Molecular dynamics study of the tautomeric equilibrium in the 4-nitro- and 2,4,6-trichloro derivatives of 2-(N,N-dialkyloaminomethyl)phenol

 Molecular dynamics thermodynamic integration (MDTI) method and quantum chemical calculations at the density functional theory B3LYP 6-31+(d,p) level, which included the Tomasi model of the solvent reaction field, were applied to study the tautomeric equilibrium of Mannich base in methanol solution. The values obtained for the free-energy difference are in good agreement with experimental data. However, the results from quantum mechanical calculations were not as good as the results of MDTI simulations owing to inappropriate treatment of intermolecular hydrogen bonds between the solute molecule and the first shell of solvent molecules in the Tomasi model of the solvent reaction field. The radial distribution functions between solute atoms and solvent atoms confirmed the formation of hydrogen bonds between the solute molecule and surrounding methanol molecules and indicated that the zwitterionic form is associated more with an organized solvent structure at the level of the first solvation shell than is the molecular form. Received: 26 April 2002 / Accepted: 9 September 2002 / Published online: 31 March 2003     

Recent advances in quantum mechanical/molecular mechanical calculations of enzyme catalysis: hydrogen tunnelling in liver alcohol dehydrogenase and inhibition of elastase by α-ketoheterocycles

 Hybrid quantum mechanical (QM)/molecular mechanical (MM) calculations are used to study two aspects of enzyme catalysis, Kinetic isotope effects associated with the hydride ion transfer step in the reduction of benzyl alcohol by liver alcohol dehydrogenase are studied by employing variational transition-state theory and optimised multidimensional tunnelling. With the smaller QM region, described at the Hartree–Fock ab initio level, together with a parameterised zinc atom charge, good agreement with experiment is obtained. A comparison is made with the proton transfer in methylamine dehydrogenase. The origin of the large range in pharmacological activity shown by a series of α-ketoheterocycle inhibitors of the serine protease, elastase, is investigated by both force field and QM/MM calculations. Both models point to two different inhibition mechanisms being operative. Initial QM/MM calculations suggest that these are binding, and reaction to form a tetrahedral intermediate, the latter process occurring for only the more potent set of inhibitors. Recieved 3 October 2001 / Accepted: 6 September 2002 / Published online: 31 January 2003 Contribution to the Proceedings of the Symposium on Combined QM/MM Methods at the 222nd National Meeting of the American Chemical Society, 2001 Correspondence to: I. H. Hillier Acknowledgements. We thank EPSRC and BBSRC for support of the research and D.G. Truhlar for the use of the POLYRATE code.     

Exploring the quantum mechanical/molecular mechanical replica path method: a pathway optimization of the chorismate to prephenate Claisen rearrangement catalyzed by chorismate mutase

 A replica path method has been developed and extended for use in complex systems involving hybrid quantum/classical (quantum mechanical/molecular mechanical) coupled potentials. This method involves the definition of a reaction path via replication of a set of macromolecular atoms. An “important” subset of these replicated atoms is restrained with a penalty function based on weighted root-mean-square rotation/translation best-fit distances between adjacent (i±1) and next adjacent (i±2) pathway steps. An independent subset of the replicated atoms may be treated quantum mechanically using the computational engine Gamess-UK. This treatment can be performed in a highly parallel manner in which many dozens of processors can be efficiently employed. Computed forces may be projected onto a reference pathway and integrated to yield a potential of mean force (PMF). This PMF, which does not suffer from large errors associated with calculated potential-energy differences, is extremely advantageous. As an example, the QM/MM replica path method is applied to the study of the Claisen rearrangement of chorismate to prephenate which is catalyzed by the Bacillus subtilis isolated, chorismate mutase. Results of the QM/MM pathway minimizations yielded an activation enthalpy ΔH ^†† of 14.9 kcal/mol and a reaction enthalpy of −19.5 kcal/mol at the B3LYP/6-31G(d) level of theory. The resultant pathway was compared and contrasted with one obtained using a forced transition approach based on a reaction coordinate constrained repeated walk procedure (ΔH ^†† =20.1 kcal/mol, ΔH _rxn = −20.1 kcal/mol, RHF/4-31G). The optimized replica path results compare favorably to the experimental activation enthalpy of 12.7±0.4 kcal/mol. Received: 16 December 2001 / Accepted: 6 September 2002 / Published online: 8 April 2003 Contribution to the Proceedings of the Symposium on Combined QM/MM Methods at the 22nd National Meeting of the American Chemical Society, 2001. Correspondence to: H.L. Woodcock e-mail: hlwood@ccqc.uga.edu Acknowledgements. The authors thank Eric Billings, Xiongwu Wu, and Stephen Bogusz for helpful discussions and related work. The authors also show grateful appreciation to The National Institutes of Health and The National Science Foundation for support of the current research.     

