3 Theoretical Chemistry By C. THOMSON Department of Chemistry University of St. Andrews St. Andrews KY16 9ST Scotland 1 Introduction As in last year’s report coverage of the literature is restricted to ab initio calculations and owing to the ever increasing number of Ipplications must be very subjective a large number of references being omitted. Two useful new text books have appeared,’32 and a recent issue of THEOCHEM3 was devoted to papers in honour of K. Fukui Nobel Laureate (with R. Hoffman) in 1981. The papers presented at the 4th International Congress in Quantum Chemistry in Uppsala have been p~blished.~ A number of useful reviews have appeared including one on substituent effect^,^ a review of the rotational barrier in C2H6,6 the interpretation of electron distributions in molec~les,~ calculation of excited state potential energy (PE) surfaces,8 and reviews on Valence Bond (VB) theory’ and its use in organic reactivity problems.” The increasing application of quantum chemistry to biochemical problems is reflected in the appearance of a new edition’ ’ of Richards’ ‘Quantum Pharmacology’.2 Advances in Theoretical Techniques Basis Sets and Integral Evaluation.-Further additions to the standard basis sets developed by Pople and co-workers have been reported. The widely used STO-3G minimal basis sets have been extended to include the first and second row transition metals,12 and appear to be useful in the description of the bonding in various organometallic compounds. Improvements to the standard first row atom STO-3G basis sets have been tested by Yurtsever et a113 These yield energies -500-1400 kJmol-’ lower than the original STO-3G basis sets.’ R. L. Flurry ‘Quantum Chemistry’ Prentice Hall New York 1983. ’ D. A. McQuarrie ‘Quantum Chemistry’ Oxford University Press Oxford 1983. ’ THEOCHEM 1983.93 1-250. Int. J. Quantum Chem. 1983 23 1-1688. R. D. Topsom Acc. Chem. Res. 1983 16 292. R. M. Pitzer Acc. Chem. Res. 1983 16 207. ’ M. B. Hall in ‘Electron Distributions and the Chemical Bond’ ed P. Coopens and M. B. Hall Plenum Press New York 1982. E. R. Davidson and L. E. McMurchie Excited States 1982 5 I. Z. S. Herman Znt. J. Quantum Chem. 1983 23 921. lo A. D. Ross and S. S. Shaik Acc. Chem. Rex 1983 16 363. I’ W. G. Richards ‘Quantum Pharmacology’ 2nd Ed.Butterworths London 1983. ’’W. J. Pietro and W. J. Hehre J. Comput. Chem. 1983 4 241. E. Yurtsever W. Schoeller and D. D. Shillady Chim. Acta Turc. 1982 10 165. 29 30 C. Thornson The standard 3-21G basis set can be augmented with a set of diffuse SP functions to give the 3-21 + G basis set which is suitable for calculating the geometries and proton affinities of molecular anions.14 A medium size energy optimized basis set (15s 1 Ip 6d) has been developed for the elements In-Xe.” Burton and co-workers16 have studied procedures for sys- tematically analysing and improving on basis set deficiencies especially for configur- ation interaction (CI) calculations Different algorithms for the calculation of the electron-electron repulsion integrals have been studied by Hegarty and Van der Velde,” particularly with respect to their use on vector computers.A recent book has appeared devoted to the problem of evaluating integrals over Slater-type orbitals.” However it seems likely that Gaussian-type orbitals (GTO) will continue to dominate polyatomic molecule calcu- lations. Rys” et al. and Harris2’ have discussed improved algorithms for GTO integrals and Habitz and Clementi” have also developed faster programmes for these integrals which should be useful for large molecules. Self-consistent Field Theory.-Further work has appeared on the convergence prob- lem in Self-consistent Field (SCF) calculations. The criteria proposed by Stanton” have been generalized for an Unrestricted (UHF) wave function,23 and related to the stability conditions.The latter have been further in~estigated.~~ A further method for accelerating SCF convergence has been propo~ed.’~ A new procedure for SCF energy minimization has been proposed and tested in RHF calculations on both closed- and open-shell systems.26 Substantial time savings were achieved. The calculation of localized orbitals has been disc~ssed,~’ as have population and the calculation of one-electron proper tie^.^' A new SCF interaction energy scheme has been proposed by Kaufman and co-workers3’ which includes the counterpoise correction. Leroy3* has examined the concept of chemical stability from the point of view of SCF results. A new and very general form of valence bond theory has been described (VB-SCF theory),33 which contains MC-SCF theory as a subclass and gives results for P.E.l4 T. Clark J. Chandrasekhar G. W. Spitznagel and P. von R. Schleyer J. Comput. Chem. 1983 4 294. Is A. Stromberg 0. Gropen and U. Wahlgren J. Compu!. Chem. 1983 4 181. I‘ P. G. Burton P. D. Gray and U. E. Senff Mol. fhys. 1982 47 785. ” D. Hegarty and G. Van der Velde Int. J. Quantum Chem. 1983 23 1135. ETO Multicentre Molecular Integrals ed. C. A. Weatherford and H. W. Jones Reidel Dordrecht 1982. l9 J. Rys M. Dupuis and H. F. King J. Comput. Chem. 1983 4 154. 20 F. Harris In!. J. Quantum Chem. 1983 23 1469. 21 P. Habitz and E. Clementi Comput. Phys. Commun. 1983 29 301. 22 R. E. Stanton J. Chem. fhys. 1981 75 5416. 23 J.C. Facelli and R. H. Contreras J. Chem. fhys. 1983 79 3421. 24 P. Karadakov and 0.Castano In!. J. Quantum Chem.. 1983 24 453. 25 I. Balint and M. 1. Ban Chem. Phys. Lett. 1983 101 153. 26 J. Fernandez Rico J. M. Garcia de la Vega J. I. FernLndez Alonso and P. Fantucci J. Comput. Chem. 1983 4 33 41. 27 J. M. Leonard and W. L. Luken 7heor. (-‘him. Actu 1982 62 107. 28 B. T. Thole and P. Th. van Duijnen Theor. Chim. Acta 1983 63 209. 29 1. Mayer Chem. fhvs. Lett. 1983 97 270. “I G. De Rrouckkre Int. J. Quantum Chern. 1983 23 1677. 31 W. A. Sokalski S. Roszak P. C. Hariharan and J. J. Kaufman In!. J. Quantum Chem. 1983 23 847. 32 G. Leroy Int. J. Quantum Chem. 1983 23 271. 33 J. H. van Lenthe and G. Balint-Kurti J. Chem. Phys.1983 78 5699. The0retical Chemistry 31 curves which are very accurate. Extensions to polyatomic molecules will be awaited with interest. There have been several papers dealing with localized bond and their use in the calculation of rotation barriers.36 Electron Correlation.