can be found in ref.4. A number of these calorimeters have been developed by Skinner’s group at SnR (1) + Br (g) -+ SnR,Br (I) + RBr (g) (2) C4H& (1) + H20 (g) + LiOH (c) + C4H,, (g) (3) 6RCH=CH2 (1) + B,H (g) -+ 2(RCH2CH,)3B (sol.) (4) Manchester and they include ones used to study reactions (2t(4).6-8 The main difficulty in the reaction calorimetry of organometallic compounds particularly with the more reactive ones of Groups I 11 and 111 is the violence of the reactions which are difficult to control. Carson et aL9 measured the energy evolved in the hydrolysis of dimethylzinc in aqueous ether solution [equation (5)]and in the decomposition of the same compound by dilute sulphuric Me2Zn(1) + 2H20 (aq. ether) + Zn(OH) (ppt.) + 2CH4 (g ether) (5) acid [equation (6)].The large uncertainties in the enthalpies of both reactions Me2Zn (1) + H2S04 (aq.) -+ ZnSO (aq.) + 2CH (g) (6) arose because of the ill-defined nature of the precipitated Zn(OH) in the former case and in the side-reactions which arose because of the violence of the main reaction in the latter case. Data for enthalpies of formation derived by the use of reaction calorimetry are discussed in Section 5. 4 Enthalpies of Vaporizationor Sublimation The standard enthalpy of formation of any compound in the solid or liquid state depends on both the chemical binding forces within the molecule and the forces between the molecules. For the discussion of the chemical binding forces only as for example in the determination of bond-energy terms it is necessary to remove the intermolecular forces from consideration.This can be achieved by conversion of AH,“(1) to AH; (g) the standard enthalpy of formation in the gas phase using equations (7) and (8). Although progress in the determination of AH; (g) = AH (1) + AHo (vaporization) (7) AH (g) = AH (c)+ AHo (sublimation) (8) J. B. Pedley H. A. Skinner and C. L. Chernick Trans. Faraday SOC.,1957 53 1612. ’ P. A. Fowell and C. T. Mortimer J. Chem. SOC.,1961 3793. * A. E. Pope and H. A. Skinner J. Chem. Soc. 1963 3704. A. S. Carson K. Hartley and H. A. Skinner Trans. Faraday SOC.,1949,45 1159. The Thermochemistry of' Organometallic Compounds 107 the standard enthalpies of formation of organometallic compounds is moving ahead albeit slowly this is not the case with enthalpies of vaporization and sublimation.In this area the data are virtually non-oxistent. General methods of determining enthalpies of vaporization and sublimation have been otlined by Cox and Pilcher. lo In the case of organometallic compounds the low vapour pressures and the possibility of aggregate molecules in the gas phase are problems which need to be taken into account in a reliable detennina- tion of AHo (vap. or sub.). The second of these possibilities is one which has not been taken into account too often in the past. The wide discrepancies in the temperature dependence of the sublimation pressures of SiPh reported by McCauley and Smith" and by Calle and Kana'an12 have been attributed to incomplete degassing in the former case.A novel method of determining the enthalpy of sublimation of diphenyl- mercury is due to Carson et a1.,13 who measured the vapour pressure over a short range of temperature near 298 K by using the Knudsen effusion method on a sample of Ph,Hg labelled with the radioactive isotope 203Hg. However using a similar technique Carson Copper and st rank^'^ studied tritium- labelled tetraphenyltin and tetraphenyl-lead obtaining a value of 66.32 kJ mol- ' for the enthalpy of sublimation of the former. Keiser and Kana'an15 have redetermined AHo (sub.) for tetraphenyltin using the techniques of simultaneous measurement of the torsional recoil and of the rate of mass effusion and they obtained a vaue of 161.1 kJ mol-'. The latter study gives a more reliable value for this quantity since the entropy of sublimation in the former case is impossibly low.The probable reason for the widely different values of the enthalpies of sublimation is that at the lower temperatures used by Carson et al. the species effusing from the Knudsen cell was polymeric in nature although this has yet to be proved. Using the mass-effusion and torsional-recoil methods simultaneous- ly it is possible to calculate the vapour pressure by both methods the results agreeing when the correct molecular weight is used for the species present in the gas phase. The agreement is excellent when the molecular weight of the monomer is used in Kana'an's work. Further examples of the use of this method to deter- mine the enthalpies of sublimation of organometallic compounds are given in the next section.Reliable information on the enthalpies of vaporization and sublimation of other compounds awaits the construction and operation of other experimental systems of this type. 5 Reliable Thennochemical Data on Organometallic Compounds The compilation of reliable values for the enthalpies of formation of organo-metallic compounds is not an easy job for the non-thermochemist. Often he is lo J. D. Cox and G. A. Pilcher 'Thermochemistry of Organic and Organometallic Com- pounds' Academic Press London 1970. ' I J. A. McCauley and N. 0. Smith J. Chem. Thermodynamics 1973,5 31. L. M. Calle and A. S. Kana'an J. Chem. Thermodynamics 1974 935. A. S. Carson D. R. Stranks and B. R.Wilmshurst Proc.Roy. Soc. 1958 A244,72. l4 A. S. Carson R. Cooper and D. R.Stranks Trans. Furuduy Soc. 1962,58 2125. I5 D. Keiser and A. S. Kana'an J. Phys. Chem. 1969 73 4264. 108 W. V. Steele confronted with two or more values all of which are different and is unable to distinguish between them. Such an example is the standard enthalpy of formation of dibenzenechromium ;here two values exist in the literature ;Fischer Cotton and Wilkinson16 gave AH C12H12Cr (c) = 89.1 f33 kJ mol-' and Fischer and S~hreiner'~ found a value of AH; CI2Hl2Cr (c) = 213.0 & 12 kJ mol-'. Both these values were obtained by static-bomb calorimetry but insufficient details are given particularly in the latter case for an objective decision to be made on the relative merit of the results.It is probable that neither are reliable in view of the unreliable results normally obtained by static measurements. Cox and Pilcher,' in their comprehensive review of the enthalpies of formation of organic and organometallic compounds tabulate critically the data available to 1966. The tabulation is particularly good as it gives not only the results of the thermochemical measurements but also some indications of how the measure- ments were made and a realistic error limit on the values. Many of the values listed there bring up to date the earlier review by Skinner,I8 who gives even more detail. Here we review the data available up to December 1974 Group by Group. The reader is referred to ref. 10 to obtain values where these are relevant.Group IA.-Very few reliable thermochemical data exist on the organometallic compounds of this Group. Cox and Pilcher summarize all the data available at present. It is worth noting that the data have been obtained by static-bomb calorimetry and therefore their reliability is questionable. The enthalpies of vaporization quoted are for the formation of polymeric vapours in the gas phase and accurate bond-dissociation energies for these compounds are still in doubt. Group IIA.-Cox and Pilcher select only one piece of work on the hydrolysis dicyclopentadienylmagnesiumfor inclusion in their compilation. Since then the only measurements on the enthalpies of formation of the organometallic compounds of this Group are due to Holm.18" He has measured the enthalpies of reaction of 17 alkyl halides with magnesium metal in diethyl ether using a steady-state heat-flow calorimeter.He measured the enthalpies of the reaction RX (1) + Mg (c)ezRMgX (sol.) (9) (9),correcting for the side-reactions (10) and (1 1). RX (1) + 3Mg (c) ether_ iR-R (1) + iMgX (sol.) (10) ether RX (1) + $Mg (c) +iRH (1) + iR ( +H) (1) + MgX (sol.) The enthalpies of reaction of the hydrogen halides with Grignard reagents in ether were also measured. The results were used to calculate the enthalpies of formation of the Grignard reagents in ether along with their relative l6 A. K. Fischer F. A. Cotton and G. Wilkinson J. Phys. Chem. 1959,63 154. E. 0. Fischer and S. Schreiner Chem. Ber. 1958,91,2213. I' H.A.Skinner in 'Advances in Organometallic Chemistry' Academic Press London 1964,Vol.2 p.49. (a) T.Holm J. Organometallic Chem. 1973,56 87. The Thermochemistry of' Organometallic Compounds bond-dissociation energies. Absolute values of the dissociation energies cannot be calculated in the absence of both the standard enthalpies of formation of the RMgX compounds and their enthalpies of sublimation. Holm concluded that in relative terms the R-MgX bond strength is constant for various primary alkyl groups but is 50 kJ mol-' higher for Me and Ph groups. It is lower by 21 22 and 62 kJ mol- for isopropyl s-butyl and t-butyl respectively. Benzyl and ally1 groups gave values which were approximately 33 kJ mol- weaker than the primary groups. These results follow that which is normally observed in the variation of bond dissociation energies with alkyl groups in organometallics (see section 6).Group 1IB.-The thermochemistry of the organometallic compounds of Zn Cd and Hg has been well documented by Cox and Pilcher." The results come from two main sources ;static-bomb calorimetry and reaction calorimetry. In the case of the zinc alkyls the uncertainties in the final values obtained both by static-bomb calorimetry and hydrolysis reaction calorimetry were high owing to the lack of a well-defined thermodynamic end state and the violence of the reaction. A similar situation exists for the dialkyls of cadmium. The study of the thermochemistry of the organo-compounds of mercury has been undertaken in the main by Skinner's group at Manchester.In the early fifties a series of papers tackled the determination of AH; for R2Hg and RHgX compounds by various methods. In this case static combustion bomb calorimetry can be used with great effect to determine the standard enthalpies of combustion and hence formation since the mercury for the main part does not burn and only small traces of red HgO were formed on the bomb fittings. All these early results are tabulated by Cox and Pilcher. More recently Carson and Wilms- hurst" have remeasured AH; Ph2Hg (c) by the static-bomb method to try and remove the uncertainty which existed over its value. Their result AH; Ph2Hg (c) = 282.8 f7.9 kJ mol-' agrees well with that obtained by Skinner and Fairbrother.20 The value now seems to be well established at 281.6 f4.2 kJ mol-'.The novel method used in the determination of the enthalpy of sublima- tion of this compound has already been mentioned in Section 4. Group IIIA.4ox and Pilcher" tabulate data on 60 organometallic compounds of boron. The majority of the trialkylboron values listed were obtained either by static-bomb calorimetry or by measuring the enthalpy of addition of diborane to an olefin in 'monoglyme' solvent e.g. reaction (12). The static-bomb com- B2H6 (g) + 6C2H4 (g) + 2B(C2H,) (1) (12) bustion measurements are complicated by the fact that the boron burns to form boric oxide which becomes largely hydrated by the water formed and which is thermodynamically ill-defined. A residue which has been shown to be a mixture of B4C together with boron and carbon is also formed.Good and M&nsson2' l9 A. S. Carson and B. R. Wilmshurst J. Chem. Thermodynamics 1971,3 251. D. M. Fairbrother and H. A. Skinner Trans. Furuday Soc. 1956 52 956. W. D. Good and M. Miinsson J. Phys. Chem. 1966 ?O 97. 110 W. V. Steele have developed a rotating-bomb calorimetric technique to solve these problems in order to determine accurate values for the enthalpies of formation of boron compounds. The method involved the combustion of the boron-containing compound mixed with a fluorine-containing combustion promoter vinylidene fluoride polymer. The combustion bomb initially contained an aqueous solution of hydrofluoric acid in such concentration that the boron appeared in the reaction products in a homogeneous solution.Comparison experiments were used to minimize errors from the inexact reductions to standard states (see Section 2). In these experiments benzoic acid and/or hydrocarbon oil were used to produce the same amount of CO and temperature rise as in the main combustions. The bomb contained initially an aqueous solution of HF and HBF, which on dilution with the water formed by thc combustion of the mixture gave a solution of nearly the same amount and concentration as in the main experiments. The enthalpies of formation of orthoboric acid trimethylamineborane and diam- moniumdecaborane were determined. The energy of combustion of trimethyl- amineborane can be represented by the reaction scheme of reactions (13) and (14).B (c)+ 0.750 (g) + 18.67,HF,57.21,H20 (1) -D HBF4,14.67,HF,58.71,H,O (1) AG = -723.6 f0.8 kJ mol-' (13) C,H,,NB (c,III) + 6.750 (g) + 18.67,HF,51.21,H20 (1) -+ 3co2 (g) + 0.5N2 (8) + HBF4,14.67,HF,58.71,H,O (1) (14) AE = -3474.3 f1.9kJmol-' Combining reactions (13) and (14) with data for the enthalpies of formation of C02(g) and H20(1) and the enthalpy of dilution of aqueous HF the enthalpy of formation of trimethylamineborane was found to be AH; C3H12NB(c 111) = -142.4 4A0kJ mol-'. This method has not been applied to other boron organometallic compounds and the values for many remain suspect. Pedley22 has produced an internally consistent analysis by computer of the thermo- chemical data on boron organometallic compounds and other boron compounds.The enthalpies of formation of aluminium alkyls in the literature are internally inconsistent. They have nearly all been determined by static-bomb calorimetry with all the defects that that entails. Values reported for Et,Al differ by as much as 84kJ mol-'. The most reliable piece of work in the field appears to be that of Mortimer and who studied the reaction between Me,Al and acetic acid in toluene [reaction (15)] and obtained AH; Me,Al(I) = -150.6 f6.7 kJ mol-l. Me,A1 (1) + 3CH,C02H (toluene solution) + (CH,CO,),Al (c)+ 3CH (g) (15) Recently Smith2 has attempted to resolve the conflict in published en-thalpies of formation of aluminium alkyls by use of a one-constant equation (the 22 J. B. Pedley M. F. Guest and M. Horn,J. Chem. Thermodynamics 1969 1 345.23 C. T. Mortimer and P. W. Sellers J. Chem. Soc. 1963 1978. 24 M. B. Smith J. Organometallic Chem. 1974 76 171. The Thermochemistry of’ Organometallic Compounds 111 ‘Displacement Rule’) to formulate a self-consistent set of values. However such a set of values can only be tentative and the design of a rotating-bomb calorimetric set-up suitable for the combustion of these compounds is required to produce valid data. Smith states that the measurement of the enthalpies of acid hydrolysis appears to be particularly appropriate for aluminium compounds. Group ID.-The results from determinations of the standard enthalpies of formation of the alkyl organometallic compounds of gallium indium and thallium are also meagre. The only addition to the values quoted in ref.10 is the determination of the enthalpies of formation of Et,Ga Bu,Ga and BuiGa by Rabinovich Kol’yakova and Zorina2& by static-bomb calorimetry. They give little experimental detail and the reliability of the values is questionable. The results given are as follows Et,Ga AH;(1)= -117 f4kJmol-’ AH;(g)= -75kJmol-’ (16) Bu,Ga AH; (1) = -280 & 4 kJ mol-’ AH; (g) = -222 kJ mol-’ (17) BuiGa AH (1) = -289 f4 kJ mol-’ AH; (g) = -234 kJ mol-’ (18) Group IVB.-The difficulty of obtaining reliable thennochemical data on organosilicon compounds has often been noted. A recent paper25 ,on the bond- energy terms for Group IVB organometallic compounds does not include any values for alkylsilanes stating the reason as lack of reliable data.Quane26 has combined data from two recent experimental studies ;the electron-impact work of Potzinger and Lampe2’ and the determination of enthalpies of combustion of methyl chlorosilanes by Hajiev and Agarunov,28 to obtain values for silicon bond-energy terms which reproduce the input data within f12 kJ mol-’. The breakthrough in the field of obtaining reliable data on silicon organo- metallic compounds is due to Good et a1.,29 who determined the enthalpy of formation of hexamethyldisiloxane by a similar method to that described above for boron compounds. They showed that the combustion of the compound in the presence of aaa-trifluorotoluene resulted in the formation of gaseous silicon tetrafluoride in place of silica and a complete clean combustion resulted.Water placed initially in the bomb dissolved the silicon tetrafluoride to produce a homogeneous solution of hexafluorosilicic acid in excess hydrofluoric acid. The energy of formation of the hexafluorosilicic acid was determined in a separate experiment in which elemental silicon mixed with a sample of polyvinylidene fluoride of known energy of combustion was burned with a solution of hydro- fluoric acid placed initially in the bomb. It was thus possible to determine the 24aI. B. Rabinovich G. M. Kol’yakova and E. N. Zorina Doklady Akad. Nauk S.S.S.R. 1973 209 616. 25 A. S. Carson P. G. Laye J. A. Spencer and W. V. Steele J. Chem. Thermodynamics 1970 2 659. 26 D. Quane J. Phys. Chem. 1971,75,2480. 27 P. Potzinger and F.W. Lampe J. Phys. Chem. 1970.74 719. ” S. N. Hajiev and M. J. Agarunov J. Organometallic Chem. 1970 22 305. ’9 W. D. Good J. L. Lacina B. L. DePrater and J. P. McCullough J. Phys. Chem. 1964 68 579. 112 W. V. Steele enthalpy of formation of the hexamethyldisiloxane with respect to the particular sample of elemental silicon used in the measurements. Iseard Pedley and Tre~erton,~' using a similar method have recently deter- mined the standard enthalpies of formation of tetraethylsilicon hexamethyl- disiloxane and hexamethyldisilane. The agreement between the two values for hexamethyldisilane is excellent and augurs well for the use of this method in the future. The enthalpies of formation determined by the Sussex group were AH; Me6Si20 (1) = -812.5 f19.7 kJ mol-' (19) AH; Me,Si (1) = -403.3 & 7.1 kJ mol-' (20) AH; Et,Si (1) = -277.8 _+ 18.8 kJmol-' (21) The accurate determination of the enthalpies of formation of a number of organogermanium compounds has appeared in the literature since the publication of ref.10. The work by Bills and Cotton31 on the determination of the enthalpy of formation of tetraethylgermanium by rotating-bomb calorimetry has led the way in this field. They used 10% hydrofluoric acid as solvent to dissolve the .~~ products of combustion. Since then Carson et ~1 at Leeds have determined the standard enthalpies of formation of tetraphenylgermanium tetrabenzyl- germanium and hexaphenyldigermanium by rotating-bomb calorimetry using 1M-potassium hydroxide as solvent.Small unburnt residues which produced C02 on heating in oxygen were observed but these were so small that their exact composition was dficult to determine. The results were calculated on the assumption that this residue was a 50 %mixture ofcarbon and unburnt compound. The resultant derived enthalpies of formation are AH Ph,Ge (c) = 281.2 & 13.8 kJ mol-' (22) AH Ph&e (c) = 446.4 f10.5 kJ mol-' (23) AH; Bz,Ge (c) = 219.7 10.5 kJ mol-' (24) Kana'an33 has determined the sublimation pressures and the associated thermo- chemical quantities for tetraphenylgermanium and hexaphenyldigermanium by simultaneous measurement of the torsional recoil and rate of mass effusion. He obtained values of AH:", Ph,Ge = 156.9 & 4.6 kJ mol-' (25) AH:", Ph,Ge = 209.2 4.2 kJ mol-' (26) and combining these values with those in equations (22) and (23) respectively 39 B.S. Iseard J. B. Pedley and J. A. Treverton J. Chem. Soc. (A) 1971 3071. 31 J. L. Bills and F. A. Cotton J. Phys. Chem. 1964 68 806. 32 (a) G. P. Adams A. S. Carson and P. G. Laye Trans. Furuduy Soc. 1969 65 113; (6) A. S. Carson E. M. Carson P. G. Laye J. A. Spencer and W. V. Steele ibid. 1970 66 2459. 33 A S. Kana'an J. Chem. Thermodynamics 1974 6 191 The Th ermoch em is try oj0rganometallic Compounds 113 we obtain AH; Ph,Ge (g) = 438.1 f14.2 kJ mo1-l (27) AH; Ph,Ge2 (g) = 655.6 _+ 11.3 kJ mol-' (28) These values differ from those quoted by Carson eta!.,who used estimated values for the enthalpies of sublimation.Using the above values for the enthalpies of sublimation it is possible to estimate that the enthalpy of sublimation of tetra-benzylgermanium should be Bz,Ge = 184 8 kJ mol-' (29) and hence AH; Bz,Ge (g) = 403.8 kJ mol-The static-bomb and reaction calorimetry of organotin compounds has been reviewed by Skinner,'* and the values obtained are listed by Cox and Pilcher." Static-bomb calorimetry appears to be able to give reliable values for tin organometallic compounds since the only products of combustion are SnO CO, and H,O with only a small amount of unburnt tin and soot. However in the case of tetraphenyltin the combustion proved difficult owing to ex-plosion~.~~ Adams Carson and overcame this problem by using an aneroid calorimeter in their combustions.Owing to the smaller heat capacity of the system they were able to use much smaller samples and still get a reasonable temperature rise. A silica chimney helped to obtain complete combustion. The agreement obtained between the two investigations was excellent. Carson et have also determined the standard enthalpy of formation of hexaphenyl- ditin in the same calorimeter. They obtained AH; Ph6Sn (c) = 660.2 f8.4 kJ mol-' (31) Keiser and Kana'an' have measured the enthalpies of sublimation of both tetraphenyltin and hexaphenylditin obtaining values of AH&, Ph,Sn = 161.1 f5.0 kJ mol-' (32) AHzubPh6Sn2= 188.3 f3.9kJmol-' (33) Combination of these values with those obtained for the standard enthalpies of formation of the compounds gives AH; Ph,Sn (g) = 571.1 f5.9 kJ mol-' (34) AH; Ph,Sn2 (g) = 848.5 _+ 9.2 kJ mol-' (35) As stated above the static-bomb calorimetry of the organometallic compounds of lead gave values which were in error by up to 150kJ mol-'.Accurate thermo- chemical values for lead alkyls have been obtained by rotating-bomb calorimetry 34 A. E. Pope and H. A. Skinner Trans. Faraday Soc. 1964 60 1402. 35 G. P. Adams A. S. Carson and P. G. Laye J. Chem. Thermodynamics 1969 1 393. 36 W. V. Steele A. S. Carson P. G. Laye and J. A. Spencer J. Chem. Thermodynamics 1973 5 477. 114 W. V. Steele by Good et al.' The bomb contained nitric acid as solvent for the solid products of the combustions and the final solution was a homogeneous one of lead nitrate in excess nitric acid.The bomb processes can be summarized by equations (36) and (37). CsH,,Pb(l) + 17.84HN03,573.6H,O + 13.502 + ISH2O + Pb(NO3),,15.84HN0,,586.1H,O + 8C02(g) (36) Pb(N03)2,15.84HN0,,586.1H,0 -+ Pb(N03),(c) + 15.84HNO3,575.IH,O + 11H20(1) (37) The derived enthalpies of formation are given in equations (38) and (39) using AH; Me,Pb (1) = 64.4 f 3.8 kJ mol-I (38) AH; Et4Pb (1) = 108.8 f 2.5 kJ mol-' (39) the most recent value for the enthalpy of formation of solid lead nitrate.36 Carson et aL3' have determined the standard enthalpy of formation of tetra- phenyl-lead using a similar method to that of Good but using yellow lead dioxide as the solid lead compound in the comparison experiments; lead nitrate is hygroscopic and requires careful handling in weighing.The following enthalpies of formation were derived from the results AH; Ph,Pb (c)= 515.0 f 15.0kJ mol-' (40) AH; Ph4Pb (g) = 709.6 f 20.0kJ mol-' (41) Group VB.-The values tabulated by Cox and Pilcher for the enthalpies of formation of the organophosphorus compounds all have large uncertainties attached to them. Recent work by Birley and Skinner3* and Head and Lewis39 on the enthalpy of formation of aqueous orthophosphoric acid should lead the way in obtaining more reliable values for all the compounds. Head and Lewis burnt white phosphorus in a rotating-bomb calorimeter ;hydrolysisof the reaction products produced a mixture of acids. When the bomb was maintained at 323 K the product was orthophosphoric acid when perchloric acid was used as solvent.Their paper outlines methods for the detection of small amounts of the phosphorus acids in the presence of a large excess of the ortho-acid. It should be used as a model by anyone undeitaking the determination of the enthalpies of these compounds by rotating-bomb calorimetry. The static-bomb calorimetry of arsenic organometallic compounds is fraught with difficulty as the products are a complex mixture of solid As203 AsZ04 unburnt As and carbon together with an aqueous solution of As"' and As" in varying concentrations within the bomb itself. The values obtained by this 3' A. S. Carson P. G. Laye J. A. Spencer and W. V. Steele J. Chem. Thermodynamics 1972,4 783. 38 G. I. Birley and H. A. Skinner Trans. Faraday SOC.,1968,64 2232.39 A. J. Head and G. 9. Lewis J. Chem. Thermodynamics 1970,2,701. The Thermochemistry of Organometallic Compounds 115 method must therefore be suspect. Mortimer and Sellers40 have used the rotating- bomb method to determine the standard enthalpy of formation of triphenyl-arsine. The solvent used in the combustions was sodium hydroxide giving a final solution of sodium arsenate sodium arsenite sodium carbonate and excess sodium hydroxide. After analysis of the solution corrections were made for the enthalpies of formation of the sodium carbonate and the sodium arsenate. The only values available for organo-antimony and -bismuth compounds were obtained by static-bomb calorimetry and are suspect. Cox and Pilcher list uncertainty intervals of +16kJmol-' for these compounds and this is probably an under-estimate.Group VIA and Group VIM.-With the exception of the triacetylacetonates of chromium and manganese(III) whose enthalpies of formation have been determined by reaction calorimetry only static-bomb calorimetry values exist for the organometallic compounds of both of these Groups.'O A rotating-bomb method of determining the standard enthalpies of formation of manganese organometallic compounds has been developed by Good et a1.,41but to date the only manganese compound studied has been dimanganese decacarbonyl. The solvent used in the rotating-bomb experiments to dissolve the products of combustion was a mixture of nitric acid and hydrogen peroxide which converted all the manganese into Mn" ions.A solution of manganese nitrate Mn(NO,), 10.3H20 encapsulated in a Pyrex ampoule was used to reproduce the same final solution in the comparison experiments. The idealized combustion reaction can be represented by equation (42),and Mn,(CO), (c) + 4HN03,16H,0 + 60 + 2Mn(N03),,10.3H,0 + 10C0 (g) + 2H,O (1) (42) AH; Mn,(CO), (c) = -1683.8 f 3.4 kJ mol-Group VIB.-The thermochemistry of organoselenium compounds is in its infancy. Barnes and M~rtimer~~ have determined the standard enthalpies of formation of selenium dioxide and diphenyl selenide by rotating-bomb calori- metry using deionized water as the solvent. The enthalpy of selenium dioxide in water was determined in separate experiments by reaction calorimetry. The following enthalpies of formation were determined AH;SeOz(c) = -226.4 & 2.1 kJmol-' (43) AH Ph,Se (c) = 227.2 6.0 kJ mol- (44) AH Ph,Se (g) = 291.0 8.4 kJ mo1-l (45) Group VIII-The data on the organometallic compounds of this Group have been summarized by Cox and Pilcher" in half a page of their tables and the field is virtually bare of kny accurate values.40 C. T. Mortimer and P. Sellers J. Chem. Soc. 1964 1965. 41 W. D. Good D. M. Fairbrother and G. Waddington J. Phys. Chem. 1958 62 853. 42 D. S. Barnes and C. T. Mortimer J. Chem. Thermodynamics 1974,6 371. 116 W. V. Steele 6 Mean Metal Bond Dissociation Energies The difference between the concepts of bond-energy terms and bond-dissociation energies is well known and will not be explained here (see for example ref.18). The enthalpies of formation of organometallic compounds can be used in con- junction with the enthalpies of formation of the free radicals and the enthalpies of formation of the gaseous metal atoms to calculate mean bond-dissociation energies of metal-carbon bonds in metallic alkyls and related compounds. If the enthalpy of process (46)can be calculated then we have equation (47) MR,(g) + M(g) + nR(g) (46) AHo = AH; M (g) + n AH; R (g) -AH; MR (g) (47) and the mean bond-dissociation energy D(M-R) is AH"/n. In general these mean bond-dissociation energies will differ from the actual metal-carbon dissociation energies D(R,-M-R) which still have not received much attention and few measured values have been reported.An exception to this is the study of the individual bond-dissociation energies in mercury dialkyls in which the inequality of the two dissociation energies was demonstrated. The whole field has been reviewed by Skinner.18 The mean bond-dissociation energies in the metal alkyls as defined above are listed in Table 3 and have been derived from the data in Tables 1 and 2 along with the enthalpies of formation of the metal alkyls from Cox and Pilcher'O or given in Section 5. Values derived from static-bomb calorimetry are given in parentheses as these can only be tentative. However certain trends are evident and these can best be shown for the organometallic compounds of Group IVB. The mean bond-dissociation energy for RMe is approximately 30 kJ mol- ' greater than that determined for other n-alkyl groups which stays virtually constant.The D value for RPh is approximately 65 kJ mol- more than that determined for the normal alkyl groups. Also D(M-R) falls progressively as we descend the Group i.e. D(C-R) > D(Si-R) > D(Ge-R) > D(Sn-R) > D(Pb-R). The comments made in the last paragraph apply to a number of other values in Table 3 and parallel those made by Holm'8a in his discussion of the relative bond-dissociation energies of R-MgX compounds (see Section 5). Cox and Pilcher" list values for bond-energy terms for organometallic com- pounds which reproduce the data reasonably well (within f12 kJ mol- '). It is therefore not proposed to set out these values here again but the interested reader is referred to their book.It is also worth noting the scheme derived by Carson et u/.19736*37 for the organometallic compound of Group IVB. 7 Conclusions The thermochemistry of organometallic compounds has progressed in the past two decades since the advent of the rotating-bomb calorimeter. A number of workers notably Good and Skinner have pioneered methods of determining The Thermochemistry of Organometallic Compounds Table 1 Enthalpies of formation of gaseous atoms at 298.15 K" Atom AH; (g)/kJ mol- Atom AH (g)/kJ mol-' H 217.997 f0.006 cu 338.5 f2.1 Li 161 f2 Zn 130.54 f0.21 Be 322 f2 Ga 272 & 2 B 559 f 15 Ge 283 f2 C 716.7 f0.4 AS 288 f12 N 472.7 f0.4 Se 207.5 f4.2 0 249.17 f0.10 Br 111.88 f0.12 F 78.5 f10.0 Rb 79.5 & 2.1 Na 108.43 f0.63 Sr 165 f2 MgA1 143.68 f0.20 332.6 f0.2 Y Zr 420 f2 593 f10 Si 453.5 f12.6 Nb 753 f8 P 316.2 f0.6 Mo 659 f2 S 277.8 f0.3 Tc 661 17 C1 121.290 f0.008 Ru 650 f10 K 89.60 f0.21 Rh 558 f8 Ca 179 & 2 Pd 373.2 & 3.3 sc 380.7 & 2.1 Ag 284.9 f0.8 Ti 467.97 & 1.72 Cd 111.56 f0.10 V 514.6 f1.0 In 236.73 f0.42 Cr 397 f2 Sn 300.7 & 0.3 Mn 284.9 f1.7 Sb 265 f8 Fe 415 f7 Te 193 f8 co 422.6 f0.8 I 106.762 f0.040 Ni 421.86 f0.29 CS 78.6 f1.3 Ba 185 f2 Au 368 f4 Hf 619 f4 Hg 61.329 & 0.054 Ta 782 f10 T1 181.2 f2.1 w 851.4 f0.8 Pb 194.97 f0.84 Re 778.0 f2.7 Bi 208.8 f0.8 0s 790 f6 Ra 162 f10 Ir 669 f8 Th 597.5 f4.6 Pt 564.5 f2.1 U 536 f8 a All values are taken from 'Bond Energies.Data and Methodology' by W. V. Steele Butterworths London in the press. In this monograph the values listed above are those accepted as the 'best' available from a review of literature data up to July 1974. Table 2 Enthalpies of formation of free radicals at 298.15 K Radical AH:/kJ mol-' Reference CH 145.6 f0.4 a Et 106.7 f4.2 b Pr" 85.8 f7.5 b Bun 67 f10 b Pr' 76 f7.5 b Bu' 54 f9 C Bu' 33 f6 c Ph 324.3 f10.0 d Bz 188 f13 e cyc10-CSH.j 188 k40 e a W. A. Chupka J. Chem. Phys. 1968 48,2337; J. A. Kerr Chem. Rev. 1966 66 465; H. E. O'Neil and S. W. Benson Chapter 17 in 'Free Radicals' ed. J. K. Kochi Wiley-Interscience 1973 vol. 11; G. A. Chamberlain and E. Whittle Trans. Furuday SOC.,1971,67 2077; J.S. Roberts and H. A. Skinner Trans. Furaduy SOC.,1949 45 339. 118 W. V. Steele Table 3 Mean bond-dissociation energies in MR,,D(M-R)/kJ mol-'a Bond D/kJ mol-Bond D/kJ mol-Li-Me (248) Ga-Bu 232 & 8? Li-Bu (253) Ga-Bu' 223 f 8? Mg-Cyclo-C,H 191 & 45 In-Me 168 f6 Zn-Me 183 f7 Si-Et 290 f25 Zn-Et 133 f10 Ge-Et 244 f8 Zn-Pr" 145 f25 Ge-Pr 239 f8 Zn -Bu" 157 f25 Ge-Ph 306 f16 Cd-Me 147 f4 Ge-Bz 183 f16 Cd-Et 111 f 8 Sn-Me 226 & 4 Hg-Me 124 f4 Sn-Et 193 f 8 Hg-Et 100 f8 Sn-Pr 197 & 8 Hg-Pr" 99 f 9 Sn-Pr' 182 f 10 Hg-Pr' 86 f9 Sn-Bu" 198 f10 Hg-Ph 157 + 8 Sn-Ph 257 & 10 B-Me (373) Pb-Me 168 f4 B-Et (344) Pb-Et 139 f6 B-Pr" (351) Pb-Ph 196 f10 B-Pr' (346) P-Me (283) B-Bu" (349) P-Et (229) B-Bu' (334) P-Ph (319) B-Ph (466) As-Me (238) Al-Me (286) As-Et (184) AI-Et (272) or (245)b As-Ph 280 + 15 Ga-Me 252 f 8 Cr-c,H (166)-Ga-Et 223 + 8? MO-c6H6 (21 1) Sb-Me (224) Se-Et (238) Sb-Et (1 79) Se-Ph 277 f10 Sb-Ph (267) Fe -cyclo-C H 288 f40 Bi-Me (140) Ni-cyclo-C,H 237 f40 Bi-Et (109) Bi-Ph (200) a Values calculated from equation (47) Tables I and 2 and values of AK (g) from ref.10 or text; 'Value calculated from A& Et,Al(g) = -84 kJ mol-from P. A. Fowler Ph.D. Thesis University of Manchester 1961. the standard enthalpies of formation of these compounds but several important groups remain untackled notably organo-aluminium and -phosphorus com-pounds. Kana'an's work on the determination of the enthalpies of sublimation of the tetraphenyls of Group IVB includes virtually the first such determinations in the field and it is to be hoped that more values will be forthcoming soon.The basis of the field has been well founded and it now needs a set of dedicated scrupulous workers to continue the good work.

