3 TheoreticaI Chemist ry By H.S. RZEPA Department of Chemistry Imperial College of Science and Technology London S W7 2AY 1 Introduction A further volume in the series of Specialist Periodical Reports’ and the proceedings of a conference on computational theoretical organic chemistry’ provide reviews of recent advances in this field and Clementi3 has described in detail one approach to the study of large chemical systems of biological importance using quantum mechanical methods. Two interesting developments are the increasingly common study of organometallic systems and their reactions by ab initio SCF-MO techniques (see below) and the setting up of computer data bases for ab initio molecular wave function^^" and their literature citation^.^' 2 Advances in Theoretical Techniques Geometry Optimization.2a-Schaefer and co-workers’ have extended their study of analytical energy derivatives (i.e.with respect to the nuclear co-ordinates) by formulating expressions for the gradients of open-shell/CI wavefunctions illustrat- ing the technique by calculating the geometry and the vibrational frequencies of the ‘Al and 3B1states of methylene. The difference in the zero-point energies between the two states was then calculated and used in an estimate of the ‘most probable’ value of 41 f 6 kJ mol-’ for the singlet-triplet energy difference. Developments in theoretical techniques seem often to be reflected in calculations on this species! Improvements to the algorithms for calculating energy derivatives continue to be made6a and in one particularly elegant example6’ molecular symmetry was used to reduce the time taken for the ab initio analytical evaluation of the Hessian (i.e.the second derivative or force constant) matrix [cf.Annu. Rep. Bog. Chem. Sect. B 1980 77 161. The time was found to be proportional to 1/N ‘Theoretical Chemistry’ ed. C. Thompson (Specialist Periodical Reports) Royal Society of Chemistry 1981 Vol. 4. (a) H. B. Schlegel Nato Adu. Study Inst. Set. Ser. C Comput. Theor. Org. Chem. 1981 67 129 J. D. Goddard ibid. p. 161; (b)R. A. Poirier ibid. p. 15; (c)M. A. Robb and R. H. A. Eade ibid. p. 21. E. Clementi Lecture Notes in Chemistry. Vol. 16 Computational Aspects for Large Chemical Systems Springer-Verlag New York 1980. (a)R. A. Whiteside J.S. Binkley R. Krishnan D. J. DeFrees,,H. B. Schiegel and J. A. Pople Carnegie Melfon Quantum Chemistry Archive Carnegie-Mellon University Pittsburgh PA (USA) 1980; (6)Y. Osamura S. Yamabe F. Hirota H. Hosoya S. Iwata H. Kashiwagi K. Morokuma M. Togasi and S. Obara J. Chem. Znf. Comput. Sci. 1981,21 86. Y. Osamura Y. Yamaguchi and H. F. Schaefer J. Chem. Phys. 1981,75 2919. (a) L. R. Kahn J. Chem. Phys. 1981 75 3962; (a) T. Takada M. Dupuis and H. F. King ibid. 1981,75 332. 39 H. S. Rzepa where N is the order of the point group corresponding to the molecular symmetry and in this way the vibrational frequencies of ethane could be calculated in ca. 20 times less time than more conventional methods. It is also important to use efficient energy-minimization algorithms for the optimization of molecular geometries.Iterative algorithms based on variable-metric methods [such as the Davidon- Fletcher-Powell (DFP) or the generally more robust Broyden-Fletcher-Goldfarb-Shanno (BFGS) procedure],' in which only a local approximation to the inverse Hessian matrix is evaluated were foundga to be faster or at least equal in speed to the force relaxation method of Pulay,g6 where the inverse Hessian is obtained via numerical differentiation of the first derivatives. The force relaxation method may yet prove to be superior if the inverse Hessian is obtained analytically as in the example of ethane above. BasisSets.26-New minimum and extended basis sets for use in ab initio calculations continue to be recommended for specific applications.The Schleyer groupg have developed STO (4-31+G) sets in which extra p functions are added to all the first row atoms and which are claimed to be suitable for calculations involving anionic species. Such basis sets were used inter alia in studying proton affinities. Morokuma's group" have shown how effective core potentials (ECP) for the first row elements can be used in the calculation of geometries and energies of molecules and the transition states for their interconversion. They used a STO 31G valence basis set in conjunction with analytical gradients and found that the energies differed by less than 8 kJ mol-' and the geometries by less than 4 pm or 0.5" from the values obtained using the all electron 4-31G basis set.This approach promises to decrease