Polarizable Atomic Multipole Water Model for Molecular Mechanics Simulation

CHARMM at 45: Enhancements in Accessibility, Functionality, and Speed

Since its inception nearly a half century ago, CHARMM has been playing a central role in computational biochemistry and biophysics. Commensurate with the developments in experimental research and advances in computer hardware, the range of methods and applicability of CHARMM have also grown. This review summarizes major developments that occurred after 2009 when the last review of CHARMM was published. They include the following: new faster simulation engines, accessible user interfaces for convenient workflows, and a vast array of simulation and analysis methods that encompass quantum mechanical, atomistic, and coarse-grained levels, as well as extensive coverage of force fields. In addition to providing the current snapshot of the CHARMM development, this review may serve as a starting point for exploring relevant theories and computational methods for tackling contemporary and emerging problems in biomolecular systems. CHARMM is freely available for academic and nonprofit research at https://academiccharmm.org/program.

NMR Spectroscopy and Multiscale Modeling Shed Light on Ion-Solvent Interactions and Ion Pairing in Aqueous NaF Solutions

The balance between ion solvation and ion pairing in aqueous solutions modulates chemical and physical processes from catalysis to protein folding. Yet, despite more than a century of investigation, experimental determination of the distribution of ion-solvation and ion-pairing states remains elusive, even for archetypal systems like aqueous alkali halides. Here, we combine nuclear magnetic resonance (NMR) spectroscopy and multiscale modeling to disentangle ion-solvent interactions from ion pairing in aqueous sodium fluoride solutions. We have developed a high-accuracy method to collect experimental NMR resonance frequencies for both ions as functions of temperature and concentration. Comparison of these data with resonance frequencies for nonassociating salts allows us to differentiate the influence of solvation and ion pairing on NMR spectra. These high-quality experimental NMR data are used to validate our modeling framework comprising polarizable force field molecular dynamics (MD) simulations and quantum chemical calculations of NMR resonance frequencies. Our experimental and theoretical resonance frequency shifts agree over a wide range of temperatures and concentrations. Structural analysis reveals how both trends are dominated by interactions with water molecules. For the more sensitive 19F nucleus, the NMR resonance frequency decreases as hydrogen bonds between fluoride and water molecules are reduced in number with increased temperature and molality. Through a detailed analysis of the theoretical NMR resonance frequencies for both ions, we show that NMR spectroscopy can distinguish both contact ion pairs and single-solvent-separated ion pairs from free ions. This quantitative framework can be applied directly to other systems.

Development of an anisotropic polarizable model for the all-atom AMOEBA force field

For planar and rigid π-conjugated molecular systems, electrostatic and inductive interactions are pivotal in governing molecular packing structures and electron polarization energies. These electrostatic interactions typically exhibit an anisotropic nature within π-conjugated systems. In this study, we utilize the atoms in molecules (AIM) theory in conjunction with linear response theory to decompose molecular polarizability into distributed atomic polarizability tensors. On the basis of atomic polarizability tensors, we extended an anisotropic polarizable model into the AMOEBA polarizable force field. Both anisotropic and isotropic polarizable models in combination with various density functional theory (DFT)-derived atomic multipoles were applied to optimize the experimental crystals of naphthalene and anthracene. Furthermore, these two types of electrostatic models, coupled with the evolutionary algorithm USPEX program, are utilized to predict the crystal structures of oligoacenes. Our findings demonstrate that the anisotropic polarizable model exhibits superior performance in crystal refinement and crystal structure prediction. This enriched anisotropic polarizable model is seamlessly integrated into the AMOEBA polarizable force field and readily applicable within our modified Tinker program.

Calculation of solvation force in molecular dynamics simulation by deep-learning method

Electrostatic calculations are generally used in studying the thermodynamics and kinetics of biomolecules in solvent. Generally, this is performed by solving the Poisson-Boltzmann equation on a large grid system, a process known to be time consuming. In this study, we developed a deep neural network to predict the decomposed solvation free energies and forces of all atoms in a molecule. To train the network, the internal coordinates of the molecule were used as the input data, and the solvation free energies along with transformed atomic forces from the Poisson-Boltzmann equation were used as labels. Both the training and prediction tasks were accelerated on GPU. Formal tests demonstrated that our method can provide reasonable predictions for small molecules when the network is well-trained with its simulation data. This method is suitable for processing lots of snapshots of molecules in a long trajectory. Moreover, we applied this method in the molecular dynamics simulation with enhanced sampling. The calculated free energy landscape closely resembled that obtained from explicit solvent simulations.

Polarizable atomic multipole-based force field for cholesterol

Cholesterol is one of the essential component of lipid in membrane. We present a polarizable atomic multipole force field (FF) for the molecular dynamic simulation of cholesterol. The FF building process follows the computational framework as the atomic multipole optimized energetics for biomolecular applications (AMOEBA) model. In this framework, the electronics parameters, including atomic monopole moments, dipole moments, and quadrupole moments calculated from ab initio calculations in the gas phase, are applied to represent the charge distribution. Furthermore, the many-body polarization is modeled by following the same pattern of distributed atomic polarizabilities. Then, the bilayers composed of two typical phospholipid molecules, 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC), and 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC), in a range of different cholesterol concentrations are built and implemented by molecular dynamics (MD) simulations based on the proposed polarizable FF. The simulation results are statistically analyzed to validate the feasibility of the proposed FF. The structural properties of the bilayers are calculated to compare with the related experimental values. The MD values show the same trend of experimental values changes.Communicated by Ramaswamy H. Sarma.

Water-glycan interactions drive the SARS-CoV-2 spike dynamics: insights into glycan-gate control and camouflage mechanisms

To develop therapeutic strategies against COVID-19, we introduce a high-resolution all-atom polarizable model capturing many-body effects of protein, glycan, solvent, and membrane components in SARS-CoV-2 spike protein open and closed states. Employing μs-long molecular dynamics simulations powered by high-performance cloud-computing and unsupervised density-driven adaptive sampling, we investigated the differences in bulk-solvent-glycan and protein-solvent-glycan interfaces between these states. We unraveled a sophisticated solvent-glycan polarization interaction network involving the N165/N343 glycan-gate patterns that provide structural support for the open state and identified key water molecules that could potentially be targeted to destabilize this configuration. In the closed state, the reduced solvent polarization diminishes the overall N165/N343 dipoles, yet internal interactions and a reorganized sugar coat stabilize this state. Despite variations, our glycan-solvent accessibility analysis reveals the glycan shield capability to conserve constant interactions with the solvent, effectively camouflaging the virus from immune detection in both states. The presented insights advance our comprehension of viral pathogenesis at an atomic level, offering potential to combat COVID-19.

A new method to calculate broadband dielectric spectra of solvents from molecular dynamics simulations demonstrated with polarizable force fields

Simulating the dielectric spectra of solvents requires the nuanced definition of inter- and intra-molecular forces. Non-polarizable force fields, while thoroughly benchmarked for dielectric applications, do not capture all the spectral features of solvents, such as water. Conversely, polarizable force fields have been largely untested in the context of dielectric spectroscopy but include charge and dipole fluctuations that contribute to intermolecular interactions. We benchmark non-polarizable force fields and the polarizable force fields AMOEBA03 and HIPPO for liquid water and find that the polarizable force fields can capture all the experimentally observed spectral features with varying degrees of accuracy. However, the non-polarizable force fields miss at least one peak. To diagnose this deficiency, we decompose the liquid water spectra from polarizable force fields at multiple temperatures into static and induced dipole contributions and find that the peak originates from induced dipole contributions. Broadening our inquiry to other solvents parameterized with the AMOEBA09 force field, we demonstrate good agreement between the experimental and simulated dielectric spectra of methanol and formamide. To produce these spectra, we develop a new computational approach to calculate the dielectric spectrum via the fluctuation dissipation theorem. This method minimizes the error in both the low and high frequency portions of the spectrum, improving the overall accuracy of the simulated spectrum and broadening the computed frequency range.

