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.     

Generalized hybrid orbital for the treatment of boundary atoms in combined quantum mechanical and molecular mechanical calculations using the semiempirical parameterized model 3 method

The application of combined quantum mechanical (QM) and molecular mechanical methods to large molecular systems requires an adequate treatment of the boundary between the two approaches. In this article, we extend the generalized hybrid orbital (GHO) method to the semiempirical parameterized model 3 (PM3) Hamiltonian combined with the CHARMM force field. The GHO method makes use of four hybrid orbitals, one of which is included in the QM region in self-consistent field optimization and three are treated as auxiliary orbitals that do not participate in the QM optimization, but they provide an effective electric field for interactions. An important feature of the GHO method is that the semiempirical parameters for the boundary atom are transferable, and these parameters have been developed for a carbon boundary atom consistent with the PM3 model. The combined GHO-PM3/CHARMM model has been tested on molecular geometry and proton affinity for a series of organic compounds.Acknowledgement We thank the National Institutes of Health for support of this research.Contribution to the Jacopo Tomasi Honorary Issue     

A combined quantum mechanical and molecular mechanical method using modified generalized hybrid orbitals: implementation for electronic excited states

The generalized hybrid orbital (GHO) method is implemented at the second-order approximate coupled cluster singles and doubles (CC2) level for quantum mechanical (QM)/molecular mechanical (MM) electronic excited state calculations. The linear response function of CC2 in the GHO scheme is derived and implemented. The new implementation is applied to the first singlet excited states of three aromatic amino acids, phenylalanine, tyrosine, and tryptophan, and also bacteriorhodopsin for assessment. The results obtained for aromatic amino acids agreed well with the full QM CC2 calculations, while the calculated excitation energies of bacteriorhodopsin and its chromophore, all-trans retinal, reproduced the environmental shift of the experimental data. For the bacteriorhodopsin case, the environmental shift of GHO also showed good agreements with the experimental data. The contribution of the quantum effect of certain moieties in the excited states is elucidated by changing the partitioning of QM and MM regions.     

The dynamo library for molecular simulations using hybrid quantum mechanical and molecular mechanical potentials

The Dynamo module library has been developed for the simulation of molecular systems using hybrid quantum mechanical (QM) and molecular mechanical (MM) potentials. Dynamo is not a program package but is a library of Fortran 90 modules that can be employed by those interested in writing their own programs for performing molecular simulations. The library supports a range of different types of molecular calculation including geometry optimizations, reaction‐path determinations and molecular dynamics and Monte Carlo simulations. This article outlines the general structure and capabilities of the library and describes in detail Dynamo's semiempirical QM/MM hybrid potential. Results are presented to indicate three particular aspects of this implementation—the handling of long‐range nonbonding interactions, the nature of the boundary between the quantum mechanical and molecular mechanical atoms and how to perform path‐integral hybrid‐potential molecular dynamics simulations. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 1088–1100, 2000     

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.     

Implementation of the IMOMM methodology for performing combined QM/MM molecular dynamics simulations and frequency calculations

A technique for implementing the integrated molecular orbital and molecular mechanics (IMOMM) methodology developed by Maseras and Morokuma that is used to perform combined quantum mechanics/molecular mechanics (QM/MM) molecular dynamics simulations, frequency calculations and simulations of macromolecules including explicit solvent is presented. Although the IMOMM methodology is generalized to any coordinate system, the implementation first described by Maseras and Morokuma requires that the QM and MM gradients be transformed into internal coordinates before they are added together. This coordinate transformation can be cumbersome for macromolecular systems and can become ill-defined during the course of a molecular dynamics simulation. We describe an implementation of the IMOMM method in which the QM and MM gradients are combined in the cartesian coordinate system, thereby avoiding potential problems associated with using the internal coordinate system. The implementation can be used to perform combined QM/MM molecular dynamics simulations and frequency calculations within the IMOMM framework. Finally, we have examined the applicability of thermochemical data derived from IMOMM framework. Finally, we have examined the applicability of thermochemical data derived from IMOMM frequency calculations. Received: 11 May 1998 / Accepted: 14 August 1998 / Published online: 16 November 1998     

Mixed ab initio QM/MM modeling using frozen orbitals and tests with alanine dipeptide and tetrapeptide

Methodology is discussed for mixed ab initio quantum mechanics/molecular mechanics modeling of systems where the quantum mechanics (QM) and molecular mechanics (MM) regions are within the same molecule. The ab initio QM calculations are at the restricted Hartree–Fock level using the pseudospectral method of the Jaguar program while the MM part is treated with the OPLS force fields implemented in the IMPACT program. The interface between the QM and MM regions, in particular, is elaborated upon, as it is dealt with by “breaking” bonds at the boundaries and using Boys-localized orbitals found from model molecules in place of the bonds. These orbitals are kept frozen during QM calculations. Results from tests of the method to find relative conformational energies and geometries of alanine dipeptides and alanine tetrapeptides are presented along with comparisons to pure QM and pure MM calculations. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 1468–1494, 1999     

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.     