significantly the time taken by ab initio calculations. The last year has seen a proliferation of basis sets for elements of higher rows of the periodic table such as for Rb Sr In-Xe,"" Sc-Cu,"* and the transition metals of the first and second series,"' greatly facilitating studies involving organometallic species. Electron Correlation.2c-This immensely difficult problem continues to attract interest. The CASSCF (Complete Active Space SCF) method has been developed12 and is an MCSCF scheme [cf. Annu. Rep. Prog. Chern. Sect. B 1980 77 171 in which no selection of individual configurations is required. This selection problem has also been tackled using many-body-perturbation theory. A coupled-cluster- singles-doubles (CCSD) method is reported13 to be a good approximation to a 'full' Configuration Interaction (CI) approach in which th 7 number of terms is limited to a function of N6 (where N is the number of basis functions).These types of ' R. W. H. Sargent ACSSymp. Ser. 1980,124,37. (a) F. Bernardi A. Bottoni and G. Tonachini J. Mof.Sfrucr. Themhem. 1981 86 123; (6)P. Pulay G. Fogarasi F. Pang and J. E. Boggs J. Am. Chem. SOC.,1979,101,2550. J. Chandrasekhar J. G. Andrade and P. von R. Schleyer J. Am. Chem. SOC.,1981,103 5609. S. Obara K.Kitaura and K. Morokuma Theor. Chim. Actu 1981,60 227. (a)W.J. Pietro E. S. Blurock R. F. Hout W. J. Hehre D. J. DeFrees and R. F. Stewart Inorg. Chem. 1981,20 3650; (b)A. K. Rappe T. A. Smedley and W.A. Goddard J. Phys. Chem. 1981 85 2607;(c) I. Hyla-Kryspin J. Demuynck A. Strich and M. Bknard J. Chem. Phys. 1981 75 3954;(d)W. R. Wadt J. Am. Chem. SOC.,1981,103,6053. l2 P. E. M. Siegbahn J. Almlof A. Heiberg and B. 0.Roos J. Chem. Phys. 1981,74,2384. l3 (a) G.D. Purvis and R. J. Bartlett J. Chem. Phys. 1982,76 1910;(b)R. J. Bartlett Annu. Reu. Phys. Chem. 1981 32,359. Theoretical Chemistry 41 methods enable in some cases more than 98% of the correlation energy to be recovered although at considerable computational expense. Semi-empirical and Other More Approximate Methods.-Thie114" has presented a modified version (MNDOC) of the MNDO method which has been parameterized for the elements C H N and 0.The problem of electron correlation is dealt with explicitly rather than in the averaged parametric manner of MNDO and for molecules in which electron correlation effects are not unusual MNDOC was found to give results similar to MNDO.Significant differences were found for e.g. cyclo-butadiene at a square (D4h) geometry where MNDOC predicts the singlet state to be ca. 42 kJ mol-' more stable than the triplet apparently in violation of Hundt's rule (!) but in agreement with ab initio calculations. This is purely a correlation effect since the two states are formally degenerate in the NDDO approximation upon which MNDO is based. Another interesting result was that the most stable geometry of [18]annulene is predicted to have D6h rather than D3hSYX'nmetry. Although this agrees with the X-ray structure it differs from other semi-empirical and ab initio calculations that have been made using uncorreluted wavefunctions [cf.Annu.Rep. Prog. Chem. Sect. B 1980,77,22]. It is ironic that current SCF-MO theory has such problems in dealing correctly with the types of molecules with which molecular orbital theory at the Huckel level began! Thie114' has also applied the MNDOC method to the study of excited states finding that although vertical excitation energies are calculated to be too low by cu. 1eV singlet-triplet energy separations are predicted very well. A related in~estigation'~' into the use of split valence shell basis sets at the NDDO level was not encouraging yielding results that were no better than the original MNDO procedure for the prediction of molecular energies.MNDO parameters for aluminium have been reported'' and the results of calculations for species containiig lithium have been cited,I6 although the parameters have unfortunately not yet been published. A method based on a new formalism for U/Tseparability (QCFF/PI) has been parameterized for molecules containing nitrogen and oxygen" and it appears to be useful in calculating the equilibrium conformations electronic spectra vibra- tional spectra and resonance Raman spectra of large biological chromophores and for studying the effect of solvent or protein environment on these properties. One curious property of semi-empirical methods and CND0/2 in particular is the high degree of charge alternation predicted for polar molecules.An experi- mental study was found not to support this although an indication was given that the MNDO method may give more physically reasonable results.18 3 Electronic Structure and Geometries of Molecules Conformations and Intermolecular Interactions.