AMOEBA+ Classical Potential for Modeling Molecular Interactions

Energetics and J-coupling constants for Ala, Gly, and Val peptides demonstrated using ABEEM polarizable force field in vacuo and an aqueous solution

The development of an atom-bond electronegativity equalisation method at the σπ-level (ABEEM) polarisable force field (PFF) for peptides is presented. ABEEM PFF utilises a fluctuating charge model to explicitly describe...

Inter-anion chalcogen bonds: Are they anti-electrostatic in nature?

Inter-anion hydrogen and halogen bonds have emerged as counterintuitive linkers and inspired us to expand the range of this unconventional bonding pattern. Here, the inter-anion chalcogen bond (IAChB) was proposed and theoretically analyzed in a series of complexes formed by negatively charged bidentate chalcogen bond donors with chloride anions. The kinetic stability of IAChB was evidenced by the minima on binding energy profiles and further supported by ab initio molecular dynamic simulations. The block-localized wave function (BLW) method and its subsequent energy decomposition (BLW-ED) approach were employed to elucidate the physical origin of IAChB. While all other energy components vary monotonically as anions get together, the electrostatic interaction behaves exceptionally as it experiences a Coulombic repulsion barrier. Before reaching the barrier, the electrostatic repulsion increases with the shortening Ch⋯Cl^- distance as expected from classical electrostatics. However, after passing the barrier, the electrostatic repulsion decreases with the Ch⋯Cl^- distance shortening and subsequently turns into the most favorable trend among all energy terms at short ranges, representing a dominating force for the kinetic stability of inter-anions. For comparison, all energy components exhibit the same trends and vary monotonically in the conventional counterparts where donors are neutral. By comparing inter-anions and their conventional counterparts, we found that only the electrostatic energy term is affected by the extra negative charge. Remarkably, the distinctive (nonmonotonic) electrostatic energy profiles were reproduced using quantum mechanical-based atomic multipoles, suggesting that the crucial electrostatic interaction in IAChB can be rationalized within the classical electrostatic theory just like conventional non-covalent interactions.

Simulating the binding of key organic functional groups to aqueous calcium carbonate species

The interaction of organic molecules with mineral systems is relevant to a wide variety of scientific problems both in the environment and minerals processing. In this study, the coordination of small organics that contain the two most relevant functional groups for biomineralisation of calcium carbonate, namely carboxylate and ammonium, with the corresponding mineral ions are examined in aqueous solution. Specifically, two force fields have been examined based on rigid-ion or polarisable models, with the latter being within the AMOEBA formalism. Here the parameters for the rigid-ion model are determined to target the accurate reproduction of the hydration structure and solvation thermodynamics, while both force fields are designed to be compatible with the corresponding recently published models for aqueous calcium carbonate. The application of these force fields to ion pairing in aqueous solution is studied in order to quantitatively determine the extent of association.

Classical Electrostatics Remains the Driving Force for Interanion Hydrogen and Halogen Bonding

Interanion hydrogen bonding (IAHB) and halogen bonding (IAXB) have emerged as a counterintuitive linker in a range of fascinating applications. Despite the overall repulsive (positive) binding energy, anions are trapped in a local minimum with its corresponding transition state (TS) preventing dissociation. In other words, the adduct of anions is metastable. Seemingly, the electrostatic paradigm and force field description of hydrogen/halogen bonding (HB/XB) are challenged, because of the preconceived Coulombic repulsion. Aiming at an insightful understanding of these interanion phenomena, we employed the energy decomposition approach based on the block-localized wavefunction method (BLW-ED) to investigate a series of exemplary interanion complexes. As expected, the key distinction from the conventional HB/XB lies in the electrostatic interaction, which is not increasingly repulsive as anions gradually approach to each other. Rather, there is a Coulombic barrier at a certain point. After this point, the electrostatic repulsion diminishes with the decreasing distance between anions. Differently, other energy components vary monotonically just like in conventional cases. The nonmonotonic characteristic of the electrostatic interaction in interanion complexes was reproduced using the multipole expansion in AMOEBA polarizable force field in which the state-specified atomic multipoles were adopted. This suggests that the nonmonotonicity can be well interpreted by classical electrostatic theory and there is no conceptual difference between conventional HB/XB and IAHB/IAXB. The stability of IAHB/IAXB depends on the competition between the local attractive HB/XB and the global Coulombic repulsion of net charges, though there is cooperativity between these two contrasting forces. This concise model was supported by the attractive IAHB/IAXB in modified molecular capsules, which exhibit strong quadruple HB/XBs and a considerable distance between charged substituents.

