2 Theoretical organic chemistry By JIALI GAO Department of Chemistry State University of New York at Buffalo Buffalo New York 14260 USA 1 Introduction Theoretical organic chemistry encompasses a wide range of topics spanning from high level electronic structural calculations of simple organic molecules using well-established ab initio molecular orbital or density functional theory techniques to computer simulations of chemical reactions and interactions in solution. This article is divided into two sections theoretical developments and applications. In the former theoretical advances in linear scaling electronic structure methods for large systems are briefly addressed. The focus however is on the development of solvation models and simulation techniques particularly those using hybrid quantum and classical methods.In the latter section topics covered in this review include transition structure modeling aromaticity conformational and tautomeric equilibria host–guest modeling pericyclic reactions and photochemical processes. 2 Theoretical developments Theoretical treatments of organic molecules may be roughly classified in terms of electronic structure theories and empirical force fields. The former describe an organic system by quantum chemical methods which include Hartree–Fock (HF) theory post-Hartree–Fock methods density functional theory (DFT) and multiconfiguration self-consistent field (MCSCF) techniques. On the other hand empirical force fields represent a molecular system by van der Waals spheres and partial atomic charges and the potential energy surface is simply expressed by empirical potential functions.Of particular interest is the syntheses of these approaches for treatments of large molecules and solvation e§ects. In this section the significant developments in theoretical treatments for large molecular systems solvation modeling and free-energy simulation techniques will be presented. Theoretical treatment for large molecular systems The bottleneck for HF and DFT calculations is often considered to be the computation of two-electron repulsion integrals. In large systems a large number of the electron repulsion integrals are insignificant and their computation can be avoided with sophisticated screening methods. Using fast multipole methods and tree codes near- Royal Society of Chemistry–Annual Reports–Book B 3 linear scaling for the construction of the Coulomb matrix has been achieved.1–3 White and Head-Gordon have introduced a new method for DFT and HF calculations with Cartesian Gaussian basis functions by summing the density matrix into the underlying Gaussian integral formulas without explicit formation of the full set of two electron integral intermediates.Testing indicates a speedup of greater than four times for the (ppDpp) class of integrals and over 10 times for (ffDff) integrals.4 Because exchange interactions in insulators are local computation of the exchange matrix can be made to scale linearly with the system size. Indeed linear-scaling has been achieved in local density functional calculations by using real-space cuto§s. Schwegler and Challacombe have introduced a threshold criterion obtained from an asymptotic form of the density matrix which explicitly assumes an exponential decay at large distances.5 Restricted HF/3-21G calculations on a series of water clusters and polyglycine a-helices demonstrated the O(N) scaling of the algorithm.Using the fast multipole method for the Coulomb matrix with only slight modification of this procedure Burant et al. obtained the near-field exchange matrix. Since the exchange interaction for insulators is localized only small errors are introduced by its neglect in theFMMfar field. The near-field exchange method was demonstrated for HF calculations in time-scaling near-linearly with system size. Benchmark calculations on polyglycine chains water clusters and diamond pieces show microhartree accuracy and speed up to 10 times over traditional calculations for systems of greater than 300 atoms.6 In other areas Hernandez et al.proposed a linear-scaling scheme for densityfunctional pseudopotential calculations based on a formulation of density-functional theory in which the ground state energy is determined by minimization with respect to the density matrix subject to the constraints of idempotency (p2\p) and the correct number of electrons in the system. Linear scaling is achieved by assuming that the density matrix should vanish at a distance greater than a chosen cuto§.7 The algorithm is based on a method developed by Li Nunes and Vanderbilt and energy minimization is performed using the conjugated-gradient method.8 The method avoids matrix diagonalization which scales as O(N3) and has a memory requirement of O(N2).The method has also been used in extended Hu� ckel calculations.9 The idea of working with the density matrix has also been applied in other forms to DFT and semiempirical molecular orbital calculations.10–14 The treatment of large molecular systems has also been described by implementation of scalable HF calculations using a massively parallel computer.15 On a di§erent note Peng et al. described a redundant internal coordinate system constructed from all bonds valence angles and dihedral angles for optimizing molecular geometries. Redundant internal coordinates provide substantial improvements in optimization e¶ciency over Cartesian and non-redundant internal coordinates especially for flexible and polycyclic molecules. Transition structure searches are also improved.16 Baker and Chan compared various approaches towards optimization of geometry using Cartesian Z-matrix and natural internal coordinates.It is claimed that the Z-matrix representation is superior for optimization of transition structure.17 Solvation The importance of solvent e§ects in organic chemistry is emphasized by the facts that the vast majority of organic reactions are carried out in solution and that processes related to life itself occur in an aqueous environment. To characterize the reactivity of 4 Jiali Gao organic molecules and to predict the rates for organic reactions it is essential to include solvent e§ects in the theoretical treatments. However the inclusion of explicit solvent molecules means a significant increase in the size of the system and requires a statistical mechanical description of the physical properties.Methods for the treatment of solvent e§ects may be divided into two categories a continuum depiction of the solvent system characterized by its relative permittivity and a classical yet explicit representation of the solvent molecules through the use of empirical potential functions. Continuum models have been used both in quantum mechanical calculations and in classical simulations of biological macromolecules and continue to enjoy popularity thanks to their computational e¶ciency. However as the computational power increases the advantages o§ered by continuum models will continue to diminish. Explicit solvent simulations may now be routinely carried out for large scale systems including solutions and biological molecules.Even with pentium-processor based personal computers fluid simulations are now possible.18 Furthermore the accuracy and quality of empirical potential functions used in molecular dynamics and Monte Carlo calculations have tremendously increased in the past decade and these treatments may be further enhanced by the combined use of quantum mechanical methods and empirical force field as well as full ab initio potentials.19,20 Continuum models There have been several recent reviews on the theory and prospective applications of continuum models.21 Because of their computational simplicity and the possibility of parametrizing specific models there has been significant refinement and improvement of continuum models in 1996. In the past developments of continuum solvation models have been focused on aqueous solution due to its central importance in chemistry.This trend has persisted in the past year. The extremely successful semiempirical solvation model deloped by Chambers et al. which is based on the generalized Born model has been extended with the use of Class IV atomic charges.22 Chambers et al. described a new parametrization in this series of solvation models featuring a new set of geometry-based functional form for e§ective Coulomb radii and atomic surface tension terms. In addition atomic charges are obtained by both the AM1-CM1A and PM3-CM1P Class IV charge model which is a multilinear parametric method derived from Mulliken population analysis and bond orders. Of the 215 neutral solutes containing H C N O F S Cl Br and I and a wide variety of organic functionalities the mean unsigned error in the free energy of hydration is only 0.50 kcal mol~1 using CM1A charges and 0.55 kcal mol~1 using CM1P charges.The predicted solvation energies for 12 cations and 22 anions have deviations of 4.4 and 4.3 kcal mol~1 for models based on AM1 and PM3. The implementation of the polarizable continuum model (PCM) in Gaussian 94 has been further improved by including higher-order electrostatic interactions and a more realistic shape of the solute cavity defined by an isosurface of the total electron density.23 Although physically appealing it is not clear if such a cavity definition can yield such accurate results as parametrized atomic radii. The importance of these factors is assessed by comparing theoretical results to the experimentally known conformational equilibrium between syn and anti forms for furfuraldehyde and the C–C rotational barrier of 2-nitrovinylamine.Foresman et al. found that the correlation to experiment is improved when an infinite-order PCM method is used.23 An alternative implementation builds upon an early SCRF model which combines the 5 Theoretical organic chemistry PS-GVB (pseudo-spectra generalized valence bond) electronic structure calculations and electrostatic potential (ESP) fitted charges with the DelPhi Poisson-Boltzmann equation solver.24 The performance and failures of this continuum model in several well-known cases including the solvation of the methylated amines have been examined. 