3 Theoretical Organic Chemistry By I. H.WILLIAMS School of Chemistry University of Bath Bath BA2 7AY A comprehensive review of the year’s literature in this thriving area might fill the remainder of this volume the latest supplement to the bibliography of ab initio calculations alone has 1842 entries.’ What follows in this report is necessarily very selective and subjective but aims to highlight significant theoretical developments as applied to organic chemistry. 1 Computational Methods Despite the increasing capabilities of ab initio quantum-chemical methods on ever more powerful computers (e.g. calculation of the SCF electrostatic potential around an undecapeptide cyclosporin derivative with 199 atoms and 1000 basis functions2) semi-empirical MO methods remain important tools for the study of organic and bio-organic molecules.The AM1 method has been parameterized for halogens3 and phosph~rus,~ and is even included as an option in the GAUSSIAN38 suite of ab initio programs. Besides being useful in its own right for explorations of energy surfaces AM1 provides an economical means of obtaining geometries for species whose energies may then be determined by single-point calculations using high-level ab initio method^.^ A new and efficient technique for optimization of the parameters in semi-empirical MO methods has been developed and applied by Stewart to the modified neglect of diatomic overlap scheme.6 The result is PM3 (parametric method three following MNDO and AMl) available in MOPAC version 5.0 for the elements H C N 0 F Al Si P S C1 Br and I.The average difference between calculated and experimental heats of formation for 657 compounds is 33 kJ mol-I (CJ 58 and 53 kJ mol-’ respectively for MNDO and AMl) with the most dramatic improve- ments being for hypervalent compounds. Since PM3 probably represents an optimum parameterization (within the limitations of accuracy of the reference data employed) errors which remain -e.g. square-planar cyclobutadiene -are likely to be errors associated with the form of the Hamiltonian itself.6 PM3 hydrogen bonds are linear6 and the utility of this new method has been demonstrated by its use in a study of reaction pathways and specific solvation effects upon phosphoryl transfer reactions.’ ’ Quantum Chemistry Literature Database.Supplement 8. Bibliography of ab initio calculations for 1988 ed. K. Ohno K. Morokuma and H. Hosoya THEOCHEM 1989 62 1. ’S. L. Price R.J. Harrison and M. F. Guest J. Comput. Chem. 1989 10 552. M. J. S. Dewar and E. G. Zoebisch THEOCHEM 1988,49 1. M. J. S. Dewar and C. Jie THEOCHEM 1989 56 1. ’ M. J. S. Dewar A. J. Holder E. F. Healy and S. Olivella J. Chem. Soc. Chem. Commun. 1989 1452. J. J. P. Stewart J. Compur. Chem. 1989 10 209 221. ’H. S. Rzepa and M. Y. Yi J. Chem. Soc. Chem. Commun. 1989 1502. 33 34 I. H.Williams PM3 energy surfaces for the Beckmann rearrangement of oximes' and for additions of phosphaalkenes and phosphonium ylides to formaldehyde are in good agreement with the results of ab initio methods.' On the subject of third editions Allinger's heralded MM3 molecular mechanics force field for hydrocarbons has arrived; lo this corrects known deficiencies of MM2 and provides reliable estimates of many properties including vibrational frequencies for the purpose of evaluating absolute and relative entropies.The MM3 van der Waals parameters for C and H make these atoms slightly larger and softer than in MM2 and the introduction of a torsion-stretch interaction term enables the lengths of eclipsed C-C bonds to be evaluated correctly as in norbornane and dodeca- hedrane." MM2 parameters have been reported for furan thiophene and related compounds siloxanes nitriles organoselenium and tellurium compounds,12 chlorosilanes and di~ilanes,'~ epoxides,16 and pentacoordin- amides,14 di~xetanes,'~ ate phosphorus compounds." In applying computational quantum chemistry to organic molecules using ab initio methods three major areas of difficulty arise basis sets electron correlation and the multidimensional nature of potential energy surfaces.Practical schemes intended to provide accurate results must consider all three aspects. The use of second-order Moller-Plesset theory (MP2) to estimate electron correlation effects on molecular geometries is becoming standard; for this purpose it is necessary to include polarization basis functions on non-hydrogen atoms," as in the MP2/6-3 lG* method. Basis sets specifically designed for correlated molecular calculations have been