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

Abstract

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.

A Gaussian wave packet phase-space representation of quantum canonical statistics

“…(7) and (17) were evaluated using our thermostatted GWP dynamic approach described in Ref. 31. The algorithms and parameters used during equilibration and subsequent propagation of the GWPs are given in Section IX A of Ref.…”

“…The algorithms and parameters used during equilibration and subsequent propagation of the GWPs are given in Section IX A of Ref. 31. Equilibration was performed for 1 × 10 5 a.u.…”

“…The classical value is recovered at high temperature by virtue of the behaviour of the Gaussian phase-space density in a, which tends to increasingly narrow Gaussians and thus suppresses (r 2 i j ) ncl (see Ref. 31 for an analytic expression for the most probable a as a function of temperature for a harmonic system).…”

“…The existence of this well defined GWP dynamic on an effective potential means that the NHC and NHLC thermostats of Ref. 31 can be applied unaltered to sample the canonical phase-space density on H eff .…”

“…(1) is applied explicitly using the imaginary-time formulation of MCTDH, before applying the real-time propagators using the conventional formulation. [27][28][29][30] Our recent work has focused on a Gaussian wavepacket (GWP) approach to approximate quantum canonical statistics, 31 where the quantum thermal average is approximated using the extended phase-space of thawed Gaussian parameters. Much of the recent work on thermal quantum statistical averages of real-time properties is within the framework of RPMD, CMD, and semi-classical approaches.…”