Force-matching Approach Research Articles

How close are the classical two-body potentials to abinitio calculations? Insights from linear machine learning based force matching.

In this work, we propose a linear machine learning force matching approach that can directly extract pair atomic interactions from abinitio calculations in amorphous structures. The local feature representation is specifically chosen to make the linear weights a force field as a force/potential function of the atom pair distance. Consequently, this set of functions is the closest representation of the abinitio forces, given the two-body approximation and finite scanning in the configurational space. We validate this approach in amorphous silica. Potentials in the new force field (consisting of tabulated Si-Si, Si-O, and O-O potentials) are significantly different than existing potentials that are commonly used for silica, even though all of them produce the tetrahedral network structure and roughly similar glass properties. This suggests that the commonly used classical force fields do not offer fundamentally accurate representations of the atomic interaction in silica. The new force field furthermore produces a lower glass transition temperature (Tg ∼ 1800K) and a positive liquid thermal expansion coefficient, suggesting the extraordinarily high Tg and negative liquid thermal expansion of simulated silica could be artifacts of previously developed classical potentials. Overall, the proposed approach provides a fundamental yet intuitive way to evaluate two-body potentials against abinitio calculations, thereby offering an efficient way to guide the development of classical force fields.

A Mori–Zwanzig Dissipative Particle Dynamics Approach for Anisotropic Coarse Grained Molecular Dynamics

Coarse grained (CG) molecular dynamics simulations are widely used to accelerate atomistic simulations but generally lack a formalism to preserve the dynamics of the system. For spherical particles, the Mori-Zwanzig approach, while computationally complex, has ameliorated this problem. Here we present an anisotropic dissipative particle dynamics (ADPD) model as an extension of this approach, which accounts for the anisotropy for both conservative and nonconservative interactions. For a simple anisotropic system we parametrize the coarse grained force field representing ellipsoidal CG particles from the full-atomistic simulation. To represent the anisotropy of the system, both the conservative and dissipative terms are approximated using the Gay-Berne (GB) functional forms via a force-matching approach. We compare our model with other CG models and demonstrate that it yields better results in both static and dynamical properties. The inclusion of the anisotropic nonconservative force preserves the microscopic dynamical details, and hence the dynamical properties, such as diffusivity, can be better reproduced by the aspherical model. By generalizing the isotropic DPD model, this framework is effective and promising for the development of the CG model for polymers, macromolecules, and biological systems.

Extension of the force-matching method to coarse-grained models with axially symmetric sites to produce transferable force fields: Application to the UNRES model of proteins.

The force-matching approach to coarse graining, in which the forces that act on site centers are fitted to the respective average forces computed from all-atom molecular dynamics simulations, provides a link between coarse-grained and all-atom molecular dynamics. In the existing implementations, radial site-site interaction potentials are assumed, thus precluding extensive coarse-graining that usually requires anisotropic potentials. In this work, we extended the force-matching approach to coarse-grained models with axially symmetric sites and implemented it to the UNRES model of polypeptide chains developed in our laboratory, in which the only interaction sites are united peptide groups and united side chains, the α-carbon atoms serving as anchor points. The optimizable parameters were those of the UNRES energy function and not whole potential profiles, which provide better transferability. We tested the implementation with the 20-residue tryptophan-cage miniprotein, selected as the training protein, starting from the NEWCT-9P variant of UNRES. The reference forces were obtained from implicit- and explicit-solvent simulations. Using a target function composed of a force-matching term and a maximum-likelihood term that drives the force field at reproducing the NMR-determined conformational ensembles at three selected temperatures, force fields were obtained which did not produce site-site clashes for the structures simulated with all-atom molecular dynamics with AMBER, and modeled the structures of α-helical proteins with resolution comparable to that of the NEWCT-9P force field. The new force fields also produced the free-energy landscapes of tryptophan cage similar to those obtained from the all-atom molecular dynamics runs.

Application of Screening Functions as Cutoff-Based Alternatives to Ewald Summation in Molecular Dynamics Simulations Using Polarizable Force Fields.

