3 Theoretical Organic Chemistry By C.A. REYNOLDS Department of Chemistry and Siulogical Chemistry University of €sex Wivenhue Park Colchester C04 3SQ UK 1 Introduction Theoretical organic chemistry is a wide ranging topic; theoretical chemists approach this discipline from a number of diverse perspectives ranging from extremely accurate methods applied to small model systems through to methods applicable to large biological molecules where the aim is to seek insight into complex processes rather than to produce quantitative results. Fortunately the author of the review has been encouraged to be selective rather than exhaustive. Consequently the topics covered reflect the author's interests and have been grouped into three sections density functional theory (DFT) because the author believes this will have a tremendous impact on theoretical organic chemistry in the years to come (for the reasons outlined below); calculations involving solvation since although sohation is still largely neglected it is clearly important in organic chemistry; and transition structures because they are the key to understanding mechanism.To conclude a short section is appended at the end on neural networks since these represent just one of many new computational techniques which are beginning to be applied in interesting ways to Chemistry. Indeed one of the criteria for including articles for review is the author's perception of the future potential of the methods for use in application to organic chemistry. 2 Density Functional Theory In the opinion of the author density functional theory (DFT)' is poised to make a revolutionary contribution to theoretical organic chemistry.The reasons for this are that it is potentially exact,2 it scales very favourably with size (usually N3where N is the number of basis functions though there is currently much research on order N methods in quantum chemistry) and it has recently been shown to give very promising results (seeTable 1). Since the method may be unfamiliarto many readers the relevant features are discussed below followed by an overview of a selected proportion of the interesting results published in 1993. Background.-Within traditional molecular orbital (MO) methods where the total R.G.Parr and W. Yang 'Density Functional Theory ofAtoms and Molecules' Oxford University Press New York 1989.P. Hohenkrg and W. Kohn Phys. Reix B 1964 136 864. 51 C.A. Reynolds wavefunction 'B is constructed as a product (actually determinant) of N one-electron molecular orbitals # !P = t4rdr#,-#NI (11 the total energy of a molecule is composed ofone-electron terms (the kinetic energy and the electron-nucIear potential terms) and two-electron terms. The two-electron terms consist of the coulomb energy and the exchange energy. All of these terms involve integraIs over basis functions and the integrals are evaluated analyticaIIy. In addition accurate calculations require evaluation of the correlation energy which is not present in self-consistent field (SCF) MO calculations.Generally the correlation energy is evaluated by including excited states and so effectively the total wavefunction is now a linear combination of a large number of determinants similar to that on the right hand side of Equation (1). Such multi-determinant wavefunctions are essential for the accurate description of many chemical processes particularly dissociation and so they are also essential for a reliable description of transition states. It is the calculation of the correlation energy which render impossible accurate ab initio calculationsfor systems ofreal chemical interest because the calculations scale according to N5for the simplest approach [second order Maller-Plesset theory (MP2)] which does not even describe dissociation correctly and according to N7 for the more reliable approaches such as higher order M~rller-Plesset perturbation theory or coupled cluster calculations.In the light of this unfavourable scaling density functional theory possibly o@rs the only reliable alternative. The essentials of the method are given below. Density Functional Methods.-Within the local density approximation (LDA) the exchange energy is evaluated as follows J r EtDA= C dr~(r)~'~ where C is a constant and p is the electron density. The integral is now usually evaluated numerically over a grid. A key question when assessing DFT calculations is whether this integral has been evaluated accurately; a reasonable check is aIso to integrate p(r) over the grid which should give the total number of electrons in the molecule.Probably the most significant change came in 1988 when Becke proposed that the gradient of the density was also important in evaluating the exchange energy.3(Such methods involving Vp(r)are termed non-local or gradient methods.) ..2 where p is a constant and x = I Vp(r)l/p4/3.The correlation energy can be evaluated in a similar manner using local or non-local functionals. The non-local methods are usually denoted by a combination of letters to denote the combination of functionals for exchange and correlation; thus B-LY P denotes the Becke '88 exchange functional3 plus the Lee Yang and Patr correlational f~nctional;~ B-VWN denotes the Becke A.D. Becke Phys. Rev. A 1988 38 3098. C. Lee W. Yang and R.G. Pan Phys. Reu. B 1988,37,785;B.Miehlich A. Savin H. StolI and H. Preuss Chem. Phys. Lett. 1989 157,200. Theoretical Organic Chemistry exchange functional plus the Vosko Wilk and Nussair correlational f~nctional.~ There is currentIy much research into new functionals and we can certainly expect the current functionals to be superseded. A number of choices exist as to how the density is evaluated. The integrals in Equations (2) and (3) may be evaluated using any density and results show that the answers may not differ significantly whether the density is evaluated in a manner which is self consistent with equation (2) or (3)$ alternatively any other density such as an SCF density may be used. In chemical applications the density is usually constructed from atom-centred basis functions as in traditional molecular orbital methods though the resultant orbitals thus produced by the Kohn-Sham method may not have the same physicaI meaning.In studies ofmolecules interacting with surfaces it is common to construct the density from plane waves (see section on Carr-Parrinello methods). Model Studies on Small Molecules.