ISSN:0308-6003    

DOI:10.1039/PR9747100103

出版商:RSC    

年代:1974

数据来源: RSC

摘要:

7 The High-temperature Thermodynamics of Inorganic Substances By G. V. JAGANNATHAN G. R. WOOLLEY and P. A. H. WYATT Department of Chemistry The University of St. Andrews Scotland 1 Introduction The extension of chemical thermodynamics to reactions at high temperatures is of course by no means new and is in principle straightforward. Indeed the preference in the past for working within 100K or so of room temperature reflected in many publications in the purely chemical literature (with notable exceptions) has obviously been dictated by experimental convenience and many metallurgists have probably felt with some justification that they had a broader vision of the scope of chemical thermodynamics than the average chemist. Despite the experimental difficulties substances which react at useful rates only at high temperatures have nevertheless frequently demanded practical attention because of their economic importance and consequently much of the informa- tion on metals and other inorganic substances and their mixtures has been widely scattered through the specialist literature in subjects outside the arbitrary con- fines of mainstream chemistry.It is therefore particularly useful when books like F. D. Richardson’s ‘Physical Chemistry of Melts in Metallurgy’(in two volumes)’ appear and provide an up-to-date key to reviews and other references in a well- defined and important area of this large field. Although supplementary information about the behaviour of mixtures is often essential it is still broadly true that the principal object of thermodynamic studies at high temperatures is to permit the calculation of yields of chemical reactions (McGlashan2) and for this purpose free-energy information on pure substances over wide temperature ranges will continue to be of paramount importance.While third-law determinations and statistical calculations continue the free-energy values for many compounds still depend upon the measurement of a chemical or phase equilibrium at a high temperature if only for checking internal consistency and here a good feeling for the possibility of chemical complications and even kinetic constraints is obviously vital. Since dozens of elements are potentially important economically and every element in spite of F. D. Richardson ‘Physical Chemistry of Melts in Metallurgy’ Volumes I and 11 Academic Press London 1974.* ‘Chemical Thermodynamics’ ed. M. L. McGlashan (Specialist Periodical Reports) The Chemical Society London 1973 Vol. I. 119 G. V. Jagannathan G. R. Woolley,and P. A. H. Wyatt family resemblances has largely its own distinctive chemistry there will always be important questions of detail to settle experimentally even after the broad framework of consistent free-energy data throughout the Periodic Table has largely been set up. In particular nonstoicheiometry will always bring special problems of its own wherever it occurs. During the past two decades a good introduction to the general physico- chemical background and the high-temperature techniques involved has been provided by successive editions of ‘Metallurgical Thermochemistry’ by Kubaschewski Evans and Al~ock,~ and by the Discussions of the Faraday Society on ‘The Physical Chemistry of Process Metallurgy’ (No.4 1948) ‘The Structure and Properties of Ionic Melts’ (No. 32 1961) and ‘The Vitreous State’ (No. 50 1970). Calculations of reaction yields vapour pressures etc. have also been greatly facilitated by the replacement of laborious expressions involving tempera- ture series by compilations of -(G* -HF)/T values or often more usefully still of AG? values over a wide range of temperatures as in the JANAF table^.^ In recent years however the whore field has expanded considerably largely for two reasons. On the one hand alongside the steady progress in the traditional fields of metallurgy glass technology and ceramics considerable research effort has been directed towards investigations of the properties of materials in any way connected with nuclear power rocket fuels and semiconductors.On the other hand advances in mass spectrometry and the development of the matrix-isolation technique (ironically taking advantage of very low-temperature properties) have produced a revolution in our knowledge of the constitution of the vapour phase over high-temperature melts and solids. In preparing this Report a few hundred references have been traced for the past two years alone and it will clearly be impracticable and probably also pointless to cover all of them adequately since they will in any case be familiar to specialists in the various fields.We have therefore designed our Report rather for those approaching this subject from the traditionally ‘chemical’ end and have aimed at giving an adequate introductory bibliography and a survey both of the standard methods of investigation and of the novel experimental techniques that are gain- ing favour. The selection of examples chosen to illustrate lines of research cannot be exhaustive but it will give some indication of the problems one can expect to meet. 2 Sources of Information Between 1956 and 1966 seven reviews appeared of high-temperature chemical studies. The first fo~r~-~ covered mainly experimental techniques while the 0. Kubaschewski E. L. Evans and C. B. Alcock ‘Metallurgical Thermochemistry’ 4th edn.Pergamon Press Oxford 1967. D. R. Stull and H. Prophet ‘Joint Army Navy and Air Force Thermochemical Tables’ U.S. Govt. Printing Office Washington 2nd edn. 1971. L. Brewer and A. W. Searcy Ann. Rev. Phys. Chem. 1956 7 259. J. L. Margrave Ann. Rev. Phys. Chem. 1959 10 457. ’ P. W. Gilles Ann. Rev. Phys. Chem. 1961 12 355. R. F. Porter Ann. Rev. Phys. Chem. 1959 10 219. The High-temperature Thermodynamics of Inorganic Substances 121 later ones9- l1 have in addition discussed the status of high-temperature topics" and have turned towards the correlation of result.sg-" and the discussion of structures and stabilities of species and the adequacy of theoretical treatments." The dissociation energies of diatomic the attainment and measurement of high temperatures,6 and the kinetics of high-temperature reactions6 and heterogeneous equilibria* are among the topics dealt with.The period since 1966 has seen the rapid growth of matrix-isolation spec- troscopy photoelectron spectroscopy and to a lesser extent Mossbauer spectroscopy all of which have potentially important contributions to make to the investigation of high-temperature species ;however the combination of mass spectrometry with the Knudsen effusion cell still seems to be the most widely used technique for this purpose. Reference will be made to some of these methods and their recent variants in this Report. A review of the field up to 1970 was published by Margrave et a!.," who referred to the experimental techniques available for the characterization of high-temperature species and discussed the conclusions which had been drawn about the stabilities and structures of a num- ber of the latter.More recently the first Chemical Society Specialist Periodical Report on Chemical Thermodynamics2 contains some excellent chapters of direct relevance to high temperatures. One by Kubaschewski Spencer and Dench is specifi-cally on a restricted branch of this subject ('Metallurgical Thermochemistry at High Temperatures') and surveys the thermochemical quantities required and the experimental methods for their determination while another by Frankiss and Green is on the 'Statistical Methods of Calculating Thermodynamic Functions' and sets out the requisite formulae in some detail though it must be admitted that the examples chosen for the applications are almost entirely organic molecules.The most useful chapter for present purposes however is that of Herington on 'Thermodynamic Quantities Thermodynamic Data and their Uses' which must be one of the most comprehensive yet manageable guides to the literature in any subject. Theory units symbols and measuring scales are all surveyed along with an extensive bibliography of the available tabulations of thermodynamic data and a discussion of their uses. To the Herington list of sources may now be added (i) a monograph by Mills12 on inorganic sulphides selenides and tellurides surveying the literature up to 1970 and listing the heats of formation standard entropies heat capacities en- thalpies vapour pressures and dissociation energies of over 700 compounds up to 2000 K; (ii) a special compilation by HorvathI3 of the physical properties of 31 compounds of major importance in the chemical industry including in graphical form such properties as vapour pressure density (orthobaric and J.Drowart and P. Goldfinger Ann. Rev. Phys. Chem. 1962 13 459. lo R. J. Thorn Ann. Rev. Phys. Chem. 1966 17 83. l1 J. W. Hastie R. H. Hauge and J. L. Margrave Ann. Rev. Phys. Chem. 1970 21,475. I K. C. Mills 'Thermodynamic Data for Inorganic Sulphides Selenides and Tellurides' Butterworths London 1973. l3 A. L. Horvath 'Physical Properties of Inorganic Compounds' Arnold London 1974. G. V. Jagannathan G. R. Woolley and P. A. H.Wyatt supercritical) latent heat of vaporization thermal capacity viscosity thermal conductivity surface tension and solubility; and (iii) a book by Barin and Knacke14 on inorganic substances the review of which by Skinner” implies that it does not contain much data independent of the JANAF tables Landolt- Bornstein and ‘Metallurgical Therm~chemistry’.~ The second edition of the JANAF Thermochemical Tables is welcomed in a review by F. D. Rossini,16 who makes a plea that the full notation (G* -HF)/T should be adhered to and not replaced by contractions like gef,. (On this theme the article following Rossini’s review is a guide to the IUPAC recommendations on the presentation of thermodynamic results prepared by Commission 1.2 on thermodynamics and thermochemistry under the chairmanship of E.F. Westrum jun.) Further JANAF supplements beyond the first 33 now incor- porated in the second edition are now published from time to time in J. Phys. Chem. ReJ Data (see e.g. Vol. 3 No. 2 1974). Apart from revisions for lead halides and titanium oxides the programme has continued with new tables on cobalt chlorides oxides of V Nb Ta and Cr selected carbides nitrides and alkaline-earth compounds; and it is proposed to follow on with refractory metal halides polyatomic carbon gases and sulphur-fluorine compounds. ’ The International Council of Scientific Unions (ICSU) and the Committee on Data for Science and Technology (CODATA) set up in 1968 a Task Group on Key Values for Thermodynamics with the object of producing an internationally agreed set of values for the thermodynamic properties of chemical species.Following upon the initial publication of the first report a final list has now been produced18 of recommended values in both J and thermochemical calories of AH? (298.15 K) Se (298.15 K) and [H* (298.15 K) -H*(O)] for the atomic and molecular forms of the elements 0,H C1 Br I N C (with for example AH? (298.15K) for C(g) at 716.67 kJ mol-’ or 171.29 kcaI mol-I) and the rare gases plus H,O (1 and g) and gaseous HCl HBr HI CO and CO,. It is stressed that these recommended values will not be entirely consistent with any other published set but the Task Group has as its ultimate goal the revision of the 298.15 K values for the whole field. Mention should also be made of the CODATA ‘International Compendium of Numerical Data project^','^ the CATCH (Computer Analysis of Thermochemical Data) tables available from the School of Molecular Sciences of the University of Sussex and of the quarterly current awareness bibliographies on the ‘Higher Temperature Chemistry and Physics of Materials’,’’ edited by J.J. Diamond and covering research at temperatures above 1OOO”C. It is l4 I. Barin and 0. Knacke ‘Thermochemical Properties of Inorganic Substances’ Springer-Verlag Berlin/Heidelberg 1973. Is H. A. Skinner J. Chem. Thermodynamics 1974 6 71 1. l6 F. D. Rossini J. Chem. Thermodynamics 1972 4 509. M. W. Chase personal communication. Codata Key Values Part I J. Chem. Thermodynamics 1972 4 331. l9 Codata ‘International Compendium of Numerical Data Projects’ Springer-Verlag Berlin 1969.’O ‘Bibliography on the High Temperature Chemistry and Physics of Materials’ ed. J. J. Diamond NBS Special Publ. 313-1 1968 and onwards. The High-temperature Thermodynamics of Inorganic Substances 123 divided into two parts (I) solids and liquids and (11) gases and groups the references under 15 headings such as ‘Phase equilibria above lo00 “C’ ‘Devices for achieving temperatures above 1500”C,or ‘Spectroscopy of interest to high temperature chemistry’. When investigating certain high-temperature equilibria e.g. by the Knudsen effusion technique where the residence time of the molecules in the cell may be rather short it is necessary to know which of the possible reactions have time to reach equilibrium.Kinetic information is then vital. Specifically high-tempera- ture reaction rate data (up to 5000K) for homogeneous gas reactions are critically surveyed by Baulch et with O.S.T.I. support and a paper on current compila- tions and evaluations of kinetic data is also available.22 3 Enthalpy Measurements The established methods of attaining and measuring high temperatures are well re~iewed.~*~*~ A new International Practical Temperature Scale was adopted in 1968 (IPTS 68) being higher by 1.24K at lo00 “C and 5.9 K at 3000 “C than the older (IPTS 48) scale further information is given by Herington.2 Improvements have been made in the traditional resistive and inductive heat- ing of furnaces but novel methods are constantly being introduced or such as arc and solar imaging shock tubesz4 and lasers,25 flames augmented by electric power adiabatic expansion,26 and the radio-frequency heating associ- ated with electromagnetic levitation.The latter technique with which tempera- tures above 2700 K are obtainable is particularly suited to the study of reactive alloys at high temperatures and has been shown to give results for enthalpies of mixing and other thermodynamic quantities in good agreement with former methods for the liquid Fe-Ni ~ystern,~’ but it is clearly of restricted application to inorganic substances in general. Calorimetry.-The various forms of calorimeter are well reviewed and classi- fied,2,3*28,29 and details of specifically high-temperature devices can be found in specialist books3 and re~iews.2~ To judge from recent publications the most popular method of determining thermal capacities and enthalpies is still drop calorimetry.Here a capsule con- taining the specimen is heated in a furnace to a determined temperature and then dropped into a calorimeter of known heat capacity kept near room temperature ’I D. L. Baulch ‘High Temperature Reaction Rate Data Reports’ Department of Physical Chemistry Leeds University Leeds England 1970. 22 L. H. Gevantman and D. Garvin Internat. J. Chem. Kinetics 1973 5 213. Chemical Society Faraday Symposium No. 8 ‘High Temperature Studies in Chemistry’ London 1973. 24 W. T. Rawlins and W. C. Gardiner jun. J. Phys. Chem. 1974 78 497. 25 R. T. Meyer A.W. Lynch and J. M. Freese J. Phys. Chem. 1973 77 1083. 26 J. Berkowitz J. Chem. Phys. 1972 56 2766. ’’ K. C. Mills K. Kinoshita and P. Grieveson J. Chem. Thermodynamics 1972 4 581. ** ‘Physicochemical Measurements at High Temperatures’ ed. J. O’M Bockris J. L. White and J. D. MacKenzie Butterworths London 1959. 29 ‘Experimental Thermochemistry’ Vol. 11 ed. H. A. Skinner Interscience-Wiley London 1962. 124 G. V. Jagannathan G. R. Woolley and P. A. H. Wyatt so that the enthalpy change of the sample between the two temperatures can be determined directly and the heat capacity from the rate of change with tem- perature of the enthalpy. In this way [HO(T)-H*(298.15 K)] and CF(T){and hence sometimes [S*(T) -Se(298.15 K)] and other functions) have been deter- mined for FeSe between 300 and 853 K by Svendsen ;30 for Na,O up to 1300 K and Na(1) up to 1505 K by Fredrickson and Chasanov ;31 for UN up to 1700 K by Oetting and Leitnaker;32 and for Pt and a Pt-Rh alloy (10 mass per cent Rh) between 400 and 1700 K,33aU02.25up to 1600 K,33band LiF NaF KF RbF and CsF from 500 to 1600 K,33call by MacLeod.For the alkali-metal fluorides Ma~Leod~~' also reports the enthalpies of fusion as 26.7 kJ mol-' (LiF) 33.5 kJ mol-' (NaF) 29.5 kJ mol-' (KF) 25.9 kJ mol-' (RbF) and 14.0kJ mo1-l (CsF). With the exceptions of the KF value which is higher than other published data and that of CsF which is considerably lower than the only other published value these agree well with other determinations. Mar and have continued their studies of high-temperature enthalpies of compounds of high boron content and Spedding et aL3' report much useful data tabulated at 100 K intervals from 100 to 1600 K of ten rare-earth fluorides.By adiabatic shield calorimetry Grran~old~~ determines the following quanti- ties for liquid Se CF (1000K) = 35.62JK-'mol-' [HO (1000K) -H0 (298.15K)] = 28.593kJmol-' and [S* (lo00 K) -S* (298.15K)] = 49.81 J K mol-;and for hexagonal Se he finds the melting point to be (494.33 & 0.02)K and the enthalpy of fusion (6159 k 4) J mol- '. With his co-~orkers~~ he is also investigating the thermodynamic properties (up to 900 K and above) of selenides and tellurides of Ni Fe and Cr some of which are non-stoicheiometric com- pounds and of alkali-metal-MgC1 double chlorides.38 The Co and Ni tellurides undergo interesting structural changes and the heat capacities of phases of various composition are reported by Milk3' A neat high-temperature calori- meter (for 900-1800K) which can serve either as an adiabatic or as a heat- flow device is described by Malinsky and Claisse4' for the study of metal systems. The authors claim that it is reliable sensitive and easy to operate and have measured the enthalpy of formation at 1550 K and the heat capacity from 1100 to 1700 K of another non-stoicheiometric compound Cro.47Tmo.53. Recently high-temperature microcalorimetry has been used by Campserveux and 30 S. R. Svendsen Acta Chem. Scand. 1972 26 3834. 31 D. R. Fredrickson and M. G. Chasanov J. Chem. Thermodynamics 1973 5 485; ibid.1974 6 629. 32 F. L. Oetting and J. M. Leitnaker J. Chem. Thermodynamics 1972 4 199. 33 (a) A. C. MacLeod J. Chem. Thermodynamics 1972,4 391 ;(b)ibid. p. 699; (c)J.C.S. Faraday I 1973 69 2026. 34 R. W. Mar and N. D. Stout J. Chem. Thermodynamics 1974,6 943. " E. H. Spedding B. J. Beaudry D. C. Henderson and J. Moorman J. Chem. Phys. 1974,60 1578. 36 F. Grenvold J. Chem. Thermodynamics 1973 5 525. 37 F. Grenvold Acta Chem. Scand. 1972 26 2085; F. Grenvold N. J. Kveseth and A. Sween J. Chem. Thermodynamics 1972 4 337; F. Grenvold; ibid. 1973 5 545. 38 J. L. Holm B. J. Holm B. Rinnan and F. Grenvold J. Chem. Thermodynamics 1973 5 97. 39 K. C. Mills J.C.S. Faraday I 1974 70 2224. 40 I. Malinsky and F. Claisse J. Chem.Thermodynamics 1973 5 615. The High-temperature Thermodynamics of Inorganic Substances 125 Gerdanian4’ for determining partial molar enthalpies of solution of 0 in CeO,. and CeO at 1353 K and the less common materials used in semiconductors are attracting interest as investigations over wider ranges of temperature become possible. For example McMasters et have reported enthalpies and Gibbs free energies of formation of the europium chalcogenides EuO EuS EuSe and EuTe which become ferromagnetic or antiferromagnetic at temperatures down to 20 K. Flames.4ertain gaseous systems can be studied above 2000 K by injection of the reactants into the premixed constituent gases forming the flame and examin- ing their subsequent changes by emission spectro~copy.~~ Kinetic aspects feature prominently in such studies but equilibrium constants are also obtain- able and hence standard enthalpies of formation.Jensen and Jones44 have used H,-N,-0 flames to examine gas-phase Al-and Fe- containing species. Aluminium is an important rocket fuel and consequently knowledge of its high-temperature chemistry is essential. It was found that when A1 was present in the H,-N,-0 flame the main product was Al(OH) ,although Fe produced FeOH. The following thermodynamic information was obtained (all species are gaseous) A1 + 2H20 = Al(OH) + 2H (1) AH? = (-95 k 30) kJ mol-’ K = 3.0 exp(4300 K/T) A1 + OH = A10 +H (2) AH? = (-172 k 20) kJ mol-’ ; K = 0.67 exp(l9 200 K/T) Fe + H,O = FeOH + H (3) AH = (110 k 20) kJ mol-’ ; K = 66 exp( -16 100 K/7) Fe + OH = FeO + H (4) AH? = (22 k 20) kJ mol-’; K = 0.67exp(-3160K/T) Enthalpies of formation from the gaseous elements were also derived :Al(OH),(g) (-1005 & 30) kJ mol-’ ; AlO(g) (-349 & 20) kJ mol-’ ; FeOH(g) (69 k20) kJ mol- ’; FeO(g) (259 & 20) kJ mol- ’.The derived A10 bond energy (596 k 20) kJ mol-’ is at variance with some former estimates. Similar studies on Ba by Jones and Br~ida~~ have produced information on the population of states of BaO and shown that Ba gives rise to a greater proportion of charged species in the flame than Al. A discussion of the formation of inorganic oxide aerosols of controlled dimen- sions and generated from anhydrous chlorides in H,-02 flames is contained in 4‘ J.Campserveux and P. Gerdanian J. Chem. Thermodynamics 1974 6 795. 42 0.D. McMasters K. A. Gschneidner jun. E. Kaldis and G. Sampietro J. Chem. Thermodynamics 1974 6 845. 43 (a) A. G. Gaydon “Dissociation Energies and Spectra of Diatomic Molecules’ Chapman and Hall London 1968. (b) A. G. Gaydon ‘The Spectroscopy of Flames’ Chapman and Hall London 1974. 44 (a) D. E. Jensen and G. A. Jones J.C.S. Faraday I 1972 68 259; (6) ibid. 1973 69 1448. 45 C. R. Jones and H. P. Broida J. Chem. Phvs. 1974,60 4369 4377. 126 G. V. Jagannathan G. R. Woolley and P. A. H. Wyatt the Faraday Symposium Report on Fogs and If of submicronic size these particles exhibit unusual photocatalytic properties. For example Ti0246 allows the catalytic photo-oxidation (in the U.V.range) of organic and inorganic compounds at ambient temperature. Enthalpy Information from Other Sources.