24 A new approach is proposed in which short-range empirical corrections based upon solvent accessibility are made for specific functional groups.This leads to a reduction in the mean error of the calculated solvation free energies for 29 test compounds by a factor of 2 to 0.37 kcal mol~1. The implementation and parametrization of calculations based on the boundary element method have been described by Horvath,25 Tawa26 and their co-workers. In the later calculations the average error in the computed free energies of solvation for 14 simple molecules is about 2.5 kcal mol~1 at the HF and DFT levels using the 6-31G* basis set. The e§ect of aqueous solvation on equilibrium geometry was also studied using a parametrized continuum model.27 Several studies have been reported on the derivation of analytical derivative methods within continuum models in electronic structure calculations.These developments have led to the calculation of static polarizability and hyperpolarizabilities for formaldehyde N-methylacetamide and methyl formate in aqueous solution,28 and provided convenient tools for the analysis of solvent e§ects on reaction paths.29 Using analytical second derivatives of the generalized conductor-like screening model (GCOSMO) Stefanovich and Truong calculated vibrational frequency shifts for several molecules including acetone methylamine formic acid acetic acid and N-methylacetamide in water.30 For acetone and methylamine the continuum model performs very well in reproducing the experimental spectral shifts. However for strong hydrogen bonding molecules like formic acid and acetic acid it is found that at least one explicit water molecule should be included in the GCOSMO calculations.For organic solvents it might be expected that continuum solvation models developed for water may be directly applied by simply changing the relative permittivity from 78 for water to that for the corresponding organic solvent. However there is no guarantee that the solute cavity size will be identical in di§erent solvents. This is further complicated by the dispersion and cavitation energies. Thus it is necessary to reoptimize the empirical parameters involved in continuum model calculations. The issue of non-aqueous solvation modeling has been addressed by several groups. Luque et al. extended the PCM method to CCl 4 solution in both ab initio HF/6-31G* and semiempirical self-consistent reaction field (SCRF) calculations.31 Parametrization of the solute–solvent interface and of the hardness atomic parameters was performed against experimental data and Monte Carlo simulation results.Errors in calculated free energies of solvation for a series of neutral organic solutes using the optimized atomic radius were less than 1 kcal mol~1. Schaefer and Karplus have introduced an analytical continuum electrostatic (ACE) model for the treatment of electrostatic solvation energies of small molecules as well as proteins.32 The method features a Gaussian charge distribution for electrostatic interactions and a novel treatment of the self-energy of the molecule in solution. Combined with the generalized Born equation for charge–charge interactions it was possible to determine analytically electrostatic contributions to the solvation energy thereby allowing the method to be applicable in molecular dynamics and molecular mechanics calculations.The error in the computed solvation free energy using the 6 Jiali Gao ACE method is 15% for small molecules (10–20 atoms) and 5.4% for the protein BPTI using the results from finite-di§erence calculations as the reference. Luo and Tucker have described a compressible solvation model based on a numerical grid algorithm for solving Poisson’s equation. The method is applicable to arbitrary charge distribution in cavities of arbitrary shape.33 Thus the local permittivity is treated as a function of the field-dependent local density [eqn. (1)] e4(R,T)\e4(o[E(R)],T) (1) where T is temperature o is density of the solvent and E(R) is the electric field at position R. e4(o[E(R)],T) and p[E(R)] are properties of the pure solvent.The electric field is determined through self-consistent solution of Poisson’s equation. Application of this method to the hydrolysis of anisole in supercritical water shows that the e§ect of solvent compression lowers the free energy barrier of reaction by as much as 14 kcal mol~1. It was found that inclusion of compression e§ects improves the agreement between the calculated and experimental dependence of the activation barrier on pressure. In closing this section Lim and Jorgensen used five sets of geometries and atomic charges derived from ab initio SCRF calculations with relative permittivities of 1.0 2.23 and 35.94 at HF/6-31G* MP2 and B3LYP levels for Monte Carlo simulations of the [2]2] cycloaddition of 1,1-dicyanoethylene (DCNE) and methyl vinyl ether (MVE).34 Thus partial atomic charges used in empirical potential functions may reflect the average charge polarization in various solvents.The best results are obtained using the charges and geometries from B3LYP/6-31G* gas-phase calculations. Explicit description of the solvent Significant progress has been made in the development of methods for explicit solvent representations in computer simulations in the past year. A large amount of e§ort has been devoted to the development of hybrid quantum mechanical and molecular mechanical (QM/MM) potentials which will be the emphasis in this section. For earlier applications the reader is referred to a recent article on the study of solvent e§ects in organic chemistry using hybrid QM/MM potentials.35 Bakowies and Thiel have presented a hierarchy of three models for hybridQM/MM calculations.36 In the simplest model A a large molecular system is reduced into a smaller QM fragment which is saturated by hydrogen link atoms in a way similar to that described by Field et al.37 The QM fragment is mechanically embedded in the remainder of the empirically treated fragment and the interactions between QM and MM fragments are purely determined by molecular mechanical force field calculations.In general the MM fragment may be regarded as solvent molecules. The more refined models B and C include a quantum mechanical treatment of electrostatic interactions between the two fragments and a semiempirical description of MM polarization. A key feature in Bakowies and Thiels treatment of electrostatic interactions is that semiempirical electrostatic potentials and MM charges derived on the basis of electronegativity equalization are used.38 Incorporation of the MNDO method and the MM3 force field allowed a number of test applications including computations of heats of formation of hydrocarbons proton a¶nities and deprotonation energies of alcohols.Transition structure determinations for a hydride transfer reaction and ring cleavage of oxiranes by nucleophiles were also described. 