3 Theoretical Organic Chemistry By JONATHAN W. ESSEX Department of Chemistry University of Southampton High field Southampton SO17 lBJ UK 1 Introduction Theoretical organic chemistry spans a wide range of interests from the well-established calculations of the electronic properties for very small systems using ab initio techniques to the computer simulation of large hydrated systems many of bioorganic interest using molecular dynamics and Monte-Carlo methods. This review is broadly divided into two sections theoretical advances and applications. In the former the importance of including solvation in calculations is emphasized both through continuum treatments and explicit solvent models applied within computer simulations. Computer-simulation methodology is also addressed as are the calculation of transition states and reaction pathways; the latter are of particular importance since they control chemical reactivity.In the applications sections a special emphasis is placed on reviewing host-guest chemistry as through this discipline organic chemists are investigating the fundamental interactions that control biochemistry. Pericyclic reactions and the S,2 reaction are also reviewed since despite the considerable theoretical effort devoted to these areas in the past they are still providing challenges that stretch current theory to its limits. The calculation of equilibrium properties is also addressed as is photochemistry. It is arguably impossible for any one individual in a short article to review exhaustively the entire literature and the author has therefore been selective in presenting what he considers to be the most interesting advances in the past year.Undoubtedly this is a subjective procedure and this review is likely to be flavoured by the author’s personal research interests. 2 Theoretical Advances The theoretical techniques applied to organic chemistry can be roughly classified in terms of electronic-structure calculations and computer simulations. The former include Hartree-Fock and post-Hartree-Fock methods density functional calcula- tions and semi-empirical methods and typically provide energetic and structural information for both electronic ground states and transition states. Computer simulations usually involve empirical potential-energy functions coupled with molecu- lar dynamics or Monte-Carlo simulations and provide thermodynamic and structural data often in the condensed phase.This distinction between electronic-structure 25 Jonathan W. Essex calculations and computer simulations is becoming somewhat blurred by the development of simulation techniques using quantum mechanical potentials such as Car-Parrinello and mixed molecular-mechanics/quantum-mechanics, and by the use of classical force-fields to determine transition states. In this section the significant advances in solvation modelling computer simulations and free-energy calculations and transition state and reaction pathway searching will be presented. Solvation.-The role of solvent in influencing chemical equilibria and rates of reaction cannot be understated.However the inclusion of solvation effects in theoretical calculations is plagued by difficulties of accuracy and computational cost. The currently available techniques can be divided into two main areas those relying on a continuum description of the solvent and those in which the structure of the solvent molecules is considered explicitly. Continuum models are frequently used to model the effect of bulk solvent on quantum mechanical calculations. The alternative method of introducing a large number of water molecules into the calculation is very expensive. However in cases where the solvent participates in a reaction through a specific interaction then a continuum treatment is inadequate and that solvent molecule will need to be included explicitly in the calculation for example in the aldol condensation.' Continuum models are also finding increasing use in classical simulations especially of proteins and peptides where the expense of including a large number of solvent molecules can prove prohibitive.Increasing computer power does however make the use of explicit solvent treatments more feasible and indeed in most classical simulations explicit solvent models are the method of choice especially given the increasing use of polarizable intermolecular potential-energy functions. The progress made in each of these two areas during 1994 will be considered separately in this review and the reader is referred to two general reviews of solvation treatments for additional inf~rmation.~.~ Continuum Descriptions of Solvation.-In continuum modelling the solvent is treated as a polarizable structureless continuum; the electrostatic contribution of the free energy of solvation is usually evaluated separately from the dispersive and cavitation terms.The principal advantages of this approach are the treatment of solute-solvent polarization effects and the speed of the calculation as compared with explicit solvent models. However information on the solvent structure is unavailable and moreover the underlying assumption that the solvent can be treated as a continuum may not be valid. Uncertainties regarding the appropriate size and shape of the solute cavity also exist. While the loss of solvent structural information is unavoidable significant progress concerning the other difficulties has been made.Several reviews describing the current state of continuum modelling of solvent were published during 1994.4,5 Of particular interest is the paper by Tomasi and Persico4 in which the current state of the field was comprehensively presented both from the methodological view point and from the perspective of the chemical problems to which the approach has been E. L. Coitino J. Tomasi and 0.N. Ventura J. Chem. SOC.,Faraday Trans. 1994 90,1745. P. E. Smith and B. M. Pettitt J. Phys. Chem. 1994 98 9700. W. F. van Gunsteren F.J. Luque D. Timms and A. E. Torda Annu. Rev. Biophys. Biomol. Struct. 1994,23 847. J. Tomasi and M. Persico Chem. Rev. 1994 94 2027. A.A.Rashin and M.A. Bukatin Biophys. Chem. 1994 51 167. Theoretical Organic Chemistry successfully applied. The issue of the appropriate choice of cavity size in continuum calculations was addressed extensively by Orozco Luque and Bachs in both ab initio6" and semi-empirical treatments.' Errors in calculated free energies of hydration for a range of molecules derived using the recommended cavities were of the order of 1kcal mol- '. Continuum models applied in conjunction with empirical treatments of the solute were also found to give results sensitive to cavity size.g Agreement between the free energy of hydration of a water molecule obtained using the Poisson-Boltzmann continuum treatment with that obtained using an explicit solvent model could only be achieved by making the cavity radius charge dependent.This suggests that electrostriction is a significant problem in continuum models. In a related study using an empirical solute description cavity radii and atomic charges were optimized to reproduce experimental free energies of hydration using the Poisson-Boltzmann approach.' The possibility of combining an explicit solvent description of the solute's first hydration shell with a continuum description of subsequent hydration spheres was raised.' ',''This approach is justified since simulations using an explicit water model suggest that water beyond the first solvation shell essentially behaves as part of the bulk phase.I2 Furthermore electrostriction and dielectric saturation are explicitly treated and the sensitivity of the results to subtle changes in cavity size are reduced since the dielectric interface is further removed from the region of interest the solute.' I Perhaps this hybrid procedure offers the 'best of both worlds'; namely a continuum treatment but with explicit solvent in the critical region near the solute.A number of other methodological developments in the area of continuum solvation have been made in the past year. These include the introduction of a distance- dependent dielectric constant to the polarizable continuum model thereby eliminating the sharp discontinuity of the dielectric constant at the cavity b~undary.'~ A fast technique for solving the non-linear form of the Poisson-Boltzmann equation has been developed and applied to a number of protein systems; use of the non-linear form of the equation is particularly important in cases where the solute molecule is highly charged.'4.' The non-linear form of the Poisson-Boltzmann equation has also been solved independently using a boundary element method.' Boundary element procedures have been used to investigate the sensitivity of free energies of solvation to such parameters as cavity size and the level of sophistication of the quantum- mechanical component. " A new method for modelling solvation effects through induced atom-centred multipoles has been presented and was shown to be as accurate as finite-difference approaches but with greater efficiency.' * There has been considerable effort in the past year in combining treatments of M.Bachs F.J. Luque and M. Orozco J. Comput. Chem. 1994 15 446. ' M. Orozco and F.J. Luque Chem. Phys. 1994 182 237. F. J. Luque M. Bachs and M. Orozco J. Comput. Chem. 1994 15 847. S.W. Rick and B. J. Berne J. Am. Chem. Soc. 1994 116 3949. lo D. Sitkoff K. A. Sharp and B. Honig J. Phys. Chem. 1994 98 1978. S.L. Chan and C. Lim J. Phys. Chem. 1994 98 692. 1.1. Vaisman F. K. Brown and A. Tropsha J. Phys. Chem. 1994,98 5559. l3 M. Cossi B. Mennucci and J. Tomasi Chem. Phys. Lett. 1994 228 165. '4 M. Holst R. E. Kozack and F. Saied S. Subramanian Proteins Struct. Func. Gen. 1994 18 231. l5 M. Holst R. E. Kozack F. Saied and S. Subramaniam J. Biornol Struct. Dyn. 1994 11 1437. l6 H.-X. Zhou J. Chem. Phys. 1994 100 3152. T. Furuki A.Umeda M. Sakurai Y. Inoue R. Chujo and K. Harata J. Comput. Chem. 1994 15 90. M. E. Davis J. Chem. Phys. 1994 100 5149. 28 Jonathan W. Essex solvation with calculations using density functional theory (DFT).' 9-23 This powerful method of performing electronic structure calculations was extensively reviewed in last year's report.24 The extension of this procedure to include solvation through the Poisson-Boltzmann self consistent reaction field (SCRF),21 and polarizable 19720 continuum models (PCM)22 will undoubtedly yield many exciting results in the future. Solvation effects have also been incorporated into generalized valence-bond calcula- tions by Tannor et through the Poisson-Boltzmann equation giving an average error for solvation free energies with respect to experiment of 0.6 kcal mol- '.The combined semi-empirical/continuum-solventmodels of Cramer and Truhlar referred to as the SMx series of models have proved very popular for calculating free energies of solvation,26 particularly because the calculations are fast and easy to perform. Dixon et al.27 have developed a similar model based on the AM1 Hamiltonian which was reported to be more efficient still and gave more accurate free energies of hydration. Explicit Solvent Models.