3 Theoretical Chemistry By G. KLOPMAN and P. ANDREOZZI Chemistry Department Case Western Reserve University Cleveland Ohio 44106 U.S.A. 1 Introduction In this chapter we review three major areas in which quantum mechanical methods have been extensively applied in the past year. The topics include the electronic structure and conformation of molecules where the contributions of quantum mechanical methods have now found widespread acceptance; the theoretical study of dynamic processes which is becoming a popular area thanks to improved computational techniques that allow the determination of fairly accurate reaction hypersurfaces; and finally the study of molecular associations which is one of the most promising new areas of quantum mechanical research.Indeed with the development of more sophisticated theoretical techniques methods are now availa- ble for investigating ‘supermolecules’ consisting of two or more aggregated molecules as in a solute-solvent cluster. 2 Electronic Structure and Conformation of Molecules Structural Properties.-Ab initio methods with extended basis sets and varying level of configuration interaction continue to be applied to the calculation of the proper- ties of the ground and excited states of small molecules. The structure of xenon difluoride has been investigated by Bagus et al.’ They found the bond distances and dissociation energies to be in reasonable agreement with the experimentally determined values. The molecular structures of ClF and ClF radicals and their ions have been investigated by Ungemach and Schaefer.2 The geometries of the ions were compared with those of the isoelectronic sulphur fluorides and interesting disparities were found.Nitrogen derivatives seem to have been particularly popular and several calculations have been published notably on the electronic structure and geometry of N2H,3 N2H2, HN02,6and NOCl and NCC1.’ The bulk of the calculations however remain associated with organic molecules. In the small carbon-containing systems these studies often aim at determining the ’ P. S. Bagus B. Liu D. H. Liskow and H. F. Schaefer tert. J. Amer. Chem. SOC. 1975,97 7216. * S. R. Ungemach and H. F. Schaefer tert. J. Amer. Chem. SOC.,1976,98 1658. 3 K. Vasudevan S. D. Peyerimhoff and R. J. Buenker J.Mol. Structure 1975,29 285. R. Ahlrichs and V. Staemmler Chem. Phys. Letters 1976 37 77. C. F. Jackels and E. R. Davidson J. Chem. Phys. 1975,63 4672. 6 S. Skaarup and J. E. Boggs J. Mol. Structure 1976,30 389. 7 A Stagard Chem. Phys. Letters 1976,40 429. 23 24 G.Klopman and P.Andreozzi geometries and wavefunctions of the ground and low-lying excited states. Examples of such calculations are those performed on CH2,8 CH0,9 HCHO," and NH2CH0.l1 The interaction between two substituents on the same carbon atom has recently attracted the attention of several research groups. Nielssen and Skancke12 found that the planar form of CH2Li2 is only 8.7 kcal mol-' less stable than the tetrahedral one. A systematic study of a large series of CH2XY molecules where X and Y can be any of the Li BeH BH2 CH3 NH2 OH or F groups was presented by Dill Schleyer and P0p1e.l~ These authors found large bond-separation energies (for the isodesmic reaction XCH2Y + CH -+CH3X+ CH3Y) only if both substituents were strongly electronegative or both strongly electropositive.Rotational barriers have also been discussed in the cases where Y is either BH or NH,. Barriers to internal rotation have also been determined in the groundl4 and excited states of glyoxal (OHC-CHO)." In the ground state the trans-form was found to be 5.9kcalmol-' more stable than the cis-form. The structure of ethylidene (CH3-CH) and its transformation into ethylene was studied by Gordon et a1.,16using MIND0/2 and INDO methods and by Altman et al.," from an ab initio viewpoint.MIND0/2 finds no energy minimum for singlet ethylidene while INDO predicts a non-classical bridged structure (l),and the ab initio calculations point towards a classical staggered geometry (2). Other small organic systems of interest have been investigated such as methyleneimide and its fluoro-derivatives,18 keten,19*20 and acrolein21 (both in the ground and excited states) md trimethylenemethane.22 Single-determinant ab initio MO theory has also bgen applied to all possible singlet and triplet states of the C3H2 isomers23 and to C4 hydrocarbon^.^^ The structure of cyclobutadiene continues to arouse controver~y.~~*~~ The latest entry is a Multi Configuration LCAO-MO calculation by Nakayama et ~l.,~' H HH H -H-'H H (1) (2) * J.H. Meadows and H. F. Schaefer tert. J. Amer. Chem. SOC.,1976,98,4383. 9 P. I. Bruna R. J. Buenker and S. D. Peyerimhoff J. Mol. Structure 1976,32 217. 10 L. B. Harding and W. A. Goddard tert. J. Amer. Chem. SOC.,1975,97,6293. 11 L. B. Harding and W. A. Goddard tert. J. Amer. Chem. Soc. 1975 97 6300. " E. W. Nielssen and A. Skancke J. Organometallic Chem. 1976 116 251. 13 J. D. Dill P. von R. Schleyer and J. A. Pople J. Amer. Chem. SOC.,1976,98 1663. 14 C. E. Dykstra and H. F. Schaefer tert. J. Amer. Chem. SOC.,1975,!?7 7210. 15 C. E. Dykstra and H. F. Schaefer tert. J. Amer. Chem. SOC., 1976 98 401. 16 M. S. Gordon P. M. Saatzer and R. D. Koob Chem. Phys. Letters 1976 37 217. 1' J. A. Altmann 1. G. Csizmadia and K. Yates Chem. Phys.Letters 1976,41 500. 18 J. M. Howell J. Amer. Chem. SOC.,1976 98 886. 19 L. B. Harding and W. A. Goddard tert. J. Amer. Chem. SOC.,1976,98 6093. 20 C. E. Dykstra and H. F. Schaefer tert. J. Amer. Chem. SOC.,1976 98 2689. 21 C. E. Dykstra J. Amer. Chem. SOC., 1976,98 7182. 22 W. T. Borden J. Amer. Chem. Soc. 1976,98 2695. 23 W. J. Hehre J. A. Pople W. A. Lathan L. Radom E. Wasserman and A. R. Wasserman J. Amer. Chem. SOC.,1976,98 4378. 24 W. J. Hehre and J. A. Pople J. Amer. Chem. SOC.,1975 97 6941. 25 W. T. Borden J. Amer. Chem. SOC., 1975,97 5968. 