-A large number of papers have appeared concerning the various methods of including electron correlation in quantum chemistry calculations. Space permits only a brief mention of some of these. The configuration interaction method (CI) is in principle capable of yielding the exact non-relativistic wave function and much recent work has appeared. One important aspect is the convergence characteristics of the e~pansion,~’ which has been studied by Cooper and Pounder.Payne has investigated the use of a basis of biorthogonal states.38 Multi-reference CI techniques have been implemented by several groups and references are to be found in a recent article by Ahlri~hs~~ in the Proceedings of a meeting devoted to computational methods in quantum chemistry. An important implementation of the shape-driven graphical unitary group approach has been reported by Schaefer’s A variational calculation on C2H4 included more than lo6 configurations and examined the contributions of triple and quadruple excitations. Several other a~thors~~,~’,~~ have discussed the unitary group method and its relationship to the symmetric group approach. The paper by Schaefer marks the beginning of a series of full CI calculations (where all possible N-tuple excitations are included for N-electrons) on molecules with small or medium-size basis sets.A full CI double zeta (DZ) basis calculation on H2043 was followed by DZ + P calculations on BH,44 HF NH3 and more recently Be and ( H2)2 with large basis sets.45 Bartlett and co-~orkers~~ have compared the results with calculations including correlation by different methods in particular the coupled-cluster doubles (CCD) and many body perturbation theory (MBPT) methods at the full fourth-order level. The agreement with the full CI is to within <8 kJ mol-’ for CCD and to -40 kJ mol-’ for the MBPT(4) method. A similar comparison of full CI to a CI extrapolation method has been reported for H20by Burton and Gray.47 Schweig and co-~orkers~~ have looked at the effect of triple and quadruple excitations on one-electron densities in CI calculations.34 V. Barone. G. del Re A. Lami and G. Abbate THEOCHEM 1983 105 198. ’’ V. Barone G. del Re A. Lami and G. Abbate THEOC‘HEM 1983 105 IY I. 36 G. F. Musso G. Figari and V. Magnasco J. Chem. Soc. Faraduy Trans. 2 1983 79 93 1283. ” 1. L. Cooper and C. N. M. Pounder J. Chem. Phys. 1982 77 5045. 3x P. W. Payne J. Chem. Phys. 1982 77 5630. 39 R. Ahlrichs 5th Seminar on Computational Methods in Quantum Chemistry Max Planck Institute Groningen 198 1. 40 P. Saxe D. J. Fox H. F. Schaefer 111 and N. C. Handy J. Chem. Phys. 1982 77 5584. 4’ P. W. Payne lnr. J. Quantum Chem. 1982 22 1085. 42 W. Duch and J. Karwowski Inr. J. Quantum Chem. 1982 22 783.43 P. Saxe H. F. Schaefer 111 and N. C. Hardy Chem. Phys. Lett. 1981 79 202. 44 R. J. Harrison and N. C. Handy Chem. Phys. Lerr. 1983 95 386. 45 R. J. Harrison and N. C. Handy Chem. Phys. Lett. 1983 98 97. 46 R. J. Bartlett H. Sekino and G. D. Purvis Ill Chem. Phys. Lett. 1983 98 66. 47 P. G. Burton and P. D. Gray Chem. Phys. Lett. 1983 96,453. 48 H Meyer A. Schweig and W. Zittlau. Chem. Phvs. Lett. 1982 92 637. 32 C. Thornson Interest continues in developing the Multi-Configuration SCF (MC-SCF) method particularly since the earlier problems with convergence seem to have largely been solved. The recent developments have been reviewed,49 and several later papers by the same group have a~peared.~'-~~ A different convergence method has been proposed by Yurtsever and shill ad^^^ and tested.MC-SCF equations for excited states have been in~estigated,~~ and also time-dependent aspects of MC-SCF problem^.^^,^^ R~eggen~~ has further developed his extended geminal method6' and in an application to F2 obtained excellent agreement with experiment for the dissociation energy and bond length. There have been various developments in coupled cluster theory.61 Potential Energy (PE) Surfaces.-The recent efforts in this area are expected ulti- mately to be of enormous benefit to the chemist in the understanding of reaction mechanisms and much current research is concerned with the problem of the analysis of the molecular potential energy hypersurfaces. Mezey in particular has made important contributions in the description of chemical structure based on the topology of the nuclear configuration spa~e,6~~' have also and other a~thors~~-~' studied this aspect of PE surfaces.The problems of locating saddle points on such surfaces have been the subject of several paper^.^"^^ S~hafer~~ has reviewed the use of gradient methods in structural chemistry and Miller74 has similarly reviewed the dynamic aspects of reaction path studies. Sim~ns~~ and co-workers have described an interesting new automated method for walking on PE surfaces. This should enable one to locate stationary points at lower cost and has been successfully implemented. Central to this problem is that of determining the first and second derivatives of the potential energy surface.A very clear review of the analytic calculation of 49 D. L. Yeager D. Lynch J. Nichols P. Jbrgensen and J. Olsen J. Phys. Chem. 1982 86 2140. 50 A. Igawa D. L. Yeager and H. Fukutome J. Chem. Phys. 1982 76 5388. 5' P. J~rgensen,P. Swanstrom and D. L. Yeager J. Chem. Phys. 1983 78 347. 52 J. Olsen and P. Jbrgensen J. Chem. Phys. 1982 77 6109. 53 P. Jbrgensen P. Swanstrom D. L. Yeager and J. Olsen Int. J. Quantum Chem. 1983 23 959. 54 J. Olsen P. Jbrgensen and D. L. Yeager Int. J. Quant. Chem. 1983 23 25. 55 E. Yurtsever and D. Shillady Chem. Phys. Lett. 1983 94 316. 56 R. Colle and 0.Salvetti Mol. Phys. 1982 47 959. 57 R. McWeeny Int. J. Quantum Chem. 1983 23 405. 58 R. McWeeny THEOCHEM 1983,93 1. 59 I.Roeggen J. Chem. Phys. 1983 78 2496. 60 I. Roeggen Int. J. Quantum Chem. 1982 22 149. 6' W. H.Fink A Banerjee and J. Simons J. Chem. Phys. 1983 79 3104. 62 P. G. Mezey Int. J. Quanrum Chem. 1982 22 101. 63 P. G. Mezey THEOCHEM 1983 103 81. h4 P. G. Mezey Theor. Chim. Acra 1982 62 131. 65 P. G. Mezey J. C'hem. Phys. 1983 78 6182. 66 M. V. Basilevsky THEOCHEM 1983 103 139. 67 M. V. Basilevsky Chem. Phys. 1982 67 337. 68 R. B. King Theor. Chim. Acta 1983 63 103. '" P. G. Mezey Can. J. Chem. 1983 61 956. 70 M. R. Peterson I. G. Csizmadia and R. W. Sharpe THEOCHEM 1983 94 127. 7' I. Balint and M. I. Ban Theor. Chim. Acta 1983 63 255. 12 I. Balint and M. I. Ban Int. J. Quantum Chem. 1983 24 161. 73 L. Schafer J.Mol. Struct. 1983 100 51. 74 W. H. Miller J. Phys. Chern. 1983 87 3811. 