-This category of solvation modelling can be subdivided into the integral-equation methods and the models in which solvent molecules are explicitly included in the calculation. The latter are particularly popular in classical computer simulations since specific interactions such as hydrogen bonding are treated.Arguably the most significant deficiency of the majority of these studies is the failure to include polarization explicitly although this is now being addressed by a number of groups. Integral-equation methods introduce the effect of solvent through the calculation of distribution functions given an empirical pair potential-energy function.28 The method has been extended to ab initio calculation^,^^ representing an interesting development in the treatment of solvation within a quantum-mechanical framework since the structure of the solvent is included in the calculation. In terms of classical treatments of solute and solvent conventional empirical potential-energy parameters continue to be developed and refined.In particular the OPLS force-field derived by Jorgensen has been extended to cover all-atom treatments of simple hydrocarbon^,^' and class I1 force-fields that incorporate anharmonic effects and intramolecular coupling interactions have been developed for alkanes3 1,32 and poly~arbonates.~~ However these approaches all include polarization in an average sense and in situations involving charged systems a force-field that explicitly includes polarization may be preferable. Emphasis is being placed on the development and l9 K. Baldridge R. Fine and A. Hagler J. Comput. Chem. 1994 15 1217. 2o J. L. Chen L. Noodleman D. A. Case and D. Bashford J. Phys. Chem. 1994 98 11 059. 21 M. F. Ruiz-Lopez F. Bohr M.T. C. Martins-Costa and D. Rinaldi Chem.Phys. Lett. 1994 221 109. 22 A. Fortunelli and J. Tomasi Chem. Phys. Lett. 1994 231 34. 23 A.A. Rashin M.A. Bukatin J. Andzelm and A.T. Hagler Biophys. Chem. 1994 51 375. 24 C.A. Reynolds Ann. Rep. Prog. Chem. Sect. 8 1993 90 51. 25 D.J. Tannor B. Marten R. Murphy R. A. Friesner D. Sitkoff A. Nicholls M. Ringnalda W. A. Goddard 111 and B. Honig J. Am. Chem. SOC. 1994 116 11 875. 26 C.J. Cramer and D.G. Truhlar J. Comput. Aid. Mol. Des. 1992 6 629. R. W. Dixon J. M. Leonard and W. J. Hehre Isr. J. Chem. 1994 33,427. 28 J. Perkyns and B. M. Pettitt Biophys. Chem. 1994 51 129. 29 S. Ten-no F. Hirata and S. Kato J. Chem. Phys. 1994 100 7443. 30 G. Karninski E. M. Duffy T. Matsui and W. L. Jorgensen J. Phys. Chem. 1994 98 13077. 31 M.J. Hwang T.P. Stockfisch and A.T.Hagler J. Am. Chem. SOC. 1994 116 2515. 32 J.R. Maple M.-J. Hwang T. P. Stockfisch and A.T. Hagler Isr. J. Chem. 1994 34 195. 33 H. Sun S. J. Mumby J. R. Maple and A.T. Hagler J. Am. Chem. SOC.,1994 116 2978. 2' Theoretical Organic Chemistry 29 validation of polarizable water model^,^^.^' since this solvent is of course very important in living systems. Furthermore a new approach for introducing polariz- ation has been developed by Rick et based on the concept of electronegativity equalization and applied to the simulation of water. The method gave accurate predictions of gas and liquid-phase properties for a small increase in computational expense over pairwise-additive potentials and thus its extension to bioorganic simulations is very attractive.A notable area of interest in contemporary theoretical organic chemistry is the calculation of relative free energies of s~lvation,~~ allowing such diverse properties as binding constants and tautomeric equilibria to be evaluated. Absolute free energies of hydration of the acetate and methylammonium ions have been calculated in the past year using a polarizable water The calculated free energies of hydration were shown to be in good agreement with experiment without the need to invoke any reparameterization; this was not the case when a conventional pairwise-additive water model was used. It is possible to progress beyond the traditional approximation of pairwise-additive interaction potentials in computer simulations by using either the hybrid molecular- mechanics/quantum-mechanics (MM/QM) scheme or by the Car-Parrinello (CP) procedure.In recent years Gao has been instrumental in developing and applying a MM/QM procedure in which Monte-Carlo simulations are performed on a solute modelled using the semi-empirical AM 1 Hamiltonian and a solvent represented through the empirical TIP3P Further studies have been reported in 1994 investigating a range of processes including tautomeric eq~ilibria,~' the influence of solvent on the Claisen rearrangement,41 and the effect of solvent on the n+n* electronic transition of acetone.42 This approach of Gao does however suffer from the disadvantages arising from the choice of solute Hamiltonian and the absence of polarization of the solvent.The issue of the solute Hamiltonian has been addressed through the use of other models. Stanton et have used a MM/QM technique based on the PM3 Hamiltonian combined with molecular-dynamics simulations with the TIP3P water model. Relative free energies of hydration between different solute molecules were calculated. Wei and Salahub used DFT to model a solute water molecule in a combined MM/QM procedure although the response of the classical solvent to polarization of the quantum-mechanical solute was not ~onsidered;~~ it would be expected that an MM/QM approach using DFT would be ultimately more reliable than that using a semi-empirical Hamiltonian. The CP scheme is able to address both the deficiencies of the common MM/QM procedures; a DFT approach is used which is arguably preferable to a semi-empirical model and both solute and solvent are treated identically thereby allowing 34 D.N. Bernado Y. Ding K. Krogh-Jespersen and R. M. Levy J. Phys. Chem. 1994,98 4180. 35 S.-B. Zhu and C. F. Wong J. Phys. Chem. 1994 98,4695. 36 S. W. Rick S.J. Stuart and B. J. Berne J. Chem. Phys. 1994 101 6141. 37 P.A. Kollman Chem. Rev. 1993 93 2395. 38 E.C. Meng P. Cieplak J. W. Caldwell and P.A. Kollman J. Am. Chem. SOC.,1994 116 12061. 39 J. Gao and X. Xia Science 1992 258 631. 40 J. Gao and L. Shao J. Phys. Chem. 1994,98 13772. 41 J. Gao J. Am. Chem. Soc. 1994 116 1563. 42 J. Gao J. Am. Chem. SOC.,1994 116 9324. 43 R.V. Stanton L. R. Little and K. M. Merz Jr. J. Phys. Chem. 1995 99 483. 44 D. Wei and D.R. Salahub Chem. Phys. Lett. 1994 224 291. 30 Jonathan W.Essex polarization of the solvent. Owing to the computational expense of performing these calculations simulations of several picoseconds are the norm considerably less than is accessible through simulations using classical potentials. However during the course of the year a multiple time-scale method has been derived which provides the possibility of increasing simulation speed by up to a factor of 10 without compromis- ing ac~uracy.~’ Laasonen and Klein have used the CP scheme to study the dissociation of hydrochloric acid in water.46 They were able both to observe the breaking of the H-C1 bond and to characterize the solvent structure around the two ions after dissociation. CP simulations have also been used to study a metallocene-catalysed ethylene polymerization reaction.47 The simulations were able to follow the reaction from the initial complex through to propyl formation over 150 fs and suggest that the insertion step of the reaction does not have an energy barrier.Curioni et ~21.~~ investigated the protonation of 1,3,S-trioxane and 1,3-dioxolane monomers in isolation using CP simulations. The protonation of trioxane was not immediate but rapid release of formaldehyde was then observed. Dioxolane underwent rapid protonation followed by ring opening but no loss of formaldehyde followed. The implication of these results for the polymerization reactions of these molecules was discussed. Computer Simulation and Free-energy Methodologies.-In this section the advances in computer simulation and free-energy methodologies that are of particular relevance to organic systems will be addressed.It should be self-evident that since free energies determine the position of equilibria their accurate calculation must be a major goal in theoretical organic chemistry. Undoubtedly one of the most difficult problems in calculating precise free energies via condensed-phase molecular dynamics or Monte-Carlo simulations is that of adequately sampling the available conformational space of the system. Relative free energies can be evaluated using either the thermodynamic integration (equation 1)or perturbation equations (equation 2).37 I= 1 AG=S 1=0 (g),dA The free-energy difference between two states A (A = 0) and B (A = l),AG is evaluated as the integral of the ensemble average of dH/dA where H is the Hamiltonian.AG = -RTln (exp( -AH/RT)) (2) R and T are the ideal gas constant and temperature respectively and AH is the difference in Hamiltonian between states A and B. In both cases an ensemble average is evaluated (the term inside the angular brackets) and if the conformational sampling is incomplete then this average may be inadequately converged or have converged to the wrong result. A combined Monte-Carlo/molecular-dynamics scheme has been proposed which in conjunction with a continuum treatment of solvation goes some way to addressing this issue.49 Large-step Monte-Carlo moves are able to cross high 45 M. E. Tuckerman and M.Parrinello J. Chem. Phys. 1994 101 1316. 46 K. Laasonen and M. L. Klein J. Am. Chem. SOC. 1994 116 11 620. 47 R. J. Meier G.H. J. van Dorernaele S. Iarlori and F. Buda J. Am. Chem. SOC. 1994 116 7274. 48 A. Curioni W. Andreoni J. Hutter H. Schiffer and M. Parrinello J. Am. Chem. SOC. 1994 116 11 251. 49 F. Guarnieri and W.C. Still J. Comput. Chem. 1994 15 1302. Theoretical Organic Chemistry 31 energy barriers whereas molecular dynamics or in this particular implementation stochastic dynamics is able to sample well the environment of the current local minimum. Using a combination of alternate Monte-Carlo and stochastic-dynamics steps it is possible to search the conformational space of flexible molecules more efficiently than with either method in isolation.The combined Monte-Carlo/molecu- lar-dynamics scheme has been applied to the study of the conformational ther- modynamics of a series of diamides.” The simulations were able to reproduce the experimental enthalpic and entropic data for intramolecular hydrogen-bond forma- tion while at the same time demonstrating complete convergence. A similar procedure has been developed by Clamp et al.” It is perhaps worth commenting that this approach relies for its success on either having no solvent present or using a continuum treatment. If an explicit solvent model were used then the large-step Monte-Carlo component would be less efficient and perhaps yield almost zero acceptance of moves. Ewing and LybrandS2 demonstrated that poor sampling can cause significant errors in the calculation of relative solvation free energies.They estimated the free energies of hydration of a range of organophosphorus compounds and found that a conventional molecular-dynamics simulation with explicit solvent was unable to explore adequately the conformational space of the molecule. The use of a continuum treatment of solvation applied to the minimum energy conformations of the molecule was their solution to this difficult problem and gave free energies consistent with related experimental data. Straatsma and M~Cammon~~ have addressed the sampling problem by an alternative route; they calculated potentials of mean force for rotation about the peptide dihedral angles of alanine dipeptide in water and used these results as umbrella biasing potentials in simulations of larger peptides.A significant increase in sampling efficiency resulted. Beutler and van Gunsteren have developed a procedure for overcoming energy barriers by extending the simulation into a fourth dimen~ion;’~ the approach was shown to work when calculating the change in density of an atomic fluid although less efficiently than conventional procedures. The technique may however prove useful when applied to organic and biological systems. Pearlman has developed a technique for assessing the convergence of free-energy calculations by evaluating ‘free-energy derivatives’ with respect to the individual parameters in the force field.’ ’ The need to perform very long simulations to achieve reliable convergence and precise free-energy results was apparent.One way of obtaining relative free energies rapidly is to estimate the total free energy change for a process from only a single simulation. Aqvist et al.56 report a method based on linear-response theory whereas Smith and van Gunsteren use a Taylor expansion of the free energy.57 A particular difficulty in free-energy calculations arises when an atom or group of atoms is created or annihilated as in for example the mutation of ethanol to methanol in water to calculate the difference between their free energies of hydration. At the point 50 D.Q. McDonald and W.C. Still J. Am. Chem. SOC.,1994 116,11550. ” M.E. Clamp P.G. Baker C. J. Stirling and A. Brass J. Comput. Chem. 1994 15 838. ” T. J. A. Ewing and T.P. Lybrand J. Phys. Chem. 1994 98 1748. 53 T.P. Straatsma and J.A. McCammon J. Chem. Phys. 1994 101 5032. 54 T.C. Beutler and W. F. van Gunsteren J. Chem. Phys. 1994 101 1417. 5s D.A. Pearlman J. Cornput. Chem. 1994 15 105. ” J. Aqvist C. Medina and J.-E. Samuelsson Protein Engineering 1994 7 385. 57 P.E. Smith and W. F. van Gunsteren J. Chem. Phys. 1994 100 577. 32 Jonathan W. Essex in the simulation where the atoms appear or disappear the calculation can become very unstable and ill-behaved. Zacharias et aLS8overcame this difficulty by scaling the Lennard-Jones interaction potential that is usually used to describe van der Waals interactions smoothly to zero in the course of the simulation. Using conventional methodology the steeply repulsive component of the potential was present up until the .~~ atom was annihilated.Beutler et ~1proposed a similar solution although they used a soft-core potential at the point of annihilation/creation. The decomposition of calculated free-energies into contributions arising either from individual components of the force field or from groups of atoms within the molecule has proved popular in recent years since it would allow the calculated free-energy change to be interpreted in chemically meaningful terms. However it has been argued that such a decomposition is meaningless owing to the path dependence of the free-energy components. Smith and van Gunsteren presented a convincing demonstra- tion of this phenomenon for the mutation of p-cyanophenol to p-methoxyphenol in solution.60 Boresch et aL6’ agreed that free-energy decompositions are path depend- ent but they considered this approach useful and able to provide insight provided the pathway adopted in the free-energy calculation was defined.Transition States and Reaction Pathways.-The calculation of transition states and reaction routes is of considerable interest to organic chemists; this section will review recent methodological developments in this area. Although the first stage in exploring a potential energy surface is to determine stationary points-reactants transition state and products-it may prove necessary to confirm that the reaction mechanism does indeed link these stationary points. In practice this can be achieved using ‘reaction-path following’ in which the path of steepest descent from the transition state is calculated in mass-weighted Cartesian coordinates.Schlege16’ addressed some of the deficiencies of this procedure and in particular examined ways of dealing with bifurcation of reaction paths and developed more efficient algorithms that make maximal use of gradient and Hessian information. A disadvantage of conventional methods of transition-state searching is the expense associated with the large number of steps required to map the path completely together with the necessary expensive second-derivative calculation at the transition state. To .~~ address these issues Chiu et ~1 adopted a procedure described by Elber and Karpld4 in which an energy function of the entire path was minimized.The method was demonstrated to perform well in comparison with the traditional approaches of reaction path calculation and offers the possibility of efficiently calculating reaction pathways for large systems. Barnes et have investigated reaction mechanisms from the perspective of More O’Ferrall-Jencks diagrams a commonly used method for rationalizing reactivity trends and found that these diagrams successfully predicted transition-state structural variations on changing the reactants. 58 M. Zacharias T. P. Straatsma and J. A. McCammon J. Chem. Phys. 1994 100 9025. 59 T. C. Beutler A. E. Mark R. C. van Schaik P. R. Gerber and W. F. van Gunsteren Chem. Phys. Lett. 1994 222 529. P. E. Smith and W. F. van Gunsteren J. Phys. Chem. 1994 98 13 735.61 S. Boresch G. Archontis and M. Karplus Proteins Struct. Func. Gen. 1994 20 25. 62 H.B. Schlegel J. Chem. SOC. Faraday Trans. 1994 90,1569. 63 S.S.-L. Chiu J.J. W. McDouall I.H. Hillier J. Chem. SOC.,Faraday Trans. 1994 90,1575. 64 R. Elber and M. Karplus Chem. Phys. Lett. 1987 139 375. 65 J.A. Barnes J. Wilkie and I.H. Williams J. Chem. Soc. Faraday Trans. 1994 90,1709. Theoretical Organic Chemistry 33 The calculation of transition-state structures and energies can prove expensive because of the need to evaluate second-derivative information and difficult since the transition-state search may not actually find a transition state if the starting geometry is poorly chosen. Two groups have addressed this issue using methods that predict the transition state given energies geometries and force constants of the reactants and produ~ts.~~,~~ Given the level of approximation these calculations performed well generating qualitatively correct transitions states which at the very least were useful starting points for more rigorous procedures.Shaik et have proposed a method ~1.~~7~~ of finding transition states based on valence-bond theory; the transition-state wave function was approximated to that at the avoided crossing state (ACS) between reactants and products. The reliability of this approach was determined by studying various S,2 reactions and it was found that the ACS was a useful approximation to the transition state. Houk et ~1.~’ have pioneered a molecular-mechanics based approach for determin- ing the structure of transition states.Molecular-mechanics parameters for transition states are derived from ab initio results. The structure obtained by energy minimization using these parameters is presumed to represent the transition state and the difference in energy between this structure and the reactants then corresponds to the activation energy of the reaction. This approach has been criticized on a number of grounds including the fact that transition states are saddle points not minima and that electronic stabilization of the transition state can be difficult to incorporate into the model. Specifically Menger and Sherrod71 have raised the issue of the arbitrary nature of the parameters adopted and have suggested that a random method of parameter optimization rather than a rational approach may be more efficient.Eurenius and Houk7’ have investigated intramolecular hydride transfers and demonstrated that a rational approach to transition-state parameter development was effective provided that care was taken in the parameterization. Molecular-mechanical modelling of transition states has also been applied to the addition of boronates to aldehydes with considerable SUCC~SS.’~ The issue of calculating rates of reaction given knowledge of a reaction’s potential energy surface with the inclusion of tunnelling effects has been extensively addressed .~~ by Truhlar et ~ 1 A notable feature or this work was the use of high-level ab initio calculations to calculate energies at three of four points along the reaction pathway typically including reactants and transition states to correct the entire reaction swath evaluated using cheaper semi-empirical calculations.This method has been applied to the reaction of the hydroxide radical with ethane an important process in both atmospheric chemistry and combu~tion.~~ The method was able to reproduce to within a factor of two the experimental rate constants and also demonstrated the importance of including tunnelling effects; in the temperature range 25WOO K more than half the reactive events were predicted to occur by tunnelling. Furthermore this technique of 66 F. Jensen J. Comput. Chem. 1994 15 1199. 67 K. Ruedenberg and J.-Q. Sun J. Chem. Phys. 1994 101 2168. 68 S. Shaik and A.C. Reddy J. Chem. SOC.,Faraday Trans. 1994 90 1631. 69 S. Shaik A. Ioffe A.C. Reddy and A. Pross J. Am. Chem. SOC. 1994 116 262. 70 K.P. Eurenius and K.N. Houk J. Am. Chem. SOC. 1994 116 9943. 71 F. M. Menger and M. J. Sherrod J. Am. Chem. SOC. 1990 112 8071. 72 C. Gennari E. Fioravanzo A. Bernardi and A. Vulpetti Tetrahedron 1994 50 8815. 73 W.-P. Hu Y.-P. Liu and D.G. Truhlar J. Chem. SOC. Faraday Trans. 1994 90 1715. 74 V. S. Melissas and D.G. Truhlar J. Phys. Chem. 1994 98 875. 34 Jonathan W. Essex calculating reaction rates with the inclusion of tunnelling has recently been extended to the solution phase." The relative merits of transition states evaluated using ab initio semi-empirical and density-functional theories have been compared in a series of papers.Abashkin and R~sso~~ reported a method for finding transition states implemented within a density functional formulation and Stanton and Mer~~~ compared the transition states of organic and organometallic reactions found using density functional theory with those derived from ab initio and semi-empirical calculations. Non-local density functional calculations were observed to yield energetic results of similar quality to post Hartree-Fock calculations although the DFT geometries were generally less reliable. Deng and Ziegler reported the implementation of reaction-path following within DFT and tested its performance on a range of reactions including an SN2 displacement and an elimination reaction.78 It was found that the reaction paths were in qualitative agreement with ab initio results and that where discrepancies occurred between local and non-local DFT reactant and product geometries the non-local geometries were generally in better agreement with experiment.Energies of stationary points were found to be of comparable quality to MP4SDTQ results. Andres et studied the reaction of CO with CH,NHCONH using ab initio and semi-empirical calculations and found that the four-membered-ring transition state was observed at all levels of theory although there were clearly differences in geometry and energetics. Mulholland and Richards" investigated the transition states for unimolecular hydrogen fluoride elimination from a series of methylene and vinyl halides using both semi-empirical and ab initio calculations.The geometries of the transition states at the AM1 and PM3 levels were very different from the MP2/6-31 lG(d,p) results although the calculated activation energies were generally in better agreement. 