Streamlining and Optimizing Strategies of Electrostatic Parameterization

PyPE_RESP: A Tool to Facilitate and Standardize Derivation of RESP Charges

We introduce PyPE_RESP, a tool to facilitate and standardize partial atomic charge derivation using the Restrained Electrostatic Potential (RESP) approach. PyPE_RESP builds upon the open-source Python package RDKit for chemoinformatics and the AMBER suite for molecular simulations. PyPE_RESP provides an easy setup of multiconformer and multimolecule RESP fitting while allowing a comprehensive definition of charge constraint groups through multiple methods. As a command line tool, PyPE_RESP can be integrated into batch processes. The software enables the derivation of partial atomic charges for additive and polarizable force fields. It outputs constraint group and nonconstraint group charges to give an immediate overview of the fit result. PyPE_RESP will be distributed with AmberTools and compatible with most computing platforms.

Isotropic Periodic Sum for Polarizable Gaussian Multipole Model

The isotropic periodic sum (IPS) method provides an efficient approach for computing long-range interactions by approximating distant molecular structures through isotropic periodic images of a local region. Here, we present a novel integration of IPS with the polarizable Gaussian multipole (pGM) model, extending its applicability to systems with Gaussian-distributed charges and dipoles. By developing and implementing the IPS multipole tensor theorem within the Gaussian multipole framework, we derive analytical expressions for IPS potentials that efficiently handle both permanent and induced multipole interactions. Our comprehensive validation includes energy conservation tests in the NVE ensemble, potential energy distributions in the NVT ensemble, structural analysis through radial distribution functions, diffusion coefficients, induced dipole calculations across various molecular systems, and ionic charging free energies. The results demonstrate that the pGM-IPS approach successfully reproduces energetic, structural, and dynamic properties of molecular systems with accuracy comparable to the traditional particle mesh Ewald method. Our work establishes pGM-IPS as a promising method for simulations of polarizable molecular systems, achieving a balance between computational efficiency and accuracy.

Automated Refinement of Property-Specific Polarizable Gaussian Multipole Water Models Using Bayesian Black-Box Optimization

The critical importance of water in sustaining life highlights the need for accurate water models in computer simulations, aiming to mimic biochemical processes experimentally. The polarizable Gaussian multipole (pGM) model, recently introduced for biomolecular simulations, improves the handling of complex biomolecular interactions. As an integral part of our initial exploration, we examined a minimalist fixed geometry three-center pGM water model using ab initio quantum mechanical calculations of water oligomers. However, our final model development was based on liquid-phase water properties, leveraging automated machine learning (AutoML) techniques for optimization. This allows the development of a framework to refine both van der Waals and electrostatic parameters of the pGM model, aiming to accurately reproduce specific properties such as the oxygen-oxygen radial distribution function, density, and dipole moment, all at 298 K and 1.0 bar pressure. The efficacy of the optimized three-center pGM water model, pGM3P-25, was assessed through simulations of a water box of 512 water molecules, showcasing marked enhancements in both accuracy and practical utility. Notably, the model accurately reproduces thermodynamic properties not explicitly included in training while significantly reducing the time and human effort required for optimization. It was found that pGM3P-25 can reproduce temperature-dependent properties such as density, self-diffusion constants, heat capacity, second virial coefficient, and dielectric constant, which are important in biomolecular simulations. This study underscores the potential of AutoML-driven frameworks to streamline parameter refinement for molecular dynamics simulations, paving the way for broader applications in computational chemistry and beyond.

Refinement of Atomic Polarizabilities for a Polarizable Gaussian Multipole Force Field with Simultaneous Considerations of Both Molecular Polarizability Tensors and In-Solution Electrostatic Potentials

Atomic polarizabilities are considered to be fundamental parameters in polarizable molecular mechanical force fields that play pivotal roles in determining model transferability across different electrostatic environments. In an earlier work, the atomic polarizabilities were obtained by fitting them to the B3LYP/aug-cc-pvtz molecular polarizability tensors of mainly small molecules. Taking advantage of the recent PCMRESPPOL method, we refine the atomic polarizabilities for condensed-phase simulations using a polarizable Gaussian Multipole (pGM) force field. Departing from earlier works, in this work, we incorporated polarizability tensors of a large number of dimers and electrostatic potentials (ESPs) in multiple solvents. We calculated 1565 × 4 ESPs of small molecule monomers and dimers of noble gas and small molecules and 4742 × 4 ESPs of small molecule dimers in four solvents (diethyl ether, ε = 4.24, dichloroethane, ε = 10.13, acetone, ε = 20.49, and water, ε = 78.36). For the gas-phase polarizability tensors, we supplemented the molecule set that was used in our earlier work by adding both the 4252 monomer and dimer sets studied by Shaw and co-workers and the 7211 small molecule monomers listed in the QM7b database to a combined total of 13,523 molecular polarizability tensors of monomers and dimers. The QM7b polarizability set was obtained from quantum-machine.org and was calculated at the LR-CCSD/d-aug-cc-pVDZ level of theory. All other polarizability tensors and all ESPs were calculated at the ωB97X-D/aug-cc-pVTZ level of theory. The atomic polarizabilities were developed using all polarizability tensors and the 1565 × 4 ESPs of small molecule monomers and were then assessed by comparing them to the 4742 × 4 ab initio ESPs of small molecule dimers. The predicted dimer ESPs had an average relative root-mean-square error (RRMSE) of 9.30%, which was only slightly larger than the average fitting RRMSE of 9.15% of the monomer ESPs. The transferability of the polarizability set was further evaluated by comparing the ESPs calculated using parameters developed in another dielectric environment for both tetrapeptide and DES monomer data sets. It was observed that the polarizabilities of this work retained or slightly improved the transferability over the one discussed in earlier work even though the number of parameters in the present set is about half of that in the earlier set. Excluding the gas-phase data, for the DES monomer set, the average transfer RRMSEs were 16.25% and 10.83% for pGM-ind and pGM-perm methods, respectively, comparable to the average fitting RRMSEs of 16.03% and 10.54%; for tetrapeptides, the average transfer RRMSEs were 5.62% and 3.95% for pGM-ind and pGM-perm methods, respectively, slightly larger than 5.41% and 3.61% of the fitting RRMSEs. Therefore, we conclude that the pGM methods with updated polarizabilities achieved remarkable transferability from monomer to dimer and from one solvent to another.