Transition state structure invariance to model system size and calculation levels: a QM/MM study of the carboxylation step catalyzed by Rubisco

The present study elucidates structural features related to the molecular mechanism in the carboxylation step of the reaction catalyzed by Rubisco. Starting from the initial X-ray Protein Data Bank structure of a Rubisco monomer, the reactive subsystem in vacuo is subjected to quantum chemical semiempirical and ab initio studies, while the effects of the protein environments are included by means of a hybrid quantum mechanical/molecular mechanical (QM/MM) approach. The QM/MM is used to characterize the transition structure for carboxylation inside the protein. The calculations were made with the AM1/CHARMM/GRACE scheme. Comparisons between the in vacuo and in situ transition structures show remarkable invariance with respect to geometric parameters, index and transition vector amplitudes. The transition state couples the carbon dioxide attack to the C2 center of the substrate in its dienol form with a simultaneous intramolecular hydrogen transfer from the C2 atom to the hydroxyl group linked to the C3 center. This study suggests that carboxylation may be simultaneously coupled to the activation of the C3 center in the enzyme. Received: 24 March 1998 / Accepted: 3 September 1998 / Published online: 10 December 1998     

Enzyme mechanisms with hybrid quantum and molecular mechanical potentials. I. Theoretical considerations

The application of hybrid quantum mechanical and molecular mechanical (QM/MM) potentials to the study of chemical reactions in enzymes is outlined. The discussion is general and addresses the difficulties encountered in an enzyme QM/MM study. First, general criteria for determining whether a particular enzyme is an appropriate candidate for a QM/MM approach are outlined. Methods for obtaining starting structures are detailed. The importance of choosing appropriate levels of ab initio or semiempirical theory is emphasized. Approaches for interfacing the QM and MM regions are briefly discussed, with greater detail given to describing our CHARMM-GAMESS interface. Techniques for partitioning the system into QM and MM regions are explored. Link atom placement, as distant from reacting atoms as possible within the confines of computational efficiency, is examined in some detail. Methods for determining reaction paths are also discussed. © 1996 John Wiley & Sons, Inc.     

Performance assessment of semiempirical molecular orbital methods in describing halogen bonding: quantum mechanical and quantum mechanical/molecular mechanical-molecular dynamics study

The performance of semiempirical molecular-orbital methods--MNDO, MNDO-d, AM1, RM1, PM3 and PM6--in describing halogen bonding was evaluated, and the results were compared with molecular mechanical (MM) and quantum mechanical (QM) data. Three types of performance were assessed: (1) geometrical optimizations and binding energy calculations for 27 halogen-containing molecules complexed with various Lewis bases (Two of the tested methods, AM1 and RM1, gave results that agree with the QM data.); (2) charge distribution calculations for halobenzene molecules, determined by calculating the solvation free energies of the molecules relative to benzene in explicit and implicit generalized Born (GB) solvents (None of the methods gave results that agree with the experimental data.); and (3) appropriateness of the semiempirical methods in the hybrid quantum-mechanical/molecular-mechanical (QM/MM) scheme, investigated by studying the molecular inhibition of CK2 protein by eight halobenzimidazole and -benzotriazole derivatives using hybrid QM/MM molecular-dynamics (MD) simulations with the inhibitor described at the QM level by the AM1 method and the rest of the system described at the MM level. The pure MM approach with inclusion of an extra point of positive charge on the halogen atom approach gave better results than the hybrid QM/MM approach involving the AM1 method. Also, in comparison with the pure MM-GBSA (generalized Born surface area) binding energies and experimental data, the calculated QM/MM-GBSA binding energies of the inhibitors were improved by replacing the G(GB,QM/MM) solvation term with the corresponding G(GB,MM) term.     