Improvement of the Gaussian Electrostatic Model by separate fitting of Coulomb and exchange-repulsion densities and implementation of a new dispersion term

The description of each separable contribution of the intermolecular interaction is a useful approach to develop polarizable force fields (polFFs). The Gaussian Electrostatic Model (GEM) is based on this approach, coupled with the use of density fitting techniques. In this work, we present the implementation and testing of two improvements of GEM: the Coulomb and exchange-repulsion energies are now computed with separate frozen molecular densities and a new dispersion formulation inspired by the Sum of Interactions Between Fragments Ab initio Computed polFF, which has been implemented to describe the dispersion and charge-transfer interactions. Thanks to the combination of GEM characteristics and these new features, we demonstrate a better agreement of the computed structural and condensed properties for water with experimental results, as well as binding energies in the gas phase with the ab initio reference compared with the previous GEM* potential. This work provides further improvements to GEM and the items that remain to be improved and the importance of the accurate reproduction for each separate contribution.

Nuclear Quantum Effects in Liquid Water at Near Classical Computational Cost Using the Adaptive Quantum Thermal Bath

We demonstrate the accuracy and efficiency of a recently introduced approach to account for nuclear quantum effects (NQEs) in molecular simulations: the adaptive quantum thermal bath (adQTB). In this method, zero-point energy is introduced through a generalized Langevin thermostat designed to precisely enforce the quantum fluctuation-dissipation theorem. We propose a refined adQTB algorithm with improved accuracy and report adQTB simulations of liquid water. Through extensive comparison with reference path integral calculations, we demonstrate that it provides excellent accuracy for a broad range of structural and thermodynamic observables as well as infrared vibrational spectra. The adQTB has a computational cost comparable to that of classical molecular dynamics, enabling simulations of up to millions of degrees of freedom.

CONI-Net: Machine Learning of Separable Intermolecular Force Fields

Noncovalent interactions (NCIs) play an essential role in soft matter and biomolecular simulations. The ab initio method symmetry-adapted perturbation theory allows a precise quantitative analysis of NCIs and offers an inherent energy decomposition, enabling a deeper understanding of the nature of intermolecular interactions. However, this method is limited to small systems, for instance, dimers of molecules. Here, we present a scale-bridging approach to systematically derive an intermolecular force field from ab initio data while preserving the energy decomposition of the underlying method. We apply the model in molecular dynamics simulations of several solvents and compare two predicted thermodynamic observables-mass density and enthalpy of vaporization-to experiments and established force fields. For a data set limited to hydrocarbons, we investigate the extrapolation capabilities to molecules absent from the training set. Overall, despite the affordable moderate quality of the reference ab initio data, we find promising results. With the straightforward data set generation procedure and the lack of target data in the fitting process, we have developed a method that enables the rapid development of predictive force fields with an extra dimension of insights into the balance of NCIs.

A Quantum Chemical Topology Picture of Intermolecular Electrostatic Interactions and Charge Penetration Energy

Based on the Interacting Quantum Atoms approach, we present herein a conceptual and theoretical framework of short-range electrostatic interactions, whose accurate description is still a challenging problem in molecular modeling. For all the noncovalent complexes in the S66 database, the fragment-based and atomic decomposition of the electrostatic binding energies is performed using both the charge density of the dimers and the unrelaxed densities of the monomers. This energy decomposition together with dispersion corrections gives rise to a pairwise approximation to the total binding energy. It also provides energetic descriptors at varying distance that directly address the atomic and molecular electrostatic interactions as described by point-charge or multipole-based potentials. Additionally, we propose a consistent definition of the charge penetration energy within quantum chemical topology, which is mainly characterized in terms of the intramolecular electrostatic energy. Finally, we discuss some practical implications of our results for the design and validation of electrostatic potentials.

