3 Theoretical Organic Chemistry By I. H. WILLIAMS School of Chemistry University of Bristol Bristol BS8 1TS 1 Introduction The growth in this area of the chemical literature has continued there are 1846 entries in the 1987 bibliography of ab initio calculations’ which of course does not include semi-empirical and molecular mechanics calculations nor results of the ‘pencil and paper’ variety. The aim of this chapter is not to report comprehensively on all areas but to highlight the various themes of interest and importance which have emerged from the year’s published literature. 2 Computational Methods The development of analytical gradient methods for ab initio wavefunctions has been crucial to the application of computational quantum chemistry to organic chemical problems.Owing to the importance of geometry optimization and potential energy (PE) surface exploration the practical utility of any method is severely limited until analytical first (and maybe second) derivatives of the energy are available. Moreover it is becoming increasingly apparent that the treatment of many interesting problems in even a qualitatively correct manner requires the inclusion of electron correlation. It has been suggested that this might soon become an essential requirement for publication of theoretical studies on molecules with up to five first-row atoms; good agreement with experimental geometries and vibrational frequencies is obtained for ‘medium-sized’ organic molecules (three first-row atoms!) using second-order Moller-Plesset perturbation theory (MP2) and configuration interaction with all single and double excitations (CISD) approaches to electron correlation.* Large-scale calculations with the third-order MP3 method are not recommended it is better to use MP2 with a large basis.3 Analytical gradients have been developed for full MP4 wavefunctions (including triple excitations)? The CISD method is neither size-consistent (the energy of a supermolecule AB with A and B at infinite separation is not equal to the sum of the individual energies of two fragments A and B) nor size-extensive (the energy does not scale linearly ’ Quantum chemistry literature database.Supplement 7. Bibliography of ab initio calculations for 1987 ed. K. Ohno and K. Morokuma THEOCHEM 1988,51 1.E. D. Simandiras R. D. Amos N. C. Handy T. J. Lee J. E. Rice R. B. Remington and H. F. Schaefer J. Am. Chem. SOC.,1988 110 1388. I. L.Alberts and N. C. Handy J. Chem. Phys. 1988 89 2107. J. Gauss and D. Cremer Chem. Phys. Lett. 1988 153 303; G. W. Trucks J. D. Watts E. A. Salter and R. J. Bartlett ibid. p. 490. 27 28 I. H. Williams with the number of electrons). There is current interest in methods which overcome these deficiencies such as the coupled-pair functional (CPF) method' and the quadratic configuration interaction (QCISD) method,6 for both of which analytical gradients are now available and the family of coupled-cluster methods e.g. CCSD,7 CCSDT,' etc. which are superior to CI methods for equivalent truncation levels. The above methods are appropriate -at varying degrees of cost! -for the evalu- ation of the dynarnical electron correlation for closed-shell molecules in which the wavefunction is dominated by a single reference determinant i.e.a single pattern of occupation of molecular orbitals by electrons. There is growing awareness however that a single electronic configuration is qualitatively inadequate for the description of many bond breaking and bond making processes and for structures involving highly stretched bonds in these instances a multiconfigurational method is necessary to treat the non-dynamical electron correlation effects. Examples are given in later sections. However there still remains the need to evaluate dynamical correlation arising from a multideterminantal reference.To this end a simple MCSCF perturbation theory -orthogonal valence bond second-order Moller- Plesset (OVB MP2)9-has been described and a unitary multiconfigurational coupled cluster method" has been developed for chemically accurate studies of PE hypersurfaces on which the electronic configurations providing the essential description of the wavefunction change with nuclear geometry. Algorithms have been described for following reaction paths over PE surfaces by steepest descent methods," by gradient extremal walking,I2 and by the local quad- ratic appro~imation,'~,'~ for determining accurate paths leading away from saddle points,13 and for the location of branching points (at which it is energetically favourable for a system to break symmetry) on reaction paths." A novel method for finding saddle points has been suggested,16 involving the generation of an 