-Since DFT is a reasonably new technique for chemists (but not for physicists who generally look at much larger energy differences) it has been important to estabiish the reliability of density functional theory in chemical problems. It is this area where significant and exciting progress has been made in the last twelve months. To date there have been few genuine application studies that have significantly enhanced our understanding of chemistry.However there have been many significant studies on model systems. Some studies have considered the performance of DFT in predicting molecular properties for a large number of molecules; understandably the most systematic study by Johnson et al.,came out of the Pople group.’ The general findings are for bond lengths the €3-LYP functional gives bond lengths which are too long by about 0.018 A -the error is comparable to that of Hartree-Fock methods but the sign of the error is reversed; for dipole moments the errors are similar to those of Hartree-Fock methods except that DFT has some success fur difficult molecules like CO and NO; atomization energies are extremely well predicted by both the B-LYP and B-VWN methods with a mean error close to zero; and harmonic frequencies are generally well produced with the errors generaIly less than those obtained using MP2 methods.Studies on bond breaking processes have also found that non-local DFT is valid for multideterminant problems,8 and this is a very significant observation (see also transition state references in Table 1). For energetics the majority of researchers find that density functional theory generally performs as well as MP2 (in the cases where MP2 is vaIid). This appears to be at odds with Johnson et who generaIly find it vastly superior. However as Johnson shows the errors in traditional approaches tend to be systematic whereas the errors in DFT methods tend to be random and this tends to account for why DFT performs simiiarly to MP2.Not all ofthe studies in Table 1are significant by themselves. However the weight of the evidence presented in this selection of papers is extremely strong particularly for those involving calculations of dissociation energies or transition structures. More- over given the volume of research into new functionals the preference for density functional theory over traditional approaches will grow and we wiil surely see DFT having a very profound influence on theoretical organic chemistry. Partly as a warning S. H. Vosko L. Wilk and M. Nusair Con. J. Phys. 1980 58 1200. C.T. Lee G. Fitzgerald and W.T. Yang J. Chem. Phys. 1993,98,2971. ’ B.G. Johnson P. M. W. Gill and J.A. Pople J. Chern. Phys. 1993 98 5612. C. W. Murray N.C.Handy and R. D. Amos 1.Chem. Phys. I993,98 7145. C.A. Reynolds some of the articles in Table 1 are based on local density functional theory which the table shows may give good results. However a closer look will show that reliable results often require non-local methods. (Needless to say the table does not show the cases where density functional theory performs badly.) Applications.-At this point it is helpful to review briefly two applications that illustrate the power of density functional methods. The first is a study ofthe isomers of N,H and illustrates how favourably the energy barriers connecting the various isomersofN,H calculated using non-local density functional theory compared to those calculated using high level ab initio methods such as G2 theory?*" The potential energy surface is illustrated in Figure 1 in which the relative energies given (in kcalmol-') are for Hartree-Fock; non-local DFT; G2 theory respectively.) 89;70;70 H -;49;50 /\ H H/N=N N=N H / H' N=N 6N=N H/N=N H 20;22;24 0;o;o 7;5$ Figure 1 The use of DFT to study organometaIlics is aptly illustrated by studies on H-H and C-H bond activation by the a-bond metathesis reaction (Scheme 11." The bond dissociation energies of the cornpIex have been caiculated to within 2&30 kJ mol -(4.5-7.5 kcal mold ') of experiment.The transition structures for the above reaction have been located and the activation energies are consistent with the experimentally observed rate constants thus the results are generally in line with experiment.Scheme I J. Andzelm C. Sosa and R.A. Eades,J. Chem. Phys. 19!?3,97,4664. B.J. Smith J. Phys. Chem. 1993 9,10513. *l T. Zieglcr E. Folga and A. Berces J. Am. Chem. Suc. 1993,115,536. Theoretical Organic Chemistry C z em me -I? me 0 L. emee em emmm mm - d c$ *+ 5P em Ii ‘C om me e w eeeeew C. A. Reynolds Finally it is appropriate to note that DFT methods are now available in the popular GAUSSIAN’2 and CADPAC13 traditional quantum chemical codes as well as from other commercial sources. Carr-Parridlo Methods.-Carr-ParrineIlo methods combine quantum mechanical methods with molecular dynamics. (The local density approximation is usually used along with pseudopotentials to represent the cure electrons and the basis set is typically constructed from plane-waves rather than atomic orbital-like basis functions.) The inherent advantage is that molecular dynamics can be performed without the need for crude force-fields containing parameters which may be far from ideal.In addition bond breaking processes can be followed. The potential of this method for studying reactions is tremendous. However to date there are a number of technical problems and applications have largely been applied to cluster chemistry and related problems. References 14 and 15 illustrate the method and show how it can be used in combination with simulated annealing to overcome the multiple minimum problem and determine the global minimum for molecular structures.Excited States.-The Hohenberg-Kohn theorem2 is in principle valid only for the ground state electron density so there is as yet no universally held justification for applying DFT methods to excited states despite much research in this area. However a number of authors for example Dual et have shown that DFT can yield meaningfuI results when applied to excited states. 3 Solvation Backgromd.