3 Selected Applications Owing to the amount of literature published in the past year describing applications of theory to problems of organic chemistry only selected topics will be reviewed here. Host-guest chemistry is an area of increasing interest since the factors influencing molecular recognition can be studied in systems of tractable size. This is particularly important when trying to understand the processes that determine binding in biochemistry. The calculation of physical properties of molecules such as conforma- tional tautomeric and redox equilibria are also presented.These properties influence molecular reactivity and their calculation often requires the combination of accurate gas-phase energies with condensed-phase simulations. Finally pericyclic and SN2 reactions are reviewed. Not only are these reactions of considerable synthetic utility but they also represent a significant challenge to theory. The author believes that these areas represent a broad cross-section of the currently interesting topics. Host-Guest Chemistry.-The investigation of molecular recognition processes through the development of synthetic host molecules is an area of increasing interest in 75 D.G. Truhlar Y.-P. Liu G. K. Schenter and B.C. Garrett J. Phys. Chem. 1994 98,8396. l6 Y. Abashkin and N.Russo J. Chem. Phys. 1994 100 4417. 77 R.V. Stanton and K. M. Merz J. Chem. Phys. 1994 100,434. 78 L. Deng and T. Ziegler Int. J. Quant. Chem. 1994 52 731. 79 J. Andres V. Moliner J. Krechl and E. Silla J. Phys. Chem. 1994 98 3664. A. J. Mulholland and W. G. Richards Int. J. Quant. Chem. 1994 51 161. Theoretical Organic Chemistry organic chemistry. These systems provide the opportunity to study noncovalent interactions in relatively small molecules thereby providing information applicable to larger biological systems. The ultimate goals of these studies are the rational design of synthetic catalysts with selectivities comparable to enzymes and the design of large-scale molecular aggregates with specific physical properties. Theoretical chemis- try is increasingly being applied to these systems to assist first in the interpretation of experimental data and second in the rational design process.The binding of alkali cations to synthetic receptors was studied in some detail by a number of authors during 1994.These systems are of considerable practical interest in nuclear-waste reprocessing because of their potential for the separation of radioactive ions. In two studies Kollman et a1.81,82 investigated the binding to a synthetic cavitand consisting of eight anisole subunits in water and methanol. The cavity is complement- ary in size to Cs+ which is observed to bind the most tightly of all to the alkali ions in water-saturated chloroform. However the cavitand also shows an unusual secondary binding preference in that Na' binds more strongly than Li' and K+.83Bayly and Kollman" investigated the binding behaviour of the cavitand with the alkali metal cations through a combination of molecular-dynamics simulations and free-energy calculations under aqueous conditions.Water was adopted as solvent for this study rather than the experimental solvent of water-saturated chloroform since the composition of the water/chloroform mixture was not known and the ions would undoubtedly act as water scavengers leading to a locally water-rich environment. The relative binding-constants of the various ions with the cavitand were calculated using the thermodynamic cycle given in Figure 1. Ion binding is characterized by the free energies AGl and AG2.However these processes are difficult to simulate in practice whereas the other legs of the cycle corresponding to the free-energy change on mutating between two ions whilst bound and in solution are much easier to evaluate. H + G1 AGl * H:G1 I I AG" AGb .) t H + G2 AG2 H:G2 Figure 1 Free-energy cycle for the binding of guests G1 and G2 to the host H. AGu and AG correspond to the free-energy changes on perturbing between guests GI and G2 whilst unbound and bound to the host respectively Given AGu and AG, the difference in binding free energy between the two ions AG2 -AGl can be calculated. The practical calculation of equilibrium constants in the course of condensed-phase simulations almost invariably relies on the use of such thermodynamic cycles.The simulations reproduced the experimentally observed binding order and the calculated binding affinities were in semiquantitative agreement with experiment. Inspection of the host/guest geometries in the course of the simulations revealed that for Li+-Rb+ two water molecules accompanied the ion into *' C.I. Bayly and P. A. Kollman J. Am. Chem. SOC.,1994 116 697. B.E. Thomas IV and P. A. Kollman J. Am. Chem. SOC.,1994 116 3449. 83 D. J.Crarn R. A. Carmack M. P.deGrandpre,G. M. Lein I. Goldberg,C. B. Knobler E. F. Maverick and K.N. Trueblood J. Am. Chem. SOC. 1987 109 7068. 36 Jonathan W. Essex the cavity. However only in the case of Na’ were the ion and water molecules able to form an optimal arrangement in the cavity thereby rationalizing the increased binding constant of Na’ compared with Li’ and K ’.In the second investigations2 Thomas and Kollman repeated the calculations but using methanol as solvent. In this case the binding preference for Na’ was not observed despite the presence of two methanol molecules in the cavity with Li + and Na’ .This was attributed to the fact that methanol forms fewer hydrogen-bond interactions than water and is sterically more bulky. The 18-crown-6 cation host has been investigated by a number of research groups using a range of techniques. Troxler and WipP4 performed molecular-dynamics simulations of this species in acetonitrile and observed that the range of conformations sampled depended upon whether water or acetonitrile was used as solvent. The solvent structure in the vicinity of the isolated crown ions and in the complex was also investigated.Cieplak et studied this system under aqueous conditions using molecular dynamics and free-energy calculations. They applied the new technique of free-energy derivatives” to ascertain the size of the ion giving optimum binding to this molecule; an ion intermediate in size between Na’ and K+ was predicted to form the strongest complex. Glendening et aLS6approached this molecule from a quantum- mechanical perspective. Ab initio calculations were performed on the isolated crown and on the complexed species. The affinity of alkali metal ions for this molecule arose largely from electrostatic interactions between the cation and the nucleophilic ether backbone.Moreover these gas-phase calculations suggested that the smallest ions should bind most strongly in conflict with experiment. However when four water molecules were included in the calculations the experimental preference for K ’ binding was reproduced. This system was also studied using the combined MM/QM pr~cedure.~’ The crown was modelled by the AM1 Hamiltonian and K’ and water by molecular-mechanics potentials. Molecular-dynamics simulations were performed and the results showed the utility of this method as applied to this system. In particular the magnitude of the crown polarization was significant suggesting that ideally this contribution should be explicitly treated. It should however be noted that simulations using pairwise-additive potentials include polarization in an average sense and have .~~ proven successful in studying this type of system.Marrone et ~1also observed crown polarization in their calculation of the potential of mean force for K+ binding to 18-crown-6. The potential of mean force for the association of Cs+ to this host was evaluated using molecular dynamics by Dang;89 this study is notable in that a chloride counter-ion was included in the simulation. The calculated binding free-energies of -0.5 and -1.3 kcal mol- depending on the position of the counter ion are in good agreement with experimental results of between -1.1 and -1.4 kcal mol- ’.Metal ion complexation to aliphatic ethers a component in stabilizing cationxrown complexes was investigated through ab initio calculations on model system^,'^ with the goal of parameterizing the MM3 force-field for these molecules.The calculations showed that for stable complexes the extent to which ligand coordination reproduces a trigonal 84 L. Troxler and G. Wipff J. Am. Chem. Soc. 1994 116 1468. 85 P. Cieplak D.A. Pearlman and P.A. Kollman J. Chem. Phys. 1994 101 627. 86 E.D. Glendening D. Feller and M. A. Thompson J. Am. Chem. Soc. 1994 116 10657 ” M.A. Thompson E.D. Glendening and D. Feller J. Phys. Chem. 1994 98 10465. 8R T. J. Marrone D. S. Hartsough and K. M. Merz Jr. J. Phys. Chem. 1994 98 1341. 89 L. X. Dang Chem. Phys. Lett. 1994 27 21 1. 90 B.P. Hay and J.R. Rusad J. Am. Chem. Soc. 1994 116 6316. Theoretical Organic Chemistry 31 planar geometry is perhaps more important than the extent to which the preferred M-0 bond length is adopted.Troxler and WipP4 also performed molecular dynamics and free-energy calcula- tions on cryptand [2223 and its alkali metal complexes in acetonitrile. Whilst quantitative agreement of the calculated relative binding constants with experiment was not reproduced K+ was predicted to bind most strongly in accord with experiment. Ross and Hardin” investigated the stabilizing influence of alkali metal ions on a Guanine-rich-DNA quadruplex. The cation is considered trapped inside the quadruplex in a cavity lined by eight hydrogen-bonded carbonyl oxygen atoms. The change in binding free energy as a function of the cation was calculated in the course of molecular-dynamics simulations.Although experiment gave the most stable quadru- plex with K + and simulation gave Na’ a free-energy minimum as a function of cation size was predicted reflecting the competition between ion solvation and binding within the DNA cavity. A number of other studies were reported during the year which involved the calculation of relative free energies of binding. Duffy and J~rgensen~~ readdressed the issue of pyrazine and pyridine binding to Rebek’s acridine diacid in light of a recent crystal structure. Previous sir nu la ti on^^^ suggested that the relatively small experimen- tal preference for pyrazine over pyridine arose from the host cleft being too small to accommodate simultaneous two-point binding of pyrazine. However a crystal structure of this host with q~inoxaline~~ demonstrated that two-point binding was possible.Duffy and Jorgensen performed a new set of Monte-Carlo simulations using an all-atom parameter set and with increased host flexibility. If was found that the host was able to accommodate two-point binding by undergoing deformation and that the unexpected pyrazine/pyridine preference arose from favourable interactions between pyridine and the distant non hydrogen-bonding acid group. The simulations were able to reproduce the experimental relative free energies of binding very well. The earlier failed to predict two-point binding since full host flexibility was not included in the calculation. In Figure 2 the gas-phase minimum-energy structures for pyrazine pyridine and quinoxaline bound to the acridine host are presented; two-point binding is clearly observed for pyrazine and quinoxaline.Mark et ~1.