Abstract
The numerical advantage of quantum Monte Carlo simulations of rigid bodies relative to the flexible simulations is investigated for some simple systems. The results show that if high frequency modes in molecular condensed matter are predominantly in the ground state, the convergence of path integral simulations becomes nonuniform. Rigid body quantum parallel tempering simulations are necessary to accurately capture thermodynamic phenomena in the temperature range where the dynamics are influenced by intermolecular degrees of freedom; the stereographic projection path integral adapted for quantum simulations of asymmetric tops is a significantly more efficient strategy compared with Cartesian coordinate simulations for molecular condensed matter under these conditions. The reweighted random series approach for stereographic path integral Monte Carlo is refined and implemented for the quantum simulation of water clusters treated as an assembly of rigid asymmetric tops.
Highlights
In a series of articles[38,39,40,41,42] we have introduced and refined methodologies to carry out PIMC methods in rotational and torsional manifolds based on the DeWitt formula.[2]
It is well known that rigid body simulations improve the efficiency of thermodynamic estimators in Metropolis simulations
We anticipate that in quantum simulations the efficiency of the rigid body algorithms will have two contributions; the first should be a similar decrease in statistical fluctuations of the estimated thermodynamics properties, and the second, and probably more important contribution is the convergence with respect to the number of path variables of the properties, at temperatures where the high frequency modes are predominantly in the ground state
Summary
The present article has two main purposes. Firstly, we investigate the efficiency gained in PIMC simulations of molecular condensed matter when holonomic constraints are used. We anticipate that in quantum simulations the efficiency of the rigid body algorithms will have two contributions; the first should be a similar decrease in statistical fluctuations of the estimated thermodynamics properties, and the second, and probably more important contribution is the convergence with respect to the number of path variables of the properties, at temperatures where the high frequency modes are predominantly in the ground state. In this case, one expects the path integral Monte Carlo approach based on Cartesian coordinates to experience nonuniform convergence.
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