75 J. Simons P. Jbrgensen H. Taylor and J. Ozment J. Phys. Chem. 1983 87 2745. Theoretical Chemistry 33 molecular gradients and Hessians has been given by Jargensen and Simon~,~~ who derived the relevant equations for several different classes of wave functions using exponential unitary operator methods. A more recent paper77 dealt with third and fourth derivatives which relate to anharmonicities on PE surfaces. P~lay~~ has also discussed gradients and coupled electron pair theories. Schaefer and co-~orkers~~ have also obtained expressions for analytic second derivatives for high-spin open-shell RHF wave functions and also for the simplest" two-configuration post-SCF wave function.A new approach" to the solution of the coupled perturbed HF equations has been described which avoids the four index transformation. The rotational invariance properties of the analytic first second and third energy derivative integrals have been exploiteds2 to save time in the integral derivative computations. King and co-workersS3 have also investigated the use of symmetry in the coupled- HF formalism and an alternative expression for MCSCF force constants was de~cribed.'~ An alternative to gradient methods has been proposed by Nakatsuji et aLS5in a series of papers. An extension of the usual basis set by inclusion of derivative basis functions gives a wave function which satisfies the Hellman-Feynman theorem and this yields additional insight into the driving force in chemical reactions.However it is substantially more expensive than gradient methods,8688 but there will probably be increased interest in such approaches. 3 Applications Applications of the methods referred to in earlier sections are increasing enormously every year and this section will be of necessity very subjective. Small Molecule PE Surfaces and Reactions.-A large basis set CI calculation includ- ing all single and double excitations has been reporteds9 for the reaction (1) C(3P)+ H -+ CH2(3B,) (1) The reaction proceeds through a weakly avoided crossing of the 3A2and 3B,potential energy surfaces the lowest energy pathway giving a barrier height of -4 kJ mol-' 76 P. J~rgensen and J. Simons J.Chem. Phys. 1983 79 334. 77 J. Simons and P. J~rgensen,J. Chem. Phys. 1983 79 3599. 7x P. Pulay THEOCHEM 1983 103 57. 79 P. Saxe Y. Yamaguchi and H. F. Schaefer 111 J. Chem. Phys. 1982 77 5647. no Y. Yamaguchi Y. Osamura G. Fitzgerald and H. F. Schaefer Ill J. Chem. Phys. 1983 78 1607. " Y. Osamura Y. Yamaguchi P. Saxe D. J. Fox M. A. Vincent and H. F. Schaefer Ill THEOCHEM 1983 103 183. '* M. A. Vincent P. Saxe and H. F. Schaefer 111 Chem. Phys. Lett. 1983 94 351. 133 T. Takada M. Dupuis and H. F. King J. Comput. Chem. 1983 4 234. 84 R. N. Camp H. F. King J. W. Mclver jun. and D. Mullally J. Chem. Phys. 1983 79 1088. 85 H. Nakatsuji M. Hada K. Kanda and T. Yonezawa Int. J. Quantum Chem. 1983,23,357 and references therein.86 P. Pulay J. Chem. Phys. 1983 79 2491. 87 H. Nakatsuji K. Kanda M. Hada and T. Yonezawa J. Chem. Phys. 1983 79 2493. xn H. Nakatsuji M. Hada and T. Yonezawa Chem. Phys. Lett. 1983 95 573. x9 L. B. Harding J. Phys. Chem. 1983 87 441. 34 C. Thomson but the value is very sensitive to the basis set. A similar study of the reaction B+(]S) + H + BH'(21;+) + H (2) using an MRD-CI wave functiong0 was reported by Hirst. The best available calculations on the electron affinity of CH29' yield a value corrected for zero-point vibrational energy of 0.42 eV and it is estimated that this value is low by -0.2 eV. The source of this remaining error has yet to be determined. The singlet-triplet gap of 37 kJ mol-' is in good agreement with other estimates.The insertion of Be into H2 has been studiedg2 using the coupled cluster singles and doubles (CCSD) method and compared to full CI results. The method provides an excellent description of this process in good agreement with full CI results. The structure and stability of a large number of dicationsg3 XHF(X = N 0 P or S) fourteen in all have been studied using large basis sets in RHF calculations and the calculated activation barriers and deprotonation energies were in reasonable agreement with charge stripping experiments. Botschwina has used the Self Con- sistent Electron Pairs (SCEP) method to calculate the PE surface and vibrational frequencies of FH2+ C1H2+,94 and H30+ 95 The i.r. intensities were also predicted for H30+. The minimum energy pathway for the reaction (3)96 H,O + OH + H (3) has been calculated using a variety of methods and a DZ + P basis.It was concluded that the MC-SCF procedure without CI is the simplest way to obtain reliable dissociation curves. A detailed study of the reaction surface for the addition of C(3Por ID) to H20 has a~peared.~' Geometries were optimized at the 3-21G level and single point UMP3/6-3 1G** calculations carried out at the stationary points. The calculations agree with experiment in predicting that only the singlet state of C is reactive towards H2O. Carbenoids involving Li have been studied by several groups starting with CLi and Li2C.98 The former has a 'Z ground state in contrast to the 2rI state of CH. Various isomeric structures of CH2LiF have been studied with a better than DZ + P basis set and their vibrational frequencies calculated at the SCF level.The PE surface is extremely flat and the lowest energy isomer is the ion pair H,CLi+-..F- at both SCF levels and also with CI calculation^.^^ Related organometallic molecules are H2CBe and HCBeH where the low lying singlet and triplet states have been studied by Pople's group."' Calculated energy 90 D. M. Hirst Chem. Phys. Lett. 1983 95 591. 9' D. Feller L. E. McMurchie W. T. Borden and E. R. Davidson J. Chem. Phys. 1982 77 6134. 92 G. D. Purvis 111 R. Shepard F. B. Brown and R. J. Bartlett Int. J. Quantum Chem. 1983 23 835. 93 S. A. Pope I. H. Hillier M. F. Guest and J. Kendric Chem. Phys. Lett. 1983 95 247. 94 P.Botschwina 'Molecular Ions' ed. J. Berkowitz and K. 0. Groeneveld Plenum Press 1983 p. 41 I. 95 P. Botschwina P. Rosmus and E. A. Reinsch Chem. Phys. Lett. 1983 102 299. 96 S. A. Alexander and F. A. Matsen Int. J. Quantum Chem. 1982 516 445. 97 S. N. Ahmed M. L. McKee and P. B. Shevlin J. Am. Chem. SOC.,1983 105 3942. 98 A. Mavridis and J. F. Harrison J. Am Chem. SOC.,1982 104 3827. 99 M. A. Vincent and H. F. Schaefer 111 J. Chem. Phys. 1982 77 6103. I00 B. T. Luke J. A. Pople and P. von R. Schleyer Chem. Phys. Lett. 1983 97 265. Theoretical Chemistry differences were obtained using the 6-31G** basis set and the MP4 procedure following 6-3 1G* geometry optimizations at the SCF level. The first computation of the structure of a transition state in the reactions of carbenoids has been reported."l The reaction of LiCH2F with C2H4 has been studied using a 3-21G basis set.The computed transition state structure (I) is related to the butterfly structure (2) proposed for the Simmons-Smith reaction where the car- benoid is IZnCH,I and L,L' are ligands. The structure (1) also resembles the transition-state structure for the isomerization of LiCH2F to H2CLiF which is nearly linear.99 L' I . ,CH2 a. R,C-CR A very detailed study has appeared of CH;+ which has shown that this is a viable species of hexaco-ordinated carb~n.'