An open-chain imaginary-time path-integral sampling approach to the calculation of approximate symmetrized quantum time correlation functions.

We introduce a scheme for approximating quantum time correlation functions numerically within the Feynman path integral formulation. Starting with the symmetrized version of the correlation function expressed as a discretized path integral, we introduce a change of integration variables often used in the derivation of trajectory-based semiclassical methods. In particular, we transform to sum and difference variables between forward and backward complex-time propagation paths. Once the transformation is performed, the potential energy is expanded in powers of the difference variables, which allows us to perform the integrals over these variables analytically. The manner in which this procedure is carried out results in an open-chain path integral (in the remaining sum variables) with a modified potential that is evaluated using imaginary-time path-integral sampling rather than requiring the generation of a large ensemble of trajectories. Consequently, any number of path integral sampling schemes can be employed to compute the remaining path integral, including Monte Carlo, path-integral molecular dynamics, or enhanced path-integral molecular dynamics. We believe that this approach constitutes a different perspective in semiclassical-type approximations to quantum time correlation functions. Importantly, we argue that our approximation can be systematically improved within a cumulant expansion formalism. We test this approximation on a set of one-dimensional problems that are commonly used to benchmark approximate quantum dynamical schemes. We show that the method is at least as accurate as the popular ring-polymer molecular dynamics technique and linearized semiclassical initial value representation for correlation functions of linear operators in most of these examples and improves the accuracy of correlation functions of nonlinear operators.

Competing quantum effects in the free energy profiles and diffusion rates of hydrogen and deuterium molecules through clathrate hydrates.

Clathrate hydrates hold considerable promise as safe and economical materials for hydrogen storage. Here we present a quantum mechanical study of H2 and D2 diffusion through a hexagonal face shared by two large cages of clathrate hydrates over a wide range of temperatures. Path integral molecular dynamics simulations are used to compute the free-energy profiles for the diffusion of H2 and D2 as a function of temperature. Ring polymer molecular dynamics rate theory, incorporating both exact quantum statistics and approximate quantum dynamical effects, is utilized in the calculations of the H2 and D2 diffusion rates in a broad temperature interval. We find that the shape of the quantum free-energy profiles and their height relative to the classical free energy barriers at a given temperature, as well as the rate of diffusion, are strongly affected by competing quantum effects: above 25 K, zero-point energy (ZPE) perpendicular to the reaction path for diffusion between cavities decreases the quantum rate compared to the classical rate, whereas at lower temperatures tunneling outcompetes the ZPE and as a result the quantum rate is greater than the classical rate.

Hydrophobic hydration and the anomalous partial molar volumes in ethanol-water mixtures.

The anomalous behavior in the partial molar volumes of ethanol-water mixtures at low concentrations of ethanol is studied using molecular dynamics simulations. Previous work indicates that the striking minimum in the partial molar volume of ethanol VE as a function of ethanol mole fraction XE is determined mainly by water-water interactions. These results were based on simulations that used one water model for the solute-water interactions but two different water models for the water-water interactions. This is confirmed here by using two more water models for the water-water interactions. Furthermore, the previous work indicates that the initial decrease is caused by association of the hydration shells of the hydrocarbon tails, and the minimum occurs at the concentration where all of the hydration shells are touching each other. Thus, the characteristics of the hydration of the tail that cause the decrease and the features of the water models that reproduce this type of hydration are also examined here. The results show that a single-site multipole water model with a charge distribution that mimics the large quadrupole and the p-orbital type electron density out of the molecular plane has "brittle" hydration with hydrogen bonds that break as the tails touch, which reproduces the deep minimum. However, water models with more typical site representations with partial charges lead to flexible hydration that tends to stay intact, which produces a shallow minimum. Thus, brittle hydration may play an essential role in hydrophobic association in water.

The molecular charge distribution, the hydration shell, and the unique properties of liquid water.