'image' surface on which valley floors become cols and vice versa; the saddle region therefore possesses all positive curvatures on the image surface and may be found by standard minimization techniques.It is recommended that the 'precise' ~ption'~ and the BFGS Hessian update schemeI8 should always be employed in geometry optimiz- ations using the popular MOPAC and AMPAC programs for semi-empirical MO calculations. The AM1 semi-empirical method has been found to give good results for geometries and for many properties but opinions differ as to its ability to describe hydrogen bonds. Some find it an unreliable tool which 'fails to reproduce the energy J.E. Rice T. J. Lee and N. C. Handy J. Chem. Phys. 1988 88 7011. J. Gauss and D. Cremer Chem. Phys. Lett. 1988 150 280. T. J. Lee and J. E. Rice Chem. Phys. Lett. 1988 150 406. G. E. Scuseria and H. F. Schaefer Chem. Phys. Lett 1988 152 382. J. J. W. McDouall K. Peasley and M. A. Robb Chem. Phys. Lett. 1988 148 183. 10 M. R. Hoffmann and J. Simons J. Chem. Phys. 1988 88 993. 'I B. C. Garrett M. J. Redmon R. Steckler D. G. Truhlar K. K. Baldridge D. Bartol M. W. Schmidt and M. S. Gordon J. Phys. Chem. 1988 92 1476. 12 P. Jprrgensen H. J. A. Jensen and T. Helgaker Theor. Chim. Acfa 1988 73,55. l3 M. Page and J. W. McIver J. Chem. Phys. 1988 88 922. 14 J. Ischtwan and M. A. Collins J. Chem. Phys. 1988 89 2881.J. Baker and P. M. W. Gill J. Comput. Chem. 1988 9 465. 16 C. M. Smith Theor. Chim. Acta 1988 74 85. l7 D. B. Boyd D. W. Smith J. J. P. Stewart and E. Wimmer J. Comput. Chem. 1988 9 387. W. Thiel THEOCHEM 1988 40 415; D. K. Agrafiotis and H. S. Rzepa J. Chem. Res. fS). 1988 100. Theoretical Organic Chemistry 29 and structure of hydrogen bonds in charged systems with useful acc~racy”~ and suggest that ‘conclusions regarding its efficacy . . .need reconsideration’,20 whereas others find its energetic predictions qualitatively acceptable*l and indeed quite adequate for the description of (NH,+) nNH clusters.22 Dannenberg finds the gas-phase hydration energies of protonated diamines to be good and regards the predicted bifurcated hydrogen bonds as genuine; moreover he finds trifurcated structures for the water dimer very similar the AM1 geometry in high-level ab initio calculations and suggests that the experimental geometry may be determined entr~pically.~~ Thiel has provided an overview of the current status of and perspectives for semi-empirical MO methods outlining their theoretical justification and suggesting various options for future improvements but Lindholm has different views regarding the way to develop better methods.24 Watch this space for news of the recently announced PM3 method from J.J. P. Stewart! MM2 molecular mechanics parameters have been reported for hydrogen bonds conjugated nitrogen-containing heterocycles silanes divinyl ethers and aromatic halide derivative^,^^ and for peptides and penicillins.26 Various schemes have been devised for obtaining charges for molecular mechanics calculation^.^^ 3 Structure Bonding and Properties In its diamond jubilee year the concept of hybridization is alive and well.It does not explain molecular geometry but it does ‘happen’ in response to physical interactions between atoms and is therefore not an arbitrary concept; allowing for optimal non-orthogonal hybrids leads to a picture of chemical bonding incorporating most of the familiar concepts of qualitative chemistry such as the VSEPR theory of molecular geoxetry.28 Equally the physical basis for the latter may be found by the analysis of the Laplacian of the electronic charge density local concentrations of charge in the valence shell of an atom in a molecule faithfully duplicate the spatially localized electron pairs of the VSEPR The spin-coupled descrip- tion of methane yields ‘hybridization without preconception^'^' -the optimized orbitals on carbon are sp3-like but are not orthogonal their overlap with each other being 0.48.Bent bonds are a common occurrence and angles between bond paths (the paths of maximum electron density between atoms) are in good accord with common hybridization arguments. Thus the FCH angle in fluoromethane is expected 19 A. A. Bliznyuk and A. A. Voityuk THEOCHEM 1988 41 343. 20 W. C. Herndon and T. P. Radhakrishnan Chem. Phys. Lett. 1988 148 492. 21 G. Buemi F. Zuccarello and A. Raudino THEOCHEM 1988 41 379. 22 S. Galera J. M. Lluch A.Oliva and J. BertrPn THEOCHEM 1988 40 101. 23 J. J. Dannenberg and L. K. Vinson J. Phys. Chem. 1988 92 5635; J. J. Dannenberg ibid. p. 6869. 24 W. Thiel Tetrahedron 1988 44,7393; E. Lindholrn ibid. p. 7461. 