Optimizing efficiency of perturbative Monte Carlo method

We introduce error weighting functions into the perturbative Monte Carlo method for use with a hybrid ab initio quantum mechanics/molecular mechanics (QM/MM) potential. The perturbative Monte Carlo approach introduced earlier provides a means to reduce the number of full SCF calculations in simulations using a QM/MM potential by evoking perturbation theory to calculate energy changes due to displacements of an MM molecule. The use of weighting functions, introduced here, allows an optimal number of MM molecule displacements to occur between the performance of the full self-consistent field calculations. This will allow the ab initio QM/MM approach to be applied to systems that require more accurate treatment of the QM and/or MM regions. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1632–1638, 1998     

Geometry optimization based on linear response free energy with quantum mechanical/molecular mechanical method: applications to Menshutkin-type and Claisen rearrangement reactions in aqueous solution

The authors present a method based on a linear response theory that allows one to optimize the geometries of quantum mechanical/molecular mechanical (QM/MM) systems on the free energy surfaces. Two different forms of linear response free energy functionals are introduced, and electronic wave functions of the QM region, as well as the responses of electrostatic and Lennard-Jones potentials between QM and MM regions, are self-consistently determined. The covariant matrix relating the QM charge distribution to the MM response is evaluated by molecular dynamics (MD) simulation of the MM system. The free energy gradients with respect to the QM atomic coordinates are also calculated using the MD trajectory results. They apply the present method to calculate the free energy profiles of Menshutkin-type reaction of NH3 with CH3Cl and Claisen rearrangement of allyl vinyl ether in aqueous solution. For the Menshutkin reaction, the free energy profile calculated with the modified linear response free energy functional is in good agreement with that by the free energy perturbation calculations. They examine the nonequilibrium solvation effect on the transmission coefficient and the kinetic isotope effect for the Claisen rearrangement.     

Modeling of serine protease prototype reactions with the flexible effective fragment potential quantum mechanical/molecular mechanical method

A complete cycle of chemical transformations for the serine protease prototype reaction is modeled following calculations with the flexible effective fragment quantum mechanical/molecular mechanical (QM/MM) method. The initial molecular model is based on the crystal structure of the trypsin–bovine pancreatic trypsin inhibitor complex including all atoms of the enzyme within approximately 15–18 Å of the oxygen center O of the catalytic serine residue. Several selections of the QM/MM partitioning are considered. Fractions of the side chains of the residues from the catalytic triad (serine, histidine and aspartic acid) and a central part of a model substrate around the C–N bond to be cleaved are included into the QM subsystem. The remaining part, or the MM subsystem, is represented by flexible chains of small effective fragments, whose potentials explicitly contribute to the Hamiltonian of the QM part, but the corresponding fragment–fragment interactions are described by the MM force fields. The QM/MM boundaries are extended over the C–C bonds of the peptides assigned to the QM subsystem in the enzyme, C–C and C–N bonds in model substrates. Multiple geometry optimizations have been performed by using the RHF/6-31G method in the QM part and OPLSAA or AMBER sets of MM parameters, resulting in a series of stationary points on the complex potential-energy surfaces. All structures generally accepted for the serine protease catalytic cycle have been located. Energies at the stationary points found have been recomputed at the MP2/6-31+G^* level for the QM part in the protein environment. Structural changes along the reaction path are analyzed with special attention to hydrogen-bonding networks. In the case of a model substrate selected as a short peptide CH₃(NHCO-CH₂)₂ – HN–CO–(CH₂–NHCO)CH₃ the computed energy profile for the acylation step shows too high activation energy barriers. The energetics of this rate-limiting step is considerably improved, if more realistic model for the substrate is considered, following the motifs of the ThrI11–GlyI12–ProI13-–CysI14–LysI15–AlaI16–ArgI17–IleI18–IleI19 sequence of the bovine pancreatic trypsin inhibitor.     

Transition structure selectivity in enzyme catalysis: a QM/MM study of chorismate mutase

Two different transition structures (TSs) have been located and characterized for the chorismate conversion to prephenate in Bacillus subtilis chorismate mutase by means of hybrid quantum-mechanical/molecular-mechanical (QM/MM) calculations. GRACE software, combined with an AM1/CHARMM24/TIP3P potential, has been used involving full gradient relaxation of the position of ca. 3300 atoms. These TSs have been connected with their respective reactants and products by the intrinsic reaction coordinate (IRC) procedure carried out in the presence of the protein environment, thus obtaining for the first time a realistic enzymatic reaction path for this reaction. Similar QM/MM computational schemes have been applied to study the chemical reaction solvated by ca. 500 water molecules. Comparison of these results together with gas phase calculations has allowed understanding of the catalytic efficiency of the protein. The enzyme stabilizes one of the TSs (TS_OHout) by means of specific hydrogen bond interactions, while the other TS (TS_OHin) is the preferred one in vacuum and in water. The enzyme TS is effectively more polarized but less dissociative than the corresponding solvent and gas phase TSs. Electrostatic stabilization and an intramolecular charge-transfer process can explain this enzymatically induced change. Our theoretical results provide new information on an important enzymatic transformation and the key factors responsible for efficient selectivity are clarified. Received: 25 March 2000 / Accepted: 7 August 2000 / Published online: 23 November 2000