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Kohn-Sham density functional theory (DFT) is a standard tool in most branches of chemistry, but accuracies for many molecules are limited to 2-3 kcal ⋅ mol-1 with presently-available functionals. Ab initio methods, such as coupled-cluster, routinely produce much higher accuracy, but computational costs limit their application to small molecules. In this paper, we leverage machine learning to calculate coupled-cluster energies from DFT densities, reaching quantum chemical accuracy (errors below 1 kcal ⋅ mol-1) on test data. Moreover, density-based Δ-learning (learning only the correction to a standard DFT calculation, termed Δ-DFT ) significantly reduces the amount of training data required, particularly when molecular symmetries are included. The robustness of Δ-DFT  is highlighted by correcting "on the fly" DFT-based molecular dynamics (MD) simulations of resorcinol (C6H4(OH)2) to obtain MD trajectories with coupled-cluster accuracy. We conclude, therefore, that Δ-DFT  facilitates running gas-phase MD simulations with quantum chemical accuracy, even for strained geometries and conformer changes where standard DFT fails.

Determining collective variables (CVs) for conformational transitions is crucial to understanding their dynamics and targeting them in enhanced sampling simulations. Often, CVs are proposed based on intuition or prior knowledge of a system. However, the problem of systematically determining a proper reaction coordinate (RC) for a specific process in terms of a set of putative CVs can be achieved using committor analysis (CA). Identifying essential degrees of freedom that govern such transitions using CA remains elusive because of the high dimensionality of the conformational space. Various schemes exist to leverage the power of machine learning (ML) to extract an RC from CA. Here, we extend these studies and compare the ability of 17 different ML schemes to identify accurate RCs associated with conformational transitions. We tested these methods on an alanine dipeptide in vacuum and on a sarcosine dipeptoid in an implicit solvent. Our comparison revealed that the light gradient boosting machine method outperforms other methods. In order to extract key features from the models, we employed Shapley Additive exPlanations analysis and compared its interpretation with the "feature importance" approach. For the alanine dipeptide, our methodology identifies ϕ and θ dihedrals as essential degrees of freedom in the C7ax to C7eq transition. For the sarcosine dipeptoid system, the dihedrals ψ and ω are the most important for the cisαD to transαD transition. We further argue that analysis of the full dynamical pathway, and not just endpoint states, is essential for identifying key degrees of freedom governing transitions. [ABSTRACT FROM AUTHOR]

Last year, at least 30,000 scientific papers used the Kohn-Sham scheme of density functional theory to solve electronic structure problems in a wide variety of scientific fields. Machine learning holds the promise of learning the energy functional via examples, bypassing the need to solve the Kohn-Sham equations. This should yield substantial savings in computer time, allowing larger systems and/or longer time-scales to be tackled, but attempts to machine-learn this functional have been limited by the need to find its derivative. The present work overcomes this difficulty by directly learning the density-potential and energy-density maps for test systems and various molecules. We perform the first molecular dynamics simulation with a machine-learned density functional on malonaldehyde and are able to capture the intramolecular proton transfer process. Learning density models now allows the construction of accurate density functionals for realistic molecular systems.Machine learning allows electronic structure calculations to access larger system sizes and, in dynamical simulations, longer time scales. Here, the authors perform such a simulation using a machine-learned density functional that avoids direct solution of the Kohn-Sham equations.

Advanced potential energy surfaces are defined as theoretical models that explicitly include many-body effects that transcend the standard fixed-charge, pairwise-additive paradigm typically used in molecular simulation. However, several factors relating to their software implementation have precluded their widespread use in condensed-phase simulations: the computational cost of the theoretical models, a paucity of approximate models and algorithmic improvements that can ameliorate their cost, underdeveloped interfaces and limited dissemination in computational code bases that are widely used in the computational chemistry community, and software implementations that have not kept pace with modern high-performance computing (HPC) architectures, such as multicore CPUs and modern graphics processing units (GPUs). In this Feature Article we review recent progress made in these areas, including well-defined polarization approximations and new multipole electrostatic formulations, novel methods for solving the mutual polarization equations and increasing the MD time step, combining linear-scaling electronic structure methods with new QM/MM methods that account for mutual polarization between the two regions, and the greatly improved software deployment of these models and methods onto GPU and CPU hardware platforms. We have now approached an era where multipole-based polarizable force fields can be routinely used to obtain computational results comparable to state-of-the-art density functional theory while reaching sampling statistics that are acceptable when compared to that obtained from simpler fixed partial charge force fields.