26 R. C. Haddon and G. R. J. Williams J. Amer. Chem. SOC.,1975,97,6582. z7 M. Nakayama M. Nishihira and Y. J. I'Haya Bull. Chem. SOC.Japan 1976,49 1502. Theoretical Chemistry indicating not only that a Jahn-Teller distortion favours a rectangular (&) ground state (by 0.3-0.9 eV) but that even in the square form (D4,,), the singlet would be more stable than the triplet by ca.0.3 eV. The influence of single methyl and fluoro substituents on the conformation of cyclopentane and cyclohexane was studied by Cremer Binkley and Pople.28 They found that methyl groups tend to exist in the equatorial positions while the fluoro-group prefers the equatorial position in cyclohexane but the axial position in cyclopentane. The importance of non-bonded attractions in determini g the prefer- .~~ red conformation of molecules has been stressed by Epiotis et ~ 1 Thee showed that the preferred geometry depends not only on steric effects but also on one-electron non-bonded attractive effects that are determined by the symmetry of the inherent orbitals.The structures of various ketones have been investigated by several groups. Fitzpatrick and Fanning using STO-3G found that the length and dipole of the CO bond in disubstituted cyclopropenones reflect both the n-and cr-effects of the s~bstituents.~' The influence of substituents on the electron density of the oxygen of the CO bond of a series of compounds of the type X-Ar-COR was also investigated but here a CND0/2 approximation was ~sed.~' A large number of ring systems containing one or more heteroatoms have also been investigated recently. The MIND0/3 method was used to study the stability of a series of possible intermediates in the u.v.-initiated decomposition of (3).32 The reaction occurs with loss of C02 and is believed to yield the lactone (4) rather than (5).The stabilities and geometries of a number of meso-ionic species derived from m oxazole and imida~ole~~ were also calculated with MIND0/3. The meso-ionic compounds were found to be highly polar and much less stable than their classical counterparts. The technique of using molecular fragments in the ab initio calculation of large .~~ molecules was used by Christoffersen et ~ 1to calculate with some success various properties of the ground and excited states of carbazole. The electronic structures of phosphole (6)35and thieno[3,4-~]thiophen (7)36were also studied but by semi- empirical methods only. Both systems are postulated to be aromatic despite their unusual geometrical constraints.Phosphole possesses a pyramidal structure and is aromatic only because strong hypercon jugation exists between the PR orbital and 28 D. Cremer J. S. Binkley and J. A. Pople J. Amer. Chem. Soc. 1976,98 6836. 29 N. D. Epiotis R. L. Yates and F. Bernardi J. Amer. Chem. SOC. 1975,97 5961. 30 N. J. Fitzpatrick and M. 0.Fanning J. Mol. Structure 1976 33 257. 31 D. Beauptre J. P. Stguin R. Urzan and J. P. Doucet Canad. J. Chem. 1976 54 297. 32 C. S. C. Chung J. Mol. Structure 1976 30 189. 33 M. J. S. Dewar and I. J. Turchi J.C.S. Perkin 11 1976 548. 34 L. E. Nitzche C. Chabalowski and R. E. Christoffersen J. Amer. Chem. Soc. 1976,98,4794. 35 W. Schafer A. Schweig and F. Mathey J. Amer. Chem.Soc. 1976,98 407. 36 C. Muller A. Schweig M. P. Cava andM. V. Lakshmikantham J. Amer. Chem. SOC.,1976,98,7187. G. Klopman and P.Andreozzi R the 7r-system of the cis-butadiene fragment. In the case of the thienothiophen it is found that although the 7r-system is strongly stabilized (aromatic) the molecule as a whole is not particularly stable because of the unfavourable arrangement of its molecular orbitals. The ability of the sulphur atom to interact with 7r-systems has also been considered by Chen and Hoffman37 in a study of the structure of sulphurane SR,. The molecule which is found to exist in a C, geometry (B) bears many similarities to the corresponding phosphorane molecule. Both seem to generate the same axial preference for electronegative substituents.However the site preference of 7r-substituents is different in the two molecules presumably because of the presence of the lone pair in an equatorial position of the sulphurane. 0 R -Sb-R (axial) 4 '*. R R (equatorial) Carbocations. Both semi-empirical an ab initio methods continue to be used to calculate the structure of carbocations. Thus it was found to no one's surprise that both CH3+ and CH2F+ cations tend to ex% in a planar form.38 On the other hand the structure of the ethyl cation (C2Hs+) continues to be debated. Thus the energies of both the classical and hydrogen-bridged structures were calculated using various quantum methods and evaluated with respect to each other by Heidrich and his collaborators.39 Wilcox et aL40not only calculated the stability of the bridged ethyl cation but also determined the stretching force constants that apply to the migrating hydrogen atom.This calculation allowed an estimate to be made of the deuterium kinetic isotope effect to be observed in the reactions involving the ethyl cation. The stabilities of the classical and hydrogen-bridged vinyl cation (C&+) were also The a6 initio plus CI indicated that both structures are equally stable. Finally it was also found by STO-3G and 4-31G methods that among the various isomers of the C3H3+ cation,,' the most stable is the cyclopropenium ion (9) H H 3-1 M. M. L. Chen and R. Hoffmann J. Amer. Chem. SOC.,1976,98 1647. 38 J. Burdon D. W. Davies and G. D. Conde J.C.S. Perkin ZI 1976 1193.39 D. Heidrich M. Grimmer and H. J. Kohler Tetrahedron 1976 32 1193. 40 C. F. Wilcox I. Szele and D. E. Sunko Tetrahedron Letters 1975 4457. 41 J. Weber M. Yoshimine and A. D. Mclean J. Chem. Phys. 1976,64,4159. 42 L. Radom P. C. Hariharan J. A. Pople and P. von R. Schleyer J. Amer. Chem. Soc. 1976.98 10. 27 Theore tica 1 Chemistry +CH,-C~CH followed at ca. 34 kcal mol-’ by the propargyl cation (10). A similar study involving C2H6N+ isomers resulted in the following order of ~tabilities:~~ Other interesting studies involving carbocations include the STO-3G/4-3 1G calcu- lation of the electronic structure of the phenyl cation44 and that of a series of pyridylmethyl and pyrimidylmethyl cations by an INDO appr~ximation.