A Feynman Path Centroid Effective Potential Approach for the Study of Low Temperature Parahydrogen Clusters and Droplets

The quantum simulation of large molecular systems is a formidable task. We explore the use of effective potentials based on the Feynman path centroid variable in order to simulate large quantum clusters at a reduced computational cost. This centroid can be viewed as the “most” classical variable of a quantum system. Earlier work has shown that one can use a pairwise centroid pseudo-potential to simulate the quantum dynamics of hydrogen in the bulk phase at 25 K and 14 K [Chem. Phys. Lett. 249, 231, (1996)]. Bulk hydrogen, however, freezes below 14 K, so we focus on hydrogen clusters and nanodroplets in the very low temperature regime in order to study their structural behaviours. The calculation of the effective centroid potential is addressed along with its use in the context of molecular dynamics simulations. The effective pseudo-potential of a cluster is temperature dependent and shares similar behaviour as that in the bulk phase. Centroid structural properties in three dimensional space are presented and compared to the results of reference path-integral Monte Carlo simulations. The centroid pseudo-potential approach yields a great reduction in computation cost. With large cluster sizes, the approximate pseudo-potential results are in agreement with the exact reference calculations. An approach to deconvolute centroid structural properties in order to obtain real space results for hydrogen clusters of a wide range of sizes is also presented. The extension of the approach to the treatment of confined hydrogen is discussed, and concluding remarks are presented