-AIthough it is widely understood by organic chemists that solvent effects can have a dramatic effect on reactivity it is rather surprising that most theoreticai studies stiIl do not include the effects of solvation as a matter of course. There are a number of reasons for this. One is the lack of suitable software though this reason is rapidly becoming out of date.Another is that while solvation effects are indeed important the errors due to the limitations of semiempirical treatments the errors due to basis set size limitations and the errors due to inadequate treatment of electron correlation (see above) are all still the largest potential errors in any calculation. A third reason is the lack of realistic models for treating solvation since all the models are defective in one way or another despite much research in recent years. A find reason is that some methods particufarly those involving computer simulations require specialist skills different to those required for accurate gas-phase studies of potentia1 energy surfaces. One notable contribution towards providing readily available software for solvation ’’ ‘GAUSSIAN 92/DFT’ Gaussian Inc 4415 Fifth Avenue Pittsburgh PA 15213 USA.l3 R.D. Amos ‘CADPAC 5.1’ University Chemical Laboratories Lensfield Road Cambridge UK CB2 1EW. K. Laasonen M. Parrinello R. Car C.Y. Lee and D. Vanderbilt Chem. Phys. Lett. 1993,207,208. Is R.O. Jones J. Chem. Phys. 1993,99 1194. l6 C. Dual H.U. Gudel and J. Weber J. Chem. Phys. 1993,98 4023. Theoretical Organic Chemistry 57 studies is the AMSOL program,51 which is available through QCPE.52The authors of AMSOL Cramer and Truhlar have published an excellent review53 of solvation models and despite the title (‘Continuum solvation models classical and quantum mechanical implementations’) both empirical and explicit water simulation models are discussed in addition to Poisson-Boltzmann reaction-field methods and generalized Born methods which are discussed in some detail.The review also includes a comparison (with experiment) of the various methods for determining free energies of hydration. (Cramer and Truhlar’s own generalized Born method54 certainly does well in this cornparison). An excellent review of Poisson-Boltzmann methods55 has also been published in the last year. A particular advantage of this method is that it is applicable to large systems and can inctude ionic strength in the caIculations. TypicaI uses inctude calculating the molecular electrostatic potential around macromolecules and calculating pK shifts in enzymes but as yet there have been few applications to l7 L.A.Eriksson S. Lunell and R.J. Boyd J. Am. Chem. SOC. 1993 115 6896. la A. D. Becke J. Chem. Phys. 1993,98 5648. l9 A.D. Becke J. Chem. Phys. 1993,97,9173. 2o H. Chen M. Krasowski and G. Fitzgerald J. Chem. Phys. 1993 98 8710. 21 R. M. Dickson and A. D. Becke J. Chem. Phys. 1993,99 3898. 22 L. Goodwin and D.R. Salahub Phys. Rev. A 1993 47 R774. 23 D. P. Chong D. Papousek Y.T. Chen and P. Jensen J. Chem. Phys. 1993,98 1352. 24 M.S. Stave and J. 3.Nicholas J. Phys. Chem. 1993 97 9630. 25 E. Folga and T. Ziegler 1.Am. Chem. Soc. 1993 115 5169. 26 I. Papai J. Mink R. Fournier and D.R. Salahub .I.Phys. Chem. 1993 97 9986. ’’ K. 0.Christe W. W. Wilson D. A. Dixon S. I. Khan R. Bau,T. Metzenthin and R. Lu,~. Am. Chem.SOC. 1993 115 1836.28 K.O. Christe D. A. Dixon J. C. P. Sanders,G.J. SchrobiIgen and W. W. Wilson,J. Am. Chem.Soc. 1993 115 9461. 29 K. 0.Christe D. A. Dixon I. B. Goldberg C.J. Schack B. W. Walther J.T. Wang and F. WiIliams,J. Am. Chern. Soc. 1993 115 1129. 30 A. Berces and T. Ziegler J. Chem. Phys. 1993 98,4793. 31 C. W. Murray G.J. Laming N.C. Hamdy and R. D. Amos J. Phys. Chem. 1993 97 1868. 32 1.G. Guan P. Duffy J.T. Carter D. P. Chong K. C. Casida M. E. Casida and M. Wrinn J. Chem.Phys. 1993,98 4753. 33 M. M.Huhn R. D. Amos R. Kobayashi and N.C. Handy J. Chem. Phys. 1993,98 7107. ” D. P. Chong and C.Y. Ng J. Chem. Phys. 1993 98 759. 35 P. Duffy and D.P. Chong Org. Mass. Spec. 1993 28 321. 36 D. Heinernann and A. Rosen Theor. Chirn. Acta. 1993 85 249.37 f.Politzer 3. M. Serninario M.C. Concha and J.S. Murray Theor. Chirn. Acta. 1993 85 127. ’’ C.Sosa C. Lee G. Fitzgerald and R. A. Eades Chem. Phys. Lett. 1993,211 265. 39 P. FIeukiger J. Weber R. Chiarelli A. Rassat and Y. Ellinger Int. J. Quant. Chem. 1993 45 649. 40 A. Berces and T. Ziegler Chem. Phys. Lett. 1993,203 592. 41 D.P. Chong and A.V. Bree Chem. Phys. Lett. 1993 210 443. 42 C. Mijoule 2. Latajka and D. Borgis Chem. Phys. Lett. 1993 208 364. 43 C. Lee and D. VanderbiIt Chern. Phys. Lett. 1993 210 279. 44 A. Ghosh and J. AlrnIof Chem. Phys. Lett. 1993 213 519. 45 J. M. Seminario Chem. Phys. Lett. 1993 206 547. 46 S. M. Colwell C. W. Murray N. C. Handy and R. D. Amos Chem. Phys. Lett. 1993 210 261. 47 I.A. Topoi and S. K. Burt Chem. Phys.Letr. 1993 204 61 1. 48 K. Waizurni H. Masuda H. Einaga and N. Fukushima Chem. Lett. 1993 7 1145. 49 R. D. Amos C. W. Murray and N.C. Handy Chern. Phys. Lett. 1993 202 489. T. Ziegler E. Folga and A. Berces J. Am. Chem. Soc. 1993 115 636. 51 C.3. Cramer G.C. Lynch G.D. Hawkins D.G. Truhlar and D. A. Liotard AMSOL 4.0 QCPE 606 QCPE BulIetin 1993 13(4). 52 Quantum Chemistry Program Exchange Creative Arts Building 181 Indiana University Bloomington IN 47405 USA. 53 C.J. Crarner and D.G. Truhlar Reviews in Computational Chemistry in the press. 54 C.J. Cramer and D.G. Truhlar 1.Cornput.-Aided MoI. Des. 1992,6 629. 55 B. Honig K. Sharp and A.S. Yang J. Phys. Chem. 1993 97 1101. 58 C.A. Reynolds organic chemistry despite recent encouraging results referred to in the review.One recent application has been to non-natural DNA triplex-forming olig~nucleotides.~~ Computer Simuiation Methods.-References to computer simulation reviews and texts are given in reference 19. Free energy methods57 have yielded very high levels of agreement between calcdated and experimental free energies including free energies of hydrati~n.~~ The real advantage of these methods is the treatment of specific solvent molecules. Jorgensen has shown how these methods implemented within a Monte Carlo framework can be useful for characterizing the hydration patterns of molecules. In particular the solute-water hydrogen bonding patterns can be n~ted.~~-~' Such effects may be important in determining mechanistic effects and conformational preferences in solution.62An algorithm for calculating residence times at particular hydration sites has been presented and may be helpful for anaIysing such structural features particularly for biorn~lecules.