reported;" the 6-311G basis is not of triple-zeta quality (as claimed) in the valence region." Pople et al.have prescribed a general procedure for predictions of total energies of molecules at equilibrium geometries using methods implemented in GAUSSIAN88 with accuracies of *8 kJ mol-' in atomization energies for molecules containing two first-row atoms.21 This 'Gaussian- 1' procedure treats electron correla- tion effects at the MP4SDTQ level (with single double triple and quadruple excitations) using the 6-31 1G** basis for geometries optimized at the MP2/6-31G* level and then augments this by corrections (assumed to be additive) for zero-point energy additional diffuse sp and higher polarization basis functions on non-P. A. Hunt and H. S. Rzepa J. Chem. SOC.,Chem. Commun. 1989 623. H. S. Rzepa J.Chem. Soc. Perkin Trans. 2 1989 2115. 10 N. L. Allinger Y. H. Yuh and J.-H. Lii J. Am. Chem. SOC.,1989 111 8551; J.-H. Lii and N. L. Allinger ibid. pp. 8566 8576. N. L. Allinger H. J. Geise W. Pyckhout L. A. Paquette and J. C. Gallucci J. Am. Chem. Soc. 1989 111 1106. 12 J. C. Tai J.-H. Lii and N. L. Allinger J. Comput. Chem. 1989 10 635; M. R. Frierson and N. L. Allinger J. Phys. Org. Chem. 1989 2 573; E. Goldstein and N. L. Allinger THEOCHEM 1989 57 149; N. L. Allinger J. A. Allinger and L. Q. Yan ibid. 1989 60,363. l3 S. G. Cho R. J. Unwalla F. K. Cartledge and S. Profeta J. Compul. Chem. 1989 10 832; S. Profeta R. J. Unwalla and F. K. Cartledge ibid. p. 99. 14 D. M. Schnur Y. H. Yuh and D. R. Dalton J. Org. Chem. 1989 54 3779. l5 W.H. Richardson J. Org. Chem. 1989 54 4677. 16 B. L. Podlogar and D. J. Raber J. Org. Chem. 1989 54 5032. G. Robinet M. Barthelat V. Gasni and J. Devillers J. Chem. Soc. Chem. Commun. 1989 1103. l8 H. Guo and M. Karplus J. Chem. Phys. 1989,91 1719. 19 T. H. Dunning J. Chem. Phys. 1989,90 1007. 20 R. S. Grev and H. F. Schaefer J. Chem. Phys. 1989 91 7305. 21 J. A. Pople M. Head-Gordon D. J. Fox K. Raghavachari and L. A. Curtiss J. Chem. Phys. 1989,90 5622. Theoretical Organic Chemistry 35 hydrogen atoms so-called quadratic C1 and for 'higher-level' effects. A scheme has also been presented for simultaneous optimization of wavefunction and geometry by an efficient quadratically convergent method.22 It is well known that the UHF method for open-shell species does not in general give pure spin states this causes problems when using perturbation methods to determine correlation energies.Spin projection techniques have been proposed by several groups recently to annihilate the contaminating spin states either as part of the SCF procedure,23 or afterwards giving PMPn 24 or PUMPn 25 wavefunctions. Configuration interaction is an important method for evaluating electron correla- tion effects but it suffers from a lack of size consistency; this feature introduces significant errors into calculated interaction energies26 and barrier heights2' for associative or dissociative reactions. This problem can be side-stepped by treating the dissociated species not as isolated molecules but as a supermolecule whose components are separated by a large distance.Coupled-cluster methods are being used increasingly and have the great advantage of being guaranteed size consistent;28 These methods differ from Moiler-Plesset methods (which are also size consistent) in that they treat certain classes of excitation to all orders of perturbation theory whereas the MPn methods treat all classes of excitation to a certain order n. The importance of higher-than-double excitations in determining chemical reaction barriers is illustrated by a study29 of the unimolecular triple dissociation of glyoxal into 2CO + H2.CI with single and double excitations reduced the activation energy from its SCF value by 29 kJ mol-' but the coupled-cluster singles-and-doubles method reduced it by 56 kJ mol-' and inclusion of triple excitations caused a further reduction of 24 kJ mol-'.If the SCF wavefunction provides a qualitatively adequate description for a molecule and if the perturbation series converges well then MP4SDQ and MP4SDTQ give roughly equivalent results to CCSD and CCSDT re~pectively.~' As yet however high-level methods such as these can be applied in practice only to systems containing no more than four first-row atoms. Schlegel has reported3' an improved algorithm for reaction-path following (as implemented in GAUSSIAN88) and Koseki and Gordon have discussed32 modifications to intrinsic reaction coordinate methods (available in the Iowa/ North Dakota version of GAMESS) suitable for very flat potential energy surfaces.Ab initio reaction paths may be interfaced with calculations of chemical reaction rate constants using the POLYRATE program for variational transition-state theory and semiclassical tunnelling calculation^.