A theoretical investigation of the mechanism for the reaction between a quebrachitol derivative and N3−

The reaction between a mesylated compound and sodium azide was previously studied experimentally at a temperature of 140 °C using dimethylformamide as a solvent. The product was assigned on the basis of the analysis of the NMR spectra. In this work semiempirical (AM1 and PM3), ab initio (Hartree–Fock and MP2) and density functional theory (BLYP functional) quantum mechanical calculations, using continuum models for describing the solvent effect, were carried out for this process to better understand the reaction mechanism. Three distinct mechanisms involving a carbocation and epoxide intermediates, and a transition-state structure for direct attack of the N₃ ⁻ species to the reactant were investigated. The theoretically calculated preferred reaction pathway passing through an epoxide intermediate agrees nicely with the experimental proposal, providing a good example of where theoretical calculations can be of great help to definitively elucidate the reaction mechanism. Received: 10 July 2001 / Accepted: 20 December 2001 / Published online: 8 April 2002     

Semiempirical QM/MM potential with simple valence bond (SVB) for enzyme reactions. Application to the nucleophilic addition reaction in haloalkane dehalogenase

 We present a method for the correction of errors in combined QM/MM calculations using a semiempirical Hamiltonian for enzyme reactions. Since semiempirical models can provide a reasonable representation of the general shape of the potential energy surface for chemical reactions, we introduce a simple valence bond-like (SVB) term to correct the energies at critical points on the potential energy surface. The present SVB term is not a stand-alone potential energy function, but it is used purely for introducing small energy corrections to the semiempirical Hamiltonian to achieve the accuracy needed for modeling enzymatic reactions. We show that the present coupled QM-SVB/MM approach can be parameterized to reproduce experimental and ab initio results for model reactions, and have applied the PM3-SVB/MM potential to the nucleophilic addition reaction in haloalkane dehalogenase. In a preliminary energy minimization study, the PM3-SVB/MM results are reasonable, suggesting that it may be used in free energy simulations to assess enzymatic reaction mechanism. Received: 1 November 2001 / Accepted: 6 September 2002 / Published online: 19 February 2003 Contribution to the Proceedings of the Symposium on Combined QM/MM Methods at the 222nd National Meeting of the American Chemical Society, 2001 Correspondence to: Lakshmi S. Devi-Kesavan e-mail: kesavan@chem.umn.edu Acknowledgments. The work is partially supported by the NIH and the NSF.     

The search for stationary points on a quantum mechanical/molecular mechanical potential-energy surface

 We propose a methodology to locate stationary points on a quantum mechanical/molecular mechanical potential-energy surface. This algorithm is based on a suitable approximation of an initial full Hessian matrix, either a modified Broyden–Fletcher–Goldfarg–Shanno or a Powell update formula for the location of, respectively, a minimum or a transition state, and the so-called rational function optimization. The latter avoids the Hessian matrix inversion required by a quasi-Newton–Raphson method. Some examples are presented and analyzed. Received: 16 July 2001 / Accepted: 9 October 2001 / Published online: 9 January 2002     

Dipole–reaction field interaction model for the solvent reorganization energy and its application to the benzoquinone–benzoquinone anion radical system