~’ investigated the binding of para-substituted phenols to a-cyclodextrin. This study demonstrated the importance of careful analysis in the calculation of free energies. In particular the need to demonstrate closed thermodynamic cycles was emphasized as was the fact that without a reliable assessment of simulation error agreement with experimental binding-constants may be fortuitous. Free-energy calculations in host-guest chemistry have even taken on a predictive role. In a notable study Burger et ~1.~~ predicted that a specific modification of a podand ionophore host should yield high enantioselectivity between a particular D and L-amino-acid derivative.The calculations used the continuum GB/SA solvent model of chloroform 91 W.S. Ross and C.C. Hardin J. Am. Chem. SOC. 1994 116 6070. 92 E. M. Duffy and W. L. Jorgensen J. Am. Chem. SOC. 1994 116 6337. 93 W. L. Jorgensen S. Boudon and T. B. Nguyen J. Am. Chem. SOC. 1989 111 755. 94 R.A. Pascal Jr. and D. M. Ho J. Am. Chem. Soc. 1993 115 8507. 95 A. E. Mark S. P. van Helden P. E. Smith L. H. M. Janssen and W. F. van Gunsteren J. Am. Chem. SOC. 1994 116 6293. 96 M.T. Burger A. Armstrong F. Guarnieri D. Q. McDonald and W. C. Still J. Am. Chem. SOC.,1994,116 3593. Jonathan W. Essex (4 Figure 2 Gas-phase energy minima for the acridine diacid host with (a)pyrazine (b)pyridine and (c) quinoxaline (Reproduced with permission from J.Am. Chem. SOC. 1994 116 6337. 0 1994 American Chemical Society.) together with the mixed Monte-Carlo/stochastic-dynamicsmethod.49 The predicted enantioselectivity was found to agree with experiment to within 0.3 kcal mol- ’ a remarkable achievement. Theoretical methods have also been used to investigate the various specific interactions that stabilize complex formation including hydrogen bonding cation-.n interactions and hydrophobic interactions. Ab initio calculations have been used to investigate the hydrogen bonding between formic acid and f~rmamide,~~ since this complex is a model for a frequently adopted molecular recognition motif. It was found that the weakest hydrogen-bond between the carbonyl oxygen of formic acid and the formyl hydrogen contributed approximately 2.5-3.5 kcal Mol -to the complex interaction energy.Thus the formyl proton may indeed participate in hydrogen bonding and this should be remembered when designing synthetic hosts. It has been suggested that cation-.n interactions are responsible for the binding of acetylcholine to acetylcholinesterase. Ab initio calculations have been performed on the tetramethylam- monium and ammonium cations complexed with benzene and water to investigate the ’’ T. Neuheuser B.A. Hess C. Reutel and E. Weber J. Phys. Chem. 1994 98 6459. Theoretical Organic Chemistry 39 strength ofthis type ~finteraction.~~ It was found that cation-n interactions were indeed strong and in the case of the tetramethylammonium cation stronger binding to benzene than water was observed.Free-energy calculations of the binding of acetylcholine to a synthetic host99 supported the assertion that cation-n interactions are significant. The potential-energy surface of the benzene dimer has been investigated using ab initio calculations.'00 This can be regarded as the prototype system for aromatic-aromatic interactions in biochemistry. The calculations suggested that the parallel-displaced structure has the lowest energy lower than the T-shaped although entropic effects are likely to favour the T-shaped geometry with increasing temperature. On a more qualitative level molecular-dynamics simulations have been used to justify trends in binding constant without the explicit calculation of free energies.Huang et a[."' rationalized the trends in binding constant of different cyclohexanet- riols with a synthetic polyaza cleft in terms of the relative strengths of intramolecular hydrogen bonds within the triol. Chin et were able to reproduce the experimental trend in aggregate stability by determining the amount of distortion from planarity in the aggregates in the course of a molecular dynamics simulation. Finally molecular dynamics Monte-Carlo simulations and energy minimizations have been used to predict the geometry of host-guest binding in peptide'03 and glycoside' O4 binding systems and in the rational design of synthetic hosts for peptides'05 and bis- imidazoles.' O6 Conformational Equilibria.-The issue of molecular conformation is of critical importance to organic chemists since a molecule's reactivity is intimately related to the shape it adopts.Such a large amount of work has been published in the past year on conformation that it is impossible to review the entire subject exhaustively. Three areas will therefore be presented in more detail the effect of solvent on conformation the role of intramolecular hydrogen-bonding and the anomeric effect. These areas are of particular importance in determining the conformational stability of carbohydrate molecules a topic of considerable current interest. Ethane-1,2-diol is usually the molecule of choice for the investigation of intra- molecular hydrogen-bonding. Both ab initio and density-functional methods have been used to investigate the gas-phase conformations of this molecule and the effect of solvent has been introduced through the SMx series of models.'07-' Ab initio calculations at the MP4/6-31 lG**//MP2/6-31G** level showed that the two lowest energy gas-phase conformations have an intramolecular hydrogen-bond demonstrat- ing the importance of hydrogen-bonding in stabilizing conformation although a total 98 K. S. Kim J. Y. Lee S.J. Lee T.-K. Ha and D. H. Kim J. Am. Chem. Soc. 1994 116 7399. 99 P. H. Axelsen Isr. J. Chem. 1994 34 159. ''' P. Hobza H. L. Selzle and E. W. Schlag J. Am. Chem. SOC. 1994 116 3500. lo' C. Y. Huang L. A. Cabeil and E.V. Anslyn J. Am. Chem. Soc. 1994 116 2778. D. N. Chin D. M. Gordon and G. M. Whitesides J. Am. Chem. SOC. 1994 116 12033. A. Borchardt and W.C.Still J. Am. Chem. SOC. 1994 116 7467. G. Das and A. D. Hamilton J. Am. Chem. Soc. 1994 116 11 139. *05 M.F. Cristofaro and A.R. Chamberlin J. Am. Chem. Soc. 1994 116 5089. S. Mallik R.D. Johnson and F.H. Arnold J. Am. Chem. Soc. 1994 116 8902. lo' T. Oie I. A. Topol and S. K. Burt J. Phys. Chem. 1994,98 1121. C.J. Cramer and D.G. Truhlar J. Am. Chem. SOC.,1994 116 3892. 109 B. J. Teppen M. Cao R. F. Frey C. van Alsenoy D. M. Miller and L. Schafer J. Mol. Struct. (Theochem) 1994 314 169. 'lo T.S. Yeh Y. P. Chang T. M. Su and I. Chao J. Phys. Chem. 1994 98 8921. Jonathan W. Essex of ten stable conformations were identified all within approximately 4.5 kcal mol- 'of each other. Non-local density functional methods gave reasonable agreement with ab initio MP4 cal~ulations,'~~ but at less computational cost.There appears to be a concensus that this system is particularly challenging for ab initio methods; the energies of each conformation are very sensitive to basis set and level-of-correlation treat- merit.108,109Furthermore semi-empirical methods were not suitable for the confor- mational analysis of this molecule. The MM3 empirical potential-energy function was able to reproduce the ab initio potential-energy for conformations involving intra- molecular hydrogen-bonds but performed less adequately for the other conforma- tions.' lo The inclusion of solvation effects through the SMx series of models gave a free-energy of solvation in excellent agreement with experiment and the predicted aqueous conformational populations agreed with available experimental data sup- porting the use of these continuum solvation treatments in conformational analysis.lo8 Competition for hydrogen-bonding by the solvent would be expected to reduce the amount of intramolecular hydrogen-bonding in solution and this was supported by theory.Polyamines have also been used to study intramolecular hydrogen-bond- ing,' ' ' although diols are perhaps of more relevance because this motif is present in sugars. The anomeric effect is the preference of six-membered heterocycles substituted at C-2 with an electronegative group X to adopt the axial conformation (Scheme 1).Perhaps the simplest molecules that show this effect are the 2-substituted tetrahydropyrans.This series of molecules has been investigated both from the perspective of the gas-phase preference for the axial over equatorial conformation and to determine the role of solvation in affecting the conformational equilibrium. A series of ab initio calculations on tetrahydropyran derivatives have been carried out by Tvaroska and Carver.' '371 l4 Calculations of 2-fluoro and -chloro derivatives' ' provided an estimate for the gas-phase energy difference between axial and equatorial conforma- X Scheme 1 tions of approximately 2.5 kcal mol- '. The inclusion of solvent by a continuum method reduced the preference for the axial conformation by between 1 and 2 kcal mol-2-Methoxytetrahydropyran can be regarded as a model for the glycosidic linkage of carbohydrates.Not only can this system be expected to show the anomeric effect but also the exo-anomeric effect. The latter is the observed preference for the methyl group to adopt a gauche orientation with respect to the ring oxygen atom. Ab initio calculations carried out on this molecule' l4 gave a gas-phase free-energy difference between axial and equatorial conformations of 0.84 kcal mol- ' at room temperature in good agreement with the experimental result of between 0.7 and 0.9 kcal mol- ' in nonpolar solvents. Furthermore the calculations reproduced the ''I S.J. Lee B.J. Mhin S.J.Cho J.Y. Lee and K.S. Kim J. Phys. Chem. 1994 98 1129. 'I2 M. R. Kazerouni L. Hedberg and K. Hedberg J. Am. Chem. Soc. 1994 116 5279. 'l3 I. Tvaroska and J. P. Carver J. Phys.Chem. 1994 98 6452. 'I4 I. Tvaroska and J. P. Carver J. Phys. Chem. 1994 98 9477. Theoretical Organic Chemistry 41 experimentally observed exo-anomeric effect. The inclusion of solvent into the calculation reduced the magnitude of the axial preference to 0.23 kcal mol- for water in reasonable agreement with experiment. The performance of a range of molecular- mechanics force-fields was also investigated and it was found that MM3 with a dielectric constant of 1.5 was best able to reproduce the ab initio axiakquatorial conformational energy difference but was unable to calculate barriers of rotation correctly. This and related molecules have also been investigated both experimentally and theoretically by Wiberg and Marquez,"' and Jorgensen et ~1."