-Molecular mechanics calcula- tions seem capable of quite subtle indications of molecular deformations and 14 (a) W. Thiel J. Am.Chem. SOC.,1981,103,1413 1420; (b) A.Schweig and W. Thiel ibid. p. 1425; (c) W. Thiel Theor. Chim. Acra 1981,59,191. L. Davis R.M. Guidry J. R. Williams M. J. S. Dewar and H. S. Rzepa J. Compur. Chem. 1981,2 1s 433. 16 J. Chandrasekhar and P. von R. Schleyer J. Chem. Soc. Chem. Commun. 1981,260. 17 A.Warshel and A. Lappicirella J. Am.Chem.Soc. 1981,103,4664. 18 R. D. Stolow P. W. Samal and J. W. Giants J. Am. Chem. SOC.,1981,103 197. H. S. Rzepa reactivities. Ab initio calculations had indicated [cf.Annu. Rep. Prog. Chern. Sect. B 1980,77,21] that norbornadiene has non-planar double bonds with the hydrogen atoms on the endo-side of the molecule and this finding is also now reproduced by MM2 molecular mechanics calculati~ns.'~ This suggests that these deformations to not occur as a result of orbital repulsions for which the MM2 method is of course not parameterized. Other applications of this method include a study of the conformation of valerolactone,20 in which the calculated rotational constants of the half-chair form were found to be in better accord with those obtained from the microwave spectrum than those calculated for the boat form.A study2' (using the molecular mechanics method) of the formation of acylchy- motrypsins as a model for enzyme-substrate interactions involved considering more than 40000 non-bonding interactions alone! Ac-L-Trp-X (X = NH,) is a good substrate binding some lo5times faster than the D-isomer which corresponds to a difference in free energy between the two species at the transition state of ca. 29 kJ mol-'. The calculations indicated that coulombic terms for the three major hydrogen bonds accounted for 20 kJ mol-' of this energy while van der Waals repulsions accounted for 8-13 kJ mol-'. This study is claimed to be the first success- ful computer evaluation of enzyme-substrate specificity! The force field of uracil has now been calculated using an ab initio procedure and a STO-3G basis set with the force constants being corrected to '4-31G basis set quality'.22" Many uncertainties in the force field of benzene appear to have been resolved using 4-21G basis set calculations,22b and sxh studies of the force fields of medium-sized molecules are now becoming fairly routine.As well as being of great help in applications such as the molecular mechanics calculations cited above they can often help to interpret complex experimental spectra. Neutral Species.-Several challenges to experimentalists have been made on the basis of theoretical calculations. Mislow and co-workersZ3 find no theoretical support for the surprisingly short (147 pm) central C-C bond length in hexaphenylethane suggested by a recent X-ray structural determination on a related compound.The molecular mechanics and MNDO methods both predict a value of ca. 168 pm. A class of bridged 'hyperstable' olefins which should display decreased reactivity of the bridgehead double bond (e.g.a smaller than normal heat of hydrogenation) have been [i.e. (l)]and molecular mechanics calculations have indicated l9 U. Burkert Angew. Chem. Int. Ed. Engl. 1981 20 574. T. Philip. R. L. Cook T. B. Malloy N. L. Allinger S. Chang and Y. Yuh J. Am. Chem. Soc. 1981 103,2151. D. F. DeTar J. Am. Chem. Soc. 1981,103 107. 22 (a) Y. Nishimura M. Tsuboi S. Kato and K. Morokuma J. Am. Chem. Soc. 1981 103 1354; (b) P. Pulay G. Fogarasi and J. E. Boggs J.Chem. Phys. 1981,14 3999. 23 E. Osawa Y. Onuki and K. Mislow J. Am. Chem. Soc. 1981,103,7475. 24 W. F. Maier and P. von R. Schleyer J. Am. Chem. Soc. 1981,103,1891. Theoretical Chemistry H H (4) several unknown polycyclic compounds containing 3,4 or 5-membered rings which should be reasonably stable [e.g. (2)and (3)JZ5 Schleyer and his group in a continuing search for compounds containing planar tetraco-ordinate carbon found that (4) was predicted by the MNDO method to prefer a planar geometry. Unfortunately an X-ray study of 2,6-dimethoxyphenyl-lithium showed it to be hexameric and not dirneric.I6 A MNDO studyz6 of [2.2.2.2]paddlane (5) revealed an extraordinary central C-C bond of length 148pm. Planar tetraco-ordinate carbon is sp2 hybridized with a lone pair of electrons in the p orbital perpendicular to the molecular plane and a LUMO with S symmetry located on the substituents.The central bond in (5) is formed from the appropriate