 Based on the spherical cavity approximation and the Onsager model, a dipole–reaction field interaction model has been proposed to elucidate the solvent reorganization energy of electron transfer (ET). This treatment only needs the cavity radius and the solute dipole moment in the evaluation of the solvent reorganization energy, and fits spherelike systems well. As an application, the ET reaction between p-benzoquinone and its anion radical has been investigated. The inner reorganization energy has been calculated at the level of MP2/6–31+G, and the solvent reorganization energies of different conformations have been evaluated by using the self-consistent reaction field approach at the HF/6–31+G level. Discussions have been made on the cavity radii and the values are found to be reasonable when compared with the experimental ones of some analogous intramolecular ET reactions. The ET matrix element has been determined on the basis of the two-state model. The fact that the value of the ET matrix element is about 10 times larger than RT indicates that this ET reaction can be treated as an adiabatic one. By invoking the classical Marcus ET model, a value of 4.9 × 10⁷M⁻¹s⁻¹ was obtained for the second-order rate constant, and it agrees quite well with the experimental one. Received: 19 October 2001 / Accepted: 17 January 2002 / Published online: 3 May 2002     

The performance of the rapid estimation of basis set error and correlation energy from partial charges method on new molecules of the G3/99 test set

Experimental enthalpies of formation have been approximated using single-point Hartree–Fock (HF)–self-consistent-field (SCF) total energies plus the rapid estimation of basis set error and correlation energy from partial charges (REBECEP) energy corrections. The energy corrections are calculated from the HF–SCF partial atomic charges and optimized atomic energy parameters. The performance of the method was tested on 51 closed-shell neutral molecules (50 molecules from the G3/99 thermochemistry database plus urea, composed of H, C, N, O, and F atoms). The predictive force of the method is demonstrated, because these larger molecules were not used for the optimization of the atomic parameters. We used the earlier RECEP-3 [HF/6-311+G(2d,p)] and REBECEP [HF/6-31G(d)] atomic parameter sets obtained from the G2/97 thermochemistry database (containing small molecules) together with natural population analysis and Mulliken partial charges. The best results were obtained using the natural population analysis charges, although the Mulliken charges also provide useful results. The root-mean-square deviations from the experimental enthalpies of formation for the selected 51 molecules are 1.15, 3.96, and 2.92 kcal/mol for Gaussian-3, B3LYP/6-11+G(3df,2p), and REBECEP (natural population analysis) enthalpies of formation, respectively (the corresponding average absolute deviations are 0.94, 7.09, and 2.27 kcal/mol, respectively). The REBECEP method performs considerably better for the 51 test molecules with a moderate 6-31G(d) basis set than the B3LYP method with a large 6-311+G(3df,2p) basis set. Received: 10 March 2001 / Accepted: 5 July 2001 / Published online: 11 October 2001     

Comparison of solvent reaction field representations

 Alternative ways are examined for representing a reaction field to treat the important effects of long-range electrostatic interaction with a solvent in electronic structure calculations on the properties of a solute. Several extant boundary element methods for approximate representation of the solvent reaction field in terms of surface charge distributions are considered, and analogous new methods for approximate representation in terms of surface dipole distributions are introduced. Illustrative computational results are presented on representative small neutral and ionic solutes to evaluate the relative accuracy of various methods. Received: 2 July 2001 / Accepted: 10 September 2001 / Published online: 19 December 2001     

Monte Carlo simulation of 2-ethoxyethanol in continuum configurational biased procedure: conformational analysis and association in aqueous and non-aqueous media

 Monte Carlo simulations have been carried out for 2-ethoxyethanol (C₂E₁) in isothermal-isobaric ensemble (NPT) at different temperatures and 1 atm pressure with a continuum configurational biased procedure in water and chloroform media. Hydrogen bond bridges were formed between adjacent oxygen atoms in C₂E₁ (CH₃CH₂OCH₂CH₂OH) through water molecules. We also found that the stable conformers of C₂E₁ in water and CHCl₃ are different and the effect of temperature on solute-solvent interaction energies is considerable. The self-association of C₂E₁ in aqueous and nonaqueous media has been studied by statistical perturbation theory, and the relative free energy has been obtained at different reaction coordinates by double-wide sampling method. Two minima were found in water solvent in the potential of mean force (PMF), corresponding to the contact and solvent-separated pairs, but only one minimum was found in CHCl₃ solvent corresponding to a contact pair complex. Received: 18 January 2001 / Accepted: 22 October 2001 / Published online: 21 January 2002     

