Systematic improvement of a classical molecular model of water

Computer Simulation of Three-Phase Equilibria for Some Water/n-Alkane Binary Systems

In this work, the vapor-liquid-liquid equilibrium (VLLE) of the water/n-pentane, water/n-hexane, water/n-octane, and water/n-decane binary systems is calculated by computer simulation using the NVT-Gibbs ensemble (in the version of three simulation boxes) combined with the configurational bias Monte Carlo method. The combination of both methods, the molecular potential models used, and the simulation details allowed us to calculate the triphasic equilibrium properties of the systems studied: the densities of the three phases in equilibrium, their compositions, and potential energies. In previous works, these simulations were not carried out at a temperature range nor water/n-alkanes systems simulated in this work, probably because they are highly nonideal systems; so, to the best of our knowledge, this is the first time that this phenomenon is studied in detail. The results from VLLE simulations of the water/n-pentane system for temperatures from 343.2 to 435 K, the water/n-hexane system for temperatures from 373.11 to 473.15 K, the water/n-octane system for temperatures from 310.9 to 500 K, and for the water/n-decane system for temperatures from 374.15 to 525 K are reported here. The temperature range was selected in concordance with the experimental data available for an adequate study of the VLLE simulation results. The subcritical densities (vapor and liquid rich in n-alkane phases) at various temperatures fit well with the scaling law and the law of rectilinear diameters, allowing the estimation of upper critical end point temperature and density of the VLLE. The simulation results show a good prediction with experimental data reports in the literature.

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.

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.

A Fast, Convenient, Polarizable Electrostatic Model for Molecular Dynamics

We present an efficient polarizable electrostatic model, utilizing typed, atom-centered polarizabilities and the fast direct approximation, designed for efficient use in molecular dynamics (MD) simulations. The model provides two convenient approaches for assigning partial charges in the context of atomic polarizabilities. One is a generalization of RESP, called RESP-dPol, and the other, AM1-BCC-dPol, is an adaptation of the widely used AM1-BCC method. Both are designed to accurately replicate gas-phase quantum mechanical electrostatic potentials. Benchmarks of this polarizable electrostatic model against gas-phase dipole moments, molecular polarizabilities, bulk liquid densities, and static dielectric constants of organic liquids show good agreement with the reference values. Of note, the model yields markedly more accurate dielectric constants of organic liquids, relative to a matched nonpolarizable force field. MD simulations with this method, which is currently parametrized for molecules containing elements C, N, O, and H, run only about 3.6-fold slower than fixed charge force fields, while simulations with the self-consistent mutual polarization average 4.5-fold slower. Our results suggest that RESP-dPol and AM1-BCC-dPol afford improved accuracy relative to fixed charge force fields and are good starting points for developing general, affordable, and transferable polarizable force fields. The software implementing these approaches has been designed to utilize the force field fitting frameworks developed and maintained by the Open Force Field Initiative, setting the stage for further exploration of this approach to polarizable force field development.

Tuning Potential Functions to Host-Guest Binding Data

Software to more rapidly and accurately predict protein-ligand binding affinities is of high interest for early-stage drug discovery, and physics-based methods are among the most widely used technologies for this purpose. The accuracy of these methods depends critically on the accuracy of the potential functions that they use. Potential functions are typically trained against a combination of quantum chemical and experimental data. However, although binding affinities are among the most important quantities to predict, experimental binding affinities have not to date been integrated into the experimental data set used to train potential functions. In recent years, the use of host-guest complexes as simple and tractable models of binding thermodynamics has gained popularity due to their small size and simplicity, relative to protein-ligand systems. Host-guest complexes can also avoid ambiguities that arise in protein-ligand systems such as uncertain protonation states. Thus, experimental host-guest binding data are an appealing additional data type to integrate into the experimental data set used to optimize potential functions. Here, we report the extension of the Open Force Field Evaluator framework to enable the systematic calculation of host-guest binding free energies and their gradients with respect to force field parameters, coupled with the curation of 126 host-guest complexes with available experimental binding free energies. As an initial application of this novel infrastructure, we optimized generalized Born (GB) cavity radii for the OBC2 GB implicit solvent model against experimental data for 36 host-guest systems. This refitting led to a dramatic improvement in accuracy for both the training set and a separate test set with 90 additional host-guest systems. The optimized radii also showed encouraging transferability from host-guest systems to 59 protein-ligand systems. However, the new radii are significantly smaller than the baseline radii and lead to excessively favorable hydration free energies (HFEs). Thus, users of the OBC2 GB model currently may choose between GB cavity radii that yield more accurate binding affinities and GB cavity radii that yield more accurate HFEs. We suspect that achieving good accuracy on both will require more far-reaching adjustments to the GB model. We note that binding free-energy calculations using the OBC2 model in OpenMM gain about a 10× speedup relative to corresponding explicit solvent calculations, suggesting a future role for implicit solvent absolute binding free-energy (ABFE) calculations in virtual compound screening. This study proves the principle of using host-guest systems to train potential functions that are transferrable to protein-ligand systems and provides an infrastructure that enables a range of applications.

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.

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.

Molecular Dynamics Studies of the Ho(III) Aqua-tris(dibenzoylmethane) Complex: Role of Water Dynamics

The seven-coordinate Ho(III) aqua-tris(dibenzoylmethane)(DBM) complex, referred to as Ho-(DBM)₃·H₂O, was first reported in the late 1960s. It has a threefold symmetric structure, with Ho at the center of three dibenzoylmethane ligands and hydrogen-bonded water to ligands. It is considered that the hydrogen bonds between the water molecule and the ligands surrounding Ho play an important role in the formation of its symmetrical structure. In this work, we developed new force-field parameters for classical molecular dynamics (CMD) simulations to theoretically elucidate the structure and dynamics of Ho-(DBM)₃·H₂O. To develop the force field, structural optimization and molecular dynamics were performed on the basis of ab initio calculations using the plane-wave pseudopotential method. The force-field parameters for CMD were then optimized to reproduce the data obtained from ab initio calculations. Validation of the developed force field showed good agreement with the experimental crystalline structure and ab initio data. The vibrational properties of water in Ho-(DBM)₃·H₂O were investigated by comparison with bulk liquid water. The vibrational motion of water was found to have a characteristic mode originating from stationary rotational motion along the c-axis of Ho(III) aqua-tris(dibenzoylmethane). Contrary to expectations, the hydrogen-bond dynamics of water in Ho-(DBM)₃·H₂O were found to be almost equivalent to those of bulk liquid water except for librational motion. This development route for force-field parameters for CMD and the establishment of water dynamics can advance the understanding of water-coordinated metal complexes with high coordination numbers such as Ho-(DBM)₃·H₂O.