The range-dependent screening of the charge-charge, charge-induced dipole, and induced dipole-induced dipole interactions was examined for a variety of liquids modeled using polarizable force fields. A cutoff-based method for calculation of the electrostatic interactions in molecular dynamics (MD) is presented as an alternative to Ewald-type summation for simulations of the disordered materials modeled using many-body polarizable force fields with permanent charges and induced point dipoles. The proposed approach was tested on bulk water, room-temperature ionic liquids, and solutions of ions in polar solvents. The smooth, short-range, and atom-type independent screening functions for interactions between the charges and induced dipoles were obtained using the force matching approach. An excellent agreement for both the magnitude and directionality of forces, structural and dynamic properties, was found in MD simulations utilizing the developed screening functions, compared to those with Ewald summation. While similar in shape and range, the charge-charge screening functions were somewhat dependent on the material chemistry. On the other hand, the charge-induced dipole and induced dipole-induced dipole screening functions were found to be nearly universal for the tested materials.

Using Force Matching To Determine Reactive Force Fields for Water under Extreme Thermodynamic Conditions.

We present a method for the creation of classical force fields for water under dissociative thermodynamic conditions by force matching to molecular dynamics trajectories from Kohn-Sham density functional theory (DFT). We apply our method to liquid water under dissociative conditions, where molecular lifetimes are less than 1 ps, and superionic water, where hydrogen ions diffuse at liquid-like rates through an oxygen lattice. We find that, in general, our new models are capable of accurately reproducing the structural and dynamic properties computed from DFT, as well as the molecular concentrations and lifetimes. Overall, our force-matching approach presents a relatively simple way to create classical reactive force fields for a single thermodynamic state point that largely retains the accuracy of DFT while having the potential to access experimental time and length scales.

A new embedded-atom method approach based on the pth moment approximation

Large scale atomistic simulations with suitable interatomic potentials are widely employed by scientists or engineers of different areas. The quick generation of high-quality interatomic potentials is urgently needed. This largely relies on the developments of potential construction methods and algorithms in this area. Quantities of interatomic potential models have been proposed and parameterized with various methods, such as the analytic method, the force-matching approach and multi-object optimization method, in order to make the potentials more transferable. Without apparently lowering the precision for describing the target system, potentials of fewer fitting parameters (FPs) are somewhat more physically reasonable. Thus, studying methods to reduce the FP number is helpful in understanding the underlying physics of simulated systems and improving the precision of potential models. In this work, we propose an embedded-atom method (EAM) potential model consisting of a new manybody term based on the pth moment approximation to the tight binding theory and the general transformation invariance of EAM potentials, and an energy modification term represented by pairwise interactions. The pairwise interactions are evaluated by an analytic-numerical scheme without the need to know their functional forms a priori. By constructing three potentials of aluminum and comparing them with a commonly used EAM potential model, several wonderful results are obtained. First, without losing the precision of potentials, our potential of aluminum has fewer potential parameters and a smaller cutoff distance when compared with some constantly-used potentials of aluminum. This is because several physical quantities, usually serving as target quantities to match in other potentials, seem to be uniquely dependent on quantities contained in our basic reference database within the new potential model. Second, a key empirical parameter in the embedding term of the commonly used EAM model is found to be related to the effective order of moments of local density of states. This may provide a way to improve the precision of EAM potentials further through more precise approximations to tight binding theory. In addition, some critical details about construction procedures are discussed.

Nuclear quantum effects in liquid water from path-integral simulations using an ab initio force-matching approach

We have applied path integral simulations, in combination with new ab initio based water potentials, to investigate nuclear quantum effects in liquid water. Because direct ab initio path integral simulations are computationally expensive, a flexible water model is parameterised by force-matching to density functional theory-based molecular dynamics simulations. Static and dynamic properties of liquid water at ambient conditions are presented and the role of nuclear quantum effects, exchange-correlation functionals and dispersion corrections are discussed in regards to reproducing the experimental properties of liquid water.

The force matching approach to multiscale simulations: Merits, shortcomings, and future perspectives

Among the various approaches to multiscale simulations, in recent years, force matching has been known for a quick growth. The method is based on a least‐square fit of reference properties obtained from simulations at a certain scale, to parameterize the force field for coarser‐grained scale simulations. Its advantage with respect to conventional schemes used for parameterizing force fields, lies in that only physically accessible configurations are sampled, and that the number of reference data per configuration is large. In this perspective article, we discuss some recent findings on the tailoring of the objective function, on the choice of the empirical potential, and on the way to improve the quality of the reference calculations. We present pros and cons of the algorithm, and we propose a road map to future developments. © 2014 Wiley Periodicals, Inc.