-A feature of the Jensen and Jones work mentioned above44a is their careful comparison of the second- and third- law estimates of the thermodynamic quantities involved. A similar comparison has been made in a closely related study by Farber Srivastava and Uy47 of the vapour species over A1,03 at temperatures near 2000 K. Estimates are given of the partial pressures of all the gaseous species Al 0,A10 A1,0 A1,0, A102 and (provisionally) A1,0 between 1900 and 2600 K and internally consistent heats of formation and equilibrium constants are derived. The vapour species were determined mass spectrometrically after emission in a collimated beam from an elongated orifice in an effusion cell constructed from alumina itself and not from metals such as tungsten and molybdenum reactions with which are demonstrated to account reasonably for the former discrepancies between mass spectrometric and weight-loss evidence.However despite the internal consistency achieved separately in the completely independent flame and mass- spectrometric investigations the derived thermodynamic values are not yet completely consistent between themselves. For example the bond energy of A10 quoted by Farber et ~1.:~ though higher than some earlier estimates is still at about 510 kJ mol-' significantly lower than the 600 kJ mol-' figure mentioned ~' by Jensen and Jones.440 Farber et ~ 1 . ~discuss this discrepancy further and refer to the work of Newman and Page:' who also reported a 'high' value for the dissociation energy of A10 of 601 kJ mol-' (second law) and 589 kJ mol-' (third law) from a spectroscopic study similar to that of Jensen and Jones.The establishment of equilibrium concentrations in the flame is felt to be acceptable although Jensen and Jones state that their H OH and 0 concentrations were slightly above the equilibrium values. The discrepancy is apparently more likely to lie in the intensitysoncentration calibration of AlO which was assumed to be the only Al-containing species present at 4200K other than A1 itself. If this is not the case and the suboxides of A1 are more stable at increased temperatures this leads to an uncertain electronicf number for the 0-0 band and a consequent error in D(A1-0).Although one cannot draw further definite conclusions it is interesting to note that Das et have examined A10 theoretically and report (along with data on CN) a value of 4.24 eV (ie. only 409 kJ mol-' !) for D for the ground state of A10. The next excited states are assigned D,values of 3.70 eV (354 kJ mol-') and 3.55 eV (342 kJ mol- '). Clearly further high-temperature work on A1 and its oxides should solve the problem. 46 (a)F. Juillet F. Lecomte H. Mozzanega S.J. Teichner A. Thevenet and P. Vergnon Chemical Society Faraday Symposium No. 7 'Fogs and Smokes' Swansea 1973 p. 57; (6) A. P. George R. D. Murley and E. R. Place ibid. p. 63. 47 (u)M. Farber R. D. Srivastava and 0. M. Uy J.C.S.Faruday I 1972 68 249; (6)J.C.S. Faraduy 11 1972 68 1388. 48 R. N. Newman and F. M. Page Combustion and Flame 1971 17 149. 49 G. Das T. Janis and A. C. Wahl J. Chem. Phys. 1974 61 1274. The High-temperature Thermodynamics of Inorganic Substances 4 Free-energy Measurements Vapour Pressures Vapour-pressure measurements of one form or another are still the most abundant source of direct equilibrium information at high temperatures. Despite their closer relationship to free energy vapour pressures are conveniently deter- mined at several temperatures and enthalpy values are thereby also derived as mentioned above for the aluminium oxide system.,’ A somewhat arbitrary selection of ‘second law’ enthalpy information derived in this way therefore falls naturally into this section for illustrative purposes.Such second-law enthalpy values are in any case now commonly compared with third-law values to check the overall consistency of the thermodynamic interpretation. This has often been done in the investigations referred to below though it is not specifically mentioned here. The well-established Knudsen effusion techniques acquired new versatility when combined with mass spectrometry in the 1960’s and more recently with low-temperature matrix-isolation methods for characterizing the vapour species. These important developments have been well reviewed.’ It has always been necessary to characterize the vapour species before the measured vapour pressure could be quantitatively interpreted and even with purely mechanical methods such as weight loss and torsion effusion ingenious combinations of results could in principle give some indication of the molecular weight of the effusing species.However as a result of the much greater power of the newer techniques both to determine the species present and to estimate their concentra- tions not only has a wealth ofnew vapour-pressure information accumulated but there has also been a complete revolution in our ideas about the degree of chemical complication of the species which can exist in the vapour phase. Mass Spectrometry.-Our first example of unexpectedly complicated vapour species also illustrates the problems that can be introduced by having a temporary embarrassment of information from the modern highly sensitive instruments.In a mass-spectrometric investigation of the species evaporating from V205-WO mixtures at 1255-1465 K evidence was obtained for the existence of more than 60 ions by Gilles and co-worker~,~~ who identified many previously unknown ternary species of high molecular weight such as V2W201,+ and V3W2OI3+ some of which disappeared however as effusion progressed and the composition of the sample approached the V02/W02 + WO solid-solution region. The system was unfortunately too complex to derive thermodynamic results. By contrast the vapour species over solid and liquid WOCl is regarded as WOCl by Enghag and Staffan~son,~~ who determined the vapour pressure by a trans- piration method and also reported heats of fusion and sublimation of 10.13 and 72.22 kJ mol- ’,respectively at the melting point (478 K) and of vaporization 62.09 kJ mol-’ at 501 K.‘The Characterization of High Temperature Vapours’ ed. J. L. Margrave Wiley New York 1967. * ‘Vibrational Spectroscopy ofTrapped Species’ ed. H. E. Hallam Wiley London 1973. ’’ S. L. Bennett S. S. Lin and P. W. Gilles J. Phys. Chem. 1974 78 266. 53 P. Enghag and L. Staffansson Acru Chem. Scand. 1972 26 1067. 128 G. V.Jagannathan,G. R. Woolley and P. A. H. Wyatt Other examples of recently identified species are SiON detected by M~enow~~ (who has also investigated Ge,N and GeSiN) and Hf" which was identified above 2800 K by Kohl and st earn^,^^" who report AH? = (60.5 & 30) kJ mo1-l for the reaction HfN = Hf(g) + $N,(g) (5) together with free-energy values at 2885 and 2969K and deduce D(Hf-N) = (531 k 30) kJ mol-'.Continuing their studies of the thermodynamics of aluminium-containing molecules and of the vaporization of metal carbides the same authors55b report dissociation energies of AIC, AI,C, and AIAuC obtained with the use of a tantalum effusion cell. Two papers report the presence of carbon species in the vapour when certain substances are heated in graphite Knudsen cells. Thus Hilden brand5 found gaseous SCF in addition to SF and SF on investigating the effect at 1500 K on a graphite cell of SF, which he was led to examine because of its possible use as an electron scavenger in plasmas and also as a source of fluorine atoms for use in lasers.Standard enthalpies of formation of all three gaseous species are given along with S-F bond dissociation energies. Guido and Gigli5'"qb have similarly identified the species CeSiC effusing from a graphite-lined cell contain- ing CeSi,. The same authors describe in the more recent paper cited the use of a double-oven technique for the study of gaseous GaCN in the range 1398- 1783K and give tables of -(GF -HF)/Tand enthalpies. The sublimation of graphite itself has been further investigated by Zavitsanos and CarlsonS8 using a technique involving r.f. heating of the Knudsen cell which they show to be convenient and compatible with high-temperature time-of-flight mass spectrometry. With 450 kHz heating at 25 kW temperatures in excess of 2700 K are possible and all the vapour species C ,C, C3 ,and C were detected in the range 232G3000 K.The partial pressures of the C and C species over graphite varied in this temperature range according to the equations log, [P(C,)/N m-'1 = 14.977 -44 230 K/T (6) log, [P(C,)/N m-'1 = 14.950 -40 670 K/T (7) and the entropy change for vaporization to C is quoted as 190.6 J K-mol-at 2740 K. The temperature range has been extended still further to 4000 K and above by Meyer et ~l.,,~ who have investigated reactions with H, 0, and CH of carbon species (C,)from the laser-induced evaporation of graphite and tantalum carbide. Among several recent papers by Gingerich and co-~orkers~~ there is a study of the reactions between carbon and phosphorus in a graphite-lined Ta cell and 54 D.W. Muenow J. Phys. Chem. 1973 77 970; J. Chem. Phys. 1974,60 3382. 55 (a) F. J. Kohl and C. A. Stearns J. Phys. Chem. 1974 78 273; (b)ihid. 1973 77 136. 56 H. D. Hildenbrand J. Phys. Chem. 1973 77 897. 57 (a) M. Guido and G.Gigli J. Chem. Phys. 1973 59 3437; (b) ibid. 1974 60 721. '* P. D. Zavitsanos and G. A. Carlson J. Chem. Phys. 1973,59 2966. 59 J. Kordis and K. A. Gingerich J. Chem. Phys. 1973 58 5058; ibid. 1973 58 5141; K. A. Gingerich and G. D. Blue ihid. 1973,59 185; D. L. Cocke and K. A. Gingerich, ibid.,1974 60 1958 J. Kordis and K. A. Gingerich J. Phvs. Chem. 1973 77 700; K. A. Gingerich D. L. Cocke and J. Kordis ibid. 1974 78 603. The High-temperature Thermodynamics of Inorganic Substances 129 there are others of equilibria involving gaseous Sb, Sb, Sb4 SbP SbP, and P,; of AIAu; of TiRh Rh, and Ti,Rh; of Eu and EuAg; and of ASPand BiP.Free-energy enthalpy and bond-energy values are given for many of the com- pounds and in the case of the europium compounds the authors test the Pauling polar compound model (in which respect see also the recent work of Neubert and Zmbov6' on CuLi AgLi and AuLi). They also give methods of estimating the heats of formation of as yet unknown diatomic lanthanides. A different europium compound has been studied by Hariharan and Eick,61 who find the sublimation vapour pressure of Eu"Se over the range 1808-2131 K to be log, (PIN m-2) = (8.53 ? 0.096) -(2.26 k 0.02) x lo4 K/T (8) using W and Mo Knudsen cells and time-of-flight mass spectrometry.The disso- ciation energies of the gaseous oxides of another rare-earth metal CeO and Ce,O, are reported by Piacente and co-workers,62 who also measured the vapour pressure of rubidium in the range 402-551 K and the dissociation energy of the Rb molecule. Ackermann and Ra~h,~~ who in their later papers report several free-energy and enthalpy results for the oxides Y203 YO ZrO and HfO have determined the vapour pressures over the pure solid or liquid metals Th Hf and Zr which fit the following equations in the ranges stated log, [P(Th,l)/N m-2] = (11.032 k 0.098) -(29 769 & 219) K/T (9) at 2020-2500 K ; log, [P(Hf,l)/Nm-2] = (11.312 & 0.085) -(30446 k 240)K/T (10) at T > 2464K; log, [P(Hf,s)/N m-2] = (1 1.862 5 0.072) -(31 801 f.153) K/T (1 1) at 194&2464 K ; log,,[P(Zr,l)/Nm-2] = (11.548 k 0.081) -(29944 i-240)K/T (12) at 2 134-2550 K. The standard heats of sublimation at 298 K are rather similar Th (597.5 & 4.6) Hf (620.9 f 5.0),and Zr (560.0 5.0)kJ mol-'. The gaseous oxides Tho and Tho have been investigated recently in the range 17&1900 K by Hildenbrand and M~rad.~~ Among the Group V elements elementary arsenic has been studied in the vapour phase over solid MoAs, Mo,As3 GaAs and InAs by Murray Pupp and P~ttie.~' Excellent agreement between second- and third-law estimates is reported and the equilibrium constant for the reaction As4(g) 2As,(g) is derived with values varying from 4 x atm at 1048 K to 1.1 x lo-' atm at 807 K. Two simple oxide species of phosphorus PO and PO, have had their atomization energies determined as (593.0 k 8)kJmol-' and (1086.2 f 11) " A.Neubert and K. F. Zmbov J.C.S. Faraday I 1974 70 2219. 61 A. V. Hariharan and H. A. Eick J. Chem. Thermodynamics 1974 6 373. " V. Piacente G. Bardi L. Malaspina and A. Desideri J. Chem. Phys. 1973 59 31; V. Piacente G. Bardi and L. Malaspina J. Chem. Thermodynamics 1973 5 219. h3 R. J. Ackermann and E. G. Rauh J. Chem. Thermodynamics 1972 4 521; ibid. 1973 5 331 ;J. Chem. Phys. 1974 60 2266. h4 D. L. Hildenbrand and E. Murad J. Chem. Phys. 1974 61 1232. 65 J. J. Murray C. Pupp and R. F. Pottie J. Chem. Phys. 1973 58 2569; J. Chem. Thermodynamics 1974 6 123. 1 30 G. V. Jagannathan G. R. Woolley and P. A. H. Wyatt kJ mol- ',respectively and the equilibrium constants have been determined in the range 1200-2500 K for some of their reactions with Y,Gd and Sn all in the gas phase by Drowart et Uy and Drowart66b find dissociation energies free-energy functions and equilibrium constants at 1200-1700K for the reactions of compounds of A1 and Cu with the Group V1 elements S Se and Te.Rosenqvist and Tunge~vik~~ 2ZnS(s) = 2Zn(g) + S,(g) (13) ZnS(s) + Si(s) = Zn(g) + SiS(g) (14) have examined the equilibria (13)and (14),Farber and Srivastava68 the vaporiza- tion of VN and V and very recently Sigai and Wiedemeier69 the activities of CdSe and MnSe in their solid solutions. Gas-phase Negative Ions in Mass Spectrometry.-Negative ions attract attention both when they can be found as equilibrium vapour species at the very high temperatures (above 2000 K) now accessible to investigation and when they can be used to determine electron affinities.In such investigations Srivastava Uy and Farber7' employ a dual vacuum-chamber mass spectrometer-furnace assembly and enhance the formation of negative oxide ions by adding preheated KCl from a second boiler to take advantage of the excellent electron-donor properties of the alkali metal. Equilibrhm constants are then determined for such reactions as (15) and (16) at 1623-2100K whence electron affinities are BO(g) + CI-(g) = BO-(g) + Cl(g) (15) BO,(g) + c]-(g) = BO;(g) + CNg) (16) derived as (300.8 & 8.4)kJ mol-' for BO and (344.3 & 12.55)kJ mol-' for BO,. A similar investigation with the corresponding A1 compounds in the somewhat higher temperature range 208-2222 K leads to electron affinities of (354.8 & 12.55)kJ mol-' for A10 and (396.2 & 12.55)kJ mol-' for AlO (greater than that of C1) and has already been mentioned in connection with the discrepancy between the mass spectrometric and flame spectroscopic results for the AlO(g) heat of formation and bond energy.47 Margrave and his co-workers7 have recently measured the heat of formation of GeF,(g) and its electron affinity from the appearance potential of the negative ion in the usual way.They emphasize the importance of determining the kinetic energies of the fragments from the electron impact since allowance for this excess energy makes an appreciable difference to the estimated heats of formation of 66 (a)J.Drowart C. E. Myers R. Szwarc A. V. Auwera-Mahieu and 0.M. Uy J.C.S. Faraday U,1972 68 1749; (b) 0. M. Uy and J. Drowart Trans. Faraday Soc. 1971 67 1293. 67 T. Rosenqvist and K. Tungesvik Trans. Faraday SOC.,1971 67 2945. 68 M. Farber and R. D. Srivastava J.C.S. Faraday I 1973 69 390. 69 A. G. Sigai and H. Wiedemeier J. Chem. Thermodynamics 1974 6 983. 70 R. D. Srivastava 0. M. Uy and M. Farber Trans. Faraday SOC.,1971 67 2941. 71 J. L. Wang J. L. Margrave and J. L. Franklin J. Chem. Phys. 1974,60 2158. The High-temperature Thermodynamics of Inorganic Substances 131 GeF, GeF, and GeF,-. The present values of the bond-dissociation energies of the Group IV fluorides are summarized in a table.71 Negative ions are also being considered as intermediates in the pyrolytic decomposition of inorganic substances.From e.s.r. evidence Harrison and Ng7 deduce that NO3,- occurs as an intermediate in the decomposition of strontium and barium nitrates while Cordes and Smith73 find evidence for ClO,-when LiC10 decomposes to LiCl and 0 (with some C10 also formed) and compare the behaviour of LiClO with that of other alkali-metal perchlorates. Tang and Fenn7 sublimed NH,ClO and examined the vapour by time-of-flight mass spectrometry. This substance is of some importance since it is used as the oxidizer in most solid-fuel rockets and contributes about half the total weight of most ballistic missiles. Tang and Fenn do not consider negative ions at this stage but they do report that quite different results were obtained depending upon the form of the solid.Whereas a single crystal loses NH and HClO on heating a vapour of lower molecular weight is obtained from a compressed powder. The authors suggest that sublimation processes may be classified as associative disso- ciative or destructive and regard the behaviour of the compressed solid as indicative of decomposition in the vapour after initial dissociation sublimation. If this dependence of vapour constitution upon the state of aggregation of the solid proves at all common it points to a variable that will have to be taken into account in projected work and may possibly be a factor in explaining some of the dis- crepancies which arise from time to time between the results of different groups of investigators.Matrix Isolation.-While the use of matrix isolation as a technique for the trapping identification and estimation of concentration of vapour species is now well e~tablished,~'.~ there have been few recent studies specifically directed 1,75 towards this application most of the activity having been channelled into i.r. and other purely spectroscopic investigations of the species conveniently isolated in that and of the reactions between such species in the matrix itself. (For recent examples see the work of Spiker and Andrews on reactions of alkali metals with N,O ;77a with NO ;77b of Rb and Cs with 0 ;77c of NiF and NiCl with CO N, and 02;77d and of CO with CaF, CrF, MnF, and ZnFz;77d and the work of Bos Ogden and on Ge + 0 vapour reactions).From that point of view vapour-pressure cells are simply sources of supply of the required molecular beams but the results of such work will have a direct 72 L. G. Harrison and H. N. Ng J.C.S. Furuduy I 1973,69 1432. 73 H. F. Cordes and S. R. Smith J. Phys. Chem. 1974 78 773 776. 74 S. P. Tang and J. B. Fenn J. Phys. Chem. 1973 77 940. 75 A. J. Barnes and H. E. Hallam Quart. Rev. 1969 23 392; H. E. Hallam Ann. Reports 1970 67 (A) 117. 76 S. D. Gabelnick G. T. Reedy and M. G. Chasanov J. Chem. Phys. 1974 60,1167. 77 (a)R. C. Spiker jun. and L. Andrews J. Chem. Phys. 1973 58 702 713; (6) L. Andrews and D. E. Tevault J. Phys. Chem. 1973,77,1640,1646 (c)R. R. Smardzewski and L. Andrews ibid.p. 801 ;L. Andrews J. T. Hwang and C. Trindle ibid. p. 1065; (6)D. A. Van Leirsburg and C. W. DeKock ibid. 1974,78,134; (e)A. Bos J. S. Ogden and L. Orgee ibid. p. 1763. 132 G. V.Jagannathan G. R. Woolley,and P. A. H. Wyatt bearing on the high-temperature field both by indicating which species to look for in experimental work (and supplying a technique for their identification and measurement) and by providing the detailed molecular information for a reliable statistical mechanical calculation of their thermodynamic functions. For example in the absence of anharmonicity constant data a simple harmonic model must be used and this could introduce significant errors at high tempera- tures. Margrave and co-workers” review the situation and list geometries and frequencies for a wide range of oxides and halides.Her~berg’~ and Gayd~n~~ give spectroscopic data on many species present in high-temperature environ- ments. A new evaluation of the molecular constants of 16 bent symmetric SY,-type molecules is given by Thirugnanasambandam and Mohan.” Since many of the species trapped in matrices often contain only 2 or 3 atoms they are attracting the interest of the theoretical chemists. For example O’Neil et dBO report an ab initio calculation on the LiO radical giving a bond angle of 44.5” in the ground state. Theoretical treatments of small molecules are discussed by Thomson elsewhere in this volume. Many references to the spectra of matrix-trapped species could be cited but only one or two of the recent technical developments will be mentioned here.Schoch and Kays1 recommend a triode sputtering source for substances which are difficult to vaporize and have used it to prepare samples of Ag Ta W and Mo trapped in Ar and Xe for spectroscopy; and PerutL and TurnerB2 compare the properties of matrices prepared by ‘slow spray on’ (SSO) and pulsed matrix isolation (PMI) methods. Most of the isolated species up to the present have been examined by i.r. spectroscopy. As a recent example of the combination of i.r. with Mossbauer spectroscopy we cite the study of SnO Sn2P2 Sn Sn, and higher polymers of both in N matrices by Bos et who give references to earlier work in the past three or four years. They point out that the Mossbauer technique is better than other forms of spectroscopy for the study of low-tempera- ture diffusion and reactivity because the area of the absorption peaks is compara- tively independent of the chemical environment of the resonance-active nuclei.Photoelectron Spectroscopy.Xonventiona1photoelectron spectrometers are too insensitive to deal with the low concentrations of vapour species commonly encountered over inorganic substances at high temperatures but Berkowitz has increased the detection efficiency by increasing the acceptance angle with a cylindrical mirror arrangement and can thereby operate satisfactorily with an effective sample gas pressure in the ionization region of the order of lo- N mP2. In this way photoelectron spectra have been mapped out and interesting in- ferences about bonding have been drawn for the high-temperature vapour species 78 G.Herzberg ‘The Spectra and Structures of Simple Free Radicals’ Cornell Univ. Press Ithica New York 1971. 79 P. Thirugnanasambandam and S.Mohan J. Chem. Phys. 1974,61,470. 80 S. V. O’Neil H. F. Schaefer tert. and C. F. Bender J. Chem. Phys. 1973 59 3608. 81 F. Schoch and E. Kay J. Chem. Phys. 1973,59 718. 82 R. N. Perutz and J. J. Turner J.C.S. Faraday II 1973 69 452. 