Realistic phase diagram of water from "first principles" data-driven quantum simulations

Since the experimental characterization of the low-pressure region of water's phase diagram in the early 1900s, scientists have been on a quest to understand the thermodynamic stability of ice polymorphs on the molecular level. In this study, we demonstrate that combining the MB-pol data-driven many-body potential for water, which was rigorously derived from "first principles" and exhibits chemical accuracy, with advanced enhanced-sampling algorithms, which correctly describe the quantum nature of molecular motion and thermodynamic equilibria, enables computer simulations of water's phase diagram with an unprecedented level of realism. Besides providing fundamental insights into how enthalpic, entropic, and nuclear quantum effects shape the free-energy landscape of water, we demonstrate that recent progress in "first principles" data-driven simulations, which rigorously encode many-body molecular interactions, has opened the door to realistic computational studies of complex molecular systems, bridging the gap between experiments and simulations.

A Deep Potential model for liquid-vapor equilibrium and cavitation rates of water

Computational studies of liquid water and its phase transition into vapor have traditionally been performed using classical water models. Here, we utilize the Deep Potential methodology-a machine learning approach-to study this ubiquitous phase transition, starting from the phase diagram in the liquid-vapor coexistence regime. The machine learning model is trained on ab initio energies and forces based on the SCAN density functional, which has been previously shown to reproduce solid phases and other properties of water. Here, we compute the surface tension, saturation pressure, and enthalpy of vaporization for a range of temperatures spanning from 300 to 600 K and evaluate the Deep Potential model performance against experimental results and the semiempirical TIP4P/2005 classical model. Moreover, by employing the seeding technique, we evaluate the free energy barrier and nucleation rate at negative pressures for the isotherm of 296.4 K. We find that the nucleation rates obtained from the Deep Potential model deviate from those computed for the TIP4P/2005 water model due to an underestimation in the surface tension from the Deep Potential model. From analysis of the seeding simulations, we also evaluate the Tolman length for the Deep Potential water model, which is (0.091 ± 0.008) nm at 296.4 K. Finally, we identify that water molecules display a preferential orientation in the liquid-vapor interface, in which H atoms tend to point toward the vapor phase to maximize the enthalpic gain of interfacial molecules. We find that this behavior is more pronounced for planar interfaces than for the curved interfaces in bubbles. This work represents the first application of Deep Potential models to the study of liquid-vapor coexistence and water cavitation.

Incorporating Polarization and Charge Transfer into a Point-Charge Model for Water Using Machine Learning

Rigid nonpolarizable water models with fixed point charges have been widely employed in molecular dynamics simulations due to their efficiency and reasonable accuracy for the potential energy surface. However, the dipole moment surface of water is not necessarily well-described by the same fixed charges, leading to failure in reproducing dipole-related properties. Here, we developed a machine-learning model trained against electronic structure data to assign point charges for water, and the resulting dipole moment surface significantly improved the predictions of the dielectric constant and the low-frequency IR spectrum of liquid water. Our analysis reveals that within our atom-centered point-charge description of the dipole moment surface, the intermolecular charge transfer is the major source of the peak intensity at 200 cm^-1, whereas the intramolecular polarization controls the enhancement of the dielectric constant. The effects of exact Hartree-Fock exchange in the hybrid density functional on these properties are also discussed.

Influence of the Lennard-Jones Combination Rules on the Simulated Properties of Organic Liquids at Optimal Force-Field Parametrization

We recently introduced the CombiFF scheme [Oliveira et al., J. Chem. Theory Comput. 2020, 16, 7525], an approach for the automated refinement of force-field parameters against experimental condensed-phase data for large compound families. Using this scheme, once the time-consuming task of target-data selection and curation has been performed, the force-field optimization itself is both straightforward and fast. As a result, CombiFF provides an ideal framework for evaluating the influence of functional-form decisions on the accuracy of a force field at an optimal level of parametrization. We already used this approach to assess the effect of using an all-atom representation compared to united-atom representations in the force field [Oliveira et al., J. Chem. Theory Comput. 2022, 18, 6757]. Here, CombiFF is applied to assess the effect of three Lennard-Jones combination rules, geometric-mean (GM), Lorentz-Berthelot (LB), or Waldman-Hagler (WH), on the simulated properties of organic liquids. The comparison is performed in terms of the experimental liquid density ρ_liq, vaporization enthalpy ΔH_vap, surface-tension coefficient γ, static relative dielectric permittivity ϵ, and self-diffusion coefficient D. The calibrations of the three force-field variants are carried out independently against 2044 experimental values for ρ_liq, and ΔH_vap concerning 1516 compounds. The resulting root-mean-square deviations from experiment are 30.0, 26.9, and 36.7 kg m^-3 for ρ_liq and 2.8, 2.8, and 2.9 kJ mol^-1 for ΔH_vap, when applying the GM, LB, and WH combination rules, respectively. In terms of these (and the other) properties, the three combination rules perform comparatively well, with the GM and LB results being more similar to each other and slightly more accurate compared to experiment. In contrast, the use of distinct combination rules for the parameter calibration and property calculation leads to much larger errors.

An extensive assessment of the performance of pairwise and many-body interaction potentials in reproducing ab initio benchmark binding energies for water clusters n = 2-25

