Partial hessian fitting for determining force constant parameters in molecular mechanics

We present a new protocol for deriving force constant parameters that are used in molecular mechanics (MM) force fields to describe the bond‐stretching, angle‐bending, and dihedral terms. A 3 × 3 partial matrix is chosen from the MM Hessian matrix in Cartesian coordinates according to a simple rule and made as close as possible to the corresponding partial Hessian matrix computed using quantum mechanics (QM). This partial Hessian fitting (PHF) is done analytically and thus rapidly in a least‐squares sense, yielding force constant parameters as the output. We herein apply this approach to derive force constant parameters for the AMBER‐type energy expression. Test calculations on several different molecules show good performance of the PHF parameter sets in terms of how well they can reproduce QM‐calculated frequencies. When soft bonds are involved in the target molecule as in the case of secondary building units of metal‐organic frameworks, the MM‐optimized geometry sometimes deviates significantly from the QM‐optimized one. We show that this problem is rectified effectively by use of a simple procedure called Katachi that modifies the equilibrium bond distances and angles in bond‐stretching and angle‐bending terms. © 2016 Wiley Periodicals, Inc.

[1]  W. Goddard,et al.  UFF, a full periodic table force field for molecular mechanics and molecular dynamics simulations , 1992 .

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

[3]  M. Castier,et al.  Molecular Simulation Studies of the Diffusion of Methane, Ethane, Propane, and Propylene in ZIF-8 , 2015 .

[4]  Ross C. Walker,et al.  Paramfit: Automated optimization of force field parameters for molecular dynamics simulations , 2015, J. Comput. Chem..

[5]  Tore Brinck,et al.  Force field parameterization of copper(I)-olefin systems from density functional calculations , 1997 .

[6]  Joseph A. Bank,et al.  Supporting Online Material Materials and Methods Figs. S1 to S10 Table S1 References Movies S1 to S3 Atomic-level Characterization of the Structural Dynamics of Proteins , 2022 .

[7]  J. Berg,et al.  Molecular dynamics simulations of biomolecules , 2002, Nature Structural Biology.

[8]  Kristina Nilsson,et al.  An automatic method to generate force-field parameters for hetero-compounds. , 2003, Acta crystallographica. Section D, Biological crystallography.

[9]  Junmei Wang,et al.  Development and testing of a general amber force field , 2004, J. Comput. Chem..

[10]  Peter A. Kollman,et al.  FREE ENERGY CALCULATIONS : APPLICATIONS TO CHEMICAL AND BIOCHEMICAL PHENOMENA , 1993 .

[11]  Per-Ola Norrby,et al.  Automated molecular mechanics parameterization with simultaneous utilization of experimental and quantum mechanical data , 1998 .

[12]  Renxiao Wang,et al.  Systematic Derivation of AMBER Force Field Parameters Applicable to Zinc-Containing Systems. , 2010, Journal of chemical theory and computation.

[13]  Lars Olsen,et al.  General Transition-State Force Field for Cytochrome P450 Hydroxylation. , 2007, Journal of chemical theory and computation.

[14]  Jorge M. Seminario,et al.  Calculation of intramolecular force fields from second‐derivative tensors , 1996 .

[15]  J. Seminario,et al.  Ab Initio Analysis of Silicon Nano-Clusters , 2014 .

[16]  Toon Verstraelen,et al.  Automated Parametrization of AMBER Force Field Terms from Vibrational Analysis with a Focus on Functionalizing Dinuclear Zinc(II) Scaffolds. , 2012, Journal of chemical theory and computation.

[17]  Olivia Wise,et al.  New force field parameters for metalloproteins I: Divalent copper ion centers including three histidine residues and an oxygen‐ligated amino acid residue , 2014, J. Comput. Chem..

[18]  Junmei Wang,et al.  Automatic parameterization of force field by systematic search and genetic algorithms , 2001, J. Comput. Chem..