Atomistic Polarizable Embeddings: Energy, Dynamics, Spectroscopy, and Reactivity

The computational modeling of realistic extended systems, relevant in, e.g., Chemistry and Biophysics, is a fundamental problem of paramount importance in contemporary research. Enzymatic catalysis and photoinduced processes in pigment-protein complexes are typical problems targeted by computer-aided approaches, to complement experiments as interpretative tools at a molecular scale. The daunting complexity of this task lies in between the opposite stringent requirements of results' reliability for structural/dynamical properties and related intermolecular interactions, and a mandatory principle of realism in the modeling strategy. Therefore, in practice, a truly realistic computational model of a biologically relevant system can easily fail to meet the accuracy requirement, in order to balance the excessive computational cost necessary to reach the desired precision.To address such an "accuracy vs reality" dualistic requirement, mixed quantum mechanics/classical mechanics approaches within Atomistic (i.e., preserving the discrete particle configuration) Polarizable Embeddings (QM/APEs) methods have been proposed over the years. In this Account, we review recent developments in the design and application of general QM/APE methods, targeting situations where a local intrinsically quantum behavior is coupled to a large molecular system (i.e., an environment), often involving processes with different dynamical time scales, in order to avoid brute-force, unpractical quantum chemistry calculations on the complete system.In the first place, our interest is devoted to the available APEs models presently implemented in computational software, highlighting the quantum chemistry methods that can be used to treat the QM subsystem. We review the coupling strategy between the QM subsystem and the APE, which requires to examine the way the QM/MM mutual interactions are accounted for and how the polarization of the classical environment is considered with respect to (wrt) the quantum variables. Because of the need of reliable molecular and macromolecular structures, a pivotal aspect to address here is the handling of the system dynamics (i.e., gradients wrt nuclear positions are required), especially for large molecular assemblies composed by an overwhelming number of atoms, exploring many conformations on a complex energy landscape.Alongside, we highlight our views on the necessary steps to take toward more accurate general-purposes and transferable explicit embeddings. The main objective to achieve here is to design a more physically grounded multiscale approach. To do so, one should apply advanced new generation classical models to account for refined induction effects that are able to (i) improve the quality of QM/MM interaction energies; (ii) enhance transferability by avoiding the compulsory partial (or total) reparameterization of the classical model. Moreover, the extension of recent developments originating from the field of advanced classical molecular dynamics (MD) to the realm of QM/APE methods is a key direction to improve both speed and efficiency for the phase space exploration of systems of growing size and complexity.Lastly, we point out specific research topics where an advanced QM/APE dynamics can certainly shed some light. For example, we discuss chemical reactions in "harsh" environments and the case of spectroscopic theoretical modeling where the inclusion of refined environment effects is often mandatory.

Advanced Electrostatic Model for Monovalent Ions Based on Ab Initio Energy Decomposition

Ions play important roles in the structures and functions of biomolecules. In biomolecular simulations, ions either directly interact with biomolecules or provide an ionic environment that influences electrostatic interactions of solutes. The AMOEBA+ water model has demonstrated significant advancement of the classical force field for describing molecular interactions due to its improvements on the functional forms to account for essential physics. This work expands the applicability of the AMOEBA+ model toward alkali metal (Li, Na, K, Rb, and Cs) and halogen (F, Cl, Br, and I) ions. Various quantum chemical data on ion-ion and ion-water interactions, experimental ion hydration free energies, and lattice energies of salt crystals are used in the parametrization. The final parameters are verified with other properties outside of the parametrization data, including lattice energies of additional salt crystals and ionic activity coefficients in solution. The new model captures a wide range of ion properties from the gas phase to solution phase and crystals. More importantly, AMOEBA+ provides energy components that are consistent with ab initio energy decomposition. Thus, we expect AMOEBA+ to be more general, transferable, and valuable for the interpretation of intermolecular forces in efficient classical simulations.