7 Theoretical organic chemistry In the spirit of Thiel’s model A Matsubara et al. applied an integrated molecular orbital plus molecular mechanics (IMOMM) method to investigate the organometallic reaction of Pt(PR 3 ) 2 with H 2 (R\H Me But and Ph).39 Using the Gaussian 92/DFT and MM3 programs this computation proceeds by performing of full MM geometry optimization with fixed MO atom positions.Then an ab initio gradient calculation is carried out for the QM molecule plus link atoms. A comparison of the full MO(RHF) optimized and the IMOMM(RHF/MM3) optimized structures of the reactant transition state and products for a simple hydrogenation reaction H 2 ]Pt(PR 3 ) 2 ](H) 2 Pt(PR 3 ) 2 for R\H Me But and Ph shows that the IMOMM optimization can reproduce the MO optimized structures. However the IMOMM calculations fail to reproduce some (up to 5 kcal mol~1) of the electronic e§ect of a methyl for hydrogen substitution for this model system. The energetics obtained at the IMOMM(MP2/MM3) level for the present reaction is consistent with the experimental findings. Morokuma and co-workers have also described an integrated molecular orbital plus molecular orbital (IMOMO) method for integration of two di§erent levels ofMO approximation instead of combiningMOandMMtreatments.40,41 In this approach only the active or more complex part of a molecule is treated at a higher level of theory and the rest of the molecule is modeled at a lower level of approximation.The high-level portion of the molecule is embedded in the lower-level fragment. The integrated total energy and derivatives are defined from three di§erent calculations the two independent fragments at high and low levels and the whole molecule at low levels. Thus the interaction between the two fragments is obtained from the calculation employing a low level of approximation. The structure of the transition state as well as the equilibrium structure can be optimized using the integrated energy.Model calculations for the conformation energy of ethane and n-butane the barrier for S N 2 reactions of alkyl chlorides and Cl~ and for the expoxidation of benzene indicated that these methods have a tremendous potential. The methods described above use a link atom approach to satisfy the free valencies resulting from the division of a large molecular system intoQMandMM(or separate QM) fragments. The question of continuity between the two subsystems is addressed by Rivail and co-workers through the use of a strictly localized bond orbital which is assumed to have transferable properties since the parameters for the localized bond orbitals are determined on model compounds (Scheme 1).42,43 The hybrid bond orbital pointing toward the classical atom is excluded in the QM/SCF calculation with fixed charge density (bond order).The method is physically appealing and has been used in full energy minimization for the proton exchange process between the histidine and aspartic acid system of the catalytic triad of human neutrophil elastase. In contrast to classical force fields the results obtained from this approach are found to be in good agreement with the crystallographic data. Tunon et al. have presented a coupled density functional–molecular mechanics Monte Carlo simulation method which was demonstrated for the solvation of a water molecule in liquid water.44 Using a double-zeta basis set plus polarization orbitals and non-local exchange-correlation corrections the computed atom–atom radial distribution functions are found to be in accord with the experimental data and the instantaneous and average polarization of the QM molecule has been analyzed.Frozen density functional theory (FDFT) has been used by Wesolowski et al. in a 8 Jiali Gao frozen orbital QM MM Scheme 1 Schematic representation of the localized bond orbital method study of the proton transfer reaction in water F~]HF]FH]F~.45 The method treats the solute–solvent system as a supermolecule but constrains the electron density of the solvent molecules. Thus the solvent molecules are treated quantum mechanically; however the electron densities of these molecules are kept fixed. The performance of this model is verified by comparing full and frozen DFT calculations of solute–solvent clusters.In fluid simulations an empirical valence bond (EVB) mapping potential is used to carry out molecular dynamics simulations. Next the free energy di§erence between the FDFT and the EVB potential surfaces is determined via an umbrella sampling technique. It was suggested that the FDFT method provides a convenient approach for ‘solving’ the hybrid QM/MM link atom problem although the details are not given. In order to address the interaction between QM and MM atoms in a hybrid QM/MM approach Freindorf and Gao optimized the empirical Lennard-Jones parameters for use in hybrid ab initio HF/3-21G and MM simulations.46 These parameters are associated with hybrid QM/MM potentials which should be optimized for a new combination of QM and MM methods. With a single set of parameters typically two per atom the computed hydrogen bonding geometries and energies from the hybrid HF/3-21G and OPLS potential are in excellent accord with ab initio HF/6-31G data with an rms deviation of less than 0.5 kcal mol~1 in energy and 0.1Å in hydrogen bond distance for over 80 bimolecular complexes.The e§ect of electrostatic interactions in integrated electronic structure calculations may be treated via an e§ective fragment method as demonstrated by Day et al.47 This method makes use of the perturbing Hamiltonians referred to as e§ective fragment potentials. The solvent which may consist of discrete water molecules protein or other materials is treated explicitly using a model potential that incorporates electrostatics polarization and exchange repulsion e§ects. In addition to energy calculations analytical gradients and numerical second derivatives can be determined.The method was shown to yield good accord with full ab initio calculations for the water dimer and water–formamide complex. Moriarty and Karlstrom have proposed a method to describe the exchange repulsion arising from the overlap between the wave functions ofQMandMMmolecules.48 To account for this e§ect an extra term is added to the Hamiltonian [eqn. (2)] Hij \Hij(1]sij) (2) where sij is a correction term which depends on the overlap between the wave functions of the QM system and the MM molecules. The method was tested by a computer simulation of a QM water in a classical liquid water. Wang Boyd and Laaksonen proposed another scheme to measure the interaction betweenQMandMMregions by using vibrational frequency shifts from the gas phase into solution.49 The 12 vibra- 9 Theoretical organic chemistry tional modes for methanol in its pure liquid form are derived from correlation data in molecular dynamics simulations at the ab initio HF/3-21G** level.It was found that weak coupling between the QM and MM regions yields the best agreement with experimental spectral shifts. The e§ects of solvent on the geometrical parameters of methanol were also investigated in this study. A treatment of the mutual charge polarization between theQMandMMparts of a system has been developed by Thompson by incorporating point dipole polarizabilitities into hybrid QM/MM calculations.50 A consistent treatment of the interaction between theMMpolarizable dipoles and the fullQMwave function was presented in a fashion that allows for energy conservation in molecular dynamics simulations.The implementation details are given for the NDDO semiempirical QM Hamiltonians. The method was applied to the estimation of the spectroscopic blue shift for the n–p* electronic excited states of a series of carbonyl solutes. Computed spectral shifts are in good accord with experiment and previous theoretical studies. In a somewhat di§erent approach solvent e§ects on molecular spectra have been investigated for the n–p* excited states of pyridazine in water by Zeng et al.51 This approach involves two independent calculations. First fluid simulations were performed using empirical potentials with ESP-fitted charges for the ground and excited states to generate an ensemble of configurations representing the equilibrium structure of the solvent around the chromophore.Then the liquid structure is taken and the change in the vertical excitation energy is calculated by considering solute–solvent electronic interactions. In the solvent-shift calculations the solute is treated as being polarizable with the ground and excited state molecular polarizabilities derived from finite field CNDO/S-CI calculations. Zeng et al. have examined a number of di§erent ways of deriving the ESP-fitted charges for use in spectral calculations. The best estimate of the spectral shift of the first singlet excited state is 4100cm~1 in good agreement with the observed value of 3800 cm~1. This work follows earlier calculations of Zeng et al. of the solvent spectral shifts of other diazine compounds including pyridazine pyrimidine and pyrazine.52 A hybrid QM/MM approach has been used to calculate the di§erence in the pK! values of the ground and excited state of phenol in water.This method couples gas-phase excitation energies determined using the CASPT2 method and free energy perturbation calculations to obtain the di§erence in the free energy of solvation of the ground and excited state. The calculation of the solvation energy of the excited state used a semiempirical configuration interaction method to represent phenol in Monte Carlo simulations.53 The computed acidity