Path integral density matrix dynamics: A method for calculating time-dependent properties in thermal adiabatic and non-adiabatic systems

NQCDynamics.jl: A Julia package for nonadiabatic quantum classical molecular dynamics in the condensed phase

Accurate and efficient methods to simulate nonadiabatic and quantum nuclear effects in high-dimensional and dissipative systems are crucial for the prediction of chemical dynamics in the condensed phase. To facilitate effective development, code sharing, and uptake of newly developed dynamics methods, it is important that software implementations can be easily accessed and built upon. Using the Julia programming language, we have developed the NQCDynamics.jl package, which provides a framework for established and emerging methods for performing semiclassical and mixed quantum-classical dynamics in the condensed phase. The code provides several interfaces to existing atomistic simulation frameworks, electronic structure codes, and machine learning representations. In addition to the existing methods, the package provides infrastructure for developing and deploying new dynamics methods, which we hope will benefit reproducibility and code sharing in the field of condensed phase quantum dynamics. Herein, we present our code design choices and the specific Julia programming features from which they benefit. We further demonstrate the capabilities of the package on two examples of chemical dynamics in the condensed phase: the population dynamics of the spin-boson model as described by a wide variety of semiclassical and mixed quantum-classical nonadiabatic methods and the reactive scattering of H₂ on Ag(111) using the molecular dynamics with electronic friction method. Together, they exemplify the broad scope of the package to study effective model Hamiltonians and realistic atomistic systems.

Harmonic-phase path-integral approximation of thermal quantum correlation functions

We present an approximation to the thermal symmetric form of the quantum time-correlation function in the standard position path-integral representation. By transforming to a sum-and-difference position representation and then Taylor-expanding the potential energy surface of the system to second order, the resulting expression provides a harmonic weighting function that approximately recovers the contribution of the phase to the time-correlation function. This method is readily implemented in a Monte Carlo sampling scheme and provides exact results for harmonic potentials (for both linear and non-linear operators) and near-quantitative results for anharmonic systems for low temperatures and times that are likely to be relevant to condensed phase experiments. This article focuses on one-dimensional examples to provide insights into convergence and sampling properties, and we also discuss how this approximation method may be extended to many-dimensional systems.

Concerted transfer of multiple protons in acid-water clusters: [(HCl)(H2O)]2 and [(HF)(H2O)]4

Molecular dynamics simulations using directly ab initio potentials are carried out for the ionically bonded clusters [(Cl^-)(H₃O⁺)]₂ and [(F^-)(H₃O⁺)]₄ to explore their transitions to the hydrogen-bonded [(HCl)(H₂O)]₂ and [(HF)(H₂O)]₄ structures during the first picosecond of simulation. Both the ionic and the H-bonded structures that are formed are highly symmetric. It is found that proton transfers are concerted in all trajectories for [(Cl^-)(H₃O⁺)]₂. For [(F^-)(H₃O⁺)]₄, the fully concerted mechanism is dominant but partially concerted transfers of two or three protons at the same time also occur. The concerted mechanism also holds for the reverse process of ionization of neutral acid molecules. It is suggested that the high symmetry of the ionic and the H-bonded structures plays a role in the preference for concerted transfers. Possible implications of the results for proton transfers in other systems are discussed.

The Nosé-Hoover looped chain thermostat for low temperature thawed Gaussian wave-packet dynamics

We have used a generalised coherent state resolution of the identity to map the quantum canonical statistical average for a general system onto a phase-space average over the centre and width parameters of a thawed Gaussian wave packet. We also propose an artificial phase-space density that has the same behaviour as the canonical phase-space density in the low-temperature limit, and have constructed a novel Nosé-Hoover looped chain thermostat that generates this density in conjunction with variational thawed Gaussian wave-packet dynamics. This forms a new platform for evaluating statistical properties of quantum condensed-phase systems that has an explicit connection to the time-dependent Schrödinger equation, whilst retaining many of the appealing features of path-integral molecular dynamics.