2s N. L. Allinger R. A. Kok and M. R. Iman J. Comput. Chem. 1988,9 591; J. C. Tai and N. L. Allinger J. Am. Chem. Soc. 1988 110 2050; M. R. Frierson M. R. Iman V. B. Zalkow and N. L. Allinger J. Org. Chem. 1988,53,5248; J. P. Bowen V. V. Reddy D. G. Patterson and N. L. Allinger ibid.,p. 5471. 26 S. Wolfe D. F. Weaver and K. Yang Can. J. Chem. 1988 66 2687; S. Wolfe M. Khalil and D. F. Weaver ibid. p. 2715. 27 R. J. Abraham and G. H. Grant J. Cornput. Chem. 1988 9 244 709; R. J. Abraham and P. E. Smith ibid. p. 288; J. Mullay ibid. pp. 399 764; L.-G.Hammarstrom T. Liljefors and J. Gasteiger ibid. p. 424. 28 D. B. Cook THEOCHEM 1988 46 79. 29 R. F. W. Bader R. J. Gillespie and P. J. MacDougall J. Am. Chem. Soc. 1988 110 7329. 30 F. Penotti J. Gerratt. D. L. Cooper and M. Rairnondi THEOCHEM 1988 46 421. 30 I. H. Williams to be less than the tetrahedral value since the electronegative fluorine atom should prefer to bond to a carbon hybrid orbital with considerable p character. In reality it is 109.2”,but the angle between the CF and CH bond paths is indeed only 106.7’; such comparisons frequently reveal the nature of intramolecular interaction^.^' Altona and co-workers use non-orthogonal strictly local molecular orbitals as the basis for analysis of intramolecular interactions -such as the anomeric effect -in terms of ‘quasi-classical’ (overlap independent) and ‘interference’ (overlap depen- dent) contribution^.^^ Weinhold however argues for the importance of maintaining strict orbital orthogonality in applying perturbation-style analysis to the physical interpretation of wave function^.^^ In his view natural bond orbitals defined by a simultaneous requirement for maximum electron occupancy and orthonormality correspond better to the classical concept of a transferable localized bond than does a localized molecular orbital; the breakdown of bond transferability may be regarded as arising from interactions between a localized bond and its chemical environment namely rehybridization (Bent’s rule) effects orthogonality (steric) effects and chemical delocalization (hyperconjugative) eff e~ts.~~ Whereas classical valence bond (VB) theory would describe the C-Li bond in methyl lithium as a mixture of covalent and ionic structures involving orbitals localized on each centre the spin-coupled VB method uses a different language in describing this bond as a purely covalent interaction between orbitals allowed to be delocalized.By projecting their spin-coupled VB wavefunction on to a classical VB basis of localized atomic orbitals however Hiberty and Cooper have shown that the ‘covalent’ picture for methyl lithium with delocalized orbitals implicitly contains ionic structures and reveals about 76% ionic character for the C-Li bond (organic chemists will be reassured to learn!).35 Why are carboxylic acids stronger acids than are alcohols? The standard textbook answer (‘because the carboxylate anion is stabilized by resonance delocalization’) is wrong say Siggel Thomas and Streit~ieser.~~ Normal inductive effects which polarize the acid account for most of the enhanced acidity of a carboxylic acid.Different methods of electron population analysis all agree that the carbonyl group in carboxylic acids is highly polarized and is the major factor affecting their acidity relative to alcohols. The total charge in the carboxylate anion is delocalized but the carbonyl oxygen is already so negatively charged in the acid that it can accept very little extra charge by allylic resonance in the v-system as conventionally represented. Not surprisingly this proposition has aroused some debate!37 The question of the origin of the anomalously high acidity of Meldrum’s acid (l),which the previous year had been suggested as ‘a worthy target for theoretical el~cidation’,~~ has been answered much less contr~versially.~~ The syn conformation of an ester 31 K.B. Wiberg and M. A. Murcko THEOCHEM 1988 46 355. 32 G. F. Smits M. C. Krol and C. Altona Mol. Phys. 1988 65 513. 33 F. Weinhold and J. E. Carpenter THEOCHEM 1988 42 189. 34 J. E. Carpenter and F. Weinhold J. Am. Chem. SOC.,1988 110 368. 35 P. C. Hiberty and D. L. Cooper THEOCHEM 1988,46 437. 36 T. D. Thomas M. R. F. Siggel and A. Streitwieser THEOCHEM 1988 42 309; M. R. F. Siggel A. Streitwieser and T. D. Thomas J. Am. Chem.SOC.,1988 110 8022. 37 0. Exner J. Org. Chem. 1988 53 1810; T. D. Thomas T. X. Carroll and M. R. F. Siggel ibid. p. 1812. E. M. Arnett and J. A. Harrelson J. Am. Chem. SOC.,1987 109 809. X. Wang and K. N. Houk J. Am. Chem. Soc. 1988,110,1870; K. B. Wiberg and K. E. Laidig ibid. p. 1872. 