~~ Combining Quantum MechanicaI Calculations with Computer Simulatiom-Com-puter simulations are of necessity based on molecular mechanics (but see above for references to Carr-Parrinello methods).They cannot in general therefore describe bond-breaking processes. However a number of studies have described the combined use of quantum chemical studies with free energy perturbation (FEP)methods.'' Such approaches have been used to study the mechanism ofcarbonic anhydrase (by studying the underlying elementary reaction^)^^*^^ and the Mentshutkin reaction.66 The effect of solvation in reference 65 is quite marked although the gas phase reaction is barrierless the barrier in solution is over 19kcalmol-' and is mainly due to desolvation effects.Reference 64actually describes the use of an empirical valence bond method but the results are compared to ab initio calculations. The main value of this particular study is probably in illustrating the catalytic effect of the environment. The solvent was found to have a marked effect on the energetics the structure of the transition state in the type I1 S,2 Mentshutkin reaction and the charge distribution in the transition structure demonstrating the value of combined quantum mechan- ical-molecular mechanical calculations. Combined calculations have also been applied to the torsional barrier in 71-ethylimidaz~le."~ Here it was found that the torsional barrier was raised in sdution by nearly 2 kcal mol-and that the position of the barrier moved.Attempts were made to rationalize the effects in terms of solute-solvent hydrogen bonds but the effects were considerably more complex than expected. TuutomericEquilibria. Tautomeric equilibria provide very popular test systems for the 'I3 V.Mohan Y. K. Cheng G.E. Marlow and B. M.Pettitt Eiopoiymers 1993-33,1317. " D. L. Beveridge and F.M. DiCapua Annu. Rev. Biophys. Biophys Chem. 1989 IS,431. 58 C.A. Reynolds P.M. King and W.G. Richards Mol. Phys. 1992,76 251. 59 W.L. Jorgensen and T.B Nguyen J. Comput. Chem. 1993 14 195. 6o H.A. Carlson T. B. Nguyen M.Orozco and W. L. Jorgensen J. Camput. Chem. 1993 14 1240. 61 P.I. Nagy G.J. Durant and D.A. Smith J. Am. Chem. Soc. 1993 115 2912. 62 P.I. Nagy W. J. Dunn G. Alagona arid C. Ghio J. Phys. Chem. 1993,!?7 4628. 63 A.E. Garcia and L. Stiller J. Cornput. Chem. 1993 14 1396. 15' J. Aqvist M. Fothergilt and A. Warshel J. Am. Chem. Soc. 1993 115,631. 65 Z. Peng and K.M. Men J. Am. Chem. Soc. 1993,115,9640. 66 J.L. Gao and X. F. Xia J. Am. Chem. SOC. 1993 115 9667. 13' D. R. Lowis J. W. Essex and W.G. Richards Molec. Sim. 1993 9 349. Theoretical Organic Chemistry reliability of sohation free energy calculations because of the chemical interest of the underlying problem; however the results are frequently ambiguous as they require solvation calculations to be combined with high-level quantum chemical calculations.Thus Burton et al. studied the tautomeric equilibria between the dihydroxy (l) monohydroxy-monoketo (2) and the diketo (3) forms of maleic hydrazide; they showed that both FEP methods and self-consistent-reaction field (SCRF)methods (see below) predict the monohydroxy-monoketo to be the most stable and that solvation stabilizes the diketo form but that the dihydroxyform is unlikely to be observed in agreement with experiment.68 In contrast however the same group showed that neither the FEP method nor the polarized continuum method (PCM),69 nor the SCRF method yield results that are totally adequate fur modelling the equilibria involving 3-hydroxypyrazole (4) and its tautomers f5)-(7) even though the errors were not large.70 The calculations do show that poIarization of the solute is important (which is not generally included in FEP methods).These two examples clearly show that great care is still required in applying these methods despite much recent progress. ComputationalCost.In contrast to many implementations of the SCRF methods FEP methods remain computationally very expensive though a particularly imaginative method for reducing the cost of FEP calculations is given in reference 71. However many drawbacks of the method remain and some are listed in reference 72. If CPU time is a real issue then the lower-level implementations of continuum methods remain more promising for small molecules; a real advantage of continuum methods is that the calculations are frequently much more easy to set up.Continuum Methods-The Kirkwood-Onsager result for the free energy of solvation in a medium of relative dielectric constant E of a dipole p centred in a sphere of radius 01 is given by Equation (4). N.A. Burton D.V. S. Green I. H. Hillier P. J. Taylor M. A. Vincent and S. Woodcock J. Chem. Soc. Perkin Trans. 2 1993 33 1. 69 S. Miertus E.Scrocco and J. Tornasi Chem. Phys. 1981,55 117. '* O.G. Parchment D.V.S. Green P.J. Taylor and I. H. Hillier J. Am. Chem. Soc. 1993 115 2352. 71 G. King and R.A. Barford J. Phys. Chem. 1993,97,8798. '2 C.A. Reynolds J. W. Essex and W. G. Richards Chem. Phys. Lett. 1992 199 257. 60 C.A. Reynolds The result includes polarization of the soIvent by the solute.Quantum mechanical reaction field methods are frequently based on this result through modification of the self-consistent field (SCF) equations and are termed self-consistent reaction-field (SCRF) methods. Limitations of this approach frequently include truncation of the multipole series at the dipok level; the use of a spherical forellipsoidal) cavity which is frequently unrealistic; the wavefunction Y is approximate and does not usually include electron correlation (it may even be semiempirical); and the results depend markedly on the choice of cavity radius cc. In recent work the quantum mechanical dipole approximation has been extended to higher muhipoles within arbitrarily shaped cavities.73 However the convergence of such methods with regard to the multipole series and size/shape of cavity has recently been q~estioned;~~ in this work a distributed multipole series has been used -this approach certainly dues need a molecular-shaped cavity.39 A number of studies have aiso extended the SCRF method beyond the SCF level to the Msller-Plesset second order level (MP2I7’ and to the configuration interaction (CI) level;76 while this latter approach like all