Quantum time correlation functions (TCFs) involving two states are important for describing nonadiabatic dynamical processes such as charge transfer (CT). Based on a previous single-state method, we propose an imaginary-time open-chain path-integral (OCPI) approach for evaluating the two-state symmetrized TCFs. Expressing the forward and backward propagation on different electronic potential energy surfaces as a complex-time path integral, we then transform the path variables to average and difference variables such that the integration over the difference variables up to the second order can be performed analytically. The resulting expression for the symmetrized TCF is equivalent to sampling the open-chain configurations in an effective potential that corresponds to the average surface. Using importance sampling over the extended OCPI space via open path-integral molecular dynamics, we tested the resulting path-integral approximation by calculating the Fermi's golden rule CT rate constant within a widely used spin-boson model. Comparing with the real-time linearized semiclassical method and analytical result, we show that the imaginary-time OCPI provides an accurate two-state symmetrized TCF and rate constant in the typical turnover region. It is shown that the first bead of the open chain corresponds to physical zero-time and that the endpoint bead corresponds to final time t; oscillations of the end-to-end distance perfectly match the nuclear mode frequency. The two-state OCPI scheme is seen to capture the tested model's electronic quantum coherence and nuclear quantum effects accurately. [ABSTRACT FROM AUTHOR]

Collective variable (CV)‐based enhanced sampling techniques are widely used today for accelerating barrier‐crossing events in molecular simulations. A class of these methods, which includes temperature accelerated molecular dynamics (TAMD)/driven‐adiabatic free energy dynamics (d‐AFED), unified free energy dynamics (UFED), and temperature accelerated sliced sampling (TASS), uses an extended variable formalism to achieve quick exploration of conformational space. These techniques are powerful, as they enhance the sampling of a large number of CVs simultaneously compared to other techniques. Extended variables are kept at a much higher temperature than the physical temperature by ensuring adiabatic separation between the extended and physical subsystems and employing rigorous thermostatting. In this work, we present a computational platform to perform extended phase space enhanced sampling simulations using the open‐source molecular dynamics engine OpenMM. The implementation allows users to have interoperability of sampling techniques, as well as employ state‐of‐the‐art thermostats and multiple time‐stepping. This work also presents protocols for determining the critical parameters and procedures for reconstructing high‐dimensional free energy surfaces. As a demonstration, we present simulation results on the high dimensional conformational landscapes of the alanine tripeptide in vacuo, tetra‐N‐methylglycine (tetra‐sarcosine) peptoid in implicit solvent, and the Trp‐cage mini protein in explicit water. [ABSTRACT FROM AUTHOR]

Predictions of the structures of stoichiometric, fractional, or nonstoichiometric hydrates of organic molecular crystals are immensely challenging due to the extensive search space of different water contents, host molecular placements throughout the crystal, and internal molecular conformations. However, the dry frameworks of these hydrates, especially for nonstoichiometric or isostructural dehydrates, can often be predicted from a standard anhydrous crystal structure prediction (CSP) protocol. Inspired by developments in the field of drug binding, we introduce an efficient data-driven and topologically aware approach for predicting organic molecular crystal hydrate structures through a mapping of water positions within the crystal structure. The method does not require a priori specification of water content and can, therefore, predict stoichiometric, fractional, and nonstoichiometric hydrate structures. This approach, which we term a mapping approach for crystal hydrates (MACH), establishes a set of rules for systematic determination of favorable positions for water insertion within predicted or experimental crystal structures based on considerations of the chemical features of local environments and void regions. The proposed approach is tested on hydrates of three pharmaceutically relevant compounds that exhibit diverse crystal packing motifs and void environments characteristic of hydrate structures. Overall, we show that our mapping approach introduces an advance in the efficient performance of hydrate CSP through generation of stable hydrate stoichiometries at low cost and should be considered an integral component for CSP workflows. [ABSTRACT FROM AUTHOR]

A method for calculating the free energy difference between two structurally defined conformational states of a chemical system is developed. A path is defined using a previously reported collective variable that interpolates between two or more conformations, and a restraint is introduced in order to keep the system close to the path. The evolution of the system along the path, which typically presents a high free energy barrier, is generated using enhanced sampling schemes. Although the formulation of the method in terms of a path is quite general, an important advance in this work is the demonstration that prior knowledge of the path is, in fact, not needed and that the free energy difference can be obtained using a simplified definition of the path collective variable that only involves the endpoints. We first validate this method on cyclohexane isomerization. The method is then tested for an extensive conformational change in a realistic molecular system by calculating the free energy difference between the α-helix and β-hairpin conformations of deca-alanine in solution. Finally, the method is applied to a biologically relevant system to calculate the free energy difference of an observed and a hypothetical conformation of an antigenic peptide bound to a major histocompatibility complex. [ABSTRACT FROM AUTHOR]