overlap of pairs of these orbitals to give a cr bond with some S (!) character i.e. correspondingly shorter than a normal C-C bond. However the energy of this system was so high that it is unlikely to be detected experimentally. S~haefer~~~ has thrown down the gauntlet regarding the structure of dimethyl silaethene. Ab initio calculations using a very large basis set and a substantial configuration interaction (CI) predicted a bond length of 169pm for the Si=C bond compared with the surprisingly long exrerimental value of 183 pm. Morokuma and co-workers independently calculated this bond to be 173 pm long finding also a Si=C vibrational wavenumber (about 1000cm-') in good agreement with that observed.28 Schaefer has also challenged276 a suggestion based on experi- mental evidence that (6) rearranges rapidly at low temperatures to the silylene (7)z7c with an implied barrier of less than 20 kJ mol-'.Ab initio calculations on the parent silaethene using a large basis set and extensive CI indicated a barrier to a [1,2]-hydrogen shift of 170 kJ mol-'! The possibility that addition of one methyl group to silaethene would account for this discrepancy was considered to be remote implying that this reaction may not be a simple hydrogen shift. Many other calculations of species containing silicon continue to be 25 P.Gund and T. M. Gund J. Am. Chem. SOC.,1981,103,4458. 26 E. U. Wurthwein J. Chandrasekhar E. D. Jemmis and P. von R. Schleyer Tetrahedron Lett. 1981 22 843. '' (a) Y. Yoshioka J. D. Goddard and H. F. Schaefer J. Am. Chem. SOC.,1981,103,2452;(b) Y. Yoshioka and H. F. Schaefer ibid. p. 7366;(c) R. T. Conlin and D. L. Wood ibid. p. 1843;T. J. Drahnak J. Michl and R. West ibid. p. 1845. '* K.Morokuma S. Nagase and M. Hanamura Tetrahedron Lett. 1981,22 1813. 29 (a) R. A. Poirier and J. D. Goddard. Chem. Phys. Lett. 1981,80 37;(b) M. H. Lien and A. C. Hopkinson ibid. p. 114;(c)M. S. Gordon and R. D. Koob J. Am. Chem. SOC.,1981 103 2939; (d) M. S. Gordon and J. A. Pople ibid. 1981 103 2945; (e)G.Trinquier and J.-P. Malrieu ibid. p. 6313.44 H. S. Rzepa ~~ H H H \ / .. 1 Si-C -H B Me/si=c\ /\ A H Me H Ab initio calculations indicate3' that the unknown and formally aromatic com- pounds (8) and (9) have about 70% of the resonance energy of the isoelectronic carbocyclic cations and a STO-3G study31 of the recently synthesized dodecahe- drane indicated that although a proton could easily pass through one of the faces into and out from the centre this would not be possible for Li'. Although theoretical calculations are often of great help in the study of molecules with unusual bonding Schaefer and co-workers have shown how difficult it can be to interpret wavefunctions in simple bonding An MCSCF calculation with 13 413 configurations indicated that ozone has 23% biradical character compared with a value of 5.2% obtained using 'only' 6825 configurations and 46% such character obtained using a simple SCF/2 X 2CI procedure.The first value was suggested to be the most soundly based and it was also emphasized that the MCSCF procedure is readily applied to the analytical calculation of first and second deriva- tives enabling the facile optimization of molecular geometries and th,e vibrational analysis of stationary points so located. Such an analysis has often proved useful. Despite being formally aromatic (10) was in this manner to actually correspond to the transition state for racemization of the chiral species (ll)! Charged Species.-Homoaromaticity in cyclic carbanions is considered by several groups of workers to be an over-rated phenomenon.MNDO and STO-3G calcula-tions on (12) show no evidence of the effect and it has been concluded34 that such effects may only arise in carbonium ions. Simple Huckel theory has been used to study the resonance energy in delocalized polycarbanions and oxocarbanion~.~~ Although such theory includes no terms for electron repulsion which is known to be especially important in anionic species it was concluded that of the oxocar- banions only the deltate dianion was highly 30 K. Krogh-Jespersen D. Cremer J. D. Dill J. A. Pople and P. von R. Schleyer J. Am. Chem. Soc. 1981,103,2589. 31 R. L. Disch and J. M. Schulman J. Am. Chem. SOC.,1981,103,3297. 32 W. D. Laidig and H. F. Schaefer J Chem. Phys. 1981,74 3411. 33 E.E. Waali J. Am. Chem. Soc. 1981,103,3604. 