3 Theoretical Chemistry By M. GODFREY Department of Chemistry University of Southampton Southampton SO9 5NH 1 Introduction There is a wide variety of theoretical models designed for the description of chemical properties in terms of the behaviour of nuclei and electrons in molecules. The models differ in the extent to which accuracy is sacrificed in favour of simplicity or feasibility. Some are designed for viewing individual trees and others are designed for viewing the wood as a whole. In compiling this year's report material concerning the nature and the application of all types of model was considered. The main criterion for selection from many hundreds of relevant references was the perceived general interest to organic chemists. Hence advances in computational methods are not usually reported unless they are exemplified by application to some important problem in organic chemistry.2 Models Concepts and Rules In this section the material considered concerns innovations in and criticisms of theoretical models the concepts used in them and rules generated from them. A special issue of Croatica Chernica Acta' was devoted to critical review articles on various models of the electronic structure of molecules. Many distinguished theoretical chemists contributed. Several interesting review papers on fundamental aspects of reaction mechanisms are among the proceedings of a colloquium on the mechanisms of elementary physicochemical processes held at Sorrento Italy in May 1983.2 Simonetta3 discussed the theoretical approach to organic reaction paths in his RSC Centenary Lecture.Calculations for isolated molecules for molecules present in a solvent and reactions in the solid state were reviewed. Ponec4 has proposed and exemplified a topological analysis of chemical reactions which he claims is more attractive for classification of reactivity in computer designed synthesis than existing techniques. Sinanoglu' has proposed a theorem and two simple rules derived from it which permit the qualitative behaviour of molecules to be predicted vis-Ci-vistheir relative stabilities deformations or reactions in a simple pictorial way. ' Croat. Chem. Acta 1984 57 765. Int. J. Quantum. Chem. 1984 26 563-964. M. Simonetta Chem. SOC.Rev. 1984 13 1. R. Ponec Collect.Czech. Chem. Commun. 1984 49 455. 0. Sinanoglu Chem. Phys. Lett. 1984 103 315. 17 18 M. Godfrey Some clarification of the properties of minimum energy paths on the potential energy surfaces (PES) of chemically reacting systems has been given6 'Structural stability' has been established as an intrinsic property of PES that holds within the adiabatic appr~ximation:~ structural stability restriction has been shown to rule out certain frontside SN2paths.* Dewar et aL9 have described a general method for the location of transition states in reaction mechanisms. The procedure is fully automatic once reactants and prod- ucts are characterized and no assumptions as to the geometry of the transition state or of the mechanism are necessary.Dewar" has also proposed the rule that syn-chronous multibond mechanisms are normally prohibited they occur only in exceptional cases where special factors operate. The best description of the reaction path may often involve co-ordinates other than the obvious one. Agmon" has shown that it is possible to generalize models for energy profiles along the reaction co-ordinate by adding an upside-down profile which describes the energy perpendicular to the reaction co-ordinate. His model involves three simple assumptions concerning the relationship between the two curves. Northrup and McCammon'* use the term 'gated' to describe reactions in which the rate of a local reaction is controlled on a larger scale by the formation of permissive structural configurations within which the local transformation can proceed relatively rapidly.Theoretical models for specific types of gated reactions have been described in previous work and a general model for analysing the kinetics of such reactions is now being developed. Houk and Rondan13 have developed a new hypothesis to show how negative activation energies and entropy control of reactivity can arise in reactions having no inherent PE barrier. The analysis of adiabatic surfaces in terms of diabatic components plays an important role in the interpretation of organic phen~mena.'