CLIFF: A component-based, machine-learned, intermolecular force field

Computation of intermolecular interactions is a challenge in drug discovery because accurate ab initio techniques are too computationally expensive to be routinely applied to drug-protein models. Classical force fields are more computationally feasible, and force fields designed to match symmetry adapted perturbation theory (SAPT) interaction energies can remain accurate in this context. Unfortunately, the application of such force fields is complicated by the laborious parameterization required for computations on new molecules. Here, we introduce the component-based machine-learned intermolecular force field (CLIFF), which combines accurate, physics-based equations for intermolecular interaction energies with machine-learning models to enable automatic parameterization. The CLIFF uses functional forms corresponding to electrostatic, exchange-repulsion, induction/polarization, and London dispersion components in SAPT. Molecule-independent parameters are fit with respect to SAPT2+(3)δMP2/aug-cc-pVTZ, and molecule-dependent atomic parameters (atomic widths, atomic multipoles, and Hirshfeld ratios) are obtained from machine learning models developed for C, N, O, H, S, F, Cl, and Br. The CLIFF achieves mean absolute errors (MAEs) no worse than 0.70 kcal mol^-1 in both total and component energies across a diverse dimer test set. For the side chain-side chain interaction database derived from protein fragments, the CLIFF produces total interaction energies with an MAE of 0.27 kcal mol^-1 with respect to reference data, outperforming similar and even more expensive methods. In applications to a set of model drug-protein interactions, the CLIFF is able to accurately rank-order ligand binding strengths and achieves less than 10% error with respect to SAPT reference values for most complexes.

Testing the Limitations of MD-Based Local Electric Fields Using the Vibrational Stark Effect in Solution: Penicillin G as a Test Case

Noncovalent interactions underlie nearly all molecular processes in the condensed phase from solvation to catalysis. Their quantification within a physically consistent framework remains challenging. Experimental vibrational Stark effect (VSE)-based solvatochromism can be combined with molecular dynamics (MD) simulations to quantify the electrostatic forces in solute-solvent interactions for small rigid molecules and, by extension, when these solutes bind in enzyme active sites. While generalizing this approach toward more complex (bio)molecules, such as the conformationally flexible and charged penicillin G (PenG), we were surprised to observe inconsistencies in MD-based electric fields. Combining synthesis, VSE spectroscopy, and computational methods, we provide an intimate view on the origins of these discrepancies. We observe that the electric fields are correlated to conformation-dependent effects of the flexible PenG side chain, including both the local solvation structure and solute conformational sampling in MD. Additionally, we identified that MD-based electric fields are consistently overestimated in three-point water models in the vicinity of charged groups; this cannot be entirely ameliorated using polarizable force fields (AMOEBA) or advanced water models. This work demonstrates the value of the VSE as a direct method for experiment-guided refinements of MD force fields and establishes a general reductionist approach to calibrating vibrational probes for complex (bio)molecules.

Implicit Solvents for the Polarizable Atomic Multipole AMOEBA Force Field

Computational protein design, ab initio protein/RNA folding, and protein-ligand screening can be too computationally demanding for explicit treatment of solvent. For these applications, implicit solvent offers a compelling alternative, which we describe here for the polarizable atomic multipole AMOEBA force field based on three treatments of continuum electrostatics: numerical solutions to the nonlinear and linearized versions of the Poisson-Boltzmann equation (PBE), the domain-decomposition conductor-like screening model (ddCOSMO) approximation to the PBE, and the analytic generalized Kirkwood (GK) approximation. The continuum electrostatics models are combined with a nonpolar estimator based on novel cavitation and dispersion terms. Electrostatic model parameters are numerically optimized using a least-squares style target function based on a library of 103 small-molecule solvation free energy differences. Mean signed errors for the adaptive Poisson-Boltzmann solver (APBS), ddCOSMO, and GK models are 0.05, 0.00, and 0.00 kcal/mol, respectively, while the mean unsigned errors are 0.70, 0.63, and 0.58 kcal/mol, respectively. Validation of the electrostatic response of the resulting implicit solvents, which are available in the Tinker (or Tinker-HP), OpenMM, and Force Field X software packages, is based on comparisons to explicit solvent simulations for a series of proteins and nucleic acids. Overall, the emergence of performative implicit solvent models for polarizable force fields opens the door to their use for folding and design applications.

Tinker-HP: Accelerating Molecular Dynamics Simulations of Large Complex Systems with Advanced Point Dipole Polarizable Force Fields Using GPUs and Multi-GPU Systems