^^ A strategy for dealing with branching points on such reaction paths has been devised.34 22 M. Head-Gordon J. A. Pople and M. J. Frisch Int. J. Quantum Chem. Symp. 1989 23 291. 23 J. Baker Chem. Phys. Lett. 1988 152 227; J. Chem. Phys. 1989 91 1789. 24 H. B. Schlegel J. Phys. Chem. 1988 92 3075; J. J. W. McDouall and H. B. Schlegel J. Chem. Phys. 1989 90 2363. 25 P. J. Knowles and N. C. Handy J. Chem. Phys. 1988 88 6991. 26 J. E. Del Bene and I. Shavitt Int. J. Quantum Chem. Symp. 1989 23 445. 27 T. P. Hamilton and H.F. Schaefer J. Chem. Phys. 1989 90,6391. 28 R. J. Bartlett J. Phys. Chem. 1988 92 1697. 29 G. E. Scuseria and H. F. Schaefer J. Am. Chem. Soc. 1989 111 7761. 30 J. F. Stanton R. J. Bartlett D. H. Magers and W. N. Lipscomb Chem. Phys. Lett. 1989 163 333. 3' C. Gonzales and H. B. Schlegel J. Chem. Phys. 1989 90 2154. 32 S. Koseki and M. S. Gordon J. Phys. Chem. 1989 93 118. 33 K. K. Baldridge M. S. Gordon R. Steckler and D. G. Truhlar J. Phys. Chem. 1989 93 5107. 34 E. Bosch M. Moreno J. M. Lluch and J. BertrLn Chem. Phys. Lett. 1989 160 543. I. H. Williams 2 Structure Bonding and Properties Orbital based schemes for population analysis of wavefunctions (Mulliken analysis or natural population analysis) predict oxygen atomic charges of about -0.6 in a range of oxygenated compounds whereas spatially based analyses (integrated Bader populations or integrated projected populations) predict charges about twice this size implying very polar C-0 bonds; the charge is not centred on the oxygen nucleus and is not spherically di~tributed.~~ Bader analysis of phosphorus com- pounds indicates polarization in the sense -C-P+ i.e.opposite to that for C-N bonds.36 Correlation effects do not significantly affect the topological and atomic properties of electron density distributions and MP2 provides a practical method for many molecule^.^' In natural population analysis correlation at the MP2 level acts consistently to reduce charge ~eparations.~' A new population analysis based on atomic polar tensors has been proposed.39 Allen has suggested an extension of the formula for Lewis-Langmuir formal atomic charges providing a more realistic manifestation of bond polarity a more natural balance between covalent and ionic extremes is achieved by a fractional weighting using the electronegativities of the atoms.40 Furthermore he has proposed an alternative definition of electronegativity as the average one-electron energy of the valence-shell electrons in ground-state free atoms.41 Pearson has discussed the application to organic chemistry of the concepts of absolute electronegativity and absolute hardness,42 and Parr has used the latter quantity (together with relative hardness with respect to an acyclic reference) to assess aromaticity in cyclic conjugated molecules.43 A study of rr-electron delocalization in azines suggests there is essentially the same delocalization in all the compounds considered and essentially the same resonance energies for benzene pyridine pyrazine and ~yrimidine.~~ The authors disagree with the assertion of Shaik and Hiberty that electron delocalization is seldom a driving force in conjugated systems involving C N and 0 atoms.However Wiberg et al. have elsewhere discussed the limitations of resonance interactions in acyclic systems pointing out for example that the barrier to internal rotation in allyl cation arises from electron delocalization and electrostatic contributions but in allyl anion is largely electrostatic in origin.45 The spin-coupled descriptions of the .rr-systems of na~hthalene~~ are similar to that of benzene.and heteroar~matics~' The bonding in hypervalent molecules such as sulphuranes can be described qualitatively without invoking d-orbital participation in the valence shell by either 35 S. M. Bachrach and A. Streitwieser J. Comput. Chem. 1989 10 514. 36 S. M. Bachrach J. Comput. Chem. 1989 10 392. 37 R. J. Boyd and L.-C. Wang J. Comput. Chem. 1989 10 367; L.-C. Wang and R. J. Boyd J. Chem. Phys. 1989 90,1083. 38 J. E. Carpenter M. P. McGrath and W. J. Hehre J. Am. Chem. SOC.,1989 111 6154. 39 J. Cioslowski J. Am. Chem. SOC.,1989 111 8333. 40 L. C. Allen J. Am. Chem. SOC.,1989 111 9115. 41 L. C. Allen 1.Am. Chem. SOC.,1989 111 9003. 