We assess the performance of 7 pairwise additive (TIP3P, TIP4P, TIP4P-ice, TIP5P, OPC, SPC, SPC/E) and 8 families of many-body potentials (q-AQUA, HIPPO, AMOEBA, EFP, TTM, WHBB, MB-pol, MB-UCB) in reproducing high-level ab initio benchmark values, CCSD(T) or MP2 at the complete basis set (CBS) limit for the binding energy and the many-body expansion (MBE) of water clusters n = 2-11, 16-17, 20, 25. By including a large range of cluster sizes having dissimilar hydrogen bonding networks, we obtain an understanding of how these potentials perform for different hydrogen bonding arrangements that are mostly outside of their parameterization range. While it is appropriate to compare the results of ab initio based many-body potentials directly to the electronic binding energies (D_e's), the pairwise additive ones are compared to the enthalpies at T = 298 K, ΔH(298 K), as the latter class of force fields are parametrized to reproduce enthalpies (implicitly accounting for zero-point energy corrections) rather than binding energies. We find that all pairwise additive potentials considered overestimate the reference ΔH values for the n = 2-25 clusters by >13%. For the water dimer (n = 2) in particular, the errors are in the range 83-119% for the pairwise additive potentials studied since these are based on an effective rather than the true 2-body interaction specifically designed as a means of partially accounting for the missing many-body terms. This stronger 2-body interaction is achieved by an enhanced monomer dipole moment that mimics its increase from the gas phase monomer to the condensed phase value. Indeed, for cluster sizes n ≥ 4 the percent deviations become slightly smaller (albeit all exceeding 13%). In contrast, we find that the many-body potentials perform more accurately in reproducing the electronic binding energies (D_e's) throughout the entire cluster range (n = 2-25), all reproducing the ab initio benchmark binding energies within ±7% of the respective CBS values. We further assess the ability of a subset of the many-body potentials (MB-UCB, q-AQUA, MB-pol, and TTM2.1-F) to also reproduce the magnitude of the ab initio many-body energy terms for water cluster sizes n = 7, 10, 16 and 17. The potentials show an overall good agreement with the available benchmark values. However, we identify characteristic differences upon comparing the many-body terms at both the ab initio-optimized geometries and the respective potential-optimized geometries to the reference ab initio values. Additionally, by applying this analysis to a wide range of cluster sizes, trends in the MBE of the potentials with increasing cluster size can be identified. Finally, in an attempt to draw a parallel between the pairwise additive and many-body potentials, we report the analysis of the individual molecular dipole moments for water clusters with 1 to ∼4 solvation shells with the TTM2.1-F potential. We find that the internally solvated water molecules have in general a larger molecular dipole moment ranging from 2.6-3.0 D. This justifies the use of an enhanced, with respect to the gas-phase value, molecular dipole moment for the pairwise additive potentials, which is intended to fold in the many body terms into an effective (enhanced) pairwise interaction through the choice of the charges. These results have important implications for the development of future generations of efficient, transferable, and highly accurate classical interaction potentials in both the pairwise additive and many-body categories.

Force Decomposition Analysis: A Method to Decompose Intermolecular Forces into Physically Relevant Component Contributions

Computational quantum chemistry can be more than just numerical experiments when methods are specifically adapted to investigate chemical concepts. One important example is the development of energy decomposition analysis (EDA) to reveal the physical driving forces behind intermolecular interactions. In EDA, typically the interaction energy from a good-quality density functional theory (DFT) calculation is decomposed into multiple additive components that unveil permanent and induced electrostatics, Pauli repulsion, dispersion, and charge-transfer contributions to noncovalent interactions. Herein, we formulate, implement, and investigate decomposing the forces associated with intermolecular interactions into the same components. The resulting force decomposition analysis (FDA) is potentially useful as a complement to the EDA to understand chemistry, while also providing far more information than an EDA for data analysis purposes such as training physics-based force fields. We apply the FDA based on absolutely localized molecular orbitals (ALMOs) to analyze interactions of water with sodium and chloride ions as well as in the water dimer. We also analyze the forces responsible for geometric changes in carbon dioxide upon adsorption onto (and activation by) gold and silver anions. We also investigate how the force components of an EDA-based force field for water clusters, namely MB-UCB, compare to those from force decomposition analysis.

A scheme for rapid evaluation of the intermolecular three-body polarization effect in water clusters

The ability to accurately and rapidly evaluate the intermolecular many-body polarization effect of the water system is very important for computer simulations of biomolecule in aqueous. In this paper, a scheme is proposed based on the polarizable dipole-dipole interaction model and used to rapidly estimate the intermolecular many-body polarization effect in water clusters. We use a bond-dipole-based polarization function to evaluate the polarization energy. We regard two OH bonds of a water molecule as two bond-dipoles and set the permanent OH bond-dipole moment of a water molecule to be 1.51 Debye. We estimate the induced OH bond-dipole moment via a simple formula in which only one correction factor is needed. This scheme is then applied to tens of water clusters to calculate the three- and four-body interaction energies. The three-body interaction energies of 93 water clusters produced by our scheme are compared with those produced by the counterpoise-corrected CCSD(T)/aug-cc-pVDZ, MP2/aug-cc-pVDZ, M06-2X/jul-cc-pVTZ methods, by the AMOEBApro13, iAMOEBA, AMOEBA+, AMOEBA+(CF) methods, and by the MB-pol method. The four-body interaction energies of 47 water clusters yielded by our scheme are compared with those yielded by the counterpoise-corrected MP2/aug-cc-pVDZ and M06-2X/ jul-cc-pVTZ methods, by the AMOEBApro13, AMOEBA+, AMOEBA+(CF) methods, and by the MB-pol method. The comparison results show that the scheme proposed in this paper can reproduce the counterpoise-corrected CCSD(T)/aug-cc-pVDZ three-body interaction energies and reproduce the counterpoise-corrected MP2/aug-cc-pVDZ four-body interaction energies both accurately and efficiently. We anticipate the scheme proposed here can be useful for computer simulations of liquid water and aqueous solutions.

Phase diagrams-Why they matter and how to predict them

Understanding the thermodynamic stability and metastability of materials can help us to, for example, gauge whether crystalline polymorphs in pharmaceutical formulations are likely to be durable. It can also help us to design experimental routes to novel phases with potentially interesting properties. In this Perspective, we provide an overview of how thermodynamic phase behavior can be quantified both in computer simulations and machine-learning approaches to determine phase diagrams, as well as combinations of the two. We review the basic workflow of free-energy computations for condensed phases, including some practical implementation advice, ranging from the Frenkel-Ladd approach to thermodynamic integration and to direct-coexistence simulations. We illustrate the applications of such methods on a range of systems from materials chemistry to biological phase separation. Finally, we outline some challenges, questions, and practical applications of phase-diagram determination which we believe are likely to be possible to address in the near future using such state-of-the-art free-energy calculations, which may provide fundamental insight into separation processes using multicomponent solvents.

Dynamics of Aqueous Electrolyte Solutions: Challenges for Simulations

This Perspective article focuses on recent simulation work on the dynamics of aqueous electrolytes. It is well-established that full-charge, nonpolarizable models for water and ions generally predict solution dynamics that are too slow in comparison to experiments. Models with reduced (scaled) charges do better for solution diffusivities and viscosities but encounter issues describing other dynamic phenomena such as nucleation rates of crystals from solution. Polarizable models show promise, especially when appropriately parametrized, but may still miss important physical effects such as charge transfer. First-principles calculations are starting to emerge for these properties that are in principle able to capture polarization, charge transfer, and chemical transformations in solution. While direct ab initio simulations are still too slow for simulations of large systems over long time scales, machine-learning models trained on appropriate first-principles data show significant promise for accurate and transferable modeling of electrolyte solution dynamics.

