Paramfit: Automated optimization of force field parameters for molecular dynamics simulations

The generation of bond, angle, and torsion parameters for classical molecular dynamics force fields typically requires fitting parameters such that classical properties such as energies and gradients match precalculated quantum data for structures that scan the value of interest. We present a program, Paramfit, distributed as part of the AmberTools software package that automates and extends this fitting process, allowing for simplified parameter generation for applications ranging from single molecules to entire force fields. Paramfit implements a novel combination of a genetic and simplex algorithm to find the optimal set of parameters that replicate either quantum energy or force data. The program allows for the derivation of multiple parameters simultaneously using significantly fewer quantum calculations than previous methods, and can also fit parameters across multiple molecules with applications to force field development. Paramfit has been applied successfully to systems with a sparse number of structures, and has already proven crucial in the development of the Assisted Model Building with Energy Refinement Lipid14 force field. © 2014 Wiley Periodicals, Inc.     

New force field for calcium binding sites in annexin-membrane complexes

For accurate classical molecular dynamics (MD) simulations of the calcium mediated bound complexes of annexin and membrane we have developed new force-field parameters correctly describing the interaction of the Ca ion with its environment. We have used quantum chemical calculations to investigate the potential energy surface experienced by the Ca ion within the three different binding sites found in domain 1 of annexin V (ANX V/1). Based on these calculations we were able to quantify the charge polarization of atoms within the binding sites, and to determine the geometry and force constants of harmonic restraints between the Ca ion and its coordinating oxygen atoms. Harmonic restraints were introduced to compensate for the deviations between the quantum mechanical potential energy surface and that of the classical force field. Our analysis has shown that using the refined force field for the Ca binding sites enables long-time MD simulations that conserve the initial structure of ANX V/1 significantly better than MD simulations using the standard force field.     

A molecular mechanics force field for lignin

A CHARMM molecular mechanics force field for lignin is derived. Parameterization is based on reproducing quantum mechanical data of model compounds. Partial atomic charges are derived using the RESP electrostatic potential fitting method supplemented by the examination of methoxybenzene:water interactions. Dihedral parameters are optimized by fitting to critical rotational potentials and bonded parameters are obtained by optimizing vibrational frequencies and normal modes. Finally, the force field is validated by performing a molecular dynamics simulation of a crystal of a lignin fragment molecule and comparing simulation-derived structural features with experimental results. Together with the existing force field for polysaccharides, this lignin force field will enable full simulations of lignocellulose.     

QuanPol: A full spectrum and seamless QM/MM program

The quantum chemistry polarizable force field program (QuanPol) is implemented to perform combined quantum mechanical and molecular mechanical (QM/MM) calculations with induced dipole polarizable force fields and induced surface charge continuum solvation models. The QM methods include Hartree–Fock method, density functional theory method (DFT), generalized valence bond theory method, multiconfiguration self‐consistent field method, Møller–Plesset perturbation theory method, and time‐dependent DFT method. The induced dipoles of the MM atoms and the induced surface charges of the continuum solvation model are self‐consistently and variationally determined together with the QM wavefunction. The MM force field methods can be user specified, or a standard force field such as MMFF94, Chemistry at Harvard Molecular Mechanics (CHARMM), Assisted Model Building with Energy Refinement (AMBER), and Optimized Potentials for Liquid Simulations‐All Atom (OPLS‐AA). Analytic gradients for all of these methods are implemented so geometry optimization and molecular dynamics (MD) simulation can be performed. MD free energy perturbation and umbrella sampling methods are also implemented. © 2013 Wiley Periodicals, Inc.     

Derivation of class II force fields. VIII. Derivation of a general quantum mechanical force field for organic compounds

A class II valence force field covering a broad range of organic molecules has been derived employing ab initio quantum mechanical "observables." The procedure includes selecting representative molecules and molecular structures, and systematically sampling their energy surfaces as described by energies and energy first and second derivatives with respect to molecular deformations. In this article the procedure for fitting the force field parameters to these energies and energy derivatives is briefly reviewed. The application of the methodology to the derivation of a class II quantum mechanical force field (QMFF) for 32 organic functional groups is then described. A training set of 400 molecules spanning the 32 functional groups was used to parameterize the force field. The molecular families comprising the functional groups and, within each family, the torsional angles used to sample different conformers, are described. The number of stationary points (equilibria and transition states) for these molecules is given for each functional group. This set contains 1324 stationary structures, with 718 minimum energy structures and 606 transition states. The quality of the fit to the quantum data is gauged based on the deviations between the ab initio and force field energies and energy derivatives. The accuracy with which the QMFF reproduces the ab initio molecular bond lengths, bond angles, torsional angles, vibrational frequencies, and conformational energies is then given for each functional group. Consistently good accuracy is found for these computed properties for the various types of molecules. This demonstrates that the methodology is broadly applicable for the derivation of force field parameters across widely differing types of molecular structures. Copyright 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1782-1800, 2001     