34 (a)E. Kaufmann H. Mayr J. Chandrasekhar and P. von R. Schleyer J. Am. Chem. Soc. 1981,103 1375; (b)J. B. Grutzner and W. L. Jorgensen J. Am. Chem. Soc. 1981,103 1372. '' (a) R.B. Bates B. A. Hess C. A. Ogle and L. J. Schaad J. Am. Chem. Soc. 1981 103 5052; (6) J. Aihara ibid. p. 1633. Theoretical Chemistry An interesting conflict has appeared over whether fluorine can stabilize car- banions by hyperconjugation. Apel~ig,~" found that ab initio 4-31G calculations predict (13a X = F) (in which hyperconjugation is possible) is 47 kJ mol-' more stable than (13b) (in which it is not). A similar difference in energy was found for X = CF,. This and the results of a Mulliken population analysis was taken as evidence that both F and CF can stabilize carbanions by hyperconjugation.However Streitwieser and co-w~rkers~~~ have criticized the Mulliken population analysis as being inter alia basis-set dependent. By carrying out a specific integra- tion of the calculated electron density they show that a H-C bond is as effective as a F-C bond if charge transfer is taken as a criterion of hyperconjugation. They conclude that the concept of negative fluorine hyperconjugation is not significant and that the calculated barrier to rotation in (13a) is more correctly explained in terms of a charge-induced polarization of the appropriate (T bond rather than actual charge transfer to the fluorine. 0 (134 (13b) (14) A great deal of attention has been devoted to other ways of stabilizing carbanions.In the system XCH; substituents such as X = Li BH2 CF etc. exert a significant stabilizing effect whereas X = NH2 OH F CH have only a weak stabilizing Anions of the type (14) have been to be stabilized by 'dipole interactions' and an even greater effect was shown if lithium was present (15) being 55 kJ mo1-I more stable than (16). In systems such as LiCH2X (X = OH or NH2) stabilization is achieved by the formation of a non-classical carbene-like species (17).37c The Schleyer group3* has investigated the rather elusive acyl carbanions using MNDO and ab initio 4-31+G calculations. These indicated that bridgehead aldehydes such as 1-adamantyl carboxaldehyde aromatic aldehydes and disub- stituted formamides were best suited for experimental studies of proton abstraction from CHO groups.Clark39 has rationalized the experimental e.s.r. observation that whereas the radical anions formed from CH3X (X= F or Cl) have three-fold symmetry the analogous silicon compounds have lower symmetry with one unique hydrogen. Ab initio 3-21G calculations indicated that the most stable form of CH3XL was best considered as a loose complex between CH; and X-and that the silicon compound had a 'T' structure (18). A suggestion has been made that the observed exchange between CN- and CH3CN is not a simple S,2 substitution but involves nucleophilic addition/elimina- tion with an intermediate [1,2]methyl shift. MNDO calculation^^^ indicate that this (a)Y. Apeloig J. Chem. SOC.,Chem. Commun.1981 396; (b)A. Streitwieser C. M. Berke and G. W. Schriver Tetrahedron (Suppl. 9),1981,37,345. 37 (a)A. Pross D. J. DeFrees B. A. Levi S. K. Pollack L. Radom and W. J. Hehre J. Org. Chem. 1981,46 1693; (b) N. G. Rondan K. N. Houk P. Beak W. J. Zajdel J. Chandrasekhar and P. von R. Schleyer ibid. 1981 46 4108; (c) T. Clark P. von R. Schleyer K. N. Houk and N. G. Rondan J. Chem. SOC.,Chem. Commun. 1981,579. 38 J. Chandrasekhar J. G. Andrade and P. von R. Schleyer J. Am. Chem. SOC.,1981,103,5612. 39 T. Clark J. Chem. SOC.,Chem. Commun. 1981,515. 'O J. G. Andrade T. Clark J. Chadrasekhar and P. von R. Schleyer Tetrahedron Lett. 1981 22 2957. H.S. Rzepa (15) (16) (17) (18) may be the least favourable pathway. The route shown in Scheme 1 is about 68 kJ mol-' lower in energy and makes an interesting suggestion for experimental study.'C HH H-*j Scheme 1 The mechanism of nucleophilic reactions that proceed via electron transfer to form radical intermediates has been investigated using ab initio 3G and 4-31G calculations using CHzNO; + CICHzNOz as a m0de1.~' The species resulting from electron transfer (CICHzNO;) was predicted to dissociate spontaneously to CH,NO; and C1-. A simple point-charge model was used to represent the effects of solvation by a dipolar solvent and the activation energy for electron transfer (in which the nitro-groups act as relays) was estimated at about 104 kJ mol-' or less. An important study of gas-phase SN2reactions using ab initio wavefunctions has shown4* that whereas the geometry of the transition state correlates very well with the heat of reaction (i.e.the Bell-Evans-Polanyi-Leffler-Hammond effect) the activation energy as is well known does not. The calculations enabled a quantitative test of the Marcus theory of such reactions which emerged with flying colours. Interestingly these authors observe that the calculated gas-phase behaviour of HOO- was entirely normal discussing the implications of this finding in terms of the so called a-effect. Lest the impression be given that studies of positively charged species have been neglected the impressive study by the Pople group Qf the C1-C3 carbocations should be The geometries have been optimized at the 6-31G* basis set level correlation energy corrections have been made at the MP4 level and zero- point-energy terms have been included.This definitive study of simple carbocations is claimed to predict relative energies to an accuracy of at least *20 kJ mol-'. Carbenes and Open-Shell Species.