for phenol in its first singlet excited state (pK! \1.4) is significantly stronger than for the ground state (pK! \10). The computational results were analyzed in terms of equilibrium solvation and vertical excitation energy and comparisons with experimental data were made.A method that lies between continuum models and explicit solvent representation is the integral equation method and in particular the reference interaction site model (RISM) for the treatment of liquid states. Continuing their development of the combined RISM and HF-SCF method Hirata and co-workers applied the technique to a classical problem in physical organic chemistry the reversal of the acidity of haloacetic acid upon transfer from the gas phase into aqueous solution.54 The computed results are in good accord with experiment. This study demonstrates that the combined RISM-SCF methods are a viable approach to the study of solvation e§ects which 10 Jiali Gao complements the traditional continuum solvation model and explicit simulation methods.In addition Sato et al. formulated an analytical energy gradient method for hybrid RISM-MCSCF calculations and this method has been applied to the study of the cis and trans conformational equilibrium for 1,2-difluoroethylene in aqueous solution.55 On the ‘classical side’ several groups have used polarizable intermolecular potential functions (PIPF) for free energy calculations and liquid simulations. Gao et al. reported a PIPF potential for simulations of pure liquid amides.56 The parameters for the empirical potential functions are consistently optimized by iterative Monte Carlo simulations to reproduce experimental thermodynamic and structural data. The final parameter set yields heats of vaporization and liquid density within 3% of experimental data.A second feature of this study is that polarization energies obtained from hybrid QM/MM simulations have been used to guide parameter development. Meng et al. applied a polarizable potential to represent both the solute and solvent in free energy perturbation calculations in an e§ort to model a peculiar trend of amine hydration.57 Contrary to the intuitive expectation of an increase in hydrophobicity successive methylation of ammonia (NH 3 ) does not yield a monotonic change in the observed solvation free energies. In fact methylamine is found to be more soluble than NH 3 in aqueous solution. Previous free energy calculations using pairwise potentials have not been able to reproduce experimental trends. Although the computed increase in solvation free energy from ammonia to methylamine (**Gs \0.38 kcal mol~1; exp [0.3 kcal mol~1) is smaller than the value predicted with a pairwise-additive model,58 methylamine is still more hydrophobic than ammonia.The computed solvation free energies are found to be in agreement with another study by Ding et al. using a di§erent implementation of polarizable potential functions.59 The e§ects of polarizability on the hydration of the chloride ion in Cl(H 2 O)~n clusters for np255 have been studied by Stuart and Berne using a fluctuating charge polarization model.60,61 The issue of particular interest is the surface vs. interior solvation of the chloride ion. It was found in this calculation that even for the largest clusters simulations with polarizable water models show a preference for solvation of the chloride ion near the surface of the cluster.This behavior is however not observed with a non-polarizable model with which interior solvation occurs for clusters of nq18. The reason for this di§erence was attributed to the polarizability of water for facilitating a larger average dipole moment on the water model rather than the many-body e§ects. New developments in empirical force fields will be briefly described in closing this section. In a series of articles Halgren describes the Merck molecular force field (MMFF94) including the method used in the parametrization.62MMFF94 is aimed at achieving an accuracy similar to that of theMM3 force field for organic molecules and proteins. It is also consistently derived for simulation of condensed phase processes. The database that is used to parametrize the MMFF94 force field was primarily derived from high-quality computational results along with some extension to include experimental results including crystal structures extracted from the Cambridge Structural Database.Overall MMFF94 reproduces experimental data with root mean square deviations of 0.014Å for bond lengths 1.2° for bond angles 61 cm~1 for vibrational frequencies 0.38 kcal mol~1 for conformational energies and 0.39 kcal mol~1 for rotational barriers. The results for hydrogen bonded systems 11 Theoretical organic chemistry closely resemble those predicted by the OPLS (optimized potential for liquid simulations) potential. Allinger and co-workers have introduced an improved force field MM4 for hydrocarbons including conjugated systems and hyperconjugative e§ects.63 The new force field is designed to improve the calculation of vibrational frequencies rotational barriers and to correct small errors in the previousMM3force field.Geometries are fit to within 0.004Å for bond lengths 1° for bond angles 4° for torsional angles and 0.5% for moments of inertia. Although the MM4 force field retains most of the formalism present in MM3 several cross-terms have been added in MM4 mainly to improve vibrational frequencies which have an rms di§erence of 25–31cm~1 from the experimental values in MM4. Empirical force fields for delocalized carbocations have been improved by Reindl et al. by introduction of additional terms into AllingersMMP2program and a quantum chemical term is implemented into force field calculations for the first time.64 The calculated heats of formation are in excellent agreement with a wide range of experimental data with the largest deviation of 3.5 kcal mol~1.Calculated structures and conformations are found to be in good accord with those obtained from ab initio MP2(full)/6-31G* calculations. Free energy simulations Because of its importance there has been a continued e§ort to refine existing methods and to formulate new procedures for accurate and e¶cient evaluation of free energies in computer simulations. Chipot et al. investigated the convergence behavior of the potential of mean force (pmf) calculations using three di§erent free energy computation techniques namely the free energy perturbation method (FEP) thermodynamic integration (TI) and the slow growth (SG) technique.65 For the three model systems tested with as much as 1 ns of molecular dynamics sampling it was found that FEP and TI yield results with comparable accuracy while SG is less robust.Kumar et al. have presented an iterative approach for estimating multidimensional free energy maps.66 The method is based on a weighted histogram analysis and is demonstrated by generating the Ramachandran free energy plots for several polypeptides. A method for conformational free energy calculations in one and multidimensions was also proposed by Krzysztof.67 Kong and Brooks presented a novel and e¶cient method for performing free energy calculations.68 In this approach the conventional ‘j’ variable associated with the ‘progress’ in chemical coordinates in FEP simulations is treated dynamically and the free energy calculations are transformed into potential of mean force calculations in the j-space.This extended Hamiltonian formalism utilizes the umbrella sampling technique and the weighted histogram analysis method. The method was illustrated by computing free energies of hydration and by using a model for competitive binding. One of the most important problems in computer simulations is the use of spherical cuto§ schemes to evaluate atomic pair interaction energies. The e§ect of truncating long-range electrostatic interactions in free energy calculations is particularly signifi- cant and has been analyzed by several groups. The Born equation of solvation has often been used to correct such errors introduced by eliminating long range electrostatic interactions for ionic solutes. However it cannot be used for molecular structures other than a spherical ion and often is complicated by boundary e§ects.Kalko et 12 Jiali Gao al. performed molecular dynamics simulations using both the spherical truncation scheme and the Ewald lattice-sum method to estimate the free energy changes for the charging process of Na` Ca`` and Cl~ in water.69 Smith and Pettitt examined the problem of the anisotropic nature of the Ewald method.70 A transition between hindered and free rotation for two simple charge distributions was observed in aqueous solution; however the energy change is well below k B T (0.3 kcal mol~1). Consequently it is argued that Ewald artifacts of enforced periodicity are small and may be safely ignored. The use of the Ewald method does give better agreement with experimental results.In an alternative approach Resat and McCammon showed that numerical methods for solving the Poisson equation provide a general approach to correct the long-range electrostatic e§ects in molecular dynamics simulations.71 Aqvist has utilized a recently developed free energy simulation procedure to estimate binding free energies of two charged benzamidine inhibitors with trypsin.72 The paper showed a way of dealing with di¶culties in calculation of the absolute binding free energies due to spherical truncation of electrostatic interactions. The e§ect of neglecting truncation of dipole–dipole interactions between the solvent molecules surrounding the charged ligand on the calculated energy has been examined in particular detail and found to be significant.This study illustrates the typical problems associated with annihilation/creation of ions inside a protein. 