We present the extension of the Tinker-HP package (Lagardère, Chem. Sci. 2018, 9, 956-972) to the use of Graphics Processing Unit (GPU) cards to accelerate molecular dynamics simulations using polarizable many-body force fields. The new high-performance module allows for an efficient use of single- and multiple-GPU architectures ranging from research laboratories to modern supercomputer centers. After detailing an analysis of our general scalable strategy that relies on OpenACC and CUDA, we discuss the various capabilities of the package. Among them, the multiprecision possibilities of the code are discussed. If an efficient double precision implementation is provided to preserve the possibility of fast reference computations, we show that a lower precision arithmetic is preferred providing a similar accuracy for molecular dynamics while exhibiting superior performances. As Tinker-HP is mainly dedicated to accelerate simulations using new generation point dipole polarizable force field, we focus our study on the implementation of the AMOEBA model. Testing various NVIDIA platforms including 2080Ti, 3090, V100, and A100 cards, we provide illustrative benchmarks of the code for single- and multicards simulations on large biosystems encompassing up to millions of atoms. The new code strongly reduces time to solution and offers the best performances to date obtained using the AMOEBA polarizable force field. Perspectives toward the strong-scaling performance of our multinode massive parallelization strategy, unsupervised adaptive sampling and large scale applicability of the Tinker-HP code in biophysics are discussed. The present software has been released in phase advance on GitHub in link with the High Performance Computing community COVID-19 research efforts and is free for Academics (see https://github.com/TinkerTools/tinker-hp).

Extension of an Atom-Atom Dispersion Function to Halogen Bonds and Its Use for Rational Design of Drugs and Biocatalysts

A dispersion function Das in the form of a damped atom-atom asymptotic expansion fitted to ab initio dispersion energies from symmetry-adapted perturbation theory was improved and extended to systems containing heavier halogen atoms. To illustrate its performance, the revised Das function was implemented in the multipole first-order electrostatic and second-order dispersion (MED) scoring model. The extension has allowed applications to a much larger set of biocomplexes than it was possible with the original Das. A reasonable correlation between MED and experimentally determined inhibitory activities was achieved in a number of test cases, including structures featuring nonphysically shortened intermonomer distances, which constitute a particular challenge for binding strength predictions. Since the MED model is also computationally efficient, it can be used for reliable and rapid assessment of the ligand affinity or multidimensional scanning of amino acid side-chain conformations in the process of rational design of novel drugs or biocatalysts.

Melting Points of OPC and OPC3 Water Models

A recently introduced family of globally optimal water models, OPC, has shown promise in a variety of biomolecular simulations, but properties of these water models outside of the liquid phase remain mostly unexplored. Here, we contribute to filling the gap by reporting melting temperatures of ice I _h of OPC and OPC3 water models. Through the direct coexistence method, which we make available in the AMBER package, the melting points of OPC and OPC3 are estimated as 242 and 210 K, similar to TIP4P-Ew and SPC/E models, respectively, and appreciably below the experimental value of 273.15 K under 1 bar pressure. Water models of the OPC family were optimized to best reproduce water properties in the liquid phase where these models offer noteworthy accuracy advantages over many models of previous generations. It is not surprising that the accuracy of OPC models in describing the phase transition to the solid state does not appear to offer similar improvements. The new anisotropic barostat option implemented in AMBER may benefit system preparation and simulation outside of the direct coexistence applications, such as modeling of membranes or very long DNA strands.

Fine-Tuning of the AMBER RNA Force Field with a New Term Adjusting Interactions of Terminal Nucleotides

Determination of RNA structural-dynamic properties is challenging for experimental methods. Thus, atomistic molecular dynamics (MD) simulations represent a helpful technique complementary to experiments. However, contemporary MD methods still suffer from limitations of force fields (ffs), including imbalances in the nonbonded ff terms. We have recently demonstrated that some improvement of state-of-the-art AMBER RNA ff can be achieved by adding a new term for H-bonding called gHBfix, which increases tuning flexibility and reduces risk of side-effects. Still, the first gHBfix version did not fully correct simulations of short RNA tetranucleotides (TNs). TNs are key benchmark systems due to availability of unique NMR data, although giving too much weight on improving TN simulations can easily lead to overfitting to A-form RNA. Here we combine the gHBfix version with another term called tHBfix, which separately treats H-bond interactions formed by terminal nucleotides. This allows to refine simulations of RNA TNs without affecting simulations of other RNAs. The approach is in line with adopted strategy of current RNA ffs, where the terminal nucleotides possess different parameters for terminal atoms than the internal nucleotides. Combination of gHBfix with tHBfix significantly improves the behavior of RNA TNs during well-converged enhanced-sampling simulations using replica exchange with solute tempering. TNs mostly populate canonical A-form like states while spurious intercalated structures are largely suppressed. Still, simulations of r(AAAA) and r(UUUU) TNs show some residual discrepancies with primary NMR data which suggests that future tuning of some other ff terms might be useful. Nevertheless, the tHBfix has a clear potential to improve modeling of key biochemical processes, where interactions of RNA single stranded ends are involved.