gmak: A Parameter-Space Mapping Strategy for Force-Field Calibration

In the context of classical molecular simulations, the accuracy of a force field is highly influenced by the values of the relevant simulation parameters. In this work, a parameter-space mapping (PSM) workflow is proposed to aid in the calibration of force-field parameters, based mainly on the following features: (i) regular-grid discretization of the search space; (ii) partial sampling of the search-space grid; (iii) training of surrogate models to predict the estimates of the target properties for nonsampled parameter sets; (iv) post hoc interpretation of the results in terms of multiobjective optimization concepts; (v) attenuation of statistical errors achieved via empiric extension of the duration of the simulations; (vi) iterative search-space translation according to a user-defined scalar objective function that measures the accuracy of the force field (e.g., the weighted root-mean-square deviation of the target properties relative to the reference data). This combination of features results in a hybrid of a single- and a multiobjective optimization strategy, allowing for the approximate determination of both a local minimum of the chosen objective function and its neighboring Pareto efficient points. The PSM workflow is implemented in the extensible Python program gmak, which is made available in the Git repository at http://github.com/mssm-labmmol/gmak. Using this implementation, the PSM workflow was tested in a proof-of-concept fashion in the recalibration of the Lennard-Jones parameters of the 3-point Optimal Point Charge (OPC3) water model for compatibility with the GROMOS treatment of nonbonded interactions. The recalibrated model reproduces typical pure-liquid properties with an accuracy similar to the original OPC3 model and represents a significant improvement relative to the Simple Point Charge (SPC) model, which is the official recommendation for simulations using GROMOS force fields.

Personal Precise Force Field for Intrinsically Disordered and Ordered Proteins Based on Deep Learning

Intrinsically disordered proteins (IDPs) are proteins without a fixed three-dimensional (3D) structure under physiological conditions and are associated with Parkinson's disease, Alzheimer's disease, cancer, cardiovascular disease, amyloidosis, diabetes, and other diseases. Experimental methods can hardly capture the ensemble of diverse conformations for IDPs. Molecular dynamics (MD) simulations can sample continuous conformations that might provide a valuable complement to experimental data. However, the accuracy of MD simulations depends on the quality of force field. In particular, the evolutionary conservation and coevolution of IDPs introduce that current force fields could not precisely reproduce the conformation of IDPs. In order to improve the performance of force field, deep learning and reweighting methods were used to automatically generate personal force field parameters for intrinsically disordered and ordered proteins. At first, the deep learning method predicted more accuracy φ/ψ dihedral of residue than the previous method. Then, reweighting optimized the personal force field parameters for each residue. Finally, typical representative systems such as IDPs, structure protein, and fast-folding protein were used to evaluate this force field. The results indicate that two personal force field parameters (named PPFF1 and PPFF1_af2) could better reproduce the experimental observables than ff03CMAP force field. In summary, this strategy will provide feasibility for the development of precise personal force fields.

State averaged CASSCF in AMOEBA polarizable water model for simulating nonadiabatic molecular dynamics with nonequilibrium solvation effects

This paper presents a state-averaged complete active space self-consistent field (SA-CASSCF) in the atomic multipole optimized energetics for biomolecular application (AMOEBA) polarizable water model, which enables rigorous simulation of non-adiabatic molecular dynamics with nonequilibrium solvation effects. The molecular orbital and configuration interaction coefficients of the solute wavefunction, and the induced dipoles on solvent atoms, are solved by minimizing the state averaged energy variationally. In particular, by formulating AMOEBA water models and the polarizable continuum model (PCM) in a unified way, the algorithms developed for computing SA-CASSCF/PCM energies, analytical gradients, and non-adiabatic couplings in our previous work can be generalized to SA-CASSCF/AMOEBA by properly substituting a specific list of variables. Implementation of this method will be discussed with the emphasis on how the calculations of different terms are partitioned between the quantum chemistry and molecular mechanics codes. We will present and discuss results that demonstrate the accuracy and performance of the implementation. Next, we will discuss results that compare three solvent models that work with SA-CASSCF, i.e., PCM, fixed-charge force fields, and the newly implemented AMOEBA. Finally, the new SA-CASSCF/AMOEBA method has been interfaced with the ab initio multiple spawning method to carry out non-adiabatic molecular dynamics simulations. This method is demonstrated by simulating the photodynamics of the model retinal protonated Schiff base molecule in water.

Stability and Metastability of Liquid Water in a Machine-Learned Coarse-Grained Model with Short-Range Interactions

Coarse-grained water models are ∼100 times more efficient than all-atom models, enabling simulations of supercooled water and crystallization. The machine-learned monatomic model ML-BOP reproduces the experimental equation of state (EOS) and ice-liquid thermodynamics at 0.1 MPa on par with the all-atom TIP4P/2005 and TIP4P/Ice models. These all-atom models were parametrized using high-pressure experimental data and are either accurate for water's EOS (TIP4P/2005) or ice-liquid equilibrium (TIP4P/Ice). ML-BOP was parametrized from temperature-dependent ice and liquid experimental densities and melting data at 0.1 MPa; its only pressure training is from compression of TIP4P/2005 ice at 0 K. Here we investigate whether ML-BOP replicates the experimental EOS and ice-water thermodynamics along all pressures of ice I. We find that ML-BOP reproduces the temperature, enthalpy, entropy, and volume of melting of hexagonal ice up to 400 MPa and the EOS of water along the melting line with an accuracy that rivals that of both TIP4P/2005 and TIP4P/Ice. We interpret that the accuracy of ML-BOP originates from its ability to capture the shift between compact and open local structures to changes in pressure and temperature. ML-BOP reproduces the sharpening of the tetrahedral peak of the pair distribution function of water upon supercooling, and its pressure dependence. We characterize the region of metastability of liquid ML-BOP with respect to crystallization and cavitation. The accessibility of ice crystallization to simulations of ML-BOP, together with its accurate representation of the thermodynamics of water, makes it promising for investigating the interplay between anomalies, glass transition, and crystallization under conditions challenging to access through experiments.

Improving Condensed-Phase Water Dynamics with Explicit Nuclear Quantum Effects: The Polarizable Q-AMOEBA Force Field

We introduce a new parametrization of the AMOEBA polarizable force field for water denoted Q-AMOEBA, for use in simulations that explicitly account for nuclear quantum effects (NQEs). This study is made possible thanks to the recently introduced adaptive Quantum Thermal Bath (adQTB) simulation technique which computational cost is comparable to classical molecular dynamics. The flexible Q-AMOEBA model conserves the initial AMOEBA functional form, with an intermolecular potential including an atomic multipole description of electrostatic interactions (up to quadrupole), a polarization contribution based on the Thole interaction model and a buffered 14-7 potential to model van der Waals interactions. It has been obtained by using a ForceBalance fitting strategy including high-level quantum chemistry reference energies and selected condensed-phase properties targets. The final Q-AMOEBA model is shown to accurately reproduce both gas-phase and condensed-phase properties, notably improving the original AMOEBA water model. This development allows the fine study of NQEs on water liquid phase properties such as the average H-O-H angle compared to its gas-phase equilibrium value, isotope effects, and so on. Q-AMOEBA also provides improved infrared spectroscopy prediction capabilities compared to AMOEBA03. Overall, we show that the impact of NQEs depends on the underlying model functional form and on the associated strength of hydrogen bonds. Since adQTB simulations can be performed at near classical computational cost using the Tinker-HP package, Q-AMOEBA can be extended to organic molecules, proteins, and nucleic acids opening the possibility for the large-scale study of the importance of NQEs in biophysics.

