Parameterization of semiempirical methods to treat nucleophilic attacks to biological phosphates: AM1/d parameters for phosphorus

 This paper reports a new AM1/d model for phosphorus that can be used to model nucleophilic attack of phosphates relevant for biological phosphate hydrolysis reactions. The parameters were derived from a quantum dataset calculated with hybrid density-functional theory [B3LYP/6-311++G(3df,2p)//B3LYP/6-31++G(d,p)] of phosphates and phosphoranes in various charge states, and on transitions states for nucleophilic attacks. A suite of non-linear optimization methods is outlined for semiempirical parameter development based on integrated evolutionary (genetic), Monte Carlo simulated annealing and direction set minimization algorithms. The performance of the new AM1/d model and the standard AM1 and MNDO/d models are compared with the density-functional results. The results demonstrate that the strategy of developing semiempirical parameters specific for biological reactions offers considerable promise for application to large-scale biological problems. Received: 15 January 2002 / Accepted: 6 September 2002 / Published online: 28 March 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: D.M. York e-mail: york@chem.umn.edu Acknowledgements. D.M.Y. is grateful for financial support provided by the National Institutes of Health (grant 1R01-GM62248-01A1) and the Donors of The Petroleum Research Fund, administered by the American Chemical Society, and the Minnesota Supercomputing Institute through a 6-month research scholar award (X.L.). Computational resources were provided by the Minnesota Supercomputing Institute.     

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     

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 new look at the reduced-gradient-following path

 The mathematical structure of the reduced-gradient-following (RGF) path introduced by Quapp et al. (1988 J. Comput. Chem. 19:1087) is reviewed and analyzed. We report two new algorithms to evaluate the RGF path. The RGF path is also compared mathematically and computationally with the gradient extremals path. An example of the evaluation of the RGF path is also reported. Received: 21 May 2001 / Accepted: 27 September 2001 / Published online: 9 January 2002     

A charge-scaling method to treat solvent in QM/MM simulations

 We present a method to treat the solvent efficiently in hybrid quantum mechanical/molecular mechanical simulations of chemical reactions in enzymes. The method is an adaptation of an approach developed for molecular-mechanical free-energy simulations. The charges of each of the exposed ionizable groups are scaled, and the system is simulated in the presence of a limited number of explicit solvent molecules to obtain a reasonable set of structures. Continuum electrostatics methods are then used to correct the energies. Variations in the procedure are discussed with an emphasis on modifications from the original protocol. We illustrate the method by applying it to the study of a hydrolysis reaction in a highly charged system comprising a complex between the base excision repair enzyme uracil-DNA glycosylase and double-stranded DNA. The resulting adiabatic reaction profile is in good agreement with experiment, in contrast to that obtained without scaling the charges. Received: 5 October 2001 / Accepted: 6 September 2002 / Published online: 28 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: M. Karplus e-mail: marci@tammy.harvard.edu     

Molecular dynamics, density functional and second-order Møller–Plesset theory study of the structure and conformation of acetylcholine in vacuo and in solution

 Molecular mechanics minimizations based on the CVFF force field and molecular dynamics simulation for a time of 2.5 ns were performed to examine the conformational behaviour and the molecular motion of acetylcholine in vacuo and in aqueous solution. Five low-lying conformations, namely the TT, TG, GG, G*G and GT, were obtained from molecular mechanics computations with the GT structure as the absolute minimum. Molecular dynamics trajectories in vacuo and in water show that only four (GT, GG, G*G and TG) and three (TG, TT and GT) conformations are present in the simulation time, respectively. Density functional B3LYP and second-order M?ller–Plesset (MP2) methods were then used to study all the five lowest-lying conformers of acetylcholine neurotransmitter in vacuo and in water by the polarizable continuum model approach. The B3LYP and MP2 computations show that in the gas phase all minima lie in a narrow range of energy with the G*G conformer as the most stable one. The relative minima GG, GT, TG and TT are located at 1.1 (3.3), 1.8 (4.2), 2.1 (4.5) and 4.3 (7.3) kcal/mol above the absolute one at the B3LYP (MP2) level. The preferred conformation in water is the TG. Solvation reduces the relative energy differences between the five minima in both computations. Received: 4 April 2001 / Accepted: 5 July 2001 / Published online: 30 October 2001     