-Borden and Da~idson~~ have discussed some of the considerable theoretical problems associated with the quantitative calculation of wavefunctions of diradicals illustrating this with species such as cyclobutadiene 41 B. Bigot D. Roux and L. Salem J. Am. Chem. SOC.,1981,103 5271. 42 S.Wolfe D. J. Mitchell and H. B. Schlegel J. Am. Chem. SOC.,1981 103 7692 7694. K. Raghavachari R. A. Whiteside J. A. Pople and P. von R. Schleyer J. Am. Chem. Soc. 1981, 103,5649. 4* W. T. Borden and E. R. Davidson Ace. Chem. Res.1981,14,69. Theoretical Chemistry 47 cyclopentadienyl cation trimethylenemethane and cyclopropenyl anion. Despite a common belief that the square singlet (*Big) ground state of cyclobutadiene is obliged by the Jahn-Teller theorem to distort to a rectangular species this is not formally correct. They show that distortion can occur by mixing with a higher 'A1 state (uia a vibration of bl symmetry) and such a 'second-order Jahn-Teller effect' can either merely reduce the force constant for this vibration (as in tetra-t-butylcyc- lobutadiene) or actually make it negative (as in cyclobutadiene itself). A detailed consideration of the problems involved in calculations of cyclopropenyl anion makes illuminating reading. The singlet is unlikely to prefer a planar geometry much less one of D3hsymmetry.Related problems were enco~ntered~~ in a study of the degree of dipolar character in methylenecyclopropene. Using ab initio MCSCF wavefunctions calculated at the geometries predicted by the MNDO method states were found for the twisted species (19) that had both diradical and pronounced zwitterionic character. The calculated properties and energies of these states were highly sensitive to the method of calculation although in general the MCSCF approach was concluded to be more reliable than the SCF/CI method. The four basic types of n-orbital initialized photoreactions of ketones (hydrogen- atom abstraction cycloaddition to double bonds a-cleavage and electron transfer) have been analysed using 'natural' orbital correlations.The first two examples belong to a class in which a new (T bond is formed to the ketone whilst in the second two examples a (T bond possessed by the ketone is ruptured. The role of triplet states and charge-transfer states in these reactions was Organometallic Species.-Schaefer has reviewed the state of the art regarding non-correlated ab initio wavefunctions for metals prognosticating that the 1980s will see a large increase in such calc~lations.~~ To illustrate what is currently feasible Schaefer quotes his group's study of (20) (21) and (22) in which the calculated geometries showed good agreement with the experimental structures. An orbital correlation diagram for (20) is presented which has interesting pedagogic possibility.:0.' H U That such calculations can be of genuine interest to organic chemists is illustrated by the theoretical study of trimethylenemethane-bis(phosphine)Pdcomplexes car- ried out by the Fenske-Hall procedure.48 Trost and co-workers had found that the species (23)was formed rather than the isomeric (24),contrary to chemical intuition regarding the relative stability of primary and secondary carbanions. The calcula- tions confirmed that indeed (23) is the more stable this being rationalized in terms of the bonding of the trimethylenemethane fragment with the metal. A cyano-group 45 R. P. Johnson and M. W. Schmidt J. Am. Chem. Soc. 1981,103,3244. 46 B. Bigot A. Devaquet and N. J. Turro J. Am. Chem. SOC.,1981,103,6. 47 (a)H. F. Schaefer J.Mol. Struct. Theochem. 1981 1 117; (b) R. M. Pitzer J. D. Goddard and H. F. Schaefer J. Am. Chem. SOC.,1981 103 5681. 