38 39 Theoretical Organic Chemistry such as methyl acetate is preferred over the anti because of a more favourable orientation of the carbonyl and ester-oxygen dipoles. The main effect of deproton- ation is to transfer negative charge not to the carbonyl oxygen but to the carbonyl carbon atom thereby reducing the carbonyl dipole and attenuating the syn-anti energy difference by 23 kJ mol-’. The presence of two syn ester moieties in Meldrum’s acid therefore leads to an enhancement of acidity by about 46 kJ mol-’ relative to malonic ester.Wiberg also notes however that the acidity of esters is due to the strong polarization of the carbonyl group in complete accord with the results of Siggel and Thomas for carboxylic acids. The pros and cons of the concept of a-aromaticity have been critically assessed by Cremer. Application of the same criteria commonly used to define maromaticity reveals that the properties of cyclopropane qualify it as a a-aromatic system the term cannot be rejected simply on the grounds that aromaticity is a property of v-electrons only.40 Electron count rules for a-aromaticity in small cyclic compounds have been form~lated.~~ Stabilization of a quasi-cyclic ‘bent’ hydride-transfer transi- tion structure (2) by 68 kJ mol-’ relative to an acyclic ‘linear’ geometry has been rationalized in terms of five-centre six-electron b~nding;~’ transition state a-aroma- ticity? H,C...H* *.C/ \\ I1 N :N H / H (2) Haddon has reviewed the topic of welectrons in three dimensions arguing that ?r-orbital overlap in non-planar conjugated organic molecules may be vastly improved at the small cost of slight rehybridi~ation.~~ Use of his POAV method and 3D-HMO theory allows for analysis of valence tautomers of 1,6-methano[ 101an- nulene and of structures along the reaction path for the Cope rearrangement jn terms of hybridization changes in the making and breaking bondsM These methods have been applied45 to the homotropylium cation (3) which has also been studied 40 D.Cremer Tetrahedron 1988 44 7427. 41 V. I. Minkin M. N. Glukhovtsev and B. Ya. Simkin THEOCHEM 1988 50 93. 42 A. E. Pain and I. H. Williams J. Chem. SOC.,Chem. Commun. 1988 1367. 43 R. C. Haddon Acc. Chem. Res. 1988 21 243. 44 R. C. Haddon Tetrahedron 1988,44 7611. 45 R. C. Haddon J. Am. Chem. Soc.. 1988 110 1108. I. H. Williams by others.46 Calculations at the SCF level suggest a double-minimum potential in the 1,7-bond co-ordinate but electron correlation changes the shape of the surface to a broad single minimum with a 1,7-bond length somewhere between 1.7 and 2.0 A; (3) is described as the ‘ideal homoaromatic species’.45 Prizes for the most highly strained molecules might go to structures (4)-(7) related to bicycle[ 1 .l.l]pentane all of which are predicted by high-level calculations (MP2/6-3 lG* optimizations with zero-point energies evaluated using HF/6-3 lG* vibrational frequencies) to be stable in low-temperature inert gas mat rice^.^' Three-membered silane rings are more highly strained than four-membered silane rings which are also less strained than their carbocyclic analogues.48 Unsaturated silicon hydrides have a tendency to pucker unlike their hydrocarbon analogues due to a smaller difference between sp2 and sp3 hybridization for Si than for C; Sax et al.regard aromaticity as a feature of the exceptional behaviour of first-row elements.49 Although hexasilabenzene is planar at the SCF level CI calculations predict a puckered Qdstructure the puckering being due to correlation effects on the 0-framework; the lowest energy Si6H6 isomer is hexa~ilaprismane.~~ 4 Reactivity and Mechanism Theories of Reactivity.-Arteca and Mezey have formulated conditions for the validity of the Hammond postulate in terms of bounds on the internal forces and force constants of nuclear arrangements along a reaction path and have identified a broad class of constraints under which it would be ~iolated.~’ Formosinho has also examined the validity of several reactivity relationships (including the Ham- mond postulate and the reactivity-selectivity principle) according to his intersecting- state model and has discussed various factors leading to their breakdown5’ Murdoch has shown how transformation from Cartesian to bond order co-ordinates reveals many molecular phenomena as low-order perturbations.Scaling relationships can be found which map energies and interatomic distances on to a ‘universal’ bond dissociation curve. Bond order transformations enable PE surfaces for reacting systems to be expressed in simple low-order forms obeying Marcus-like relationships. The intrinsic (non-thermodynamic) contributions to reaction barriers arise from interactions not present in the isolated reactants and products. The transferability of intrinsic contributions between different reactions highlights the low-order nature 46 M. Barzaghi and C. Gatti THEOCHEM 1988,43,431; ibid. 1988,44,275; R. V. Williams H. A. Kurtz and B. Farley Tetrahedron 1988 44 7455.47 V. Balaji and J. Michl Pure Appl. Chem. 1988 60 189. 