~~'~ Bernardi and Robb16 have described a procedure for the computation of diabatic surfaces defined in the framework of an ab initio CI approach. The main feature of this procedure is that each diabatic surface is associated with a specific bonding situation and thus with a specific packet of configurations built from the valence orbitals of the fragments.The importance of HOMO-HOMO interactions and of T-u interactions in frontier orbital treatments of nucleophilic attack has been stressed in several studie~.'~ Parr and Yang18 have demonstrated that most of the frontier-electron theory of W. Quapp and D. Heidrich Theor. Chim. Actu 1984 66 245. A. Fernandez and 0. Sinanoglu Theor. Chim. Acta 1984 65 179. A. Fernandez and 0.Sinanoglu Theor. Chim. Actu 1984 66 147. M. J. S. Dewar E. F. Healy and J. J. P. Stewart 1. Chem Soc. Furuduy Trans. 2 1984 227. 10 M. J. S. Dewar J. Am. Chem. SOC. 1984 106 209. N. Agmon J. Am. Chem. SOC.,1984 106 6960.I2 S. H. Northrup and J. A. McCammon J. Am. Chem. SOC. 1984 106 930. l3 K. N. Houk and N. G. Rondan J. Am. Chem. Soc. 1984 106,4293. 14 R. B. Woodward and R. Hoffman 'The Conservation of Orbital Symmetry' Academic Press New York 1970. l5 N. D. Epiotis 'Theory of Organic Reactions' Springer-Verlag Heidelberg 1978. 16 F. Bernardi and M. A. Robb J. Am. Chem. Soc. 1984 106 54. 17 C. L. Liotta E. M. Burgess and W. H. Eberhardt J. Am. Chem. SOC.,1984 106 4849; S. Yamaba T. Minato and Y. Kawabata Can. J. Chem. 1984 62 235; R. D. Bach M. L. Braden and G. J. Wolber J. Org. Chem 1983 48 1439; R. D. Bach G. J. Wolber and A. Pross Isr. J. Chem. 1983 23 97; R. D. Bach and G. J. Wolber J. Am. Chem. Soc. 1984 106 1401 1410. 18 R. G. Parr and W.Yang J. Am. Chem. SOC.,1984 106 4049. Theoretical Chemistry 19 chemical reactivity can be rationalized from the density functional theory of the electronic structure of molecules. Hori et al.” have proposed a new method for the partitioning of interaction energy. It is now well established that SN2reactions of anions commonly take place with little or no activation in the gas phase indicating that the barriers in solution are due primarily to desolvation of the ion. However the rates of SN2reactions usually vary little with changes in the solvent. Carrion and Dewa8’ have proposed a resolution of this paradox. Shaik” has attempted to show that the VB state correlation diagram model2’ can provide a conceptual basis for both solvent effects and intrinsic reactivity trends in the SN2reaction.The general problem of formulating theories of nucleophilic reactivity has been discussed by Rit~hie.~~ A knowledge of the energy-transfer rates in molecular collisions is required for a basic understanding of the kinetics of gas-phase chemical reactions. A systematic method for calculating rate constants for the excitation and relaxation of the individual vibrational modes of organic molecules in collisions with atoms has been described.24 The method involves the approximate solution of the 3D quantum- dynamical equations of motion for the atom-molecule system. Siebrand and co- workersz5 have elaborated on a method26 of non-classical hydrogen atom transfer which employs a formalism analogous to that used for radiationless transitions rather than the usual tunnelling formalism.The HSAB (hard and soft acids and bases) principle27 has been proved from a simple model utilizing the concept of ‘absolute hardness’.28 An operational definition electron affinity of the species in question. Tables of values are given for a number of free atoms Lewis acids and Lewis bases. The role of c7-conjugative interactions has been considered in detail