~~ Carbanions Carbenes and Free Radicals.Owing to the difficulties associated with electron correlation carbanions are among the most difficult carbon derivatives to be studied by ab initio methods. Although some studies have been undertaken most attempts to determine the structural characteristics of carbanions are made by semi-empirical methods. For example the MIND0/2 method was used by Shan~hal~~ to determine the structure energy and barrier to pyramidal inversion of a series of cyclic carbanions ranging from the cyclopropyl to the norbornyl carbanion. A modified Pariser-Parr-Pople program was also used to calculate the electron affinity of a series of conjugated systems including some with heteroatom~.~’ An excellent correlation was found between the energy of the lowest unoccupied MO and some recently obtained values of adiabatic electron affinities.The electronic structure of carbenes presents an equally interesting challenge. The difficulty here comes from the degeneracy of the frontier orbitals resulting some- times in the existence of a triplet ground state. Unrestricted Hartree-Fock calcula- tions are often applied to this problem and this has been done again by Takabe el ~l.,~* using a MIND0/2’ framework to determine the electronic properties of CH2 CHF and CF,. It was shown however that a simple analysis can be sufficient to determine most properties or at least the trends in properties of carbene~.~~ Indeed Liebman Politzer and Sanders showed that their method of structural fragments allows valuable information to be gained about the species merely by counting the number of electrons in the appropriate fragments.Amongst relatively few studies of moderately sized free radicals Rossi and WoodS0 examined the conformational preferences of p -substituted alkyl radicals. They found that hyperconjugative substituents tend to favour eclipsed conforma- tions while bulky substituents prefer quite predictably a staggered arrangement. Barriers to Inversion and Rotation.-The relation between the barrier to inversion of AH3 molecules and the nature of the central atom A has been discussed in terms of 43 F. Jordan J. Phys. Chem. 1976,80 76. 44 J. D. Dill P. von R. Schleyer J. S. Binkley R. Seeger J. A. Pople and E. Haselbach J. Amer. Chem. SOC.,1976,98 5428.” C. U. Pittman M. R. Smith G. D. Nichols K. Wuu Shing and L. D. Kispert J.C.S. Perkin 11 1975 1515. 46 M. Shanshal Z. Naturforsch. 1976 3111,494. 47 J. M. Younkin L. J. Smith and R. N. Compton Theor. Chim. Acta 1976,41 157. 48 T. Takabe M. Takahashi and H. Fukutome Progr. Theor. Phys. 1976,56 349. 49 J. F. Liebman P. Politzer and W. A. Sanders J. Amer. Chem. SOC.,1976,98 5115. A. R. Rossi and D. E. Wood I. Amer. Chem. SOC.,1976,98 3452. 28 G.Klopman and P.Andreozzi Walsh-type diagrams" and one-electron MO An ab initio method has been used to calculate an inversion barrier of 2.6 kcal mol-' for dimethylamine and of 3442 kcal mol-' for diff oro oar nine,^^ the value of 42 kcal mol-' being obtained when the nitrogen d-orbitals were included in the basis set.The inversion barriers of a series of simple amines have also been calculated by several semi-empirical methods,54 but in general they compared poorly with the experimentally deter- mined values. The deformation of methane has been investigated at a STO-3G and 4-31G level and the deformation modes were related to those involved in the formation of a few small-ring The intriguing possibility of finding stable tetraco-ordinated planar carbon systems has been investigated by a STO-3G method.56 It was found that several systems might indeed be more stable in a planar configuration than in the ordinary tetrahedral one. Among these the most favourable structures appear to be the planar 1,l-dilithiocyclopropane(1 l) more stable than the tetra- hedral form by 7 kcal mol-' and the planar 3,3-dilithiocyclopropene (12) stabilized by ca.10 kcal mol-'. The dilithio-derivatives also exhibit extraordinary structural properties in other respects; for example the 1,l-dilithioethylene molecule tends to exist as a triplet in a perpendicular geometry (13).57 H Li Li Li H Li (11) (12) (13) The barrier to internal rotation has been studied in several more derivatives such as in nitrous and in a series of molecules of the type XH3YH3,where X and Y were C Si or Ge.59 The ability of the MIND0/3 method to predict rotational barriers and ring puckering of strained ring compounds was tested by Combs and his collaborators. Barriers on all systems studied were under-estimated by MIND0/3 as well as by its predecessors.60 However a re-parameterization of the INDO technique gave dramatically improved results.61 The relative energies of several conformers of 1,3-diene~~~ have been calculated by ab initio and cy~lohexane~~ methods while the use of the PCILO method demonstrated that dimethylcyclohep- tan one^^^ prefer to exist in twist-chair conformations.The early semi-empirical methods rarely provide a satisfactory quantitative measure of internal rotation energies yet for large systems their results are often 51 C. C. Levin J. Amer. Chem. SOC.,1975,97 5649. 52 W. Cherry and N. Epiotis J. Amer. Chem. SOC.,1976,98 1135. 53 S. Skaarup L. L. Griffin and J. E. Boggs J. Amer. Chem. Soc. 1976,98 3140. 34 K. Ohkubo Y. Azuma and M. Okada Bull. Chem. SOC.Japan 1976,49,1397.55 K. B. Wiberg G.B. Ellison and J. J. Wendoioski J. Amer. Chem. Soc. 1976,98 1212. s6 J. B. Collins J. D. Dill E. D. Jemmis Y. Apeloig P. von R. Schleyer R. Seeger and J. A. Pople J. Amer. Chem. SOC.,1976,98 5419. 57 Y. Apeloig P. von R. Schleyer J. S. Binkley and J. A. Pople J. Amer. Chern.Soc. 1976,98,4332. 58 P. Benioff D. Gurupada and A. Wahl J. Chem. Phys. 1976,64 710. 39 G. Nicolas J. C. Barthelat and Ph. Durand J. Amer. Chem. SOC.,1976,98 1346. 60 L. L. Combs and M. Rossei J. Mol. Structure 1976 32 1. 61 L. L. Combs and M. Holloman J. Mol. Structure 1976 33 289. 62 A. J. P. Devaquet R. E. Townshend and W. J. Hehre J. Amer. Chem. Soc. 1976,98,4068. 63 T. D. Davis and A. A. Frost J. Amer. Chem. SOC.,1975,97 7410. 64 M. St.-Jacques C.Vaziri D. A. Frenette A. Goursot and S. Fliszar J. Amer. Chem. SOC.,1976 98 5759. Theoretical Chemistry qualitatively useful. Thus CND0/2 calculations have been carried out to determine the molecular conformation of phenylcyclopropane and those of various of its hetero-substituted derivatives (14),65of benzoyl(diazo)phenylmethane (15),% of di-2-pyridyl sulphide (16),67and of a series of phosphate esters.68 The effect of optimization of the geometry of the conformers on the rotational barriers was seen to be of fundamental importance in an INDO study of butadiene glyoxal benzal- dehyde and 2,2’-difl~orobiphenyl.