SAPT codes for calculations of intermolecular interaction energies

Symmetry-adapted perturbation theory (SAPT) is a method for calculations of intermolecular (noncovalent) interaction energies. The set of SAPT codes that is described here, the current version named SAPT2020, includes virtually all variants of SAPT developed so far, among them two-body SAPT based on perturbative, coupled cluster, and density functional theory descriptions of monomers, three-body SAPT, and two-body SAPT for some classes of open-shell monomers. The properties of systems governed by noncovalent interactions can be predicted only if potential energy surfaces (force fields) are available. SAPT is the preferred approach for generating such surfaces since it is seamlessly connected to the asymptotic expansion of interaction energy. SAPT2020 includes codes for automatic development of such surfaces, enabling generation of complete dimer surfaces with a rigid monomer approximation for dimers containing about one hundred atoms. These codes can also be used to obtain surfaces including internal degrees of freedom of monomers.

Psi4 1.4: Open-source software for high-throughput quantum chemistry

PSI4 is a free and open-source ab initio electronic structure program providing implementations of Hartree-Fock, density functional theory, many-body perturbation theory, configuration interaction, density cumulant theory, symmetry-adapted perturbation theory, and coupled-cluster theory. Most of the methods are quite efficient, thanks to density fitting and multi-core parallelism. The program is a hybrid of C++ and Python, and calculations may be run with very simple text files or using the Python API, facilitating post-processing and complex workflows; method developers also have access to most of PSI4's core functionalities via Python. Job specification may be passed using The Molecular Sciences Software Institute (MolSSI) QCSCHEMA data format, facilitating interoperability. A rewrite of our top-level computation driver, and concomitant adoption of the MolSSI QCARCHIVE INFRASTRUCTURE project, makes the latest version of PSI4 well suited to distributed computation of large numbers of independent tasks. The project has fostered the development of independent software components that may be reused in other quantum chemistry programs.

Three-site and five-site fixed-charge water models compatible with AMOEBA force field

In a typical biomolecular simulation using Atomic Multipole Optimized Energetics for Biomolecular Applications (AMOEBA) force field, the vast majority molecules in the simulation box consist of water, and these water molecules consume the most CPU power due to the explicit mutual induction effect. To improve the computational efficiency, we here develop two new nonpolarizable water models (with flexible bonds and fixed charges) that are compatible with AMOEBA solute: the 3-site AW3C and 5-site AW5C. To derive the force-field parameters for AW3C and AW5C, we fit to six experimental liquid thermodynamic properties: liquid density, enthalpy of vaporization, dielectric constant, isobaric heat capacity, isothermal compressibility and thermal expansion coefficient, at a broad range of temperatures from 261.15 to 353.15 K under 1.0 atm pressure. We further validate our AW3C and AW5C water models by showing that they can well reproduce the radial distribution function g(r), self-diffusion constant D, and hydration free energy from the AMOEBA03 water model and the experimental observations. Furthermore, we show that our AW3C and AW5C water models can greatly accelerate (>5 times) the bulk water as well as biomolecular simulations when compared to AMOEBA water. Specifically, we demonstrate that the applications of AW3C and AW5C water models to simulate a DNA duplex lead to a threefold acceleration, and in the meanwhile well maintain the structural properties as the fully polarizable AMOEBA water. We expect that our AW3C and AW5C water models hold great promise to be widely applied to simulate complex bio-molecules using the AMOEBA force field.

A FFLUX Water Model: Flexible, Polarizable and with a Multipolar Description of Electrostatics

Key to progress in molecular simulation is the development of advanced models that go beyond the limitations of traditional force fields that employ a fixed, point charge-based description of electrostatics. Taking water as an example system, the FFLUX framework is shown capable of producing models that are flexible, polarizable and have a multipolar description of the electrostatics. The kriging machine-learning methods used in FFLUX are able to reproduce the intramolecular potential energy surface and multipole moments of a single water molecule with chemical accuracy using as few as 50 training configurations. Molecular dynamics simulations of water clusters (25-216 molecules) using the new FFLUX model reveal that incorporating charge-quadrupole, dipole-dipole, and quadrupole-charge interactions into the description of the electrostatics results in significant changes to the intermolecular structuring of the water molecules. © 2019 The Authors. Journal of Computational Chemistry published by Wiley Periodicals, Inc.