Multiple insights call for revision of modern thermodynamic models to account for structural fluctuations in water

Modern thermodynamic models incorporate the concept of association (hydrogen bonding) and they can describe very satisfactorily many properties of water containing mixtures. They have not been successful in representing water's anomalous properties and this work provides a possible explanation. We have analyzed and interpreted recent experimental data, molecular simulation results, and two-state theory approaches and compared against the predictions from thermodynamic models. We show that the dominance of the tetrahedral structure implemented in modern thermodynamic models may be the reason for their failure for describing water systems. While this study does not prove the two-state theories for water, it indicates that a high level of tetrahedral structure of water is not in agreement with water's anomalous properties when used in thermodynamic models.

Fast Polarizable Water Model for Atomistic Simulations

Simulating water accurately has been a major challenge in atomistic simulations for decades. Inclusion of electronic polarizability effects holds considerable promise, yet existing approaches suffer from significant computational overheads compared to the widely used nonpolarizable water models. We have developed a globally optimal polarizable water model, OPC3-pol, that explicitly accounts for electronic polarizability with minimal impact on the computational efficiency. OPC3-pol reproduces five key bulk water properties at room temperature with an average relative error of 0.6%. In atomistic simulations, OPC3-pol's computational efficiency is in between that of 3- and 4-point nonpolarizable models; the model supports increased (4 fs) integration time step. OPC3-pol is tested in simulations of globular protein ubiquitin and a B-DNA dodecamer with several AMBER force fields, ff99SB, ff14SB, ff19SB, and OL15, demonstrating structure stability close to reference on multi-microsecond time scale. Simulation of an intrinsically disordered amyloid β-peptide yields an ensemble with the radius of gyration of a random coil. The proposed water model can be trivially adopted by any package that supports standard nonpolarizable force fields and water models; its intended use is in long classical atomistic simulations where water polarization effects are expected to be important.

M-Chem: a Modular Software Package for Molecular Simulation that Spans Scientific Domains

We present a new software package called M-Chem that is designed from scratch in C++ and parallelized on shared-memory multi-core architectures to facilitate efficient molecular simulations. Currently, M-Chem is a fast molecular dynamics (MD) engine that supports the evaluation of energies and forces from two-body to many-body all-atom potentials, reactive force fields, coarse-grained models, combined quantum mechanics molecular mechanics (QM/MM) models, and external force drivers from machine learning, augmented by algorithms that are focused on gains in computational simulation times. M-Chem also includes a range of standard simulation capabilities including thermostats, barostats, multi-timestepping, and periodic cells, as well as newer methods such as fast extended Lagrangians and high quality electrostatic potential generation. At present M-Chem is a developer friendly environment in which we encourage new software contributors from diverse fields to build their algorithms, models, and methods in our modular framework. The long-term objective of M-Chem is to create an interdisciplinary platform for computational methods with applications ranging from biomolecular simulations, reactive chemistry, to materials research.

Comparison of the United- and All-Atom Representations of (Halo)alkanes Based on Two Condensed-Phase Force Fields Optimized against the Same Experimental Data Set

The level of accuracy that can be achieved by a force field is influenced by choices made in the interaction-function representation and in the relevant simulation parameters. These choices, referred to here as functional-form variants (FFVs), include for example the model resolution, the charge-derivation procedure, the van der Waals combination rules, the cutoff distance, and the treatment of the long-range interactions. Ideally, assessing the effect of a given FFV on the intrinsic accuracy of the force-field representation requires that only the specific FFV is changed and that this change is performed at an optimal level of parametrization, a requirement that may prove extremely challenging to achieve in practice. Here, we present a first attempt at such a comparison for one specific FFV, namely the choice of a united-atom (UA) versus an all-atom (AA) resolution in a force field for saturated acyclic (halo)alkanes. Two force-field versions (UA vs AA) are optimized in an automated way using the CombiFF approach against 961 experimental values for the pure-liquid densities ρ_liq and vaporization enthalpies ΔH_vap of 591 compounds. For the AA force field, the torsional and third-neighbor Lennard-Jones parameters are also refined based on quantum-mechanical rotational-energy profiles. The comparison between the UA and AA resolutions is also extended to properties that have not been included as parameterization targets, namely the surface-tension coefficient γ, the isothermal compressibility κ_T, the isobaric thermal-expansion coefficient α_P, the isobaric heat capacity c_P, the static relative dielectric permittivity ϵ, the self-diffusion coefficient D, the shear viscosity η, the hydration free energy ΔG_wat, and the free energy of solvation ΔG_che in cyclohexane. For the target properties ρ_liq and ΔH_vap, the UA and AA resolutions reach very similar levels of accuracy after optimization. For the nine other properties, the AA representation leads to more accurate results in terms of η; comparably accurate results in terms of γ, κ_T, α_P, ϵ, D, and ΔG_che; and less accurate results in terms of c_P and ΔG_wat. This work also represents a first step toward the calibration of a GROMOS-compatible force field at the AA resolution.

Polarizable Force Field of Intrinsically Disordered Proteins with CMAP and Reweighting Optimization

Intrinsically disordered proteins (IDPs) are highly structurally heterogeneous without a specific tertiary structure under physiology conditions and play key roles in the development of human diseases. Due to the characteristics of diverse conformations, as one of the important methods, molecular dynamics simulation can complement information for experimental methods. Because of the enrichment for charged amino acids for IDPs, polarizable force fields should be a good choice for the simulation of IDPs. However, current polarizable force fields are limited in sampling conformer features of IDPs. Therefore, a polarizable force field was released and named Drude2019IDP based on Drude2019 with reweighting and grid-based potential energy correction map optimization. In order to evaluate the performance of Drude2019IDP, 16 dipeptides, 18 short peptides, 3 representative IDPs, and 5 structural proteins were simulated. The results show that the NMR observables driven by Drude2019IDP are in better agreement with the experiment data than those by Drude2019 on short peptides and IDPs. Drude2019IDP can sample more diverse conformations than Drude2019. Furthermore, the performances of the two force fields are similar to the sample ordered proteins. These results confirm that the developed Drude2019IDP can improve the reproduction of conformers for intrinsically disordered proteins and can be used to gain insight into the paradigm of sequence-disorder for IDPs.