Determination of side‐chain‐rotamer and side‐chain and backbone virtual‐bond‐stretching potentials of mean force from AM1 energy surfaces of terminally‐blocked amino‐acid residues,for coarse‐grained simulations of protein structure and folding. I. The method

In this and the accompanying article, we report the development of new physics‐based side‐chain‐rotamer and virtual‐bond‐deformation potentials which now replace the respective statistical potentials used so far in our physics‐based united‐reside UNRES force field for large‐scale simulations of protein structure and dynamics. In this article, we describe the methodology for determining the corresponding potentials of mean force (PMF's) from the energy surfaces of terminally‐blocked amino‐acid residues calculated with the AM1 quantum‐mechanical semiempirical method. The approach is based on minimization of the AM1 energy for fixed values of the angles λ for rotation of the peptide groups about the C^α ··· C^α virtual bonds, and for fixed values of the side‐chain dihedral angles χ, which formed a multidimensional grid. A harmonic‐approximation approach was developed to extrapolate from the energy at a given grid point to other points of the conformational space to compute the respective contributions to the PMF. To test the applicability of the harmonic approximation, the rotamer PMF's of alanine and valine obtained with this approach have been compared with those obtained by using a Metropolis Monte Carlo method. The PMF surfaces computed with the harmonic approximation are more rugged and have more pronounced minima than the MC‐calculated surfaces but the harmonic‐approximation‐and MC‐calculated PMF values are linearly correlated. The potentials derived with the harmonic approximation are, therefore, appropriate for UNRES for which the weights (scaling factors) of the energy terms are determined by force‐field optimization for foldability. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

A supervised fitting approach to force field parametrization with application to the SIBFA polarizable force field

A supervised, semiautomated approach to force field parameter fitting is described and applied to the SIBFA polarizable force field. The I‐NoLLS interactive, nonlinear least squares fitting program is used as an engine for parameter refinement while keeping parameter values within a physical range. Interactive fitting is shown to avoid many of the stability problems that frequently afflict highly correlated, nonlinear fitting problems occurring in force field parametrizations. The method is used to obtain parameters for the H₂O, formamide, and imidazole molecular fragments and their complexes with the Mg²⁺ cation. Reference data obtained from ab initio calculations using an auc‐cc‐pVTZ basis set exploit advances in modern computer hardware to provide a more accurate parametrization of SIBFA than has previously been available. © 2014 Wiley Periodicals, Inc.     

Force field development for organic molecules: Modifying dihedral and 1–n pair interaction parameters

We comprehensively illustrate a general process of fitting all‐atom molecular mechanics force field (FF) parameters based on quantum mechanical calculations and experimental thermodynamic data. For common organic molecules with free dihedral rotations, this FF format is comprised of the usual bond stretching, angle bending, proper and improper dihedral rotation, and 1–4 scaling pair interactions. An extra format of 1–n scaling pair interaction is introduced when a specific intramolecular rotation is strongly hindered. We detail how the preferred order of fitting all intramolecular FF parameters can be determined by systematically generating characteristic configurations. The intermolecular Van der Waals parameters are initially taken from the literature data but adjusted to obtain a better agreement between the molecular dynamics (MD) simulation results and the experimental observations if necessary. By randomly choosing the molecular configurations from MD simulation and comparing their energies computed from FF parameters and quantum mechanics, the FF parameters can be verified self‐consistently. Using an example of a platform chemical 3‐hydroxypropionic acid, we detail the comparison between the new fitting parameters and the existing FF parameters. In particular, the introduced systematic approach has been applied to obtain the dihedral angle potential and 1–n scaling pair interaction parameters for 48 organic molecules with different functionality. We suggest that this procedure might be used to obtain better dihedral and 1–n interaction potentials when they are not available in the current widely used FF. © 2014 Wiley Periodicals, Inc.     

The IR spectrum of supercritical water: Combined molecular dynamics/quantum mechanics strategy and force field for cluster sampling

Supercritical water was analyzed recently as a gas of small clusters of waters linked to each other by intermolecular hydrogen‐bonds, but unexpected “linear” conformations of clusters are required to reproduce the infra‐red (IR) spectra of the supercritical state. Aiming at a better understanding of clusters in supercritical water, this work presents a strategy combining classical molecular dynamics to explore the potential energy landscape of water clusters with quantum mechanical calculation of their IR spectra. For this purpose, we have developed an accurate and flexible force field of water based on the TIP5P 5‐site model. Water dimers and trimers obtained with this improved force field compare well with the quantum mechanically optimized clusters. Exploration by simulated annealing of the potential energy surface of the classical force field reveals a new trimer conformation whose IR response determined from quantum calculations could play a role in the IR spectra of supercritical water. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

