Excitation levels and magic numbers of small para-Hydrogen clusters (N$ \le 40$)

TL;DR

This study systematically calculates excitation energies of small para-hydrogen clusters (3 to 40 molecules) using diffusion Monte Carlo, revealing their complex spectra, magic numbers at N=13, 36, and enhanced production at N=13, 31, 36.

Contribution

First comprehensive calculation of excitation energies for para-hydrogen clusters up to 40 molecules, identifying magic numbers and thermal effects.

Findings

Clusters with N=13 and 36 show peaks in chemical potential and large energy gaps.

Enhanced production predicted at N=13, 31, and 36, consistent with experimental data.

Rich spectra with angular momentum excitations up to L=13 for larger clusters.

Abstract

The excitation energies of parahydrogen clusters have been systematically calculated by the diffusion Monte Carlo technique in steps of one molecule from 3 to 40 molecules. These clusters possess a very rich spectra, with angular momentum excitations arriving up to L=13 for the heavier ones. No regular pattern can be guessed in terms of the angular momenta and the size of the cluster. Clusters with N=13 and 36 are characterized by a peak in the chemical potential and a large energy gap of the first excited level, which indicate the magical character of these clusters. From the calculated excitation energies the partition function has been obtained, thus allowing for an estimate of thermal effects. An enhanced production is predicted for cluster sizes N=13, 31 and 36, in agreement with experiment.