Development of the Quantum-Inspired SIBFA Many-Body Polarizable Force Field: Enabling Condensed-Phase Molecular Dynamics Simulations

We present the extension of the Sum of Interactions Between Fragments Ab initio Computed (SIBFA) many-body polarizable force field to condensed-phase molecular dynamics (MD) simulations. The quantum-inspired SIBFA procedure is grounded on simplified integrals obtained from localized molecular orbital theory and achieves full separability of its intermolecular potential. It embodies long-range multipolar electrostatics (up to quadrupole) coupled to a short-range penetration correction (up to charge-quadrupole), exchange repulsion, many-body polarization, many-body charge transfer/delocalization, exchange dispersion, and dispersion (up to C10). This enables the reproduction of all energy contributions of ab initio symmetry-adapted perturbation theory (SAPT(DFT)) gas-phase reference computations. The SIBFA approach has been integrated within the Tinker-HP massively parallel MD package. To do so, all SIBFA energy gradients have been derived and the approach has been extended to enable periodic boundary conditions simulations using smooth particle mesh Ewald. This novel implementation also notably includes a computationally tractable simplification of the many-body charge transfer/delocalization contribution. As a proof of concept, we perform a first computational experiment defining a water model fitted on a limited set of SAPT(DFT) data. SIBFA is shown to enable a satisfactory reproduction of both gas-phase energetic contributions and condensed-phase properties highlighting the importance of its physically motivated functional form.

Melting points of water models: Current situation

By using the direct coexistence method, we have calculated the melting points of ice I h at normal pressure for three recently proposed water models, namely, TIP3P-FB, TIP4P-FB, and TIP4P-D. We obtained T m = 216 K for TIP3P-FB, T m = 242 K for TIP4P-FB, and T m = 247 K for TIP4P-D. We revisited the melting point of TIP4P/2005 and TIP5P obtaining T m = 250 and 274 K, respectively. We summarize the current situation of the melting point of ice I h for a number of water models and conclude that no model is yet able to simultaneously reproduce the melting temperature of ice I h and the temperature of the maximum in density at room pressure. This probably points toward our both still incomplete knowledge of the potential energy surface of water and the necessity of incorporating nuclear quantum effects to describe both properties simultaneously.

Quantitative molecular simulations

All-atom simulations can provide molecular-level insights into the dynamics of gas-phase, condensed-phase and surface processes. One important requirement is a sufficiently realistic and detailed description of the underlying intermolecular interactions. The present perspective provides an overview of the present status of quantitative atomistic simulations from colleagues' and our own efforts for gas- and solution-phase processes and for the dynamics on surfaces. Particular attention is paid to direct comparison with experiment. An outlook discusses present challenges and future extensions to bring such dynamics simulations even closer to reality.

Open Force Field Evaluator: An Automated, Efficient, and Scalable Framework for the Estimation of Physical Properties from Molecular Simulation

Developing accurate classical force field representations of molecules is key to realizing the full potential of molecular simulations, both as a powerful route to gaining fundamental insights into a broad spectrum of chemical and biological phenomena and for predicting physicochemical and mechanical properties of substances. The Open Force Field Consortium is an industry-funded open science effort to this end, developing open-source tools for rapidly generating new high-quality small-molecule force fields. An integral aspect of this is the parameterization and assessment of force fields against high-quality, condensed-phase physical property data, curated from open data sources such as the NIST ThermoML Archive, alongside quantum chemical data. The quantity of such experimental data in open data archives alone would require an onerous amount of human and computational resources to both curate and estimate manually, especially when estimations must be obtained for numerous sets of force field parameters. Here, we present an entirely automated, highly scalable framework for evaluating physical properties and their gradients in terms of force field parameters. It is written as a modular and extensible Python framework, which employs an intelligent multiscale estimation approach that allows for the automated estimation of properties from simulation and cached simulation data, and a pluggable API for estimation of new properties. In this study, we demonstrate the utility of the framework by benchmarking the OpenFF 1.0.0 small-molecule force field and GAFF 1.8 and GAFF 2.1 force fields against a test set of binary density and enthalpy of mixing measurements curated using the framework utilities. Further, we demonstrate the framework's utility as part of force field optimization by using it alongside ForceBalance, a framework for systematic force field optimization, to retrain a set of nonbonded van der Waals parameters against a training set of density and enthalpy of vaporization measurements.

Maximum in density of electrolyte solutions: Learning about ion-water interactions and testing the Madrid-2019 force field

In this work, we studied the effect of Li⁺, Na⁺, K⁺, Mg²⁺, and Ca²⁺ chlorides and sulfates on the temperature of maximum density (TMD) of aqueous solutions at room pressure. Experiments at 1 molal salt concentration were carried out to determine the TMD of these solutions. We also performed molecular dynamics simulations to estimate the TMD at 1 and 2 m with the Madrid-2019 force field, which uses the TIP4P/2005 water model and scaled charges for the ions, finding an excellent agreement between experiment and simulation. All the salts studied in this work shift the TMD of the solution to lower temperatures and flatten the density vs temperature curves (when compared to pure water) with increasing salt concentration. The shift in the TMD depends strongly on the nature of the electrolyte. In order to explore this dependence, we have evaluated the contribution of each ion to the shift in the TMD concluding that Na⁺, Ca²⁺, and SO₄ ^2- seem to induce the largest changes among the studied ions. The volume of the system has been analyzed for salts with the same anion and different cations. These curves provide insight into the effect of different ions upon the structure of water. We claim that the TMD of electrolyte solutions entails interesting physics regarding ion-water and water-water interactions and should, therefore, be considered as a test property when developing force fields for electrolytes. This matter has been rather unnoticed for almost a century now and we believe it is time to revisit it.

DFT-based QM/MM with Particle-Mesh Ewald for Direct, Long-Range Electrostatic Embedding

We present a DFT-based, QM/MM implementation with long-range electrostatic embedding achieved by direct real-space integration of the particle mesh Ewald (PME) computed electrostatic potential. The key transformation is the interpolation of the electrostatic potential from the PME grid to the DFT quadrature grid, from which integrals are easily evaluated utilizing standard DFT machinery. We provide benchmarks of the numerical accuracy with choice of grid size and real-space corrections, and demonstrate that good convergence is achieved while introducing nominal computational overhead. Furthermore, the approach requires only small modification to existing software packages, as is demonstrated with our implementation in the OpenMM and Psi4 software. After presenting convergence benchmarks, we evaluate the importance of long-range electrostatic embedding in three solute/solvent systems modeled with QM/MM. Water and BMIM/BF4 ionic liquid were considered as ``simple' and ``complex' solvents respectively, with water and p-phenylenediamine (PPD) solute molecules treated at QM level of theory. While electrostatic embedding with standard real-space truncation may introduce negligible error for simple systems such as water solute in water solvent, errors become more significant when QM/MM is applied to complex solvents such as ionic liquids. An extreme example is the electrostatic embedding energy for oxidized PPD in BMIM/BF4 for which real-space truncation produces severe error even at 2-3 nm cutoff distances. This latter example illustrates that utilization of QM/MM to compute redox potentials within concentrated electrolytes/ionic media requires carefully chosen long-range electrostatic embedding algorithms, with our presented algorithm providing a general and robust approach.