~~,~~~ The geometry (3) was obtained in RHF/6- 3 1G* gradient calculations and the relative energies on the surface by single point MP3/6-31G** calculations.Results were also reported for CH;+ which has D4h symmetry and C,Hi+. The structure of the latter has each carbon pentaco-ordinate (4). There is a large barrier -119 kJ mol-' to deprotonation of CHi+. It was suggested that both CHi+ C,Hi+ and C,Hi+ might be observable in the gas phase. A related paperIo4 dealt with the PE surface for C,H:+ which has the perpendicular structure (5). The rotational barrier to the D2h transition state (6) is high (115 kJ mol-I). Other workerslo5 have studied CH4+. Transition-state structures for the neutral cationic and anionic vinylidene-acetyleneIo6 rearrangement have been found using the 4-3 1G basis and relative energies computed at the MP3 level with a 6-31 +G** basis set with added diffuse functions for the anions.Rearrangement of the anion proceeds with a high activation energy (193 kJ mol-I) uia a perpendicular transition state (7). J. Mareda N. G. Rondan K. N. Houk T. Clarke and P. von R. Schleyer J. Am. Chem. SOC.,1983 105 6997. ItIZ K. Lamrnemma G. A. Olah M. Rar~aphi and M. Simonetta J. Am. Chem. Soc. 1982 104 6851. I03 K. Lammertsma M. Barzaghi G. A. Olah J. A. Pople P. von R. Schleyer and M. Simonetta J. Am. Chem. SOC.,1983 105 5258. I04 K. Lammertsma M. Barzaghi G. A. Olah J. A. Pople A. J. Kos and P. von R. Schleyer J. Am. Chem. SOC.,1983 105 5252. I05 J. M. Garcia de la Vega J. Fernandez Rico M. Paniagua and J. J. Fernandez-Alonso THEOCHEM 1983 105 31. lo' G. Frenking Chem. Phys. Lerr. 1983 100 484. 36 C.Thornson A comprehensive study of the PE surfaces for the set of compounds H,ABH (A B = C N 0 and F) has been p~b1ished.l~' A wealth of important information is contained in this paper. Cations containing oxygen have been much studied recently. Isotope effects have been investigatedlo8 in the protonation and deprotonation of CH30H a problem studied earlier in detail,'" together with the transition-state structures. Various dications such as CH30H2+ CH,OH;+ CH202+ HCOHZf and other related species have been studied by Bouma and Radom."' CH,OH;+ is much more stable than CH30H2+ in agreement with experiment. The structures and stabilities of the species C2H30t,'l' C2H50+,Ii2 have been studied by the same and C2H60+113 group. The lowest energy isomer of C2H,0f is the acetyl cation CH3CO+ but CH2COH is also predicted to be stable.In the case of C2H60+ the two lowest energy isomers are the oxonium ions (8) and (9). The acidity of the acetylenic proton in 21 mono-substituted acetylenes has been investigated the STO-3G geometries being fully optimized and the acidities calcu- lated at the 4-31G//3G Potential energy surface calculations become more expensive as the number of atoms increases and a thorough search of the surface is not feasible except for quite small basis sets. Nevertheless several larger systems have been studied and we refer to a few of these results. An investigation of the reactions of 'Aa O2 with C2H4 with the CASSCF method shows that the pathway via a peroxirane intermediate has a lower activation energy than the biradical pathway.' The mechanism of hydroboration in ether has been studied using as a model H3B-OH2.The reaction with C2H4 was studied and shown to resemble an SN2 displacement of the solvent by the olefin."6 A large scale calculation in the dissociation of H,C0"7 gives an H,CO -CO + H (4) I07 J. A. Pople K. Raghavachari M. J. Frisch J. S. Brinkley and P. von R. Schleyer J. Am. Chem. Soc. 1983 105 6389. Io8 I. H. Williams THEOCHEM 1983 105 105. I IIY R. H. Nobes and L. Radom Org Mass Specfrom. 1982 17 340. I10 W. J. Bouma and L. Radom J. Am. Chem. Soc. 1983 105 5484. 'I1 R. H. Nobes W. J. Bouma and L. Radom J. Am. Chem. Soc. 1983 105 309. I I2 R. H. Nobes and L. Radom Chem. Phys. Leu. 1983 99 107.I13 W. J. Bouma R. H. Nobes and L. Radom J. Am. Chem. Soc. 1983 105 1743. I14 M. F. Powell M. R. Peterson and I. G. Csizmadia THEOCHEM 1983 9 323. 1 I5 M. Hotokka B. Roos and P. Siegbahn J. Am. Chem. Soc. 1983 105 5263. 1 I6 T. Clark D. Wilhelm and P. von R. Schleyer J. Chem. Soc. Chem. Commun. 1983 606. I I7 M. Dupuis W. A. Lester jun. B. H. Lengsfield 111 and B. Liu J. Chem. Phys. 1983 79 6167. Theoretical Chemistry 37 activation energy of 322 * 13 kJ mol-' and accurate structures and harmonic frequencies were also calculated. A similar MC-SCF study was carried out by Feller and Davidson"' of the D2hdissociation of the 'A excited state of C2H4. C2H -+ 2CH,('A,) (5) Several authors have calculated fundamental vibrational frequencies for optimized structures.Among these we mention calculations on the formate anion,'I9 and on cyclobutadiene.12' A more recent development is the ability to calculate infrared intensities and the application to H30+ H2DO' HD20+ and D20+.I2l Schaefer and co-workers'22 have examined the (C,H,) surface. The absolute minimum corresponds to vinylacetylene but singlet cyclobutyne is a relative minimum lying some 320 kJ mol-' above the absolute minimum. The [1,3] dipolar cycloaddition of fulminic acid to C2H2 has been investigated at the 4-3 IG basis level including ~orrelation'~~ with -2 x lo6 configurations! Exten- sive CI is necessary for biradical problems. The transition-state structure for the [ 1 51 sigmatropic hydrogen transfer in cis-1 3-pentadiene has been determined,'24 and in the case of the 1,2-hydride shift in C6H5+ a high quality calculation predicts a very large barrier of -170 kJ m01-I.'