48 S. Nagase and M. Nakano Angew. Chem. Int. Ed. Engl. 1988,27,1081;S. Nagase and T. Kudo J. Chem. SOC.,Chem. Commun. 1988 55. 49 A. F. Sax J. Kalcher and R. Janoschek J. Compuf.Chem. 1988 9 564. 50 G. A. Arteca and P. G. Mezey J. Comput. Chem. 1988 9 728. 51 S. J. Formosinho J. Chem. Soc. ferkin Trans. 2 1988 839. Theoretical Organic Chemistry 33 of many chemical reactions and is useful for constructing new PE surfaces from existing calculations and experimental data.52 Warshel and co-workers have used their empirical VB method together with the free-energy perturbation technique to perform simulations of free-energy relation- ships (and dynamics) of SN2reactions in aqueous solution; a Marcus-like relation- ship was found between the thermodynamic free energy of reaction and the solvent contribution to the activation free energy.53 A Marcus-theory treatment of MP2/6-3 lG*//HF/3-21G calculated energetics for several hydrogen atom transfer reactions has shown that the coefficient a (=dAE*/dAE) is an index of selectivity but not always a reliable measure of transition state structure.Variation in the Marcus intrinsic barrier is an important factor in determining the magnitude of a whose value may become anomalously sizeable when a new interaction occurs between the reacting fragments in the transition state.54 An AM1 theoretical simulation of a Bransted correlation for an acyl transfer reaction has shown that a linear rate-equilibrium correlation is not incompatible with the ‘Bema Hapothle’ and with variable transition state structure and that Brfinsted coefficients are not direct measures of transition state structure; a transformation to bond order co-ordinates is the key feature of a simple intersecting curves model which reproduces this behaviour in predicting an essentially constant value for a and a variable transition state location along the reaction ~o-ordinate.’~ A novel theoretical analysis of substituent effects has been proposed and applied to Hammett and Bransted and related plots.Structural changes along the reaction co-ordinate are controlled by a requirement to make charge transfer between the species joined by the making/breaking covalent bond as facile as possible.Changes in electronic structure do not smoothly follow geometrical changes and as a consequence the global pattern of rate-equilibrium and rate-rate relationships is not expected to be very simple. However the permissible changes in electronic structure suggest that this pattern should exhibit certain simple local features notably straight lines with slopes close to particular values.56 The idea that a chemical reaction may be considered in terms of the interaction between reactant-like and product-like ‘diabatic’ states just as in the Heitler-London VB method the hydrogen molecule is treated in terms of coulomb and exchange interactions between hydrogen atoms was originally proposed by M. G. Evans in 1938.Now rigorous methods have been developed by which adiabatic PE surfaces may be ‘diabatized’ to enable their analysis within this simple VB scheme. Bernardi et al. have described a procedure for transforming an accurate complete-active-space self-consistent-field (CASSCF) wavefunction to this Heitler-London VB form uia an effective Hamiltonian and have applied their method to some previously com- puted transition structures for cycloaddition reaction^.^' Malrieu and co-~orkers~~ have used a different method to obtain nearly diabatic surfaces from MO CI 52 J. R. Murdoch THEOCHEM 1988 40 447. 53 J.-K. Hwang G. King S. Creighton and A. Warshel J. Am. Chem. Soc. 1988 110 5297. 54 H. Yamataka and S. Nagase J. Org. Chem. 1988 53 3232. 55 I. H. Williams Bull.Soc. Chim. Fr. 1988 192; R. B. Hammond and I. H. Williams J. Chem. SOC.,Perkin Trans. 2 1989 59. 56 G. F. Fadhil and M. Godfrey J. Chem. SOC.,Perkin Trans. 2 1988 133; M. Godfrey ibid. p. 139. 57 F. Bernardi M. Olivucci J. J. W. McDouall and M. A. Robb J. Chem. Phys. 1988 89 6365. sx 0. K. Kabbaj F. Volatron and J.-P. Malrieu Chem. Phys. Lerr. 1988 147 353. 34 I. H. Williams calculations for the simplest sN2 process H-+ HZ,which support Shaik’s qualita-tive VB model for this system. The relationship between reaction barriers and transition state looseness defined both thermochemically and geometrically has been discussed.59 SN2Reactions.