Getting the intermolecular forces correct: introducing the ASTA strategy for a water model

Having a force field for water providing good bulk properties is paramount for modern studies of most biological systems. Some of the most common three-site force fields are TIP3, SPC/ε or OPC3, providing a decent range of bulk properties. That does not mean though, that they have realistic inter-atomic forces. These force fields have been parameterized with a top-down approach, meaning, by fitting the force field parameters to the experimental bulk properties. This approach has been the governing strategy also for many variants of four- and more-site models. We test a bottom-up approach, in which the force field is parameterized by optimizing the non-bonded inter-atomic forces. Our philosophy is that correct inter-atomic forces lead to correct geometrical and dynamical properties. The first system we try to optimize with the accurately system tailored atomic (ASTA) approach is water, but we aim to eventually probe other systems in the future as well. We applied our ASTA strategy to find a good set of parameters providing accurate bulk properties for the simple three-site force field forms, and also for AMOEBA, a more detailed and polarizable force field. Even though our bottom-up approach did not provide satisfactory results for the simple three-site force fields (with fixed charges), for the case of the AMOEBA force field it led to a modification of the original strategy, giving very good intra- and inter-molecular forces, as compared to accurate quantum chemically calculated reference forces. At the same time, important bulk properties, in this study restricted to the density and diffusion, were accurately reproduced with respect to the experimental values.

Dynamic Ion Correlations and Ion-Pair Lifetimes in Aqueous Alkali Metal Chloride Electrolytes

Electrolytes are central to many technological applications, as well as life itself. The behavior and properties of electrolytes are often described in terms of ion pairs, whereby ions associate as either contact ion pairs (in which ions are "touching") solvent-separated ion pairs (in which ions' solvent shells overlap) or solvent-solvent-separated ion pairs (in which ions' solvent shells are distinct). However, this paradigm is generally restricted to statistically averaged descriptions of solution structure and ignores temporal behavior. Here we elucidate the time-resolved dynamics of these ion-ion interactions in aqueous metal chloride electrolytes using the partial van Hove correlation function, based on polarizable molecular dynamics simulations. Our results show that the existence and persistence of ion pairs in aqueous metal chloride electrolytes should not be assumed a priori, but in fact are ion specific features of the solution with lifetimes on subpicosecond time scales.

A Polarizable QM/MM Model That Combines the State-Averaged CASSCF and AMOEBA Force Field for Photoreactions in Proteins

This study presents the polarizable quantum mechanics/molecular mechanics (QM/MM) embedding of the state-averaged complete active space self-consistent field (SA-CASSCF) in the atomic multipole optimized energetics for biomolecular applications (AMOEBA) force field for the purpose of studying photoreactions in protein environments. We describe two extensions of our previous work that combine SA-CASSCF with AMOEBA water models, allowing it to be generalized to AMOEBA models for proteins and other macromolecules. First, we discuss how our QM/MM model accounts for the discrepancy between the direct and polarization electric fields that arises in the AMOEBA description of intramolecular polarization. A second improvement is the incorporation of link atom schemes to treat instances in which the QM/MM boundary goes through covalent bonds. A single-link atom scheme and double-link atom scheme are considered in this work, and we will discuss how electrostatic interaction, van der Waals interaction, and various kinds of valence terms are treated across the boundary. To test the accuracy of the link atom scheme, we will compare QM/MM with full QM calculations and study how the errors in ground state properties, excited state properties, and excitation energies change when tuning the parameters in the link atom scheme. We will also test the new SA-CASSCF/AMOEBA method on an elementary reaction step in NanoLuc, an artificial bioluminescence luciferase. We will show how the reaction mechanism is different when calculated in the gas phase, in polarizable continuum medium (PCM), versus in protein AMOEBA models.

FeNNol: An efficient and flexible library for building force-field-enhanced neural network potentials

Neural network interatomic potentials (NNPs) have recently proven to be powerful tools to accurately model complex molecular systems while bypassing the high numerical cost of ab initio molecular dynamics simulations. In recent years, numerous advances in model architectures as well as the development of hybrid models combining machine-learning (ML) with more traditional, physically motivated, force-field interactions have considerably increased the design space of ML potentials. In this paper, we present FeNNol, a new library for building, training, and running force-field-enhanced neural network potentials. It provides a flexible and modular system for building hybrid models, allowing us to easily combine state-of-the-art embeddings with ML-parameterized physical interaction terms without the need for explicit programming. Furthermore, FeNNol leverages the automatic differentiation and just-in-time compilation features of the Jax Python library to enable fast evaluation of NNPs, shrinking the performance gap between ML potentials and standard force-fields. This is demonstrated with the popular ANI-2x model reaching simulation speeds nearly on par with the AMOEBA polarizable force-field on commodity GPUs (graphics processing units). We hope that FeNNol will facilitate the development and application of new hybrid NNP architectures for a wide range of molecular simulation problems.

Accuracy limit of non-polarizable four-point water models: TIP4P/2005 vs OPC. Should water models reproduce the experimental dielectric constant?

The last generation of four center non-polarizable models of water can be divided into two groups: those reproducing the dielectric constant of water, as OPC, and those significantly underestimating its value, as TIP4P/2005. To evaluate the global performance of OPC and TIP4P/2005, we shall follow the test proposed by Vega and Abascal in 2011 evaluating about 40 properties to fairly address this comparison. The liquid-vapor and liquid-solid equilibria are computed, as well as the heat capacities, isothermal compressibilities, surface tensions, densities of different ice polymorphs, the density maximum, equations of state at high pressures, and transport properties. General aspects of the phase diagram are considered by comparing the ratios of different temperatures (namely, the temperature of maximum density, the melting temperature of hexagonal ice, and the critical temperature). The final scores are 7.2 for TIP4P/2005 and 6.3 for OPC. The results of this work strongly suggest that we have reached the limit of what can be achieved with non-polarizable models of water and that the attempt to reproduce the experimental dielectric constant deteriorates the global performance of the water force field. The reason is that the dielectric constant depends on two surfaces (potential energy and dipole moment surfaces), whereas in the absence of an electric field, all properties can be determined simply from just one surface (the potential energy surface). The consequences of the choice of the water model in the modeling of electrolytes in water are also discussed.

Force Field X: A computational microscope to study genetic variation and organic crystals using theory and experiment

Force Field X (FFX) is an open-source software package for atomic resolution modeling of genetic variants and organic crystals that leverages advanced potential energy functions and experimental data. FFX currently consists of nine modular packages with novel algorithms that include global optimization via a many-body expansion, acid-base chemistry using polarizable constant-pH molecular dynamics, estimation of free energy differences, generalized Kirkwood implicit solvent models, and many more. Applications of FFX focus on the use and development of a crystal structure prediction pipeline, biomolecular structure refinement against experimental datasets, and estimation of the thermodynamic effects of genetic variants on both proteins and nucleic acids. The use of Parallel Java and OpenMM combines to offer shared memory, message passing, and graphics processing unit parallelization for high performance simulations. Overall, the FFX platform serves as a computational microscope to study systems ranging from organic crystals to solvated biomolecular systems.