~~ l~~ Bicerano et ~ 1 .in an interesting paper on malonaldehyde have determined the geometry and vibrational frequencies of the asymmetric equilibrium structure and also that of the transition state. The geometry and frequencies were evaluated at the SCF level and the barrier height using C1 calculations the latter quantity being 33 kJ mol-l. Finally the dynamical tunnelling has been calculated using a simple one-dimensional model with results in good agreement with experiment. (10) (1 1) (12) The question of the structure of the 2-norbornyl cation has been addressed once more with high quality CI calculations.127 Optimization of the various structures was performed and the classical structure (10) is the minimum energy structure at the 4-3 1G level with C- and H-bridged structures corresponding to saddle points.Correlation calculations with up to 1.5 million configurations stabilize the bridged structure relative to the classical as was also the case with 6-3 1G" SCF calculations. It was concluded that the C-bridged structure should be a true minimum and that there is no true minimum corresponding to the classical structure (10). Similar results were reported by other workers.12* I IX D. Feller and E. R. Davidson J. Phys. Chem. 1983 87 2721. 1 I9 A. R. Gregory K. G Kidd and G. W. Burton THEOCHEM 1983 104 9. I20 B. A. Hess jun.P. Chrsky and L. J. Schaad J. Am. Chem. SOC.,1983 105 695. 12' M. E. Colvin G. P. Raine H. F. Schaefer Ill and M. Dupuis. J. Chem. Phys. 1983 79 1551. 122 G. Fitgerald P. Saxe and H. F. Schaefer 111 J. Am. Chem. SOC.,1983 105 690. I23 P. C. Hiberty G. Ohanessian and H. B. Schlegel J. Am. Chem. SOC.,1983 105 719. I24 B. A. Hess jun.and L. J. Schaad J. Am. Chem. SOC.,1983 105 7185. I25 P. von R. Schleyer A. J. Kos and K. Raghavachari J. Chem. SOC.,Chem. Commun. 1983 1296. I26 J. Bicerano H. F. Schaefer 111 and W. H. Miller J. Am. Chem. SOC.,1983 105 2550. I27 M. Yoshimine A. D. McLean B. Liu D. J. DeFrees and J. S. Binkley J. Am. Chem. SOC.,1983,105,6185. 128 K. Raghavachari R. C. Haddon P. von R. Schleyer and H. F. Schaefer 111 J. Am.Chem. SOC.,1983 105 5915. 38 C. Thomson The structures of various C9H9+ cations and their interconversions have been studied both with MNDO and STO-3G ab initio ~tudies.'~' The cation of C symmetry is the most stable in agreement with experiment. Calculations on the molecular ions of allene and propyne have been rep~rted.'~~~'~' Transition structures for reactions representative of the additions of model nucleophiles electrophiles and radicals to propene have been reported by Houk and ~o-workers.'~~ Finally the question of cyclic N6of Dshsymmetry'33 (hexa-azabenzene) has been explored at the SCF level. The cyclic structure is predicted to be a relative minimum and the energy surface is very flat. Radical and Other Open-shell Species and Reactions.-We restrict the coverage in this section to radicals of interest primarily in organic chemistry.has reviewed his various papers on the structure of free radicals and the use of the Unrestricted Hartree Fock (UHF) method. An extensive comparison of structural predictions for small radicals using a wide variety of basis sets and correlation up to the MP3 level has been reported by P0p1e.l~~ Provided spin contamination is small the UHF and ROHF predictions are in good agreement and spin contamina- tion is least for the largest basis sets. The radicals considered in this study were mainly diatomic or triatomic molecules apart from CH3. The ammonium radical' 36 undergoes dissociation by tunnelling through a low barrier the ground state being the 3s 'A Rydberg state.Havriliak and King'37 have also studied this species. The reactions of singlet and triplet NH radicals'38 have been studied using a MRD-CI wave function and 4-31G or 4-31G** basis set. The calculation^'^^ on HCO show it to have a a-ground-state and a low lying 7r-excited-state. Transition states for the fragmentation to H + COz were determined. Two papers deal with different aspects of the structure of methoxy CH,O. MBPT calculations'40 of the geometry Jahn-Teller energy surfaces spin orbit splitting and Zeeman effects have been reported. A very detailed study of the surface for CH30 and its rearrangement to CH,OH together with vibrational frequencies and transition-state structures has appeared.141 CH20H lies some 21 kJ mol-' lower than CH30 and the favoured isomerization mode is uia an intramolecular rearrangement.Theoretical studies'42 on [CH,COH]+ agree with experiment in predicting that it does exist as a stable C2H40+ isomer and as a key intermediate in the isomerization- dissociation processes of the cation radical of gaseous vinyl alcohol. 129 M. B. Huang 0.Goskinski G. Jonsall and P. Ahlberg J. Chem. Soc. Perkin Trans. 2 1983 305. 130 G. Frenking and H. Schwartz 2. Naturforsch. Teil B 1982 37 1602. 131 G. Frenking and H. Schwartz Znt. J. Mass Spectrom. Ion Phys. 1983 52 131. 132 M. N. Paddon-Row N. G. Rondan and K. N. Houk J. Am. Chem. Soc. 1982 104 7162. 133 P. Saxe and H. F. Schaefer 111 J. Am Chem. SOC. 1983 105 1760. 134 G. Leroy J. Mol. Struct.1983 93 175. 135 L. Farnell J. A. Pople and L. Radom J. Phys. Chem. 1983 87 79. 136 B. N. McMaster J. Mrozek and V. H. Smith jun. Chem. Phys. 1982 73 131. 137 S. Havnliak and H. F. King J. Am. Chem. SOC.,1983 105 4. 138 T. Fueno V. BonaEiE-Kouteckf and J. KouteckL J. Am. Chem. SOC. 1983 105 5547. 139 D. Feller E. S. Huyser W. T. Borden and E. R. Davidson J. Am. Chem. SOC.,1983 105 1459. 140 G. D. Bent G. F. Adams R. H. Bartram G. D. Purvis and R. J. Bartlett J. Chem. Phys. 1982,76,4144. 141 S. Saebo L. Radom and H. F. Schaefer 111 J. Chem. Phys. 1983 78 845. 142 Y. Apeloig M. Karni B. Gommer G. Depke G. Frenking S. Meyn J. Schmidt and H. Schwarz J. Chem. SOC. Chem. Commun. 1983 1497. Theoretical Chemistry (13) (14) (15) Calculations on five different states'43 of CH2N have been reported and a study on CH2CN.144 The frequencies and i.r.spectrum intensities have been calculated for C2H5,145 and a vibrational analysis performed from an MC SCF wave function for all~l.'~~ Correlation effects in several small radicals including C2H5 have been studied by Nakatsuji et ~21'~' Two important papers by Schlegel and co-workers have dealt with the reactions H + C2H4 S C2H5 (5) F +CZH4 + C2H4F + H + C2H3F (6) using fully optimized structures at HF/3-21G HF/6-31G* and MP2/3-21G levels. The geometries are relatively insensitive to basis set variations unlike the energies and the transition-state structures have geometries which are reactant-like (13). Energy differences computed at the MP4 and including zero-point energy corrections were compared with experimental data where available for instance AH for reaction (6) was computed to be -61 *9 kJ mol-'.The structures of a variety of radicals derived from addition of F to substituted ethylenes have been studied at the SCF level with a 3-21G basis set,'50 and the radicals formed in the reaction of OH with pyridine and pyridinium ion with a minimal STO-3G basis.'" Several P-substituted cyclopropyl radicals have been studied by Clark el A variety of radical ions have been the subject of calculations. Hyperfine coupling constants inversion barriers and geometries have been computed'53 for CF3 NFf and BFJ. There is a continuing controversy over the structure of the radical cation derived from C2H,.Calculations by Merry and Thomson predict C2HZ to be planar at the 6-31G*'54 SCF level of theory a conclusion confirmed by Belville and Ba~ld,'~~ but an extensive CI cal~ulation'~~ predicted a twisted structure (by -23") in agreement with MNDO results155 and the analysis of the photoelectron ~pectra.'