continuum methods is generally considered to be unable to treat strong specific solvation effects such as hydrogen bonds it can treat excited states.An implementation of the pofarizible continuum method of Miertus et al. including electron correlation up to third order has also been proposed.77 However given the rather crude description of the molecular shape usually used (but not in the PCM approach) and noting that the choice of radius has a marked effect on the predicted AG value it is questionable whether the more accurate treatment of Ip yields more accurate free energies of solvation particularly given the other known errors in continuum methods.In defence of traditional SCRF methods Young et al. noted that the method gave resuits of comparable quality to those from molecular dynamics simulations when applied to tautorneric equilibria partition coefficients and amine basicity. However the continuum methods systematically overestimated the free energies of hydration though the errors tended to cancel upon taking differences. Moreover they also found that going beyond the dipole in the SCRFmethod did not increase the accuracy.Good agreement with experiment was also found by the same group in studies on the conformatiunal preferences of the alanine di~eptide.~’ Clearly the performance of these continuum methods like any other method depends on the problem to which it is applied. A good illustration of the use of the PCM method is given by Tunon et al. who have combined the PCM method with high level ab initio studies (up to MP4) to look at the difference in acid/base behaviour of a series of alcohols in both the gas phase and soiution. 73 V. Dillet D. Rinaldi J. G. Anguyan and J. L. Rivail Chem. Phys. Lett. 1993,202 18. ’‘ R. R. Pappalardo E. S. Marcos M. F. Ruiz-Lopez D. Rinaldi and J. L. Rivail J. Am. Chem. Sac. 1993 115 3722.7s J.G. Anguyan Int. J. Quant. Chem. 1993,47,469. ’‘ M.V. Basilevsky G. E. Chudinov D. V. Napolov and L. M. Tirnofeeva Chem. Phys. 1993 173,345. 77 F.J.O. klvalle and M. A. AguiIar 1.Mol. Struct. (THEOCHEM),1993,99 25. 78 P. Young D.V. S. Green I.H. Hillier and N. A. Burton Mot. Phys. 1993 80 503. 79 I.R. Gould and I.H. Hillier 1.Chem. Soc. Chem. Commun. 1993 951. I. Tunon E. Silla and J.L. Pascualahuir J. Am. Chem. Soc. 1993 115 2225. Theoreticat Organic Chemistry Semiempirical and Classical Implementations of Continuum Methods.-In terms of agreement with experiment in real applications semiempirical continuum methods have probably given results as reliable as their ab initio quantum mechanical counterparts. The use of INDO/S-CI for studying excited states and spectra is quite widespread; in combination with a continuum method it has given quite good predictions of solvatochromic shifts of organic molecules.Another semiempirical method formulated within the NDDO framework has given very encouraging results on excited states and again can predict solvatochromic shifts quite well. The particular advantages of this method8* are the inclusion of the dispersion energy (which is not included in most continuum methods) as well as the cavity energy and very fast computation of the molecular electrostatic potential on the surface;83 the dispersion energy calculations are relatively time-consuming but are essential to model correctly certain solvatochromic shifts. This latter method is again based on the poIarizabie continuurn method of Miertus et ~1.,~'which dues use realistic molecular cavity shapes.Rather than trying to increase the level of treatment of !P in the method the Tomasi group have shown that a classical implementation of the method using point charges (provided that they are potential-derived charges) can give quite good calculated solvation energies. This observation could be quite significant for studying macro- molecules where a full molecular dynamics or quantum mechanical treatment could be very expensive.84 (Pappalardo et aL8 have also modelled the solvatochromic shift for the n -,n* transition of acetone using an MCSCF implementation of a continuum model with an ellipsoidal cavity). Due to its implementation within MOPAC93,86 the new COSMO methods7 is IikeIy to become very popular.However apart from showing that the glycine zwitterion is more stable in aqueous solution than the neutral form and a very small number of comparisons with experimental values as yet there is little indication of its general reliability. Applications.-Efiect of Hydration on Cycloadditions. The (2 + 2) cycloaddition of t-butylcyanoketene (8) to phenylethene (9) (Scheme 2) was studied using a four-orbital four-electron CAS-MCSCF method using earlier studies as a guide. Scheme 2 The most favourable route was found to proceed via a biradical intermediate in which steric interactions between the three substituents are minimized despite the observation that this mechanism does not produce the most stable product.The effect 'I T. Fox and N. Rosch J. Mol. Struct. (THEOCHEM) 1992 95,279. 82 G. Rauhut T. Clark and T. Steinke J. Am. Chem. Soc. 1993 115 9174. 83 G. Rauhut and T. CLark J. Comput. Chem. 1993 14 503. '* R. Montagnani and J. Tomasi J. Mol. Struct. (THEOCHEM) 1993,98 131. 85 R. R.Pappatardo M. Reguero M.A. Rabb and M. Frish Chem. Phys. Lett. 1993,212 12. 86 J. J. P. Stewart MOPAC 93 QCPE Bull. 1993 13. A. Klamt and G. Schuurmann J. Chem. SOC.,Perkin Trans. 2 1993 799. 62 C.A. Reynolds ofmodelling hydration by a multipolar expansion (to order six) in an elIipsoidal cavity was found to enhance the gas phase product preference,88 -though convergence problems in the multipolar expansion were noted. Significantly the differential solvation energy corrections for such asynchronous pericycIic reactions are sufficiently large to have a marked effect on selectivity.Nucteophiiic Additions and the SupermoIecuk Approach to Sohation. The nucleophilic addition of ammonia to small molecules with activated double bonds such as acrolein has been calculated at the MP2 level with stationary points optimized at the HF/6-3lG* level. The purpose of these calculations was to gain some understanding of the possible biological effects of such reactions involving DNA. Hydration energies were caIculated using a polarizabk dielectric continuum. However the major reduction in the barrier height on solvation was found only when an explicit catalytic water molecule was included in the quantum mechanical treatment.89 Such a supermolecule approach is currently the only viable method of studying solvent- assisted mechanisms.However the calculation of hydration energies by the continuum method is probably not feasible except in the AMSOL method which is designed to treat explicit water molecufes consistently. Potential of Mean Force Calculations.