Isothermal-isobaric ensemble simulations of melting in quantum solids

Abstract

An isothermal-isobaric ensemble version of the Fourier path-integral Monte Carlo method is formulated and applied to study melting in quantum solids. Experimental molar volumes of solid ortho-${\mathrm{D}}_{2},$ para-${\mathrm{H}}_{2},$ and HD are shown to be reasonably well reproduced by simulations using a Lennard-Jones potential. The fcc and hcp solid structures of ortho-${\mathrm{D}}_{2}$ are compared at 14 K and 0.85 MPa. The large quantum effects in solid ${\mathrm{D}}_{2}$ are demonstrated by the fact that the quantum solid at 14 K and 0.85 MPa has an average kinetic energy per particle which is 3.2 times its classical value and a density which is 21% less than that for the corresponding classical solid. The 0.85 MPa isobar, starting with an fcc solid at 14 K, is mapped out between 14 and 30 K. Changes in the various structural and energetic quantities with temperature have been monitored as a function of temperature. The instantaneous normal-mode spectrum of the quantum system is followed as a function of temperature and shown to undergo significant changes on melting of the quantum solid. In particular, the Einstein frequency and the average participation ratio of the real branch is shown to decrease sharply on melting while the fraction of imaginary frequencies increases.