by De~ar,~~ with special reference to bond localization and aromaticity the structures of radicals and diradicals triplet carbenes stabilities of conformers including the gauche and anorneric effects and chelotropic reactions. Borden and co-workers3’ have shown using second-order Jahn-Teller theory that allylic resonance in radicals will decrease in importance with increasing differences between the electronegativities of the central and terminal heavy atoms and that electron repulsion effects will cause allylic resonance to be more important in diradicals than in the corresponding radical species containing one less .rr-electron.They have also shown how the same conclusions can be reached within the context of resonance theory provided that no-bond resonance structures which localize electron pairs on the most electronegative atoms are considered. Starting from a 19 K. Hori,Y. Asai and T. Yamabe Theor. Chim. Acta 1984 66 77. 2o F. Carrion and M. J. S. Dewar J. Am. Chem. Soc. 1984 106 3531. ” S. S. Shaik J. Am. Chem SOC.,1984 106 1227. 22 A. Pross and S. S. Shaik Acc.Chem. Res. 1983 16 363. 23 C. D. Ritchie J. Am. Chem. SOC.,1983 105 7313. 24 D. C. Clary J. Am. Chem. SOC. 1984 106 970. 25 W. Siebrand T. A. Wildman and M. 2.Zgierski J. Am. Chem. Soc. 1984 106 4083 4089. 26 J.-P. Laplante and W. Siebrand Chem. Phys. Lett. 1978 59 433. 27 R. G. Pearson J. Am. Chem. SOC.,1963 85 3535. 28 R. G. Parr and R. G. Pearson J. Am. Chem. SOC.,1983 105 7512. 29 M. J. S. Dewar J. Am. Chem. SOC.,1984 106 669. 30 D. Feller E. R. Davidson and W. T. Borden J. Am. Chem. Soc. 1984 106 2513. are the ionization potential and the AandIwhereI-A) ;( of absolute hardness is 20 M. Godfrey VB approach Howeler and Klessingefl' have developed a simple model for non-polar radical reactions which extends beyond the possibilities offered by known MO considerations.K~wajima~~ has presented an extension of the classical VB theory of aromaticity that can account for both antiaromaticity and magnetic effects. According to Wennerstrom and co-~orkers~~ the r-system of a macrocycle with 2-fold rotational symmetry and 2n conjugated nelectrons can conveniently be regarded as the sum of two cyclic n .rr-electron systems having Huckel and Mobius topology respectively. Two studies show that through-resonance is less significant than many organic chemists assume. In the influence of the mesomeric interactions of .rr-donor para-substituents on nitrobenzene was examined by means of analyses in VB terms of ab initio SCF wavefunctions. In the other,35 it was shown by ab initio MO calculations that the length of the double bond in mono- and di-substituted ethylenes is almost constant even in compound (1).This result is in keeping with previous studies36 on benzene derivatives. 02NINHz Magn~sson~~ has reconsidered sp hydridization in the light of results of an ab initio MO study of bonding by first and second row main-group elements. He finds no justification for retaining the familiar model of a strict relationship between bond angle and the participation of s and p orbitals in bonding. The Walsh-Bent hypothesis that the attachment of electronegative groups favours the use of p rather than s orbitals in bonding by a central atom is also not supported. Gready3' has re-examined the nature of the relationship between .rr-bond order and bond length in the prediction of molecular geometry and the interpretation of chemical bonding.In an extension of earlier Jug4* has suggested a generaliz- ation of the quantum-mechanical definition of valence of atoms in molecules. Valence is considered as the expectation value of diatomic parts of density operators. A novel approach to the description of chemical bonds has been reported41 which confirms indications from X-ray diffraction results that the formation of covalent bonds does not necessarily bring about an increase in electron density in the bonding region. The weakness ofthe Mulliken population formalism in determining the ionic character of the C-Li bond in organolithium compounds has been 31 U. Howeler and M. Klessinger Angew.Chem Int. Ed. Engl. 1984 23 985. 