-The free energy profile for the rotationaf isomerization of N,N-dimethylformamide has been determined using a combined quantum mechanical-molecular mechanical approach. The hybrid AM l/TIP?P model was used with the AM 1 energies scaled to reproduce high level ab initio results. The potential of mean field was determined by statistical perturbation theory implemented within a Monte Carlo frame~ork.’~ The difference in polarity between the ground state and the transition state emphasizes the desirability of inchding polarization effects in such calculations.4 Transition Structures The theme of the majority of the articles reviewed in this section is inclusion of reports of calculated transition structures. Calculated transition structures and their asso- ciated barrier heights offer from theory a unique contribution to the study of organic reactivity. A useful general review on the interplay between experiment and calculated transition structures is given by Williams:’ who remarks that the transition structure is frequently calculated more accurately than the energy barrier -as judged against very high level ab initio calculations. For this reason the reader may wish to review the work reported below in the light of the earlier comments on ab initio methods and density functional theory; these ideas on the difficulty of obtaining definitive energy barriers are superbly illustrated in the high-quality articles described in the next section.Diels-Alder Reactions.-The long running controversy as to whether DieIs-Alder reactions occur via concerted or other mechanisms continues. Li and Houk9’ have M.Reguero R.R. Pappalardo M. A. Robb and H.S. Rzepa J. Chem. SOC. Perkin Trans. 2 1993 1499. 89 L. Pardo R. Osman H. Weinstein and J.R. Rabinowitz J. Am. Chem. Soc. 1993 115 8253. 90 J.L. Gao. J. Am. Chem. Soc. 1993 115,2930. 91 I.H. Williams Chem. Soc. Rev. 1993,22,277. 92 Y. Li and K.N. Houk,J. Am.Chem. SOC. 1993 115 7478. Theoretical Organic Chemistry applied state-of-the-art calculations to this problem and come down very firmly along the lines of the generally (but still nut universalIy held) view that the process is indeed concerted for the reaction between butadiene (10)and ethylene (I 1)(Scheme 3). Their calculations on the reactants concerted transition state (TS) biradical TS and biradical intermediate for the reaction between butadiene and ethylene are sum-marized in Table 2. -L Buadical Scheme 3 The difference in energy of 5.8 kcal rno1-l between the concerted and stepwise transition structures calculated using the 3-21G basis set falls to 3.4 kcaI mol- when zero-point energies are taken into account. For the 6-3tG* basis set the difference falls even further to 0.5kcal mol-* ;thus when entropy is taken into account the biradical process is predicted to be more favourable.Since the CASSCF calculations include six electrons in six active orbitals a good representation was indeed given. However the MCSCF method overestimates the stability of biradical species. The more reliable quadratic CI results favour concerted pathways and the overall conclusion based on several pieces of evidence is given in the final column of the above table. As discussed elsewhere in this article it should be noted that sotvation may have a marked effect on these relative energies and also that substituents may affect the pathway for analogues of either reactant in this reaction. For butadiene dirnerization a concerted mechanism is probably preferred but the calculations inchding eight electrons in eight active orbitals are not sufficiently accurate to make such definitive statements.This particular controversy probably has a few more years to run! There have been fewer studies of hetero-Diels-Alder reactions. The same group has studied the reaction of ten dienophiles uia seventeen transition structures by assuming the reaction is concerted but not necessariIy synchrono~s.~~ The reactivity differences and stereochemical preferences are discussed on the basis of the geometries and relative energies of the transition structures. It was shown that the lone pair orbitals on the dienophiIes can exert a large destabilizing influence on the filled orbitals of the butadiene and that these lone-pair-n-electron interactions can have a large influence on stereoselectivities.In some cases it is found that solvation by dichloromethane modelled by the Onsager reaction field can actually stabilize the reactants more than the transition state despite the large dipole moment in the transition state. Likewise there have been relatively few studies ofinverse Diels-Alder reactions. An interesting cjairn to emerge from the reaction shown in Scheme 4 is that the regioselectivity of the reaction is controlled primarily by the (estimated) attractive 93 M.A. McCarrick Y.D. Wu,and K.N.Houk J. Org. Chem. 1993 I,3330. Table 2 Relative energies (kcal mol -of reactants transition structures and intermediates calculated and determined experimentally for the reaction of ethylene with butadiene (Scheme 3) CASSCF/ CASSCFj Molecples 3-216 6-31G* UQCISD(T) RQCISD(T) Expt.Conclusions React ants 0.0 0.0 0.0 0.0 0.0 Concerted TS 37.3 43.8 29.4 25.5 25.1 & 2 0 Biradical TS 43.1 45.7 39.2 35.7 5 Biradical intermediate 41.1 40.7 30.3 29.8 27.3 3 Theoretical Organic Chemistry 65 dispersion interactions between the phenyI rings of the reactants.94 Semiempirical and Hartree-Fock methods are nut able to take these factors into account (though molecular mechanics based transition state studies could -see below) and hence the treatment at the MP2 level was necessary to explain the experimental findings. P P + -+ H-CrC-Pb Scheme 4 An interesting AM 1semiempirical study (with limited configuration interaction) of the reaction between acrylonitrile (12)and allene (13) (Scheme5) has been undertaken to help to explain the origin of the kinetic isotope effect observed with gem-dide~terioallene.’