-Shaik et al. have analysed HF/4-3 1G geometrical and energetic data for methyl transfer between a range of nucleophiles and leaving groups and have found extended linear correlations between (a) the magnitude of the barrier and the fractional elongation of the carbon-to-leaving-group bond in the transition structure and (b) the sum of the forward and reverse barriers and the transition state ‘looseness’.The more extensive the bond cleavage in the transition structure the higher the barrier to reaction.60 Electron correlation has a very substantial influence on sN2 barrier heights. Single and triple excitations make important contributions to reducing barriers for reactions of a range of nucleophiles with methyl fluoride at the MP4SDTQ level.61Multi-reference-determinant CI calculations62 confirm this for the reaction H--CH3F-CH4 * * -F-.The barrier for this same reaction is very basis-set dependent at the SCF level; electron correlation by MPn methods tends to decrease the barrier but the convergence with the order n of the perturbation expansion is not smooth. Transition state structures optimized at the MP2/6-311G** level are similar to those at the HF/3-21G level; C, symmetry is not maintained all along the reaction path which trifurcates in the product region on its way to a vertex-bound CH3-H --F-ion-molecule complex. Energy profiles have been calculated also with MCSCF + CI and CEPA methods. Calculated rate constants agree with experi-ment when based on MP2 and MP4 theoretical barrier heights but not on the MCSCF + CI value.63The CEPA-1 method predicts the D3,,trigonal bipyramidal structure for CH,-to be not a saddle point but a local minimum;64the degenerate transition structures for its sN2 formation and breakdown were not determined.Additions to Double Bonds.-Ab initio HF/3-2 1G studies65for gas-phase halogena-tion of ethene predict three-centre halonium-ion-like transition structures (8) for C12 and Br, but an asymmetric four-centre transition structure for concerted syn addition of F2.Quasi-classical trajectory calculations66for the ethene + F2 reaction have shown that 1,2-difluoroethane is only an intermediate on the way to X- + ...f X .. ,.. . . ............. 59 S. S. Shaik J. Am. Chern. Soc. 1988 110 1127. 60 S. S. Shaik H. B. Schlegel and S. Wolfe J. Chem. SOC.,Chem. Commun.,1988 1322. 61 I.cernuiak and M. Urban Collect. Czech. Chem. Commun.,1988 53 2239. 62 R. Vetter and L. Zulicke THEOCHEM 1988 47 85. 63 Z. Havlas A. Merkel J. Kalcher and R. Zahradnik Chem. Phys. 1988 127 53; A. Merkel Z. Havlas and R. Zahradnik J. Am. Chem. SOC.,1988 110 8355. 64 J. Kalcher THEOCHEM 1988 44 235. 65 S. Yamabe T. Minato and S. Inagaki J. Chem. SOC.,Chem. Commun. 1988 532. 66 L. M. Raff J. Phys. Chem. 1988.92. 141. Theoretical Organic Chemistry 35 CH,=CHF + HF products. Bromochlorination involves a bromonium-ion-like transition structure.67 Bridged structures are predicted for chloronium ions from ethene and cis- and trans-but-2-ene whereas those from propene but-1-ene 2-methylpropene and 2-methylbut-2-ene have open structures (in accord with experiment) at the HF/3-21G level; however contrary to observation an open structure is predicted at this level for the chloronium ion from 2,3-dimethylbut-2- ene.68 These results might be expected to be rather sensitive to the inclusion of electron correlation together with a more flexible basis set.Addition of C1+ or Br+ to cyclopropane leads to a four-membered ring intermediate which may rearrange in a zigzag fashion to a 3-halogenopropyl cation.69 In contrast to nucleophilic addition of OH- approach of SH- to formamide involves only an ion-molecule complex and does not lead to formation of a tetrahedral adduct; thiolate addition to amides probably proceeds by initial O-prot~nation.’~ Hydride addition to formaldehyde has been the prototype of nucleophilic addition to a carbonyl group; previous SCF calculations have suggested no barrier to gas-phase formation of methanolate.However inclusion of diffuse basis functions leads to the prediction of a maximum in the SCF PE profile. Electron correlation has an appreciable effect (even for this closed-shell system) in reducing this barrier to less than 4 kJ mol-* and shifting the location of the transition structure by 0.4 A along the reaction co-~rdinate.~~ Hydroxide addition to formaldehyde and to ethene has been treated by MCSCF calculations which permit the description of both heterolytic and homolytic processes; it is found that the constraints implicit in SCF treatments are not serious qualitatively but do lead to quantitatively different energies and geometries7 The kinetic stereoelectronic effect of antiperiplanar lone pairs assisting hydride transfer from methanimine to formonitrilium is revealed only by calculations which include electron ~orrelation.~~ Multibond Reactions.