Development of a Force Field for the Simulation of Single-Chain Proteins and Protein-Protein Complexes

The accuracy of atomistic physics-based force fields for the simulation of biological macromolecules has typically been benchmarked experimentally using biophysical data from simple, often single-chain systems. In the case of proteins, the careful refinement of force field parameters associated with torsion-angle potentials and the use of improved water models have enabled a great deal of progress toward the highly accurate simulation of such monomeric systems in both folded and, more recently, disordered states. In living organisms, however, proteins constantly interact with other macromolecules, such as proteins and nucleic acids, and these interactions are often essential for proper biological function. Here, we show that state-of-the-art force fields tuned to provide an accurate description of both ordered and disordered proteins can be limited in their ability to accurately describe protein-protein complexes. This observation prompted us to perform an extensive reparameterization of one variant of the Amber protein force field. Our objective involved refitting not only the parameters associated with torsion-angle potentials but also the parameters used to model nonbonded interactions, the specification of which is expected to be central to the accurate description of multicomponent systems. The resulting force field, which we call DES-Amber, allows for more accurate simulations of protein-protein complexes, while still providing a state-of-the-art description of both ordered and disordered single-chain proteins. Despite the improvements, calculated protein-protein association free energies still appear to deviate substantially from experiment, a result suggesting that more fundamental changes to the force field, such as the explicit treatment of polarization effects, may simultaneously further improve the modeling of single-chain proteins and protein-protein complexes.

Evaluation of the AMOEBA force field for simulating metal halide perovskites in the solid state and in solution

In this work, we compare the existing nonpolarizable force fields developed to study the solid or solution phases of hybrid organic-inorganic halide perovskites with the AMOEBA polarizable force field. The aim is to test whether more computationally expensive polarizable force fields like AMOEBA offer better transferability between solution and solid phases, with the ultimate goal being the study of crystal nucleation, growth, and other interfacial phenomena involving these ionic compounds. In the context of hybrid perovskites, AMOEBA force field parameters already exist for several elements in solution, and we decided to leave them unchanged and to only parameterize the missing ones (Pb²⁺ and CH₃NH₃ ⁺ ions) in order to maximize transferability and avoid overfitting to the specific examples studied here. Overall, we find that AMOEBA yields accurate hydration free energies (within 5%) for typical ionic species while showing the correct ordering of stability for the different crystal polymorphs of CsPbI₃ and CH₃NH₃PbI₃. Although the existing parameters do not accurately reproduce all transition temperatures and lattice parameters, AMOEBA offers better transferability between solution and solid states than existing nonpolarizable force fields.

Implementation of Geometry-Dependent Charge Flux into the Polarizable AMOEBA+ Potential

Molecular dynamics (MD) simulations employing classical force fields (FFs) have been widely used to model molecular systems. The important ingredient of the current FFs, atomic charge, remains fixed during MD simulations despite the atomic environment or local geometry changes. This approximation hinders the transferability of the potential being used in multiple phases. Here we implement a geometry-dependent charge flux (GDCF) model into the multipole-based AMOEBA+ polarizable potential. The CF in the current work explicitly depends on the local geometry (bond and angle) of the molecule. To our knowledge, this is the first study that derives energy and force expressions due to GDCF in a multipole-based polarizable FF framework. Due to the inclusion of GDCF, the AMOEBA+ water model is noticeably improved in terms of describing the monomer properties, cluster binding/interaction energy, and a variety of liquid properties, including the infrared spectra that previous flexible water models were not able to capture.

Accurate Biomolecular Simulations Account for Electronic Polarization

In this perspective, we discuss where and how accounting for electronic many-body polarization affects the accuracy of classical molecular dynamics simulations of biomolecules. While the effects of electronic polarization are highly pronounced for molecules with an opposite total charge, they are also non-negligible for interactions with overall neutral molecules. For instance, neglecting these effects in important biomolecules like amino acids and phospholipids affects the structure of proteins and membranes having a large impact on interpreting experimental data as well as building coarse grained models. With the combined advances in theory, algorithms and computational power it is currently realistic to perform simulations with explicit polarizable dipoles on systems with relevant sizes and complexity. Alternatively, the effects of electronic polarization can also be included at zero additional computational cost compared to standard fixed-charge force fields using the electronic continuum correction, as was recently demonstrated for several classes of biomolecules.