~’ (14) X =CH2 0,S NH or CC12 (15) (16) Semi-empirical potential mapping is becoming an important tool in the arsenal of theoreticians interested in the chemical behaviour of biologically important molecules.The influence of the molecular configuration of a molecule on the potential field seen by an approaching reagent is a particularly significant problem that can be studied by such a technique. Jordan7’ applied it to the study of 2-(a!-hydroxyethyl)thiamine (17) in an effort to assess the importance of a sub- stituent at position 2. Me OH (17) In another study related to natural products Popkie Koski and Kaufman’l presented an impressive ab initio calculation of the conformation of morphine and some if its derivatives. The eigenvalues were in satisfactory agreement with rneas- ured photoelectron spectral data and the charge densities were compatible with experimental ESCA results.A report on theoretical conformational analysis would not be complete without mention of some of the excellent work performed with the force-field or molecular- mechanics methods. These methods are extremely powerful in dealing with confor- rnational problems and can easily be used to study very large systems. However these techniques are still in their infancy and considerable work is now aimed at 6s S. Sorriso and F. Stefani J.C.S. Perkin 11 1976 374. S. Sorriso and A. Stggard J.C.S. Perkin 11 1976 538. 67 C. Chachaty G. Pappalardo and G. Scarlata,J.C.S. Perkin 11 1976 1234. 68 D. G. Gorenstein D. Kar B. A. Luxon and R. K. Momii J. Amer. Chem. SOC.,1976,98 1668. 69 J. C. Rayez and J. J. Dannenberg Chem. Phys. Letters 1976,41,492.70 F. Jordan J. Amer. Chem. SOC.,1976,98 808. H. E. Popkie W. S. Koski and J. J. Kaufman J. Amer. Chem. SOC.,1976,98 1342. G.Klopman and P. Andrmzzi developing appropriate potential functions mostly for non-bonding intera~tion,~~ such as the H--H potential.73 The methods however provide rapid and often reliable values for the conformational energies of hydrocarbons and have recently been used to calculate the most favourable conformations of sterically hindered hydrocarbon^,^^ 1,2-disubstituted ethane~,~' and a series of alcohols and ether^,'^ the latter with mitigated success. A unique case has been described by Hagler et aZ.,77 where both ab initio and molecular mechanics methods were used to determine the barriers to rotation about the N-C and C-C bonds (4 and 4)in amides and peptides (18).The values of 4 and 4were determined experimentally to be 180"and O" respectively. Interestingly enough both theoretical methods yielded the correct value for 4 but both also gave an incorrect value for (I. 3 Theoretical Studies of Dynamic Processes Isomerization Reactions.-The possible rearrangement paths of cyclopropane have been It was found that the radical cation79 opens along a disrotatory mode and then fragments into CH,*+ and ethylene. The fragmentation into CH and CH2=CH2*+ is energetically more favourable but could occur only along a forbid- den pathway. The degenerate circumambulatory rearrangement of the homocyclo- propenyl cation (19)has been investigated by Hehre and Devaquet" and explained as being due to subjacent orbital control.Jorgensen'l performed MIND0/3 calculations for various conformations of trishomocyclopropenyl cations (20) and found that the most favourable rearrangement yields (21) rather than (22). The (19) (20) (21) (22) photochemical disrotatory ring closure of butadiene has been investigated by an ab initio method,82 and the possible rearrangements of C6HIo hydrocarbons have been studied by MIND0/2." In the latter case 1,4-cyclohexylene (23) emerged as the 72 S. Fitzwater and L. S. Bartell J. Amer. Chem. SOC.,1976 98 5107. 73 D. N. J. White and M. J. Bovill J. Mol. Structure 1976 33 273. 74 H. Braun and W. Luttke J. Mol. Structure 1976 31 97. 75 A. W. Burgess L. L. Shipman R. A. Nemenoff and H. A. Scheraga J.Amer. Chem. SOC.,1976,98,23. 76 N. L. Allinger and D. Y. Chung J. her. Chem. SOC.,1976,98,6798. 77 A. T. Hagler L. Leiserowitz and M. Tuval J. Amer. Chem. SOC.,1976 98 4600. 78 X. Chapuisat and Y. Jean J. Amer. Chem. Soc. 1975,97,6325. 79 S. Beran and R. Zahradnik Coll. Czech. Chem. Comm. 1976,41 2303. 80 W. J. Hehre and A. J. P. Devaquet J. Amer. Chem. SOC.,1976,98,4370. 81 W. L. Jorgensen Tetrahedron Letters 1976 3029. 82 D. Grimbert G. Segal and A. Devaquet J. Amer. Chem'. Soc. 1975.97,6629. 83 A. Komornicki and J. W. McIver jun. J. Amer. Chem. Soc. 1976,98 4553. Theoretical Chemistry central structure involved both in the Cope rearrangement of hexa- 1,5-diene (24) and in the cleavage and inversion of bicyclo[2,2,0]hexane (25). (23) (24) (25) Ab initio methods have been used in studies of other ring formations.The energy of the oxiren molecule (26) postulated to be an intermediate in the Wolff rearrangement was shown to be 11.8 kcal mol-' greater than that of the isomeric formylmethylene molecule (27) and the interconversion ring-opening reaction was (26) (27) found to carry an activation energy of 7.3 kcal m01-l.'~ A study of the interconver- sion of the azido-tetrazole (29) has also been made.85 From the STO-3G results it was postulated that polar solvents should activate the cyclization reaction in spite of the fact that the open chain possesses more charge separation. (28) (29) The cis-trans isomerization of diazenes (R'-N=N-R2) was investigated by an ab initio method by Howell and Kirschenbaum.86 They found that unless both R' and R2 are fluorine atoms the trans-form is always favoured.cis-trans Isomeriza- tion was seen to occur by inversion rather than rotation. Some tautomerism equilibria have also been investigated recently; the CND0/2 method was used to study the enamine-imine equilibriums7 and the use of the INDO technique allowed Westhof and Flossman8' to postulate that the imidazole radical anion generated within an argon matrix by photoelectron transfer is in reality the radical (30) obtained by addition of H to C-5 of imidazole and not the (Y -pyrrolamine (31). (30) (3 1) Cycloaddition Reactions.