A fast Variational Gaussian Wave-packet method: Size-induced structural transitions in large neon clusters

TL;DR

This paper introduces a significantly accelerated Variational Gaussian Wavepacket (VGW) method that efficiently computes thermodynamic properties of large many-body systems, demonstrated on neon clusters with up to 6500 atoms, revealing size-induced structural transitions.

Contribution

The authors develop a fast VGW method with reduced computational complexity from O(N^3) to O(N^2) by focusing on relevant short-range correlations, enabling large-scale quantum cluster simulations.

Findings

Efficiently models large neon clusters up to 6500 atoms.

Reveals size-dependent competition between icosahedral and decahedral structures.

Achieves accurate thermodynamic calculations with reduced computational cost.

Abstract

The Variational Gaussian wavepacket (VGW) method is an alternative to Path Integral Monte-Carlo (PIMC) 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) $3N\times 3N$ Gaussian width matrix without sacrificing the accuracy of the fully-coupled VGW method. This results in the reduction of the original $\mathcal{O}(N^3)$ scaling to $\mathcal{O}(N^2)$. 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.