Exploring optimization strategies for improving explicit water models: Rigid n-point model and polarizable model based on Drude oscillator

Rigid n-point water models are widely used in atomistic simulations, but have known accuracy drawbacks. Increasing the number of point charges, as well as adding electronic polarizability, are two common strategies for accuracy improvements. Both strategies come at considerable computational cost, which weighs heavily against modest possible accuracy improvements in practical simulations. In an effort to provide guidance for model development, here we have explored the limiting accuracy of "electrostatically globally optimal" n-point water models in terms of their ability to reproduce properties of water dimer-a mimic of the condensed state of water. For a given n, each model is built upon a set of reference multipole moments (e.g. ab initio) and then optimized to reproduce water dimer total dipole moment. The models are then evaluated with respect to the accuracy of reproducing the geometry of the water dimer. We find that global optimization of the charge distribution alone can deliver high accuracy of the water model: for n = 4 or n = 5, the geometry of the resulting water dimer can be almost within 50 of the ab initio reference, which is half that of the experimental error margin. Thus, global optimization of the charge distribution of classical n-point water models can lead to high accuracy models. We also find that while the accuracy improvement in going from n = 3 to n = 4 is substantial, the additional accuracy increase in going from n = 4 to n = 5 is marginal. Next, we have explored accuracy limitations of the standard practice of adding electronic polarizability (via a Drude particle) to a "rigid base"-pre-optimization rigid n-point water model. The resulting model (n = 3) shows a relatively small improvement in accuracy, suggesting that the strategy of merely adding the polarizability to an inferior accuracy water model used as the base cannot fix the defects of the latter. An alternative strategy in which the parameters of the rigid base model are globally optimized along with the polarizability parameter is much more promising: the resulting 3-point polarizable model out-performs even the 5-point optimal rigid model by a large margin. We suggest that future development efforts consider 3- and 4-point polarizable models where global optimization of the "rigid base" is coupled to optimization of the polarizability to deliver globally optimal solutions.

Ewald-based methods for Gaussian integral evaluation: application to a new parameterization of GEM

The development of accurate potentials for computational simulations has been an active area of research. Our group has been involved in the development of the Gaussian electrostatic model (GEM), a force field based on molecular densities. The philosophy of GEM is based on the pioneering work of N. Gresh and co-workers of the reproduction of individual inter-molecular interaction components obtained from quantum mechanical (QM) energy decomposition analysis (EDA). The molecular densities used in GEM are represented by fitting accurate QM molecular densities using auxiliary basis sets (comprised of Hermite Gaussians). The use of these molecular densities results in the need to evaluate a large number of Gaussian integrals. We have previously shown that the particle-mesh Ewald (PME), and fast Fourier Poisson (FFP) methods can be used for efficiently evaluating these types of integrals. Here, we present the latest parameterization of GEM* and its application for an extensive study of PME and FFP for molecular dynamics (MD) simulations using a hybrid version of our potential, GEM*. The temperature dependence of various bulk properties is presented and discussed, as well as the effect of various parameters affecting the performance/accuracy of both methods.

Molecular Dynamics Simulations of Ionic Liquids and Electrolytes Using Polarizable Force Fields

Many applications in chemistry, biology, and energy storage/conversion research rely on molecular simulations to provide fundamental insight into structural and transport properties of materials with high ionic concentrations. Whether the system is comprised entirely of ions, like ionic liquids, or is a mixture of a polar solvent with a salt, e.g., liquid electrolytes for battery applications, the presence of ions in these materials results in strong local electric fields polarizing solvent molecules and large ions. To predict properties of such systems from molecular simulations often requires either explicit or mean-field inclusion of the influence of polarization on electrostatic interactions. In this manuscript, we review the pros and cons of different treatments of polarization ranging from the mean-field approaches to the most popular explicit polarization models in molecular dynamics simulations of ionic materials. For each method, we discuss their advantages and disadvantages and emphasize key assumptions as well as their adjustable parameters. Strategies for the development of polarizable models are presented with a specific focus on extracting atomic polarizabilities. Finally, we compare simulations using polarizable and nonpolarizable models for several classes of ionic systems, discussing the underlying physics that each approach includes or ignores, implications for implementation and computational efficiency, and the accuracy of properties predicted by these methods compared to experiments.