Interfacing ab initio Quantum Mechanical Method with Classical Drude Osillator Polarizable Model for Molecular Dynamics Simulation of Chemical Reactions.

In order to further improve the accuracy and applicability of combined quantum mechanical/molecular mechanical (QM/MM) methods, we have interfaced the ab initio QM method with the classical Drude oscillator polarizable MM force field (ai-QM/MM-Drude). Different coupling approaches have been employed and compared: 1. the conventional dual self-consistent-field (SCF) procedure; 2. the direct SCF scheme, in which QM densities and MM Drude positions are converged simultaneously; 3. the micro-iterative SCF scheme, in which the Drude positions of the polarizable model are fully converged during each self-consistent field (SCF) step of QM calculations; 4. the one-step-Drude-update scheme, in which the MM Drude positions are updated only once instead of fully converged during each molecular dynamics (MD) step. The last three coupling approaches are found to be efficient and can achieve the desired convergence in a similar number of QM SCF steps comparing with the corresponding QM method coupled to a non-polarizable force field. The feasibility and applicability of the implemented ai-QM/MM-Drude approach have been demonstrated by carrying out Born-Oppenheimer molecular dynamics simulations with the umbrella sampling method to determine potentials of mean force for both the methyl transfer reaction of the methyl chlorine-chlorine ion system and the glycine intra-molecular proton transfer reaction in aqueous solution. Our results indicate that the ai-QM/MM-Drude approach is very promising, which provides a better description of QM/MM interactions while can achieve quite similar computational efficiency in comparison with the corresponding conventional ab initio QM/MM method.

[1]  Gregory K. Schenter,et al.  Excited States of the Bacteriochlorophyll b Dimer of Rhodopseudomonas viridis: A QM/MM Study of the Photosynthetic Reaction Center That Includes MM Polarization , 1995 .

[2]  Richard A. Bryce,et al.  A solvation model using a hybrid quantum mechanical/molecular mechanical potential with fluctuating solvent charges , 1997 .

[3]  M. Levitt,et al.  Theoretical studies of enzymic reactions: dielectric, electrostatic and steric stabilization of the carbonium ion in the reaction of lysozyme. , 1976, Journal of molecular biology.

[4]  A. Fernández-Ramos,et al.  A direct-dynamics study of the zwitterion-to-neutral interconversion of glycine in aqueous solution , 2000 .

[5]  Arieh Warshel,et al.  Polarizable Force Fields:  History, Test Cases, and Prospects. , 2007, Journal of chemical theory and computation.

[6]  Guohui Li,et al.  Development of effective quantum mechanical/molecular mechanical (QM/MM) methods for complex biological processes. , 2006, The journal of physical chemistry. B.

[7]  W. Thiel,et al.  Hybrid Models for Combined Quantum Mechanical and Molecular Mechanical Approaches , 1996 .

[8]  Walter Thiel,et al.  QM/MM studies of enzymes. , 2007, Current opinion in chemical biology.

[9]  Jacopo Tomasi,et al.  An Integrated Effective Fragment—Polarizable Continuum Approach to Solvation: Theory and Application to Glycine , 2002 .

[10]  Michiel Sprik,et al.  A polarizable model for water using distributed charge sites , 1988 .

[11]  P. Kollman,et al.  A Second Generation Force Field for the Simulation of Proteins, Nucleic Acids, and Organic Molecules , 1995 .

[12]  J. Ponder,et al.  Force fields for protein simulations. , 2003, Advances in protein chemistry.

[13]  Yingkai Zhang,et al.  How do SET-domain protein lysine methyltransferases achieve the methylation state specificity? Revisited by Ab initio QM/MM molecular dynamics simulations. , 2008, Journal of the American Chemical Society.

[14]  Hao Hu,et al.  Free energies of chemical reactions in solution and in enzymes with ab initio quantum mechanics/molecular mechanics methods. , 2008, Annual review of physical chemistry.

[15]  Qiang Cui,et al.  Importance of van der Waals Interactions in QM/MM Simulations. , 2004, The journal of physical chemistry. B.

[16]  Benoît Roux,et al.  Modeling induced polarization with classical Drude oscillators: Theory and molecular dynamics simulation algorithm , 2003 .