A point-charge force field for molecular mechanics simulations of proteins based on condensed-phase quantum mechanical calculations

Molecular mechanics models have been applied extensively to study the dynamics of proteins and nucleic acids. Here we report the development of a third-generation point-charge all-atom force field for proteins. Following the earlier approach of Cornell et al., the charge set was obtained by fitting to the electrostatic potentials of dipeptides calculated using B3LYP/cc-pVTZ//HF/6-31G** quantum mechanical methods. The main-chain torsion parameters were obtained by fitting to the energy profiles of Ace-Ala-Nme and Ace-Gly-Nme di-peptides calculated using MP2/cc-pVTZ//HF/6-31G** quantum mechanical methods. All other parameters were taken from the existing AMBER data base. The major departure from previous force fields is that all quantum mechanical calculations were done in the condensed phase with continuum solvent models and an effective dielectric constant of epsilon = 4. We anticipate that this force field parameter set will address certain critical short comings of previous force fields in condensed-phase simulations of proteins. Initial tests on peptides demonstrated a high-degree of similarity between the calculated and the statistically measured Ramanchandran maps for both Ace-Gly-Nme and Ace-Ala-Nme di-peptides. Some highlights of our results include (1) well-preserved balance between the extended and helical region distributions, and (2) favorable type-II poly-proline helical region in agreement with recent experiments. Backward compatibility between the new and Cornell et al. charge sets, as judged by overall agreement between dipole moments, allows a smooth transition to the new force field in the area of ligand-binding calculations. Test simulations on a large set of proteins are also discussed.     

Derivation of class II force fields. I. Methodology and quantum force field for the alkyl functional group and alkane molecules

A new method for deriving force fields for molecular simulations has been developed. It is based on the derivation and parameterization of analytic representations of the ab initio potential energy surfaces. The general method is presented here and used to derive a quantum mechanical force field (QMFF) for alkanes. It is based on sampling the energy surfaces of 16 representative alkane species. For hydrocarbons, this force field contains 66 force constants and reference values. These were fit to 128,376 quantum mechanical energies and energy derivatives describing the energy surface. The detailed form of the analytic force field expression and the values of all resulting parameters are given. A series of computations is then performed to test the ability of this force field to reproduce the features of the ab initio energy surface in terms of energies as well as the first and second derivatives of the energies with respect to molecular deformations. The fit is shown to be good, with rms energy deviations of less than 7% for all molecules. Also, although only two atom types are employed, the force field accounts for the properties of both highly strained species, such as cyclopropane and methylcyclopropanes, as well as unstrained systems. The information contained in the quantum energy surface indicates that it is significantly anharmonic and that important intramolecular coupling interactions exist between internals. The representation of the nature of these interactions, not present in diagonal, quadratic force fields (Class I force fields), is shown to be important in accounting accurately for molecular energy surfaces. The Class II force field derived from the quantum energy surface is characterized by accounting for these important intramolecular forces. The importance of each 4.2 to 18.2%. This fourfold increase in the second derivative error dramatically demonstrates the importance of bond anharmonicity in the ab initio potential energy surface. The Class II force field derived from the quantum energy surface is characterized by accounting for these important intramolecular forces. The importance of each of the interaction terms of the potential energy function has also been assessed. Bond anharmonicity, angle anharmonicity, and bond/angle, bond/torsion, and angle/angle/ torsion cross-term interactions result in the most significant overall improvement in distorted structure energies and energy derivatives. The implications of each energy term for the development of advanced force fields is discussed. Finally, it is shown that the techniques introduced here for exploring the quantum energy surface can be used to determine the extent of transferability and range of validity of the force field. The latter is of crucial importance in meeting the objective of deriving a force field for use in molecular mechanics and dynamics calculations of a wide range of molecules often containing functional groups in novel environments. © 1994 by John Wiley & Sons, Inc.     

分子力场进展

分子力学（简称ＭＭ）是近年来化学家常用的一种计算方法。与量子力学从头计算和半经验方法相比，用分子力学处理大分子可以大大节省计算时间，而且，在大多数情况下，用分子力学方法计算得到的分子几何构型参数与实验值之间的差值可在实验误差范围之内。所以，分子力学是研究生物化学体系的有效和可行的手段。分子力学的核心是分子力场。本文介绍了分子力场的量子力学背景、分子力场和光谱力场之间的关系。分子力场的一般形式、分力     