32 S. Kuwajima 1. Am. Chem. SOL,1984 106 6496. 33 U. Norrinder 0. Wennerstrom and H. Wennerstrom Tetrahedron Lett. 1984 25 1397. 34 P. C. Hiberty and G. Ohanessian J. Am. Chem. Soc. 1984 106,6963. 35 S. Marriott and R. D. Topsom THEOCHEM 1984 18 305. 36 E. von Nagy-Felsobuki R. D. Topsom S. Pollack and R. W. Taft J. Mol. Stnrct. 1982 88 255. 37 E. Magnusson J. Am. Chem. Soc. 1984 106 1177 1185. 38 J. E. Gready J. Comput. Chem. 1984 5 411. 39 M. S. Gopinathan and K. Jug Theor. Chim.Act4 1983 63 491 511. 40 K. Jug J. Comput. Chem. 1984 5 555. 41 D. Cremer and E. Kraka Angew. Chem. Int. Ed. Engl. 1984 23 627. 42 S. M. Bachrach and A. Streitwieser J. Am. Chem. Soc. 1984 106 2283. Theoretical Chemistry 21 Visual representations of electron densities can be instrumental in helping in the understanding of both the structures of molecular systems and their potential reactivity.Practical problems in representing electron densities by surfaces are being tackled by Hehre and co-worker~.~~ 3 Simple Quantitative Relationships The material considered in this section is that which contributes to the understanding of the bases of simple quantitative free energy relationships. The relationship between the free energy of activation and the free energy of reaction in electron proton atom and group-transfer reactions has attracted much attention. Murdoch’s theoretical equation,44 (l) expresses barrier heights (or well depths) in terms of kinetic and thermodynamic contributions.In equation (l),AE* describes the barrier height for a reaction AE the overall energy change AE; the intrinsic barrier and g and g are functions which govern the relative contributions of the kinetic term and the thermodynamic term. It has been shown4’ that previous empirical equations (including those of and of Agmon and Le~ine~~) obtained by a wide variety of apparently unrelated assumptions are special cases of equation (1). Murdoch and co-workers have argued4’ that applications of Marcus- like equations to double-well potential surfaces might fail and have proposed49 a new method for obtaining the height of the intrinsic barrier that can be applied to processes which have no corresponding identity reactions.AE* = AEi(1 -g2) + $AE(l + gl) (1) WolfeSo has pointed out that if Marcus’ equation is valid no stationary point should exist between the reactant state and the product state when IAEl z= 4AEi. This prediction has been confirmed by ab initio MO calculations on the deprotonation of carbon acids. Wiseman and Kestner” have made some modifications to the model of Agmon and Levine.4’ They conclude that the Bronsted coefficient is not equal to the transition state bond order in violation of the Leffler-Grunwald post~late.’~ The mechanistic significance of the Bronsted parameter has been studied by Pross within the framework of a qualitative VB Although the correlation between total N-atom charge and gas-phase basicities is poor in heteroaromatic systems there is good correlation of N lone-pair charge and protonation energy.54 An experimental result which has implications for the interpretation of Bronsted coefficients is that the slopes of log k versus pK, for 43 M.M. Franc] R. F. Hout and W. J. Hehre J. Am. Chem. SOC.,1984 106 563. 44 J. R. Murdoch and D. E. Magnoli 1. Am. Chem. SOC.,1982 104 3792. 45 J. R. Murdoch 1.Am. Chem. SOC.,1983 105 2159. 46 R. A. Marcus J. Chem. Phys. 1956 24 966. 47 N. Agmon and R. D. Levine J. Chem. Phys. 1979,71 3034. 48 J. Donnella and J. R. Murdoch J. Am. Chem. SOC 1984 106,4724. 49 M. Y. Chen and J. R. Murdoch J. Am. Chem. SOC.,1984 106 4735. 50 S. Wolfe Can. J. Chem. 1984 62 1465. 51 F. W. Wiseman and N. R. Kestner J. Phys. Chem. 1984 88,4354.52 J. E. Leffler and E. Grunwald ‘Rates and Equilibria of Organic Reactions’ Wiley New York 1963. 53 A. Pross J. Org. Chem 1984 49 1811. 