-Cycloaddition reactions are among the most amenable to theoretical calculations and continue to arouse the interest of theoreticians.84 0.P. Strausz R. K. Gosavi A. S. Denes and I. G. Csizmadia J. Amer. Chern. Suc. 1976,98 4784. L. A. Burke J. Elguero G. Leroy and M. Sana J. Amer. Chem. Suc. 1976,98 1685. 86 J. M. Howell and L. J. Kirschenbaum J. Amer. Chem. Suc. 1976,98 877. 87 J. Teysseyre J. Arriau A. Dargelos J. Elguero and A. R. Katritzky Bull. SUC.chim. belges 1976,85 39. 88 E. Westhof and W. Flossmann J. Amer. Chem. Suc. 1975 97 6622. G. Klopman and P.Andreozzi Several tudies have been carried out for 1,3-dipolar cycloaddition reactions such as the addision of a carbonyl-ylide to ethylene*’ and the ozonolysis of 01efins.~**~’ Ab initio calculations using STO-3Gand 4-3 1G basis sets have also been carried out for the 1,3-dipolar additions of fulminic acid (HCNO) to ethylene acetylene ethynamine and pr~pynenitrile.~~ These calculations indicated that as predicted by the rules of conservation of symmetry the reactions occur along a synchronous path.It was also found that the geometry of the transition state is insensitive to substitu- tion. The forbidden 2 +2 cycloaddition reaction has also received some attention. Epiotis et ~21.~~ found in contrast to experimental results that the most favourable path for approach by the two cycloaddends of a polar 2+2 reaction is along a transoid configuration. Tatsumi and his ~011aborator~’~ found in their study of the metal-catalysed 2 +2 cyclodimerization of ethylene and acetylene that the rectan- gular approach of the reagents is accompanied by the appearance of significant biradical character.This occurred in spite of the fact that the transition-metal catalyst removed the formal restrictions imposed by orbital symmetry on the geometry of the transition state. Finally an interesting study of the effect of cyano substituents in dienophiles on the rate of 2 +4 cycloadditions has been reported by Houk and M~nchausen.~~ Protonation Reactions.-The protonation of benzene to form a Wheland inter- mediate has been studied by several groups. Ermler Mulliken and Clemer~ti~~ have determined the geometry of the benzenium ion using a large contracted gaussian basis set. They also determined a value of 189 kcal mol-’ for the proton affinity of benzene as compared with an experimental value of 183.1 kcal mol-’.The proton affinity of benzene as well as those of toluene and other benzene derivatives has also been calculated by Gleghorn and McConkey using the MIND0/2’ techniq~e,~’ and by Devlin et al.98 and McKelvey and his collaborator^,'^ using the STO-3G method. In the latter study,99 the authors found that there is a good correlation between the AE value for the isodesmic process [equation (l)] and the value of sigma plus (Brown’s sigma values) used to correlate electrophilic aromatic substitution. X X 89 G. Leroy M.-T. Nguyen and M. Sana Tetrahedron 1976,32 1529. 90 P. C. Hiberty J. Amer. Chem. SOC.,1976,98,6088. 91 G. Leroy and M. Sana Tetrahedron 1976,32 1379. 92 D. Poppinger Austral. J. Chem. 1976,29,465. 93 N. D. Epiotis R.L. Yates D. Carlberg and F. Bernardi J. Amer. Chem. SOC.,1976,98 453. q4 K. Tatsumi K. Yamaguchi and T. Fueno Tetrahedron 1975,31 2899. 9s K. N. Houk and L. L. Munchausen J. Amer. Chem. SOC.,1976,98,937. 96 W. C. Ermler R. S. Mulliken and E. Clementi J. Amer. Chem. SOC. 1976,98,388. 97 J. T. Gleghorn and F. W. McConkey J.C.S. Perkin IZ 1976 1078. 98 J. L. Devlin tert. J. F. Wolf R. W. Raft and W. J. Hehre J. Amer. Chem. SOC.,1976 98 1990. 99 J. M. McKelvey S. Alexandratos A. Streitwieser jun. J. L. M. Abboud and W. J. Hehre J. Amer. Chem. SOC.,1976,98,244. TheoreticaI Chemistry 33 Other protonation studies include that of cyclobutane,'OO where an ub initio calculation found both the edge- and corner-protonated forms to be essentially similar in energy and lying 126 kcalmol-' below that of cyclobutane and a proton.Although this value is quite large it is still significantly lower than that found for cyclopropane and is thus consistent with the fact that protonated cyclobutane is seldom seen experimentally. The electronic structure of protonated methanol has been studied by Flood and Nilssen,'" and that of methyl-anisoles by Greenberg and collaborators,102 who found predominance of ring protonation over oxygen protona- tion for all three anisole isomers. Protonation at oxygen has been found to be energetically more favourable than N-protonation in urea,1o3 and C-protonation is favoured over N-protonation in dia~omethane.''~ The proton affinity of a series of amines has been measured by an equilibrium ion cyclotron resonance technique by Aue and his c~llaborator~''~ and found to correlate reasonably well with values from ab initio and CNDO calcula-tions.The influence of alkyl substituents on the proton affinity of a series of amines as well as alcohols and ethers was also investigated by Umeyama and Morokuma,106 by the energy-decomposition technique using an ab initio method. They found the order of proton affinity to be controlled predominantly by the inductive and polarization stabilization effects of the methyl groups attached to the protonated atom. Finally MO calculationsof the controversial BHS molecule the protonated form of BH4- continue to be performed. BH5 is isoelectronic with CHSC and while in the SCF approximation it is found to be unstable with respect to BH3 and H2,107 the inclusion of correlation energy yields a slightly bonding situation (ca.2 kcal mol-') in the C,configuration."* Nucleophilic Substitution Reactions.