Structural characteristics of low-density environments in liquid water

The existence of two structural forms in liquid water has been a point of discussion for a long time. A phase transition between these two forms of liquid water has been proposed based on evidence from molecular simulations, and experiments have also been very recently able to track the proposed transition of the low-density liquid form to the high-density liquid form. We propose to use the average angle an oxygen atom makes with its neighbors to describe the structural environment of a water molecule. The distribution of this order parameter is observed to have two peaks with one peak at ∼109.5^{∘}, corresponding to the internal angle of a regular tetrahedron, indicating tetrahedral arrangement. The other peak corresponds to an environment with a tighter arrangement of neighboring molecules. The distribution of O-O-O angles is decomposed into two skewed distributions to estimate the fractions of the two liquid forms in water. A good similarity is observed between the temperature and pressure trends of fractions of locally favored tetrahedral structure (LFTS) form estimated using the new order parameter and the reports in the literature, over a range of temperatures and pressures. We also compare the structural environments indicated by different order parameters and find that the order parameter proposed in this paper captures the structure of first solvation shell of the LFTS accurately.

Using atomic charges to model molecular polarization

We review different models for introducing electric polarization in force fields, with special focus on methods where polarization is modelled at the atomic charge level. While electric polarization has been included in several force fields, the common approach has been to focus on atomic dipole polarizability. Several approaches allow modelling electric polarization by using charge-flow between charge sites instead, but this has been less exploited, despite that atomic charges and charge-flow is expected to be more important than atomic dipoles and dipole polarizability. A number of challenges are required to be solved for charge-flow models to be incorporated into polarizable force fields, for example how to parameterize the models and how to make them computational efficient.

Singular value decomposition analysis of the electron density changes occurring upon electrostatic polarization of water

In-depth elucidation of how molecules are electrically polarized would be one key factor for understanding the properties of those molecules under various thermodynamic and/or spatial conditions. Here this problem is tackled for the case of hydrogen-bonded water by conducting singular value decomposition of the electron density changes that occur upon electrostatic polarization. It is shown that all those electron density changes are approximately described as linear combinations of ten orthonormal basis “vectors”. One main component is the interatomic charge transfer through each OH bond, while some others are characterized as the atomic dipolar polarizations, meaning that both of these components are important for the electrostatic polarization of water. The interaction parameters that reasonably well reproduce the induced dipole moments are derived, which indicate the extent of mixing of the two components in electrostatic polarization.

The main features of the electron density changes that occur upon electrostatic polarization of water are elucidated by conducting singular value decomposition analysis of those changes.

RNA-Specific Force Field Optimization with CMAP and Reweighting

RNA plays a key role in a variety of cell activities. However, it is difficult to capture its structure dynamics by the traditional experimental methods because of the inherent limitations. Molecular dynamics simulation has become a valuable complement to the experimental methods. Previous studies have indicated that the current force fields cannot accurately reproduce the conformations and structural dynamics of RNA. Therefore, an RNA-specific force field was developed to improve the conformation sampling of RNA. The distribution of ζ/α dihedrals of tetranucleotides was optimized by a reweighting method, and the grid-based energy correction map (CMAP) term was first introduced into the Amber RNA force field of ff99bsc0χOL3, named ff99OL3_CMAP1. Extensive validations of tetranucleotides and tetraloops show that ff99OL3_CMAP1 can significantly decrease the population of an incorrect structure, increase the consistency between the simulation results and experimental values for tetranucleotides, and improve the stability of tetraloops. ff99OL3_CMAP1 can also precisely reproduce the conformation of a duplex and riboswitches. These findings confirm that the newly developed force field ff99OL3_CMAP1 can improve the conformer sampling of RNA.

Comparison of molecular dynamics simulations of water with neutron and X-ray scattering experiments

The atomistic structure and dynamics obtained from molecular dynamics (MD) simulations with the example of TIP3P (rigid and flexible) and TIP4P/2005 (rigid) water is compared to neutron and X-ray scattering data at ambient conditions. Neutron and X-ray diffractograms are calculated from the simulations for four isotopic substitutions as well as the incoherent intermediate scattering function for neutrons. The resulting curves are compared to each other and to published experimental data. Differences between simulated and measured intermediate scattering functions are quantified by fitting an analytic model to the computed values. The sensitivity of the scattering curves to the parameters of the MD simulations is demonstrated on the example of two parameters, bond length and angle.

Anomalous temperature dependence of the experimental x-ray structure factor of supercooled water

The structural changes of water upon deep supercooling were studied through wide-angle x-ray scattering at SwissFEL. The experimental setup had a momentum transfer range of 4.5 Å^-1, which covered the principal doublet of the x-ray structure factor of water. The oxygen-oxygen structure factor was obtained for temperatures down to 228.5 ± 0.6 K. Similar to previous studies, the second diffraction peak increased strongly in amplitude as the structural change accelerated toward a local tetrahedral structure upon deep supercooling. We also observed an anomalous trend for the second peak position of the oxygen-oxygen structure factor (q₂). We found that q₂ exhibits an unprecedented positive partial derivative with respect to temperature for temperatures below 236 K. Based on Fourier inversion of our experimental data combined with reference data, we propose that the anomalous q₂ shift originates from that a repeat spacing in the tetrahedral network, associated with all peaks in the oxygen-oxygen pair-correlation function, gives rise to a less dense local ordering that resembles that of low-density amorphous ice. The findings are consistent with that liquid water consists of a pentamer-based hydrogen-bonded network with low density upon deep supercooling.