Edge-sharing water prisms

Regular-shaped water clusters and nanostructures can be of particular interest for the self-assembly of complex structures and functional materials involving water molecules. Polyhedral water clusters are the most well studied. The low-energy structures of water hexamer, octamer and decamer are shaped like right prisms. The cavities of gas hydrates also have a polyhedral shape. Ice nanotubes are of no less interest both as configurations of global energy minima and in terms of possible applications. This article presents the results of the first systematic study of the structure and properties of a special class of water clusters. It reveals different combinations of three right prisms sharing an edge. According to modern calculations, the configurations of global energy minima of water clusters with the number of molecules being eighteen and twenty have this structure precisely. The topological characteristics of the edge-sharing water prisms are studied and the formulas for estimating the residual entropy are obtained. For these clusters (3-prisms), the usefulness of using a discrete model of intermolecular interaction [strong-weak-effective-bond model], previously developed for polyhedral water clusters, is shown. Calculations of the binding energy were performed using the non-additive Amoeba potential. To understand the relative stability of 3-prisms among other cluster forms, we use the structures recently reported in a published database containing over 3 × 106 unique water cluster networks (H2O)N of size N = 3-25 [Rakshit et al., J. Chem. Phys., 2019, 151(21), 214307, DOI: 10.1063/1.5128378].

Simulation of Linear and Cyclic Alkanes with Second-Order Møller-Plesset Perturbation Theory through Adaptive Force Matching

Predicting ensemble properties, such as density and heat of vaporization, of small hydrocarbons is challenging due to the dispersion-dominated weak interactions between these molecules. With the adaptive force matching (AFM) method, the bonded and short-range nonbonded interactions are fitted to second-order Møller-Plesset perturbation theory (MP2) references computed with the def2-TZVP basis set. The dispersion is modeled using symmetry adapted perturbation theory (SAPT) at MP4 accuracy using the def2-TZVPD basis set. A new charge matrix decomposition technique is described to obtain partial charges in AFM. Although the models developed do not have any empirical parameters, several properties of the resulting models are compared with experiments as validations. The density, heat of vaporization, pressure dependence of density, diffusion constants, and surface tensions all show quantitative agreement with experiments. Although the density shows a very small systematic error, which could be due to missing three-body dispersion, the heat of vaporization agrees with experiments of within 0.5%. The paper shows that AFM can be used as a reliable tool to enable simulations at post-Hartree-Fock quality at the cost of molecular mechanics force fields.

Lambda-ABF: Simplified, Portable, Accurate, and Cost-Effective Alchemical Free-Energy Computation

We introduce the lambda-Adaptive Biasing Force (lambda-ABF) method for the computation of alchemical free-energy differences. We propose a software implementation and showcase it on biomolecular systems. The method arises from coupling multiple-walker adaptive biasing force with λ-dynamics. The sampling of the alchemical variable is continuous and converges toward a uniform distribution, making manual optimization of the λ schedule unnecessary. Contrary to most other approaches, alchemical free-energy estimates are obtained immediately without any postprocessing. Free diffusion of λ improves orthogonal relaxation compared to fixed-λ thermodynamic integration or free-energy perturbation. Furthermore, multiple walkers provide generic orthogonal space coverage with minimal user input and negligible computational overhead. We show that our high-performance implementations coupling the Colvars library with NAMD and Tinker-HP can address real-world cases including ligand-receptor binding with both fixed-charge and polarizable models, with a demonstrably richer sampling than fixed-λ methods. The implementation is fully open-source, publicly available, and readily usable by practitioners of current alchemical methods. Thanks to the portable Colvars library, lambda-ABF presents a unified user interface regardless of the back-end (NAMD, Tinker-HP, or any software to be interfaced in the future), sparing users the effort of learning multiple interfaces. Finally, the Colvars Dashboard extension of the visual molecular dynamics (VMD) software provides an interactive monitoring and diagnostic tool for lambda-ABF simulations.

Exploring Biomolecular Conformational Dynamics with Polarizable Force Field AMOEBA and Enhanced Sampling Method Milestoning

Conformational dynamics play a crucial role in determining the behavior of the biomolecules. Polarizable force fields, such as AMOEBA, can accurately capture electrostatic interactions underlying the conformational space. However, applying a polarizable force field in molecular dynamics (MD) simulations can be computationally expensive, especially in studying long-time-scale dynamics. To overcome this challenge, we incorporated the AMOEBA potential with Milestoning, an enhanced sampling method in this work. This integration allows us to efficiently sample the rare and important conformational states of a biomolecule by using many short and independent molecular dynamics trajectories with the AMOEBA force field. We applied this method to investigate the conformational dynamics of alanine dipeptide, DNA, and RNA A-B form conversion. Well-converged thermodynamic and kinetic properties were obtained, including the free energy difference, mean first passage time, and critical transitions between states. Our results demonstrate the power of integrating polarizable force fields with enhanced sampling methods in quantifying the thermodynamic and kinetic properties of biomolecules at the atomic level.

Water Solvent Reorganization upon Ultrafast Resonant Stimulated X-ray Raman Excitation of a Metalloporphyrin Dimer

We propose an X-ray Raman pump-X-ray diffraction probe scheme to follow solvation dynamics upon charge migration in a solute molecule. The X-ray Raman pump selectively prepares a valence electronic wavepacket in the solute, while the probe provides information about the entire molecular ensemble. A combination of molecular dynamics and ab initio quantum chemistry simulations is applied to a Zn-Ni porphyrin dimer in water. Using time-resolved X-ray diffraction and pair distribution functions, we extracted solvation shell dynamics.

Impact of an Ionic Liquid Solution on Horseradish Peroxidase Activity

Horseradish peroxidase (HRP) is an enzyme that oxidizes pollutants from wastewater. A previous report indicated that peroxidases can have an enhancement in initial enzymatic activity in an aqueous solution of 0.26 M 1-ethyl-3-methylimidazolium ethyl sulfate ([EMIm][EtSO4]) at neutral pH. However, the atomistic details remain elusive. In the enzymatic landscape of HRP, compound II (Cpd II) plays a key role and involves a histidine (H42) residue. Cpd II exists as oxoferryl (2a) or hydroxoferryl (2b(FeIV)) forms, where 2a is the predominantly observed form in experimental studies. Intriguingly, the ferric 2b(FeIII) form seen in synthetic complexes has not been observed in HRP. Here, we have investigated the structure and dynamics of HRP in pure water and aqueous [EMIm][EtSO4] (0.26 M), as well as the reaction mechanism of 2a to 2b conversion using polarizable molecular dynamics (MD) simulations and quantum mechanics/molecular mechanics (QM/MM) calculations. When HRP is solvated in aq [EMIm][EtSO4], the catalytic water displaces, and H42 directly orients over the ferryl moiety, allowing a direct proton transfer (PT) with a significant energy barrier reduction. Conversely, in neat water, the reaction of 2a to 2b follows the previously reported mechanism. We further investigated the deprotonated form of H42. Analysis of the electric fields at the active site indicates that the aq [EMIm][EtSO4] medium facilitates the reaction by providing a more favorable environment compared with the system solvated in neat water. Overall, the atomic level supports the previous experimental observations and underscores the importance of favorable electric fields in the active site to promote catalysis.