-The SN2reaction path has been investigated by Dannenberg"' for the reactions between water and protonated alcohols and between F-and alkyl fluorides. The results obtained from an INDO method seem to over-emphasize hydrogen bonding in the transition state. Keil and Ahlrichs,"' using an ab initio method studied several SN2reactions of the kind ACH,+ B-+ A-+ CH3B where A and B are H F or C1. They found that electron correlation contributes up to 7 kcal mol-' to the activation energy and consequently should not be neglected. The importance of non-bonded attraction in the stereochemistry of the SN2'reaction has been emphasized by Yates et aZ.," while De Tar and Tenpas112 showed using molecular mechanics that steric hindrance must be taken into account in order to correlate the rate of ester hydrolysis.loo T. Pakkanen and J. L. Whitten J. Amer. Chem. SOC.,1975,97,6337. lol E. Flood and E. W. Nilssen J. Mol. Structure 1976 30 129. lo* R. S. Greenberg M. M. Bursey and L. G. Pedersen J. Amer. Chem. SOC.,1976.98 4061. Io3 Y.A. Panteleev and A. A. Liporskii Zhur. strukt. Khim. 1976.17 2. lo4 H. M. Niemeyer Helu. Chim. Acta 1976 59 1133. loS D. H. Aue H. M. Webb and M. T. Bowers J. Amer. Chem. SOC.,1976,98 311. lo6 H. Umeyama and K. Morokuma J. Amer. Chem. SOC.,1976,98,4400. lo7 I. M. Pepperberg T. A. Halgren and W.N. Lipscomb J. Amer. Chem. SOC.,1976,98 3442. Io8 C. Hoheisel and W. Kutzelnigg J. Amer. Chem. SOC.,1975,97 6970. lo9 J. J. Dannenberg J. Amer. Chem. SOC.,1976 98 6261. 110 F. Keil and R. Ahlrichs J. Amer. Chem. SOC.,1976 98 4787. R. L. Yates N. D. Epiotis and F. Bernardi J. Amer. Chem. SOC., 1975 97 6615. 112 D. F. DeTar and C. J. Tenpas J. Amer. Chem. Soc. 1976 98 4567. 34 G.Klopman and P.Andreozzi Nucleophilic attack on carbonyl systems has also been investigated by MO methods. For example Lipscomb and his ~~llaborator~"~ studied the reactions of F- and OH- with FCHO NH,+HCHO and CH,O-+H,NCHO with a minimal basis set using the PRDDO procedure. A complete potential surface for the reaction between OH- and H2NCH0 has been calculated by Tomasi et by a STO-3G procedure.They found that the tetrahedral intermediate is 104 kcal mol-' more stable than the reagents in the gas phase. The nucleophilicity of the hydride ion has been investigated by Allen et al."' in the POH3+H-reactions and by Olah et al.' l6 in the H4Nf +H- reaction. In both cases a trigonal bipyramidal intermediate is postulated where the central atom (P and N respectively is pentaco-ordinated (32) and (33). In the case of the phosphine oxide it was also found that the oxygen prefers to exist in the equatorial position [see (32)] rather than in the axial position [see (34)]. HH HH HO \I \I P-0 N-H 'PLH ,// I // I /' I HH HH HH The aromatic nucleophilic substitution reaction has also received some attention as Epiotis and Cherry"' showed that a perturbation method allowed them to rationalize the substitution pattern encountered in molecules of the type C&Y where X is a halogen and Y any other substituent.Dissociation and Recombination Reactions.-Ab initio calculations have been used to study the dissociation of diazomethane"* into CH,('A,) and N, of keten'" into CH and CO and the insertion reaction of CH into H2 to give methane.',' The interaction of H2 with a large series of Lewis acids (H+ Li' BeH' . . . )has also been investigated,12' and binding energies were found to range from high values of 109.5 kcal mol-' for the system H2+H' and 43.2 kcal mol-' for H,+CH,' to low values of 2-5 kcal mol-' for H2 +BeH' BH2+ LiH and BH,. In general it was found that the ability of electron-deficient species to bind a hydrogen molecule is entirely governed by charge polarizability.The photodissociation of formaldehyde into H2and CO was seen to proceed with an activation energy of 4.5 eV.12* Since this value is considerably larger than the experimentally determined threshold energy (3.66 eV) it was suggested that either energy pooling occurs to produce H2C0 with energy in excess of the exciting radiation or that dissociation occurs uiu a catalysed bimolecular pathway. 113 S. Scheiner W. N. Lipscomb and D. A. Kleier J. Amer. Chem. SOC., 1976 98 4770. 114 G. Alagona E. Scrocco and J. Tomasi J. Amer. Chem. SOC.,1975,97,6976. 115 C. A. Deakyne and L. C. Allen J. Amer. Chem. SOC.,1976,98,4076. 116 G. A.Olah D. J. Donovan J. Chen and G. Klopman J. Amer. Chem. SOC.,1975 97 3559. 117 N. D. Epiotis and W. Cherry J. Amer. Chem. SOC. 1976 98 5432. 118 J. Lievin and G. Verhaegen Theor Ckim. Acta 1976,42 47. 119 P. Pendergast and W. H. Fink J. Amer. Chem. SOC.,1976,98 648. 120 C. W. Bauschlicher jun. H. F. Schaefer tert. andC. F. Bender J. Amer. Chem. SOC.,1976,98,1653. 121 J. B. Collins P. von R. Schleyer J. S. Binkley J. A. Pople and L. Radom J. Amer. Chem. SOC.,1976,98 3436. 122 R. L. Jarre and K. Morokuma J. Chem. Phys. 1976,64 4881. Theoretical Chemistry The deoxygenation of ethylene oxide by atomic carbon [equation (2)] has been investigated by the MIND0/3 method.lZ3 The reaction was found to occur downhill (via path i) all the way by direct oxygen abstraction by the carbon atom to form carbon monoxide.Other abstraction reactions that were investigated by ab initiu methods are the reaction of triplet methylene CH2(3B,)with hydrogen and with methane,124 and the abstraction reaction between chlorine and methane. lZ5 ko'-c-+ 11 + co 4 Solvation and Other Molecular Associations Solvation.-The past couple of years have seen the birth of new kinds of quantum mechanical calculations. Once it had been established that the methods are satisfac- tory for dealing with bonds and that the algorithm had been made sufficiently flexible to deal with relatively large systems people started to look at intermolecular interactions such as chemical reactions. More recently molecular associations such as those encountered in molecules in solution have begun to be dealt with by relatively sophisticated quantum mechanical methods.A review of the various existing molecular models for the solvation of small ions and polar molecules has recently been published by Schuster Jakubetz and Marius.126 Considerable interest also presently exists in determining physical properties of gas-phase molecules such as the basicity of alkylamine~~~' and pyridines128 or the acidity of halogenoacetic acids,lZ9 in order to compare these values with the corresponding solution values in an attempt to establish a data base for the study of hydration enthalpies. McCreery Christoffersen