Machine learning phase space quantum dynamics approaches.

Derived from phase space expressions of the quantum Liouville theorem, equilibrium continuity dynamics is a category of trajectory-based phase space dynamics methods, which satisfies the two critical fundamental criteria: conservation of the quantum Boltzmann distribution for the thermal equilibrium system and being exact for any thermal correlation functions (even of nonlinear operators) in the classical and harmonic limits. The effective force and effective mass matrix are important elements in the equations of motion of equilibrium continuity dynamics, where only the zeroth term of an exact series expansion of the phase space propagator is involved. We introduce a machine learning approach for fitting these elements in quantum phase space, leading to a much more efficient integration of the equations of motion. Proof-of-concept applications to realistic molecules demonstrate that machine learning phase space dynamics approaches are possible as well as competent in producing reasonably accurate results with a modest computation effort.

Unified Efficient Thermostat Scheme for the Canonical Ensemble with Holonomic or Isokinetic Constraints via Molecular Dynamics.

We have recently proposed a new unified theoretical scheme (the "middle" scheme) for thermostat algorithms for efficient and accurate configurational sampling of the canonical ensemble. In this paper, we extend the "middle" scheme to molecular dynamics algorithms for configurational sampling in systems subject to constraints. Holonomic constraints and isokinetic constraints are used for demonstration. Numerical examples indicate that the "middle" scheme presents a promising approach to calculate configuration-dependent thermodynamic properties and their thermal fluctuations.

Path integral molecular dynamics for exact quantum statistics of multi-electronic-state systems.

An exact approach to compute physical properties for general multi-electronic-state (MES) systems in thermal equilibrium is presented. The approach is extended from our recent progress on path integral molecular dynamics (PIMD), Liu et al. [J. Chem. Phys. 145, 024103 (2016)] and Zhang et al. [J. Chem. Phys. 147, 034109 (2017)], for quantum statistical mechanics when a single potential energy surface is involved. We first define an effective potential function that is numerically favorable for MES-PIMD and then derive corresponding estimators in MES-PIMD for evaluating various physical properties. Its application to several representative one-dimensional and multi-dimensional models demonstrates that MES-PIMD in principle offers a practical tool in either of the diabatic and adiabatic representations for studying exact quantum statistics of complex/large MES systems when the Born-Oppenheimer approximation, Condon approximation, and harmonic bath approximation are broken.

A unified thermostat scheme for efficient configurational sampling for classical/quantum canonical ensembles via molecular dynamics.

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 thermostats, such as the Andersen thermostat and Nosé-Hoover chain, regardless of whether the thermostat is deterministic or stochastic. In addition to analytical analysis, two 1-dimensional models and three typical real molecular systems that range from the gas phase, clusters, to the condensed phase are used in numerical examples for demonstration. Accuracy may be increased by an order of magnitude for estimating coordinate-dependent properties in molecular dynamics (when the same time interval is used), irrespective of which type of thermostat is applied. The scheme is especially useful for path integral molecular dynamics because it consistently improves the efficiency for evaluating all thermodynamic properties for any type of thermostat.

A simple and accurate algorithm for path integral molecular dynamics with the Langevin thermostat.

We introduce a novel simple algorithm for thermostatting path integral molecular dynamics (PIMD) with the Langevin equation. The staging transformation of path integral beads is employed for demonstration. The optimum friction coefficients for the staging modes in the free particle limit are used for all systems. In comparison to the path integral Langevin equation thermostat, the new algorithm exploits a different order of splitting for the phase space propagator associated to the Langevin equation. While the error analysis is made for both algorithms, they are also employed in the PIMD simulations of three realistic systems (the H2O molecule, liquid para-hydrogen, and liquid water) for comparison. It is shown that the new thermostat increases the time interval of PIMD by a factor of 4-6 or more for achieving the same accuracy. In addition, the supplementary material shows the error analysis made for the algorithms when the normal-mode transformation of path integral beads is used.