Beyond isotropic repulsion: Classical anisotropic repulsion by inclusion of p orbitals

Accurate modeling of intermolecular repulsion is an integral component in force field development. Although repulsion can be explicitly calculated by applying the Pauli exclusion principle, this approach is computationally viable only for systems of limited sizes. Instead, it has previously been shown that repulsion can be reformulated in a "classical" picture: the Pauli exclusion principle prohibits electrons from occupying the same state, leading to a depletion of electronic charge between atoms, giving rise to an enhanced nuclear-nuclear electrostatic repulsion. This classical picture is called the isotropic S2/R approximation, where S is the overlap and R is the interatomic distance. This approximation accurately captures the repulsion of isotropic atoms such as noble gas dimers; however, a key deficiency is that it fails to capture the angular dependence of the repulsion of anisotropic molecules. To include directionality, the wave function must at least be a linear combination of s and p orbitals. We derive a new anisotropic S2/R repulsion model through the inclusion of the anisotropic p orbital term in the total wave function. Because repulsion is pairwise and decays rapidly, it can be truncated at a short range, making it amenable for efficient calculation of energy and forces in complex biomolecular systems. We present a parameterization of the S101 dimer database against the ab initio benchmark symmetry-adapted perturbation theory, which yields an rms error of only 0.9 kcal/mol. The importance of the anisotropic term is demonstrated through angular scans of water-water dimers and dimers involving halobenzene. Simulation of liquid water shows that the model can be computed efficiently for realistic system sizes.

The role of charge in microdroplet redox chemistry

In charged water microdroplets, which occur in nature or in the lab upon ultrasonication or in electrospray processes, the thermodynamics for reactive chemistry can be dramatically altered relative to the bulk phase. Here, we provide a theoretical basis for the observation of accelerated chemistry by simulating water droplets of increasing charge imbalance to create redox agents such as hydroxyl and hydrogen radicals and solvated electrons. We compute the hydration enthalpy of OH- and H+ that controls the electron transfer process, and the corresponding changes in vertical ionization energy and vertical electron affinity of the ions, to create OH• and H• reactive species. We find that at ~ 20 - 50% of the Rayleigh limit of droplet charge the hydration enthalpy of both OH- and H+ have decreased by >50 kcal/mol such that electron transfer becomes thermodynamically favorable, in correspondence with the more favorable vertical electron affinity of H+ and the lowered vertical ionization energy of OH-. We provide scaling arguments that show that the nanoscale calculations and conclusions extend to the experimental microdroplet length scale. The relevance of the droplet charge for chemical reactivity is illustrated for the formation of H2O2, and has clear implications for other redox reactions observed to occur with enhanced rates in microdroplets.

Unraveling thermodynamic anomalies of water: A molecular simulation approach to probe the two-state theory with atomistic and coarse-grained water models

Thermodynamic and dynamic anomalies of water play a crucial role in supporting life on our planet. The two-state theory attributes these anomalies to a dynamic equilibrium between locally favored tetrahedral structures (LFTSs) and disordered normal liquid structures. This theory provides a straightforward, phenomenological explanation for water's unique thermodynamic and dynamic characteristics. To validate this two-state feature, it is critical to unequivocally identify these structural motifs in a dynamically fluctuating disordered liquid. In this study, we employ a recently introduced structural parameter (θavg) that characterizes the local angular order within the first coordination shell to identify these LFTSs through molecular dynamics simulations. We employ both realistic water models with a liquid-liquid critical point (LLCP) and a coarse-grained water model without an LLCP to study water's anomalies in low-pressure regions below 2 kbar. The two-state theory consistently describes water's thermodynamic anomalies in these models, both with and without an LLCP. This suggests that the anomalies predominantly result from the two-state features rather than criticality, particularly within experimentally accessible temperature-pressure regions.

Redefined ion association constants have consequences for calcium phosphate nucleation and biomineralization

Calcium orthophosphates (CaPs), as hydroxyapatite (HAP) in bones and teeth are the most important biomineral for humankind. While clusters in CaP nucleation have long been known, their speciation and mechanistic pathways to HAP remain debated. Evidently, mineral nucleation begins with two ions interacting in solution, fundamentally underlying solute clustering. Here, we explore CaP ion association using potentiometric methods and computer simulations. Our results agree with literature association constants for Ca2+ and H2PO4-, and Ca2+ and HPO42-, but not for Ca2+ and PO43- ions, which previously has been strongly overestimated by two orders of magnitude. Our data suggests that the discrepancy is due to a subtle, premature phase separation that can occur at low ion activity products, especially at higher pH. We provide an important revision of long used literature constants, where association of Ca2+ and PO43- actually becomes negligible below pH 9.0, in contrast to previous values. Instead, [CaHPO4]0 dominates the aqueous CaP speciation between pH ~6-10. Consequently, calcium hydrogen phosphate association is critical in cluster-based precipitation in the near-neutral pH regime, e.g., in biomineralization. The revised thermodynamics reveal significant and thus far unexplored multi-anion association in computer simulations, constituting a kinetic trap that further complicates aqueous calcium phosphate speciation.

A Many-Body Perspective of Nuclear Quantum Effects in Aqueous Clusters

Nuclear quantum effects play an important role in the structure and thermodynamics of aqueous systems. By performing a many-body expansion with nuclear-electronic orbital (NEO) theory, we show that proton quantization can give rise to significant energetic contributions for many-body interactions spanning several molecules in single-point energy calculations of water clusters. Although zero-point motion produces a large increase in energy at the one-body level, nuclear quantum effects serve to stabilize higher-order molecular interactions. These results are significant because they demonstrate that nuclear quantum effects play a nontrivial role in many-body interactions of aqueous systems. Our approach also provides a pathway for incorporating nuclear quantum effects into water potential energy surfaces. The NEO approach is advantageous for many-body expansion analyses because it includes nuclear quantum effects directly in the energies.

Constant-pH Simulations with the Polarizable Atomic Multipole AMOEBA Force Field

Accurately predicting protein behavior across diverse pH environments remains a significant challenge in biomolecular simulations. Existing constant-pH molecular dynamics (CpHMD) algorithms are limited to fixed-charge force fields, hindering their application to biomolecular systems described by permanent atomic multipoles or induced dipoles. This work overcomes these limitations by introducing the first polarizable CpHMD algorithm in the context of the Atomic Multipole Optimized Energetics for Biomolecular Applications (AMOEBA) force field. Additionally, our implementation in the open-source Force Field X (FFX) software has the unique ability to handle titration state changes for crystalline systems including flexible support for all 230 space groups. The evaluation of constant-pH molecular dynamics (CpHMD) with the AMOEBA force field was performed on 11 crystalline peptide systems that span the titrating amino acids (Asp, Glu, His, Lys, and Cys). Titration states were correctly predicted for 15 out of the 16 amino acids present in the 11 systems, including for the coordination of Zn2+ by cysteines. The lone exception was for a HIS-ALA peptide where CpHMD predicted both neutral histidine tautomers to be equally populated, whereas the experimental model did not consider multiple conformers and diffraction data are unavailable for rerefinement. This work demonstrates the promise polarizable CpHMD simulations for pKa predictions, the study of biochemical mechanisms such as the catalytic triad of proteases, and for improved protein-ligand binding affinity accuracy in the context of pharmaceutical lead optimization.