Molecular recognition by β-cyclodextrin derivatives: molecular dynamics, free-energy perturbation and molecular mechanics/ Poisson–Boltzmann surface area goals and problems

 The complexation of p-tert-butylphenyl p-tert-butylbenzoate and N-(p-tert-butylphenyl)-p-tert-butylbenzamide with a β-cyclodextrin derivative formed by two cyclodextrin units linked by a disulfide bridge on one of the C6 atoms has been studied by computational methods. The better amide solubility and the better internal interactions of the ester complex explain the experimentally observed better association constant for the ester. The free-energy perturbation methodology and molecular mechanics/Poisson–Boltzmann surface area analysis have been used to explain the problem and to compare the results. Received: 14 April 2002 / Accepted: 11 August 2002 / Published online: 4 November 2002 Acknowledgements. The Kollman group at the University of California San Francisco is gratefully acknowledged for support and encouragement throughout all this study. The authors thank UAB for inland and outland fellowships to I.B.. Financial support was obtained from grant no. PPQ2000-0369 from the “Ministerio de Ciencia y Tecnologia” (Spain). Intensive computations were performed either with the computers of the Kollman group or with those of CESCA-C⁴ (Catalonia, Spain). Correspondence to: C. Jaime e-mail: carlos.jaime@uab.es     

Model studies of the chemisorption of hydrogen and oxygen on the Au (1 0 0) surface

 The convergence of chemisorption energy for hydrogen and oxygen on gold clusters is studied. Two theoretical approaches have been employed; wavefunction methods at the self-consistent-field second–order M?ller–Plesset level and density functional theory and the two methods are compared. Relativistic effective core potentials exploited in the former approach were developed in this work. Received: 25 October 1999 / Accepted: 21 February 2001 / Published online: 11 October 2001     

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     

NMR chemical shifts in the low–pH form of a-chymotrypsin. A QM/MM and ONIOM–NMR study

 The relationship between hydrogen bonding and NMR chemical shifts in the catalytic triad of low-pH α-chymotrypsin is investigated by combined use of the effective fragment potential [(2001) J Phys Chem A 105:293] and ONIOM–NMR [(2000) Chem Phys Lett 317:589] methods. Our study shows that while the His57 N^δ1−H bond is stretched by a relatively modest amount (to about 1.060 ?) this lengthening, combined with the polarization due to the molecular environment, is sufficient to explain the experimentally observed chemical shifts of 18.2 ppm. Furthermore, the unusual down-field shift of H^ɛ1 (9.2 ppm) observed experimentally is reproduced and shown to be induced by interactions with the C=O group of Ser214 as previously postulated. The free-energy cost of moving H^δ1 from His57 to Asp102 is predicted to be 5.5 kcal/mol. Received: 26 September 2001 / Accepted: 6 September 2002 / Published online: 21 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: J. H. Jensen e-mail: jan-jensen@uiowa.edu Acknowledgements. This work was supported by a Research Innovation Award from the Research Corporation and a type G starter grant from the Petroleum Research Fund. The calculations were performed on IBM RS/6000 workstations obtained through a CRIF grant from the NSF (CHE-9974502) and on supercomputers at the National Center for Supercomputer Applications at Urbana-Champaign. The authors are indebted to Visvaldas Kairys for help with the CHARMM program, and to Daniel Quinn for many helpful discussions.     

Strategies for computing chemical reactivity indices

 Two recent articles [(2000) J Am Chem Soc 122: 2010, (2001) J Am Chem Soc 123: 2007] have explored electron-density-based and external-potential-based chemical reactivity indices. In this article, methods are presented for computing these indices from the output of a Kohn–Sham density functional theory calculation. Received: 18 October 2000 / Accepted: 4 April 2001 / Published online: 9 August 2001     

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     

Molecular structure and Bader's theory

 It is shown that a supposed catastrophe of Bader's theory of atoms in molecules, suggested by Cassam-chena? and Jayatilaka [Theor Chem Acc (2001) 105: 213] is merely a consequence of the approximate character of the adiabatic Born–Oppenheimer theory of molecular structure, and that nonadiabatic approaches could be in accordance with Bader's ideas. Received: 4 April 2001 / Accepted: 5 September 2001 / Published online: 3 June 2002     

Electron-pairing analysis from localization and delocalization indices in the framework of the atoms-in-molecules theory