~ Wiberg and Marquez' '' were able to reproduce the experimental anomeric effect using ab initio Hartree-Fock calculations at the 6-3 lG* level.It was found experimentally that increasing the polarity of the solvent reduced the axial preference and that this could be largely rationalized by considering the dipole moments of the axial and equatorial forms. It was also demonstrated that hydrogen bonding plays a role in the effect of solvation and this will have implications for modelling solvation using continuum treatments which exclude such specific interactions. Jorgensen et al.' l6 investigated the effect of solvent on the anomeric equilibrium of 2-methoxytetrahydropyran using Monte-Carlo free-energy calculations with explicit solvent molecules.The calculated preference for the equatorial conformation in water of 0.4 k0.2kcal mol- agreed well with experiment and was interpreted in terms of the changing dipole moment of the solute molecule. Simple continuum treatments of solvation such as SM2 and a dipolar SCRF calculation were unable to reproduce this result. Salzner and Schleyer' investigated a range of molecules using ab initio calculations in an attempt to determine which of the explanations for the anomeric effect was the most plausible namely dipolar repulsion or hyperconjugation. On balance their calculations supported the hyperconjugation explanation as being the most consistent with their results. The effect of solvent on conformation has been partly addressed in the discussion of the anomeric effect and intramolecular hydrogen-bonding.However there is a large amount of literature on this particular subject applied to other systems and in particular to peptide conformation. There is obviously great interest in the ultimate goal of predicting protein structure in solution and preliminary studies on small peptides are seen as a way of addressing the effect of solvent on conformation using a system of tractable size. Studies of dipeptides have been reported by Gould et al. ''* and Shang and Head-Gordon.' '' In both cases continuum models were used although explicit solvent has been used to calculate potentials of mean force for alanine dipeptide by Straatsma and M~Cammon.'~ demonstrated the The work of Gould et ~1."~ profound effect solvent can have on molecular conformation.Furthermore by comparison with the paper of Shang and Head-Gordon"' they demonstrated the importance of using continuum treatments that extend beyond a consideration of the molecular dipole moment. For an SCRF treatment the inclusion of terms up to 1 = 7 is advised as well as the use of a more realistic non-spherical cavity. Chan and Lim12' investigated the conformational space of a tetrapeptide using a random search coupled with energy minimization. An empirical description of the molecular energetics was I" K.B. Wiberg and M. Marquez J. Am. Chem. SOC. 1994 116 2197. W. L. Jorgensen P. I. Morales de Tirado and D. L. Severance J. Am. Chem. SOC. 1994 116 2199. U. Salzner and P. v. R. Schleyer J. Org. Chem. 1994 59 2138.I. R. Gould W. D. Cornell and I.H. Hillier J. Am. Chem. SOC. 1994 116 9250. H.S. Shang and T. Head-Gordon J. Am. Chem. SOC.,1994 116 1528. 120 S. L. Chan and C. Lim J. Phys. Chem. 1994 98 12 805. 42 Jonathan W. Essex adopted together with a finite-difference Poisson-Boltzmann treatment of solvation. It was found that the inclusion of solvation reduced the tendency for opposite charges to associate thereby increasing the number of favourable conformations considerably. The effect of solvent on the conformational equilibria of a number of organic molecules has been investigated including cocaine and derivatives,' ' amiloride,' 22 diarylguanidines,' 23 and phosphoryl choline and ethanolamine.' 24 These studies used both continuum and explicit representations of solvent together with ab initio semi-empirical and molecular mechanical descriptions of molecular energetics.Of particular note the solvation free energies obtained using a continuum model in conjunction with ab initio calculations were in fair agreement with the results obtained using the GB/SA solvent treatment with the AMBER force-field for diaryl- guanidines.' 23 GB/SA is a particularly fast method for calculating solvation free energies and these results suggest that it can be expected to work reasonably well in calculating relative conformational energies. However reservations concerning the reliability of the GB/SA model in treating n-stacking interactions were expressed. Nagy et al.' 25 performed a number of calculations on conformational equilibria comparing the performance of the GB/SA model applied in conjunction with the AMBER force-field to the results obtained using ab initio calculations to give gas-phase torsional-energy profiles followed by Monte-Carlo free-energy calculations with explicit solvent molecules to determine the solvation contribution.Their results for histamine and ethane- 1,2-diol suggested that the GB/SA solvation treatment applied with the AMBER force-field was not reliable for predicting conformational equilibria when intramolecular hydrogen bonds could form. The authors suggested that the molecular-mechanics parameters used in this procedure may need revising for this type of system. Redox Potentials and Tautomeric Equilibria.-The calculation of these physicochemi- cal properties represents a significant challenge to theory particularly when aqueous- phase equilibria are required.Two papers reporting the calculation of one-electron reduction potentials appeared in 1994. Neural networks were used by Wolfe et to predict the one-electron electrode potentials for a range of nitrobenzenes nitrofurans and nitroimidazoles. The input data to the neural network were the compound heats of formation evaluated semi-empirically and the free energies of hydration calculated using the AMl-SM2 model. An average accuracy of 70mV was reported from the calculations. A combination of quantum-mechanical calculations of gas-phase free energies together with classical computer simulations giving solution-phase free energies was adopted by Wheeler to calculate the one-electron reduction potential of p-benzoq~inone.'~~ This combination was used by Reynolds et to calculate successfully two-electron reduction potentials.One-electron potentials on the other hand are more problematic because of difficulties arising from the radical anion; the 12' B. Yang J. Wright M. E. Eldefrawi S. Pou and A.D. MacKerell J. Am. Chem. SOC. 1994 116 8722. 12* R.A. Buono T.J. Venanzi R. J. Zauhar V. B. Luzhkov and C.A. Venanzi J. Am. Chem. SOC. 1994,116 1520. 123 G. Alagona C. Ghio P.I. Nagy and G.J. Durant J. Phys. Chem. 1994 98 5422. 124 T.B. WooLf and B. Roux J. Am. Chem. SOC. 1994. 116 5916. 125 P.I. Nagy J.E. Bitar and D.A. Smith J. Comput. Chem. 1994 15 1228. 12' J. J. Wolfe J.D. Wright C.A. Reynolds and A. C. G. Saunders Anti-Cancer Drug Design 1994 9 85. 12' R. A. Wheeler J. Am. Chem. SOC.,1994,116 1 1 048. 12* C.A. Reynolds P. M. King and W. G. Richards Nature (London) 1988 334 80. Theoretical Organic Chemistry 43 gas-phase electron affinities require sophisticated treatments of electron correlation and the aqueous-phase relative free energy of hydration must consider the long-range electrostatic contribution arising from the creation/annihilation of charge. The calculated and experimental reduction potentials agreed to within 100mV.' 27 Tautomeric equilibria are fundamentally important in organic chemistry and especially in condensation reactions. Lammertsma and Pra~ad'~~ investigated the imine/enamine tautomeric equilibrium using a combination of ab initio calculations together with the SCRF continuum treatment of solvation.The calculations demon- strated the importance of using high-level basis sets together with a good description of electron correlation in these systems. Cao et al.13* investigated the tautomeric equilibria of 3-hydroxypyrazole; this represents a particularly challenging system since eight tautomers are possible. High-level ab initio calculations were performed up to MP4 and CCSD to calculate the gas-phase energies of the tautomers. The effect of solvent was introduced by first SCRF continuum calculations truncated as the dipolar term and second by Monte-Carlo free-energy perturbation calculations using explicit solvent molecules. The convergence of the ab initio results with increasing basis-set size and sophistication of correlation treatment suggests that great care needs to be taken when studying these systems to ensure reliable results.In the solution-phase Monte-Carlo simulations the authors used partial charges derived from the SCRF calculations. In this fashion they hoped to include both solute polarization and first-hydration-shell effects in the calculated free energies. The authors did however point out that the Hartree-Fock (HF) wavefunctions used to derive the charges usually overestimate gas-phase dipole moments and that by using HF/SCRF charges the solute may become too polarized. The combined ab initiolfree-energy perturbation results predicted the dominant solution-phase tautomer that was in agreement with experiment.Use of the SCRF free energies of hydration incorrectly predicted the dominant tautomer and furthermore the energies were demonstrated to be sensitive to cavity size. This discrepancy was attributed to the failure of continuum models to include an explicit description of the first hydration-shell together with the truncation of the solute multipole-expansion at the dipolar level. Histamine is an important molecule in biological systems; it not only stimulates smooth muscle contraction but also regulates the secretion of acid in the stomach. It has a very large range of accessible conformational tautomeric and protonation states and is therefore a very interesting theoretical target. These equilibria have been addressed by two separate research groups in the past year again using a combination of ab initio calculation and free-energy perturbation simulations.Worth and Richards' 3' studied the histamine monocation from the perspective of investigating the sensitivity of the simulation results to protocol. Difficulties associated with sampling and parameter generation were investigated and discussed. Nagy et al.132 performed a very comprehensive investigation of histamine conformational and tautomeric equilibria and also related their results to the proposed binding mechanism of histamine to the H receptor; they found that their equilibrium results were consistent with the thermodynamic requirements for this mechanism. 129 K. Lammertsma and B. V. Prasad J.Am. Chem. Soc. 1994 116 642. 130 M. Cao B. J. Teppen D. M. Miller J. Pranata and L. Schafer J. Phys. Chem. 1994 98 11 353. 13' G.A. Worth and W.G. Richards J. Am. Chem. Soc. 1994 116 239. 132 P.I. Nagy G.J. Durant W.P. Hoss D.A. Smith J. Am. Chem. Soc. 1994 116 4898. Jonathan W. Essex Pericyclic Reactions.