3 Applications Catalysts and transition structures Theoretical characterization of the geometry and energetics of transition structures for organic reactions plays a central role in computational organic chemistry. The availability of accurate functional in DFT calculations has further widened the scope of these applications particularly to reactions involving transition metals. This is illustrated by the DFT study of Morokuma and co-workers of the remarkable osmiumcatalyzed dihydroxylation of olefins.73 Although extensive experimental studies as well as theoretical investigations have been carried out the central question of the problem remains the distinction between two alternative reaction mechanisms (i) a concerted [3]2] cycloaddition path and (ii) an initial [2]2] mechanism followed by isomerization to the [3]2] intermediate.Morokuma and co-workers obtained the transition structures and intermediates for the [2]2] and [3]2] cycloaddition pathways in the osmium-catalyzed dihydroxylation of olefins at the B3LYP/LANL2DZ level. The activation energy for the [2]2] process is 43.3 and 50.4 kcal mol~1 respectively for reactions in the presence and absence of ammonia as the ligand base. The [3]2] process proceeds through an early transition structure with an energy only 1.9 and 1.4 kcal mol~1 higher than the respective free and ammonia-liganded reactants. Addition of a second molecule of ammonia eliminates the barrier to the [3]2] addition. Remarkably the free and ammonia-liganded osmaoxetane intermediates of the [2]2] process are of significantly higher energy than the transition structure of the [3]2] process.It was therefore concluded that the osmium-catalyzed dihydroxylation of olefins cannot proceed through a [2]2] intermediate. Yamabe et al.74 examined the epoxidation of olefins by peracids [eqn. (3)] 13 Theoretical organic chemistry H2C ZnI I + CH2 ZnI I ZnI2 + Scheme 2 HCO 3 H]CH 2 ––CH 2 ]HCO 2 H]ethylene oxide (3) at the MP4/6-311G**//MP2/6-311G** level. The reaction is found to proceed via a two step mechanism with the initial formation of one C–O bond and the O–H bond retained. This transition structure leads to an unprecedented transient intermediate featuring aHCOO· · ·H 2 C–(OH)–CH 2 complex which is converted to another hydrogen bonded intermediate between ethylene oxide and formic acid with a hydrogen bond distance of only 1.62Å.The activation energy from the peracid–ethene complex is about 17 kcal mol~1. Electron-donating substituents were found to cause a large reduction in the activation energy for the reaction. In a separate study the reaction of (E)-1-(phenylseleno)-2-(trimethylsilyl)ethene 1 with vinyl ketone in the presence of a chiral TiCl 2 (binaphtholate) catalyst to form enantiomerically enriched cis-cyclopropanes as products was investigated through geometry optimization in RHF/LAN1MB calculations.75 The approach of 1 from the si face of the C1 position of a vinyl ketone results in strong steric repulsion between the naphthalene ring and the trimethylsilyl group. In contrast approach from the re face is free of steric congestion and leads to the formation of the experimentally observed (1S,2R) isomer.Wu et al. have modeled the unimolecular and bimolecular elimination of methane from TiMe 4 using ab initio MO methods and the 3-21G and HW3 basis sets and predicted a high activation energy for unimolecular elimination of methane and a lower activation energy for the bimolecular elimination reaction.76 For Ti(CH 2 –CMe 3 ) 4 a preference for a-hydrogen abstraction over c-hydrogen abstraction was predicted. Frankcombe et al. have examined four possible reaction channels for the carbonylation reaction of palladium(II) complexes of mixed bidentate anionic ligands using DFT and MP2/6-31G*/Hay&Wadt methods.77 A novel pathway for isomerization via a five-coordinate transition structure from the square-pyramidal intermediate with a modest barrier of 4.2 kcal mol~1 has been identified.The Simmons–Smith cyclopropanation reaction has been studied using DFT calculations including relativistic e§ects either through e§ective core potentials or an explicit quasi-relativistic approach.78 Assuming that the reactive alkyl zinc–iodine species is monomeric a concerted mechanism was found to be the most favorable pathway for the reaction of ethene with CH 2 ZnI 2 (Scheme 2). The reaction involves an initial electrophilic attack with an activation energy of 11.5 to 14.6 kcal mol~1 while the overall reaction is exothermic by 33.5–37.8 kcal mol~1 using the BP and BLYP functions respectively. The transition structure has geometrical features similar to the intermediate structure for the barrierless addition of singlet carbene to ethene.The reaction of singlet methylene with water was studied by Gonzalez et al.79 Methylene reacts in a barrierless fashion to produce the ylide-like intermediate methyleneoxonium H 2 C~–`OH 2 which in turn undergoes a 1,2-hydrogen shift to produce CH 3 OH. Results at the QCISD(T)/6-311]]G** level indicate that the gas phase ylide and the transition state are located 6.4 and 4.9 kcal mol~1 below the reactants with an intrinsic barrier for the 1,2-hydrogen shift of 1.4 kcal mol~1. In the presence of 14 Jiali Gao the solvent the ylide is 5.5 kcal mol~1 more stable than reactants while the barrier for the hydrogen shift is increased to 7.5 kcal mol~1. Moss et al. have examined the stability and reactivity of oxa-substituted carbenes.80 The profound influence of these substituents is illustrated by the observation that the ground state of methylene is a triplet whereas that of dimethoxycarbene is a singlet calculated to lie 76 kcal mol~1 below the triplet.81 Moreover dimethoxycarbene is strongly nucleophilic while the electrophilic reactivity of methylene and the halocarbenes is suppressed.82 Kawashima et al.have found evidence both from experiment and HF/4-31G* computations indicating that 1,2-oxathietanes can be intermediates of the reaction of sulfur ylides with carbonyl compounds and decompose to form the oxirane with retention of configuration.83 It was suggested that this process may be treated as a salt-free Corey–Chaykovsky reaction. Ab initio calculations revealed that the formation of the oxirane proceeds by a concerted mechanism through a polarized transition state and an activation energy of 53.8 kcal mol~1.Yliniemela et al. performed ab initio MP2/6-31G*//HF/3-21G* calculations to locate the transition structure for the Darzens reaction of benzaldehyde and an a-haloester.84 The reaction proceeds via a two-step mechanism with initial aldol-type addition followed by cyclization to form the a,b-epoxy ester. The rate limiting step of this reaction appears to be keto–enol tautomerization since the enol intermediate reacts with benzaldehyde with a barrier of only 10–15 kcal mol~1. It has been proposed that the stereochemistry is determined by the steric requirements for the aldol addition step. In an interesting study Yamamoto et al. found that 5-endo cyclization is remarkably e§ective for the cyclisation of the 5-oxapenta-2,4-dienoyl radical even though this pathway is disfavored by Baldwin’s rules.85 Ab initio UHF/6-31G* calculations suggest that this acyl radical has a flat U-shaped geometry and can be represented as a ketene-substituted a-carbonyl radical.Aromaticity The concept of aromaticity and antiaromaticity occupies a unique position in organic chemistry. There has been considerable recent interest both in the definition of these basic concepts and in the application to the study of chemical problems. This renaissance was led by the work of Schleyer et al. who have identified the unique association of the magnetic susceptibility with cyclic delocalization of electrons. This work introduces the use of absolute magnetic shieldings computed at ring centers (non-weighted mean of the heavy atom coordinates) using quantum mechanical methods as a new aromaticity/antiaromaticity criterion.86 Negative ‘nucleus-independent