Learning neural network potentials from experimental data via Differentiable Trajectory Reweighting

In molecular dynamics (MD), neural network (NN) potentials trained bottom-up on quantum mechanical data have seen tremendous success recently. Top-down approaches that learn NN potentials directly from experimental data have received less attention, typically facing numerical and computational challenges when backpropagating through MD simulations. We present the Differentiable Trajectory Reweighting (DiffTRe) method, which bypasses differentiation through the MD simulation for time-independent observables. Leveraging thermodynamic perturbation theory, we avoid exploding gradients and achieve around 2 orders of magnitude speed-up in gradient computation for top-down learning. We show effectiveness of DiffTRe in learning NN potentials for an atomistic model of diamond and a coarse-grained model of water based on diverse experimental observables including thermodynamic, structural and mechanical properties. Importantly, DiffTRe also generalizes bottom-up structural coarse-graining methods such as iterative Boltzmann inversion to arbitrary potentials. The presented method constitutes an important milestone towards enriching NN potentials with experimental data, particularly when accurate bottom-up data is unavailable.

The automated optimisation of a coarse-grained force field using free energy data

Atomistic models provide a detailed representation of molecular systems, but are sometimes inadequate for simulations of large systems over long timescales. Coarse-grained models enable accelerated simulations by reducing the number of degrees of freedom, at the cost of reduced accuracy. New optimisation processes to parameterise these models could improve their quality and range of applicability. We present an automated approach for the optimisation of coarse-grained force fields, by reproducing free energy data derived from atomistic molecular simulations. To illustrate the approach, we implemented hydration free energy gradients as a new target for force field optimisation in ForceBalance and applied it successfully to optimise the un-charged side-chains and the protein backbone in the SIRAH protein coarse-grain force field. The optimised parameters closely reproduced hydration free energies of atomistic models and gave improved agreement with experiment.

The mystery of sub-picosecond charge transfer following irradiation of hydrated uridine monophosphate

The early mechanisms by which ionizing rays damage biological structures by so-called direct effects are largely elusive. In a recent picosecond pulse radiolysis study of concentrated uridine monophosphate solutions [J. Ma, S. A. Denisov, J.-L. Marignier, P. Pernot, A. Adhikary, S. Seki and M. Mostafavi, J. Phys. Chem. Lett., 2018, 9, 5105], unexpected results were found regarding the oxidation of the nucleobase. The signature of the oxidized nucleobase could not be detected 5 ps after the electron pulse, but only the oxidized phosphate, raising intriguing questions about the identity of charge-transfer mechanisms that could explain the absence of U⁺. We address here this question by means of advanced first-principles atomistic simulations of solvated uridine monophosphate, combining Density Functional Theory (DFT) with polarizable embedding schemes. We contrast three very distinct mechanisms of charge transfer covering the atto-, femto- and pico-second timescales. We first investigate the ionization mechanism and subsequent hole/charge migrations on a timescale of attoseconds to a few femtoseconds under the frozen nuclei approximation. We then consider a nuclear-driven phosphate-to-oxidized-nucleobase electron transfer, showing that it is an uncompetitive reaction channel on the sub-picosecond timescale, despite its high exothermicity and significant electronic coupling. Finally, we show that non-adiabatic charge transfer is enabled by femtosecond nuclear relaxation after ionization. We show that electronic decoherence and the electronic coupling strength are the key parameters that determine the hopping probabilities. Our results provide important insight into the interplay between electronics and nuclear motions in the early stages of the multiscale responses of biological matter subjected to ionizing radiation.

Systematic optimization of a fragment-based force field against experimental pure-liquid properties considering large compound families: application to oxygen and nitrogen compounds

The CombiFF approach is a workflow for the automated refinement of force-field parameters against experimental condensed-phase data, considering entire classes of organic molecules constructed using a fragment library via combinatorial isomer enumeration. One peculiarity of this approach is that it relies on an electronegativity-equalization scheme to account for induction effects within molecules, with values of the atomic hardness and electronegativity as electrostatic parameters, rather than the partial charges themselves. In a previous article [M. P. Oliveira, M. Andrey, S. R. Rieder, L. Kern, D. F. Hahn, S. Riniker, B. A. C. Horta and P. H. Hünenberger, J. Chem. Theory. Comput. 2020, 16, 7525], CombiFF was introduced and applied to calibrate a GROMOS-compatible united-atom force field for the saturated acyclic (halo-)alkane family. Here, this scheme is employed for the construction of a corresponding force field for saturated acyclic compounds encompassing eight common chemical functional groups involving oxygen and/or nitrogen atoms, namely: ether, aldehyde, ketone, ester, alcohol, carboxylic acid, amine, and amide. Monofunctional as well as homo-polyfunctional compounds are considered. A total of 1712 experimental liquid densities ρliq and vaporization enthalpies ΔHvap concerning 1175 molecules are used for the calibration (339 molecules) and validation (836 molecules) of the 102 non-bonded interaction parameters of the force field. Using initial parameter values based on the GROMOS 2016H66 parameter set, convergence is reached after five iterations. Given access to one processor per simulated system, this operation only requires a few days of wall-clock computing time. After optimization, the root-mean-square deviations from experiment are 29.9 (22.4) kg m-3 for ρliq and 4.1 (5.5) kJ mol-1 for ΔHvap for the calibration (validation) set. Thus, a very good level of agreement with experiment is achieved in terms of these two properties, although the errors are inhomogeneously distributed across the different chemical functional groups.

Preparing and Analyzing Polarizable Molecular Dynamics Simulations with the Classical Drude Oscillator Model

Molecular dynamics (MD) simulations performed with force fields that include explicit electronic polarization are becoming more prevalent in the field. The increasing emergence of these simulations is a result of continual refinement against a range of theoretical and empirical target data, optimization of software algorithms for higher performance, and availability of graphical processing unit hardware to further accelerate the simulations. Polarizable MD simulations are likely to be most impactful in biomolecular systems in which heterogeneous environments or unique microenvironments exist that would lead to inaccuracies in simulations performed with fixed-charge, nonpolarizable force fields. The further adoption of polarizable MD simulations will benefit from tutorial material that specifically addresses preparing and analyzing their unique features. In this chapter, we introduce common protocols for preparing routine biomolecular systems containing proteins, including both a globular protein in aqueous solvent and a transmembrane model peptide in a phospholipid bilayer. Details and example input files are provided for preparation of the simulation system using CHARMM, performing the simulations with OpenMM, and analyzing interesting dipole moment properties in CHARMM.

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.

Nuclear Quantum Effect and Its Temperature Dependence in Liquid Water from Random Phase Approximation via Artificial Neural Network

We report structural and dynamical properties of liquid water described by the random phase approximation (RPA) correlation together with the exact exchange energy (EXX) within density functional theory. By utilizing thermostated ring polymer molecular dynamics, we examine the nuclear quantum effects and their temperature dependence. We circumvent the computational limitation of performing direct first-principles molecular dynamics simulation at this high level of electronic structure theory by adapting an artificial neural network model. We show that the EXX+RPA level of theory accurately describes liquid water in terms of both dynamical and structural properties.