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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]

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]

Higher order factorization schemes are developed for path integral molecular dynamics in order to improve the convergence of estimators for physical observables as a function of the Trotter number. The methods are based on the Takahashi-Imada and Susuki decompositions of the Boltzmann operator. The methods introduced improve the averages of the estimators by using the classical forces needed to carry out the dynamics to construct a posteriori weighting factors for standard path integral molecular dynamics. The new approaches are straightforward to implement in existing path integral codes and carry no significant overhead. The Suzuki higher order factorization was also used to improve the end-to-end distance estimator in open path integral molecular dynamics. The new schemes are tested in various model systems, including an ab initio path integral molecular dynamics calculation on the hydrogen molecule and a quantum water model. The proposed algorithms have potential utility for reducing the cost of path integral molecular dynamics calculations of bulk systems. [ABSTRACT FROM AUTHOR]

In this paper (Paper I) and a companion paper (Paper II), novel new algorithms and applications of the isokinetic ensemble as generated by Gauss' principle of least constraint, pioneered for use with molecular dynamics 20 years ago, are presented for biophysical, path integral, and Car-Parrinello based ab initio molecular dynamics. In Paper I, a new "extended system" version of the isokinetic equations of motion that overcomes the ergodicity problems inherent in the standard approach, is developed using a new theory of non-Hamiltonian phase space analysis [M. E. Tuckerman et al., Europhys. Lett. 45, 149 (1999); J. Chem. Phys. 115, 1678 (2001)]. Reversible multiple time step integrations schemes for the isokinetic methods, first presented by Zhang [J. Chem. Phys. 106, 6102 (1997)] are reviewed. Next, holonomic constraints are incorporated into the isokinetic methodology for use in fast efficient biomolecular simulation studies. Model and realistic examples are presented in order to evaluate, critically, the performance of the new isokinetic molecular dynamic schemes. Comparisons are made to the, now standard, canonical dynamics method, Nosé-Hoover chain dynamics [G. J. Martyna et al., J. Chem. Phys. 97, 2635 (1992)]. The new isokinetic techniques are found to yield more efficient sampling than the Nosé-Hoover chain method in both path integral molecular dynamics and biophysical molecular dynamics calculations. In Paper II, the use of isokinetic methods in Car-Parrinello based ab initio molecular dynamics calculations is presented. [ABSTRACT FROM AUTHOR]

Investigates the double proton transfer in the formic acid dimer using ab initio path integral molecular dynamics (PIMD). Description of the electronic structure by Kohn-Sham formulation of the density functional theory; Details on the PIMD approach of Tuckerman; Results of the thermal and quantum fluctuations around the equilibrium structure.

In path integral molecular dynamics, efficient sampling of the phase space is not guaranteed due to the stiff harmonic part of the action arising from the quantum kinetic energy. This problem has been eliminated by incorporating a sufficient number of thermostats into the dynamical scheme and by introducing a transformation of the path ‘‘bead’’ variables. In this paper, an efficient Car–Parrinello path integral molecular dynamics algorithm, sufficiently general to include the use of ultrasoft pseudopotentials is introduced. Difficulties encountered when combining thermostats and transformations of the Cartesian ‘‘bead’’ coordinates with the generalized orthonormality condition are circumvented by employing a constrained nonorthogonal orbital method. © 1996 American Institute of Physics. [ABSTRACT FROM AUTHOR]

New path integral molecular dynamics (PIMD) and path integral hybrid Monte Carlo (PIHMC) algorithms are developed. It is shown that the use of a simple noncanonical change of variables that naturally divides the quadratic part of the action into long and short wavelength modes and multiple time scale integration techniques results in very efficient algorithms. The PIMD method also employs a constant temperature MD technique that has been shown to give canonical averages even for stiff systems. The new methods are applied to the simple quantum mechanical harmonic oscillator and to electron solvation in fluid helium and xenon. Comparisons are made with PIMC and the more basic PIMD and PIHMC methods. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Equilibrium fractionation of stable isotopes is critically important in fields ranging from chemistry, including medicinal chemistry, electrochemistry, geochemistry, and nuclear chemistry, to environmental science. The dearth of reliable estimates of equilibrium fractionation factors, from experiment or from natural observations, has created a need for accurate computational approaches. Because isotope fractionation is a purely quantum mechanical phenomenon, exact calculation of fractionation factors is nontrivial. Consequently, a severe approximation is often made, in which it is assumed that the system can be decomposed into a set of independent harmonic oscillators. Reliance on this often crude approximation is one of the primary reasons that theoretical prediction of isotope fractionation has lagged behind experiment. A class of problems for which one might expect the harmonic approximation to perform most poorly is the isotopic fractionation between solid and solution phases. In order to illustrate the errors associated with the harmonic approximation, we have considered the fractionation of Li isotopes between aqueous solution and phyllosilicate minerals, where we find that the harmonic approximation overestimates isotope fractionation factors by as much as 30% at 25 °C. Lithium is a particularly interesting species to examine, as natural lithium isotope signatures provide information about hydrothermal processes, carbon cycle, and regulation of the Earth's climate by continental alteration. Further, separation of lithium isotopes is of growing interest in the nuclear industry due to a need for pure 6Li and 7Li isotopes. Moving beyond the harmonic approximation entails performing exact quantum calculations, which can be achieved using the Feynman path integral formulation of quantum statistical mechanics. In the path integral approach, a system of quantum particles is represented as a set of classical-like ring-polymer chains, whose interparticle interactions are determined by the rules of quantum mechanics. Because a classical isomorphism exists between the true quantum system and the system of ring-polymers, classical-like methods can be applied. Recent developments of efficient path integral approaches for the exact calculation of isotope fractionation now allow the case of the aforementioned dissolved Li fractionation properties to be studied in detail. Applying this technique, we find that the calculations yield results that are in good agreement with both experimental data and natural observations. Importantly, path integral methods, being fully atomistic, allow us to identify the origins of anharmonic effects and to make reliable predictions at temperatures that are experimentally inaccessible yet are, nevertheless, relevant for natural phenomena. [ABSTRACT FROM AUTHOR]