An Efficient Integrator Scheme for Sampling the (Quantum) Isobaric–Isothermal Ensemble in (Path Integral) Molecular Dynamics Simulations

Because most chemical or biological experiments are performed under conditions of controlled pressure and temperature, it is important to simulate the isobaric-isothermal ensemble at the atomic level to reveal the microscopic mechanism. By extending our efficient configuration sampling approach for the canonical ensemble, we propose a unified "middle" scheme to sample the coordinate (configuration) and volume distribution, which can accurately simulate either classical or quantum isobaric-isothermal processes. Various barostats and thermostats can be employed in the unified "middle" scheme for simulating real molecular systems with or without holonomic constraints. In particular, we demonstrate the recommended "middle" scheme by employing the Martyna-Tuckerman-Tobias-Klein barostat and stochastic cell-rescaling barostat, with the Langevin thermostat, in molecular simulation packages (DL_POLY, AMBER, GROMACS, and so forth). Benchmark numerical tests show that, without additional numerical effort, the "middle" scheme is competent in increasing the time interval by a factor of 5 ∼ 10 to achieve the same accuracy of converged results for most thermodynamic properties in (path integral) molecular dynamics simulations.