83 A. Bos A. T. Howe B. W. Dale and L. W. Becker J.C.S. Faraday II 1974 70 440; A. Bos and A. T. Howe ibid. p. 451. The High-temperature Thermodynamics of Inorganic Substances 133 TlC1 TlBr and T118" (all of which were chosen because they were previously known to give rise to simple monatomic vapour species); Group 111 monohalides InCl InBr and In1 ;846 monomer and dimer photoelectron spectra of TlF ;84c the halides of CS;~~ the trihalides of In and Ga;84e and the halides (except F) of Zn Cd and Hg.8" Static Dynamic and Simple Effusion Methods.-Most of the classical vapour- pressure methods have been adapted at some time or other for high-temperature work.Elliott et a/.*' have described an isopiestic balance for measurements between 939 and 1037K and used it to determine cadmium vapour pressures over Cd-Au alloys. More recently transpiration methods have been used by De Maria and Piacente86 in determining the vapour pressure of Ca from 1126 to 1300 K for which equation (17) is valid and Sr from 1086 to 1310 K for which log, (PIN m-') = (9.94 k 0.13) -(8SSO +_ 158) K/T (17) log, (PIN m-') = (9.76 k 0.14) -(7720 k 161)K/T (18) equation (18) applies and by Battat et aLg7 on systems involving Ga As HC1 and H,O after first testing their novel apparatus with water at the lower tempera- tures and lead at 12S1400K.Static gauges have been used by Greenberg et to study the sublimation of Zn,P,(s) at 890-1 130 K and by DeLong and Ro~enberger~~ for reaction (19) at 670-1 170 K. Topor" reports the vapour pressures and enthalpies of vaporization of the liquid chlorides bromides and iodides of Na K Rb and Cs measured by the quasistatic Rodebush-Dixon method and derives equilibrium constants for the dimerization reactions at 1300K and compares them with theoretical calculations. Another study of several alkali-metal halides by Ewing and Stern,g' contains a valuable theoretical and experimental investigation of the change-over from molecular to hydrodynamic flow from a Knudsen cell as the pressure becomes higher.Observed rates of vapour loss are shown to be greater in the hydro- dynamic and transitional regions than those predicted by the Hertz-Knudsen theory for molecular flow ;but vapour pressures are nevertheless still found to be 84 (a) J. Berkowitz J. Chem. Phys. 1972 56 2766; (b)J. Berkowitz and J. L. Dehmer. ibid. 1972 57 3194; (c) J. J. Dehmer J. Berkowitz and L. C. Cusachs ibid. 1973 58 5681; (d)J. Berkowitz J. L. Dehmer and T. E. H. Walker ibid. 1973 59 3645; (e) J. L. Dehmer J. Berkowitz L. C. Cusachs and H. S. Aldrich ibid.1974 61 594; (f) J. Berkowitz ibid. p. 407. 85 0. R. B. Elliott C. C. Herrick J. F. Lemons and P. C. Nordine High Temp. Sci. 1969 1 58. 86 G. De Maria and V. Piacente J. Chem. Thermodynamics 1974 6 1. 87 D. Battat M. M. Faktor I. Garrett and R. H. Moss J.C.S. Furaday I 1974 70 2267 2280 2293 2302. 88 J. H. Greenberg V. B. Lazarev S. E. Kozlov and V. J. Shevchenko J. Chem. Thermo- dynamics 1974 6 1005. 89 M. C. DeLong and F. Rosenberger J. Chem. Thermodynamics 1974 6 877. L. Topor J. Chem. Thermodynamics 1972 4 739. C. T. Ewing and K. H. Stern J. Phys. Chem. 1974 78 1998. 134 G. V.Jagannathan,G. R. Woolley and P.A.H. Wyatt calculable from flow rates in these higher pressure regions and the results agree well with those derived from standard thermodynamic procedures.The ratio of actual flow/(hypothetical) Knudsen flow in the transition region depends only on the mean free path and is independent of the diameter of the orifice. A detailed comparison is given of the new data with those recorded in the JANAF tables. The gap of several hundred degrees in the experimental data on which the latter were based was one reason for undertaking this investigation. If effusion measurements alone are being relied upon for vapour-pressure values it is important to know how dissociation in the vapour affects the results. Knox and Wyatt9 reformulate this problem taking a proper account of the steady-state condition within the Knudsen cell. Ha~chke,~ however finds that equilibrium pressures of EuBr are not attained in Knudsen cells at 502423 K and resorts instead to spectrophotometry to determine the vapour concentration.Several systems have been examined by the classical Knudsen technique. Nagai et find that equation (20) applies for the reaction (21) at 1823-1983 K AGF/kJ mol-= (761.70 & 10.46)-0.2439 T/K (20) SiO,(s) = SiO(g) + +o,(g) making allowance for the dissociation of O, and obtain the enthalpy of forma-tion of SiO(g) at 298 K as (-116.7 5 14.6) kJ mol-' and a vaporization coeffi- cient of about 0.02 for SiO,(s) in the experimental temperature range. The related Si(s) + SiO,(s) = 2SiO(g) (22) equilibrium (22) has according to Kubaschewski and Chart,95 an equilibrium SiO vapour pressure given by equation (23). log, (PINm-2) = 13.613 -1.785 x lo4 K/T (23) For the oxides As,O (arsenolite) Sb,O (valentinite) and SeO, Behrens and co-~orkers~~ find the vapour pressures to satisfy equation (24) at 367429 K log, [P(AS406)/N m-,] = (14.91 & 0.32) -(6067 & 125)K/T (24) equation (25) at 627-732 K (in these cases the vapour species being the doubled log, [P(Sb,06)/N mP2]-(14.39 & 0.30) -(10066 & 203) K/T (25) formula as shown) and equation (26) at 374-427 K.In all cases useful ranges log, [P(SeO,,s)/N m-,] = (14.547 f 0.450) -(5785 & 180)K/T (26) of thermodynamic data are given. Biefeld and Eick9' also used the Knudsen method to investigate the sublimation of ZnF from 901 to 1125 K but collected 92 J. H. Knox and P. A. H. Wyatt J.C.S. Faraday I 1973 69 1961.93 J. M. Haschke J. Chem. Thermodynamics 1973 5 283. 94 S. Nagai K. Niwa M. Shimmei and T. Yokokawa J.C.S. Faraday I 1973,69 1628. 9s 0. Kubaschewski and T. G. Chart J. Chem. Thermodynamics 1974 6 467. 96 R. G. B. Behrens and G. M. Rosenblatt J. Chem. Thermodynamics 1972 4 175; ibid. 1973 5 173; R. G. Behrens R. S. Lemons and G. M. Rosenblatt ibid. 1974 6 457. 97 R. M. Biefeld and H. A. Eick J. Chem. Thermodynamics 1973,5 353. The High-temperature Thermodynamics of Inorganic Substances the sublimate on a target. They deduced equation (27) along with other derived thermodynamic information. log, [P(ZnF,)/Nm-’] = (13.443k 0.071) -(13 185 f 72)K/T (27) Metal Su1phates.-Richardson reviews the thermodynamic aspects of many of the pure and mixed solid and liquid inorganic salts of industrial importance.Sulphates are selected here for special mention partly because they are not treated extensively in Richardson’s book but mainly because their investigation illus- trates some of the problems encountered in interpreting vapour-pressure measurements when several possibilities seem open for the choice of vapour species. Intuitively most chemists would probably suppose that a solid or liquid sulphate on heating simply dissociates to the oxide plus SO, which itself disso- ciates further into SO and 0 to an extent that is dependent upon the tempera- ture. The extent of dissociation of SO3 might also depend upon the time of residence of the vapour in the cell and the accessibility of catalytic surfaces in effusion or transpiration techniques and detailed kinetic information is obviously necessary to settle that point.To complete the story the fate of the metal oxide has also to be considered. At moderate temperatures at least the oxides of most transition and alkaline-earth metals are expected to form a new solid phase while those of the alkali metals might be expected to vaporize and then perhaps to dissociate further into the free metals and oxygen. Not all recent investigators would find this description compatible with their experimental findings though it does seem to accord well with work on Fe,(SO,) CuSO, Al,(SO,), CaSO, and MgSO,. Halstead and Laxtong8 have used both static and dynamic methods to obtain vapour pressures in the Fe,(SO,),-Fe,O,-SO system and have examined the solid residues from their cells by X-ray diffraction and X-ray fluorescence spectroscopy always finding only Fe,(SO,) and a-Fe,O,.Traces of y-Fe,O (probably present as a thin film) were nevertheless detectable in samples in which only a small degree ( <2 76) of sulphate decomposition had occurred. Further pressures given by such relatively oxide-free ( < 2 %) Fe,(SO,) were similar to those obtained using y-Fe,O as a starting material while pressures given by more decomposed (>4”,)sulphate samples were similar to those given by partially sulphated a-Fe203. On this basis Halstead and Laxton explain discrepancies in the literature and summarize their vapour-pressure values in the equations (28) for log, [P(SO,)/N m-’1 = (14.18 k 1.39) -(0.95 k 0.11) x lo4 K/T (28) the a-Fe20,-Fe2(S0,) system and (29) for the y-Fe,O,- Fe,(SO,) system.log, [P(SO,)/N m-’] = (13.17 k 1.10)-(0.91 k 0.09) x lo4 K/T (29) Their dynamic technique resembles that of Dewing and Richardson :” pre-heated and equilibrated mixtures of SO, SO, and O, diluted with N, were 98 W. D. Halstead and J. W. Laxton J.C.S. Faraday I 1974 70 807. 99 E. W. Dewing and F. D. Richardson Trans.Faraday SOC.,1959,55 61 1. G. V. Jagannuthan,G. R. Woolley and P. A. H. Wyatt passed over samples in the cell and the temperature at which no weight change occurred was recorded. In their study of CaSO and MgSO, Dewing and Richardson detected the onset of decomposition by a sharp discontinuity in differential thermocouple readings during heating.Supporting the sample in a spiral of Pt-13 "/,Rh thermocouple wire presumably helped to ensure that SO and SO were at equilibrium. Earlier work on the alkaline-earth sulphates illustrates the care with which static and dynamic determinations have to be compared if inconsistencies are to be avoided. In particular Dewing and Richardson mention objections to the interpretation of Knopf and Staude,"' whose results were nevertheless taken into account in the MgSO entry in the JANAF 1966 supplement (PB 168 37&1). According to Collins et al.,"' both CuSO and A12(SO,) decompose initially to give the metal oxides and SO, though they obtained a different pattern of results for alunite [presumably KAI,(SO,),(OH),] and suggest that the sulphate ion dissociates by at least two different mechanisms.On the other hand Papazian et ~1.'~~" believe that the primary gaseous products in the decomposition of AI,(SO,) and Hf(SO,) are SO and O, and that SO and SO are subsequently formed from these. Their interpretation has since been criticized by Johnson and Gallagher and defended by the authors themselves.lo2' This unexpected view stems mainly from the fact that SO,' peaks have been hard to detect in the mass spectrometer while SO' and SO2' show up quite clearly. The question then arises as to whether or not the observed SO2/SOratios are compatible with breakdown of SO3 and SO in the mass spectrometer. The alkali-metal sulphates are known to vaporize congruently i.e.the vapour has the composition M2S0, but a new feature that now emerges is that K,SO, Rb2S04 and Cs2S0 appear to be present largely as the sulphate molecules in the vapour phase." The results for Li,SO and Na,SO indicate more extensive dissociation however. Cubicciotti and Fene~hea"~" found that their Na,SO vapour-pressure results determined by a transpiration technique using N as carrier gas were greater than those calculated from the literature for the decom- position equilibrium (30) and therefore made further measurements in the Na,SO,(l) = 2Na(g) + SO,(g) + 0 (30) presence of SO2 and 0,to suppress the dissociation and allow the measurement of the pressure of Na,SO,(g) alone. In this way they obtained the equation (31) log, (PINm-,)= (10.964 f0.15) -(15 540 k 380) K/T (31) for the vapour species Na,SO over the liquid at 140@-1625 K.Extrapolation of their overall pressures down to lower temperatures produces values an order of magnitude lower than those recorded by an effusion technique by Powell and loo H. K. Knopf and H. Staude 2.phys. Chem. (Leipzig) 1955 204 265. lol L. W. Collins E. K. Gibson and W. W. Wendlandt Thermochim. Acta 1974 9 15. lo* (a) H. A. Papazian P. J. Pizzolato and R. R. Orrell Thermochim. Acra 1972 4 97; (6) J. W. Johnson jun. and P. K. Gallagher ibid. p. 105; H. A. Papazian P. J. Pizzolato and R. R. Orrell ibid. p. 109. lo3 (a) D. Cubicciotti and F. J. Feneshea High Temp. Sci. 1972 4 32; (b) D. G. Powell and P. A. H. Wyatt J. Chem. SOC.(A) 1971 3614.The High-temperature Thermodynamics of Inorganic Substances Wyatt,"3b whose results were however complicated by the appearance of changes of slope in the In P us. l/Tplots for Na,SO and Li,SO which have not yet been satisfactorily explained. The presence or absence of the oxides Na,O and Li,O in the vapour also raises once again the question of the cracking pat- terns to be expected in the mass spectrometer.'04 Sulphates are being studied from a different angle by Rosen and Wittung,'" who equilibrate the solids with known mixtures of gaseous S and 0 to deter- SPbO(s) + $S,(g) + $02(g)= 4PbO,PbSO,(s) (32) log, (Klatm-') = 43 260 K/T -18.51 (33) mine thermodynamic results for the reaction (32) for which they find equation (33) is valid at 973-1073 K.5 Free-energy Measurements :Electromotive Force Mass-spectrometric and matrix-isolation techniques effective as they are at providing detailed information about vapour species are nevertheless expensive. It is therefore encouraging that similar information can sometimes be arrived at by ingenious variants on conventional physicochemical devices. Ratchford and Rickert have developed an electrochemical Knudsen ce111°6 in which the rate of effusion of a species is governed in the steady state by a small electrolysing current and the slope of a graph of the logarithm of the latter against the e.m.f. depends directly upon the number of atoms (x) in such molecular species as S and Sex. Figure 1 shows the form of cell used for the study of sulphur vapour species between 500 and 800K at which temperatures the decomposition of Ag,S is negligible.Sulphur molecules then only effuse as a result of the passage of an electric current which is the only measure of the effusion rate here; i.e.no weight- loss measurements are made. An applied positive potential at the Pt electrode next to the Ag,S pellet releases sulphur at this electrode and thence into the vapour and forces silver ions into the solid electrolyte AgI from which silver is then deposited onto the negative Pt electrode. When the current has settled down to its steady-state value the Knudsen cell maintains a definite sulphur vapour pressure over the Ag,S the fixed activity of which ensures that the prevailing e.m.f. E of the solid-state cell measuring the silver activity relative to pure silver also measures the square rooi of the S activity or the 1/2x power of the vapour pressure of the species S,.It then follows that the vapour pressure of S is related to its value po(S,) over pure liquid sulphur by the expression (34) E" p(S,) = po(S,) exp [2x(E -Eo)F/RT] (34) lo4 P. J. Ficalora 0. M. Uy D. W. Muenow and J. L. Margrave J. Amer. Ceram. SOC. 1968 51 574; T. Kosugi Kogyo Kagaku Zasshi 1970 73 1087. lo5 E. Rosen and L. Wittung Acra Chem. Scand. 1972 26 2427. lo6 H. Rickert in 'Condensation and Evaporation of Solids' ed. E. Rutner P. Goldfinger and J. P. Hirth; Gordon and Breach London 1964. G. V.Jagannathan,G. R. Woolley and P. A. H. Wyatt Thermocouple Figure 1 The electrochemical Knudsen cell (Reproducedby permission from 'Condensation and Evaporation of Solids' ed.E. Rutner P. Goldfinger and J. P. Hirth Gordon and Breach London 1964 p. 209) being the e.m.f. of the cell when Ag,S is in equilibrium with liquid sulphur. It is the appearance of x in the exponent that permits its determination since p(S,) is directly proportional to the effusion rate which is in turn governed here by the electric current (with x only appearing as a multiplier). Hence the logarithm of the current is related to E through x provided that one of the possible S species predominates in the vapour over a certain temperature and pressure range. Rickert finds that this proves to be the case for both S and Se the diatomic forms show up clearly at the lower e.m.f.values for 600-800K and there are good indications of higher forms (particularly Se,) at lower temperatures. The derived sulphur vapour pressures are in quantitative agreement with the values obtained by other methods. (For recent information on sulphur and selenium see H. Rau et al.''') This subtle technique obviously has some rather stringent requirements in the way of solid electrolytes and workable cells but could perhaps inspire further exploration along similar lines. Since later developments"' incorporate mass lo' H. Rau T. R. N. Kutty and J. R. F. Guedes de Carvalho J. Chem. Thermodynamics 1973 5 291 833; H Rau ibid. 1974 6 525. lo* D. Detry J. Drowart P. Goldfinger H. Keller and H. Rickert Z. phys. Chern. (Frankfurt) 1967 55 314; ibid.1971 75 273; H. Rickert and K. H. Tostmann Werkstofe und Korrosion 1970 965. The High-temperature Thermodynamics of Inorganic Substances spectrometry it is probably too optimistic to regard the electrochemical Knudsen cell asa serious competitor though it clearly gives very useful supplementary information in favourable cases. Galvanic cells continue to be used in more conventional ways at high tempera- tures particularly for the study of alloys,2 in which application molten halides have been popular electrolytes though they have other uses.lo9 Thus Nguyen- Duy and Rigaud"' used the LiCl-KCl eutectic in cells such as Zn(l)lZn2+ in LiCl + KCl (1 eutectic)lZn+ Ag + Sn (1) to examine the effects of small additions of Ag (or Cu or Au) on the thermo- dynamic properties of dilute solutions of Zn in molten Sn in the temperature range 723-923 K.Similar work by Neethling and co-workers on the Na-Cd-In and Na-Pb-In systems' '' employed the slightly more complicated cell NalPyrex glasslNaC1 + ZnC1 ,(1 eutectic)lPyrex glasslNa alloy and required a supplementary determination of the ternary phase diagram as may frequently become necessary for uncommon ternary systems. Aronson and Lemont'12 have dispensed with the eutectic phase altogether leaving only the glass aselectrolyte K(l)/K-glasslK+ T1 (1) The K-TI alloy composition was varied over the complete range and values of partial molar enthalpy and entropy and also of the integral quantities are given. Curious maxima and minima (like those in the Na system) are believed to indi- cate a strong chemical interaction between the two metals.Solid electrolytes 'v2 continue to find applications. Zirconia stabilized with calcium oxide is used in the cell PtlCo xC00 + (1 -x)MgOIZrO + Ca01Co0 ColPt with which Rigaud et ~1."~have determined the activity of COO in COO-MgO mixtures. The derived COO and MgO activity coefficients show significant positive deviations from ideality. Rezukhina and Kravchenko' used thoria in a similar way for a study of Ta-Co mixtures and Klinedinst and Stevenson' ' determined the free energy of formation of /3-Ga20 with a cell involving thoria doped with yttria as the solid electrolyte and a flowing CO + C02 gas mixture as one electrode. lo9 G. Landresse and G.Duyckaerts Inorg. Nuclear Chem. Letters 1974 10 675. lo P. Nguyen-Duy and M. Rigaud J. Chem. Thermodynamics 1974,6 727,999. A. J. Neethling J. Chem. Thermodynamics 1974 6 707 1083; H. E. Bartlett A. J. Neethling and P. Crowther ibid. 1970. 2 523. l2 S. Aronson and S. Lemont J. Chem. Thermodynamics 1973,5 155. 'l ' M. Rigaud G. Giovannetti and M. Hone J. Chem. Thermodynamics 1974,6,993. (a)T. N. Rezukhina and L. I. Kravchenko J. Chem. Thermodynamics 1972 4 655; (6) T. N. Rezukhina T. F. Sisoeva L. I. Holokhonova and E. G. Ippolitov ibid. 1974,6 883. 115 K. A. Klinedinst and D. A. Stevenson J. Chem. Thermodynamics 1972 4 565. G. V. Jagannathan,G. R. Woolley and P. A. H. Wyatt As a recent example of the use of CaF as a solid electrolyte we cite the paper by Rezukhina et al.' '4b on nine cells of the type MI M'F,JCaF21M" MIIF,, where the metal MI is baser than MI' with respect to fluorine and M'F and MIIF,, are the fluorides in equilibrium with M' or with MI' respectively.The cell with M'F = MgF and M"F = AlF was used to check the experimental technique and that with M'F = CaF and M"F = MgF to confirm the absence of electronic conductivity in CaF at very small fluorine activities. The investigation covers the temperature range 710-1 120 K and provides values of AH (298.15 K)/kJ mo1-' of -1732 (LaF,) -1739 (YF,) -1712 (PrF,) -1649 (ScF,) and -859.4 (MnF,) and of S* (298.15 K)/J K-' mol-' of 99.2 79.9 117.2 92.0 and 87.4 respectively. These results are compared with calori- metric values where they are available.Finally some of the cells used by Levitski and Scolis"6 employ CaF and others thoria doped with La203 or CaO as solid electrolytes for the investiga- tion of the strontium and aluminium tungstates Sr,WO, Sr,WO, SrWO, Sr,A1,0, and SrAl,O in the range 1100-1400 K. They also give references to the recent Russian literature. The recent publication of Richardson' deals with ionic melt mixtures reference to which is conveniently included here although techniques other than e.m.f. are also employed. Examples of recent high-temperature thermodynamic mixture studies are the Ce"'C1-alkali-metal chloride and La"'C1-alkali-metal chloride systems by Papatheodorou and co-workers,' '7a bivalent basic oxide-SnO systems by Lahiri,' '7b and CaF with alkali fluorides by Kleppa and Hong.' '7c Richardson' has also discussed the interaction of gases with ionic melts.Further studies published or in progress include investigations of the solubilities of He Ar N, O, CH, H, CO CO, and NH in alkali-metal nitrate mixtures by Desimoni Paniccia and Zambonin' ' and the high-temperature thermo-dynamics of solid solutions of H in bcc V Nb and Ta by Kleppa et al. '8b Such reports commonly include useful thermodynamic mixing and solution data. 'I6 V. A. Levitski and Y. Y. Scolis J. Chem. Thermodynamics 1974 6 1181. (a) G. N. Papatheodorou and 0. J. Kleppa J. Phys. Chem. 1974 78 178; G. N. Papatheodorou and T. Ostvold ibid. p. 181 ; (6) A. K. Lahiri Trans. Faraduy Soc. 1971,67 2952; (c)0.J. Kleppa and K.C. Hong J. Phys. Chem. 1974 78 1478. 'I8 (a) F. Paniccia and P. G. Zambonin J.C.S. Faraday I 1972 68 2083; E. Desimoni F. Paniccia and P. G. Zambonin ibid. 1973,69,2014; F. Paniccia and P. G. Zambonin ibid. p. 2019; (b) 0. J. Kleppa P. Dantzer and M. E. Melnichak J. Chem. Phys. 1974,61 4048.