Accurate thermochemistry from corrected Hartree–Fock results: rapid estimation of nearly experimental quality total energy using the small 6-31G(d) basis set

Gaussian-3 ground-state total electronic energies have been approximated using single point 6-31G(d) basis set Harteee–Fock self-consistent-field (HF-SCF) total energies and partial charges based on our earlier rapid estimation of correlation energy from partial charges method. Sixty-five closed-shell neutral molecules (composed of H, C, N, O, and F atoms) of the G2/97 thermochemistry database were selected for the present study. The main feature in this work is that the␣basis set error has been treated by the least squares fit of rapid estimation of basis set error and correlation energy from partial charges (REBECEP) atomic parameters. With these parameters a rather accurate closed-shell ground-state electronic total energy can be obtained from a small basis set HF-SCF calculation in the vicinity of stationary points. The average absolute deviation of the best REBECEP enthalpies of formation from the experimental enthalpies of formation is 1.39 kcal/mol for the test set of 65 enthalpies of neutral molecules. Received: 11 December 2000 / Accepted: 6 February 2001/Published online: 11 October 2001     

Investigation of the S<Subscript>0</Subscript>S<Subscript>1</Subscript> excitation in bacteriorhodopsin with the ONIOM(MO:MM) hybrid method

 We have investigated the S₀ and S₁ electronic states in bacteriorhodopsin using a variety of QM/MM levels. The decomposition of the calculated excitation energies into electronic and electrostatic components shows that the interaction of the chromophore with the protein electric field increases the excitation energy, while polarization effects are negligible. Therefore, the experimentally observed reduction in excitation energy from solution phase to protein environment (the Opsin shift) does not come from the electrostatic interaction with the protein environment, but from either the interaction ofthe chromophore with the solvent or counter ion, or structural effects. Our high-level ONIOM(TD– B3LYP:Amber) calculation predicts the excitation energy within 8 kcal/mol from experiment, the discrepancy probably being caused by the neglect of polarization of the protein environment. In addition, we have shown that the level of optimization is extremely critical for the calculation of accurate excitation energies in bacteriorhodopsin. Received: 13 October 2001 / Accepted: 6 September 2002 / Published online: 3 February 2003 Contribution to the Proceedings of the Symposium on Combined QM/MM Methods at the 222nd National Meeting of the American Chemical Society, 2001 Correspondence to: K. Morokuma e-mail: morokuma@emory.edu     

Implementation of solvent reaction fields for electronic structure

 Methods are described to incorporate solvent reaction field effects into solute electronic structure calculations. Included are several old and new approaches based on approximate solutions of Poisson's equation through boundary element methods, wherein the solutions are represented in terms of certain apparent surface charge or apparent surface dipole distributions. Practical algorithms to set up and solve the requisite equations are described and implemented in a new general reaction field computer program. Illustrative computational results are presented to show the performance of the program. Received: 2 July 2001 / Accepted: 11 September 2001 / Published online: 19 December 2001     

Ab initio and density functional theory studies on the mechanism of nucleophilic vinylic substitution of 4<Emphasis Type="Italic">H</Emphasis>-pyran-4-one and 2-methyl-4<Emphasis Type="Italic">H</Emphasis>-pyran-4-one with ammonia

