Path integral simulations of quantum Lennard-Jones solids

Abstract

Path integral simulations are used to study the thermodynamic and structural properties of quantum Lennard-Jones solids as a function of the degree of quantum delocalization or the de Boer parameter. Simulations in the isothermal–isobaric ensemble are performed using a Fourier path integral Monte Carlo technique. Among the more striking trends in the properties of quantum solids which emerge from this study is the strong dependence of the number density on the degree of delocalization, rather than the temperature. The large lattice expansions, under NPT conditions, associated with quantum solids, are necessarily accompanied by significant decreases in the binding energies. The kinetic energies per particle indicate that even a semiclassical Lennard-Jones solid is far from the classical equipartition regime at temperatures as high as 70% of the melting temperature. The Lindemann index, the bond orientational order parameters and the structure factors are used to monitor the degree of solidlike order. The Lindemann index increases sharply with the de Boer parameter and is accompanied by a substantial decrease in the average coordination number. This local disorder in the solid phase has a significant effect on the second-order bond-orientational order parameters, but leaves the third-order rotational invariants unchanged. The intensity of structure factors dies out very rapidly as the magnitude of the wave vector increases. Trends in lattice rigidities and the deviation of typical instantaneous configurations from the equilibrium lattice geometry as a function of quantum effects are estimated from the instantaneous normal mode spectra. It is also shown that configurational properties of the quantum path centroids, when compared with observable values based on averaging over instantaneous configurations, provide insights into the relation between local disorder and the relative magnitude of thermal and quantum fluctuations.