42 R. G. Pearson J. Org.Chem. 1989 54,1423. 43 Z. Zhou and R. G. Parr J. Am. Chem. SOC. 1989 111 7371. 44 K. B. Wiberg D. Nakaji and C. M. Brenernan J. Am. Chem. SOC.,1989 111 4178. 45 K. B. Wiberg C. M. Breneman K. E. Laidig and R. E. Rosenberg Pure Appl. Chem. 1989 61 635. 46 M. Sironi D. L. Cooper J. Gerratt and M. Raimondi 1.Chem. Soc. Chem. Commun. 1989 675. 47 D. L. Cooper S. C. Wright J. Gerratt and M. Raimondi J. Chem. SOC.,Perkin Trans. 2 1989 255 263. 7'heoretica1 Organic Chemistry 37 MO or VB models.48 A VB analysis suggests two types of hypercoordinated XH,+I radicals those involving an avoided crossing between Lewis-structure curves only and those which additionally involve an 'intermediate' curve.49 This model attributes the bonding in bipyramidal SiH,- to efficient use of the axial Si-H (T*orbitals (in contrast to the situation in CH5-) rather than to hypervalency associated with d-~rbitals.~' Integrated population analysis of bonds between silicon and common non-metals indicates extensive polarization in the sense +Si-X-.In contrast to carbon the ionic nature of these bonds allows silicon to expand its coordination sphere to form stable pentacoordinate species.51 A P-SiH3 substituent stabilizes secondary and tertiary carbenium ions by 93 and 67 kJ mol-' respectively three times the effect of a P-CH group whereas both substituents have about the same influence on radical stabilitie~.~~ The tendency for hyperconjugative stabilization in carbenium ions causes the 2-pr0pyl~~ and cyclopen- ty154 cations to be chiral and distorts 2-adamantyl cation (1) away from the classical C, geometry.55 The 7-norbornyl cation (2) has a C,-symmetrical non-classical structure.56 The extremely short central C-C single bond in bitetrahedryl (3) and in bicubyl (4) is associated with increased s-character arising from the bending H (1) (2) (3) (4) back of the substituents on those atoms.57 cis-Butadiene slightly prefers a gauche c~nformation:~' conjugation is little affected by torsion of up to about 40".3 Reactivity and Mechanism Pericyclic Reactions.-A perturbational MO analysis of the C,-symmetrical transition structure for the synchronous concerted Diels- Alder addition of ethene to butadiene suggests that the barrier (AH' = 107 kJ mol-' at the MP4SDTQ/6-31G* level) is largely due to closed-shell repulsions between filled orbitals on the addends.59 The Cope rearrangement of 3,3-dicyanohexa- 1,Sdiene is predicted by RHF/ AM 1 calcu- lations to proceed by a synchronous concerted mechanism involving an aromatic 4H J.G. Angyin THEOCHEM 1989 55 61; F. Volatron ibid. p. 167. 49 A. Demolliens 0. Eisenstein P. C. Hiberty J. M. Lefour G. Ohanessian S. S. Shaik and F. Volatron J. Am. Chem. SOC.,1989 111 5623. G. Sini P. C. Hiberty and S. S. Shaik J. Chem. Soc. Chem. Commun. 1989 772. '' S. Gronert R. Glaser and A. Streitwieser J. Am. Chem. Soc. 1989 111 3111. 52 M. R. Ibrahim and W. L. Jorgensen J. Am. Chem. SOC.,1989 111 819. 53 P. von R. Schleyer W. Koch B. Liu and U. Fleischer J.Chem. Soc. Chem. Commun. 1989 1098. 54 W. Koch B. Liu and P. von R. Schleyer J. Am. Chem. Soc. 1989 111 3479. 55 R. Dutler A. Rauk T. S. Sorensen and S. M. Whitworth J. Am. Chem. SOC.,1989 111 9024. 56 M. Bremer K. Schotz P. von R. Schleyer U. Fleischer M. Schindler W. Kutzelnigg W. Koch and P. Pulay Angew. Chem. In?. Ed. Engl. 1989 28,,1042. 57 P. von R. Schleyer and M. Bremer Angew. Chem. Int. Ed. EngL 1989 28 1226; Y. Xie and H. F. Schaefer Chem. Phys. Lett. 1989 161 516. 5R J. E. Rice B. Liu T. J. Lee and C. M. Rohlfing Chem. Phys. Lerr. 1989 161 277; I. A. Alberts and H. F. Schaefer Chem. Phys. Lert. 1989 161 375. 59 R. D. Bach J. J. W. McDouall H. B. Schlegel and G. J. Wolber J. Org. Chem. 1989 54 2931. 38 I. H. Williams transition structure rather than the more usual biradicaloid path:’ Pericyclic reac- tions with small exo- or endothermicities are likely to occur by both the syn- chronous/aromatic and non-synchronous/biradicaloidpaths representing distinct mechanisms as for either boat or chair Cope rearrangements.Claisen rearrangements of ally1 vinyl ethers owing to their large exothermicities occur mostly by a single merged mechanism of intermediate type.6‘ Epiotis suggests that stabilizing charge alternation in the transition structures for allowed concerted reactions may be promoted by weak polarizable bonds in the underlying a-system. Thus the balance between concerted and stepwise biradical mechanisms may be determined by the a-bonds and replacement of