[17]  Steven J. Stuart,et al.  Dynamical fluctuating charge force fields: Application to liquid water , 1994 .

[18]  M. Karplus,et al.  How Enzymes Work: Analysis by Modern Rate Theory and Computer Simulations , 2004, Science.

[19]  Jing Kong,et al.  Lennard–Jones parameters for the combined QM/MM method using the B3LYP/6‐31G*/AMBER potential , 2005, J. Comput. Chem..

[20]  Jiali Gao,et al.  Energy components of aqueous solution: Insight from hybrid QM/MM simulations using a polarizable solvent model , 1997, J. Comput. Chem..

[21]  H. C. Andersen Rattle: A “velocity” version of the shake algorithm for molecular dynamics calculations , 1983 .

[22]  Martin J. Field,et al.  HYBRID QUANTUM MECHANICAL/MOLECULAR MECHANICAL FLUCTUATING CHARGE MODELS FOR CONDENSED PHASE SIMULATIONS , 1997 .

[23]  K. Hirao,et al.  A polarizable mixed Hamiltonian model of electronic structure for solvated excited states. II. Application to the blue shift of the H2CO 1(π*←n) excitation in water , 2002 .

[24]  Michel Dupuis,et al.  Critical assessment of the hybrid QM/MM-pol-vib approach: Small water clusters using polarizable flexible water potentials , 2000 .

[25]  Benoît Roux,et al.  Atomic Level Anisotropy in the Electrostatic Modeling of Lone Pairs for a Polarizable Force Field Based on the Classical Drude Oscillator. , 2006, Journal of chemical theory and computation.

[26]  B. T. Thole,et al.  On the quantum mechanical treatment of solvent effects , 1980 .

[27]  Jiali Gao,et al.  Optimization of the Lennard‐Jones parameters for a combined ab initio quantum mechanical and molecular mechanical potential using the 3‐21G basis set , 1996 .

[28]  I. Williams,et al.  A hybrid quantum mechanical molecular mechanical method: Application to hydration free energy calculations , 2002 .

[29]  M. Swart,et al.  Some applications of the direct reaction field approach , 1999 .

[30]  R. Friesner,et al.  Ab initio quantum chemical and mixed quantum mechanics/molecular mechanics (QM/MM) methods for studying enzymatic catalysis. , 2005, Annual review of physical chemistry.

[31]  Alexander D. MacKerell,et al.  Determination of Electrostatic Parameters for a Polarizable Force Field Based on the Classical Drude Oscillator. , 2005, Journal of chemical theory and computation.

[32]  S. Hammes‐Schiffer Quantum-classical simulation methods for hydrogen transfer in enzymes: a case study of dihydrofolate reductase. , 2004, Current opinion in structural biology.

[33]  S. Creighton,et al.  Simulation of free energy relationships and dynamics of SN2 reactions in aqueous solution , 1988 .

[34]  M. Okina,et al.  On the Ratio of Zwitterion Form to Uncharged Form of Glycine at Equilibrium in Various Aqueous Media , 1982 .

[35]  Pengyu Y. Ren,et al.  Polarizable Atomic Multipole Water Model for Molecular Mechanics Simulation , 2003 .

[36]  Wilfred F. van Gunsteren,et al.  Development of a simple, self-consistent polarizable model for liquid water , 2003 .

[37]  Jiali Gao,et al.  Solvatochromic Shifts of the n → π* Transition of Acetone from Steam Vapor to Ambient Aqueous Solution:  A Combined Configuration Interaction QM/MM Simulation Study Incorporating Solvent Polarization. , 2007, Journal of chemical theory and computation.

[38]  M. Karplus,et al.  A combined quantum mechanical and molecular mechanical potential for molecular dynamics simulations , 1990 .

[39]  I. Tuñón,et al.  On the tautomerization process of glycine in aqueous solution , 2000 .

[40]  A. Warshel,et al.  Structure/function correlations of proteins using MM, QM/MM, and related approaches: methods, concepts, pitfalls, and current progress. , 2003, Advances in protein chemistry.

[41]  W. L. Jorgensen,et al.  Comparison of simple potential functions for simulating liquid water , 1983 .