54 J. Catalan J. L. G. de Paz M. Yanez and J. Elguero J. Am. Chem. Soc. 1984 106 6552. 22 M. Godfrey SN2reactions of various sets of substituted anionic nucleophiles with benzyl chloride are identical irrespective of the nature of the donor atom.” An experimental result which has implications for the mechanistic significance of the Hammett reaction constant (rho) is that the rates of the identity methyl-transfer reactions of a set of substituted benzene sulphonates fit the Hammett equation with a non-zero (+0.6) value of rho.56 The mechanistic significance of the reaction constants (rho) and the cross-interaction constant (q) in the interactive free-energy relationship for two substituents X and Y (equation 2) have been ~tudied.’~ It is concluded that the value of q reflects at least in part a change in the position of the transition state induced by the substituent.log kXYIkHH = P%X + PzHffY + PXUY (2) Swain has recently5’ reiterated an earlier59 claim that only one resonance scale is necessary in the field and resonance analysis of substituent effects. This claim has been criticized6’ on the grounds that it provides an incomplete separation of field and resonance effects and that it fails badly for systems following the cr-scale of substituent effects. Swain has also proposed61 that a dual solvent parameter equation (3) is adequate for expressing solvent effects on molecular properties (P):the solvent parameters A and B represent respectively the solvating ability of anions and cations.However Taft Abboud and Kamlet62 have reasserted that the three solvent parameters involved in their own analysis63 are necessary in the general case. Swain has replied64 to all these criticisms. Afanas’ev6’ has also argued that different scales of resonance constants are superfluous but Kevi1f6 has given evidence that A and B are considerably inferior to the N and Y parameters of the extended Grunwald-Winstein equation67 when applied to solvolytic displacement reactions. P = Po + aA + 6B (3) The correlation of octanol/water partition coefficients with the Kamlet-Abboud- Taft parameted3 gives insights into the relative importance of molecular factors that determine solution partition coefficients.68 Brady and Cad9 are pessimistic about whether physically meaningful information is extractable from correlations involving single-parameter scales following an examination of the effects of modelling dipole-dipole and dipole-induced dipole interactions with a single lumped parameter.55 F. G. Bordwell and D. L. Hughes J. Am. Chem. SOC.,1984 106 3234. 56 E. S. Lewis and D. D. Hu J. Am. Chem. SOC.,1984 106 3292. 57 J. E. Dubois M.-F. Ruasse and A. Argile J. Am. Chem. SOC.,1984 106 4840 4846. 58 C. G. Swain S. H. Ungar N. R. Rosenquist and M. S. Swain J. Am. Chem. SOC., 1983 105 492. 59 C. G. Swain and E. C. Lupton J. Am Chem. SOC.,1968,90 4328. 60 W.F. Reynolds and R. D. Topsom J. Org. Chem. 1984,49 1989; A. J. Hoefnagel W. Oosterbeek and B. M. Wepster J. Org. Chem. 1984,49 1993; M. Charton J. Org. Chem. 1984,49 1997. 61 C. G. Swain M. S. Swain A. L. Powell and S. Alunni J. Am. Chem. SOC.,1983 105 502. 62 R. W. Taft J.-L. M. Abboud and M. J. Kamlet J. Org. Chem. 1984 49 2001. 63 M. J. Kamlet J-L. M. Abboud and R. W. Taft hog. fhys. Org. Chem. 1981 13 1080. C. G. Swain J. Org. Chem. 1984 49 2005. 65 I. B. Afanas’ev J. Chem. SOC.,ferkin Trans. 2 1984 1589. 66 D. N. Kevill J. Chem. Res. (S) 1984 86. 67 S. Winstein E. Grunwald and H. W. Jones J. Am. Chem. SOC.,1951 73 2700. M. J. Kamlet M. H. Abraham R. M. Doherty and R. W. Taft J. Am. Chem. Soc. 1984 106,464. 69 J. E. Brady and P.W. Cam J. Phys. Chem. 1984.88 5796. Theoretical Chemistry The transmission of polar substituent ,eff ects in the bicycloalkane systems (2) and (3) have been studied by Adcock et aL7’ by measuring 19F substituent chemical shifts. In each case the shifts linearly correlate with a combination of field and electronegativity parameters but the sign of the coefficient of the electronegativity parameter is different in the two cases. A qualitative explanation in terms of c+-electron delocalization mechanisms is advanced. Ab initio MO calculations on suitable model systems have been used to study the polarization of welectron systems by substituent dipoles and to construct a theoretical scale of substituent field parameters,” and to provide a simple and well-defined scale of substituent electronegativity parameter^.