~ It is concluded that the kinetic isotope effect is due to the slower rotation of the heavier CD group as it approaches the second transition structure in the stepwise biradical reaction.NC H D “I D Scheme 5 Other interesting cycloaddition studies are reported in references 96-100. Competition Between SN2and h2 Mechanisms-In a high level (MP2/6-3 IG*) study of the effect of methyl substitution on the energetics of S,2 sabstitution uersus E2 94 J. Cioslowski J. Sauer J. Hetzenegger,T. Karcher and T.Hierstetter,J.Am. Chem.SOC.,1993,115,1353 95 E.A. Halevi and M. Wolfsberg .I.Chem. SOC.Perkin Trans. 2 1993,1493. 96 D.A. Smith and C. W. UIrner J. Org. Chem. 1993,58,4118. ” R.Sustmann W. Sicking and R. Buisgen J. Org. Chem. 1993 58 82. 98 S. Yamabe S. Kawajiri T. Minato and T. Machiguchi J. Org. Chem. 1993,58 1122. 99 F. P.Cossio J. M. UgaIde X. Lopez,B. Lecea and C. Palomo J. Am. Chem. Soc. 1993,115,995. loo B.E.Thomas J. D. Evanseck and K.N. Houk J. Am. Chem. Soc. 1993,115,4165. C. A. Reynolds elimination in the reaction of F-with (CH,),CHCl or CH,CH2CH,C1 Gronert has shown101 that the syn transition state for E2 elimination adopts a synclinal rather than a syn periplanar geometry (see also reference 102). The conditions under which syn periplanar transition states would be expected are postulated to be unsubstituted systemsor systems with endothermic or marginally exothermic eliminations and hence late transition structures.The effect of methyl substitution upon the above energetics is discussed in terms of the balance between the stenc effect of the methyl group and its ability to spread charge in both the transition state and the initial ion-dipole complexes. Aspects of this problem have also been addressed above; see reference 103. Hynes and coworkers'D2 have presented an interesting observation :for the reaction (CH,),CX + (CH3)&*X-(X = C1 Br I) their calculations predict that solvent stabiIization for the ionization actually decreases with increasing solvent polarity and yet the actual free energy also decreases (ie.transition state ionic character and separation decrease) in complete contrast to conventional explanations. The calculations are based on a two-state valence-bond model and the aprotic solvents are modelled using a continuum method; the calculated activation free energies in all solvents agree to within 5 1.5 kcal mol- of experiment. Lee and coworkers'05 have studied the effects of substituents on the S,1 reactivities ofcationic benzyl and mono and disubstituted benzhydryl with neutral leaving groups. It is interesting to note that a number of excellent linear relationships have been found between the enthalpy of activation and the reaction enthalpy the length in the ground state of the bond being broken and change in the length of this bond as it goes to the transition state.Hybrid Molecular MechanicaI-Quantum Mechanical Models of the Transition State.-Fuli quantum mechanical determinations of transition state structures are now fairly commonplace but they are not always routine and can therefore be time consuming. One way to increase the applicability of transition-state modelling to real problems in organic synthesis is to model the transition state using molecular mechanics usually using the MM2 force-field. This approach has been very successful in rationalizing stereoselectivity. Recent examples of this approach include crotyl- borane addition to aldehydes,lo6 the aldol reaction of en01 b~rates,"~ and the synthesis of lor,2j3,25-trihydroxyvitaminD .lo8 Photochemistry.-In a study of the photochemistry of butadiene Olivucci et ~1.'~~ have shown that the traditional view that excitation from the ground 'A; state to the first excited state 2A',,is followed by decay from the avoided crossing region to the ground state and that the efficiency of the decay is determined by the gap between the ground state; the excited state potential needs to be replaced by a mechanism where the S.Gronert J. Am. Chem. Soc. 1993 115 452. lo' F. M. Bickelhaupt L.J. Dekoning and N. M. M. Nibbering J. Org. Chem. 1993 58 2436. Io3 F. M. Bickeihaupt E. J. Baerends,N. M.M. Nibbering and T. Ziegfer,J.Am. Chem.Soc. 1993,115,9160. Io4 J.R. Mathis H.J. Kim,and J.T.Hynes J. Am. Chem. Soc. 1993 115 8248. D. S.Chung C. K.Kim B.S. 'Lee and I. Lee Tetrahedron,1993,49 8359. lo6 A. Vulpetti M. Gardner C. Gennari A. Bernardi J. M. Goodman and 1. Paterson J. Org.Chem. 1993 58 1711. lo7 A. VuIpetti A. Bernardi C.Gennari J. M.Goodman and I. Paterson Tetrahedron,1993 49 685. Io8 T. Takahashi M. Nakazawa Y.Sakamoto and K. N. Houk Tetrahedron Lett. 1993,34,4075. Io9 M.Ulivucci I.N. Ragazos F. Bernardi and M.A. Robb,J. Am. Chem. SOC.,1993 115,3710. Theoretical Organic Chemistry funnel from the excited state to the ground state is actually a conical intersection. Since at the conical intersection the energy of the excited state and ground state are equal the processes are fuIly efficient. The criteria for locating conical intersections are discussed; the process involves a constrained optimization on the excited state surface.Rather than several avoided crossings giving different products a single conical intersection connecting the excited state to the ground state governs the formation of all products; the decay from the conical intersection to the ground state occurs within a single vibration. The work was based on hybrid molecular mechanics-valence bond calculations which allowed for the rapid calcuIation of energies over a grid of points. The hybrid calculations are however fully supported by MCSCF calculations with a 4-31G basis set. In a similar study using the MCSCF/4-31G method throughout PaImer et ai. have studied the minima transition structures and conical intersections on the So S, and S surface of benzene which includes the Kekule forms of benzene along with Dewar benzene benzvalene prismane and the bicyclopropenyl structure (Figure 2).A wonderfully complex set of stationary points and conical intersections are presented. For example on the S surface the only minimum is a D, structure anti-Kekule valence-bond isomer (8) connected to a prefulvene-like transition state (h); this is linked to a conical intersection which connects to the ground state. The mechanism for the photosensitized cycloaddition reaction of penta- 1,4-diene has been studied using the MP2/6-31G* method.'" The mechanism proceeds via an inter-system crossing followed by rearrangement on So. Minimum energy crossing points between T,and So were located and it was found that the preferred route involved the triplet cyclic intermediate crossing to So followed by internal rotation of the terminal methylene group; the latter change involved relatively minor changes in the skeletal structure.Tunnelling.