The OpenMMPol library for polarizable QM/MM calculations of properties and dynamics

We present a new library designed to provide a simple and straightforward way to implement QM/AMOEBA (Atomic Multipole Optimized Energetics for Biomolecular Applications) and other polarizable QM/MM (Molecular Mechanics) methods based on induced point dipoles. The library, herein referred to as OpenMMPol, is free and open-sourced and is engineered to address the increasing demand for accurate and efficient QM/MM simulations. OpenMMPol is specifically designed to allow polarizable QM/MM calculations of ground state energies and gradients and excitation properties. Key features of OpenMMPol include a modular architecture facilitating extensibility, parallel computing capabilities for enhanced performance on modern cluster architectures, a user-friendly interface for intuitive implementation, and a simple and flexible structure for providing input data. To show the capabilities offered by the library, we present an interface with PySCF to perform QM/AMOEBA molecular dynamics, geometry optimization, and excited-state calculation based on (time-dependent) density functional theory.

Relative cooperativity in neutral and charged molecular clusters using QM/MM calculations

QM/MM methods have been used to study electronic structure properties and chemical reactivity in complex molecular systems where direct electronic structure calculations are not feasible. In our previous work, we showed that non-polarizable force fields, by design, describe intermolecular interactions through pairwise interactions, overlooking many-body interactions involving three or more particles. In contrast, polarizable force fields account partially for many-body effects through polarization, but still handle van der Waals and permanent electrostatic interactions pairwise. We showed that despite those limitations, polarizable and non-polarizable force fields can reproduce relative cooperativity achieved using density functional theory due to error compensation mechanisms. In this contribution, we assess the performance of QM/MM methods in reproducing these phenomena. Our study highlights the significance of the QM region size and force field choice in QM/MM calculations, emphasizing the importance of parameter validation to obtain accurate interaction energy predictions.

Incorporating Neural Networks into the AMOEBA Polarizable Force Field

Neural network potentials (NNPs) offer significant promise to bridge the gap between the accuracy of quantum mechanics and the efficiency of molecular mechanics in molecular simulation. Most NNPs rely on the locality assumption that ensures the model's transferability and scalability and thus lack the treatment of long-range interactions, which are essential for molecular systems in the condensed phase. Here we present an integrated hybrid model, AMOEBA+NN, which combines the AMOEBA potential for the short- and long-range noncovalent atomic interactions and an NNP to capture the remaining local covalent contributions. The AMOEBA+NN model was trained on the conformational energy of the ANI-1x data set and tested on several external data sets ranging from small molecules to tetrapeptides. The hybrid model demonstrated substantial improvements over the baseline models in term of accuracy as the molecule size increased, suggesting its potential as a next-generation approach for chemically accurate molecular simulations.

Liquid-Vapor Coexistence and Spontaneous Evaporation at Atmospheric Pressure of Common Rigid Three-Point Water Models in Molecular Simulations

Molecular dynamics (MD) simulations are widely used to investigate molecular systems at atomic resolution including biomolecular structures, drug-receptor interactions, and novel materials. Frequently, MD simulations are performed in an aqueous solution with explicit models of water molecules. Commonly, such models are parameterized to reproduce the liquid phase of water under ambient conditions. However, often, simulations at significantly higher temperatures are also of interest. Hence, it is important to investigate the equilibrium of the liquid and vapor phases of molecular models of water at elevated temperatures. Here, we evaluate the behavior of 11 common rigid three-point water models over a wide range of temperatures. From liquid-vapor coexistence simulations, we estimated the critical points and studied the spontaneous evaporation of these water models. Moreover, we investigated the influence of the system size, choice of the pressure-coupling algorithm, and rate of heating on the process and compared them with the experimental data. We found that modern rigid three-point water models reproduce the critical point surprisingly well. Furthermore, we discovered that the critical temperature correlates with the quadrupole moment of the respective water model. This indicates that the spatial arrangement of the partial charges is important for reproducing the liquid-vapor phase transition. Our findings may guide the selection of water models for simulations conducted at high temperatures.

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.

Investigation of the stability of D5SIC-DNAM-incorporated DNA duplex in Taq polymerase binary system: a systematic classical MD approach

DNA polymerases are fundamental enzymes that play a crucial role in processing DNA with high fidelity and accuracy ensuring the faithful transmission of genetic information. The recognition of unnatural base pairs (UBPs) by polymerases, enabling their replication, represents a significant and groundbreaking discovery with profound implications for genetic expansion. Romesberg et al. examined the impact of DNA containing 2,6-dimethyl-2H-isoquiniline-1-thione: D5SIC (DS) and 2-methoxy-3-methylnaphthalene: DNAM (DN) UBPs bound to T. aquaticus DNA polymerase (Taq) through crystal structure analysis. Here, we have used polarizable and nonpolarizable classical molecular dynamics (MD) simulations to investigate the structural aspects and stability of Taq in complex with a DNA duplex including a DS-DN pair in the terminal 3' and 5' positions. Our results suggest that the flexibility of UBP-incorporated DNA in the terminal position is arrested by the polymerase, thus preventing fraying and mispairing. Our investigation also reveals that the UBP remains in an intercalated conformation inside the active site, exhibiting two distinct orientations in agreement with experimental findings. Our analysis pinpoints particular residues responsible for favorable interactions with the UBP, with some relying on van der Waals interactions while other on Coulombic forces.

Investigation of dynamical flexibility of D5SIC-DNAM inside DNA duplex in aqueous solution: a systematic classical MD approach

Incorporation of artificial 3rd base pairs (unnatural base pairs, UBPs) has emerged as a fundamental technique in pursuit of expanding the genetic alphabet. 2,6-Dimethyl-2H-isoquiniline-1-thione: D5SIC (DS) and 2-methoxy-3-methylnaphthalene: DNAM (DN), a potential unnatural base pair (UBP) developed by Romesberg and colleagues, has been shown to have remarkable capability for replication within DNA. Crystal structures of a Taq polymerase/double-stranded DNA (ds-DNA) complex containing a DS-DN pair in the 3' terminus showed a parallelly stacked geometry for the pre-insertion, and an intercalated geometry for the post-insertion structure. Unconventional orientations of DS-DN inside a DNA duplex have inspired scientists to investigate the conformational orientations and structural properties of UBP-incorporated DNA. In recent years, computational simulations have been used to investigate the geometry of DS-DN within the DNA duplex; nevertheless, unresolved questions persist owing to inconclusive findings. In this work, we investigate the structural and dynamical properties of DS and DN inside a ds-DNA strand in aqueous solution considering both short and long DNA templates using polarizable, and non-polarizable classical MD simulations. Flexible conformational change of UBP with major populations of Watson-Crick-Franklin (WCF) and three distinct non-Watson-Crick-Franklin (nWCFP1, nWCFP2, nWCFO) conformations through intra and inter-strand flipping have been observed. Our results suggest that a dynamical conformational change leads to the production of diffierent conformational distribution for the systems. Simulations with a short ds-DNA duplex suggest nWCF (P1 and O) as the predominant structures, whereas long ds-DNA duplex simulations indicate almost equal populations of WCF, nWCFP1, nWCFO. DS-DN in the terminal position is found to be more flexible with occasional mispairing and fraying. Overall, these results suggest flexibility and dynamical conformational change of the UBP as well as indicate varied conformational distribution irrespective of starting orientation of the UBP and length og DNA strand.