^^ The latter scale correlates with the JC(ipso+c(ort~o) coupling constant for many monosubstituted benzenes where the directly bonded atom is a first-row element.The impossibility of obtaining a universal scale of field parameters has been discussed.72 (2) (3) The problem of through-bond versus through-space transmission of substituent effects has been discussed by Exner and co-w~rkers~~ following the failure of electrostatic theory to account for variations in the pK values of carboxylic acids in different solvents. Doan and drag^^^ have provided an answer to why free energies which are composites of two quantities (AHand AS) with independent molecular explanations are often correlated with one or two parameters.Gie~e~~ has defined the ‘isoselective relationship’ equation (4) with TiSrepresenting the isoselective temperature and discussed its significance for linear free-energy relationships. S(AH -AH:,,) = TisS(AS:,2 -AS:,,) (4) Ruoff 77 has discussed linear free-energy relationships from the viewpoint of information theory. 4 Studies of Molecular Structures and Reaction Paths The material included in this section illustrates the state of the art of theoretical studies of molecular structures and reaction paths. A critical examination of 149 landmark papers up to 1983 is presented in a book by S~haeffer.~’ A bibliography of ab initio calculations published in 1983 is available.79 70 W. Adcock A. N. Abeywickrema and G.B. Kok,J. Org. Chem. 1984 49 1387. 71 S. Mamott and R. D. Topsom J. Chem. SOC.,Perkin Trans. 2 1984 113. 72 S. Marriott and R. D. Topsom J. Am. Chem. SOC.,1984 106 7. 73 S. Marriott W. F. Reynolds R. W. Taft and R. D. Topsom J. Org. Chem. 1984 49 959. 74 K. Kalfus Z. Fried] and 0. Exner Collect. Czech. Chem. Commun. 1984 49 179. 75 P. E. Doan and R. S. Drago J. Am. Chem. SOC. 1984 106 2772. 76 B. Giese Acc. Chem. Res. 1984 17 438. 77 P. Ruoff 2. Phys. Chem (Leipzig) 1964 265 433. 78 H. F. Schaeffer ‘Quantum Chemistry The Development of ab initio Methods in Molecular Electronic Structure Theory’ Oxford University Press Oxford 1984. 79 THEOCHEM 1984 20 1. 24 M. Godfrey A fundamental weakness of Hartree-Fock MO calculations is the neglect of electron correlation.Although the energy associated with this phenomenon is a small fraction of the total energy of a molecule it is of the same order of magnitude as most energies of chemical interest. Accurate techniques for the theoretical determi- nation of electron correlation on molecular properties are therefore vital for the quantitative accuracy of predictions. A book by Wilson" describes methods for the calculation of electron correlation effects in molecules which are now widely used. Calculations on molecular systems containing up to about six first-row atoms are feasible. Kello and co-workers" have systematically calculated correlation effects and bond-correlation energies in a series of molecules which contains C1 to C4 hydrocarbons and oxygen-containing derivatives using the many body Rayleigh- Schrodinger perturbation theory up to the fourth order.Results of studies by Cizek et aZ.82on the localization of the filled and virtual orbitals in the nucleotide bases suggest that the application of localized orbitals will open new possibilities for the calculation of correlation in extended systems. Marriot and T~psom~~ have proposed standard bond lengths for a wide variety of bonds involving first-row elements to be used in fixed geometry ab initio MO calculations. They were obtained as average values from a large number of calculations at the 4-31G level with