 Nucleophilic vinylic substitutions of 4H-pyran-4-one and 2-methyl-4H-pyran-4-one with ammonia were calculated by the B3LYP method using the 6-31G(d,p) basis set. Bulk solvent effects of aqueous solution were estimated by the polarized continuum and Poisson–Boltzmann self-consistent reaction field models using the 6-311+G(d,p) basis set. In the gas phase different mechanisms were found for the two reaction systems calculated. The reaction of 4H-pyran-4-one proceeds through enol, whereas a feasible path for the less reactive 2-methyl-4H-pyran-4-one is the mechanism through a keto intermediate. Addition of ammonia in concert with proton transfer is the rate-determining step ofthe reaction. The mechanism proceeding either by a bimolecular nucleophilic substitution (S_N2) or by one involving a tetrahedral zwitterionic intermediate is shown to be unlikely in the gas phase or nonpolar solution. The effects of bulk solvent not only consist in a reduction of the various activation barriers by about 25–40 kJ mol⁻¹ but also in a change in the reaction mechanism. Received 26 May 2002 / Accepted 26 July 2002 / Published online: 14 February 2003     

Partial Hessian vibrational analysis: the localization of the molecular vibrational energy and entropy

The partial Hessian vibrational analysis (PHVA), in which only a subblock of the Hesssian matrix is diagonalized to yield vibrational frequencies for partially optimized systems, is extended to the calculation of vibrational enthalpy and entropy changes for chemical reactions. The utility of this method is demonstrated for various deprotonation reactions by reproducing full HVA values to within 0.1–0.4 kcal/mol, depending on the number atoms included in the PHVA. When combined with the hybrid effective fragment potential method [Gordon MS, et al. (2001) J Phys Chem A 105:293–307], the PHVA method can provide (harmonic) free-energy changes for localized chemical reactions in very large systems. Received: 21 September 2001 / Accepted: 30 October 2001 / Published online: 22 March 2002     

Solvent effects on the electronic absorption spectrum of formamide studied by a sequential Monte Carlo/quantum mechanical approach

Sequential Monte Carlo/quantum mechanical calculations are performed to study the solvent effects on the electronic absorption spectrum of formamide (FMA) in aqueous solution, varying from hydrogen bonds to the outer solvation shells. Full quantum-mechanical intermediate neglect of differential overlap/singly excited configuration interaction calculations are performed in the supermolecular structures generated by the Monte Carlo simulation. The largest calculation involves the ensemble average of 75 statistically uncorrelated quantum mechanical results obtained with the FMA solute surrounded by 150 water solvent molecules. We find that the n → π* transition suffers a blueshift of 1,600 cm⁻¹ upon solvation and the π → π* transition undergoes a redshift of 800 cm⁻¹. On average, 1.5 hydrogen bonds are formed between FMA and water and these contribute with about 20% and about 30% of the total solvation shifts of the n → π* and π → π* transitions, respectively. The autocorrelation function of the energy is used to sample configurations from the Monte Carlo simulation, and the solvation shifts are shown to be converged values. Received: 14 March 2002 / Accepted: 3 April 2002 / Published online: 24 June 2002     

Evaluation of an ab initio quantum mechanical/molecular mechanical hybrid-potential link-atom method

 Hybrid potentials have become a common tool in the study of many condensed-phase processes and are the subject of much active research. An important aspect of the formulation of a hybrid potential concerns how to handle covalent bonds between atoms that are described with different potentials and, most notably, those at the interface of the quantum mechanical (QM) and molecular mechanical (MM) regions. Several methods have been proposed to deal with this problem, ranging from the simple link-atom method to more sophisticated hybrid-orbital techniques. Although it has been heavily criticized, the link-atom method has probably been the most widely used in applications, especially with hybrid potentials that use semiempirical QM methods. Our aim in this paper has been to evaluate the link-atom method for ab initio QM/MM hybrid potentials and to compare the results it gives with those of previously published studies. Given its simplicity and robustness, we find that the link-atom method can produce results of comparable accuracy to other methods as long as the charge distribution on the MM atoms at the interface is treated appropriately. Received: 27 September 2002 / Accepted: 21 October 2002 / Published online: 8 January 2003 Correspondence to: M. J. Field e-mail: mjfield@ibs.fr Acknowledgements. The authors thank the Institut de Biologie Structurale – Jean-Pierre Ebel, the Commissariat à l'Energie Atomique and the Centre National de la Recherche Scientifique for support of this work.     

