A fast variational Gaussian wavepacket method: size-induced structural transitions in large neon clusters

The variational Gaussian wavepacket (VGW) approximation provides an alternative to path integral Monte Carlo for the computation of thermodynamic properties of many-body systems at thermal equilibrium. It provides a direct access to the thermal density matrix and is particularly efficient for Monte Carlo approaches, as for an N-body system it operates in a non-inflated 3N-dimensional configuration space. Here, we greatly accelerate the VGW method by retaining only the relevant short-range correlations in the (otherwise full) 3N × 3N Gaussian width matrix without sacrificing the accuracy of the fully coupled VGW method. This results in the reduction of the original O(N(3)) scaling to O(N(2)). The fast-VGW method is then applied to quantum Lennard-Jones clusters with sizes up to N = 6500 atoms. Following Doye and Calvo JCP 116, 8307 (2002)] we study the competition between the icosahedral and decahedral structural motifs in Ne(N) clusters as a function of N.