geometry optimization. The results of even the best ab initio calculations of molecular structures may not be qualitatively correct and there is still a case for performing semi-empirical calculations on small molecular systems.The inadequacies of semi-empirical methods have been discussed recently by Freed84 and by de Bruijnx5 who have suggested ways of overcoming some of the objections to these methods. The mechanisms of reactions which involve the cyclic displacement of electrons continue to attract theoretical attention. Correlation effects favour asynchronism in reaching the transition state of the Diels- Alder reaction,86 but favour C2 symmetry for the transition state structure in the Cope rearrangemente8' The transition states for 1,5-hydrogen shifts appear to have CHC angles very different from 180°.x8A MNDO study suggests that substituents should influence electrocyclic processes markedly.89 Qualitative VB theory has been usedg0 to show how the primary elec- tronic structure of the initial transition-state determines whether or not the 1,3-dipolar cycloaddition reaction is concerted.The theory also indicates that if the first transition state is primarily an extended diradical the energy minimum for an electronically excited state of the diradical must lie immediately above and be energetically close to the transition state. 80 S. Wilson 'Electron Correlation in Molecules' Oxford University Press Oxford 1984. 81 V. Kello M. Urban J. Noga and G. H. F. Diercksen J. Am. Chem. Soc. 1984 106 5864. J. Cizek W. Forner and J. Ladik Theor. Chim.Acta 1984 64 107. 83 S. Marriott and R.D. Topsom THEOCHEM 1984 19 337. 84 K. F. Freed Acc. Chem. Res. 1983 16 137. 85 S. de Bruijn Znt. J. Quantum Chem. 1984 25 367. 86 M. Ortega A. Oliva J. M. Lluch and J. Bertran Chem. Phys. Lett. 1983 102 317; F. K. Brown and K. N. Houk Tetrahedron Lett. 1984 25 4609. 87 Y. Osamura S. Kato K. Morokuma D. Feller E. R. Davidson and W. T. Borden J. Am. Chem. Soc. 1984 106 3362. 88 B. A. Hess and L. J. Schaad J. Am. Chem. Soc. 1983 105 7185; N. G. Rondan and K. N. Houk Tetrahedron Lett. 1984 25 2519; J. W. Verhoeven Red. Truv. Chim. Pays-Bas 1984 103 143. 89 A. Jensen and H. Kunz Theor. Chim. Acta 1984 65 33. 90 R. D. Harcourt and R. D. Little J. Am. Chem. Soc. 1984 106 41. Theoretical Chemistry 25 Calculations on alkenes and related compounds are inevitably numerous because of the convenient size of the molecular systems and we can mention only a few examples.There has been a systematic ab initio MO study of the structural properties of ethylene and the all-trans conjugated polyenes C4H6 C6H8 C8H10 and C10H12.~~ The cyclopropenyl cation appears to be n~n-planar,~~ and the second stable confor- mer of buta-1,3-diene appears to be gauche rather than s-c~s.~~ Stereoselectivity in hydroborati~n?~ and directive effects and selectivity in radical addition reactionsg5 have been studied. A MO of 1,3- and 1,2-sigmatropic shifts in propene has shown that the Hartree-Fock level is inadequate for determining an energy surface whose shape is dictated by the interaction and intersection of diabatic surfaces.The phenomenon of bond length alternation in large cyclic polyenes predicted at the restricted Hartree-Fock level has been confirmed at the correlated and there has been a MNDO study of bond orders in some conjugated bicyclic and tricyclic hydrocarbon^.^^ The heavy-atom chain in cumulenones CH,=(C),=O with n 3 2 has been calculated to be bent with the direction of bending alternating between in-plane and orthogonal as a function of r1.9~The influence of the lowest double- excited a-electron configuration may be responsible for this phenomenon.'" There have been a number of ab initio MO calculations on silicon-containing molecular systems that include allowance for electron correlation. If the results are valid there is no stable linear conformation of Si2H2 analogous to acetylene,"' and the thermodynamically most stable structure of H,CSiO is methylsilanone.lo2 Other studieslo3 were concerned with silylene insertion reactions into a-bonds.There has also been a study of lithium atom insertion into the C-H bond of methane.lo4 Doubleday et ~1.'