Performance Tuning of Polarizable Gaussian Multipole Model in Molecular Dynamics Simulations

Molecular dynamics (MD) simulations are essential for understanding molecular phenomena at the atomic level, with their accuracy largely dependent on both the employed force field and sampling. Polarizable force fields, which incorporate atomic polarization effects, represent a significant advancement in simulation technology. The polarizable Gaussian multipole (pGM) model has been noted for its accurate reproduction of ab initio electrostatic interactions. In this study, we document our effort to enhance the computational efficiency and scalability of the pGM simulations within the AMBER framework using MPI (message passing interface). Performance evaluations reveal that our MPI-based pGM model significantly reduces runtime and scales effectively while maintaining computational accuracy. Additionally, we investigated the stability and reliability of the MPI implementation under the NVE simulation ensemble. Optimal Ewald and induction parameters for the pGM model are also explored, and its statistical properties are assessed under various simulation ensembles. Our findings demonstrate that the MPI-implementation maintains enhanced stability and robustness during extended simulation times. We further evaluated the model performance under both NVT (constant number, volume, and temperature) and NPT (constant number, pressure, and temperature) ensembles and assessed the effects of varying timesteps and convergence tolerance on induced dipole calculations. The lessons learned from these exercises are expected to help the users to make informed decisions on simulation setup. The improved performance under these ensembles enables the study of larger molecular systems, thereby expanding the applicability of the pGM model in detailed MD simulations.

PCMRESP: A Method for Polarizable Force Field Parameter Development and Transferability of the Polarizable Gaussian Multipole Models Across Multiple Solvents

The transferability of force field parameters is a crucial aspect of high-quality force fields. Previous investigations have affirmed the transferability of electrostatic parameters derived from polarizable Gaussian multipole models (pGMs) when applied to water oligomer clusters, polypeptides across various conformations, and different sequences. In this study, we introduce PCMRESP, a novel method for electrostatic parametrization in solution, intended for the development of polarizable force fields. We utilized this method to assess the transferability of three models: a fixed charge model and two variants of pGM models. Our analysis involved testing these models on 377 small molecules and 100 tetra-peptides in five representative dielectric environments: gas, diethyl ether, dichloroethane, acetone, and water. Our findings reveal that the inclusion of atomic polarization significantly enhances transferability and the incorporation of permanent atomic dipoles, in the form of covalent bond dipoles, leads to further improvements. Moreover, our tests on dual-solvent strategies demonstrate consistent transferability for all three models, underscoring the robustness of the dual-solvent approach. In contrast, an evaluation of the traditional HF/6-31G* method indicates poor transferability for the pGM-ind and pGM-perm models, suggesting the limitations of this conventional approach.

Assessment of Amino Acid Electrostatic Parametrizations of the Polarizable Gaussian Multipole Model

Accurate parametrization of amino acids is pivotal for the development of reliable force fields for molecular modeling of biomolecules such as proteins. This study aims to assess amino acid electrostatic parametrizations with the polarizable Gaussian Multipole (pGM) model by evaluating the performance of the pGM-perm (with atomic permanent dipoles) and pGM-ind (without atomic permanent dipoles) variants compared to the traditional RESP model. The 100-conf-combterm fitting strategy on tetrapeptides was adopted, in which (1) all peptide bond atoms (-CO-NH-) share identical set of parameters and (2) the total charges of the two terminal N-acetyl (ACE) and N-methylamide (NME) groups were set to neutral. The accuracy and transferability of electrostatic parameters across peptides with varying lengths and real-world examples were examined. The results demonstrate the enhanced performance of the pGM-perm model in accurately representing the electrostatic properties of amino acids. This insight underscores the potential of the pGM-perm model and the 100-conf-combterm strategy for the future development of the pGM force field.

AmberTools

AmberTools is a free and open-source collection of programs used to set up, run, and analyze molecular simulations. The newer features contained within AmberTools23 are briefly described in this Application note.