~' High quality calculations are needed on this species. I43 G. F. Adarns D. R. Yarkony R. J. Bartlett and G. D. Purvis Inr. J. Quantum Chem. 1983 22 437. I44 F. Delbecq Chem. Phys. Letr. 1983 99 21. '45 J. Pacansky and B. Schrader J. Chem. Phys. 1983 78 1033. I46 T. Takada and M. Dupnis J. Am. Chem. Soc. 1983 105 1713. I47 H. Nakatsuji K. Ohta and T. Yonezawa J. Phys. Chem. 1983 87 3008. I48 H. B. Schlegel J.Phys. Chem. 1982 86 4878. 149 H. B. Schlegel K. C. Bhalla and W. L. Hase J. Phys. Chem. 1982 86 4883. Is" F. Delbecq and J. M. Lefour Terruhedron Lett. 1983 24 3613. 151 M. C. Anthony W. L. Waltz and P. G. Mezey Can. J. Chem. 1982 60,813. 152 T. Clark A. J. Kos P. von R. Schleyer W. P. Cofino W. H. de Wolf and F. Bickelhaupt J. Chem. SOC.,Chem. Commun. 1983 685. IS3 M. A. Benzel A. M. Maurice R. L. Belford and C. E. Dykstra J. Am. Chem. SOC.,1983 105 3802. I54 S. Merry and C. Thomson Chem. Phys. Left. 1981 82 373. 155 D. J. Belville and N. L. Bauld J. Am. Chem. SOC.,1982 104 294. 15h R. J. Bueuker S. D. Peyerirnhoff and H. L. Hsu Chem. Phys. Lett. 1971 11 65. I57 H. Koppel W. Domke L. S. Cederbaurn and W. von Niessen J. Chem. Phys.1978 69 4252. 40 C. Thornson Calculations have been reported on several substituted ethylene cation radi~a1s.l~~ The cation radical of ethane C2H6+ contains an elongated one-electron bond ( 1.98 8 at 6-31G** Level) in this a-radi~a1.I~~ The structures of the cyclic cation radicals derived from cyclopropane,16' cyclopen- tane,I6l and cyclobutane'62 have been reported. In the case of the cyclopentane cation a non-planar C symmetry is found whereas for C4Hi the lowest energy structure is rhomboidal with a rectangular structure slightly higher in energy. Ab initio spin densities'63 have been calculated for a large number of mono- and bi-cyclic azine radical anions using both MBS and DZ basis sets. Reasonable agreement was found with experimental ratios of hyperfine coupling constants.Finally there have been two studies of Jahn-Teller distortions in C6Hi,164'165 and in C6Fl,164 in one of these papers including 7r-electron correlation. Molecules Containing Other Than First-row Atoms.-Applications to second-row molecules with ever increasing accuracy continue as a result of improvements in methodology and new programmes. Only a few of the many papers are cited in this review. There is much interest in silicon-containing compounds. Spectroscopic observa- tions on various fluorosilylenes have prompted a careful study of the three lowest lying states of SiH, SiHF and SiF2.166 Earlier theoretical work has appeared on SiH2 and SiF2I6' but it is now known that a two configuration treatment must be used for the lowest singlet state of carbenes.This DZ + P study included the three low lying states and agreement with experiment was good. Vibrational frequencies were also calculated many of these not having been observed to date. A model reaction for the insertion of singlet carbenes into alkanes is the reaction SiH + H + SiH4 (7) Following earlier work by Gordon,'68 the reaction has been re-investigated with a two configuration description of SiH2 and a DZ + P basis The barrier was 20 kJ mol-' lower than the single configuration result. The barrier was further lowered to -28 kJ mol-' with CISD which is in good agreement with experiment. The transition state is depicted in (14). has studied a variety of abstraction reactions XH, +H,+ XH,,+ +H (X =C,N,Si,orP) "'J.Kalcher and G. Olbrich THEOCHEM 1983 104 489. D. J. Bellville and N. L. Bauld J. Am. Chem. Soc. 1982 104 5700. D. D. M. Wayner R. J. Boyd and D. R. Arnold Can. J. Chem. 1983 61 2310. I6l H. B. Huang S. Lunnell and A. Lund Chem. fhys. Lett. 1983 99 201. 16* J. W. Bouma D. Pottinger and L. Radom THEOCHEM 1983 103 209. M. H. Palmer and I. Simpson Z. Nuturforsch. Teil A 1983 38 415. 164 K. Raghavachari R. C. Haddon T. A. Miller and V. E. Bondybey J. Chem. Phys. 1983 79,1387. I65 H. Kato K. Hirao and M. Sano THEOCHEM 1983 104 489. I hh M. E. Colvin R. S. Grev H. F. Schaefer 111 and J. Bicerano Chem flip Leff 1983. 99. 390 I67 C. Thomson Theor. Chim. Actu 1973 32 93. I68 M. S. Gordon J. Chem. SOC.,Chem. Commun. 1981 890.I69 R. S. Grev and H. F. Schaefer 111 J. Chem. SOC.,Chem. Commun. 1983 785. I70 M. S. Gordon D. R. Gano and J. A. Boatz J. Am. Chem. Soc. 1983 105 5771. Theoretical Chemistry 41 using a variety of methods including electron correlation. Abstraction by CH is found to proceed more easily than by silyl. The POL-CI'71 method seems to be particularly good for this type of reaction. Further calculations on the Si2H2 system have appeared. Lishka and KOh1e1-l~~ have shown that large scale calculations including correlation and d-functions are essential to get the geometry correct. In particular the twisted structure does not correspond to a local minimum as reported earlier the lowest energy singlet being a non-planar bridged structure (15).For the triplet planar H2SiSi is a global minimum. The addition of HCl to ~ilaethene'~~ differs significantly from the analogous reaction involving C2H4. Gradient calculations with a 3-2 1G basis found the transi- tion state (16) and an intermediate complex which forms early in the reaction. The transition state is two-centre-like whereas the analogous state for the C2H4 reaction is four-centre-like. A careful study (with geometry optimization at the 3-21G level) of the nine possible isomers of CH2N2' and SiH2N2 has been reported by Thomson and G1ide~ell.I~~ All the silicon-containing molecules are unstable with respect to decomposition to SiH2 + N2 and the ab initio results are in disagreement with MNDO predictions for the SiH2N2 isomers.The most stable isomer of CH2N2 is cyanamide but it seems for the Si-containing compounds that the relative energies are incorrect for the 3-2 1G basis sets and one should use the 6-3 1G* basis for these molecules. Correlation corrections do not alter the order of the stabilities but in view of the results on Si2H2 the geometric parameters probably need further investigation with larger basis sets. Hopkinson et al. have studied the singlet and triplet energy surfaces for CSiH2 and the transition states.'75 A DZ basis was used and single point DZ + P or DZ + CI calculations. A similar study of the singlet surface but with more extensive CI was carried out by Hoffmann et ~l.,'~~ who also calculated the harmonic frequencies. Finally Gordon and co-~orkers'~~ have examined the question of the aromaticity of silacyclopentadienyl and silacyclopropenyl cations using an STO-2G basis set.These molecules are not significantly stabilized by delocalization unlike ~i1abenzene.l~~ Ill I72 I73 I75 I76 I77 I78 P. J. Hay and T. H. Dunning jun. J. Chem. Phvs. 1976 64 5077. H. Lishka and H.