first-row atoms by heavier ones (e.g.substitution of Si for C) should favour concerted mechanisms.62 Asymmetric Diels-Alder additions between substituted butadienes and ethenes are predicted by RHF/AMl to be concerted but are stepwise processes at the UHF/AMl RHF/AMl and RHF/3-21G calculations for cycloadditions of butadiene and cyclopentadiene to various cyanoalkenes correctly predict substituent effects on activation energies and indicate limited asynchronicity in the transition structures but incorrectly predict the ex0 mode of addition to be favoured.64 Similarly RHF/AMl gives a generally good account of the Diels-Alder reaction between cyclopentadiene and P-angelica lactone (whereas MNDO overestimates the barrier and gives a very asynchronous transition structure) but fails to predict the observed preference for the endo addu~t.~’ An AM1 study of addition of acrolein to ethene (yielding dihydropyran) could not rule out the possibility of a biradicaloid intermediate,66 but ab initio RHF studies on the Diels-Alder addition of butadiene to acrolein (yielding 4-formylcyclohexane) correctly predict the observed endo preference and an’ appreciable asynchronicity in the concerted transition str~cture.~’ Thermal decarboxylations of 2-oxetanones are formally forbidden 7~2s+ 7~2s processes which are predicted to proceed by concerted mechanisms involving highly asynchronous zwitterion-like transition structures; AM1 calculations reproduce experimental substituent effects The corresponding acid-catalysed reactions are stepwise processes involving a carbocationic intermediate whose conformation allows the observed stereochemical outcome to be interpreted.Diastereofacial selectivity in Diels-Alder additions may be considered theoreti- cally in terms of (a) electrostatic interactions between reactants in their equilibrium geometries (b) frontier MO arguments or (c) direct calculations on transition structures. Full optimization at the RHF/AMl level of all possible transition struc- tures for additions of ethene acrolein and methyl propiolate to pentadienes with stereogenic substituents at the terminal position -for attack at each face of the diene there are three rotamers -suggests that stereoselectivity is determined by a subtle 60 M. J. S. Dewar and C.Jie J. Chem. SOC.,Chem. Commun. 1989 98. 61 M. J. S. Dewar and C. Jie J. Am. Chem. SOC.,1989 111 511. 62 N. D. Epiotis J. Org. Chem. 1989 54 953. 63 J. Y. Choi and 1. Lee J. Chem. Soc. Faraday Trans. 2 1989 85 867. 64 K. N. Houk R. J. Loncharich J. F. Blake and W. L. Jorgensen J. Am. Chem. SOC.,1989 111 9172. 6S M. Sodupe A. Oliva J. Bertrkn and J. J. Dannenberg J. Org. Chem. 1989 54 2488. 66 L. F. Tietze J. Fennen and E. Anders Angew. Chem. Znf. Ed. Engl. 1989 28 1371. 67 R. J. Loncharich F. K. Brown and K. N. Houk J. Org. Chem. 1989,54 1129; K. N. Houk Pure Appl. Chern. 1989 61 643. 68 A. Moyano M. A. Pericas and E. Valenti J. Org. Chem. 1989 54 573. Theoretical Organic Chemistry 39 combination of specific steric and electronic interaction^.^^ No single effect domi- nates and electronic effects are not clearly manifested in any simple parameter such as HOMO/ LUMO properties charges or 7r-densities.Predictions made on the assumption that undistorted reactant properties are reflected at transition-state level are not uniformly c~rrect,~~’~~ and this lack of reliability emphasizes the importance of full geometry optimization for transition structures. Dewar has criticized frontier MO theory as ‘.. . unsound unnecessary and unreliable and there are no chemical problems that cannot be solved in simpler more effective ways.’ 70 A Woodward-Hoffmann (WH) allowed pericyclic reaction involving migration of hydrogen is likely to be synchronous owing to the propensity of hydrogen to form three-centre bonds.61 AM 1 calculations for dihydrogen transfer reactions between various donors and acceptors predict synchronous concerted mechanisms whereas the MNDO method tends to favour stepwise mechanisms involving radical- pair intermediates7’ The alternative concerted and stepwise mechanisms have com- parable barriers in AM 1 for dihydrogen elimination reactions whereas MNDO again favours the latter.72 The transition structure for the concerted ene reaction between methyl acrylate and propene has less asynchronous character at the RHF/6-31G level than for the parent reaction of ethene with propene and a lower barrier.73 ‘Torquoselectivity’ is the term coined for the stereochemical preference of elec- trocyclizations