and Hall proposed to separate solvent effects into macroscopic and microscopic contributions.The macroscopic solvation eff ectI3' results essentially from electrostatic contributions related to the dielectric constant of the solvent while the contributions are due to interactions between specific sites of the solute and the solvent molecules e.g. hydrogen bonding. For both of these solvation contributions the authors have presented a possible algorithm and preliminary results. So far however most calculations of solvation energies have been conducted by considering clusters of solvent molecules around an ion and comparing the energy of formation of such supermolecules with that of its components. By properly minimizing the co-ordinates of all atoms of the system information can be gained not only about the stability of the cluster but also about its structural characteristics.'23 J. M. Figuera P. B. Shevlin and S. D. Worley J. Amer. Chem. SOC.,1976 98 3478. 124 C. W. Bauschlicher jun. C.F. Bender and H. F. Schaefer tert. J. Amer. Chem. SOC.,1976,98,3072. 125 E.L. Motel1 and W. H. Fink J. Amer. Chem. SOC.,1976,98 7152. l26 P. Schuster W.Jakubetz and W. Marius Topics Current Chem. 1975,60 1. 127 D.H.Aue H. M. Webb and M. T. Bowers J. Amer. Chem. SOC.,1976,98 318. 128 D.H. Aue H. M. Webb M. T. Bowers C. L. Liotta C. J. Alexander and H. P. Hopkins jun. J. Amer. Chem. SOC.,1976,98 854. 129 P. Haberfield and A. K. Rakshit J. Amer. Chem. SOC.,1976,98 4393. 130 J. H. McCreery R. E. Christoffersen and G.G.Hall J. Amer. Chem. SOC.,1976,98 7191. 131 J. H. McCreery R. E. Christoffersen and G. G. Hall J.Amer. Chem. Soc. 1976,98 7198. 36 G.Klopman and P.Andreozzi The hydration energies of various cations and anions have been determined in this fashion by a variety of methods ranging from empirical potential functions to ab initio quantum mechanical calculations. For example structural information as well as Gibbs free energies enthalpies and entropies were calculated by Mruzik et ~1.l~~ for a number of alkali-metal and halogen ions using semi-empirical intermolecular potential functions to evaluate the interaction of the ions with up to six water molecules. A somewhat simpler technique has been used by Spears and Kim133 to calculate (with apparently great success) the hydration energy of alkali-metal ions. Here a simple electrostatic treatment with a semi-empirical selection of different repulsion potentials for each ion was used to calculate the stability of a variety of structures involving one to six water ligands.CNDO/2 calculations were presented for the solvation of ions by methan01.l~~ For this study the stabilization energies were greatly over-estimated although differences in stabilization energies for different ion-methanol clusters agreed with experiment. The evolution of the energies of stepwise addition of NH3or H20ligands to NH4+ has been computed in a STO-3G basis These calculations reproduced all the qualitative features of the corresponding experimental data (initial preference for NH over HzO,but a crossing over of preferential affinities in the second shell) and the error in the calculated energy values was found to decrease with increasing n.The structure of H30+embedded in a solid (X-= C1- NO3- C104-) has been studied using a modified version of CND0/2. Trends in struc-tural parameters were compared with the chemical properties of hydrogen bonds and paralleled the Hammett acidity scale. The structures of the dimethylformamide fragment and its complexes with alkali metals13’ have been studied using ab initio techniques. The amide form of the ion solvate is highly favoured over the isocyanate form. Ab initio techniques have also been used to study the mechanism for formation of the hydrated electr~n,’~~ and also to eluci- date the structure and properties of hydrated and ammoniated electrons. 139 An interesting attempt to study the influence of the dielectric medium on the conformation of natural products has been presented by Kumbar and Sankar.14’ It was found that the properties of tryptamine and serotonin changed considerably as a result of solvation.In particular the potential barrier between the trans and gauche forms changes as well as the shape of the contour maps around the molecule indicating potential modifications of the reactivity. Hydrogen Bonding.-The theoretical study of hydrogen bonding continues to be of special interest as many new contributions help to enrich our knowledge in this especially important field. A simple model of hydrogen bonding has been proposed by Allen,141 based on the knowledge of three characteristics of the monomer the AH 132 M.Mruzik F. Abraham and D. E. Schreiber J. Chem. Phys. 1976,64 481. 133 K. G. Spears and S. H. Kim J. Phys. Chem. 1976,80,673. I34 M. Salomon Canad. J. Chem. 1975 53 3194. 135 A. Pullman and A. Armbruster Chem. Phys. Letters 1975.36 558. 136 M. Fournier M,Allavena and A. Potier Theor. Chim. Acta 1976.42 145. 137 B. M. Rode and R. Ahlrichs Z. Naturforsch. 1975,30a 1792. $38 B. Webster J. Phys. Chem. 1975 79 2809. 139 M. D. Newton J. Phys. Chem. 1975,79 2795. 140 M. Kumbar and D. V. Siva Sankar J. Amer. Chem. SOC.,1975,97 7411. 14* L. C. Allen J. Amer. Chem. Soc. 1975,97,6921. Theoretical Chemistry 37 dipole moment the difference between the ionization potential of the electron donor and that of the noble-gas atom in its row and the length of the hydrogen-bonding lone pair.Allen has shown that most of the properties of the hydrogen-bonded dimer can be inferred from these three properties. Amongst the most common hydrogen-bonded species are those containing at least one water molecule. For example a large-scale CI study has been made of the system HO-HOH in an effort to assess the effect of correlation energy142 on the energy barrier to proton transfer. The most stable species was found to be the symmetrical one with the hydrogen-bonding H atom midway between the two oxygen centres. This result contrasted with SCF calculations where an asymmetric configuration was found to be more stable. The potential energy for the water dimer in various geometrical configurations has also been studied.Both STO-3G'43 and C1144 methods were used and the linear motion of the water dimer was investigated by Curtiss and P~ple.'