-J. Kohler J. Am. Chem. Soc. 1983 105 6646. S. Nagase and T. Kudo J. Chem. SOC. Chem. Commun. 1983 363. C. Thomson and C. Glidewell J. Comput. Chem. 1983 4 1. A. C. Hopkinson M. H. Lieu and I. G. Csizmadia Chem. Phys. Left. 1983 95 232. M. R. Hoffmann Y. Yoshioka and H. F. Schaefer 111 J. Am. Chem. Soc. 1983 105 1084. M. S. Gordon P. Boudjouk and F. Anwari J. Am. Chem. Soc. 1983 105 4972. H. B. Schlegel B.Coleman and M. Jones J. Am. Chem. Soc. 1978 100 649. 42 C. Thornson Calculations on similar germanium-containing compounds are now appearing more frequently such as H2Ge=GeH2,'793180 H,Ge=NH H,Ge=O and related molecules.'79 Dixon et ~1.'~' have determined the structure of the ylides and the energetics of the reaction (8) CH,XH + CHYXH;, for X = P N S or 0,using the GVB-POL-CI method. Another paper by the same author'82 has dealt with the proton affinities of RNH2 ROH ROH, and RSH for R = H CH3 SiH3 using a DZ + P basis for the heavy atoms and including zero-point vibrational effects. A very detailed study has appeared of the phosphonium cyclopropylide model H3P=C(CH2)2.'83 The pyramidal carbanion centre of the ground state geometry is shown ( 17).Geometries and energy barriers were given in detail and were consistent with experimental work on more complex systems. Koopman's theorem ionization potentials for a series of hydrides methyls and silyls H,X (CH3),X (SiH3),X; X = F C1 n = 1; X = 0 S n = 2; X = N P n = 3 have been reported.IS4 Excellent agreement with experimental values is found without including d-functions and this conclusion has been verified using several different basis sets. Clark'" has continued his investigations of three-electron bonds with studies of the radical cations H3PPH; H,PSH,' H3PClH+ and HCICIHf. The optimized geometry with S and P ligands tends to be increasingly trigonal bipyramidal. Turning now to sulphur containing molecules it has been observed by ScheinerIS6 that most basis sets correctly predict that NH; has a higher proton affinity than OH2 but it is necessary to go to a 4-31G" basis before the correct ordering of OH and SH2 is obtained.In contrast to the results on the phosphines noted above complete geometry optimization results show that 3d orbitals on S are essential to describe properly the bonding in d-thiocarbanions -CH2SH and -CH2SCH3.'87 Previous work used values which were too long for the C-S bond which are obtained if 3d functions are not included in the basis set. Minimal basis sets (STO-3G) and the larger STO-3G* have been used to optimize the geometries of several sulphur di-imides,Is8 following single point MP3//6-3 1G* calculations. Several isomers and isomerization pathways were studied.A similar study has appeared of the singlet states of six isomeric forms of C2H2S by two different group^,'^^,'^^ the paper by Siegbahn et ~1.'~' using the largest basis I79 G. Trinquier J.-C. Barthelat and J. Satge J. Am. Chem. SOC.,1982 104 5931. I80 S. Nagase and T. Kudo THEOCHEM 1983 103 35. 181 D. A. Dixon T. H. Dunning jun. R. E. Eades and P. G. Gassman J. Am. Chem. Soc. 1983 105 701 1. I82 M. L. Hendewerk R. Frey and D. A. Dixon J. Phys. Chem. 1983.87 2026. I83 M. A. Vincent H. F. Schaefer 111 A. Schier and H. Shmidbaur J. Am. Chem. SOC.,1983 105 3806. 184 C. Glidewell and C. Thornson J. Compur. Chem. 1983 4 9. I85 T. Clark J. Comput. Chem. 1983 4 404. 186 S. Scheiner Chem. Phys. Lerr. 1982 93 540.187 S. Wolfe L. A. LaJohn F. Bernardi A. Mangini and G. Tonachini Tetrahedron Lett. 1983 24 3789 407 1. 188 K. Raghavachari and R. C. Haddon J. Phys. Chem. 1983 87 1308. I89 R. K. Gosavi and 0. P. Strausz Can. J. Chem. 1983 61 2596. I90 P. Siegbahn M. Yoshimine and J. Pacansky J. Chem. Phys. 1983 78 1384. 7%eoretical Chemistry 43 sets. Both singlet and triplet states were studied and the two sets of calculations agree in their main conclusions. Contrary to earlier work the lowest singlet isomer is thioketene CH2=C=S with HCrCSH 30 +70 kJ mol-' higher in energy. Thiirene exists as a minimum on the singlet surface but lies some 160 kJ mol-' above the minimum. Mezey et ~1.'~' have reported the results of a study of the minimum energy reaction paths for two thioketone-enethiol equilibria using an STO-3G basis set.Finally we mention a study of the isomers of C2H4Br+,192 a series of calculations on conformers of 2-fluoro- and 2-~hloro-ethanols,'~~ and three papers which attempt a clarification of some important organic reactions. In the first the energetics of the reactions of chromyl chloride and molybdyl chloride with alkanes alcohols and alkenes has been studied with GVB wave function^,'^^ and in the second a model for the insertion of CO into the Pt"-CH3 bond has been ~tudied.''~ The increasing power of ab initio methods is well illustrated by these two papers. The last paper'96 deals with the first stages of the Stephen Gattermann and Houben- Hoesch reactions and involved determination of the reaction pathway and a large portion of the energy hypersurface for HCl + RCN + RCIC=NH R = N,CH3 (9) Structural Investigations.-The use of ab initio methods for the investigation of the equilibrium configuration of polyatomic molecules continues to grow and only a few selected studies are mentioned.Pulay and co-workers have systematically 19' investigated the effects of basis set and electron correlation on the computation of force constants and separated out the most important effects in studies on HF HCN and NH3. A subsequent careful study of the force fields of glyoxal acrolein butadiene formaldehyde and ethylene was reported19* to reproduce very well the frequencies using a 4-21G basis set. There have been several calculations on various cyclopropanes.Dupuis et have computed the vibrational spectra of cyclopropane itself and the cyclopropyl radical. There is no significant hyperconjugative interaction between the radical centre and the P-C-H bonds in the latter. A similar study of cyclopropane ethylene oxide and ethylene imine has appeared.