chemical shifts’ (NICS) denote aromaticity while positive NICSs represent antiaromaticity.The relationship of NICS and aromatic stabilization energies has been calibrated for a set of five-membered ring heterocycles. This new definition was applied to the [10]annulene system for which ring strain precludes D 10) symmetry for the parent compound. The considerable 10p electron aromaticity is overwhelmed by the energy required to deform the CCC angles to 144°. Schleyer et al. proposed a number of theoretical structures which have been characterized as promising candidates for planar 10-membered ring systems.87 The theoretical structure energies and magnetic properties demonstrate considerable aromaticity for these higher analogs of benzene.Sulzbach et al. have explored the boundary between aromatic and olefinic character 15 Theoretical organic chemistry C C C C C2v C C C C C2v D5h D5h again using the [10]annulene system.88 Although it has been shown that the all-cis- [10]annulene adopts the boat-shaped olefinic structure with alternate single and double bonds instead of the aromatic D 10) conformation the structures and energies of compounds which contain one trans double bond have not been determined. Sulzbach et al. using MP2 and Becke3LYP methods found that a nearly planar aromatic structure which has one hydrogen pointing towards the center of the ring and a plane of symmetry which bisects the molecule (heart-shaped structure) lies at a potential energy minimum and has a lower energy than the C 2 twist conformation.These new results indicate that only high-order correlated methods will be able to correctly predict the [10]annulene potential surface and Sulzbach et al. have suggested that results obtained for similar systems using MP2 or DFT/B3LYP methods should be treated with extreme caution until verified at higher levels of theory. Using the MP4/6-31]G*//MP2/6-31]G* method Goller et al. have studied the influence of the electronegativity of ligands Y (F Cl Br I OH NH 2 CH 3 and H) on the strength of the r*-aromatic e§ect in gem-disubstituted 1H-phosphirenium cations and substituted 3-silacyclopropenes. It was found that r*-aromaticity influences the geometry of the systems.89 While there is no unique definition of absolute stabilization comparison with the ring strain energies of the corresponding carbocycles suggests that the 1H-phosphirenium cations enjoy 14–20 kcal mol~1 r*-aromatic stabilization and that silacyclopropenes are stabilized by 19–27 kcal mol~1.Glukhovstsev et al. assessed the aromatic stabilization energy of the cyclopropenyl cation to be 59.2 kcal mol~1 by computing the homodesmotic stabilization energy using G2 theory. 90 For the cyclopropenyl radical a small stabilization energy of 8.9 kcal mol~1 was obtained suggesting that this radical should not be classified as aromatic. The corresponding anion has a non-planar C4 singlet structure with a negative energy ([4.1 kcal mol~1) for the homodesmotic reaction (4).(CH) 3 ~](CH 2 ) 3 ]cyclopropene]cyclopropyl anion (4) Salts of a-sulfonyl carbanions are important intermediates in organic synthesis and have been the subject of extensive experimental and theoretical studies. Remarkably fluorination of the S-alkyl substituent has a significant e§ect on the structure and stability of a-sulfonyl carbanions. For example the pK! value of dimethyl sulfone is 31.1 whereas that of trifluoromethyl methyl sulfone is 18.8. Raabe et al. performed ab initio MP2/6-31]G*//HF/6-31]G* calculations to examine the structure of a-sulfonyl carbanions and the barrier to rotation about the Ca–S bond.91 It was found that structural changes and the conformation dependence of the rotational barrier can be explained by an interaction between the anionic lone pair orbital and the r and r* orbitals of the C–S bond through a negative hyperconjugation.Electron-withdrawing groups increase the coe¶cients at sulfur in the r* orbital and reduce its energy. There 16 Jiali Gao is also a significantly higher calculated rotational barrier for the fluorinated compound compared to dimethyl sulfone. Rauk has reported the surprising discovery that the 1-methyl-1-cyclohexyl cation has two distinct isomers and this has now been observed by B3LYP/6-31G* geometry optimizations.92 Each of the two isomers has a chair structure but with di§ering modes of hyperconjugative stabilization of the carbocation. The lowest energy structure shows C–C hyperconjugation between the empty p orbital and two C2–C3 bonds while hyperconjugation from a C–H bond is the higher energy (0.87 kcal mol~1) conformer.A transition structure which resembles the classical 1-methyl-1-cyclohexyl cation has been located at 0.25 kcal mol~1 higher in energy than the structure stabilized by C–H hyperconjugation. The elusive acepentalene radical anion was generated from a triquinacene derivative precursor in the gas phase by Haag et al.93 Computational studies at the B3LYP/6- 311]G* level with zero-point energy corrections revealed that the C4 singlet acepentalene is 3.9 kcal mol~1 lower in energy than the triplet state which has C 37 symmetry. The singlet state is stabilized by Jahn–Teller distortion and has an inversion barrier of 7.5 kcal mol~1 through a C 27 transition state. The calculated electron a¶nity of the S 0 state is 1.8 eV in accord with the experimental estimate of 1.5 eV.In a study at the BLYP/DZd level Sulzbach et al. confirmed that this is a stable molecule with a singlet ground state.94 However the C–– C double bond is twisted by 45° and the strain energy is ca. 93 kcal mol~1 in agreement with molecular mechanics results. The triplet state has a nearly perfect perpendicular arrangement at the central C––C bond (87°). It is strained by 42 kcal mol~1 and is 12 kcal mol~1 higher in energy than the singlet state. The synthesis of tetra-tert-butylethylene from di-tert-butylcarbene will be di¶cult because the barrier for dimerization (25 kcal mol~1) is much higher than for an intramolecular insertion reaction of the carbene (5 kcal mol~1). The heat of formation for 2,4,6-trinitro-1,3,5-triazine (TNTA) was predicted to be 46 kcal mol~1 using MBPT(2)//6-31G*//MBPT(2)/6-31G*]ZPE calculations.95 In a search for powerful high-energy density materials the following favorable performance properties of TNTA were reported an energy release of 304 kcal mol~1 on decomposition into N 2 and CO 2 a specific decomposition energy of 1410 cal g~1 and specific impulses of 269 s in the atmosphere and 294 s in vacuo.Conformational and tautomeric equilibria Cieplak et al. investigated the chair–twist boat equilibrium of substituted 1,3-dioxanes (Scheme 3) by use of 13CNMRspectroscopy ab initio molecular orbital and molecular mechanics methods.96 Both MP2/6-31G* and the AMBER force field yield results which are consistent with theNMRdata whereasMM3calculations fail. The calculations confirm the prediction of the critical role of electrostatic interactions in determining the barrier to chair–twist boat conversion.Gung et al. obtained relative energies for various conformers in 1,5-diene-3,4-diols at the MP2/6-31G* level which have been found to give nearly perfect diastereofacial selectivity in a number of reactions.97 The most stable conformer is found to have a gauche arrangement for the two vinyl groups and an anti orientation for the dioxyl group. The keto–enol equilibria of carboxylic acids as well as acidities of the carbon and oxygen acids have been investigated by several groups. Gordon et al. have examined the abstraction of hydrogen from both carbon and oxygen by hydride fluoride and 17 Theoretical organic chemistry O O R O O R O O R MP2 SCRF AMBER MM3 1.38 1.53 1.44 2.62 (0.0) MP2 SCRF AMBER MM3 2.98 3.18 2.04 0.26 Scheme 3 Computed energy changes (kcal mol~1) for the two equilibria at various levels of theory OH+ O H CH3 O O H CH3 CH3 O– O CH3 O O H CH2 O H O H O C+ H O H CH3 p Ka K = 26.6 p KE 2 = 21.8 p Ka E = 7.3 p KE 1 = 19.3 p Ka + = 13.1 + H+ + H+ p Ka = 4.76 (exp) p Ka = – 6.2 (exp) Scheme 4 hydroxide anions in acetic acid using ab initio MP4/6-31G]]G(dp)//6- 311]]G(dp) methods.98 The activation energy for the isomerization of acetate to enolate ion is 50.4 kcal mol~1 while the G2 values for the gas phase acidities of acetic acid at the OH and CH ends are 339.3 and 365.8 kcal mol~1 respectively.The acidity of the carbon acid in water was also investigated in hybrid Monte Carlo QM/MM simulations along with high level ab initio calculations.99 The predicted pK! and equilibrium constants which are found to be in good accord with experimental and previous theoretical estimates are summarized in Scheme 4.Wu and Lien investigated the intramolecular tautomerization of acetyl derivatives CH 3 COX (X\H BH 2 CH 3 NH 3 OH F Cl CN and NC) using ab initio molecular orbital methods at the HF and MP2/6-31G* levels and single point MP4(SDTQ)/6-311]]G** calculations. 