ISSN:0308-6003    

DOI:10.1039/PR9747100119

出版商:RSC    

年代:1974

数据来源: RSC

摘要:

8 High-pressure Chemistry By 6. CLEAVER Department of Chemistry The University Southampton SO9 5NH 1 Previous Reviews and General Publications A new journal entitled High Temperatures-High Pressures began in 1969; it contains papers and review articles reporting work either at high temperatures or at high pressures (not necessarily both simultaneously) and also brief reports on conferences and announcements about future meetings. The series Aduances in High-pressure Research continues under new Editorship ;Volume 4 appeared in June 1974 (five years after Volume 3) and contains articles on the response of solids to shock waves on X-ray diffraction studies at pressures up to 300 kbar and on diamond formation at high pressures. A bibliography of high-pressure research’ has been prepared covering the literature back to 1900; the current literature is surveyed in bimonthly bulletins.Pressure-induced electronic transi- tions are discussed in a book by Drickamer.’ References to review articles on particular aspects of high-pressure chemistry will be given in the appropriate sections below. 2 Technical Advances High-pressure research has always been experimentally difficult. More rapid progress will result as technical innovations are introduced and are eventually incorporated into commercially available equipment. Some recently described advances are reviewed in this section. Several improvements to the technique of high-pressure measurement have been described and the current state of the art has been re~iewed.~ In diamond anvil cells the frequency shift of the R fluorescence of ruby may be used to indicate the pressure; small pieces of ruby are mixed with the ample.^ In X-ray diffraction work a standard substance is mixed with the sample and ’ ‘High Pressure Bibliography’ (Published by the High Pressure Data Center Brigham Young University Provo Utah 84602 U.S.A.); 1900-1968 (2 vols.) 1968-1971 (I vol.) and annual volumes thereafter.H. G. Drickamer and C. W. Franck ‘Electronic Transitions and the High-pressure Chemistry and Physics of Solids’ (in the series ‘Studies in Chemical Physics’ ed. A. D. Buckingham) Chapman and Hall London 1973; see also H. G. Drickamer Chem. in Britain 1973 9 353. C. Y. Liu K. Ishizaki J. Paawe and I. L. Spain High Temps.-High Press.1973 5 359. S.Block and G. J. Piermarini High Temps.-High Press. 1973 5 567. 141 142 B. Cleaver the pressure is deduced from the change in the lattice parameter of the standard. NaCl is the preferred standard,' but NaF or LiF may be used if the NaCl dif- fraction lines overlap with those of the sample or if the sample is appreciably harder than NaCl. If the sample and marker differ in hardness a pressure intensification effect appears to occur6 (the pressure being higher in the harder material). Later work7 showed that this is in part due to non-hydrostatic compo- nents in the stress field notably in opposed anvil apparatus coupled with the fact that diffraction patterns are then produced only by lattice planes which are parallel with the anvil axes.Novel high-pressure equipment has been described which permits work at very low temperatures' or in high magnetic fields.' N.m.r. experiments have been performed using samples in glass tubes at pressures up to 2 kbar ;the tubes had been carefully pre-treated with HF to improve their bursting strength and reliabil- ity." Vessels transparent to neutrons have been constructed.' ' A pulsed ruby laser has been used to heat to 3000 "Ca sample held in a diamond 'opposed anvil' apparatus at 260 kbar.12 A very efficient form of thermal insulation made from thin metal foil has been described; it can be used to insulate the furnace in internally heated gas-filled pressure vessels. The performance of an apparatus employing unusually large Bridgman anvils has been inve~tigated.'~ Using anvils of 78 mm diameter and pyrophyllite gaskets samples of 5 mm thickness x 10mm diameter were compressed to over 100kbar.A large hexahedral press has been built" and operated to l00kbar. The homogeneity of pressure in the sample volume (an isosceles hexahedron) was similar to that normally achieved in tetrahedral or cubic presses (and better than the Bridgman anvil) with the advantage that access to the sample is un- obstructed in a mirror plane between the two sets of three pistons. Diffraction experiments can be carried out in this plane using the Debye-Scherrer method and the Bragg-Brentano focusing arrangement can be used. The three meridian places at 120" to each other can also be used for neutron diffraction.The highest static pressures achieved to date were reported by Kawai.16 The apparatus is described as a split sphere with double-staged pistons. Unlike most multi-piston apparatus it is simple in design and relatively cheap to construct. B. Olinger and J. C. Jamieson High Temps.-High Press. 1970 2 513; D. L. Decker J. Appl. Phys. 1971 42 3239. Y.Sato S. Akimoto and K. Inone High Temps.-High Press. 1973 5 289. ' Y. Sato Y. Ida and S. Akimoto High Temps.-High Press. 1973 5 679. J. Wittig High Temps.-High Press. 1972 4 116; J. S. Schilling U. F. Klein and W. B. Holzapfel Rev. Sci. Instr. 1974 45 1353. W. B. Holzapfel and D. Severin High Temps.-High Press. 1969 1 7 13 ;G. D. Pitt and D. A. Gunn ibid. 1970 2 547 1972 4 353. lo H. Yamada Rev.Sci. Instr. 1974 45 640. 'I 0.Blaschko and G. Ernst Rev. Sci. Instr. 1974 45 526; D. B. McWhan D. Bloch and G. Parisot ibid. p. 643. Li-Chung Ming and W. A. Bassett Rev. Sci. Instr. 1974 45 1 115. l3 P. Malbrunot P. Meunier and D. Vidal High Temps.-High Press. 1969 1 93. l4 B. Okai and J. Yoshimoto High Temps.-High Press. 1973 5 675. M. Contre High Temps.-High Press. 1969 1 339. l6 N. Kawai and S. Eudo Rev. Sci. Instr. 1970 41 1178. High-pressure Chemistry Eight similar steel pistons each with a separate tip made from carbaloy pack together to form a sphere. The inner surfaces of the tips form a regular octa- hedron. The assembled pistons are surrounded by a spherical shell made from thick rubber and the entire device is suspended in oil inside a cylindrical pressure vessel of -30 cm diameter.This vessel is closed by pistons at each end and these can be driven in by a ram to raise the oil pressure to 3 kbar. Small corner pieces at the outer meeting-points of the pistons ensure that the pistons move syn- chronously as the oil pressure is raised. Pyrophyllite is used as a gasket material and conventional tubular graphite heaters can be used to raise the sample tempera- ture to 1500 "C if desired. Pressures in the range 3&500 kbar were originally claimed but in subsequent experiments" vitreous silica was compressed irre- versibly to densities comparable with those reached by Al'tshuler in shock-wave experiments. Comparison with the equation of state indicated that pressures in excess of 2 Mbar had been achieved.In a series of papers," Kumazawa has explored the general design principles of multi-anvil sliding systems (MASS). These employ the principle of massive support yet offer a relatively large volume compression; as the pressure is raised the sample volume is reduced by a progressive sliding movement of each anvil against its neighbours. In some versions a controlled outward movement of some components is permitted by placing pads of compressible material behind them. Although few of these ideas have yet been put into practice some interest- ing possibilities appear to exist. Spectroscopic Techniques-The design of pressure cells with windows for spectroscopic studies has been reviewed," and the authors list the maximum pressures attainable with common window materials (sapphire diamond ger- manium silicon Irtran).A short-path-length cell suitable for U.V. and visible spectroscopy on corrosive liquids at high temperatures (500"C 1 kbar) was described by Liidemann.20 In a Raman cell designed for use to 12kbar,2' light scattered at 90" from the incident laser beam is collected by a prism and is re- flected in a direction parallel to the original beam but offset from it laterally. This ingenious arrangement allows work down to Av = 20 cm-' while avoiding the use of cross-bores in the vessel (which would greatly reduce its strength). 3 High-pressure Chromatography High-speed Liquid Chromatography.-In recent years the technique of liquid-solid chromatography has undergone improvements and is now capable of making separations in times as short as those used in gas chromatography.This has been done by using higher mobile-phase velocities and higher column N. Kawai S. Mochizuki and H. Fujita Phys. Letters (A) 1971 34 107. M. Kumazawa High Temps.-High Press. 1971 3 243; M. Kumazawa K. Masaki H. Sawamoto and M. Kato ibid. 1972 4 293; M. Kumazawa ibid. 1973 5 599. l9 J. M. Besson J. P. Pinceaux and R. Piotrzowski High Temps.-High Press. 1974 6 101. 2o H.-D. Liidemann and W. A. J. Mahon High Temps.-High Press. 1969 1 215. P. Figuiere M. Ghelfenstein and H. Szwarc High Temps.-High Press. 1974 6 61. 144 B. Cleaver efficiencies. The old (1-2 cm diameter) columns packed with particles of 100-150pn diameter and using gravity feed have been replaced by narrow (1-3 mm) columns with smaller particles (50pm) and the liquid phase is driven through by applying a pressure at the column inlet (typically 20&-400bar).Ionic non- volatile or thermally unstable solutes (for which gas-liquid chromatography would be unsuitable) can be separated in times of the order of a few minutues. To avoid stagnation of solution trapped in pores ‘porous layer beads’ are now being used. These have a solid inert core of -40 pm diameter coated with a 1 pm layer of the active absorbent and rapidly reach equilibrium with the liquid phase. Flow rates of 1-5 cm3 min-’ are used. Column lengths are typically 1 m and both analytical and preparative-scale columns can be made. The driving pressure is supplied by a gas cylinder (with a bellows to transmit it to the liquid) or by a variable-speed pump which may incorporate a mixing device to dispense mixed solvents (whose proportions may be changed as elution proceeds).Applica- tions of the technique are being made in the fields of steroids herbicides pesticides antibiotics dyestuffs alkaloids and nucleic acid constituents. The subject has been reviewed by Kirkland.22 Supercritical-fluid Chromatography.-In high-speed liquid chromatography pressure is used simply to boost the flow rate of the eluent ;it has virtually no effect on the adsorption equilibrium. The pressure falls linearly from its highest value at the inlet to atmospheric pressure at the outlet. Supercritical-fluid chroma- tography employs similar pressures but is based on completely different prin- ciples.The eluent is a supercritical gas at a pressure of up to a few hundred bar but the pressure gradient down the column is very small; most of the pressure drop occurs at the outlet. The solubility of compounds in the eluent is strongly dependent on the pressure especially in the vicinity of the critical point. Pressure programming is therefore of value; the pressure is held constant at first and then is increased linearly to elute the less soluble components. A good example is given by Bartmann,23 who demonstrated the separation of n-alkanes from C to C, using supercritical CO at 40 “C. Other potentially useful mobile phases are C& C2H4 freons SF, and N,O (all at room temperature).A small amount of a polar substance may be added to the supercritical eluent to increase the solubility (and so reduce the retention times) of substances to be separated. Supercritical- fluid chromatography has been reviewed recently.24 Like high-speed liquid chromatography it is an attractive alternative to gas-liquid chromatography which may be used for thermolabile compounds macromolecules polymers biochemicals and natural products. 22 ‘Modern Practice of Liquid Chromatography’ ed. J. J. Kirkland Wiley New York 1971. ” D. Bartmann Ber. Bunsengesellschaft phys. Chem. 1972 76 336; D. Bartmann and G. M. Schneider J. Chromatog. 1973 83 135. 24 M. N. Myers and J. C. Giddings Progr. Separation and Purification 1972 3 133; T. H. Houw and R. E.Jentoft J. Chromatog. 1972 68 303. High-pressure Chemistry 4 Physical Properties of Fluids Phase Studies-As part of a wider study on the properties of salts and metals in the supercritical region Franck Hensel Todheide and their colleagues have determined the vapour-pressure curves and critical points of NH,Cl BiCl caesium and potassium.25 The possible types of miscibility behaviour which may be found in binary systems at high pressures have been comprehensively described and reviewed by Schneider.26 Of particular interest in recent years have been the pressure dependence of upper or lower critical solution temperatures (or of closed misci- bility loops) and the behaviour of fluid mixtures above the critical temperature of either pure component (‘gas-gas systems’).In the former category a nice example is the study by Peter and Schneider 27 of the systems CHF3-C2H6 CF4-C2H6 and CHF,&F at temperatures down to -150 “C and pressures up to 1700 bar. The ternary system CF,-CHF,-C2H6 was also studied. In each case the systems show limited miscibility at low temperatures with an upper critical solution temperature (UCST). The range of immiscibility and the UCST both increase with increasing pressure. The pressure dependence of miscibility has been investigated for some ternary systems mainly of the type water-salt- organic compound. The addition of the salt often has the same effect on the binary water-organic system as an increase in pressure. A different type of ternary system (water-propan-2-01-benzene) was recently studied.2s This forms a single liquid phase at high temperatures and separates into two liquids on cooling.In water-rich mixtures of given composition the unmixing temperature rises with increasing pressure whereas the opposite is the case in mixtures of low water content. The importance of such studies in the technology of separation and purification of organic compounds is obvious. An interesting and novel applica- tion of the temperature-jump technique to the study of the kinetics of phase separation has been reported.29 Using the system water-KC1-pyridine a condenser discharge was used to change the temperature from a point in the one-liquid region to one in the two-liquid region at an applied pressure which could be varied in the range 1-4ooo bar.The temperature change was complete in 4 p,and the onset of turbidity was followed by measuring the optical trans- mission at a wavelength of 560 nm. Transmission remained constant for 80p then fell rapidly and finally became constant again after 1 ms. The initial delay ” M. Buback and E. U. Franck Ber. Bunsengeseilschaft phys. Chem. 1972 76 350; G. Treiber and K. Todheide ibid. 1973 77 1079; H. Renkert F. Hensel and E. U. Franck ibid. 1971 75 507; W. F. Freyland and F. Hensel ibid. 1972 76 16. 26 G. M. Schneider in ‘Chemical Thermodynamics’ ed. M. L. McGlashan (Specialist Periodical Reports) The Chemical Society London Vol. 2 1975 in preparation ; Ah. Chem. Phys. 1970 17 1 ; ‘I.U.P.A.C.; Experimental Thermodynamics’ Vol.11 Ch. 16 Butterworths in the press; Ber. Bunsengesellschaft phys. Chem. 1972 76 325; ‘Water-a Comprehensive Treatise’ ed. F. Francks Plenum Press New York London 1973 Ch. 6. ’’ K. Peter and G. M. Schneider 3rd International Conference on Chemical Thermo- dynamics Baden nr. Vienna September 1973. 28 Y. Hirose P. Engels and G. M. Schneider Chem.-ing.-Tech.,1972 13 857. 29 A. Jost personal communication; A. Jost and G. M. Schneider J. Phys. Chem. in the press; A. Jost Ber. Bunsengesellschaft phys. Chem. 1974 78 300. 146 B. Cleaver was reduced when light of shorter wavelength was used. Calculation showed that with D -cm2s-l drops would grow to a size comparable with the wavelength of the light in about 100 p. The process of phase separation appears therefore to be diffusion controlled with no retardation due to formation of the interface.The critical behaviour of binary systems continues to attract interest. Systems are classified according to the position of the critical locus in a pT projection of the equilibrium diagram. In some systems (e.g. H,C&NH,) the critical locus is a continuous curve joining the critical points of the pure components. In other cases the critical locus is in two separate parts which apparently do not meet as the pressure is raised. In systems of the 'first kind' the locus runs from the critical point of the less volatile component towards higher temperatures and pressures and in systems of the 'second kind' it runs to lower temperatures as the pressure is raised sometimes passing through a temperature minimum.Schneider,' has listed the examples studied prior to 1970. H,O-Ar and fifteen systems in which He is one component are systems of the first kind in which two fluid phases can be formed when the components are mixed at a pressure of a few hundred bar and a temperature above the critical temperature of either component. The systems H,O-Xe,,l H,O-pr~pene,~~ have recently been studied. and H,O-eth~lene~~ The first two are systems of the second kind with critical curves showing tempera- ture minima at 343 "Cand 800 bar and at 329 "Cand 1950 bar respectively. In the H,O-ethylene system polymerization of the ethylene prevented a direct study of the critical locus; the temperature and pressure were restricted to 300 "C and 900 bar.Apart from the light that these studies throw on the relationship between intermolecular forces and the form of the phase diagram they are also of great technological importance ; the systems are of interest as solvents for high- temperature chemical and electrochemical processes and are also of some signifi- cance in the field of geochemistry. One study has been reported on the effect of pressure on the reversible sol-gel transformation for solutions of 12-hydroxystearic acid in carbon tetra~hloride.,~ The transition temperature rises some 20 "C as the pressure is raised to 2 kbar. The value of (dT/dp) is related to the volume change for formation of cross-links by hydrogen-bonding between adjacent acid molecules which is negative.Structure Dynamics and Thermodynamics of Fluids.-Accurate measurements of density and permittivity have been made for compressed helium34 (to 12 kbar) and nitrogen35 (to 360 bar). The latter results were used to calculate the dielectric virial coefficients of N,; the work complements earlier studies by the same 30 G. M. Schneider Adu. Chem. Phys. 1970 17 1; Fortschr. chem. Forsch. 1970 13 559. 31 E. U. Franck H. Lentz and H. Welsch Z. phys. Chem. 1974 93,95. 32 M. Sanchez and H. Lentz High Temps.-High Press. 1973,5 689. 33 Y.Taniguchi and K. Suzuki J. Phys. Chem. 1974 78 759. 34 A. Dedit J. Brielles M. Lallemand and D. Vidal High Temps.-High Press. 1974 6 189. 35 J. F. Ely and G. C. Straty J. Chem. Phys. 1974 61 1480. High-pressure Chemistry 147 authors on 02,F, and CH,.A series of papers36 has appeared reporting systematic pV-T studies on bromo-alkanes to 6 kbar and between -70 and + 175 "C.Some discussion is given on the relationship between the intermolecular potential and the shapes of the isotherms and isobars. A spectroscopic study has been made of the A-p transition in liquid ~ulphur.~' The transition tempera- ture falls from 160"Cat atmospheric pressure to 145.5 "C at 840 bar where the transition line meets the rising freezing-point curve of monoclinic sulphur. The equation of state of liquid nitromethane has been determined by shock-wave methods to 100 kbar.38 This is claimed to be the first such determination for a liquid to this pressure based entirely on experiment.Shock compressions were carried out from a series of initial temperatures between the normal freezing and boiling points. The internal energy-volumepressure (U-V-p) equation of state was then derived using the known variation of internal energy with temperature along the atmospheric pressure isobar. The U-S-V equation was also derived by numerical integration. The liquid is metastable ('superpressed') over most of the range studied the experimental time being ca. 1-lops. The technique depends on sampling the U-V-p surface by starting at different densities (tempera- tures) and could be employed for any liquid having a large coefficient of expansion. An interesting determination of the radial distribution function (RDF) of liquid sodium by X-ray diffraction has been made.39 Measurements were made at four points along the freezing curve the highest being at 280 "Cand 43 kbar.In this way larger density changes were obtained than would have been possible by variation of temperature at atmospheric pressure. Measurement of the pres- sure dependence of the RDF under isothermal conditions would have been desirable but the method used requires that solid and liquid be present simul- taneously; the X-ray pattern due to the solid is then subtracted to eliminate the effect of background scattering. Over the pressure range studied the nearest- neighbour distance (first peak in the RDF) decreased by (12 f2)% and the peak sharpened considerably. The second peak behaved in a qualitatively similar way but was less well determined because of experimental errors.The RDF's for different pressures could not be brought into coincidence by a simple scaling operation because of the peak-sharpening effect mentioned. The study of the pressure dependence of tracer diffusion coefficients has been reviewed by Barton and Speedy.40 Their paper includes a table listing all systems studied among which are liquid argon various organic liquids and some molten salts. A diaphragm cell has been described,41 which is said to be capable of giving self-diffusion coefficients at high pressure with an accuracy of & 1 %. The volumes of the two compartments are matched at high pressure using spacer rings. The 36 G. Jenner and M. Millet High Temps.-High Press. 1973 5 145; ibid.1970 2 205; ibid. 1969 1 697. 37 G. M. Schneider Ber. Bunsengesellschaft phys. Chem. 1974 78 296. 38 P. C. Lysne and D. R. Hardesty J. Chem. Phys. 1973 59 6512. 39 K. H. Brown and J. D. Barnett J. Chem. Phys. 1972,57 2009 2016. 40 A. F. M. Barton and R. J. Speedy High Temps.-High Press. 1970 2 587. 4' M. A. McCool and L. A. Woolf High Temps.-High Press. 1972 4 85. 148 B. Cleaver compressibility of the liquid must be known so that appropriate corrections can be applied for the bulk flow which occurs through the diaphragm when the apparatus is pressurized and depressurized. A study of the temperature and pressure dependence of molecular reorienta- tion in liquid methyl iodide has been reported:2 covering the ranges 0-90"C and 0-2.5 kbar.The correlation function for reorientation about an axis per- pendicular to the symmetry axis was obtained from the anisotropic component of the Raman v3 band. The density and viscosity were also measured and a rota- tional diffusion coefficient D, was derived. The vibrational relaxation of the molecule was also studied using the isotropic component of the Raman bands. Finally the deuterium spin-lattice relaxation time was measured by n.m.r. This was used to derive a diffusion coefficient Dll for rotational movement about the C axis. The authors stress the importance of using pressure as an independent variable in investigations of this kind; D was found to be strongly density-dependent but Dll not so. In another of the proton relaxation rate in MeI and also MeCN it was shown that at temperatures above room tem- perature relaxation occurs by spin-rotation interaction.This relaxation mechan- ism was suppressed when the pressure was increased. A method for direct measurement of the volume change on mixing for two .~~ liquids under pressure was described by Schneider et ~ 1 It has been used to measure excess volumes for the systems water-acetonitrile and water-3-methyl- pyridine. The results were used to calculate the excess free energy of the mixtures as a function of pressure using the relationship GE(p) = GE(0) + Jp VEdp 0 In an outstanding series of experiments:' Franck Hensel Todheide and their co-workers have investigated the variation of physical properties with density in the critical and supercritical regions for various classes of fluid.The types of fluid studied were metals (Hg Cs K) po!ar liquids (H20,HCl) and ionic compounds (NH4Cl BiCl,). The object was to study the appearance of typical liquid-like behaviour as the density was increased from gas-like to liquid-like values. For the metals the properties measured were density electrical conduc- tivity optical absorption and thermoelectric power ; for the polar liquids den- sity permittivity electrical conductivity and i.r. spectra were measured and for the salts density and conductivity. At the critical point BiCl has a conductivity of only SZ-' cm-l and is estimated to be only ca. 1% ionized. At lower 42 J. H. Campbell J. F. Fischer and J. Jonas J. Chem. Phys. 1974 61 346.43 E. U. Franck H. G. Hertz and C. Radle 2.phys. Chem. (Frankfurt) 1970 73 18. 44 P. Engels and G. M. Schneider Ber. Bunsengesellschaft phys. Chem. 1972 76 1239; P. Engels G. Gotze and G. M. Schneider 3rd International Conference on Chemical Thermodynamics Baden nr. Vienna September 1973. 45 E. U. Franck Ber. Bunsengesellschaftphys. Chem. 1972 76 341; M. Buback and E. U. Franck ibid. 1973 77 1074; G. Treiber and K. Todheide ibid.,p. 1079; W. F. Freyland and F. Hensel ibid. 1972 76 347; R. W. Schmutzler and F. Hensel ibid. p. 531; F. Hensel Phys. Letters (A),1970 31,88. High-pressure Chemistry 149 densities the fluid becomes completely molecular but at higher densities (pres- sures) the conductivity rises to over 1 R-' cm-'. At the lower temperatures employed the conductivity-pressure plot passed through a maximum.This behaviour indicates that a state of complete ionization is approached at high pressures with the possibility that 'complex ions' such as [BiC14]- and [BiCl,] -are present in the intermediate region. In contrast to BiCl, NH4Cl has a high conductivity at its critical point indicating that it is predominantly ionic under these conditions. Correspondingly the critical exponent fi in the equation (Pliquid -gas) = const. IT -KIP had a different value for the two compounds; it was 0.33 for BiCl, but 0.50 for NH4Cl. For the alkali metals and mercury B was in the range 0.42-0.45. Water and Aqueous Solution~.