[42]  D. Truhlar,et al.  Self-Consistent Polarization of the Boundary in the Redistributed Charge and Dipole Scheme for Combined Quantum-Mechanical and Molecular-Mechanical Calculations. , 2007, Journal of chemical theory and computation.

[43]  Martin J. Field,et al.  Free energy perturbation method for chemical reactions in the condensed phase: a dynamic approach based on a combined quantum and molecular mechanics potential , 1987 .

[44]  W. V. van Gunsteren,et al.  On the Calculation of Atomic Forces in Classical Simulation Using the Charge-on-Spring Method To Explicitly Treat Electronic Polarization. , 2007, Journal of chemical theory and computation.

[45]  Mark S Gordon,et al.  Incremental solvation of nonionized and zwitterionic glycine. , 2006, Journal of the American Chemical Society.

[46]  J. Ángyán,et al.  The role of induction forces in infra-red matrix shifts: quantum chemical calculations with reaction field model hamiltonian , 1991 .

[47]  J. G. Snijders,et al.  A discrete solvent reaction field model within density functional theory , 2003 .

[48]  David van der Spoel,et al.  Molecular Dynamics Simulations of Water with Novel Shell-Model Potentials , 2001 .

[49]  Minoru Sakurai,et al.  Study of the Opsin Shift of Bacteriorhodopsin: Insight from QM/MM Calculations with Electronic Polarization Effects of the Protein Environment , 2001 .

[50]  Wilfred F van Gunsteren,et al.  Calculation of the free energy of polarization: quantifying the effect of explicitly treating electronic polarization on the transferability of force-field parameters. , 2007, The journal of physical chemistry. B.

[51]  J. Ángyán,et al.  MIXED QUANTUM-CLASSICAL CALCULATIONS ON THE WATER MOLECULE IN LIQUID PHASE: INFLUENCE OF A POLARIZABLE ENVIRONMENT ON ELECTRONIC PROPERTIES , 1996 .

[52]  Kenneth M. Merz,et al.  Calculation of solvation free energies using a density functional/molecular dynamics coupled potential , 1993 .

[53]  George A. Kaminski,et al.  Development of an Accurate and Robust Polarizable Molecular Mechanics Force Field from ab Initio Quantum Chemistry , 2004 .

[54]  Dawn A. Yarne,et al.  A dual length scale method for plane-wave-based, simulation studies of chemical systems modeled using mixed ab initio/empirical force field descriptions , 2001 .

[55]  Ursula Rothlisberger,et al.  The role and perspective of ab initio molecular dynamics in the study of biological systems. , 2002, Accounts of chemical research.

[56]  Christopher J. R. Illingworth,et al.  Classical polarization in hybrid QM/MM methods. , 2006, The journal of physical chemistry. A.

[57]  M. Thompson,et al.  QM/MMpol: A Consistent Model for Solute/Solvent Polarization. Application to the Aqueous Solvation and Spectroscopy of Formaldehyde, Acetaldehyde, and Acetone , 1996 .

[58]  Alexander D. MacKerell,et al.  Polarizable empirical force field for alkanes based on the classical Drude oscillator model. , 2005, The journal of physical chemistry. B.

[59]  R. Swendsen,et al.  THE weighted histogram analysis method for free‐energy calculations on biomolecules. I. The method , 1992 .

[60]  Haibo Yu,et al.  Accounting for polarization in molecular simulation , 2005, Comput. Phys. Commun..

[61]  Masataka Nagaoka,et al.  Potential Energy Function for Intramolecular Proton Transfer Reaction of Glycine in Aqueous Solution , 1998 .

[62]  W. V. van Gunsteren,et al.  Charge-on-spring polarizable water models revisited: from water clusters to liquid water to ice. , 2004, The Journal of chemical physics.

[63]  Yingkai Zhang,et al.  Pseudobond ab initio QM/MM approach and its applications to enzyme reactions , 2006 .

[64]  Jií Kolafa,et al.  Time‐reversible always stable predictor–corrector method for molecular dynamics of polarizable molecules , 2004, J. Comput. Chem..