-The issue of synchronicity in multibond pericyclic processes has been reviewed with emphasis on the discrepancies between the predictions of semi-empirical and a6 initio MO methods.73 Dewar’s AM1 results for the Cope rearrangement of hexa-1,5-diene have suggested distinct mechanistic pathways involving a non-synchronous biradicaloid transition structure for the boat rearrange- ment and a higher-energy synchronous aromatic transition structure for the chair rearrangement.An a6 initio CASSCF study involving all singlet configurations of six electrons in six active orbitals has now been performed with full geometry optimization and with each critical point being characterized by its Hessian (energy second derivatives).The transition structures for both the boat and chair rearrange- ments are found to have 10-15% more biradical character than the reactant but are each still very much closed-shell species. The C2,,chair transition structure has the lower energy. A second C, critical point with biradical character and a very short interallylic separation is found to be a local minimum at much higher energy.74 67 S. Yamabe and T. Minato Bull. Chem. SOC.Jpn. 1988 61 4449. 68 S. Yamabe T. Tsuji and K. Hirao Chem. Phys. Lett. 1988 146 236. 69 S. Yamabe T.Minato M. Seki and S. Inagaki J. Am. Chem. SOC.,1988 110 6047. 70 A. E. Howard and P. A. Kollman J. Am. Chem. SOC.,1988 110 7195. 71 C. I. Bayly and F. Grein Can. J. Chem. 1988 66 149. 72 F. Bernardi M. Olivucci G. Poggi M. A. Robb and G. Tonachini Chem. Phys. Letr. 1988 144 141. 73 W. T. Borden R. J. Loncharich and K. N. Houk Annu. Rev. Phys. Chem. 1988,39 213. 74 K. Morokuma W. T. Borden and D. A. Hrovat J. Am. Chem. SOC.,1988 110 4474. I. H. Williams According to Morokuma et al.,the boat and chair Cope rearrangements are therefore both concerted and synchronous. AM 1 calculations for Cope rearrangements of bullvalene (9) and related molecules in which the boat geometry is enforced predict typical aromatic transition structures while a second biradicaloid transition structure occurs at higher energy." A CASSCF/4-31G study of the Diels-Alder addition of ethene to butadiene shows the synchronous transition structure for the concerted mechanism to be favoured by about 8 kJ mol-' over the non-synchronous transition structure leading to the syn-gauche intermediate in the stepwise mechanism; dynamic electron correlation would probably further favour the synchronous addition path.Minimal basis CASSCF/ STO-3G calculations however lead to quite different prediction^.^^ A perturbational evaluation of this reaction shows the importance of frontier-orbital interactions; they account for 70% of the covalent stabilization term.77 The observed behaviour of isocyanates in 1,3-dipolar cycloadditions to olefins is reproduced in a perturbational analysis only if the distortions of the reactants to their transition state geometries are considered; misleading results are obtained if undistorted isolated-molecule geometries are used.78 0 A synchronous concerted mechanism for decarbonylation of (10) is predicted at the MP2/4-3 1G level with a C, symmetrical transition structure whereas UHF/ STO-3G predicts a non-synchronous path; the large exothermicity of this reaction manifests itself in a low activation energy.79 Other cheletropic processes are predicted to be non-synchronous by semi-empirical but synchronous by ab initio calculations." MCSCF computations of analytical Hessians for 2s + 2a cycloaddition 'transition structures' of ethene with ethene ketene and singlet oxygen reveal these to be 75 M.J. S. Dewar and C. Jie Tetrahedron 1988 44 1351. 76 F. Bernardi A. Bottoni,'M. J. Field M. F. Guest I. H. Hillier M. A. Robb and A. Venturini J. Am. Chem. Soc. 1988 110 3050. 77 R. Sustmann P. Daute R. Sauer and W. Sicking Tetrahedron Lett. 1988 29 4699. 78 R. Sustmann and W. Sicking Tetrahedron 1988 44 379. 79 D. M. Birney K. B. Wiberg and J. A. Berson J. Am. Chem. Soc. 1988 110 6631. 80 J. J. Quirante J. F. Arenas and F. J. Ramirez THEOCHEM 1988 47 233. *' H. S. Rzepa J. Chem. Rex (S) 1988 224. Theoretical Organic Chemistry 37 second-order saddle points with two imaginary frequencies and cast doubt upon whether a supra-antara path actually exists for these reactions.82 Thermally 'forbidden' pericyclic reactions require at least a two-configuration treatment to provide a satisfactory description.A two-configuration SCF MIND0/3 semi-empirical method has been developed to permit the re-evaluation of earlier SCF and 2 x 2 CI MIND0/3 studies by Dewar and co-workers; the new results differ considerably from the old but are in qualitative agreement with those of ab initio MCSCF methods