Generalized QM/MM Force Matching Approach Applied to the 11-cis Protonated Schiff Base Chromophore of Rhodopsin

We extended a previously developed force matching approach to systems with covalent QM/MM boundaries and describe its user-friendly implementation in the publicly available software package CPMD. We applied this approach to the challenging case of the retinal protonated Schiff base in dark state bovine rhodopsin. We were able to develop a highly accurate force field that is able to capture subtle structural changes within the chromophore that have a pronounced influence on the optical properties. The optical absorption spectrum calculated from configurations extracted from a MD trajectory using the new force field is in excellent agreement with QM/MM and experimental references.

Particle-based multiscale coarse graining with density-dependent potentials: Application to molecular crystals (hexahydro-1,3,5-trinitro-s-triazine)

We describe the development of isotropic particle-based coarse-grain models for crystalline hexahydro-1,3,5-trinitro-s-triazine (RDX). The coarse graining employs the recently proposed multiscale coarse-graining (MS-CG) method, which is a particle-based force-matching approach for deriving free-energy effective interaction potentials. Though one-site and four-site coarse-grain (CG) models were parameterized from atomistic simulations of non-ordered (molten and ambient temperature amorphous) systems, the focus of the paper is a detailed study of the one-site model with a brief recourse to the four-site model. To improve the ability of the one-site model to be applied to crystalline phases at various pressures, it was found necessary to include explicit dependence on a particle density, and a new theory of local density-dependent MS-CG potentials is subsequently presented. The density-dependency is implemented through interpolation of MS-CG force fields derived at a preselected set of reference densities. The computationally economical procedure for obtaining the reference force fields starting from the interaction at ambient density is also described. The one-site MS-CG model adequately describes the atomistic lattice structure of α-RDX at ambient and high pressures, elastic and vibrational properties, pressure-volume curve up to P = 10 GPa, and the melting temperature. In the molten state, the model reproduces the correct pair structure at different pressures as well as higher order correlations. The potential of the MS-CG model is further evaluated in simulations of shocked crystalline RDX.

Influence of Polarization on Structural, Thermodynamic, and Dynamic Properties of Ionic Liquids Obtained from Molecular Dynamics Simulations

Utilizing the transferable, quantum-chemistry-based, Atomistic Polarizable Potential for Liquids, Electrolytes, & Polymers (APPLE&P) force field, we have systematically investigated the influence of polarization effects on the accuracy of properties predicted from molecular dynamics simulations of various room temperature ionic liquids (ILs). Simulations of ILs in which the atom-based polarizability was set to zero for all atoms (nonpolarizable APPLE&P potential) resulted in changes in thermodynamic and dynamic properties from those predicted by the polarizable APPLE&P potential that are qualitatively different from changes observed for nonionic liquids. Investigation of structural and dynamical correlations using both the polarizable and nonpolarizable versions of APPLE&P allowed us to obtain a mechanistic understanding of the influence of polarization on dynamics in the ILs investigated. Additionally, the Force Matching (FM) approach was employed to systematically obtain nonpolarizable two-body force fields for several ILs that reproduce as accurately as possible intermolecular forces predicted by the polarizable model. Unlike water, for which the FM approach was found to yield an accurate representation of the liquid phase structure predicted by a polarizable model, the FM approach does not result in a two-body potential that accurately reproduces either structure or dynamics predicted by the polarizable IL model.

Multiscale Coarse-Graining of Monosaccharides

A systematic multiscale coarse-graining (MS-CG) algorithm is applied to build coarse-grained models for monosaccharides in aqueous solution. The methodology is demonstrated for the example of alpha-D-glucopyranose. The nonbonded interactions are directly derived from the force-matching approach, whereas the bonded interactions are obtained through Boltzmann statistical analyses of the underlying atomistic trajectory. The MS-CG model is shown to reproduce many structural and thermodynamic properties in the constant NPT ensemble. Although the model is derived at a single temperature, pressure, and concentration, it is shown to be reasonably transferable to other thermodynamic states. In this model, long-range interactions are effectively mapped into short-range forces with a moderate cutoff and are evaluated by table look-up. As a result, molecular dynamics employing the MS-CG model is approximately 3 orders of magnitude more efficient than its atomistic counterpart. Consequently, the model is particularly suitable for simulating carbohydrate systems at large length and long time scales. Results for an alpha-(1-->4)-d-glucan with 14 glucose units are also presented, demonstrating that the MS-CG algorithm is also applicable to the coarse-graining of other saccharide systems.

