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arXiv:chem-ph/9604001 · The Journal of Chemical Physics

van der Waals clusters in the ultraquantum limit: A Monte Carlo study

M. Meierovich, A. Mushinski, M. P. Nightingale

Published Oct 15, 1996• 14 citations
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Abstract

Bosonic van der Waals clusters of sizes three, four, and five are studied by diffusion quantum Monte-Carlo techniques. In particular we study the unbinding transition, the ultraquantum limit where the ground state ceases to exist as a bound state. We discuss the quality of trial wave functions used in the calculations, the critical behavior in the vicinity of the unbinding transition, and simple improvements of the diffusion Monte Carlo algorithm.

DOI
10.1063/1.472459

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Bosonic van der Waals clusters of sizes three, four, and five are studied by diffusion quantum Monte-Carlo techniques. In particular we study the unbinding transition, the ultraquantum limit where the ground state ceases to exist as a bound state. We discuss the quality of trial wave functions used in the calculations, the critical behavior in the vicinity of the unbinding transition, and simple improvements of the diffusion Monte Carlo algorithm.
The computational physics methods of various processes have become very popular during the last several years. Our interest in his field is predominantly motivated by the expectation that it will be possible to perform a detailed comparison between experimental and theoretical results obtained in the study of clusters of a variety of sizes. Algebraic invariants are employed to deal efficiently with the many-body correlations. We study the applicability of the developed trial wave functions over some range of particle masses, from Ar to He and lighter. We compute the ground and excited states energies and various geometric sizes of small clusters as a function of a continuously varied mass parameter. For sufficiently small masses the cluster can no longer support a bound state, and we are interested in particular in the behavior of the clusters in the vicinity of the critical mass, i.e., the point at which the binding energy approaches zero. We show that the use of bosonic polynomials provides enough variational freedom to approximate ground and excited states of clusters of any mass. We discuss how the properties of clusters change with mass.
Bosonic two-dimensional self-bound clusters consisting of NNN atoms interacting through additive van der Waals potentials become unbound at a critical mass m∗(N){m}_{*}^{(N)}m∗(N)​; m∗(N){m}_{*}^{(N)}m∗(N)​ has been predicted to be independent of the size of the system. Furthermore, it has been predicted that the ground state energy EN{E}_{N}EN​ of the NNN-atom system varies exponentially as the atomic mass approaches m∗{m}_{*}m∗​. This paper reports accurate numerical many-body calculations that allow these predictions to be tested. We confirm the existence of a universal critical mass m∗{m}_{*}m∗​, and show that the near-threshold behavior can only be described properly if a previously neglected term is included. We comment on the universality of the energy ratio EN+1∕EN{E}_{N+1}∕{E}_{N}EN+1​∕EN​ near threshold.
We study systems of particles with varying numbers of distinguishable species ranging from 4-species to the N-species limit, where N is the number of particles in the system itself. We examine these systems using various powerful simulation techniques that belong to the quantum Monte Carlo (QMC) family. The N-species limit is studied via Path Integral Monte Carlo (PIMC), which is a finite temperature, non-perturbative technique. At this limit, we explore the viability of two different thermal density matrices for systems that interact via hard-sphere, hard-cavity potentials. We then study the impact of finite-size effects on calculations of the energy, pressure and specific heat of the system when reaching the thermodynamic limit under periodic boundary conditions. We then move to studying a 4-species fermionic system using Variational Monte Carlo (VMC) and Diffusion Monte Carlo (DMC), which are ground state techniques. We apply these methods to the clustering problem of 4-particle and 8-particle systems. While the 4-particle, 4-species system is relatively simple to calculate as it is physically identical to a bosonic system of 4-particles, the 8-particle fermi system is more complicated. We detail the process of simulating a bound 8-particle state with respect to decay into two independent 4-particle clusters with DMC for the first time.
Over the past few decades many new and improved techniques have been developed to calculate ground and excited states of atomic clusters with varying degrees of accuracy. Together with progressively enhanced computer capabilities and the development of sophisticated techniques, the accuracy of results obtained from ab initio methods are closely approximating machine precision. In this paper, we use the finite difference method, whose precision is only governed by the machine precision, together with an optimization criterion to calculate the spectrum of two-body van der Waal clusters. This method is also shown to be robust enough to calculate energies close to the unbinding transition.