Enhanced sampling techniques that target a set of collective variables and that use molecular dynamics as the driving engine have seen widespread application in the computational molecular sciences as a means to explore the free-energy landscapes of complex systems. The use of molecular dynamics as the fundamental driver of the sampling requires the introduction of a time step whose magnitude is limited by the fastest motions in a system. While standard multiple time-stepping methods allow larger time steps to be employed for the slower and computationally more expensive forces, the maximum achievable increase in time step is limited by resonance phenomena, which inextricably couple fast and slow motions. Recently, we introduced deterministic and stochastic resonance-free multiple time step algorithms for molecular dynamics that solve this resonance problem and allow ten- to twenty-fold gains in the large time step compared to standard multiple time step algorithms [P. Minary et al., Phys. Rev. Lett. 93, 150201 (2004); B. Leimkuhler et al., Mol. Phys. 111, 3579-3594 (2013)]. These methods are based on the imposition of isokinetic constraints that couple the physical system to Nosé-Hoover chains or Nos'e-Hoover Langevin schemes. In this paper, we show how to adapt these methods for collective variable-based enhanced sampling techniques, specifically adiabatic free-energy dynamics/temperature-accelerated molecular dynamics, unified free-energy dynamics, and by extension, metadynamics, thus allowing simulations employing these methods to employ similarly very large time steps. The combination of resonance-free multiple time step integrators with free-energy-based enhanced sampling significantly improves the efficiency of conformational exploration. [ABSTRACT FROM AUTHOR]

Path integral-based methodologies play a crucial role for the investigation of nuclear quantum effects by means of computer simulations. However, these techniques are significantly more demanding than corresponding classical simulations. To reduce this numerical effort, we recently proposed a method, based on a rigorous Hamiltonian formulation, which restricts the quantum modeling to a small but relevant spatial region within a larger reservoir where particles are treated classically. In this work, we extend this idea and show how it can be implemented along with state-of-the-art path integral simulation techniques, including path-integral molecular dynamics, which allows for the calculation of quantum statistical properties, and ring-polymer and centroid molecular dynamics, which allow the calculation of approximate quantum dynamical properties. To this end, we derive a new integration algorithm that also makes use of multiple time-stepping. The scheme is validated via adaptive classical-path-integral simulations of liquid water. Potential applications of the proposed multiresolution method are diverse and include efficient quantum simulations of interfaces as well as complex biomolecular systems such as membranes and proteins. [ABSTRACT FROM AUTHOR]

Exposing anion exchange membrane (AEM) fuel cells to ambient air is known to decrease fuel cell efficiency significantly due to the presence of CO2. In this combined theoretical and experimental study, we examine the hydration conditions that promote reactions between CO2 and hydroxide ions in nano-confined AEMs, and we explore the effect of the carbonation process on the solvation structure and diffusion of hydroxide ions. Using fully atomistic ab initio molecular dynamics (AIMD) simulations, we find that increasing hydration can delay the carbonation reaction between OH− and CO2. Once reacted, HCO3− ions exist along the simulation, which significantly reduce the diffusion of the hydroxide ions. We confirm these results using 1H- and 13C-pulsed field gradient nuclear magnetic resonance. AIMD simulations further reveal that the HCO3− actively "blocks" the diffusion path of hydroxide ions along the simulation cell. We expect that elucidating the key design principles underlying the atomistic effects of carbonate ions on hydroxide ions diffusion mechanisms in model AEMs will provide useful guidelines for the synthesis and experimental characterization of novel highly conductive AEM fuel cell technologies in the presence of CO2-containing air. [ABSTRACT FROM AUTHOR]

The numerical algorithms for the discrete variable representation (DVR) basis sets based ab initio molecular dynamics (AIMD) scheme are provided and the accuracy and stability of the implementation of the DVR/AIMD scheme are tested by performing a simulation of liquid water at ambient conditions. The results show that a DVR/AIMD simulation of liquid water in the complete basis set limit is possible with a relatively small number of grid points as compared to the plane wave (PW) basis sets/AIMD method.

The theoretical study of (LiMe)(sub n) aggregates using Car-Parrinello molecular dynamics was undertaken and with respect to a quantum chemical static treatment, this approach furnishes supplementary information about the structural parameters. Results found that parameter-free ab intio molecular dynamics method is introduced.

The (super 17)O NMR parameters of an amorphous calcium aluminisilicate (CAS) is computed from first-principles. The atomic coordinates of a CAS glass of composition (CaO)0.21(Al2O3)0.12(SiO2)0.67 were obtained by quenching a liquid to room temperature by the means of ab initio molecular-dynamics simulations of the Car-Parrinello type.

Author(s): Mark E. Tuckerman (corresponding author) [1]; Dominik Marx [2]; Michele Parrinello [3, 4] Compared to other ions, protons (H[sup.+] ) and hydroxide ions (OH[sup.-] ) exhibit anomalously high mobilities [...]