An accurate and simple quantum model for liquid water

The path-integral molecular dynamics and centroid molecular dynamics methods have been applied to investigate the behavior of liquid water at ambient conditions starting from a recently developed simple point charge/flexible (SPC/Fw) model. Several quantum structural, thermodynamic, and dynamical properties have been computed and compared to the corresponding classical values, as well as to the available experimental data. The path-integral molecular dynamics simulations show that the inclusion of quantum effects results in a less structured liquid with a reduced amount of hydrogen bonding in comparison to its classical analog. The nuclear quantization also leads to a smaller dielectric constant and a larger diffusion coefficient relative to the corresponding classical values. Collective and single molecule time correlation functions show a faster decay than their classical counterparts. Good agreement with the experimental measurements in the low-frequency region is obtained for the quantum infrared spectrum, which also shows a higher intensity and a redshift relative to its classical analog. A modification of the original parametrization of the SPC/Fw model is suggested and tested in order to construct an accurate quantum model, called q-SPC/Fw, for liquid water. The quantum results for several thermodynamic and dynamical properties computed with the new model are shown to be in a significantly better agreement with the experimental data. Finally, a force-matching approach was applied to the q-SPC/Fw model to derive an effective quantum force field for liquid water in which the effects due to the nuclear quantization are explicitly distinguished from those due to the underlying molecular interactions. Thermodynamic and dynamical properties computed using standard classical simulations with this effective quantum potential are found in excellent agreement with those obtained from significantly more computationally demanding full centroid molecular dynamics simulations. The present results suggest that the inclusion of nuclear quantum effects into an empirical model for water enhances the ability of such model to faithfully represent experimental data, presumably through an increased ability of the model itself to capture realistic physical effects.

The microstructural evolution of Al12Mg17 alloy during the quenching processes

The processes of rapid solidification for three cooling rates of Al12Mg17 alloy from liquid to solid are simulated using molecular dynamics based on embedded-atom method potentials derived by the force-matching approach. The liquid structures are calculated and the structural factors are in good agreement with experimental data. During each rapid quenching, an amorphous state is obtained, and the microstructures of the liquid, supercooled liquid, and the amorphous states of Al12Mg17 alloy are analyzed using the pair analysis technique.

Development of Complex Classical Force Fields through Force Matching to ab Initio Data: Application to a Room-Temperature Ionic Liquid

Recent experimental neutron diffraction data and ab initio molecular dynamics simulation of the ionic liquid dimethylimidazolium chloride ([dmim]Cl) have provided a structural description of the system at the molecular level. However, partial radial distribution functions calculated from the latter, when compared to previous classical simulation results, highlight some limitations in the structural description offered by force field-based simulations. With the availability of ab initio data it is possible to improve the classical description of [dmim]Cl by using the force matching approach, and the strategy for fitting complex force fields in their original functional form is discussed. A self-consistent optimization method for the generation of classical potentials of general functional form is presented and applied, and a force field that better reproduces the observed first principles forces is obtained. When used in simulation, it predicts structural data which reproduces more faithfully that observed in the ab initio studies. Some possible refinements to the technique, its application, and the general suitability of common potential energy functions used within many ionic liquid force fields are discussed.

Multiscale Coarse-Graining of Ionic Liquids

A recently developed multiscale coarse-graining (MS-CG) approach for obtaining coarse-grained force fields from fully atomistic molecular dynamics simulation is applied to the challenging case of the EMIM+NO3- ionic liquid. The force-matching in the MS-CG methodology is accomplished with an explicit separation of bonded and nonbonded forces. While the nonbonded forces are adopted from this force-matching approach, the bonded forces are obtained from fitting the statistical configurational data from the atomistic simulations. The many-body electronic polarizability is also successfully broken into effective pair interactions. With a virial constraint fixing the system pressure, the MS-CG models rebuild satisfactory structural and thermodynamic properties for different temperatures. The MS-CG model developed from a modest atomistic simulation is therefore suitable for simulating much larger systems, because the coarse-grained models show significant time integration efficiency. This approach is expected to be general for coarse-graining other ionic liquids, as well as many other liquid-state systems. The limitations of the present coarse-graining procedure are also discussed.

Fast centroid molecular dynamics: A force-matching approach for the predetermination of the effective centroid forces

A fast centroid molecular dynamics (CMD) methodology is proposed in which the effective centroid forces are predetermined through a force-matching algorithm applied to a standard path integral molecular dynamics simulation. The resulting method greatly reduces the computational cost of generating centroid trajectories, thus extending the applicability of CMD. The method is applied to the study of liquid para-hydrogen at two state points and liquid ortho-deuterium at one state point. The static and dynamical results are compared to those obtained from full adiabatic CMD simulations and found to be in excellent agreement for all three systems; the transport properties are also compared to experiment and found to have a similar level of agreement.