[19]  Allan D. Headley,et al.  A scale of directional substituent polarizability parameters from ab initio calculations of polarizability potentials , 1986 .

[20]  M. Kaukonen,et al.  Lennard‐Jones parameters for small diameter carbon nanotubes and water for molecular mechanics simulations from van der Waals density functional calculations , 2012, J. Comput. Chem..

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

[22]  Alexandra T. P. Carvalho,et al.  Electronic Structure Investigation and Parametrization of Biologically Relevant Iron-Sulfur Clusters , 2014, J. Chem. Inf. Model..

[23]  G. Chang,et al.  Macromodel—an integrated software system for modeling organic and bioorganic molecules using molecular mechanics , 1990 .

[24]  Alexander D. MacKerell,et al.  Molecular mechanics. , 2014, Current pharmaceutical design.

[25]  Ulf Ryde,et al.  Comparison of Methods to Obtain Force-Field Parameters for Metal Sites. , 2011, Journal of chemical theory and computation.

[26]  P. Kollman,et al.  A well-behaved electrostatic potential-based method using charge restraints for deriving atomic char , 1993 .

[27]  P. Kollman,et al.  How well does a restrained electrostatic potential (RESP) model perform in calculating conformational energies of organic and biological molecules? , 2000 .

[28]  A. Becke.  Density-functional thermochemistry. III. The role of exact exchange , 1993 .

[29]  Pengfei Li,et al.  Parameterization of Highly Charged Metal Ions Using the 12-6-4 LJ-Type Nonbonded Model in Explicit Water , 2014, The journal of physical chemistry. B.

[30]  R. Friesner,et al.  Evaluation and Reparametrization of the OPLS-AA Force Field for Proteins via Comparison with Accurate Quantum Chemical Calculations on Peptides† , 2001 .

[31]  T. Halgren.  Merck molecular force field. I. Basis, form, scope, parameterization, and performance of MMFF94 , 1996, J. Comput. Chem..

[32]  Alexandra T. P. Carvalho,et al.  Parameters for molecular dynamics simulations of iron‐sulfur proteins , 2013, J. Comput. Chem..

[33]  U. Singh,et al.  A NEW FORCE FIELD FOR MOLECULAR MECHANICAL SIMULATION OF NUCLEIC ACIDS AND PROTEINS , 1984 .

[34]  Laxmikant V. Kalé,et al.  Scalable molecular dynamics with NAMD , 2005, J. Comput. Chem..

[35]  Kenneth M Merz,et al.  Structural Survey of Zinc Containing Proteins and the Development of the Zinc AMBER Force Field (ZAFF). , 2010, Journal of chemical theory and computation.

[36]  H. Berendsen,et al.  COMPUTER-SIMULATION OF MOLECULAR-DYNAMICS - METHODOLOGY, APPLICATIONS, AND PERSPECTIVES IN CHEMISTRY , 1990 .

[37]  Jaehoon Jung,et al.  Molecular dynamics study of the ionic conductivity of 1-n-butyl-3-methylimidazolium salts as ionic liquids , 2005 .

[38]  Wei Zhang,et al.  A point‐charge force field for molecular mechanics simulations of proteins based on condensed‐phase quantum mechanical calculations , 2003, J. Comput. Chem..

[39]  Pengfei Li,et al.  Rational Design of Particle Mesh Ewald Compatible Lennard-Jones Parameters for +2 Metal Cations in Explicit Solvent. , 2013, Journal of chemical theory and computation.

[40]  Parr,et al.  Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density. , 1988, Physical review. B, Condensed matter.

[41]  S. H. Vosko,et al.  Accurate spin-dependent electron liquid correlation energies for local spin density calculations: a critical analysis , 1980 .

[42]  Timothy Clark,et al.  Efficient diffuse function‐augmented basis sets for anion calculations. III. The 3‐21+G basis set for first‐row elements, Li–F , 1983 .