~~ have concluded that singlet tetramethylene exists in an entropy- dominated free-energy minimum even though it lacks a potential-energy minimum but Bernardi et ~l.''~have concluded that the diradical exists as a stable species in two different conformations gauche and trans. Calculations support the possibility that a and T phenyl radicals are well separated energetically and may exist as discrete chemically distinguishable species.'" There have been many other MO 91 C.W. Bock P. George and M. Trachtman THEOCHEM 1984 18 1. 92 B. A. Hess L. J. Schaad and P. Carsky Tetrahedron Lett. 1984 25 4721. 93 J. Breulet T. J. Lee and H. F. Schaefer J. Am. Chem. SOC.,1984 106 6250; C. W. Bock P.George and M. Trachtman Theor. Chim. Acra 1984 64 293. 94 K. N. Houk N. G. Rondan Y.-D. Wu J. T. Metz and M.N. Paddon-Row Tetrahedron 1984,40,2257. 95 R. Ponec J. Malek W. Kuhnel and E. Gey THEOCHEM 1984 19 293; R. Amaud Y.Ellinger R. Subra and J. Douady THEOCHEM 1984 19 203. 96 F. Bernardi M. A. Robb H. B. Schlegel and G. Tonachini J. Am. Chem. SOC.,1984 106 1198. 97 J. Paldus and M. Takahashi Int. 1. Quantum Chem. 1984 25 423; M. Takahashi and J. Paldus Int. J. Quantum. Chem. 1984. 26.349. 98 C. Glidewell and D. Lloyd Tetrahedron 1984 40 4455. 99 L. Farnell and L. Radom J. Am. Chem. Soc. 1984 106 25. 100 R. D. Brown and R. G. Dittmann Chem. Phys. 1984 83 77. 101 J. S. Binkley J. Am.Chem. Soc. 1984 106,603. 102 M. S. Gordon and C. George J. Am. Chem. SOC.,1984 106 609. 103 C. Sosa and H. B. Schlegel J. Am. Chem. SOC.,1984 106 5847; K. Raghavachari J. Chandrasekhar M. S. Gordon and K. J. Dykema 1. Am. Chem. SOC.,1984 106 5853; M. S. Gordon and D. R. Gano J. Am. Chem. SOC.,1984 106 5421. 104 J. G. McCaffrey R. A. Poirier G. A. Ozin and I. G. Csizmadia J. fhys. Chem. 1984,88 2898. 105 C. Doubleday R. N. Camp H. F. King J. W. McIver D. Mullally and M. Page J. Am. Chem. SOC. 1984 106 447. 106 F. Bernardi A. Bottoni G.Tonachini M. A. Robb and H. B. Schlegel Chem. fhys. Lett. 1984,108,599. 107 R. P. Johnson J. Org. Chem. 1984 49 4857. M. Godfrey calculations of various kinds on radicals,"* radical ions,"' ions,"O carbenes and nitrenes,"' and excited states we reference just a selection. Other interesting ab initio MO studies elucidate the barrier height for double proton transfer in the formic acid dimer,'13 show that hydrogen bonding plays an important role in explaining the relative basicities of methylamines in solution,' l4 and demonstrate that the activation energy in a reaction might be lowered by a catalyst designed to compress the reactant state more than the transition ~tate."~ The proceedings of a symposium on molecular mechanics held at Indianapolis in June 1983 have been published:'16 they include a treatment of the anomeric effect.' '' An appraisal of molecular force-fields for the representation of polypeptides has been given by Hall and Pavitt.'18 A set of procedures and guidelines has been presented"' for the estimation of bond length bond angle and torsional potential constants for molecular-mechanics force-fields.Chandrasekhar Smith and Jorgensenl2O claim the first computation of an energy profile for an SN2reaction in aqueous solution using Monte Carlo simulations of the reaction in solution. Chiles and Rossky121 have reported an alternative computationally faster method of tackling the identical problem. Cournoyer and Jorgensen'22 have studied solvent effects on the relative energies of carbocations.Kollman and co-~orkers'~~ claim the first ab initio SCF correlation energy and environmental effect calculation on all the chemical steps of an enzymatic reaction. K~llman'~~ has also proposed a new force-field for molecular methanical simulation of nucleic acids and proteins. lo' C. Glidewell J. Chem. Soc. 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