System-Specific Parameter Optimization for Nonpolarizable and Polarizable Force Fields

The accuracy of classical force fields (FFs) has been shown to be limited for the simulation of cation-protein systems despite their importance in understanding the processes of life. Improvements can result from optimizing the parameters of classical FFs or by extending the FF formulation by terms describing charge transfer (CT) and polarization (POL) effects. In this work, we introduce our implementation of the CTPOL model in OpenMM, which extends the classical additive FF formula by adding CT and POL. Furthermore, we present an open-source parametrization tool, called FFAFFURR, that enables the (system-specific) parametrization of OPLS-AA and CTPOL models. The performance of our workflow was evaluated by its ability to reproduce quantum chemistry energies and by molecular dynamics simulations of a zinc-finger protein.

Polarizable AMOEBA Model for Simulating Mg2+·Protein·Nucleotide Complexes

Molecular mechanics (MM) simulations have the potential to provide detailed insights into the mechanisms of enzymes that utilize nucleotides as cofactors. In most cases, the activities of these enzymes also require the binding of divalent cations to catalytic sites. However, modeling divalent cations in MM simulations has been challenging. The inclusion of explicit polarization was considered promising, but despite improvements over nonpolarizable force fields and despite the inclusion of "Nonbonded-fix (NB-fix)" corrections, errors in interaction energies of divalent cations with proteins remain large. Importantly, the application of these models fails to reproduce the experimental structural data on Mg2+·Protein·ATP complexes. Focusing on these complexes, here we provide a systematic assessment of the polarizable AMOEBA model and recommend critical changes that substantially improve its predictive performance. Our key results are as follows. We first show that our recent revision of the AMOEBA protein model (AMOEBABIO18-HFC), which contains high field corrections (HFCs) to induced dipoles, dramatically improves Mg2+-protein interaction energies, reducing the mean absolute error (MAE) from 17 to 10 kcal/mol. This further supports the general applicability of AMOEBABIO18-HFC. The inclusion of many-body NB-fix corrections further reduces MAE to 6 kcal/mol, which amounts to less than 2% error. The errors are estimated with respect to vdW-inclusive density functional theory that we benchmark against CCSD(T) calculations and experiments. We also present a new model of ATP with revised polarization parameters to better capture its high field response, as well as new vdW and dihedral parameters. The ATP model accurately predicts experimental Mg2+-ATP binding free energy in the aqueous phase and provides new insights into how Mg2+ associates with ATP. Finally, we show that molecular dynamics (MD) simulations of Mg2+·Kinase·ATP complexes carried out with these improvements lead to a better agreement in global and local catalytic site structures between MD and X-ray crystallography.

Force-field-enhanced neural network interactions: from local equivariant embedding to atom-in-molecule properties and long-range effects

We introduce FENNIX (Force-Field-Enhanced Neural Network InteraXions), a hybrid approach between machine-learning and force-fields. We leverage state-of-the-art equivariant neural networks to predict local energy contributions and multiple atom-in-molecule properties that are then used as geometry-dependent parameters for physically-motivated energy terms which account for long-range electrostatics and dispersion. Using high-accuracy ab initio data (small organic molecules/dimers), we trained a first version of the model. Exhibiting accurate gas-phase energy predictions, FENNIX is transferable to the condensed phase. It is able to produce stable Molecular Dynamics simulations, including nuclear quantum effects, for water predicting accurate liquid properties. The extrapolating power of the hybrid physically-driven machine learning FENNIX approach is exemplified by computing: (i) the solvated alanine dipeptide free energy landscape; (ii) the reactive dissociation of small molecules.

Cooperativity and Frustration Effects (or Lack Thereof) in Polarizable and Non-polarizable Force Fields

Understanding cooperativity and frustration is crucial for studying biological processes such as molecular recognition and protein aggregation. Force fields have been extensively utilized to explore cooperativity in the formation of protein secondary structures and self-assembled systems. Multiple studies have demonstrated that polarizable force fields provide more accurate descriptions of this phenomenon compared to fixed-charge pairwise nonpolarizable force fields, thanks to the incorporation of polarization effects. In this study, we assess the performance of the AMOEBA polarizable force field and the AMBER and OPLS nonpolarizable pairwise force fields in capturing positive and negative cooperativity recently explored in neutral and charged molecular clusters using density functional theory. Our findings show that polarizable and nonpolarizable force fields qualitatively reproduce the relative cooperativity observed in electron structure calculations. However, AMBER and OPLS fail to describe absolute cooperativity. In contrast, AMOEBA accounts for the absolute cooperativity by considering interactions beyond pairwise interactions. According to the energy decomposition analysis, it is observed that the electrostatic interactions calculated with the AMBER and OPLS force fields seem to play an important and counterintuitive role in reproducing the adiabatic interaction energies calculated with density functional theory. However, it is important to note that these force fields, due to their nature, do not explicitly incorporate many-body effects, which limits their ability to accurately describe cooperativity. On the other hand, frustration in polarizable and nonpolarizable force fields is caused by changes in bond stretching and angle bending terms of the building blocks when they are forming a complex.

Ice structures assembled from cubic water clusters of D2d and S4 symmetry

The study of self-assembly processes is of key importance for fundamental science and modern technologies. Cubic water clusters of D2d and S4 symmetry show great potential as building blocks for self-assembly. The objective of this paper is to construct possible ice structures formed by hydrogen bonding of these very stable water clusters. A number of such structures are herein presented, including quasi-2D and 3D ices as well as spatial layered and tubular ices. The energetics and structure of many configurations differing in the arrangement of hydrogen atoms in hydrogen bonds have been studied. It was established that the proton disorder of all such ices is of island type. The residual entropy of these ices is equal to ln(3)/4 in dimensionless form. For layered structures formed by the stacking of multiple bilayers, the determining role of the van der Waals interactions is shown. Note that, for all considered ices, the lowest-energy configurations are formed only by clusters of D2d symmetry.

Thermodynamics perturbation theory for solvation of nonpolar solutes in rose model

A simple model of water, called the rose model, is used in this work. The rose model is a very simple model that can provide insight into the anomalous properties of water. In the rose water model, the molecules are represented as two-dimensional Lennard-Jones disks with potentials for orientation-dependent pairwise interactions mimicking formations of hydrogen bonds. We have recently applied a Wertheim integral equation theory (IET) and a thermodynamic perturbation theory (TPT) to the rose model in bulk. These analytical theories offer the advantage of being computationally less intensive than computer simulations by orders of magnitudes. Here we have applied the TPT to study the transfer of a nonpolar solute into rose water, the so-called hydrophobic effect. Similarly as in our previous work for bulk water, we have found that the theory reproduces the computer simulation results quite well at higher temperatures, while the theories predict the qualitative trends at low temperatures.