100 The keto–enol free energy di§erences are computed to be in the range of 8.9 (X\NH 2 ) to 30.1 (X\OH)kcal mol~1 and acetaldehyde has a value of 13.6 kcal mol~1. The keto-to-enol transition has an activation barrier of 62–77 kcal mol~1 and has been correlated with the Hammett substituent resonance parameter (pR `). At the MP2 level *G‡\55.79]30.95pR `.Several studies of tautomeric equilibria in heterocyclic aromatic compounds have been reported. Hernandez et al. investigated the tautomerization of neutral hypoxan- 18 Jiali Gao thine and allopurinol in the gas phase and aqueous solution by using molecular orbital and SCRF methods.101 Hypoxanthine in the gas phase has two stable conformers of similar energy (\1 kcal mol~1) while A19 is the most stable tautomer of allopurinol and has an energy at least 4 kcal mol~1 lower than all other forms. Transfer of hypoxanthine to water reduces the di§erence in the energies of the H17 and H19 tautomers and even more favorable tautomers were identified consistent with experimental findings. The content of A19 in water is calculated to lie in the range of 38–88% of allopurinol and the di§erence between the energies of the A18 and A19 tautomers is reduced compared to the gas phase due to a stronger solvation of the former tautomer.Catalan et al. have observed that 1H-indazole is more stable than the 2H isomer by 3.6 kcal mol~1 from MP2/6-31G** calculations.102 Katritzky et al. carried out geometry optimization using a multicavity SCRF-AM1 and HF/6-31G methods for a N N O H N N H N N O H N N N N O H N N N N O H N N H17 H19 A18 A19 H H H series of molecules.103 It was demonstrated that bond lengths vary as the solvent polarity changes. Use of the Pozharski–Bird aromaticity index which is the average of bond fluctuation suggests that aromaticity is dependent on the environment of the molecule. Host–guest modeling Ion extraction by synthetic receptors has been extensively studied.Varnek and Wip§ examined the ion extraction selectivity by the ionophore calix[4]-bis-crown-6 L through molecular dynamics and free energy perturbation (FEP) calculations.104 The host molecule displays remarkable selectivity for extraction of Cs` over Na` from water to chloroform. The computational results correctly predict the larger binding free energy for Cs` with the use of standard 12-6-1 pairwise potentials without special treatment for the interaction with the ionophore. The high Cs` ionophoricity is attributed to di§erential solvation e§ects. Varnek and Wip§ also modeled the free ionophore and L·Cs` complex and L·Cs`-picrate counter ion system at the water/chloroform interface. The results of this simulation indicate that these ionophores are adsorbed at the interface and do not di§use spontaneously into the organic phase.In a combined X-ray di§raction study and molecular dynamics simulation calculation Muzet et al. have reported the structure of L·Sr(picrate) 2 ; L\tert-butyl-calix[4] arene-tetrakis(diethylamide).105 The ligand selectivity by the ionophore for Mg2` Ca2` Sr2`and Ba2` in vacuo in water and in acetonitrile was investigated. Molecular dynamics simulations show that the L·M`2 complexes are the converging type in water and in acetonitrile. This contrasts with L·M` alkali cation systems which display conformational flexibility in solution. Based on FEP calculations Muzet et al. determined a binding sequence of alkaline earth cations of Ca2`[Sr2`[Ba2`[Mg2` in accord with experiment. The relative free energies of 19 Theoretical organic chemistry association of these metal ions are Mg2`–Ca2` 29.9 kcal mol~1; Ca2`–Sr2` [6.7 kcal mol~1; and Sr2`–Ba2`,[13.8 kcal mol~1.Kollman and co-workers have performed molecular dynamics and free energy calculations to study the encapsulation of CH 4 CHCl 3 and CF 4 in a dimeric organic host in CHCl 3 as solvent.106 The host has been demonstrated to include CH 4 CH 2 Cl 2 CHCl 3 and C 2 H 2 with binding energies of[2 to[3 kcal mol~1 for methane and ethane and[1.0 to]1.8 kcal mol~1 for the chloromethanes. Using the AMBER force field Kollman and co-workers were able to reproduce the experimental trends for binding of CHCl 3 and CH 4 .107 However the binding of CF 4 was predicted to be only slightly weaker than the binding of CH 4 which conflicts with the experimental results.107 The possibility of similar 19F chemical shifts for bound and unbound CF 4 or a complex with CF 4 bound to the outside of the host has been o§ered as an explanation for the discrepancy.Kollman and co-workers also examined the interaction of the benzene dimer in solution as a model system for p–p interactions in proteins.108 Denti et al. calculated the Gibbs free energy of binding for a cyclophane –pyrene complex in water and in chloroform using the double annihilation technique.109 The computed di§erence in the free energy of binding in water and chloroform **G\10.2 kcal mol~1 favoring binding in water is slightly larger than the experimental di§erence of **G\7.1 kcal mol~1 at 303 K. The strong solvent dependence of cyclophane–pyrene complexation is due to di§erential free energies of cavitation in water and chloroform which are the result of the stronger intermolecular cohesive interactions of water compared to chloroform.McDonald and Still have applied free energy perturbation calculations to the enantioselectivity in binding of three peptide guest molecules to synthetic receptors with C 3 symmetry.110 The calculations reproduce the observed trends in enantioselectivity with errors of less than 0.7 kcal mol~1. The weakly bound guests have more conformational space in the receptor complex than do the more strongly binding guests and consequently the agreement with experiment is the best with those guests which form stronger complexes. These results indicate that obtaining the necessary converged ensemble averages is more challenging for the more weakly interacting guests because their complexes are structurally less well defined.The simulations indicate that the high enantioselectivity observed with these receptors arises in large part from the ability of the preferred guest peptides to form a greater number of hydrogen bonds with the receptor. Ivanrov et al. studied the inclusion complexes between the most commonly used cyclodextrins (a- b- and c-CD) and 1-bromoadamantane by NMR experiments and molecular dynamics (AMBER) simulations. 111 The computational results are found to be in agreement with experiment and predicted host–guest ratios of 2 1 1 1 and 1 1 for complexes to a- b- and c-CD respectively. The MM optimized structures indicate that the lowest energy complex has the guest molecule located between two a-cyclodextrins and oriented almost perpendicular to the average planes of the macrocycles.Castro et al. have determined the di§erential binding a¶nity and structural recognition between the inclusion complexes of cyclobis(paraquat-p-phenylene) P4` and 1,4-substituted phenyl or 4,4@-substituted biphenyl derivatives by spectrometric techniques and ab initio and semiempiricalMO methods.112 The computed complexation enthalpies from the PM3 method are on average within 1 kcal mol~1 of the experimental free energy and the geometry of penetration and position of the two complexes are 20 Jiali Gao Br H5 H3 H5 H3 consistent with NOE data from NMR spectroscopy. It was found that the primary basis for molecular recognition between 1,4-substituted phenyl guests and P4` is short range stabilizing electrostatic forces complemented by small amounts of polarizability and charge transfer.In contrast the recognition force for the diphenyl derivatives is dominated by polarizability with a small contribution from electrostatics. Thus the balance between molecular polarizability and electrostatics controls the di§erential binding a¶nity and structural recognition with the host P4`. Pericyclic reactions Pericyclic reactions continue to attract numerous theoretical investigations.113,114 Houk and co-workers pioneered transition structure characterization and have carried out calculations of kinetic isotope e§ects using ab initio molecular orbital and DFT methods. Recent examples include the calculation of the transition structure and the kinetic isotope e§ects on the Diels–Alder reactions of isoprene with maleic anhydride and of butadiene with ethylene.115,116 The computed kinetic isotope e§ects are typically in triple digit agreement with the experimental values.A variety of other Diels–Alder reactions have been studied by computational methods. Sustmann and Sicking investigated the reaction of amino- and hydroxysubstituted butadienes and cyano substituted ethylene at the B3LYP/6-31G* level.117 Special attention was paid to the stabilization of zwitterion intermediates by the inclusion of solvent e§ects in SCRF calculations. Solvent e§ects on two Diels–Alder reactions were also investigated by Gao and Furlani using a hybrid semiempirical AM1 and molecular mechanics potential.118 The reactions of butadiene with a number of thiocarbonyl compounds were examined using HF MP2 and B3LYP/6-31G* methods.119 The endo/exo and diastereofacial selectivity between cyclopentadiene and crotonolactone were examined by Sbai et al.through transition structure optimizations. 