-Pericyclic reactions are of fundamental importance to the synthetic organic chemist not only because a large number of atoms can be added to or modified within a molecule but also because the reactions can proceed with regio- and stereoselectivity. Theoretical calculations on this reaction type are generally devoted to rationalizing experimental behaviour and understanding the reaction mechanisms. In particular the issue of whether the reactions are concerted or proceed in a stepwise fashion has proven controversial.Owing to the interest in this general category of reactions a selective view of the work performed on the more popular pericyclic reactions will be presented. Diels-Alder Reactions.-This reaction is perhaps the most famous of all pericyclic reactions and arguably the one to which most theoretical effort has been devoted. In recent years there has been considerable controversy regarding the nature of the reaction pathway but there now appears to be general agreement that the reaction proceeds by a synchronous concerted pathway and not in a stepwise fashion (Scheme 2).133Sophisticated CASSCF calculations were used to investigate the reaction between butadiene and ethene and confirmed that the concerted pathway is the most likely reaction route; this result was backed-up by a comparison between calculated and experimental kinetic isotope effects.' 34*135 Scheme 2 The role of solvation in affecting the rate of pericyclic reactions has been extensively investigated by Jorgesen et al.' 36 Their approach involved determining the course of the reaction in the gas phase using ab initio methods calculating empirical potential- energy parameters for each frame along the reaction coordinate and then performing a classical Monte-Carlo simulation with explicit solvent molecules in which the free-energy difference between each frame was calculated using free-energy perturba- tion theory.In this fashion the experimentally observed acceleration of the Diels-Alder reaction between cyclopentadiene and methyl vinyl ketone in water was attributed to the strengthening of hydrogen bonds to the carbonyl oxygen in the transition state augmented by hydrophobic association.Justification for this result from ab initio calculations on water complexed with the above reagents has also been reported.'37 133 K.N. Houk J. Gonzalez and Y. Li Acc. Chern. Res. 1995 28 81. K. N. Houk Y. Li J. Storer L. Raimondi and B. Beno J. Chem. SOC.,Faraday Trans. 1994,90 1599. 135 J.W. Storer L. Raimondi and K.N. Houk J. Am. Chem. SOC. 1994 116,9675. 136 W. L. Jorgensen J. F. Blake D. Lim and D. L. Severance J. Chem. SOC.,Faraday Trans. 1994,90 1727. Theoretical Organic Chemistry 45 The water to carbonyl-oxygen hydrogen bond was calculated to be approximately 2 kcal mol- stronger in the transition state than the reactants.This method for calculating the effect of solvent on reaction rates relies on the gas-phase reaction profile also being the reaction coordinate followed in solution. However as Jorgensen has pointed out the use of continuum solvation treatments in determining reaction pathways in solution is not without diffi~u1ties.I~~ In an interesting study Craig and Stone have investigated Diels-Alder reactions using intermolecular perturbation theory (IMPT).13' In this approach Basis Set Superposition Error (BSSE) is eliminated and the technique has been shown to yield identical results to large basis set ab initio supermolecule calculations. Furthermore IMPT allows for the total interaction energy between fragments to be decomposed into well-characterized components allowing a reaction to be interpreted in meaningful terms.The disadvantage of the approach is that it cannot be used for molecules at close distances because the perturbation expansion is slowly convergent. Reactions must therefore be studied at large separations and the behaviour at the transition state inferred from results obtained earlier along the reaction coordinate; this assumption is probably valid when comparing closely related reactions. Furthermore the reactants are all examined at a fixed geometry. In the analysis of a range of Diels-Alder reactions reported by Craig and Stone IMPT was able to reproduce the trends in selectivity for a series of dienophile substituents in the butadiene/ethene reaction.Predictions of reactions involving unsymmetrical dienes and dienophiles were less successful and this was attributed to the fixed geometry adopted in the calculations whereas experiment is performed in solution and at finite temperature. It should however be noted that the IMPT calculations agreed quite well with ab initio calculations on the transition states. The Diels-Alder reaction has also been studied by both density functional and semi-empirical methods. Carpenter and Sosa14' applied local and non-local DFT to the reaction between ethene and butadiene. The local DFT results were found to be very poor whereas the non-local results were generally comparable with more expensive MP2 calculations although differences still existed.Jursic and Zdrav- kovski 14' studied the Diels-Alder reaction using semi-empirical methods and assumed a concerted synchronous reaction mechanism. The AM1 and PM3 methods were found to yield poor agreement with experiment suggesting that semi-empirical calculations cannot be used to study the concerted Diels-Alder reaction. Claisen and Cope Rearrangement.-The Claisen and Cope rearrangements are classified as [3,3] sigmatropic shifts. This type of reaction is illustrated in Scheme 3. When X = CH the reaction is referred to as the Cope rearrangement and when X = 0the reaction is the Claisen rearrangement. The possible transition states are also illustrated. The Claisen rearrangement is not only of intrinsic synthetic interest but is also of biochemical importance.Chorismic acid is a key intermediate in the shikimate biosynthetic pathway of phenylalanine and tyrosine; it undergoes a Claisen rearrange- 13' J. F. Blake D. Lim and W. L. Jorgensen J. Org. Chem. 1994 59 803. 13* W. T. Borden F. Williams T. Bally J. Michl M. T. Nguyen S. Shaik P. von R. Schleyer W. L. Jorgensen W. Saunders,V. Moliner Y. P. Liu D. G.Truhlar P. Paneth M. A. Rodriguez M. S. Child M. M. Francl and X. Assfeld J. Chem. SOC. Faraday Trans. 1994 90,1733. 139 S. L. Craig and A. J. Stone J. Chem. Soc. Faraday Trans. 1994 90 1663. 140 J. E. Carpenter and C. P. Sosa J. Mol. Struct. (Theochem) 1994 311 325. 141 B. S. Jursic and Z. Zdravkovski J. Mol. Struct. (Theochem) 1994 309,249. Jonathan W.Essex bis-allyl 1 bdiyl Scheme 3 C02H I OH Scheme 4 ment to prephenic acid catalysed by the enzyme chorismate mutase (Scheme 4). The effect of solvent on the Claisen rearrangement has been examined using both explicit solvent models and continuum treatments. Jorgensen et used the combination of the gas-phase reaction pathway with classical Monte-Carlo simula-tions to determine the effect of solvation on the Claisen rearrangement of ally1 vinyl ether. The experimentally observed rate enhancement of ca. lo3was reproduced by the simulations and was attributed to an increase in the number of hydrogen-bonds formed with solvent by the transition state. Gao investigated the same reaction using the MM/QM pr~cedure;~' this calculation yielded almost identical results to Jorgensen et al.' 36 although the solvent-induced rate acceleration was attributed to polarization of the transition state giving an enhanced dipole moment together with increased hydrogen bonding to the oxygen of the transition state.Davidson et ~1.l~~ investigated this system using a number ofcontinuum models in conjunction with both density functional and Hartree-Fock calculations. It was found that the PCM model with HF calculations performed well in modelling the solvent di-n-butyl ether but less satisfactorily in modelling the effect of water presumably because the continuum treatment does not explicitly consider hydrogen bonding unlike the previously described explicit-solvent methods. Interestingly the calculation of the gas-phase pathway using DFT which includes correlation gave good agreement with gas-phase experimental data.However the polarity of the transition state was considerably reduced with respect to that of the ground state resulting in a reduction in the calculated differential solvation energy. Thus the success of the gas-phase HF reaction 14' M. M. Davidson I. H. Hillier R. J. Hall and N. A. Burton J. Am. Chem. SOC. 1994 116 9294. Theoretical Organic Chemistry 47 profile applied within a classical Monte-Carlo simulation of solvent'36 may be attributed to the opposing influence of electron correlation and solvent polarization. The effect of including both correlation and solvent polarization is to yield a molecular dipole moment that is very close to that predicted at the HF level in the gas phase.Thus intermolecular potentials obtained from gas-phase HF calculation may be applied to condensed-phase simulations. Houk et a1.143,144 have been engaged in calculating kinetic isotope effects for the Claisen rearrangement as a way of interpreting experimental data in terms of a reaction pathway. As mentioned for the Diels-Alder reaction the precise nature of the reaction mechanism is controversial with aromatic and diradical transition states being postulated. Wiest Black and H~uk'~~ applied density functional theory to the calculation of the transition state for the Claisen rearrangement. The local spin density approximation was unable to describe the transition state properly whereas nonlocal methods suggested an aromatic-type transition state.The Becke3-LYP functional was able to give transition-state energies comparable with correlated molecular orbital theory and by comparison with experimental kinetic isotope effects good estimates of the transition state geometries were also obtained. Yo0 and Hou~'~~ report calculations on the same molecule but at the MCSCF/6-31G* level. The biochemically relevant Claisen rearrangement of chorismic acid and some of its derivatives have been investigated using ab initio calculations by Davidson and Hillier.'45 The relative barrier heights were in good agreement with experiment although the absolute values did not agree presumably because of the neglect of correlation and solvation in the calculations.The observed acceleration of the rearrangement reaction of chorismic acid and its derivatives with respect to ally1 vinyl ether (AVE) was attributed to both stabilization of the transition state and destabilization of the reactants. In a related the transition states for the Claisen rearrangements of AVE and chorismic acid were calculated at the HF/6-3 1 G* level extended to the MP2/6-31G* level for AVE. The calculated transition state for AVE was 'early' with little bond formation but considerable bond-cleavage and this was consistent with measured and calculated kinetic isotope effects. The transition state for chorismic acid was predicted to be more dissociative again in accord with measured kinetic isotope effects. The Cope rearrangement has been investigated by Hrovat et a1.1473148 at the CASPT2N level of theory thereby including electron correlation between the six active electrons and the other 28 valence electrons.This level of calculation represents an improvement on the CASSCF approach in which correlation between the active and inactive electrons is not evaluated. At the CASPT2N level of theory a stationary point corresponding to the transition state for the concerted reaction in which bond making and breaking are synchronous was found. No evidence for a 1,4-diyl intermediate was obtained unlike the CASSCF/6-3 lG* result. Furthermore the CASPT2N energetic results are in good agreement with experiment. These results therefore support the concerted mechanism for the Cope rearrangement.The density functional study of 143 0.Wiest K. A. Black and K.N. Houk J. Am. Chem. Soc. 1994 116 10336. 