A study was conducted to investigate the isothermal-isobaric molecular dynamics methods in system subject to holonomic constraints with the goal of devising equations of motion in which the scaling is performed on atomic positions. The result demonstrates that the Kneller-Mulders equations generate an isothermal-isobaric ensemble distribution only for systems with nonzero total force.

The different methods to calculate the accurate vibrational energy relaxation rates for high-frequency modes from classical molecular dynamics simulations are presented. The features and advantages of Fermi's golden rule, a convenient starting point for calculating the vibrational energy relaxation rate constants, are discussed.

A study was conducted to examine the structural and thermodynamic properties of a water droplet enclosed in a spherical cavity embedded in a hydrophobic material. The results indicate that the structure of water near an impenetrable and purely repulsive surface at standard conditions of temperature and pressure is described as a dry, separated state.

A study was conducted to investigate the thermodynamic and structural properties of a Lennard-Jones liquid at a state very close to the triple point as the radius of a hard sphere solute is varied. The result reveals that the oscillatory profiles arise for small, molecular sized radii, where as for large radii smooth interfaces with a drying layer of low vapor density near the solute are seen.

The numerical calculations of the concentration of interstitials in hard-sphere crystals are presented. In a three-dimensional fcc hard-sphere crystal at the melting pint, the concentration of interstitials is 2.7(4) x 10(super -8).

The various important issues related to the implementation of the nonadiabatic dynamics methods in the situation, where quasi-nonavoided crossings take place and play a crucial role in determining the dynamics, are presented. The important connection between dynamics, local environmental symmetry, and electronic structure in determining nonadiabatic relaxation is discussed.

The method of ab initio molecular dynamics was used to study the structural, dynamical, and electronic properties of ionic defects in liquid ammonia at 260 K created by the addition or removal of a proton. The result reveals that the NH4(super +) exhibits a characteristic cationic solvation pattern, in which it donates four hydrogen bonds to neighboring ammonia molecules, giving it a coordination number of 4.

Investigation of crystalline nitric acid trihydrate properties at 195 K has been carried out by means of Car-Parrinello molecular dynamics calculations. Results demonstrate that a proton requires free energy to reach the center of the oxygen-oxygen pair.

Ab initio path integral simulations, including time-independent equilibrium thermal and quantum fluctuations of nuclei, were used to determine interatomic interactions from an electronic structure. The hydrated proton was found to form a fluxional defect in the hydrogen-bonded network. This becomes delocalized over several hydrogen bonds due to quantum fluctuations. The proton is thus considered part of a low-barrier hydrogen bond where tunnelling is slight and the transition-state theory does not apply.

Extended phase-space isokinetic methods in their deterministic [Minary et al., Phys. Rev. Lett. 93, 150201 (2004)] and stochastic forms [Leimkuhler et al., Mol. Phys. 111, 3579 (2013)] have proved tremendously successful in allowing multiple time-scale molecular dynamics simulations to be performed with very large time steps. These methods work by coupling the physical degrees of freedom to a set of Nosé-Hoover chain or Nosé-Hoover Langevin thermostats via an isokinetic constraint, which has the effect of avoiding resonance artifacts that plague multiple time-step algorithms. In this paper, we introduce a new resonance-free approach that achieves the same gains in time step but without the imposition of isokinetic constraints or the introduction of extended phase-space variables. Rather, we modify the physical Hamiltonian that effects the same regulation of resonances achieved by the isokinetic constraints. In so doing, we show that sampling errors can be controlled and performance improvements are possible within a simpler Hamiltonian framework. The method is demonstrated in simulations of the structure of liquid water and, in conjunction with enhanced sampling, in generation of the Ramachandran free-energy surface of the solvated alanine dipeptide. [ABSTRACT FROM AUTHOR]

The high cost of ab initio molecular dynamics (AIMD) simulations to model complex physical and chemical systems limits its ability to address many key questions. However, new machine learning‐based representations of complex potential energy surfaces have been introduced in recent years to circumvent computationally demanding AIMD simulations while retaining the same level of accuracy. As these machine learning methods gain in popularity over the next decade, it is important to address the appropriate way to develop and integrate them with well‐established simulation methods. This paper details the parameterization and training, using accurate electronic structure calculations, of artificial neural network potentials (NNPs) to model the intermolecular interactions in a hydrogen clathrate hydrate, wherein hydrogen molecules are confined inside the cavities of the 3D crystalline framework of hydrogen‐bonded water molecules. This new NNP is used in conjunction with new path‐integral based enhanced sampling methods, for inclusion of nuclear quantum effects and promotion of free energy barrier crossing, in order to determine properties that are important for understanding the diffusion of hydrogen gas in the clathrate system. These simulations demonstrate the influence of cage occupancy on the free energy barriers that determine the diffusivity of hydrogen gas through the network of large cages. [ABSTRACT FROM AUTHOR]