Neural Network Water Model Based on the MB-Pol Many-Body Potential

The MB-pol many-body potential accurately predicts many properties of water, including cluster, liquid phase, and vapor-liquid equilibrium properties, but its high computational cost can make applying it in large-scale simulations quite challenging. In order to address this limitation, we developed a "deep potential" neural network (DPMD) model based on the MB-pol potential for water. We find that a DPMD model trained on mostly liquid configurations yields a good description of the bulk liquid phase but severely underpredicts vapor-liquid coexistence densities. By contrast, adding cluster configurations to the neural network training set leads to a good agreement for the vapor coexistence densities. Liquid phase densities under supercooled conditions are also represented well, even though they were not included in the training set. These results confirm that neural network models can combine accuracy and transferability if sufficient attention is given to the construction of a representative training set for the target system.

Accurate Calculation of Many-Body Energies in Water Clusters Using a Classical Geometry-Dependent Induction Model

We incorporate geometry-dependent distributed multipole and polarizability surfaces into an induction model that is used to describe the 3- and 4-body terms of the interaction between water molecules. The moment expansion is carried out up to the hexadecapole with the multipoles distributed on the atom sites. Dipole-dipole, dipole-quadrupole, and quadrupole-quadrupole distributed polarizabilities are used to represent the response of the multipoles to an electric field. We compare the model against two large databases consisting of 43,844 3-body terms and 3,603 4-body terms obtained from high level ab initio calculations previously used to fit the MB-pol and q-AQUA classical interaction potentials for water. The classical induction model with no adjustable parameters reproduces the ab initio 3-/4-body terms contained in these two databases with a root-mean-square error (RMSE) of 0.104/0.058 and a mean-absolute error (MAE) of 0.054/0.026 kcal/mol, respectively. These results are on par with the ones obtained by fitting the same data using over 14,000 (for the 3-body) and 200 (for the 4-body) parameters via Permutationally Invariant Polynomials (PIPs). This demonstrates the accuracy of this physically motivated model in describing the 3- and 4-body terms in the interactions between water molecules with no adjustable parameters. The triple-dipole-dispersion energy, included in the calculation of the 3-body energy, was found to be small but not quite negligible. The model represents a practical, efficient, and transferable approach for obtaining accurate nonadditive interactions for multicomponent systems without the need to perform tens of thousands of high level electronic structure calculations and fitting them with PIPs.

Angle-dependent integral equation theory improves results of thermodynamics and structure of rose water model

Orientation-dependent integral equation theory (ODIET) was applied to the rose water model. Structural and thermodynamic properties of water modeled with the rose model were calculated using ODIET and compared to results from orientation-averaged integral equation theory (IET) and Monte Carlo simulations. Rose water model is a simple two-dimensional water model where molecules of water are represented as Lennard-Jones disks with explicit hydrogen bonding potential in form of rose functions. Orientational dependency significantly improves IET, as the thermodynamic results obtained using ODIET are significantly more in agreement with results calculated using MC than in the case of the orientationally averaged version. At high temperatures, the agreement between the simulation and theory is quantitative; however, when temperatures lower, a slight deviation between results obtained with different methods appear. ODIET correctly predicts the radial distribution function; moreover, ODIet also enables the calculation of angular distributions. While the angular distributions obtained with ODIET are in qualitative agreement with distributions from MC simulations, the height of the peaks in angular distributions differs between methods. Using results from ODIET, the spatial distribution of water molecules was constructed, which aids in the interpretation of other structural properties. ODIET was also used to calculate fractions of molecules with different number of hydrogen bonds, which is in the agreement with the simulations. Overall, use of ODIET significantly improves the obtained results in comparison to standard IET.

A systematic mechanistic survey on the reactions between OH radical and CH3OH on ice

A systematic mechanistic survey was performed for the CH3OH + OH reaction on ice. ONIOM(ωB97X-D/Def2-TZVP:AMOEBA09) calculations suggested a range of binding energies for the CH2OH radical (0.29-0.69 eV) and CH3OH (0.15-0.72 eV) molecule on hexagonal water ice (Ih) and amorphous solid water (ASW). Computed average binding energies of CH2OH radical (0.49 eV) and CH3OH (0.41 eV) are relatively stronger compared to the CH3O radical binding energies (0.32 eV, Sameera et al., J. Phy. Chem. A, 2021, 125, 387-393). Thus, the CH3OH molecule, CH2OH and CH3O radicals can adsorb on ice, where the binding energies follow the order CH2OH > CH3OH > CH3O. The multi-component artificial force-induced reaction (MC-AFIR) method systematically determined the reaction mechanisms for the CH3OH + OH reaction on ice, where two reaction paths, giving rise to CH2OH and CH3O radicals, were confirmed. A range of reaction barriers, employing the ωB97X-D/Def2-TZVP level of theory, was found for each reaction (0.03-0.11 eV for CH2OH radical formation, and 0.03-0.44 eV for CH3O radical formation). Based on the lowest energy reaction paths, we suspect that both reactions operate on ice. The computed data in this study evidence that the nature of the binding site or the reaction site has a significant effect on the computed binding energies or reaction barriers. Thus, the outcomes of the present study will be very useful for the computational astrochemistry community to determine reliable binding energies and reaction barriers on ice.

Accurate SCC-DFTB Parametrization of Liquid Water with Improved Atomic Charges and Iterative Boltzmann Inversion

This work presents improvements of the description of liquid water within the self-consistent-charge density-functional based tight-binding scheme combining the use of Weighted Mulliken (WMull) charges and optimized O-H repulsive potential through the iterative Boltzmann inversion (IBI) process. The quality of the newly developed models is validated considering pair radial distribution functions (RDFs), as well as other structural, energetic, thermodynamic, and dynamic properties. The use of WMull charges certainly improves the agreement with experimental data, however leading to over-structured RDFs at short distance, that can be further improved by considering an optimized O-H repulsive potential obtained by the IBI process. Three different schemes were used to optimize this potential: (i) optimization including short O-H distances. This led to accurate RDFs as well as improved self-diffusion coefficient and heat of vaporization, while the proton transfer energy barrier is severely deteriorated; (ii) optimization starting at long distance. The proton transfer energy barrier is recovered while the heat of vaporization is deteriorated and the O-H RDF is less accurate at short distance; (iii) optimization within the path-integral molecular dynamics scheme which allows us to exclude nuclear quantum effects from the repulsive potential. The latter potential, in conjunction with the WMull improved atomic charges, provides similar results as (i) for structural, dynamic, and thermodynamic properties while recovering a large part of the proton transfer energy barrier. It therefore offers a good compromise to study both dynamic properties and chemistry within liquid water at a quantum chemical level.

Application of a Fluctuating Charge Polarization Model to Large Polyaromatic Hydrocarbons and Graphene Nanoflakes

We present a polarization model incorporating coupled fluctuating charges and point inducible dipoles that is able to accurately describe the dipole polarizabilities of small hydrocarbons and, for sufficiently large graphene nanoflakes, reproduce the classical image potential of an infinite conducting sheet. When our fluctuating charge model is applied to the hexagonal carbon nanoflake C60000 we attain excellent agreement with the image potential and induced charge distribution of a conducting sheet. With the inclusion of inducible dipole terms, the model predicts an image plane of zim = 1.3334 a0, which falls in line with prior estimates for graphene. We consider the case of two charges placed on opposite sides of C60000 and find that the fluctuating charge model reproduces classical electrostatics once again. By testing opposing and similar signs of the external charges, we conclude that an atomically thin molecule or extended system does not fully screen their interaction.