for ethene dimerization and for disrotatory ring opening of cyclobutene for which no transition structure exists.83 The AM1 method and electron-correlated ab initio MPn methods yield barrier heights for conrotatory ring opening of cyclobutene in agreement with experiment whereas this barrier is overestimated by the MNDO MIND0/3 and ab initio RHF methods.84 The barrier to automerization of rectangular cyclobutadiene by means of the square-planar anti-aromatic transition structure has been calculated by various ab initio methods; proper inclusion of non-dynamical electron correlation with a two-configuration wavefunction is found to be superior to extensive inclusion of dynamic correlation by the sophisticated CCSDT-1 method with a single-determinant referen~e.'~ The gauche conformer of the tetramethylene singlet biradical is probably the only significant intermediate in stepwise ethene dimerization; there is no PE barrier to its fragmentation but a small free-energy barrier owing to the decrease in entropy associated with a tightening of the terminal CH2 rotations as fragmentation pro- ceeds.86 Trimethylene singlet biradical does not exist as a free-energy intermediate at accessible temperatures but the possibility of a free-energy minimum at a PE maximum may occur for substituted derivative^.^^ Michl and BonaEiC-Kouteck9 have provided a unified view of biradicals and biradicaloids with examples including a-bond dissociation pericyclic reactions and geometrical isomerization.88 Solvation.-At least two specifically solvating water molecules are required to catalyse the thermal decarboxylation of p-aminosalicylic acid in aqueous solution.89 Supermolecular calc~lations~~ suggest that the Meyer-Schuster rearrangement of propargyl alcohol to asrolein is a solvent-assisted reaction with many-body bulk solvent effects having a passive role.Solvation by bulk water treated by a modified reaction-field method does not alter the conclusions of earlier supermolecular calculations of specific solvation effects on reactions of ~-nitrosamines~l or on tautomerism of dimethylpyra~ole.~~ Jorgensen has developed a set of optimized potentials for liquid simulations (OPLS) to describe intermolecular interactions particularly for proteins in their 82 F.Bernardi A. Bottoni M. Olivucci M. A. Robb H. B. Schlegel and G. Tonachini J. Am. Chem. SOC. 1988 110 5993. 83 J. M. Bofill J. Gomez and S. Olivella THEOCHEM 1988 40 285. 84 D. C. Spellmeyer and K. N. Houk J. Am. Chem. SOC. 1988 110 3412. 85 P. earsky R. J. Bartlett G. Fitzgerald J. Noga and V. Spirko J. Chem. Phys. 1988 89 3008. 86 C. Doubleday M.Page and J. W. McIver THEOCHEM 1988,40 331. 87 C. Doubleday M. Page and J. W. McIver J. Phys. Chem. 1988 92 4367. 88 J. Michl and V. BonaEit-Kouteck9 Tetrahedron 1988 44,7559. 89 P. Ruelle U. W. Kesselring H. Nam-Tran E. Ben-Rayana and A. Seddas J. Chem. Res. (S) 1988 90. 90 J. Andres R. Cardenas E. Silla and 0.Tapia J. Am. Chem. SOC.,1988 110 666. 91 R. Bonaccorsi J. Tomasi C. A. Reynolds and C. Thomson J. Compur. Chem. 1988,9 779. 92 M. HodoSEek D. Kocjan and D. Hadii THEOCHEM 1988.42 115. I. H. Williams native en~ironment.~~ Their use in Monte Carlo simulations of aqueous solvation of N-methylacetamide shows the sensitivity of such methods to the details of the potential functions; the unmodified parameters gave an incorrect result for the effect on the cis- trans energy difference in the peptide bond.94 Kollman has also developed many-body potentials for molecular interaction^,^' for use with the AMBER force field and has demonstrated the calculation of free energies of non-covalent associ- ation of nucleic acid bases in aqueous solution by free-energy perturba- tion/molecular dynamics methods.96 Redox potentials for benzoquinones have been calculated by a combination of methods MP2/6-31G* and AM1 to evaluate gas- phase free-energy differences and the free-energy perturbation method to calculate the hydration free-energy differences.Richards and co-workers suggest that ‘as the free-energy perturbation calculations and the ab initio calculations .. .require similar computational resources it appears that some treatment of hydration should now be carried out in all quantitative ab initio studies of energies of reaction in s~lution.’~’ 93 W.L. Jorgensen and J. Tirado-Rives J. Am. Chem. Soc. 1988 110 1657. 94 W. L. Jorgensen and J. Gao J. Am. Chem. SOC. 1988 110 4212. 95 A. E. Howard U. C. Singh M. Billeter and P. A. Kollman J. Am. Chem. Soc. 1988 110 6984. 96 P. Cieplak and P. A. Kollman J. Am. Chem. SOC.,1988 110 3734. 97 C. A. Reynolds P. M. King and W. G. Richards J. Chem. SOC.,Chem. Commun. 1988 1434; Nature (London) 1988 334 80.