We report an improved method for the calculation of tunneling splittings between degenerate configurations in molecules and clusters using path-integral molecular dynamics (PIMD). Starting from an expression involving a ratio of thermodynamic density matrices at the bottom of the symmetric wells, we use thermodynamic integration with molecular dynamics simulations and a Langevin thermostat to compute the splittings stochastically. The thermodynamic integration is performed by sampling along the semiclassical instanton path, which provides an efficient reaction coordinate as well as being physically well-motivated. This approach allows us to carry out PIMD calculations of the multi-well tunnelling splitting pattern in water dimer, and to refine previous PIMD calculations for one-dimensional models and malonaldehyde. The large (acceptor) splitting in water dimer agrees to within 20% of benchmark variational results, and the smaller splittings are within 10%.
Stochastic thermostats based on the Langevin equation, in which a system is coupled to an external heat bath, are popular methods for temperature control in molecular dynamics simulations due to their ergodicity and their ease of implementation. Traditionally, these thermostats suffer from sluggish behaviour in the limit of high friction, unlike thermostats of the Nosé-Hoover family whose performance degrades more gently in the strong coupling regime. We propose a simple and easy-to-implement modification to the integration scheme of the Langevin algorithm that addresses the fundamental source…
The properties of molecules and materials containing light nuclei are affected by their quantum mechanical nature. Modelling these quantum nuclear effects accurately requires computationally demanding path integral techniques. Considerable success has been achieved in reducing the cost of such simulations by using generalized Langevin dynamics to induce frequency-dependent fluctuations. Path integral generalized Langevin equation methods, however, have this far been limited to the study of static, thermodynamic properties due to the large perturbation to the system's dynamics induced by the ag…
Generalized Langevin Equation (GLE) thermostats have been used very effectively as a tool to manipulate and optimize the sampling of thermodynamic ensembles and the associated static properties. Here we show that a similar, exquisite level of control can be achieved for the dynamical properties computed from thermostatted trajectories. By developing quantitative measures of the disturbance induced by the GLE to the Hamiltonian dynamics of a harmonic oscillator, we show that these analytical results accurately predict the behavior of strongly anharmonic systems. We also show that it is possible…
Molecular dynamics with the stochastic process provides a convenient way to compute structural and thermodynamic properties of chemical, biological, and materials systems. It is demonstrated that the virtual dynamics case that we proposed for the Langevin equation [J. Chem. Phys. 147, 184104 (2017)] in principle exists in other types of stochastic thermostats as well. The recommended middle scheme [J. Chem. Phys. 147, 034109 (2017)] of the Andersen thermostat is investigated as an example. As shown by both analytic and numerical results, while the real and virtual dynamics cases approach the s…
Molecules like water have vibrational modes with a zero-point energy well above room temperature. As a consequence, classical molecular dynamics simulations of their liquids largely underestimate the energy of modes with a higher zero-point temperature, which translates into an underestimation of covalent interatomic distances due to anharmonic effects. Zero-point effects can be recovered using path integral molecular dynamics simulations, but these are computationally expensive, making their combination with ab initio molecular dynamics simulations a challenge. As an alternative to path integ…
We show a unified second-order scheme for constructing simple, robust and accurate algorithms for typical thermostats for configurational sampling for the canonical ensemble. When Langevin dynamics is used, the scheme leads to the BAOAB algorithm that has been recently investigated. We show that the scheme is also useful for other types of thermostat, such as the Andersen thermostat and Nosé-Hoover chain. Two 1-dimensional models and three typical realistic molecular systems that range from the gas phase, clusters, to the condensed phase are used in numerical examples for demonstration. Accura…
Two of the most successful methods that are presently available for simulating the quantum dynamics of condensed phase systems are centroid molecular dynamics (CMD) and ring polymer molecular dynamics (RPMD). Despite their conceptual differences, practical implementations of these methods differ in just two respects: the choice of the Parrinello-Rahman mass matrix and whether or not a thermostat is applied to the internal modes of the ring polymer during the dynamics. Here we explore a method which is halfway between the two approximations: we keep the path integral bead masses equal to the ph…
We discuss the use of a Langevin equation with a colored (correlated) noise to perform constant-temperature molecular dynamics simulations. Since the equations of motion are linear in nature, it is easy to predict the response of a Hamiltonian system to such a thermostat and to tune at will the relaxation time of modes of different frequency. This allows one to optimize the time needed to thermalize the system and generate independent configurations. We show how this frequency-dependent response can be exploited to control the temperature of Car-Parrinello-like dynamics, keeping at low tempera…
For a long time, performing converged path integral simulations at ultra-low, but finite temperatures of a few Kelvin has been a nearly impossible task. However, recent developments in advanced colored noise thermostatting schemes for path integral simulations, namely the Path Integral Generalized Langevin Equation Thermostat (PIGLET) and the Path Integral Quantum Thermal Bath (PIQTB), have been able to greatly reduce the computational cost of these simulations, thus making the ultra-low temperature regime accessible in practice. In this work, we investigate the influence of these two thermost…
We introduce a novel approach for a fully quantum description of coupled electron-ion systems from first principles. It combines the variational quantum Monte Carlo (QMC) solution of the electronic part with the path integral (PI) formalism for the quantum nuclear dynamics. On the one hand, the PI molecular dynamics includes nuclear quantum effects by adding a set of fictitious classical particles (beads) aimed at reproducing nuclear quantum fluctuations via a harmonic kinetic term. On the other hand, variational QMC can provide Born-Oppenheimer (BO) potential energy surfaces with a precision …
We derive two path integral estimators for the derivative of the quantum mechanical potential of mean force (PMF), which may be numerically integrated to yield the PMF. For the first estimator, we perform the differentiation on the exact path integral, and for the second, we perform the differentiation on the path integral after discretization. These estimators are successfully validated against reference results for the harmonic oscillator and Lennard-Jones dimer systems using constrained path integral Monte Carlo (PIMC) simulations. Specifically, the estimators reproduce both the derivative …
The authors present a new molecular dynamics algorithm for sampling the isothermal-isobaric ensemble. In this approach the velocities of all particles and volume degrees of freedom are rescaled by a properly chosen random factor. The technical aspects concerning the derivation of the integration scheme and the conservation laws are discussed in detail. The efficiency of the barostat is examined in Lennard-Jones solid and liquid near the triple point and compared with the deterministic Nosé-Hoover and the stochastic Langevin methods. In particular, the dependence of the sampling efficiency on t…
The development and implementation of increasingly accurate methods for electronic structure calculations mean that, for many atomistic simulation problems, treating light nuclei as classical particles is now one of the most serious approximations. Even though recent developments have significantly reduced the overhead for modelling the quantum nature of the nuclei, the cost is still prohibitive when combined with advanced electronic structure methods. Here we present how multiple time step integrators can be combined with ring-polymer contraction techniques (effectively, multiple time steppin…
The thermal degradation of a graphene-like two-dimensional triangular membrane with bonds undergoing temperature-induced scission is studied by means of Molecular Dynamics simulation using Langevin thermostat. We demonstrate that the probability distribution of breaking bonds is highly peaked at the rim of the membrane sheet at lower temperature whereas at higher temperature bonds break at random anywhere in the hexagonal flake. The mean breakage time $τ$ is found to decrease with the total number of network nodes $N$ by a power law $τ\propto N^{-0.5}$ and reveals an Arrhenian dependence on te…