*" Skancke and co-workers2" have investigated the strain energies in gem-difluorocyclopropanes and rotational isomers of cyclopropanecarboxaldehyde202 and vinylcyclopropane203 have been investigated. 191 A. E. Bruno R. P. Steer and P. G. Mezey J. Comput. Chem. 1983 4 104. 192 R. A. Poirier G. Demare K. Yates and 1. G. Csizmadia THEOCHEM 1983 94 137. 193 J. Murto M. Rasanen A. Aspiala and L. Homanen THEOCHEM 1983 92 45.194 A. K. Rappe and W. A. Goddard 111 J. Am. Chem. SOC.,1982 104 3287. 195 S. Sasaki K. Kitaura K. Morukuma and K. Ohkubo J. Am. Chem. Soc. 1983 105 2280. 196 G. Alagona and J. Tomasi THEOCHEM 1983,91 263. I97 P. Pulay J.-G. Lee and J. E. Boggs J. Chem. Phys. 1983 79 3382. 198 P. Pulay G. Fogarasi G. Pongor J. E. Boggs and A. Vargha J. Am. Chem. SOC.,1983 105 7037. I99 M. Dupuis and J. Pacansky J. Chem. Phys. 1982 76 251 1. 200 A. Komornicki F. Pauzat and Y. Ellinger J. Phys. Chem. 1983 87 3847. 201 A. Greenberg J. F. Liebrnan W. R. Dolbier jun. K. S. Medinger and A. Skancke Tetrahedron 1983 39 1533. 202 G. R. de Mare and M. R. Peterson THEOCHEM 1983 104 115. 203 G. R. de Mare and M. R. Peterson THEOCHEM 1982 89 213.44 C. Thornson Cyclobutane derivatives204 have been studied as have cyclopentane cyclopentene and cy~lopentadiene.~~~ Calculations on homocyclopropenylium cation206 show that highly sophisticated calculations (MP4/6-3 1G") are required to provide accurate information on this type of homoaromatic species. A similar example is provided by the 2-norbornyl cation (see earlier refs. 127 and 128). An important paper by Schleyer and K0s207has addressed the question of negative (anionic) hyperconjugation uia calculations on several fluorosubstituted molecules such as FCH,CH, F2BCH, and F2AlCH,. The stabilization energies are found to be large and it is concluded that the effect is definitely established. Hexahalogenoben~enes~~~*~~~ have been studied at DZ level and a variety of properties evaluated with different basis sets for C6H6 and C6F6.All the compounds are found to be planar at the SCF level. The C6H;' isomers2" have been studied with geometry optimization and their fragmentation to C5H3f and CH,' investigated. A full optimization study of the planar hydrogen2" maleate anion at the SCF level predicts a slightly asymmetric structure. Finally borepine (18)2'2 and its valence isomers have been studied in more accurate calculations. Molecular Interactions.-We mention a few of the many papers on this topic in this section. The important role of the solvent and H20 in particular on reactions continues to be an active area of research. For instance the influence of the solvent on the reaction ( 10) H2C0 + LiBH4 -* products (10) has been investigated using a modified SCF formalism with quite large effects on the reaction energy profile although the mechanistic conclusions are not altered appre~iably.~'~.~'~ The hydration of formaldehyde2I5 has been studied utilizing Ko10s'216suggestion to eliminate the basis set superposition error.The enthalpies of a large number of gas-phase hydration reactions X + H,O -* H,OX (X = H+ Li+ H20) (1 1) have been computed using MP3 level of theory with excellent agreement with e~periment.~" 204 T. Jonvik and J. E. Boggs THEOCHEM 1983 105 201. '05 S. Saeb~i F. R. Cordell and J. E. Boggs THEOCHEM 1983 104 221. 206 R. C. Haddon and K. Raghavachari J. Am. Chem. Soc. 1983 105 118. '07 P.von R. Schleyer and A. J. Kos Tetrahedron 1983 39 1141. 208 J. Almlof and K. Faegri jun. J. Chem. Phys. 1983 79,2284. 209 J. Almlof and K. Faegri jun. J. Am. Chem. Soc. 1983 105 2965. 210 K. Lammertsma and P. von R. Schleyer J. Am. Chem. Soc. 1983 105 1049. ZI I P. George C. W. Bock and M. Trachtman 1.Phys. Chem. 1983 87,1839. 212 R. L.Disch M. L. Sabio and J. M. Schulman Tetrahedron Lett. 1983 24 1863. 213 R. Bonnacorsi P. Pala and J. Tomasi THEOCHEM 1982 87,181. 214 R. Bonnacorsi P. Cimiraglia J. Tomasi and S. Mierths THEOCHEM 1983 94 1 I. 215 G. M. Maggiora and I. H. Williams THEOCHEM 1982 88 23. 216 W. Kolos Theor. Chim. Acta 1979 51 219. 217 J. del Bene H. D. Mettee M. J. Frisch B. T. Luke and J. A. Pople J. Phys. Chem.1983 87,3279. Theoretical Chemistry Scheiner has continued to investigate proton-transfer including effects of electron correlation and the structure of H302 has been examined221 in detail. The hydration energies for NH; and H30+ have also been studied at the SCF as well as the hydration of ketenimine with H20 and (H20)2.224 Sapse has reported studies of various complexes with HF,225and Scheiner226 has investigated the role of d-functions when the other molecule is H2S. Various authors have proposed other techniques for calculating intermolecular interaction^.^^'-^^^ Numerous papers on hydrogen bonding have appeared for example a series by Hin~hliffe,~~' and an application of a new AESCFdecomposition scheme23' to 12 hydrogen-bonded dimers has given very good results but has shown that STO-3G basis sets are very poor for this problem.There have been several calculations on dimers such as (NO)2,232(H20)2,233,234 (CO)2,235 and (CS)2.235In the latter study bound triplet ground states were predicted. Finally it is clear that with the advent of more powerful computers and improved programs for ab initio calculations these methods will have an even greater impact on chemistry in the future. Acknowledgement. The author wishes once again to thank Mrs. Maureen Thomson for her invaluable help with the literature search. 218 S. Scheiner Int. J. Quantum Chem. 1983 23 739. 219 S. Scheiner Int. J. Quantum Chem. 1983 23 739. 220 S. Scheiner Int. J. Quantum Chem. 1983 23 753. 221 C.M. Rohling L. C. Allen C. M. Cook and H. B. Schlegel J. Chem. Phys. 1983 78 2498. 222 S. Ikuta Cfiem.Phys. Lett. 1983 95 604. 223 S. Ikuta Mass Spectroscopy 1982 30,297. 224 M. T. Nguyen and A. F. Hegarty J. Am. Chem. Soc. 1983 105 381 1. 225 A. M. Sapse J. Chem. Phys. 1983 78 5733 5738. 226 S. Steiner J. Chem. Phys. 1983 78 599. 227 J. Hoinkis A. Ahlrichs and H.-J. Bohm Int. J. Quuntum Chem. 1983 23 821. 228 J. B. Peel Int. J. Quantum Chem. 1983 23 653. 229 0. Navaro Int. J. Quantum Chem. 1983 23 1611. 230 A. Hinchliffe THEOCHEM 1983 105 335 and references therein. 23 I W. A. Sokalski P. C. Hariharan and J. J. Kaufman J. Phys. Chem. 1983 87 2803. 232 R. D. Bardo J. Phys. Chem. 1982 86 4658. 233 M. D. Newton and N. R. Kestner Chem.Phys. Lett. 1983,94 198. 234 L. A. Curtiss Chem. Phys. Lett. 1983 96 442.