-Calculation of the transition state geometry is not always sufficient for inferring the rate of reaction; dynamics calculations and tunnelling corrections may also be required. In an application on the 1,5-sigmatropic rearrangement in cis-penta-1,3-diene Liu et al. have shown that the potential energy surface for dynamics can be calculated 'on-the fly' (i.e.by direct dynamics) using the semiempirical molecular orbital program MOPAC."' The advantage of direct dynamics is that it avoids the analytical representation of the potential energy function; it is this fitting problem that has prevented the application of modern dynamics theory to interesting organic and biochemical reactions.The calculations were based on variational transition-state theory (because this reduces the dynamics to contributions from reasonably localized regions of configurational space) including multidimensional semiclassical tunneling corrections. They show that tunnelling only occurred in a small region of the saddle point and that tunnelling can indeed account for the strong temperature dependence observed in the experimental kinetic isotope effect as well as accounting for the magnitude of the kinetic isotope effect. Repeating the calculations without tunnelling leads to significant errors of about 6eu in the entropy of activation and of about 4kcalmol-' in the enthalpy of activation.Although there were I. J. Palmer I.N. Ragazos F. Bernardi M. Otivucci and M. A. Robb J. Am. Chem. Soc. 1993,115,673. 'I1 M. Ohsaku N. Koga and K. Morokuma J. Chem. Soc. Perkin Trans. 2 1993 71. Y.P.Liu G.C. Lynch T.N. Truong,D. H.Lu,D. G.TruhIar and B.C. Garrett 1.Am. Chem. Soc. 1993 115 240408. C. A. Reynolds Figure 2 (Reproduced with permission from J.Am. Chem.SOC.,1993,115,673.01993American Chemical Society) differences in the results obtained with the AM1 PM3 and MIND0/3 Hamiltonians all three gave essentially the same results. The proton shift from CD,H to CF has been followed in a similar manner," -except that here it was necessary to obtain AM1 parameters specific to this reaction because the predicted enthalpy of reaction was too large and this would have resulted in the calculated barrier being erroneously too asymmetric.(The parameters were fitted to both kinetic and thermodynamic data subject to the restriction that parameters did not change by more than loo/,.) 5 Neural Networks The use of theory to predict chemical reactivity with great reliability is a clear yet distant goal for many theoreticians. Intrinsic errors in many of the models still in use ensure that much work remains to be done. In some cases an expert chemist could '13 Y.P.Liu D. H. Lu,A. Gonzalezlafont D.G. Truhlar and B.C. Garrett J. Am. Chem. SOC.,1993,115 7806. Theoretical Organic Chemistry make more reliable predictions than theory.With this in mind artificial neural networks are being applied with increasing frequency to chemical problems. Thearticle by Simon et on the use of neutral networks to predict which bonds in aliphatic molecules will break preferentially is a good example that shows where quantum chemical calculations may not be the most powerful predictive tool. However the neural network is able to learn the relationship between a number of empirical physical chemical descriptors (inputs) and reactivity (output). Schematically the neural network usually has the foIlowing form show in Figure 3 (this particular network was used to determine one-electron electrode potentials at pH 7from semiempirica1 heats of formation and free energies of hydration ).I Output Layer Hidden Layer Input Layer Figure 3 The inputs are initially multiplied by a (random) weight.The sum of the weighted inputs is then passed through a transfer function at the nodes in the hidden layer the output of which is summed to give the output. If this total output is different to that desired the weights are adjusted. When a given set of weights reproduces the desired output fur a set of data the network may be considered to have learned the underlying relationship -assuming one exists. A full introduction (specific to chemistry) is given in the excellent review' l6 and textbook117 by Zupan and Gasteiger and in the review by Rouvray.' ' The range of chemical problems that can be tackled using neural networks is probably limited only by the imagination and the availability of data suitable fur training.Recent applications include the classification of inductive and resonance effects,' l9 the prediction of I3C NMR chemical shifts,120,121 QSGR,lz2 IR spectra 'IA V. Simon J. Gasteiger and J. Zupan J. Am. Chem. SOC. 1993 115 9148. J. J. Wolfe J. D. Wright C.A. Reynolds and A.C.G. Saunders Anti-Cancer Drug Design 1994,9 85. 'I6 J. Gasteiger J. Zupan Angew. Chem. Int. Ed. Engl. 1993,32 503. 'I7 J. Zupan and J. Gasteiger 'Neural Networks for Chemists' VCH Weinheim 1993. D.H. Rouvray Ckem. Br. 1993 29 495. 'Ip V. Kvasnicka S. Sklenak and J. Pospichat J. Am. Chern. SOC. 1993,115 1495. ''* J.P. Doucet A. Panaye E. Feuilleaubous and P. Ladd 1.Chem. In$ Cornput. Sci. 1993 33 320. G.M.J.West J. Chem. In$ Comp. Sci. 1993 33 577. A.C.G. Good,S.-S. So and W.G. Richards J. Med. Chem. 1993,36 433. C.A. Reynolds interpretati~n,'~~ and HPLC retention times. The protein structure predicti~n,'~~-~*~ neural network inputs may include descriptors calculated quantum mechanically. 6 Conclusions It is appropriate to apologize to the authors of the many excellent works that have nut been included in this review due to oversight restrictions on space or otherwise but which show that theoretical organic chemistry remains a very healthy branch of chemistry. Q.C. Vanest P.J. Schoenrnakers,J. R. M. Smits and W. P.M. Nijssen Vib.Spect. 1993 4 263. 12* B. Rost and C. Sander J. Mol. Biol. 232 584. 12' G. Schneider and P.Wrede Angew. Chem.Int. Ed. Engl. 1993,32,1141.