120 The competition between [2]2] and [4]2] cycloaddition reactions of activated ketenes and a,b-unsaturated imines was examined by ab initio MP2/6-31G* calculations and with cyclopentadiene at the MP4 and CCSD(T) levels.121,122 It was found that monosubstituted ketenes yield exclusively [2]2] adducts whereas disubstituted activated ketenes react by both pathways. Yamabe et al. proposed a new mechanism for the reaction of ketenes with cyclopentadiene to form the ‘[2]2]’ adduct.123 MP3/6-31G*//MP2/6-31G* calculations demonstrate that direct [4]2] cycloaddition between the parent ketene across its C––O bond and cyclopentadiene has the smallest activation energy among all the computationally obtained cycloadditions.The [4]2] adduct can then isomerize to the formal [2]2] adduct via a [3,3] sigmatropic shift (Claisen rearrangement). The first step has a barrier of 23.6 kcal mol~1 and the [4]2] adduct lies 14.8 kcal mol~1 below the reactant. The 21 Theoretical organic chemistry Ph Ph •+ Ph Ph • + Scheme 5 Claisen rearrangement has a barrier of 38.1 kcal mol~1 from the [4]2] adduct and the final product is 29.2 kcal mol~1 below the starting material. The transition structure for the electrocyclic ring opening of a variety of substituted cyclobutenones were located by Houk and co-workers using HF/3-21G and HF/6- 31G* methods.124 Substituent e§ects on the stereochemistry and reactivity were predicted to be small.Johnson and Daoust studied the two modes of electrocyclic ring opening of Dewar benzene as well as related structures.125 CASSCF calculations predict the existence of Mobius benzene (cis,cis,trans-cyclohexa-1,3,5-triene) in a shallow minimum ca. 100 kcal mol~1 above benzene. The computational results show that trans-Dewar benzene a substance whose existence was originally suggested by Woodward and Ho§mann in 1971 has an energy of 150 kcal mol~1 higher than benzene and that isomerization to benzene occurs with an activation barrier of 13 kcal mol~1. The thermal electrocyclic ring closure of (2E,7E)-3,4,7-trialkylnona-2,4,5,7-tetraenes is regioselective occurring at the most sterically congested vinylallene subunit to a§ord the trisubstituted alkylidenecyclobutene.The ring-opening of a model aziridinimine has been investigated by Nguyen et al. with emphasis on the stereochemistry of the [2]1] retro-cycloaddition process.126 Ring closure of both divinylallenes and vinylallenes displays high torquoselectivity [exclusive formation of the (E)-alkylidenecyclobutenes]when the substituent at C4 is a sterically demanding alkyl group and the substituent at C2 is a formyl group. These properties have been thoroughly examined by Lopez et al.127 Ab initio MP2/6- 31G*//6-31G* calculations demonstrate that the Z-transition structure is 1.18 kcal mol~1 higher in energy than the E-transition structure when the substituent at the C4 position is a tert-butyl group. This is in good agreement with the E/Zproduct ratio of 83 17 determined by experiment.On the other hand when the tert-butyl group is replaced by a methyl group the torquoselectivity vanishes. The computed energy di§erence between the E and Z transition structures is only 0.08 kcal mol~1 which may be compared with the experimental product ratio for the E/Z isomers of 50 50. Finally a formyl group at C2 has an additional torquoselective influence and the e§ect is ascribed to the reluctance of the starting vinylallenal to relinquish extended p conjugation. In contrast to the 1,6-Bergman cyclization of neutral enediyne compounds under thermal conditions the radical cations of aryl derivatives generated through chemical photochemical and electrochemical oxidation do not follow the Bergman cyclization mode but react by a 1,5-cyclization process (Scheme 5).On the basis of the results of UHF/AM1 and PMP2/6-31G*//HF/3-21G calculations it was suggested that the electronic ground state is derived from a 5p configuration.128 The SHOMO (second highest occupied molecular orbital) is the antisymmetric combination of the hybrid 22 Jiali Gao orbitals at the C1 and C4 carbon centers. Hence cycloaromatization of the enediyne radical cation to 1,4-dehydrobenzene radical cation is an electronically forbidden process. Formation of the 1,5-cyclization product is predicted to be allowed. Davidson et al. have reported a hybrid QM/MM study of the Claisen rearrangement of chorismate to prephenate in the active site of the enzyme chorismate mutase.129 The interactions between the substrate and enzyme were found to be strongest at a position close to the transition structure leading to 24.5 kcal mol~1 reduction in the barrier for reaction of the enzyme-bound substrate.Walters has published an ab initio MP4/6-31G* study of the [3,3] sigmatropic rearrangement of 3-aza-Cope reactions.130 The activation energies are predicted to be 34.6 kcal mol~1 for 3-azahexa-1,5-diene; 21.4 kcal mol~1 for 3-azoniahexa-1,5-diene; and 17.7 kcal mol~1 for 3-azahexa-1,2,5-triene. Photochemistry Photochemical processes have been extensively studied by Bearpark et al. using both high level CASSCF CASMP2 and hybrid MMVB methods. The latter approach treats the active orbitals involved in the chemical process using a parametrized valence bond Hamiltonian and uses the MM2 force field to represent the inert r-framework. The method is designed to simulate CASSCF calculations for ground and covalent excited states.Using MMVB Bearpark et al. studied the S 0 and S 1 potential energy surfaces of pentalene and the dynamics and radiationless decay were investigated by characterizing a conical intersection between the S 0 and S 1 states of fulvene.131,132 The S 1 to S 0 decay was predicted to occur in femtoseconds before a single oscillation through the crossing line is completed. Celani et al. determined the potential energy paths that control the excited-state evolution of cyclohexadiene and cZc-hexatriene (cZc-HT) from the Franck–Condon region by CASSCF/6-31G* calculations.133 It was found that both cyclohexadiene and cZc-HT undergo a barrierless motion in the 1B 2 spectroscopic state until decay to the lower lying 2A 1 state occurs via two distinct 1B 2 /2A 1 conical intersections.Remarkably both conical interactions correspond to open (acyclic) molecular structures. It is concluded that although the photochemical ring-opening of cyclohexadiene occurs in femtoseconds in the spectroscopic state the associated photochemical ring-closure reaction of cZc-HT which is initiated upon decay of 2A 1 to the ground state occurs within picoseconds of the initial excitation. Z s- cis cZc-HT s- cis Dreyer and Klessinger have shown that fulvene is the primary product of the photolysis of benzene using semiempirical MNDOC-CI and CASSCF/3-21G calculations. 134 The most probable mechanism for the photochemical isomerization of benzene to fulvene involves the intermediate structure prefulvene and 1,3-cyclopentadienylcarbene which competes with the almost barrierless formation of benzvalene 23 Theoretical organic chemistry and rearomatization to benzene.Bach et al. investigated the photochromic valence isomerization of the norbornadiene (N) and quadricyclane (Q) cation radical system using PMP4 and CCSD(T) methods.135 The calculated adiabatic ionization potential was calculated to be 7.90 eV for N and 7.12 eV for Q in accord with the experimental values of 8.34–8.43 and 7.40–7.86 eV respectively. The barrier for the N·` to Q·` transition is about 16.5 kcal mol~1. Martin et al. studied the cleavage of photoexcited C–X (X\C Cl) bonds to the carbonyl group in acetyl chloride using an ab initio spin restricted CI singles method.136 The minimum energy conformations and transition structure for the C–X bond cleavage both in the S 1 and T 1 states have been determined.It is predicted that C–Cl bond cleavage in the S 1 state can take place upon photoexcitation since the vertical transition energy is greater than the energy of the transition state for C–Cl bond cleavage. References 1 C.A. White B. G. Johnson P.M. W. Gill and M. Head-Gordon Chem. Phys. Lett. 1996 253 268. 2 C.A. White B. G. Johnson P.M. W. Gill and M. Head-Gordon Chem. Phys. Lett. 1996 248 482. 3 M. Challacombe E. Schwegler and J. Almlo� f J. Chem. Phys. 1996 104 4685. 4 C.A. White and M. Head-Gordon J. Chem. Phys. 1996 104 2620. 5 E. Schwegler and M. Challacombe J. Chem. Phys. 1996 105 2726. 6 J.C. Burant G. E. Scuseria and M. J. Frisch J. Chem. Phys. 1996 105 8969. 7 E. Hernandez M. 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