-Franck~~ has summarized his work on the density permittivity conductivity viscosity and vibrational spectrum of pure water and of aqueous electrolyte solutions.Relatively accurate tracer diffusion coefficients (& 1%) for THO dissolved in H20 have been reported:' at 25 "C to 2100bar. A plot of D(p) against pressure showed a maximum at 900bar corresponding roughly to the minimum in the viscosity (at 500 bar at this tem- perature). Lee and Jonas4* have reported a number of n.m.r. studies on water and aqueous solutions. The deuteron spin-lattice relaxation time TI and the viscosity q were measured for D20 from 10 to 90 "C and up to 5 kbar. The quantity (Tlq/T)was calculated. It was found to be independent of temperature at constant density (in accordance with the Debye theory) but increased signifi- cantly with density.This indicates a change in the degree of coupling between rotational and translational motion. Similar studies were reported for water- C2H,]dioxan and D,O-dioxan mixtures and for electrolyte solutions in D20.In the latter case the variation of TIwith pressure was correlated with the structure- making or -breaking behaviour of the ions. The solubility in water of benzene (to 1.2 kbar) and toluene (to 3 kbar) have been measured between 25 and 55 "C by a spectrophotometric method.49 The solubilities of both compounds increased with pressure initially showing that the volume change on solution AVs is negative. For toluene the solubility passed through a maximum at 1.3 kbar showing that the volume change is positive above this pressure. Assuming that this high-pressure AK value corresponds to dissolution of the organic molecule in 'structureless' water the occurrence of negative AK values at low pressures indicates that the aromatic molecules have a structure-breaking effect in this region.The solubility of benzene in KNO solution was measured and was found to be enhanced when some K+ was replaced by Ag+ at constant ionic strength. This is due to the formation of a 46 E. U. Franck Pure Appl. Chem. 1970 24 13. 47 L. A. Woolf J. Chem. Phys. 1974 61 1600. 48 Y.Lee and J. Jonas J. Chem. Phys. 1972 57 4233; ibid. 1973 59 4845; Y. K. Lee J. H. Campbell and J. Jonas ibid. 1974 60 3537. 49 R. S. Bradley M. J. Dew and D. C. Munro High Temps.-High Press. 1973 5 169. 150 B. Cleaver charge-transfer complex [C,H,Ag] .The heat and volume change for formation + of the complex were deduced from the temperature and pressure dependence of the solubility. The optical absorption corresponding to electronic transitions in various aromatic molecules has been compared in the vapour phase and in solution in water and other solvents.50 In most solvents a red shift occurs when the solute is transferred from the gas phase to the solvent and this red shift increases with pressure. The shift is ascribed to the lowering of the energy of the excited state of the solute relative to the ground state due to interaction with the solvent. When water is the solvent the red shift is much reduced in magnitude and the pressure dependence of the shift is also smaller. These differences are explained in terms of water structure and of the interaction between the water dipole moment and the quadrupole moment of the solute chromophore in the ground and excited states.Several papers have appeared on the effect of pressure on ion-pair formation in aqueous solutions.51 Chatterjee et al. point out that the value of the ion-pair dissociation constant obtained (and of the corresponding volume change AV obtained from the pressure coefficient of this quantity) depends on the technique employed. In a Raman study of MgSO solution they obtained AV = -20.3 & 1.4cm3 mol-' for the dissociation of ion pairs whereas a value AV = -7.3 cm3 mol-' was reported from conductivity measurements and -7.2 to -8.5 cm3 mol- from density measurements.The confusion arises because there are different kinds of ion pair with two one or no solvent molecules held between the ions and the weighting given to each of these differs from one technique to an- other. Dist&ches2 has written a comprehensive article in which he discusses the effect of pressure on ion-pair formation ionization equilibria in weak electro- lytes and solubility of sparingly soluble electrolytes in the context of marine chemistry. The pressure dependence of electrical conductivity for aqueous electrolyte solutions continues to be studied e~tensively.'~ Franck Marshall and co-workers have reported accurate conductivity values for 0.01 demal KC1 solution at round values of temperature and pressure to 800 "C and 12 kbar which may now be used as standards.The conductivities were derived by averaging the results from eight different sets of experimental measurements all of which were carried out in the authors' laboratories at Karlsruhe and Oak Ridge respectively. The uncertainty in the smoothed data is k0.5% at 100"Cand lo00 bar increasing to 34% at 800 "C and 12 kbar. A. Zipp and W. Kauzmann J. Chem. Phys. 1973 59,4219. 51 R. M. Chatterjee W. A. Adams and A. R. Davis J. Phys. Chem. 1974 78 246; F. J. Millero and W. L. Masterson ibid.,p. 1287; F. J. Millero G. K. Ward F. K. Lepple and E. V. Hoff ibid. p. 1636. '' A. Disteche 'The Effect of Pressure on Dissociation Constants and its Temperature Dependence' in 'The Sea; Volume 5-Marine Chemistry' ed. E. D. Goldberg Wiley 1974.53 A. S. Quist W. L. Marshall E. U. Franck and W. von Osten J. Phys. Chem. 1970 74 2241 ;H. Renkert and E. U. Franck Ber. Bunsengesellschuft phys. Chern. 1970 74,40; J. U. Hwang H.-D. Ludemann and D. Hartmann High Temps.-High Press. 1970 2 651. High-pressure Chemistry 151 An interesting spectroscopic study of Cu" chloride complexes in aqueous solu- tions to 400 "C and 2 kbar has been described.' The solutions contained cupric perchlorate cupric chloride and lithium chloride in various proportions. At low temperatures and in dilute solution the hexa-aquo-complex of Cu" was the predominant species. As the temperature and pressure were increased mixed chloreaquo-ions appeared and finally the tetrahedral [CuC1,I2-complex. Comparable behaviour has previously been found for Co" and Nil' chloride solutions; rising temperature favours the substitution of H20 as ligand by C1-.Molten Salts.-Relatively few papers have appeared reporting high-pressure work on molten salts. Measurements of isothermal compressibility have been reported for molten alkali nitrates and halide^.^' The pressure dependence of electrical conductivity to 1 kbar was determined for all the molten alkali-metal halides (excluding fluorides) AgCl and AgBr.56 The volume AV,, defined as -RT(3In A/+)= was found to be zero for lithium halides and increased regu- larly as the alkali metal or halide ions were changed in the sequence Li+ Na' K' Rb' Cs' or C1- Br- I-. The 'activation energy' for molar conductivity at constant volume RT2(8In A/JT)v was compared with the corresponding quantity at constant pressure for each salt studied.The ratio Ev/E was unity for lithium salts and fell as the cation size was increased reaching 0.5 for the halides of the heavier alkali metals. Similar results had previously been reported for molten alkali nitrates. No existing theory for molten-salt conductivity was able to account satisfactorily for this behaviour although some of these theories had been used successfully to account for the temperature dependence of transport processes in molten salts at atmospheric pressure (when the temperature and density are changed simultaneously). This again highlights the advantages to be gained from the use of pressure as an independent variable. The conductivity of molten nitrates has now been measured at pressures up to 55 kbar.57 Plots of log(conductivity) against pressure were linear up to CQ.10 kbar but showed curvature at higher pressure. An interpretation of this be- haviour should await the determination of the densities of the melts at the pressures in question; to date this information is available only up to 9kbar. Barton and Speedy5* have pointed out the advantages of measuring the conduc- tivity and density simultaneously at high pressure and have done this for molten tetrafluoroborates NR,BF (R = n-butyl pentyl hexyl or heptyl). Bannard and TreiberS9 have published a very interesting study on the conduc- tivity of molten mercuric iodide to 4 kbar and 850 "C. This compound is unusual in having a negative temperature coefficient of conductivity at atmospheric 54 B.Scholz H.-D. Ludemann and E. U. Franck Ber. Bunsengesellschaft phys. Chem. 1972 76 406. 55 A. F. M. Barton G. J. Hills D. J. Fray and J. W. Tomlinson High Temps.-High Press. 1970 2 437. 56 B. Cleaver S. I. Smedley and P. N. Spencer J.C.S. Faraday I 1972 68 1720. '' V. Pilz and K. Todheide Ber. Bunsengesellschaft phys. Chem. 1973 77 29. 58 A. F. M. Barton and R. J. Speedy J.C.S. Faraday I 1974 70 506. 59 J. E. Bannard and G. Treiber High Temps.-High Press. 1973 5 177. 152 B. Cleaver pressure which has previously been ascribed to displacement of the auto-ionization equilibrium 2Hg1 HgI' + HgI; to the left with decreasing density. In accordance with this Bannard and Treiber found that the conductivity increased steeply with pressure (density) at constant temperature.As the pressure was raised the isobaric temperature coefficient became smaller and eventually changed sign; the isotherms crossed in a narrow pressure range near 2.8 kbar. At the highest pressure reached the conductivity appeared to have reached a maximum; this represents the balancing of two effects of pressure namely the increase in degree of ionization and the reduction in ionic mobility. Similar effects were earlier found for BiCI .45 Solvated Electrons.-The effect of pressure on the rates of reactions involving solvated electrons has been studied.60 In aqueous solution the rates of reaction of ea; with H30+ formamide acetamide acetoxime benzyl alcohol and 2-chloroethanol were measured up to 6kbar.The rate constants increase with pressure indicating a negative activation volume but AV * increased with pres- sure (ie.became less negative). This was attributed to a reduction with pressure of the cavity volume of eai. The partial molar volume of electrons V(ea;) and the cavity volume were estimated to be 7 and 10 cm3 mol- respectively at 29 "C and atmospheric pressure the difference of 3 cm3 mol-' being due to electro- striction of the water. These values conflict with an earlier estimate of 0 cm3 mol- for V(eaJ which was based on studies of a single reaction. In ethanolic solution the solvolysis reaction esolv+ EtOH-EtO,, + H was studied and was found to have an activation volume of -14.4 cm3 mol- '.However the bimolecular reaction of e& with scavengers such as nitrobenzene acetone and naphthalene had a positive activation volume (7.5 5.1 and 5.6 cm3 mol- ' respectively). The activation volume for diffusion of solvated elec- trons was estimated to be +7 cm3 mol- '. A semi-continuum model has been proposed for the solvated electron in ethanol and methanol to account for the pressure dependence of the absorption spectrum.61 Increasing pressure leads to a blue shift; this arises mainly from a reduction in the cavity radius and an increase in the energy of the quasi-free electron state. The model takes account of the effect of pressure on density and permittivity. In the model the first shell of solvent around the electron (M molecules) is regarded as partly oriented dipoles in thermal equilibrium inter- acting with the electron by the charge-dipole potential.The remaining solvent is treated as a continuum. When the pressure is changed the spectral changes arise mainly from changes in the short-range interactions between e- and the medium; for this reason recognition of the molecular properties of the solvent in the first co-ordination sphere is essential to the success of the theory. 6o R. R. Hentz Farhataziz and E. M. Hanson J. Chem. Phys. 1972,57 2959; K. N. Jha and G. R. Freeman ibid. p. 1408. D.-F. Feng K. Feuki and L. Kevan J. Chem. Phys. 1972 57 1253. High-pressure Chemistry 153 5 Physical Properties of Solids Phase Diagrams and Structure.-Papers on the determination of phase diagrams of solids (showing solid-solid and solid-liquid transition lines on a T-p diagram) and on the determination of crystal structures of high-pressure phases form a substantial fraction of the current literature on high-pressure research.Since it is impossible to summarize the results of all this work here selected examples will be given which illustrate the main uses to which these studies are put. The techniques used to determine transition lines are visual or spectroscopic observation (using a windowed cell or a transparent cell made from diamond or sapphire) differential thermal analysis differential scanning calorimetry (to determine heats of transition) volume measurement (to find the volume change on transition) conductivity measurement and X-ray diffraction.X-Ray or neutron diffraction is also used to find the crystal class space group unit-cell dimensions and structure of solid phases. The practice of X-ray diffraction at high pressure has been reviewed.62 A major objective of phase-diagram and structure determination is to study the T-p diagrams of a group of compounds of similar formula but containing dif- ferent elements and to seek similarities between the diagrams. It is often found that the diagrams of compounds within a group can be brought into coincidence by displacing them relatively along the pressure axis. An empirical rule is that for simple ionic substances the same succession of phase changes can be brought about either by increasing the pressure or by changing the cation to one of larger radius.Examples of groups of compounds studied are the alkali-metal nitrates and alkaline-earth carbonates the spinels AB20, complex halides of the type ABX (A = alkali metal B = Group V element X = halogen) cryolites A,MF (A = univalent metal M = tervalent and the univalent metal per- chlorates and fluoroborates (MClO and MBF,).64 In his study on the sodium cryolites Pistorius found that the phase diagrams of all the compounds were very similar ;the 1-11 phase-transition temperature at atmospheric pressure and also the unit-cell volume of the monoclinic form were smooth functions of the crystal radius of the tervalent ion M3+. Measurements were made for M = A] Fe V Ti and Co and predictions could then be made on the properties of com- pounds with M = Mn Mo Ta Nb Rh Ru and Pd.It was also possible to predict that a high-pressure synthesis of rare-earth cryolites Na3LnF6 is unlikely to be successful for lanthanide ions bigger than Sc3+. because the unit-cell dimen- sions would then be such as to make this compound unstable relative to 2NaF + NaLnF,. Apart from permitting a prediction to be made of the form of a phase diagram for compounds which have not been studied experimentally thcse com- parative studies may also allow existing diagrams to be extrapolated into pres- sure and temperature ranges which are beyond the reach of current experimental techniques. Thus the phase diagrams of germanates at moderate pressures '' M. D. Banus High Temps-High Press. 1969 1 483.63 C. W. F. T. Pistorius J. Solid Stare Chem. in the press. 64 J. B. Clark and C. W. F. T. Pistorius Z. phys. Chem. (Frankfurt) 1974 88 242. 154 B. Cleaver resemble those of silicates at much higher pressures so the germanates can be used as model compounds to predict the behaviour of silicates at pressures such as those encountered in the earth’s mantle. A discussion of this point and of other matters affecting phase relations in geochemical systems is given in a review by Edgar and Platt.65 High-pressure phases are sometimes investigated as examples of ‘new’ struc- tures for which no counterpart exists at atmospheric pressure. Conversely some complex compounds stable under ambient conditions decompose into simpler compounds or into elements when the pressure is raised.Pressure always favours changes which are accompanied by a reduction in volume ;although this often corresponds to an increase in co-ordination number in simple lattices (such as elementary lattices) some pressure-induced decompositions involve a reduc-tion in co-ordination number around the central atom in a complex group. This is accompanied of course by an overall increase in the space-filling efficiency of the atomic arrangement. A nice example of decomposition brought about by application of pressure is provided by the series of chalcogenides Ag8MX6 (M = Si Ge or Sn ;X = S Se or Te).66 These compounds (with the exception of Ag8GeS6) are decomposed at high pressure into a mixture of Ag,X and MX,. At pressures above l00kbar many ionic or semiconducting compounds be- come metallic.The transition can be detected by measuring the rapid fall in electrical resistance which accompanies it. These transitions have usually been brought about using shock waves (i.e. transient high pressures induced by the use of explosives) but one study has been reported in the Mbar range using static techniques. Ka~ai,~’ using his ‘split-sphere’ vessel showed that Fe203 Cr,03 and TiO all become metallic at pressures between 2 and 3 Mbar; the resistance of the samples fell sharply by between 3 and 6 orders of magnitude as the transition occurred at room temperature. The transitions were reversed when the pressure was removed. This observation is of great interest in relation to the composition of the core of the earth ;this is known to be highly conduct- ing and has been thought in the past to consist of metals such as iron and nickel.Kawai’s result shows that the oxides of these metals are an alternative possibility since the pressures he reached are approximately equal to those at the centre of the earth. It is an awe-inspiring thought that with his little sphere of less than 30 cm diameter he was able to reproduce the conditions inside that greater globe on which we live. Two interesting studies have been reported on the behaviour of point defects in solids under pressure.68 Stoicheiometric Ti0 is known to have the NaCl structure at atmospheric pressure but with 14.4% of cation sites and of anion sites vacant. The vacancy concentration falls as the pressure is raised and becomes zero at a pressure given by p(T -298) = 90 OOO kbar deg.The lattice 65 A. D. Edgar and R. G. Platt High Temps.-High Press. 1971 3 1 ;see also Y. Shimizu Y. Syuno and S. Akimoto ibid. 1970 2 11 3. “ C. W. F. T. Pistorius and 0. Gorochov High Temps.-High Press. 1970 2 31. ‘’ N. Kawai and S. Mochizuki Phys. Letters (A) 1971 36 54. A. Taylor and N. J. Doyle High Temps.-High Press. 1969 1 679; M. Iqbal and E. H. Baker ibid. 1973 5 265. High-pressure Chemistry 155 parameter increases from 4.1796 to 4.2062A as the vacancy concentration is reduced to zero but the density rises from 4.97 to 5.69. In the other study the behaviour of Tho and of Tho,-YO solid solutions was investigated as a function of oxygen pressure between lop7and 500 bar at temperatures from 800 to 1100 "C.The electrical conductivity IS was measured; it was independent of oxygen pressure below bar and was believed to be ionic in this range. At higher oxygen pressures the conductivity began to increase; c was then pro- portional to p) and the sample became a p-type semiconductor. In this region the following defect equilibrium is proposed $O,(g) + (Vo)** 0 + 2h (where V is a vacancy on an oxide site and h is a hole). Since [hI2 is propor- tional to p) by the law of mass action and IS is proportional to [h] the fourth-root dependence is explained. At higher oxygen pressures IS was found to be propor- tional to p3. To explain this the authors propose the following equilibrium involving paired vacancies O,(g) + (V Vo)."* (0,0,)"' + h TransportPropertiesof Solids.-Baran~wski~~has published an interesting study on the effect of hydrogen pressure on the diffusion of H atoms in b-palladium hydride.Diffusion was followed by recording the resistance of a wire as a func- tion of time following a small pressure change. At pressures up to 500bar the composition was in the range PdHo.,-PdHo~8 and octahedral vacancies pro- vide the sites for H atoms. In one run to 25 kbar evidence was obtained that tetrahedral interstitial sites were involved. The hydrogen content was relatively high in this case approaching or even exceeding the stoicheiometric composition (PdH). Bradley and his colleagues70 have measured the effect of pressure on conduc- tivity for a number of ionic solids including PbCl, AuCN CuCN AgCN CuCI and the highly conducting KAg,I and RbAg,I,.For PbCl, the en- thalpy and volume terms corresponding to defect formation and migration were deduced. It was concluded that anion Frenkel disorder was present with anion vacancies as the more mobile defect. For AuCN and AgCN the conductivity increased with pressure and was believed to be partly electronic. The conductivities of KAg,I and RbAg,I fell with increasing pressure with activation volumes of 3.4 and 2.8 cm3 mol-' respectively. In contrast the con- ductivities of Ag,SBr and Ag3SI increased with pressure (AV* = -1.3 and -2.3 cm3 mol- respectively) at 30 0C.71 69 M. Kuballa and B. Baronowski Ber. Bunsengesellschuft phys.Chem. 1974 78 335. 'O R. S. Bradley D. C. Munro and P. N. Spencer Trans. Furuduy SOC.,1969 65 1920; R. S. Bradley 'Ionic Migration in Solids at High Pressures in the Presence of an Electric Field' in 'Atomic Transport in Solids and Liquids' ed. A. Lodding and T. Lagerwall Verlag der Zeitschrift fur Naturforschung Tubingen 1971 p. 350; R. S. Bradley D. C. Munro and S. 1. Ali High Temps.-High Press. 1969 1 103; see also F. P. Bundy J. S. Kasper and M. J. Moore ibid. 1971 3 303. " H. Hoshino H. Yanagiya and M. Shimoji J.C.S. Furuduy 11 1974 70 281. 156 B. Cleaver Bundy et have studied a series of mixed-valence Pt and Pd compounds which show a remarkable increase of electronic conductivity with pressure (6 or 7 orders of magnitude over 140kbar) the maximum values recorded being in excess of 1 R-' cm-' in some cases.The compounds have the following formulae [M"(NH3)2X2][M'V(NH,),X4] (M = Pt or Pd; X = halogen) [Pt"(en)X,] [Ptiv(en)X4] and [Pt"(EtNH,),] [Pt'V(EtNH2)4X2]X4 ,4H20. In each case the M"ion has square-planar and the MIv ion octahedral co-ordination. The structure involves linear chains of M" and MIv alternately with X ions in the chains but placed nearer to MIv than M" .....M*I... ..X-M'"-X ..._.M" .....X-MIV-X ..... The remaining ligands form squares whose planes are perpendicular to the linear chains. The direction of highest conductivity is along the chains and the com- pounds show absorption bands which are attributed to transitions between the dz2 orbitals of M" and MIv.These bands shift to lower energy as the pressure rises and the M". ..X and MIV-X distances become closer to each other (though they still remain different at the highest pressure used). These changes indicate increases in delocalization of the d, electrons on MI' which is responsible for the steep increase in conductivity observed. Vibrational Spectroscopy.-A study has been made73 of the Raman spectrum of solid benzene in two crystalline modifications (I and 11). Several advantages arise from the use of pressure as a variable. Pressure tends to reduce non-bonded (intermolecular) atomic separations more than bonded (intramolecular) ones. The lattice-mode frequencies are therefore much more pressure-dependent than the internal-mode frequencies which facilitates assignments.Also pressure may remove accidental degeneracies. In this case a complete assignment of the spectra of I and I1 was made. The subject of vibrational spectroscopy at high pressure was reviewed in Annual Reports for 1972. Dri~kamer~~ has made an extensive study of the effect of pressure (to 125 kbar) on the 0-H N-H and C-H stretching frequencies of 15 hydrogen-bonded solids mainly phenols. The C-H frequencies increased at all pressures and the bands broadened slightly. A greater broadening was observed for the hydrogen- bond frequencies ; these decreased with pressure initially and sometimes in- creased at higher pressures. No systematic difference was found between the behaviour of inter- and intra-molecular hydrogen bonds.Substituent effects were discussed; the larger the initial red shift due to the substituent at atmo- spheric pressure the greater was the initial red shift with pressure. 6 Inorganic Reactions Synthesis of Inorganic Compounds.-Several chapters in a recent book7 survey the techniques of high-pressure synthesis and list some reactions that have been 72 L. V. Interrante K. W. Brownall and F. P. Bundy Irznorg. Chem. 1974 13 1158. 73 W. D. Ellenson and M. Nicol J. Chem. Phys. 1974 61 1380. l4 S. H. Moon and H. G. Drickamer J. Chem. Phys. 1974,61 48. l5 'Preparative Methods in Solid State Chemistry' ed. P. Hagenmuller Academic Press New York-London. 1972. High-pressure Chemistry carried out. The following general principles give a guide to the types of syntheses likely to be favoured by pressure (i) Pressure generally increases the coupling between d-orbitals on neigh-bouring metal atoms.(ii) Pressure favours high co-ordination number in simple compounds and so tends to stabilize high oxidation states of metals (requiring a high co-ordination number of anionic ligands). (iii) Pressure inhibits the formation of distorted structures or displacement of ions from the centre of an octahedral site (ferroelectric displacement). These two effects normally operate against the introduction of d-electrons by substitu- tion of B‘ cations for B cations in ABO structures where B has d-electrons but B does not. Pressure accordingly favours such substitutions. (iv) Pressure tends to broaden the range of composition attainable in insertion- type bronzes such as Na,WO, because it destabilizes distorted structures which would normally compete.