to involve twisting in one direction rather than the other.Ring- opening of cyclobutene-3-carboxylic acid and its conjugate base should proceed to the outside-substituted butadiene (Scheme l),but protonation of the acid is predicted X Scheme 1 to reverse the stereochemistry leading to the inward-substituted product involving the strong 7r-electron-withdrawing -C( OH),+ Similarly resonance-donor substituents are predicted to stabilize the transition structure for electrocyclization of pentadienyl cation when attached to the 1-position on the outside but resonance- acceptor substituents should stabilize the transition structure more effectively when in the inside position.75 WH forbidden reactions require multiconfigurational treatments for qualitatively correct descriptions and careful theoretical studies76 have indicated that concerted 69 N.Kaila R. W. Franck and J. J. Dannenberg J. Org. Chem. 1989 54 4206. 70 M. J. S. Dewar THEOCHEM 1989 59 301. 71 D. K. Agrafiotis and H. S. Rzepa J. Chem. Soc. Perkin Trans. 2 1989 475. 72 D. K. Agrafiotis and H. S. Rzepa J. Chem. SOC.,Perkin Trans. 2 1989 367. 73 T. Uchimara S. Tsuzuki K. Tanabe and Y. Hayashi J. Chem. Soc. Chem. Commun. 1989 1861. 74 A. B. Buda Y. Wang and K. N. Houk J. Org. Chem. 1989 54 2264. ’’E. A. Kallel and K. N. Houk J. Org. Chem. 1989 54 6006. 76 J. Breulet and H. F. Schaefer J. Am. Chem. SOC.,1984 106 1221; F. Bernardi A. Bottoni M. A. Robb H. B. Schlegel and G. Tonachini ibid. 1985 107 2260; F. Bernardi M. A. Robb H. B. Schlegel and G.Tonachini hid. 1984 106 1198. I. H. Williams pathways do not actually exist for WH forbidden disrotatory ring opening of cyclobutene 7r2s + 7r2s ethene dimerization and suprafacial 1,3-hydrogen migra- tion in propene. However a transition structure for concerted forbidden suprafacial 1,3-hydrogen migration in cyclopropene does exist at the CASSCF HF and MP2 levels although its energy is very close to the dissociation limit for cyclopropenyl radical plus atomic hydrogen.77 Multiconfigurational SCF calculations predict the walk rearrangement of bicyclo[ 2.1 .O]pent-2-ene to proceed preferentially by the allowed concerted mechanism with inversion at the methylene carbon in a transition structure with -50% biradical character; the forbidden rearrangement with retention of configuration is disfavoured by only 32 kJ mol-’ and occurs via a pure biradical i~~termediate.’~ A CASSCF and MP4 study shows the degenerate thermal rearrange- ment of methylenecyclobutane also to be a stepwise process involving a biradical intermediate stabilized by 7r-electron delocalization in the allylic m~iety.’~ Intramolecular reactivity of the carbene species cyclopropylmethylerie is determined by conformation the cis conformer (5) undergoes ring expansion to cyclobutene whereas the trans conformer (6) preferentially fragments to ethene and ethyne.80 H I Additions to Unsaturated Systems.-Cieplak et al.have discussed three categories of theoretical models for stereoelectronic effects in 7r-facial diastereoselectivity of additions to carbonyl groups viz.those which consider (a) ground-state distortior:s or (b) transition-state torsional interactions or (c) electron donation into the vacanl u+*orbital associated with the incipient bond. They have argued that only the latter Cieplak’s model can accommodate observations on the effects of electron- withdrawing and -releasing substituents in reagents and in cyclohexane-based sub- strates.” Ab initio MO studies of nucleophilic addition of organometsllic reagents to acrolein show that methyllithium prefers (charge-controlled) 1,2-addition whereas methylcopper prefers (orbital-controlled) 1,4-addition via a six-membered cyclic transition structure giving a metal enolate rather than an a-cuprio ketone.82 Stereoselectivities of addition of methylcopper to chiral a$-unsaturated carbonyl compounds are determined by a combination of steric and electronic effects there are similarities to nucleophilic addition to the carbonyl group particularly in regard to the steric requirements for addition to the E-isomers of substituted ensis.but the electronic characteristics are quite different with substituent effects being more in line with expectations for electrophilic reactions.83 Conjugate addition of dialkyl- cuprates to electron-deficient C=C bonds is predicted to involve pre-complexation 77 F. Jensen Chem. Phys. Lett. 1989 161 368. 78 F. Jensen J. Am. Chem. SOC.,1989 111 4643. 79 P. N. Skancke N. Koga and K. Morokuma J. Am. Chem. SOC.,1989 111 1559. 