Development of glycyl radical parameters for the OPLS-AA/L force field

On the basis of quantum chemical calculations C(alpha)-glycyl radical parameters have been developed for the OPLS-AA/L force field. The molecular mechanics hypersurface was fitted to the calculated quantum chemical surface by minimizing their molecular mechanics parameter dependent sum-of-squares deviations. To do this, a computer program in which the molecular mechanics energy derivatives with respect to the parameters were calculated analytically was developed, implementing the general method of Lifson and Warshel (J Chem Phys 1968, 49, 5116) for force field parameter optimization. This program, in principle, can determine the optimal parameter set in one calculation if enough representative value points on the quantum chemical potential energy surface are available and there is no linear dependency between the parameters. Some of the parameters in quantum calculations, including several new torsion types around a bond as well as angle parameters at a new central atom type, are not completely separable. Consequently, some restrictions and/or presumptions were necessary during parameter optimization. The relative OPLS-AA energies reproduced those calculated quantum chemically almost perfectly.     

Helical region of the potential energy surface of α-aminoisobutyric acid: A theoretical study

The helical region of the potential energy surface of blocked α-aminoisobutyric acid (Aib) dipeptide has been studied by using ab initio and semiempirical quantum mechanical methods, as well as force-field-derived methods. Depending on the method, an α-helix or a 3₁₀-helix is found to be the energy minimum. The conformations obtained from computations performed at the ab initio quantum mechanical level, as well as by using the AMBER force field, are in excellent agreement with X-ray data. Semiempirical results display some important differences with regard to experimental data. On the other hand, the CVFF force field predicts no energy minimum in the helical region of the Aib potential energy surface. © 1993 John Wiley & Sons, Inc.     

Grand challenges in quantum‐classical modeling of molecule–surface interactions

A detailed understanding of the adsorption of small molecules or macromolecules to a materials surface is of importance, for example, in the context of material and biomaterial research. Classical atomistic simulations in principle provide microscopic insight in the complex entropic and enthalpic interplay at the interface. However, an application of classical atomistic simulation techniques to such interface systems is a nontrivial problem, mostly because commonly used force fields cannot be straightforwardly applied, as they are usually developed to reproduce bulk properties of either solids or liquids but not the interfacial region between two phases. Therefore, a dual‐scale modeling approach has often been the method of choice in the past, in which the classical force field is parameterized such that quantum chemical information on near‐surface conformations and adsorption energies is reproduced by the classical force field. We will discuss in this review the current state‐of‐the‐art of quantum‐classical modeling of molecule–surface interactions and outline the major challenges in this field. In this context, we will, among other things, lay emphasis on discussing ways to obtain representable force fields and propose systematic and system‐independent strategies to optimize the quantum‐classical fitting procedure. © 2013 Wiley Periodicals, Inc.     

Global optimization of parameters in the reactive force field ReaxFF for SiOH

We have used unbiased global optimization to fit a reactive force field to a given set of reference data. Specifically, we have employed genetic algorithms (GA) to fit ReaxFF to SiOH data, using an in‐house GA code that is parallelized across reference data items via the message‐passing interface (MPI). Details of GA tuning turn‐ed out to be far less important for global optimization efficiency than using suitable ranges within which the parameters are varied. To establish these ranges, either prior knowledge can be used or successive stages of GA optimizations, each building upon the best parameter vectors and ranges found in the previous stage. We have finally arrive‐ed at optimized force fields with smaller error measures than those published previously. Hence, this optimization approach will contribute to converting force‐field fitting from a specialist task to an everyday commodity, even for the more difficult case of reactive force fields. © 2013 Wiley Periodicals, Inc.     

A new strategy for the evaluation of force parameters from quantum mechanical computations

A new strategy for the determination of force parameters is presented. The equilibrium values appearing in the force field equations representing the “stretching” and “bending” of bonds are directly determined from quantum mechanical calculations without geometrical restrictions. The determination of the force parameters is carried out by means of a rigorous fitting between the quantum mechanic and the molecular mechanical energy variations arising from the perturbation of the geometric variables. The strategy presented here has been incorporated into a computer program named PAPQMD, which was developed in order to provide nonquantum mechanical experts with a powerful tool for the determination of approximate force parameters. The program was developed upon the assumption that force parameters are not universal, but they strongly depend on the molecular environment. This implies that the parametrization procedure should be done in a molecular model close to the molecule or molecules to be studied by means of molecular mechanical or dynamic methods, and consequently, it is no longer supposed that the variation of one geometrical parameter does not affect the rest of the molecular geometry. PAPQMD performs the fitting between molecular mechanics and quantum mechanical energies considering all the perturbations that the modification in one geometric variable causes in all the others, enabling the parametrization even of large molecules. The ability of our method to reproduce experimentally derived force parameters is discussed and compared with the widely used Hopfinger's strategy. The study of the behavior of PAPQMD and Hopfinger's strategies for reproducing the force parameters of two complex molecules demonstrates the superiority of the methodology presented here.