(v) The range of composition of a non-stoicheiometric compound may be extended to include the stoicheiometric composition e.g. by permitting a very high oxygen activity to be used (e.g.CaMnO can be made from CaO + MnO in the presence of CrO as a source of oxygen. The conditions required are 20 kbar 500 “C 2 h). (vi) Pressure raises the internal energy of solids thus tending to stabilize structures in which metal ion-metal ion repulsion is significant. Pressure may be used in different ways to effect syntheses. Sometimes the ‘synthesis’ is just a phase transformation to a high-pressure form of a substance stable at atmospheric pressure (e.g.diamond synthesis).The compound may be formed at high pressure by chemical reaction ;the product may then be cooled and removed from the apparatus and may be metastable at atmospheric pressure. Pressure may be used to increase the rate of a reaction which is thermodynamically favoured at atmospheric pressure but which proceeds very slowly. Sometimes oxygen ‘buffers’ are required. These consist of a mixture of a metal and its oxide or of two oxides. The buffer is separated from the reaction mixture by a disc of Pt or BN with a small hole to transmit the gas. CrO, ZrO, MnO and PtO may be used as sources of oxygen. Addition of a small amount of water often improves the yield and crystallinity of the product. In the hydrothermal method the product is formed in super-critical water usually with the addition of a solubilizing agent such as NaOH.Some novel complex halides have been prepared using HCl HBr and HI under hydrothermal condition^.'^ By applying a suitable thermal gradient large crystals can be grown from fragmented ‘nutrient’. Some syntheses have been carried out using shock-wave conditions.’’ Pres-sures up to 10 Mbar and temperatures up to 10OOO K can be reached for times of the crder lops. Compounds which have been made in this way include TIC Zn,SiO, CrSe CrTe SnS SnSe SnTe K,PtX, and K,PtX,Y (X and Y being l6 A. Rabenau H. Rau and G. Rosenstein Z. anorg. Chem. 1970 374 43; Monatsh. 1971 102 1425. I58 B. Cleaver halogens; the last two compounds were made from KX and PtX or PtY respectively).A feature of shock-wave conditions is that the severe distortion causes multiplication of the dislocation density to ca. 10’o-10’2 an-’. This enhances the reaction rate so reasonable yields can be obtained in spite of the very short reaction time. The high-temperature zone following the shock front also favours high reaction rates although it can cause thermal decomposition of the initial product. In the reference previously a review is given of recent progress in the synthesis of compounds ABX (X= 0,halogen or S) and (AX),ABX,. Diamond Synthesis.-Synthetic diamonds now account for ca.40 % of the world’s supply of industrial-quality material. The subject has been reviewed by Wentorf. 77 Diamond exists in nature as a cubic form with ABCABC .. . stacking and also as a much rarer hexagonal form with ABAB . .. stacking. The hexagonal form has been synthesized from graphite and has also been found in meteorites where it is thought to have been generated during impact. The growth of gem-quality diamonds of size approaching 1 carat (ca. 5 mm diameter) has been described,78 and the conditions necessary for growth of larger stones are discussed. The diamonds were grown from solutions of carbon in molten Fe or Fe-Ni or Fe-A1 mixtures at 57 kbar and 1690-1830 K. The nutrient was diamond grit augmented by graphite (which was partly converted into diamond in situ). A temperature gradient was maintained between the nutrient and the seed and growth took place at a rate of 1-2.5 mg h-’.Times of up to one week were required for the growth of 1 carat gems. Some of the problems encountered were dissolution of the seed before the steady state had been reached spontaneous nucleation and growth of further crystals incorpora- tion of veils of metal and of other impurities in the growing crystal and forma- tion of graphite. Graphite can appear even when diamond is thermodynamically stable because of kinetic factors. The diamonds produced were sometimes coloured owing to the inclusion of foreign atoms. Nitrogen is a common impurity (as it is in natural diamonds) and imparts a yellow colour ;however it is atomically dispersed in synthetic diamonds whereas in nature it forms platelets in the (100)planes. Boron may also be incorporated ;in the absence of nitrogen this imparts a blue colour.It is believed that gem-quality crystals could be grown more rapidly by using as solvent a refractory metal with a melting point nearer to that of diamond (and which does not form stable carbides in the region of the eutectic temperature). Such a possibility is at present beyond the range of experimental techniques. The growth of gem-quality diamonds in the laboratory is said to be unecono- mic (a factor of 10 has been mentioned in the popular press). The main reason for continuing the work is to gain an understanding of the growth process and of ” R. H. Wentorfjun. ‘Diamond Formation at High Pressure’ in Ah. High Pressure Res. 1974 4; F. P. Bundy H. M. Strong and R. H. Wentorf ‘Chemistry and Physics of Carbon’ ed.P. L. Walker Marcel Dekker New York 1972 Vol. 10. 78 H. M. StrongandR. M. Chrenko,J. Phys. Chem. 1971,75 1838;seealso R. H. Wentorf ibid. p. 1833. High-pressure Chemistry the role of impurities. These affect the growth process and also the mechanical optical and electronic properties of the product. The control of impurity content is a major aim at the present time. A polycrystalline form of diamond known as carbonado (or in a purer form as ballas) is found in Brazil and West Africa. Since it is not so subject to fracture as single-crystal diamond having no natural cleavage planes it is preferred for certain applications in diamond tools. Carbonado is rather rare and attempts have been made to prepare it in the laboratory with some success.79 The tech- nique is to prepare the polycrystalline material directly from graphite or to make it by sintering diamond powder alone or in the presence of a binder.A feature of natural carbonado is that the crystals are held together by carbon-carbon bonds but in some of the synthetic material this function is performed by the binder which is less satisfactory. Wentorf considers that the processes by which carbonado and ballas are formed in nature are not under~tood.'~ Hall points out that the sintering can be carried out in the region ofdiamond stability (e.g.85 kbar 2440 K 3 min) to give a white product or in the region of graphite stability (e.g. 65 kbar 2500 K 20 s)to give a black product which still has satisfactory mechani- cal properties but which contains some non-diamond carbon.The sintered bodies could be produced in any desired simple shape up to 8 mm in length. A spherulitic form of graphite has been produced by carbonizing anthracene at a pressure of 1-2kbar and subsequently graphitizing.80 A mesophase is produced in the initial process and the authors discuss the reasons why the small spherical droplets do not coalesce. In a previous paper the authors describe a study of the effect of pressure on the rate of polymerization of anthra- cene (which precedes the carbonization reaction). The rate of disappearance of authracene is first-order and is accelerated by pressure (AV * = -17 cm3 mol- I). Paramagnetic species are thought to be involved in the early stages of the reaction; they lower the excitation energy of anthracene to the triplet state which precedes formation of anthryl radicals which in turn bring about polymerization.Kinetics of Inorganic Reactions.-Several studies have been reported on the effect of pressure on ligand-substitution reactions in transition-metal complexes. Tong and Swaddle*' studied the exchange of H,O between [Ir(NH3)5H20]3+ and water using H2'*0. They measured the rate constant to 4 kbar and found AV * = -3.2 cm3 mol- '. The authors had previously obtained similar values for the same reaction using the Rh3+ and Cr3+ complexes but for the Co3+ compound AV* was + 1.2 cm3 mol- '. This indicates that the Co3+ complex exchanges water by a dissociative mechanism whereas the other three do so by an associative mechanism.V3+ and Mo3+ hexa-aquo-complexes and Ru3+ amines also exchange ligands by associative mechanisms. Co3+ is the smallest '' H. T. Hall Science 1970,169,868; L. F. Vereshchagin A. A. Semerchan V. P. Modenov T. T. Bocharova and M. E. Dmitriev Soviet Phys. Dokfady,1971 15 1065. P. W. Whang F. Dachille and P. L. Walker High Temps.-High Press. 1974,6 127 137; S. Hirano F. Dachille and P. L. Walker ibid. 1973 5 207. " S. B. Tong and T. W. Swaddle Inorg. Chem. 1974 13 1538. 160 B. Cleaver cation in this group which may explain its anomalous behaviour. The authors stress that Co3+ octahedral complexes should not be used as model compounds representing all M3+ complexes. Jost2' has used a temperature-jump method to study the process Fe3+ + SCN--+ FeSCN" A condenser discharge was used to produce the temperature jump and the pressure could be varied up to 4kbar.Optical read-out was employed. The formation of complexes by Ni2+ Co2+,Cu2+ and Zn2+ with murexide was also studied. In all cases the volume change for reaction and the activation volume were both positive. Caldin and co-workerss2 have made extensive use of a laser temperature-jump cell to study reaction rates at pressures up to 3 kbar. Either optical or conducti- metric read-out were available; in the first case two windows at right-angles to the laser beam were used. The range of relaxation times which could be studied conveniently was 500 ps-2 s. The rate of formation of complexes between Ni2+ or Co2+and NH or pyri- ridine-2-azodimethylaniline(PADA) was measured as a function of pressure up to 2 kbar.The equilibrium constants for complex formation were also deter- mined at atmospheric pressure by an optical method and corresponding values at high pressure were found from the amplitude of the relaxation trace (using optical read-out). For each metal ion-ligand system the enthalpy entropy and volume of activation and the standard enthalpy entropy and volume changes for reaction were obtained. The activation volumes were very similar for all four reactions and were between 5 and 8 cm3 mol-'. The authors suggest that formation of the transition state involves the same process in all four cases and that this is the stretching of an M2+-water bond by between 20 and 50%.The standard volume change for reaction showed wide variations between the systems studied; the extreme values recorded were -9 and +6cm3 mol-' (both for Co2+ reactions). A similar study was made using an anionic ligand the glycinate ion with Co2+ Ni2+ Cu2+ and Zn2+. AV* was again positive and was between 7 and 12 cm3 mol- '. Since charged ligands are now involved these figures may not be compared directly with those from the previous study without making allowance for the volume change for formation of an outer-sphere complex. When this was done volumes of activation for breaking of the metal ion-water bond in the range 4-9 cm' mol- were obtained ; these are satisfyingly close to the values for Co2+ and Ni2+ reactions with NH and PADA indicating that the rate-determining step is the same in all cases.The reaction of Co2+ Ni2+ Cu2+ and Zn2+ with PADA was also studied in glycerol solution.82 In contrast to the aqueous reactions these substitutions all proceeded at the same rate within a factor of 4. The rate constants were smaller by two or three orders of magnitude than those calculated on the basis of dif- fusion control. For Zn2+ the activation enthalpy and volume were similar to 82 E. F. Caldin and M. W. Grant J.C.S. Faraday I 1973 69 1648 and references cited therein. High-pressure Chemistry 161 those for diffusion control. The low rate constant is attributed to steric factors during the substitution of glycerol by the ligand. The diffusion of a departing glycerol molecule into the bulk solvent is considered to be the main determinant of the activation parameters.For the Co2+ reaction the breaking of the Co2+-glycerol bond is also a significant factor. Hasinoff83 has reported measurements of the effect of pressure on the rates of ligand-substitution reactions of biological interest using the laser temperature- jump apparatus described above. The first reaction studied was that of iodide ion with cobalamin (Vitamin B12). The activation volumes for formation and dissociation of the iodide complex were respectively 6 and 12 cm3 mol-’. After making allowance for formation of an outer-sphere complex the volume change for the ligand-substitution reaction was 2.3 0.8 cm3 mol- This is sufficiently close to the values reported for the other aqueous ligand substitutions described above to suggest that stretching of the Co-H,O bond is again the rate-determin- ing step.(The relatively low value 1.2 cm3mol-’ for H,O exchange in the [CO(NH,),H,O]~+ complex was mentioned earlier in this section.”} There was some evidence that the substitution reaction in cobalamin was preceded by a very fast intramolecular process of unknown nature. If this is substantiated due allowance should be made for the volume change in this process when calculat- ing AV* for the Co-H,O bond-stretching process. The other reactions studied by Hasinoff were those of oxygen and carbon monoxide with haemoglobin (Hb) and myoglobin (Mb). The laser was used to photodissociate the complex and the recombination was followed spectro- photometrically.The Hb + CO reaction showed two exponential relaxations with time constants of 0.1 and 5 s. They are thought to correspond to the ‘oxy’ and ‘deoxy’ conformations of Hb respectively. The activation volumes were positive for the Mb + 0 and Hb + 0 reactiops (8 and 5 cm3 mol-’ respec- tively) but negative for the reactions of CO (-9 cm3mol-’ for Mb -3 and -21 cm3 mol-’ for the fast and slow reactions of Hb). A detailed discussion is given of the many factors contributing to the AV * values in terms of a mechan- istic model due to Perutz. Binding of the ligand and solvation of parts of the Hb molecule during subsequent conformational changes cause negative contri- butions to AV*. AV* is expected to be larger for the ‘oxy’ (fast) than for the ‘deoxy’ (slow) reaction because fewer salt bridges are broken in the former case.The positive AV* values for the 0 reactions are not easily explained; possibly they correspond to a different fit of the ligand into the heme pocket resulting in different displacements of the surrounding protein. It is evident that experi- mental determinations of A V* for reactions involving such complex molecules do not lead directly to clear conclusions about the mechanism. However they do provide some check on the validity of mechanistic proposals based on other evidence. ’’ B. B. Hasinoff Canad. J. Chem. 1974,52 910; Biochemistry 1974 13 31 1 I 84 W. B. Holzapfel High Temps.-High Press. 1970 2 241 ; see also ref. 2.162 B. Cleaver 7 Spectroscopic and Photochemical Studies Mossbauer spectroscopy at high pressures has been reviewed by H~lzapfel.~~ The conventional arrangement is used except that either the absorber or the source (mixed with powdered boron and epoxy resin) is held in a Bridgman anvil. High-pressure experiments have been reported using the nuclei '7Fe 67Zn "Sn 125Te,151Eu, and lg7Au,and extension to other isotopes is expected to follow rapidly. The reversible transformation of high-spin Fe3+ into high- spin Fe2+ by pressure has been observed in a variety of compounds. The pres- sure at which the transformation occurs depends partly on the properties of the ligand that supplies the electron. Studies of hyperfine interactions have led to a better understanding of the changes induced by pressure in the electronic arrangement or band structure.The effect of pressure on the stability of the tolueneiodine charge-transfer complex in n-hexane has been studied spectrophotometrically to 2 kbar.85 Values of AG,AH AS and AV for complex formation were obtained. AV was -6 cm3mold' at 1 atm rising to -4 cm3 mol-1 at 2 kbar. The frequency of the absorption maximum showed a red shift with rising pressure or falling temperature in line with previous studies. Offen86 has reported two photochemical studies on aromatic hydrocarbons in solid matrices at 77 K. The transfer ofenergy between excited pyrene and perylene was examined in a poly(methy1 methacrylate) matrix. The critical transfer distance at which the rates of intermolecular energy transfer and intramolecular decay are equal was reduced from 44A at atmospheric pressure to 35A at 30 kbar.This was due mainly to a reduction in the fluorescence lifetime of the donor. Other significant factors were an increase in the refractive index of the medium and a decrease in the spectral overlap between pyrene emission and perylene absorption. The applicability of the Forster dipole-dipole mechanism of energy transfer is confirmed at high pressure. The phosphorescence spectrum and triplet lifetime of [2H8]naphthalene were measured to 35 kbar in five different solid matrices. Compression resulted in spectral broadening by a factor of ca. 2 because of increased solvent inhomogeneity and enhanced coupling with the lattice.A pressure-induced red shift was observed in the triplet energy varying from 0 to 560 cm-at 30 kbar depending on the matrix. The phosphorescence lifetime was CQ. 20 s in each matrix at 77 K and decreased with pressure. A theoretical paper on the effect of pressure on molecular electronic spectra and the rates of electronic relaxation processes has been published by It was predicted that the pressure-induced frequency shift for different vibronic bands is the same; that the pressure dependence of frequency shifts is parabolic; and that the rates of non-radiative decays depend exponentially on the pressure and are also related to the frequency shift of the corresponding electronic transition. Oh Cheun Kwun and H. Lentz Z. phys. Chem. in the press.The paper contains references to other work on charge-transfer complexes. 86 P. C. Johnson and H. W. Offen J. Chem. Phys. 1972 57 1473; R. A. Beardslee and H. W. Offen ibid. 1973 59 4633. S H Lin J Chem Phys 1973. 59. 4458 High-pressure Chemistry Some comparison of these predictions is made with experimental data for aromatic hydrocarbons. 8 Organic Reactions Organic Synthesis.-Although most studies involving the use of high pressure in organic chemistry are made principally with the aim of elucidating the mechan- ism of reaction and the nature of the transition state the understanding which has come from such studies can be uscd in the preparative field. If the rate of a desired reaction is increased by pressure the product can be obtained in a shorter time or at a lower temperature (avoiding thermal decomposition) often in higher yieid by carrying out the process under pressure.Shortening of the reaction time is an important factor if the reactants are sterically hindered. (a) X = CHO Ac or C0,R; Y = NR (b) X = NR,; Y = CHO Ac or CO,R Scheme 1 In one research," a series of addition reactions (Scheme 1) were carried out at room temperature and at pressures between 8 and 20kbar. The reactants were contained in a berylliumxopper bellows and were allowed to react for times between 10min and 26 h. Twenty-four different reactions were tried. In all but five cases an enhancement of the rate was observed and yields in the region of 70 % were obtained. Kinetics and Mechanism.-Le Noble *' has published a very extensive review discussing the effect of pressure on the rates of chemical reactions.He lists the factors influencing the sign and magnitude of the activation volume and out- lines methods for making numerical estimates of this quantity. A classified tabulation is given containing details of 456 reactions whose rates have been measured as a function of pressure. Other reviewsg0 have appeared more recently ; that by Neuman considers free-radical initiator decompositions (homolytic scission reactions) while the article by McCabe and Eckert reports on the kinetics of cycloaddition reactions (Diels-Alder reactions) which have received much attention in recent years. [2 + 21 Cycloadditions are known to occur by a two-step mechanism the concerted mechanism being forbidden by orbital symmetry rules.However *' W. G. Dauben and A. P. Kozikowski J. Amer. Chem. SOC. 1974 % 3664. 89 W. J. Le Noble Progr. Phys. Org. Chem. 1968 5 208. 90 G. Kohnstamm Progr. Reaction Kinetics 1970 5 335 C. A. Eckert Ann. Rev. Phys. Chem. 1972 23,239; R. C. Neuman Accounts Chem. Res. 1972,5,381; J. R. McCabe and C. A. Eckert ibid. 1974 7 251. 164 B. Cleauer [4 + 21 additions can occur either by a two-step mechanism (i.e. one bond being formed first followed by the other the first step being rate-determining) or by a concerted mechanism in which both new bonds are formed simultaneously (see Scheme 2). These alternatives can often be distinguished by high-pressure studies the activation volume for the concerted mechanism being roughly twice that for the two-step route.Ignoring electrostriction and solvation effects the concerted two-step Scheme 2 expected values are -20 to -30 cm3 mol-' and -10 to -15 cm3 moll ' respectively (based on previous experience using the rules for estimating AV * to be found for example in ref. 89). For a wide range of [4+ 21 reactions A V * is in fact found to be between -30 and -45 cm3 mol- ',confirming the concerted mechanism. Sometimes AV* was more negative than AV for the total reaction. These secondary effects are indicative of interactions in the transition state which make it even more compact than the final product. This effect is particularly marked when there is an electron-donating group in the 1-position of the diene (e.g.Me or OMe). Such substituents also lower the activation energy signifi- cantly. When AV* is known the partial molar volume vmof the transition state can be calculated. If the actual volume v of the transition state can be estimated the dipole moment can be found using an equation due to J. G. Kirkwood Again 1-substituents such as Me and OMe have the biggest effect on polarity. However changes in solvent polarity have little effect and the reaction is con- sidered to be 'non-polar'. In some cases a [2 + 21 reaction and the [2 + 41 reaction occur simultaneously and pressure affects the two rate constants differently. In this situation product analysis is essential. The dimerization of chloroprene is such a case; for the [2 + 21 reaction AV* = -22 cm3 mol-' and for the [2 + 41 reaction AV* = -30 cm3 mol- '.The volume changes for reaction are -27 and -32 cm3 mol- respectively. These figures show clearly that only one bond is fully formed in the transition state of the [2 + 21 reaction. If the dienophile has a carbonyl group conjugated with the double bond AICl (or other Lewis acids) will complex with this and withdraw electrons from High-pressure Chemistry 165 the double bond. This promotes the rate of attack by the diene. In spite of the high polarity of the adduct which has led to the suggestion that the reaction is two-step high-pressure studies indicate that a concerted reaction takes place here also; for the addition of 2,3-dimethylbutadiene to n-butyl acrylate AV* is -29 cm3 mol-' for the uncatalysed reaction and -26 cm3 mol-' for the catalysed process.One recent studyg1 of an addition in which two competing reactions occur shows that great care must be exercised before one can draw the conclusion that the reaction with the greater pressure coefficient is the one involv- ing formation of the larger number of bonds. The reaction (Scheme 3) is the addi- + a,-& c1.4 Scheme 3 tion of tetrachlorobenzyne to norbornadiene. Previous experience suggests that the [2 + 2 + 21 reaction would have a more negative AV* than the [2 + 21 reaction. However the reverse was the case. The authors suggest that the reason for this unusual behaviour is that a highly polar (zwitterionic) transition state (1) is formed.This is consistent with an earlier observation that the product ratio is influenced by solvent polarity. As noted above this feature is absent in the majority of Diels-Alder reactions. Polymerization Reactions.-Wealeg2 has recently reviewed the influence of pressure on polymerization reactions. Apart from kinetic effects other physical effects of pressure such as freezing and phase separation are discussed. The other topics covered are radical polymerization radical addition and chain transfer 91 W. J. Le Noble and R. Mukhtar J. Amer. Chem. Soc. 1974 % 6191. 92 K. E. Weale in 'Reactivity Mechanism and Structure in Polymer Chemistry' ed. A. D. Jenkins and A. Ledwith Wiley Chichester 1974 Ch. 6. 166 B.Cleaver the effect of pressure on dissociation of radical initiators and ionic polymeriza- tion. In another the radical copolymerization of acenaphthalene (ACN) with methyl methacrylate (MMA) and with maleic anhydride (MA) was investi- gated in various solvents at pressures at up to 4 kbar. The effect of pressure on the relative rate of copolymerization was measured. For the ACN-MMA system the pressure dependence of the relative rate depends on the ratio of monomers initially present falling as the proportion of ACN is increased. For ACN-MA mixtures an alternating copolymer was found and the relative rate varied with pressure in a way which did not depend on the composition of the original mixture. The difference between the two systems is attributed to termination of growing chains in the ACN-MMA system by degradative transfer reactions with monomer yielding monomer radicals which are very inefficient at initiating new chains.In conclusion we note that J.C.S. Perkin Transactions parts I and 11 contained no reports on high-pressure work during 1974. We hope that 1975 will see greater use of high-pressure techniques by organic chemists. 93 M. N. Romani and K. E. Weale Brit. Polymer J. 1973 5 389.