~~ A value of the dimer.I4' The nature of the potential surface corresponding to the tunnelling motion of the latter dimer was investigated by Curtiss and P0p1e.l~~ A value of 1.1kcal mol-' for the barrier was obtained indicating that bond breaking occurs quite readily in the system. The stability of chains of HF molecules has also been in~estigated,'~' and it was found that some extra binding energy results from infinite chains as compared to smaller clusters. Other interesting papers report the study of hydrogen-bonded dimers containing mixtures of H20 and HF,14* of H20,H02 and NH3,149 of H20 HF and NH3,lS0 of H2S,15' and of H20,H2S,and a series of other electron donor^.'^^ An unexpected result of the latter work is that in 1:1complexes of amines with H20 neither the hydrogen-bond distance 0--H-N nor the amount of charge transfer seems to depend on the ionization potential of the lone pair of the amine.The interaction of water and carbon dioxide has also been investigated by an ab initio technique with CI and found to be repul~ive.'~~ It was thus suggested that carbonic acid (H2C03) is unlikely to be observed in the gas phase. Ab initio calculations have been used to investigate structural and conformational properties of hydrogen-bonded dimers of organic molecules also. Del Bene has continued to investigate the water complexes of substituted carbonyl derivative^"^ and nitrogen heterocycles.'55 An ab initio study of the cyclic nitrosomethane dimer indicated that the interaction between the two units is better described as a contact of the van der Waals type rather than as hydrogen bonding.ls6 On the other hand the 142 B.0.Roos Theor. Chim. Acta 1976,42 77. 143 G. Leroy G. Louterman-Leloup and P. Ruelle Bull. Soc. chim. belges 1976,85 205. 144 0.Matsuoka E. Clement and M. Yoshimine J. Chem. Phys. 1976 64 1351. 145 G. Leroy,G. Louterman-Leloup and P. Ruelle Bull. SOC. chim. belges 1976,85 229. 146 L. A. Curtiss and J. A. Pople J. Mol. Spectroscopy 1976 61 1. M. Kerttsz J. Koller and A. Azman Chem. Phys. Letters 1975,36 576. 14* G. Leroy G. Louterman-Leloup and P. Ruelle Bull. SOC.chim. belges 1976,85 393. 149 E.J. Hamilton and C. A. Naleway J. Phys. Chem. 1976,80 2037. 150 J. D. Dill L. C. Allen W. C. Topp and J. A. Pople J. Amer. Chem. Soc. 1975 97 7220. ls1 G. Leroy G. Louterman-Leloup and P. Ruelle Bull. Soc. chim. belges 1976,85 219. 152 C. N. R. Rao P. C. Dwivedi A. Gupta H. S. Randhawa H. Ratajczak M. M. Szczesniak K. Romanowska and W. J. Orville-Thomas J. Mol. Structure 1976 30 271. IS3 B. Jonsson G. Karlstrom H. Wennerstrom and B. Roos Chem. Phys. Letters 1976 41 317. Is* J. E. Del Bene J. Chem. Phys. 1975.63 4566. 155 J. E. Del Bene Chem. Phys. 1976,15 463. 156 H. J. Talberg and T. Ottersen J.Mol. Structure 1975 29 225. 14' 38 G.Klopman and P.Andreozzi dimers of both formic acid and hydroxyacrolein are satisfactorily described as being hydrogen-bdnded.15' Intramolecular hydrogen bonding has been studied by ab initio techniques for the enol tautomer of mal~ndialdehyde'~~ the latter with relatively and gly~oaldehyde,'~~ little success. Other Molecular Associations.-The lithium hydride dimer and its negative ion have been studied by Jordan.'60 The square form of (LiH) was found to be the most stable and 1.9 eV below that of two LiH molecules. The square (antiparallel) form (35) of the acetonitrile dimer was also found to be the most stable16' when compared to the head-to-tail structure (36). The stabilities of three possible geometrical vJ_C-CH3 I H3C-CrN CH~-C~N--CH,-CZN (35) (36) isomers of the hydrogen cyanide dimers [(37)-(39)] were considered by Moffat,16* using an ab initio technique.Of these iminoacetonitrile (37) was quite predictably found to be the most stable and the aminocyanocarbene (39) the least stable. H H H \/ /H \ N=C C N-C-CrN / \ 11 CZN N=C/ H H/ \N (37) (38) (39) The failure of CNDO to calculate correctly the stability and geometry of molecular pairs has been demonstrated again,'63 this time on a dimer consisting of formamide and imidazole. Several charge-transfer complexes have been investigated by Morokuma and his collaborators such as the 7.r -complex between benzene and carbonyl cyanide'64 and a series of complexes between various amines and b0~ane.l~~ A similar study involving amines and halogens was conducted by Leuchese and Schaefer. 166 Only a couple of years ago there was absolutely no way in which quantum mechanical calculations could have been carried out on molecules containing heavy elements such as transition metals.New parameterizations however now allow such calculations to be done at least with relatively simple MO methods. For example Summerville and Hoff man'67 calculated the geometries and electronic structures of a series of dimeric tetrahedral and square-planar transition-metal 157 J. E. Del Bene and W. L. Kochenour J. Amer. Chem. Soc. 1976,98,2041. G. Karlstrorn B. Jonsson B. Roos and H. Wennerstrom J. Amer. Chem. SOC.,1976,98 6851. I59 H. H. Jensen H. Mollendal and E. Wisloff-Nilssen J. Mol. Structure 1976 30 145. K. D. Jordan Chem. Phys. Letters 1976 40 441. 161 M. R. Dagnino G. LaMann and L.Paoloni Chem. Phys. Letters 1976 39 552. 162 J. B. Moffat J.C.S. Chem. Comm. 1975 888. 163 S. F. Abdulnur and R. L. Flurry jun. Chem. Phys. Letters 1975 36 586. 164 W. A. Lathan G. R.Pack and K. Morokuma J. Amer. Chem. SOC.,1975,97,6624. 165 H. Urneyama and K. Morokurna J. Amer. Chem. SOC.,1976,98,7208. 166 R. R. Lucchese and J. F. Schaefer tert. J. Amer. Chem. SOC.,1976 97 7205. 16' R. H. Summerville and R. Hoffrnann J. Amer. Chem. SOC.,1976,98,7240. Theoretical Chemistry complexes and determined the factors governing the preferred geometries. Block and his collaborators'68 showed that correlations do exist between the site of nucleophilic attack and the location and configuration of the lowest unoccupied orbital of some chromium and manganese carbonyl complexes of organic molecules.168 T. F. Block R. F. Fenske and C. P. Casey J. Amer. Chern. SOC., 1976,98 441.