48 D. J. Gordon R. F. Fenske T. N. Nanninga and B. M. Trost J. Am. Chem. SOC.,1981,103 5974. H. S. Rzepa > -,I,' 7' -7 Pd Pd' 4 '\\ L' 't LL (23) (24) perhaps not so surprisingly was predicted to show similar regioselectivity whereas a CF3group was predicted to be much less selective. Morokuma and co-~orkers~~ have illustrated a much more rigorous theoretical approach to the study of organometallic reactions e.g. Pt(PH3) +H2 = Pt(H)2(PH3)2. The calculations were carried out using a double-6 basis set with a relativistic effective core potential and a large 67 000 configuration CI. The transi- tion state for the insertion reaction was located with the aid of analytically calculated gradients and characterized by a vibrational analysis.Zero-point energy corrections led to a value of 34 kJ mol-' for the activation energy corresponding to a very early transition state in which the H-H bond was only stretched by 4%. This is no doubt the forerunner of many such calculations on organometallic systems. 4 Dynamic Processes and Energy Hypersurfaces The MIND0/3C4H4 potential energy surface has been studied by the Dewar group." This surface proved to be of immense complexity and no less than 19 minima corresponding to closed-shell species with no biradical character together with many of the transition states interconnecting them were located! Although some of these species are probably artifacts of the MIND0/3 method several isomers of surprisingly low energy were suggested as being worthy of further study (e.g.25). Such a comprehensive study of the surface of even a relatively small molecular system is still largely beyond an ab initio approach and the use of semi-empirical methods as 'pathfinders' is an obviously useful technique. H (25) A paper by Schaefer and co-w~rkers'~ on an ab initio study of the decomposition of glyoxal to CO and H2 makes very interesting reading. A symmetrical (Cz,) stationary point was located at four basis set levels; STO-3G 3-21G double-[ and double-6 +polarization and a vibrational analysis was carried out for each basis. The STO-3G stationary point had three imaginary frequencies (corresponding to the Hessian matrix having 3 negative eigenvalues) the 3-21G had only one (and was thus a genuine transition state) whereas the two double-6 basis sets had two 49 K.Kitaura S.Obara and K.Morokuma J. Am. Chem. Soc. 1981 103,2891. H. Kollmar F. Carrion M. J. S. Dewar and R. C. Bingham J. Am. Chem. Soc. 1981,103 5292. Y. Osamura H. F. Schaefer M. Dupuis and W. A. Lester J. Chem. Phys. 1981.75 5828. Theoretical Chemistry 49 such vibrations the lower one of ca. 96i cm-' corresponding to an out of plane deformation. The properties of the energy surface are seen to change qualitatively with basis set and such a result serves to emphasize the importance of carrying out a vibrational analysis on any putative transition state.Inclusion of an extensive CI (but without reoptimization of the geometries) reduced the calculated barrier by 75 kJ mol-' to ca. 250 kJ mol-'. The vibrational analyses were not then repeated using such correlated wavefunctions leaving open the question of whether the use of CI could have an effect similar to the change of basis set noted above. The transition state for the dissociation of formaldehyde to CO and H2has been located5' using a double-[ + polarization basis set both with and without the inclusion of CI and characterized by a vibrational analysis. In each case only one imaginary vibration was found although no simple relation between the magnitudes of the SCF and SCF/CI transition state vibrational frequencies was observed. The theor- etical barrier to the reaction was estimated at 364 f 21 kJmol-' compared with a barrier of ca.351 kJ mol-' estimated by the same method for the formation of hydroxycarbene by a [1,2]hydrogen shift. A vibrational analysis of the latter system enabled several predictions pertinent to the possible spectroscopic detection of HO(H)C to be made. A vibrational analysis of substituted chloroethanes and their transition states for dehydrochlorination using the MNDO method enabled the 'H/'H and 35C1/37C1 kinetic isotope effects to be calculated and compared with experiment and the '*C/13C isotope effects to be predicted.53 Although good agreement with the observed isotope effects was found the calculated structures of the transition states differed significantly from previously suggested models.These had been established largely by fitting to observed spectroscopic and kinetic data and included many rather arbitrary approximations. It was concluded that a more reliable and consistent approach may be to test quantum mechanical models against experiment rather than to derive models from kinetic and spectroscopic data alone. Kato and Morokuma have presented an impressive study of the unimolecular reactions of vinyl Ab initio calculations at the 4-31G basis set level were used to determine geometries and to carry out vibrational analyses whereas energies were determined at the 6-31G*/Cl level of theory. Ten elementary reactions such as cis-trans isomerization hydrogen migration and a/aor a/P elimination of HF were investigated on both the So and Tl surfaces in order to better understand the photosensitized photodecomposition of this species.Large basis set effects were observed in a study of the fragmentation of (26) to give CO and ethe~~e.