Non-equilibrium dynamics from RPMD and CMD

Abstract

We investigate the calculation of approximate non-equilibrium quantum time correlation functions (TCFs) using two popular path-integral-based molecular dynamics methods, ring-polymer molecular dynamics (RPMD) and centroid molecular dynamics (CMD). It is shown that for the cases of a sudden vertical excitation and an initial momentum impulse, both RPMD and CMD yield non-equilibrium TCFs for linear operators that are exact for high temperatures, in the t = 0 limit, and for harmonic potentials; the subset of these conditions that are preserved for non-equilibrium TCFs of non-linear operators is also discussed. Furthermore, it is shown that for these non-equilibrium initial conditions, both methods retain the connection to Matsubara dynamics that has previously been established for equilibrium initial conditions. Comparison of non-equilibrium TCFs from RPMD and CMD to Matsubara dynamics at short times reveals the orders in time to which the methods agree. Specifically, for the position-autocorrelation function associated with sudden vertical excitation, RPMD and CMD agree with Matsubara dynamics up to O(t4) and O(t1), respectively; for the position-autocorrelation function associated with an initial momentum impulse, RPMD and CMD agree with Matsubara dynamics up to O(t5) and O(t2), respectively. Numerical tests using model potentials for a wide range of non-equilibrium initial conditions show that RPMD and CMD yield non-equilibrium TCFs with an accuracy that is comparable to that for equilibrium TCFs. RPMD is also used to investigate excited-state proton transfer in a system-bath model, and it is compared to numerically exact calculations performed using a recently developed version of the Liouville space hierarchical equation of motion approach; again, similar accuracy is observed for non-equilibrium and equilibrium initial conditions.

Inclusion of nuclear quantum effects for simulations of nonlinear spectroscopy

“…In recent years, different efforts have been made to extend RPMD to describe nonadiabatic dynamics [86][87][88][89] and non-equilibrium conditions. 90 Very recently, Althorpe and co-workers have shown that RPMD can be viewed as an approximation to a more general type of quantum Boltzmann preserving classical dynamics, known as Matsubara dynamics. 42,43 However, so far, the formulation of RPMD has been restricted to the evaluation of the single-time Kubo transform.…”

Infrared-laser-pulse-enhanced ultrafast fragmentation of N22+ following Auger decay: Mixed quantum-classical simulations

“…Small differences in the dynamics resulting from the approximations in the sampling manifest themselves more strongly for short IR pulses than long IR pulses, due to less averaging in the former case. These shortcomings could, for example, be overcome by employing the ring polymer molecular dynamics approach [55,56] with nonequilibrium initial conditions [57] and surface hopping [58,59]. This is left for future work.…”

Thermal quantum time-correlation functions from classical-like dynamics

“…There may also be other classical-like approximations to quantum dynamics (and maybe Matsubara dynamics) that for some systems are more accurate [145]. Very recent research has obtained out-of-equilibrium RPMD and CMD from Matsubara dynamics [20], which should be useful tools for excited state quantum dynamics.…”

“…We touch upon extensions to non-adiabatic dynamics towards the end. We generally assume that the systems being described are in thermal equilibrium; application to non-equilibrium systems is an interesting area of present research [20].…”