80 P.B. Shevlin and M. L. McKee J. Am. Chem. SOC.,1989 111 519. A. S. Cieplak B. D. Tait and C. R. Johnson J. Am. Chem. SOC.,1989 111 8447. 82 A. E. Dorigo and K. Morokuma J. Am. Chem. SOC.,1989 111 4635. 533 A. E. Dorigo and K. Morokuma J. Am. Chem. SOC.,1989 111 6524. Theoretical Organic Chemistry 41 of copper implying an acute angle of attack onto the double bond which may explain the opposite stereoselectivities observed in the reactions of dialkylcuprates on the one hand and of alkylcopper reagents (and other conventional nucleophiles) on the other.84 The relative reactivities of acrylic acid methacrylic acid acrylonitrile and acrolein towards Michael addition may be predicted by the values of the Laplacian of the electron density distribution which manifests the sizes of the regions of charge depletion on the electrophiles at the site of nucleophilic attack.85 An intramolecular Michael addition has a higher barrier than its intermolecular counterpart owing to the stereoelectronic requirements in forming the six-membered cyclic transition structure.86 The chair transition structure for allylboration of formaldehyde is predicted to be 34 kJ mol-’ lower in energy than the twist-boat transition ~tructure.~’ Spin-projection (see above) halves the barrier heights calculated at the MP4 level for methyl radical addition to ethene and to formaldehyde and gives values agreeing well with experimental activation energiess8 The potential energy barrier for addition of dichlorocarbene to ethene is calculated to be very low (2.5 kJ mol-’ at MP2/6-31G*) and the free energy of activation 49 kJ mol-’ as determined by variational transition-state theory arises largely from the entropic term which is probably responsible for the selectivity of carbene additions.89 The inclusion of diffuse basis functions has a dramatic effect upon the potential energy surface for alkylation of acetaldehyde enolate anion by methyl fluoride and permits unambiguous distinction between the kinetic ( 0-alkylation) and thermody- namic ( C-alkylation) reactions.” The activating/deactivating abilities of substituent groups and their directing effects upon electrophilic aromatic substitution may be predicted by topological analysis of the electron density distributions of substituted phenyl compounds; these effects are not reflected in the total charges of the phenyl group or of its individual atoms but rather in the Laplacian of the total charge distribution in the n-populations and quadrupole moments of the ring carbons and in the ellipticities of the C-H bonds of the phenyl group.” The energetics of formation of arenium ion intermediates in electrophilic aromatic substitution may be interpreted similarly.’* The orientation of electrophilic substitution in non-alternant polycyclic fluoranthrene hydrocarbons have been predicted using a revamped PPP semi-empirical method parameterized for 7r-electrons only.93 SN2Displacements.-Topological electron density analyses at the RHF and MP2 levels with extended basis sets for SN2 methyl transfers involving a range of simple leaving groups and anionic nucleophiles demonstrate that the charges on the incoming and outgoing groups do relate to the position of the transition structure along the reaction ~oordinate;~~ however in the transition structures they do not 84 A.E. Dorigo and K. Morokuma J. Chem. SOC.,Chem. Commun. 1989 1884. as M. T. Carroll J. R. Cheeseman R. Osman and H. Weinstein J. Phys. Chem. 1989 93 5120. 86 C. I. Bayly and F. Grein Can. J. Chem. 1989 67 2173. 87 Y. Li and K. N. Houk J. Am. Chem. SOC.,1989 111 1236. 88 C. Gonzalez C. Sosa and H. B. Schlegel J. Phys. Chem. 1989 93 2435. 89 J. F. Blake S. G. Wierschke and W. L. Jorgensen J. Am. Chem. Soc. 1989 111 1919. 90 E. S. Marcos and J. Bertran J.Chem. SOC.,Furuduy Trans. 2 1989 85 1531. 91 R. F. W. Bader and C. Chang J. Phys. Chem. 1989 93 2946. 92 R. F. W. Bader and C. Chang J. Phys. Chem. 1989 93 5095. 93 M. J. S. Dewar and R. D. Dennington J. Am. Chem. SOC.,1989 111 3804. 94 Z. Shi and R. J. Boyd J. Am. Chem. SOC.,1989 111 1575. 42 I. H. Williams have equal magnitudes contrary to the assertions of Shaik and Pross. A quantitative VB computation of a curve-crossing diagram in the manner of those latter workers' qualitative VB model has been carried out for the SN2reaction H-+ CH based upon local fragment orbital^.