~~ The stationary point of CZvsymmetry was characterized as a true transition state at the 4-3 1G basis set level by a vibrational analysis and the calculated barrier (including correction for zero-point energy differences) was 127 kJ mol-' compared with 360 kJ mol-' using a minimal STO-3G basis. Inclusion of CI had little effect on this barrier although the authors then go on to suggest that a biradical intermediate involving C-0 bond cleavage is only 91 kJ mol-' above (26) and that the transition state leading to this biradical is only a little higher in energy! This apparent 52 J.D. Goddard Y. Yamaguchi and H. F. Schaefer J. Chem. Phys. 1981,75 3459. s3 H. S. Rzepa J. Chem. SOC.,Chem. Comrnun. 1981,939. s4 S. Kato and K. Morokuma J. Chem. Phys. 1981,74,6285. 55 D. Feller E. R. Davidson and W. T. Borden J Am. Chem. Soc. 1981,103 2558. H. S. Rzepa contradiction tends to suggest that a vibrational analysis of the C,,stationary point corresponding to the use of a correlated (i.e. SCF/CI or MCSCF) wavefunction may lead to an entirely different result. Such behaviour has in fact been observed at the MNDO The uncatalysed rearrangements of (27)to (28) were predicted to be concerted reactions involving synchronous attack by the nitrogen lone pair on the acyl carbon atom and concomitant C-0 bond cleavage via a planar transition state.However for the analogous acyl migration in (29) the transition state at the uncorrelated RHF/SCF level was found to be significantly non-planar. A simple 3 x 3 CI at this geometry was found to have little effect on the calculated energy [cf.(26)above] but reoptimization of this geometry using a correlated (UHF) wavefunction changed the character completely. The geometry became planar corresponding to a biradical intermediate and nut to a transition state. A 3 x 3 CI at this geometry showed a large lowering of the energy. One problem in such studies is in selecting the appropriate configurations to be used in the CI since those configurations important at the starting estimate of the geometry (i.e.that predicted using RHF/SCF theory) may not be at all important at the geometry eventually predicted using SCF/CI theory. (26) (27) (28) (29) Several studies have been concerned with the correlation of parameters derived from linear free-energy relationships with calculated electronic proper tie^.^' Non-additive substituent effects in some highly hindered pyridines were found to corre- late very well with geometrical distortions calculated using the MIND0/3 method57a and the best set of ‘normal’ Hammett substituent constants that reflect purely the inductive effect of the substituent have been deduced by a comparison with ab inifiu calculations of the charge distrib~tion.~’~ Finally we note several rather less rigorous methods that have been proposed to enable simple rationalization of regio and stereochemistry in organic reactions.Fukui and ~o-workers~~ have shown how the canonical MOs of the fragments of a composite reacting system can be transformed into a set of paired reagent and reactant hybrid MOs so as to condense the intermolecular overlap density. This is an extension of the well known Frontier Orbital approach to include the contribution of all the relevant MOs. It is hoped that the extent of localization and direction of these hybrid MOs will offer a clear and simple distinction between favourable and unfavourable reactions. Burgess and Li~tta~~ have extended the frontier orbital method to include just the major u-T interactions and have shown how this simple approach (which does not require any computer calculations) can often rationalize observed stereochemistry.56 H. S. Rzepa Tetrahedron 1981 37 3107. 57 (a)J. I. Seeman R. Galzerano K. Curtis J. C. Schug and J. W. Viers J. Am. Chem. SOC.,1981 103 5982; (6) E. R. Vorpagel A. Streitwieser and S. D. Alexandratos J. Am. Chem.SOC.,1981,103 3777. (a) K. Fukui N. Koga and H. Fujimoto J. Am. Chem. Soc. 1981 103 196; (b) H. Fujimoto N. Koga M. Endo and K. Fukui Tetrahedron Lett. 1981 22 3427. 59 E. M. Burgess and C. L. Liotta J. Org. Chem. 1981,46 1703.