The most essential features of a water molecule that give rise to its unique properties are examined using computer simulations of different water models. The charge distribution of a water molecule characterized by molecular multipoles is quantitatively linked to the liquid properties of water via order parameters for the degree (S(2)) and symmetry (ΔS(2)) of the tetrahedral arrangement of the nearest neighbors, or "hydration shell." ΔS(2) also appears to determine the long-range tetrahedral network and interfacial structure. From the correlations, some models are shown to be unable to reproduce certain properties due to the limitations of the model itself rather than the parameterization, which indicates that they are lacking essential molecular features. Moreover, since these properties depend not only on S(2) but also on ΔS(2), the long-range structure in these models may be incorrect. Based on the molecular features found in the models that are best able to reproduce liquid properties, the most essential features of a water molecule in liquid water appear to be a charge distribution with a large dipole, a large quadrupole, and negative charge out of the molecular plane, as well as a symmetrically ordered tetrahedral hydration shell that results from this charge distribution. The implications for modeling water are also discussed.

Effects of microcomplexity on hydrophobic hydration in amphiphiles.

Hydrophobic hydration is critical in biology as well as many industrial processes. Here, computer simulations of ethanol/water mixtures show that a three-stage mechanism of dehydration of ethanol explains the anomalous concentration dependence of the thermodynamic partial molar volumes, as well as recent data from neutron diffraction and Raman scattering. Moreover, the simulations show that the breakdown of hydrophobic hydration shells, whose structure is determined by the unique molecular properties of water, is caused by the microcomplexity of the environment and may be representative of early events in protein folding and structure stabilization in aqueous solutions.

Comparison of the Performance of Machine Learning Models in Representing High-Dimensional Free Energy Surfaces and Generating Observables.

Free energy surfaces of chemical and physical systems are often generated using a popular class of enhanced sampling methods that target a set of collective variables (CVs) chosen to distinguish the characteristic features of these surfaces. While some of these approaches are typically limited to low (∼1-3)-dimensional CV subspaces, methods such as driven adiabatic free-energy dynamics/temperature-accelerated molecular dynamics have been shown to be capable of generating free energy surfaces of quite high dimension by sampling the associated marginal probability distribution via full sweeps over the CV landscape. These approaches repeatedly visit conformational basins, producing a scattering of points within the basins on each visit. Consequently, they are particularly amenable to synergistic combination with regression machine learning methods for filling in the surfaces between the sampled points and for providing a compact and continuous (or semicontinuous) representation of the surfaces that can be easily stored and used for further computation of observable properties. Given the central role of machine learning techniques in this combined approach, it is timely to provide a detailed comparison of the performance of different machine learning strategies and models, including neural networks, kernel ridge regression, support vector machines, and weighted neighbor schemes, for their ability to learn these high-dimensional surfaces as a function of the amount of sampled training data and, once trained, to subsequently generate accurate ensemble averages corresponding to observable properties of the systems. In this article, we perform such a comparison on a set of oligopeptides, in both gas and aqueous phases, corresponding to CV spaces of 2-10 dimensions and assess their ability to provide a global representation of the free energy surfaces and to generate accurate ensemble averages.

The Surface Potential of the Water-Vapor Interface from Classical Simulations.

The electrochemical surface potential across the water-vapor interface provides a measure of the orientation of water molecules at the interface. However, the large discrepancies between surface potentials calculated from ab initio (AI) and classical molecular dynamics (MD) simulations indicate that what is being calculated may be relevant to different test probes. Although a method for extracting the electrochemical surface potential from AIMD simulations has been given, methods for MD simulations have not been clarified. Here, two methods for extracting the surface potential relevant to electrochemical measurements from MD simulations are presented. This potential is shown to be almost entirely due to the dipole contribution. In addition, the molecular origin of the dipole contribution is explored by using different potential energy functions for water. The results here show that the dipole contribution arises mainly from distortions in the hydration shell of the full hydrogen bonded waters on the liquid side of the interface, which is determined by the charge distribution of the water model. Disturbingly, the potential varies by 0.4 eV depending on the model. Although there is still no consensus on what that charge distribution should be, recent results indicate that it contains both a large quadrupole and negative charge out of the molecular plane, i.e., three-dimensional (3D) charge. Water models with 3D charge give the least distortion of the hydration shell and the best agreement with experimental surface potentials, although there is still uncertainty in the experimental values.