This article presents an overview of recent advances in the study of electron pairing through the use of localization and delocalization indices obtained from double integration over atomic basins of the exchange–correlation density in the framework of the atoms-in-molecules theory. These localization and delocalization indices describe the intra- and interatomic distribution of the electron pairs in a molecule. The main results of the application of these second-order indices to the analysis of molecular structure and chemical reactivity are briefly reviewed. It is shown that localization and delocalization indices represent a powerful tool to describe the electron-pair structure of molecules, which, in turn, provides deeper insight into relevant chemical phenomena such as electron correlation effects and the formation of localized α, β electron pairs. Received: 8 April 2002 / Accepted: 26 June 2002 / Published online: 6 September 2002 Acknowledgements. Financial help was furnished by the Spanish DGES projects no. PB98-0457-C02-01 and BQU2002-04112-C02-02. J.P. thanks the Departament d'Universitats, Recerca i Societat de la Informació de la Generalitat de Catalunya for benefiting from a doctoral fellowship, no. 2000FI-00582. M.S. is indebted to the Departament d'Universitats, Recerca i Societat de la Informació of the Generalitat de Catalunya for financial support through the Distinguished University Research Promotion, 2001. We also thank the Centre de Supercomputació de Catalunya for providing us with computing facilities. Correspondence to: M. Solà e-mail: miquel.sola@udg.es     

A correlation-consistent basis set for Fe

 A series of correlation-consistent basis sets are developed for Fe. Our best computed ⁵F–⁵D separation in the Fe atom is in excellent agreement with experiment. Our best estimate for the FeCO D ₀ value is in good agreement with experiment. The ⁵Σ⁻–³Σ⁻ separation in FeCO has an error of 3.6 kcal/mol; while the origin of this error is not clear, it is probably not due to the basis set. Received: 5 March 2001 / Accepted: 2 May 2001 / Published online: 9 August 2001     

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.     

Second-order Møller–Plesset perturbation theory with terms linear in the interelectronic coordinates and exact evaluation of three-electron integrals

 The second-order correlation energy of M?ller–Plesset perturbation theory is computed for the neon atom using a wave function that depends explicitly on the interelectronic coordinates (MP2-R12). The resolution-of-identity (RI) approximation, which is invoked in the standard formulation of MP2-R12 theory, is largely avoided by rigorously computing the necessary three-electron integrals. The basis-set limit for the second-order correlation energy is reached to within 0.1 mE _h. A comparison with the conventional RI-based MP2-R12 method shows that only three-electron integrals over s and p orbitals need to be computed exactly, indicating that the RI approximation can be safely used for integrals involving orbitals of higher angular momentum. Received: 9 May 2001 / Accepted: 31 October 2001 / Published online: 9 January 2002     

Gradient of the ZAPT2 energy

 An explicit expression for the analytical first derivative of the Z-averaged perturbation theory taken to second order energy, due to Lee and Jayatilaka, is presented for application to high-spin systems described by a restricted open-shell Hartree–Fock wavefunction. The use of frozen core orbitals is incorporated into the derivation. Received: 23 April 2001 / Accepted: 31 August 2001 / Published online: 9 January 2002     

Recent applications of density functional theory calculations to biomolecules

The purpose of this overview is to highlight the broad scope and utility of current applications of density functional theory (DFT) methods for the study of the properties and reactions of biomolecules. This is illustrated using examples selected from research carried out within our research group and in collaboration with others. The examples include the hyperfine coupling constants of amino acid radicals, the use of an amino acid as a chiral catalyst for the formation of carbon–carbon bonds in the aldol reaction, hydrogen-bond mediated catalysis of an aminolysis reaction, radiation-induced protein–DNA cross-links, and the mechanism by which an antitumor drug cleaves DNA. We demonstrate that DFT-based methods can be applied successfully to a broad range of problems that remain beyond the scope of conventional electron-correlation methods. Furthermore, we show that contemporary computational quantum chemistry complements experiment in the study of biological systems. Received: 19 December 2001 / Accepted: 8 April 2002 / Published online: 4 July 2002     

Comments on “Some fundamental problem with zero flux partitioning of electron densities”

 The article by P. Cassam-Chena? and D. Jayatilaka (Theor Chem Acc (2001) 105: 213) is critically analyzed. Received: 18 April 2001 / Accepted: 9 September 2001 / Published online: 3 June 2002