^' A barrier height of 239 kJ mol-' in the adiabatic potential curve was calculated and the quantum-mechanical resonance energy in the transition state i.e.the magnitude of the avoided crossing interaction was 67 kJ mol-'. MP4SDTQ and coupled-cluster energies agree to within 1 or 2 kJ mol-' for the ion-molecule complex and 4 or 5 kJ mol-' for the transition structure of the reaction H-+ CH3F; the inclusion of triple excitations was found to be essen- tia1.96 The shape of the energy profile calculated for the dihydrated reaction shown in equation 1 is closer to that for aqueous solution (from Jorgensen's simulation Cl-(H,O) + CH,Br -[HOH--(Cl--CH,--Br)--HOH]-, ClCH + Br-(H,O) (1) for C1- + CH3Cl) than to the gas-phase reaction.97 A MNDO effective charge a generalized Born dielectric continuum and the RISM integral equation methodloo have each been applied to the C1- + CH3Cl reaction and an analysis of discrete continuum and discrete-continuum models of solvation effects on SN2reactions has been presented."' Miscellaneous.-Jorgensen has reviewed his work on free energy calculations which illustrates the power and potential of molecular dynamics and statistical mechanics simulations for modelling organic chemistry in solution.102 For example Monte Carlo simulations and statistical perturbation theory can yield free energies of hydration which with use of a thermochemical cycle lead to calculated pK values for various organic acids.'03 Many-body solvation effects are important in describing the nature of the transition state for the Meyer-Schuster reaction in aqueous solution.'04 Dewar has discussed the nature of desolvation barriers to reactions in solution which are barrierless in the gas phase.'05 The degenerate double proton transfer in the formamidine dimer (7) is predicted to be a concerted process (in the gas phase),'" whereas the double proton shift in azophenine (8) proceeds by a stepwise rnechani~m.'~' Shaik and Pross have argued that in general cation radicals are likely to be less reactive than cations (of the same acceptor ability) towards nucleophilic attack; the former reactions involve product electronic configurations which are doubly excited with respect to the reactants (and so are 'forbidden') whereas the latter involve singly excited product configurations (and so are 'allowed').lo* 95 G. Sini S. S. Shaik J.-M. Lefour G. Ohanessian and P. C. Hiberty J. Phys. Chem. 1989 93 5661.96 M. Urban G. H. F. Diercksen 1. CernuSak and Z. Havlas Chem. Phys. Lett. 1989 159 155. 97 K. Hirao and P. Kebarle Can. J. Chem. 1989 67 1261. 98 T. Kozaki K. Morihashi and 0. Kikuchi J. Am. Chem. Soc. 1989 111 1547. 99 S. C. Tucker and D. G. Truhlar Chem. Phys. Left. 1989 157 164; J. Phys. Chem. 1989 93 8138. 100 S. E. Huston P. J. Rossky and D. A. Zichi J. Am. Chem. Soc. 1989 111 5680. 101 C. AICman F. Maseras A. Lledbs M. Duran and J. Bertran J. Phys. Org. Chem. 1989 2 611. I02 W. L. Jorgensen Acc. Chem. Res. 1989 22 184. 103 W. L. Jorgensen and J. M. Briggs J. Am. Chem. SOC.,1989 111 4190. 104 0. Tapia J. M. Lluch R. Cardenas and J. Andres J. Am. Chem. SOC.,1989 111 829. I05 M. J. S. Dewar and D. Storch J. Chem. SOC. Perkin Trans.2 1989 877. 106 P. Svensson N.-A. Bergman and P. Ahlberg Z. Naturforsch. A 1989 44 473. 107 M. K. Holloway C. H. Reynolds and K. M. Men J. Am. Chem. SOC.,1989,111,3466; H. Rumpel and H.-H. Limbach ibid. p. 5429. lo* S. S. Shaik and A. Pross J. Am. Chem. Soc. 1989 111 4306. Theoretical Organic Chemistry I H (7) Along a minimum-energy reaction path the principle of conservation of bond order is valid to a good approximation using ab initio bond orders computed according to Meyer’s definition.”’ The Hammond postulate and the notion of molecular similarity have been investigated by topological analysis of molecular shape changes occurring along reaction paths.”’ Menger has contended that transition-state modelling does not always model transition states better correlation with experimental activation energies for some degenerate intramolecular hydride transfers being achieved using ground-state struc- tures having all their bonds intact than using transition-state models with partial bonds and charges ‘The ability of “transition-state modelling” to predict rates in solution does not depend on the accuracy or even the existence of a transition state but rather on how closely the associated parameters coincide with one of many parameter sets that happen to provide a high correlation.’”’ G.Lendvay J. Phys. Chem. 1989 93 4422. I10 G. A. Arteca and P. G. Mezey J. Phys. Chem. 1989,93 4146. Ill M. J. Sherrod and F. M. Menger J. Am. Chem. Soc. 1989 111 2611.