Quantum mechanics and mixed quantum mechanics/molecular mechanics simulations of model nerve agents with acetylcholinesterase

 The accurate modeling of biological processes presents major computational difficulties owing to the inherent complexity of the macromolecular systems of interest. Simulations of biochemical reactivity tend to require highly computationally intensive quantum mechanical methods, but localized chemical effects tend to depend significantly on properties of the extended biological environment – a regime far more readily examined with lower-level classical empirical models. Mixed quantum/classical techniques are gaining in popularity as a means of bridging these competing requirements. Here we present results comparing two quantum mechanics/molecular mechanics implementations (the SIMOMM technique of Gordon et al. as implemented in GAMESS, and the ONIOM technique of Morokuma et al. found in Gaussian 98) as performed on the enzyme acetylcholinesterase and model nerve agents. This work represents part of the initial phase of a DoD HPCMP Challenge project in which we are attempting to reliably characterize the biochemical processes responsible for nerve agent activity and inhibition, thereby allowing predictions on compounds unrelated to those already studied. Received: 10 October 2001 / Accepted: 13 November 2002 / Published online: 1 April 2003 Contribution to the Proceedings of the Symposium on Combined QM/MM Methods at the 222nd National Meeting of the American Chemical Society, 2001 Correspondence to: M. M. Hurley e-mail: hurley@arl.army.mil     

Maxwell–Cartesian spherical harmonics in multipole potentials and atomic orbitals

 The nature of the Maxwell–Cartesian spherical harmonics S ⁽ⁿ⁾ _K and their relation to tesseral harmonics Y _nm is examined with the help of “tricorn arrays” that display the components of a totally symmetric Cartesian tensor of any rank in a systematic way. The arrays show the symmetries of the Maxwell–Cartesian harmonic tensors with respect to permutation of axes, the traceless properties of the tensors, the linearly independent subsets, the nonorthogonal subsets, and the subsets whose linear combinations produce the tesseral harmonics. The two families of harmonics are related by their connection with the gradients of 1/r, and explicit formulas for the transformation coefficients are derived. The rotational transformation of S ⁽ⁿ⁾ _K functions is described by a relatively simple Cartesian tensor method. The utility of the Maxwell–Cartesian harmonics in the theory of multipole potentials, where these functions originated in the work of Maxwell, is illustrated with some newer applications which employ a detracer exchange theorem and make use of the partial linear independence of the functions. The properties of atomic orbitals whose angular part is described by Maxwell–Cartesian harmonics are explored, including their angular momenta, adherence to an Uns?ld-type spherical symmetry relation, and potential for eliminating an angular momentum “contamination” problem in Cartesian Gaussian basis sets. Received: 9 July 2001 / Accepted: 7 September 2001 / Published online: 19 December 2001     

Density functional theory study of the mechanism of the proline-catalyzed intermolecular aldol reaction

Transition structures associated with the C-C bond-formation step of the proline-catalyzed intermolecular aldol reaction between acetone and isobutyraldehyde have been studies using density functional theory methods at the B3LYP/6-31G** computational level. A continuum model has been selected to represent solvent effects. For this step, which is the stereocontrolling and rate-determining step, four reactive channels corresponding to the syn and anti arrangement of the active methylene of the enamine relative to the carboxylic acid group of l-proline and the re and si attack modes to both faces of the aldehyde carbonyl group have been analyzed. The B3LYP/6-31G** energies are in good agreement with experiment, allowing us to explain the origin of the catalysis and stereoselectivity for these proline-catalyzed aldol reactions. Received: 2 April 2002 / Accepted: 18 July 2002 / Published online: 11 October 2002 Acknowledgements. This work was supported by research funds provided by the Ministerio de Educación y Cultura of the Spanish Government by DGICYT (project PB98–1429). All the calculations were performed on a Cray–Silicon Graphics Origin 2000 of the Servicio de Informática de la Universidad de Valencia. We are most indebted to this center for providing us with computer capabilities. Correspondence to: L. R. Domingo e-mail: domingo@utopia.uv.es