144 H.Y. Yo0 and K.N. Houk J. Am. Chem. SOC. 1994 116 12047. 14' M. M. Davidson and I. H. Hillier J. Chem. SOC. Perkin Trans. 2 1994 1415. 146 M. M. Davidson and I. H. Hillier Chem. Phys. Lett. 1994 225 293. 14' D.A. Hrovat K. Morokuma and W.T. Borden J. Am. Chem. Soc. 1994 116 1072. 148 D.A. Hrovat K. Morokuma and W. T. Borden J. Am. Chem. SOC. 1994 116 4529. Jonathan W. Essex Wiest et ~1.l~~ also yielded an 'aromatic' transition state and good estimates of the activation energies. However comparison between experimental and theoretical kinetic isotope effects supported the nonlocal DFT geometry but not that of the CASPT2N calculations of Hrovat et al.It is clear that further work is needed to determine the precise nature of this intriguing reaction. [2 + 21 Cyc1oadditions.-[2 + 21 Cycloadditions represent an important class of synthetic reaction since they represent an effective route to the formation of four-membered rings. These reactions have enjoyed extensive theoretical investigation from Woodward-Hoffmann theory through to the application of high-level ab initio calculations. Two general reaction mechanisms can be envisaged via a transoid biradical intermediate or in a pericyclic manner (Scheme 5). Bernardi et al.149 reported calculations on a range of [2 + 21 cycloadditions at the MCSCF level including calculations of the photochemical pathway. Their results indicated that for non-polar systems a concerted reaction path did not exist whereas in cases where the n system was polarized a transition state for the concerted route was found.However this transition state was higher in energy than that of the biradical pathway so that a concerted mechanism only became likely when solvent effects were considered. Interestingly the authors analysed their results in terms of a valence-bond model. Karadakov et al.' so have applied spin-coupled (SC) theory to the cycloaddition of two ethene molecules and found that the reaction proceeded via the diradical in agreement with CASSCF results. The SC wavefunctions can however be interpreted in a chemically useful fashion in terms of bonds and spin-states and in this respect they offer an advantage over molecular orbital methods.Scheme 5 The [2 + 21 cycloadditions of ketenes have proved a fertile area of theoretical investigation in the past year. The reaction of ketene with formaldimine was investigated using ab initio calculations coupled with a continuum treatment of s~lvation.'~' The reaction was predicted to proceed by a one-step process in the gas-phase whereas a zwitterionic intermediate was proposed for the solution phase in accord with experiment. Xu et ~1."~ have also investigated the reaction of fluoroketene with imines. Ketene and phosphaketene dimerization has been investigated by Salzner and Bachrach' s3 using high-level ab initio calculations. Ketene was predicted to 149 F. Bernardi A. Bottoni M.Olivucci A. Venturini and M. A. Robb J. Chem. SOC., Faraday Trans. 1994 90 1617. 150 P. B. Karadakov J. Gerratt D. L. Cooper and M. Raimondi J. Chem. SOC.,Faraday Trans. 1994,90 1643. 151 X. Assfeld M. F. Ruiz-Lopez,J. Gonzalez R. Lopez J. A. Sordo and T. L. Sordo J. Comput.Chem.,1994 15 479. 152 Z.-F. Xu D.-C.Fang and X.-Y.Fu J. Mol. Struct. (Theochem) 1994,305 191. Theoretical Organic Chemistry 49 dimerize via a polar diradicaloid intermediate in agreement with both experimental and theoretical studies. Phosphaketene on the other hand was predicted to dimerize in the classical Woodward-Hoffmann allowed [27c + 2x.J fashion because of the ability of the phosphorus derivative to accommodate strain in the cyclic transition state.S,2 Reactions.-The SN2 reaction continues to be the target of considerable theoretical and experimental interest since it represents probably the most elementary displace- ment reaction. Hase' 54 has reviewed the gas-phase SN2 reaction from the perspective of the various statistical theories computer simulations and experimental data whereas Ramsden' 55 has summarized the nature of bonding within the transition state itself. In this section the effect of solvent on the SN2 reaction will be reviewed followed by the recent results obtained from the gas phase. The effect of solvent on this reaction has been studied in a number of fashions. Billing and Mikkel~en'~~ investigated the reaction of a chloride ion with chloromethane in water. The calculated activation energy in water was found to be in good agreement with other theoretical estimates and experiment.The same reaction was studied by Mathis et ~11.l~~ using valence-bond theory together with a continuum solvation model in which the separate orientational and electronic contributions to the solvent dielectric were considered explicitly. The calculated activation free energies were in reasonable accord with experiment. Perhaps more importantly however the effect of separating the contributions to the solvent dielectric was marked. Mathis and Hyne~'~*,' 59 have investigated the S,1 decomposition of alkyl iodides using the same theoretical approach. Hu and Trular16' have investigated the reaction of fluoride with chloromethane in the presence of a single molecule of water and compared their results with experimental data from gas-phase clusters.The good agreement of rate constants and kinetic isotope effects with experiment supported their use of conventional transition state theory and the exclusion of tunnelling effects from the calculations. A large number of quantum-mechanical calculations on the S,2 reaction have been reported in the past year. In a series of papers Anh et af.161-163 investigated a range of nucleophiles and substrates using AM 1 and low level Hartree-Fock calculations (3-21Gand some 6-3 1G*). Most interestingly however they investigated the amount of distortion allowed in the transition state for an energy penalty of 1 kcal mol- ',to determine when an intramolecular displacement reaction would be feasible.Axial displacements of approximately 0.3 A were acceptable as were angular deviations of 8" off the preferred direction of attack. Identity exchange reactions where the nucleophile displaces the same leaving group from the substrate have been studied by several workers. Wladkowski et al. 164 investigated the displacement of fluoride using a range 153 U. Salzner and S. M. Bachrach J. Am. Chem. SOC. 1994 116 6850. 154 W. L. Hase Science 1994 266 998. 155 C.A. Rarnsden Chem. SOC.Rev. 1994 23 11 1. 156 G. D. Billing and K.V. Mikkelsen Chem. Phys. 1994 182 249. 15' J.R. Mathis R. Bianco and J.T. Hynes J. Mol. Liq. 1994 61 81. 15' J. R. Mathis and J.T. Hynes J. Phys. Chem. 1994 98 5445. 159 J.R. Mathis and J.T. Hynes J.Phys. Chem. 1994 98 5460. I6O W.-P. Hu and D.G. Truhlar J. Am. Chem. SOC. 1994 116 7797. 16' N.T. Anh F. Maurel B.T. Thanh H. H. Thao and Y.T. "Guessan New. J. Chem. 1994 18 473. 16' N.T. Anh F. Maurel H.H. Thao and Y.T. "Guessan New. J. Chem. 1994 18 483. 163 N.T. Anh B.T. Thanh H. H. Thao and Y. T. "Guessan New. J. Chem. 1994 18 489. 164 B. D. Wladkowski W. D. Allen and J.I. Braurnan J. Phys. Chem. 1994 98 13 532. 50 Jonathan W. Essex of basis sets and with the inclusion of correlation up to the CCSD(T) and MP4 levels; the net S,2 effective activation energy was observed to be 0.8 kcal mol- ' below the separated reactants. Deng et a1.16' studied the self-exchange reactions of the halomethanes (fluoro chloro bromo iodo) using both MP4 level ab initio and non-local density-functional calculations.The calculated activation energies were again observed to be sensitive to basis set and correlation with experiment lying between the MP4 and the non-local density functional results. Despite the simplicity of this reaction it clearly represents a very significant challenge to theory. Other systems studied include the reaction of chloride with bromomethane using Hartree-Fock calculations coupled with transition state and RRKM theorie~,'~~.'~~ and the calculation of kinetic isotope effects for a range of S,2 transition states.'68 The former' 66,'67 are particularly interesting in that an analytical potential energy function derived from the ab initio calculations was used in classical trajectory calculations and the results compared with the predictions of RRKM and transition state theories.The trajectory calculations were able to provide considerable detail concerning the course of the reaction and the partitioning of energy within the system's degrees of freedom. Photochemistry.-The nature and fate of photochemically excited species has been extensively studied by Olivucci Bernardi and Robb. The cyclohexadiene/hexatriene photochemical interconversion was studied at the CASSCF and CASSCF/MP2 levels. 69 These species are particularly interesting since the noncrossing rule which is applicable to diatomic molecules loses its validity in polyatomic systems so that two electronic states with the same symmetry may cross at a conical intersection. Indeed the 2A -+ lAl decay channel was predicted to occur via a conical intersection and with corresponding high efficiency and this result was consistent with the available experimental data.The photochemistry of buta-1,3-dienes1 70and acrolein,' carbene formation from the excited states of diazirine and dia~omethane,'~~ and the Paterno-Buchi rea~tion"~ have been studied and the fate of the excited states elucidated; all involved decay via conical intersections to some extent. 4 Conclusion Theoretical organic chemistry remains a flourishing discipline. Novel theoretical methods continue to be derived and applied to areas of contemporary interest. The more established techniques such as molecular mechanics are now easier to use on a routine basis. As computers become increasingly powerful and the methodology more refined it is clear that the application of theory to problems of organic interest can only become more important; the future is bright.Acknowledgement. JWE is a Royal Society University Research Fellow. 165 L. Deng V. Branchadell and T. Ziegler J. Am. Chem. SOC. 1994 116 10645. H. Wang L. Zhu and W.L. Hase J. Phys. Chem. 1994 98 1608. 167 H. Wang G.H. Peslherbe W. L. Hase J. Am. Chem. SOC. 1994 116 9644. R.A. Poirier Y. Wang and K.C. Westaway J. Am. Chem. SOC. 1994 116 2526. 169 P. Celani S. Ottani M. Olivucci F. Bernardi and M.A. Robb J. Am. Chem. SOC. 1994 116 10 141. 170 M. Olivucci F. Bernardi S. Ottani and M.A. Robb J. Am. Chem. SOC. 1994 116 2034. M. Reguero M. Olivucci F. Bernardi and M.A.Robb J. Am. Chem. SOC. 1994 116 2103. N. Yamamoto F. Bernardi,A. Bottoni M. Olivucci M. A. Robb and S. Wilsey,J. Am. Chem.SOC. 1994 116,2064. 173 1. J. Palmer I.N. Ragazos F. Bernardi M. Olivucci and M. A. Robb J. Am. Chem.SOC.,1994,116,2121.