ISSN:0308-6003    

DOI:10.1039/PR9747100141

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年代:1974

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PART II I N0RGANIC CHEMISTRY 9 Introduction By D. W. A. SHARP Department of Chemistry University of Glasgow Glasgow G 72 800 The general form of the 1974 Annual Reports (Vol. 71) on Inorganic Chemistry follows that of Volume 70 with the coverage of series of related complexes of transition elements and of properties that relate mainly to the ligand in a separate section rather than separately under each element. In Annual Reports specific note is taken of the existence of the Specialist Periodical Reports series and there- fore we do not attempt to provide a comprehensive coverage but rather to point out those aspects of inorganic chemistry which the Reporter feels are of particular significance. In particular we do not cover physical measurements on inorganic compounds unless these lead to significant advances in our under- standing of the structure or the bonding of the compound.Because of the necessity to keep down the length of articles in this year’s Report there has been a more conscious attempt to reduce the repetition of material between the various sections of the Report. This could mean that readers will need to consult sections other than those that they would normally use but we hope that in so doing they will find yet other information of use. Of necessity we generally exclude references to full reports when preliminary communications have already been mentioned in a previous volume of Annual Reports. We have cut down drastically on making references to review articles although a limited number of more general reviews on inorganic topics are listed in this introduction.Once again it is difficult to pick out areas of development for special mention but very significant advances continue to be made in the chemistry of the inter- action of olefins and polyolefins with metals and in the incorporation of metals and other heteroatoms into the cage structures of boranes and particularly of carbaboranes. One of the most interesting isolated observations is that Na- may be present in the product of the reaction between sodium metal and a cyclic polyaminoether (p. 172). It tends to be forgotten that addition of an electron to a gaseous atom is an exothermic process for most elements. Equally interesting is evidence for NaF and NaCl in the gas phase (p.244). Volume XV of Inorganic Syntheses is devoted principally to transition-metal compounds (including olefin dinitrogen triphenylphosphine complexes) al- though there are sections on phosphorus compounds and germanium hydride 169 D. W. A. Sharp derivatives.’ Volumes of Gmelin published during the year include coverage of oxygen (System number 3) transuranium elements (7) boron (13) carbon and organoiron derivatives (14) silicon (1 9,organonickel derivatives (17) lanthan- ides (39) tin (46) and silver (61). Amongst the more important books which have become available in 1974 should be mentioned volumes of thermodynamic data on inorganic chalcogenides,2 selenium and tell~rium,~ the actinides rare-earth inter metallic^,^ phosphine arsine and stibine comple~es,~ iron-sulphur pro-teins,’ organotransition-metal chemistry,’ and catalysis by metal cornplexe~.~ Amonst the more important general articles and reviews that have been published in 1974 are a revision of the M4+effective ionic radii,” reviews of the chemistry of the metallic elements in the ionosphere and mesosphere,’’ hydrogen bonding in solids,’ fluoride complexes in aqueous solution,’ ABX compound^,'^ the marcasite structure,” U.V.and X-ray photoelectron spectroscopy,’6 the effects of high pressure on the chemistry and spectra of inorganic compound^,'^ metalloboranes,’ metalloboroxanes,’9 various aspects of silicon chemistry,20 metalloenzymes,2 the relaxation of excited states of G. W. Parshall (Editor) Inorg.Synth. 1974 XV. ’ K. C. Mills ‘Thermodynamic Data for Inorganic Sulphides Selenides and Tellurides’ Butterworths London 1973. A. A. Kudryavtsev ‘Chemistry and Technology of Selenium and Tellurium’ Colletts London 1974. A. J. Freeman and J. B. Darby ‘The Actinides’ Vols. 1 and 2 Academic Press New York 1974. W. E. Wallace ‘Rare Earth Intermetallics’ Academic Press New York 1973. C. A. McAuliffe ‘Transition Metal Complexes of Phosphorus Arsenic and Antimony Ligands’ MacMillan London 1973. W. Lovenborg ‘Iron-Sulphur Proteins’ Vols. 1 and 2 Academic Press New York 1974. a R. F.Heck ‘Organotransition Metal Chemistry’ Academic Press New York 1974; P. W. Jolly and G. Wilke ‘The Organic Chemistry of Nickel’ Academic Press New York 1974.M. M. Taqui Khan and A. E. Martell ‘Homogeneous Catalysis by Metal Complexes’ Vols. I and 11 Academic Press New York 1974; P. N. Rylander ‘Organic Syntheses with Noble Metal Catalysts’ Academic Press New York 1974. lo 0.Knop and J. S. Carlow Canad. J. Chem. 1974,52,2175. T. L. Brown Chem. Rev. 1973 73 645. l2 A. Novak Structure and Bonding 1974 18 177. l3 G. Hefter Co-ordination Chem. Rev. 1974 12 221. l4 J. F. Ackerman G. M. Cole and S. L.Holt Inorg. Chim. Acra 1974 8 323. A. Kjekshus and T. Rakke Structure and Bonding 1974 19 85. I6 W. L. Jolly Co-ordination Chem. Rev. 1974 13 47; R. L. de Kock and D. R. Lloyd Adv. Inorg. Chem. Radiochem. 1974 16 66. l7 E. Sinn Co-ordination Chem. Rev. 1974 12 185; H. G. Drickamer Angew. Chem. Internat. Edn.1974 13 39. la N. N. Greenwood and I. M.Ward Chem. SOC.Rev. 1974 3 231. l9 S. K. Mehrotra G. Srivastava and R. C. Mehrotra J. Organometallic Chem. 1974 73,277. *O H. Burger R. Eujen G. Fritz F. Hofler and E. Hengge Topics in Current Chem. 1974 Vols. 50 and 5 1. ’I U. Weser R. R.Crichton M. Llinas and F. L. Siegel Structure and Bonding 1973 17. Introduction 171 transition-metal complexes,22 transition-metal complexes in cancer chemo-therapy,23 ligand effects on the kinetics of substitution and redox reactions,24 acid-catalysed reactions of transition-metal complexe~,~ perchlorate complexes,26 (CF,),N fluorinated peroxides,28 fluoros~lphates,~~ metal nitro- ~yls,~'transition-metal oxime derivative^,^' tripodal amine cornplexe~,~~ metalloprotein redox reactions,33 vitamin B systems,34 and cyanide phosphine complexes.35 22 M.K. De Armond Accounts Chem. Res. 1974 7 309. 2' M. J. Cleare Co-ordination Chem. Rev. 1974 12 349. 24 V. Gutmann and R. Schmid Co-ordination Chem. Rev. 1974 12 263. 25 P. J. Staples Co-ordination Chem. Rev. 1973 11 277. 26 L. Johansson Co-ordination Chem. Rev. 1974 12 241. ::H. G. Ang and Y. C. Syn Adv. Inorg. Chem. Radiochem. 1974 16 1. R.A. De Marco and J. M. Shreeve Adv. Znorg. Chem. Radiochem. 1974 16 110. 29 A. W. Jache Adv. Znorg. Chem. Radiochem. 1974 16 177. 30 J. H. Enemark and R. D. Feltham Co-ordination Chem. Rev. 1974 13 539. 31 A. Chakravorty Co-ordination Chem. Rev. 1974 13 1. 32 S. G. Zipp A. P. Zipp and S. K. Madan Co-ordination Chem. Rev. 1974 14 29. 33 L. E. Bennett Progr. Inorg. Chem. 1973 18 1. 34 D. G. Brown Progr. Inorg. Chem. 1973 18 177. 3s P. Rig0 and A. Turco Co-ordination Chem. Rev. 1974 13 133.

ISSN:0308-6003    

DOI:10.1039/PR9747100167

出版商:RSC    

年代:1974

数据来源: RSC