[65]  U. Singh,et al.  A combined ab initio quantum mechanical and molecular mechanical method for carrying out simulations on complex molecular systems: Applications to the CH3Cl + Cl− exchange reaction and gas phase protonation of polyethers , 1986 .

[66]  Y. Mo,et al.  Ab initio QM/MM simulations with a molecular orbital‐valence bond (MOVB) method: application to an SN2 reaction in water , 2000 .

[67]  M. Aida,et al.  A polarizable mixed Hamiltonian model of electronic structure for micro-solvated excited states. I. Energy and gradients formulation and application to formaldehyde (1A2) , 2002 .

[68]  Masataka Nagaoka,et al.  Origin of the Transition State on the Free Energy Surface: Intramolecular Proton Transfer Reaction of Glycine in Aqueous Solution , 1998 .

[69]  Scott F. Smith,et al.  Theoretical examination of the SN2 reaction involving chloride ion and methyl chloride in the gas phase and aqueous solution , 1985 .

[70]  James Andrew McCammon,et al.  Molecular Dynamics Simulations with Interaction Potentials Including Polarization Development of a Noniterative Method and Application to Water , 1990 .

[71]  Jiří Kolafa Numerical Integration of Equations of Motion with a Self-Consistent Field given by an Implicit Equation , 1996 .

[72]  Kurt V. Mikkelsen,et al.  Coupled Cluster/Molecular Mechanics Method: Implementation and Application to Liquid Water , 2003 .

[73]  Charles L. Brooks,et al.  CHARMM fluctuating charge force field for proteins: I parameterization and application to bulk organic liquid simulations , 2004, J. Comput. Chem..

[74]  D. Truhlar,et al.  QM/MM: what have we learned, where are we, and where do we go from here? , 2007 .

[75]  W. L. Jorgensen Free energy calculations: a breakthrough for modeling organic chemistry in solution , 1989 .

[76]  Wilfred F van Gunsteren,et al.  Combined QM/MM Molecular Dynamics Study on a Condensed-Phase SN2 Reaction at Nitrogen:  The Effect of Explicitly Including Solvent Polarization. , 2007, Journal of chemical theory and computation.

[77]  Yingkai Zhang,et al.  Ab initio quantum mechanical/molecular mechanical molecular dynamics simulation of enzyme catalysis: the case of histone lysine methyltransferase SET7/9. , 2007, The journal of physical chemistry. B.

[78]  Alexander D. MacKerell,et al.  A simple polarizable model of water based on classical Drude oscillators , 2003 .

[79]  Alexander D. MacKerell,et al.  A polarizable model of water for molecular dynamics simulations of biomolecules , 2006 .

[80]  Darrin M. York,et al.  A chemical potential equalization method for molecular simulations , 1996 .

[81]  G. Ciccotti,et al.  Numerical Integration of the Cartesian Equations of Motion of a System with Constraints: Molecular Dynamics of n-Alkanes , 1977 .

[82]  Alan M. Ferrenberg,et al.  Optimized Monte Carlo data analysis. , 1989, Physical Review Letters.

[83]  G. Voth,et al.  Hybrid Ab-Initio/Empirical Molecular Dynamics: Combining the ONIOM Scheme with the Atom-Centered Density Matrix Propagation (ADMP) Approach , 2004 .

[84]  Jacob Kongsted,et al.  Density functional self-consistent quantum mechanics/molecular mechanics theory for linear and nonlinear molecular properties: Applications to solvated water and formaldehyde. , 2007, The Journal of chemical physics.

[85]  D. Truhlar,et al.  Quantum mechanical methods for enzyme kinetics. , 2003, Annual review of physical chemistry.

[86]  Harry A. Stern,et al.  Development of a polarizable force field for proteins via ab initio quantum chemistry: First generation model and gas phase tests , 2002, J. Comput. Chem..

[87]  W. Goddard,et al.  Charge equilibration for molecular dynamics simulations , 1991 .

[88]  Claude Millot,et al.  INTRAMOLECULAR PROTON TRANSFER OF GLYCINE IN AQUEOUS SOLUTION USING QUANTUM MECHANICS : MOLECULAR MECHANICS SIMULATIONS , 1998 .