Optimal Scheme to Achieve Energy Conservation in Induced Dipole Models

Induced dipole models have proven to be effective tools for simulating electronic polarization effects in biochemical processes, yet their potential has been constrained by energy conservation issue, particularly when historical data is utilized for dipole prediction. This study identifies error outliers as the primary factor causing this failure of energy conservation and proposes a comprehensive scheme to overcome this limitation. Leveraging maximum relative errors as a convergence metric, our data demonstrates that energy conservation can be upheld even when using historical information for dipole predictions. Our study introduces the multi-order extrapolation method to quicken induction iteration and optimize the use of historical data, while also developing the preconditioned conjugate gradient with local iterations to refine the iteration process and effectively remove error outliers. This scheme further incorporates a "peek" step via Jacobi under-relaxation for optimal performance. Simulation evidence suggests that our proposed scheme can achieve energy convergence akin to that of point-charge models within a limited number of iterations, thus promising significant improvements in efficiency and accuracy.

Scalable hybrid deep neural networks/polarizable potentials biomolecular simulations including long-range effects

Deep-HP is a scalable extension of the Tinker-HP multi-GPU molecular dynamics (MD) package enabling the use of Pytorch/TensorFlow Deep Neural Network (DNN) models. Deep-HP increases DNNs' MD capabilities by orders of magnitude offering access to ns simulations for 100k-atom biosystems while offering the possibility of coupling DNNs to any classical (FFs) and many-body polarizable (PFFs) force fields. It allows therefore the introduction of the ANI-2X/AMOEBA hybrid polarizable potential designed for ligand binding studies where solvent-solvent and solvent-solute interactions are computed with the AMOEBA PFF while solute-solute ones are computed by the ANI-2X DNN. ANI-2X/AMOEBA explicitly includes AMOEBA's physical long-range interactions via an efficient Particle Mesh Ewald implementation while preserving ANI-2X's solute short-range quantum mechanical accuracy. The DNN/PFF partition can be user-defined allowing for hybrid simulations to include key ingredients of biosimulation such as polarizable solvents, polarizable counter ions, etc.… ANI-2X/AMOEBA is accelerated using a multiple-timestep strategy focusing on the model's contributions to low-frequency modes of nuclear forces. It primarily evaluates AMOEBA forces while including ANI-2X ones only via correction-steps resulting in an order of magnitude acceleration over standard Velocity Verlet integration. Simulating more than 10 μs, we compute charged/uncharged ligand solvation free energies in 4 solvents, and absolute binding free energies of host-guest complexes from SAMPL challenges. ANI-2X/AMOEBA average errors are discussed in terms of statistical uncertainty and appear in the range of chemical accuracy compared to experiment. The availability of the Deep-HP computational platform opens the path towards large-scale hybrid DNN simulations, at force-field cost, in biophysics and drug discovery.

Effects of polarizability and charge transfer on water dynamics and the underlying activation energies

A large number of force fields have been proposed for describing the behavior of liquid water within classical atomistic simulations, particularly molecular dynamics. In the past two decades, models that incorporate molecular polarizability and even charge transfer have become more prevalent, in attempts to develop more accurate descriptions. These are frequently parameterized to reproduce the measured thermodynamics, phase behavior, and structure of water. On the other hand, the dynamics of water is rarely considered in the construction of these models, despite its importance in their ultimate applications. In this paper, we explore the structure and dynamics of polarizable and charge-transfer water models, with a focus on timescales that directly or indirectly relate to hydrogen bond (H-bond) making and breaking. Moreover, we use the recently developed fluctuation theory for dynamics to determine the temperature dependence of these properties to shed light on the driving forces. This approach provides key insight into the timescale activation energies through a rigorous decomposition into contributions from the different interactions, including polarization and charge transfer. The results show that charge transfer effects have a negligible effect on the activation energies. Furthermore, the same tension between electrostatic and van der Waals interactions that is found in fixed-charge water models also governs the behavior of polarizable models. The models are found to involve significant energy-entropy compensation, pointing to the importance of developing water models that accurately describe the temperature dependence of water structure and dynamics.

Thermodynamics of Li+-Crown Ether Interactions in Aqueous Solvent

Lithium ion-based batteries are ubiquitous in modern technology due to applications in personal electronics and high-capacity storage for electric vehicles. Concerns about lithium supply and battery waste have prompted interest in lithium recycling methods. The crown ether 12-crown-4 has been studied for its abilities to form stable complexes with lithium ions (Li⁺). In this paper, molecular dynamics simulations are applied to examine the binding properties of a 12-crown-4-Li⁺ system in aqueous solution. It was found that 12-crown-4 did not form stable complexes with Li⁺ in aqueous solution due to the binding geometry which was prone to interference by surrounding water molecules. In addition, the binding properties of sodium ions (Na⁺) to 12-crown-4 are examined for comparison. Subsequently, calculations were performed with the crown ethers 15-crown-5 and 18-crown-6 to study their complexation with Li⁺ as well as Na⁺. It was determined that binding was unfavorable for both types of ions for all three crown ethers tested, though 15-crown-5 and 18-crown-6 showed a marginally greater affinity for Li⁺ than 12-crown-4. Metastable minima present in the potential of mean force for Na⁺ render binding marginally more likely there. We discuss these results in the context of membrane-based applications of crown ethers for Li⁺ separations.

Accurate Host-Guest Binding Free Energies Using the AMOEBA Polarizable Force Field

A grand challenge of computational biophysics is accurate prediction of interactions between molecules. Molecular dynamics (MD) simulations have recently gained much interest as a tool to directly compute rigorous intermolecular binding affinities. The choice of a fixed point-charge or polarizable multipole force field used in MD is a topic of ongoing discussion. To compare alternative methods, we participated in the SAMPL7 and SAMPL8 Gibb octaacid host-guest challenges to assess the Atomic Multipole Optimized Energetics for Biomolecular Applications (AMOEBA) polarizable multipole force field. Advantages of AMOEBA over fixed charge models include improved representation of molecular electrostatic potentials and better description of water occupying the unligated host cavity. Prospective predictions for 26 host-guest systems exhibit a mean unsigned error vs experiment of 0.848 kcal/mol across all absolute binding free energies, demonstrating excellent agreement between computational and experimental results. In addition, we explore two topics related to the inclusion of ions in MD simulations: use of a neutral co-alchemical protocol and the effect of salt concentration on binding affinity. Use of the co-alchemical method minimally affects computed energies, but salt concentration significantly perturbs our binding results. Higher salt concentration strengthens binding through classical charge screening. In particular, added Na+ ions screen negatively charged carboxylate groups near the binding cavity, thereby diminishing repulsive coulomb interactions with negatively charged guests. Overall, the AMOEBA results demonstrate the accuracy available through a force field providing a detailed energetic description of the four octaacid hosts and 13 charged organic guests. Use of the AMOEBA polarizable atomic multipole force field in conjunction with an alchemical free energy protocol can achieve chemical accuracy in application to realistic molecular systems.

Molecular modelling of the thermophysical properties of fluids: expectations, limitations, gaps and opportunities

This manuscript provides an overview of the current state of the art in terms of the molecular modelling of the thermophysical properties of fluids. It is intended to manage the expectations and serve as guidance to practising physical chemists, chemical physicists and engineers in terms of the scope and accuracy of the more commonly available intermolecular potentials along with the peculiarities of the software and methods employed in molecular simulations while providing insights on the gaps and opportunities available in this field. The discussion is focused around case studies which showcase both the precision and the limitations of frequently used workflows.