Monte Carlo computations of the quantum kinetic energy of rare-gas solids

Abstract

We report results from Monte Carlo computations for the average kinetic energy of rare-gas solids (neon, argon, krypton, and xenon), modeled by a Lennard-Jones all-neighbor interaction. The main motivation lies in the recent availability of direct experimental measurements of the average kinetic energy of solid neon, by means of deep-inelastic neutron scattering (DINS). In our computations we take strong advantage in using the effective potential technique, which has been proven to be very useful for systems where quantum effects are not too strong: the path-integral Monte Carlo (PIMC) can be replaced by the classical-like effective-potentia/ Monte Carlo (EPMC), in such a way that the needed computer time is strongly reduced. We resorted to PIMC in the case of neon, due to its rather high quantum effects. Our results for the low-temperature kinetic energy of neon are smaller than the measured ones. This discrepancy could be attributed to the simple model of the interaction we have used, as the agreement with previous theoretical calculations suggests. Moreover, we show that the quantum contributions to the kinetic energy, at the same temperatures used in the abovementioned experiments, are unexpectedly relevant also for argon, krypton, and xenon crystals, so that they should be experimentally detectable as well.

Rare-gas solids under pressure: A path-integral Monte Carlo simulation

“…Circles and triangles correspond to the vibrational kinetic and potential energy, respectively. Our results for the kinetic energy are close to those derived earlier from PIMC simu-lations with Lennard-Jones 13,21,38 and Aziz 38 interatomic potentials. For comparison, we present also in Fig.…”

“…The path-integral Monte Carlo (PIMC) technique has been applied earlier to study several properties of rare-gas solids. 13,14,15,16,17,18,19 In particular, it has predicted kinetic-energy values in good agreement with experimental data. 20,21 An effective-potential Monte Carlo theory 22,23 has been also applied to study thermal and elastic properties of solid neon.…”

Path-integral simulation of solids

“…The most popular is the Lennard-Jones pair potential given in Eq. (52), with parameters ǫ and σ slightly differing in several works [72][73][74][75][76][77][78] . Other model potentials have been employed for the effective interaction between noble-gas atoms, such as Aziz-type pair potentials 9,79,80 and three-body interactions [81][82][83][84] .…”

Analytical and Numerical (Monte Carlo) Studies of Point and Space Group Symmetry-Breaking in the Liquid–Solid Phase Transition

“…For natural argon, which we investigate numerically in this work, one has m = 39.95 amu, where amu is the atomic mass unit, and ε LJ = 119.8 K and σ LJ = 3.405Å [52,53]. At finite temperatures T > 0 all microscopic and macroscopic thermodynamic quantities may be derived from the canonical density operator [54] …”

“…Formula (93) holds for distinguishable quantum-mechanical particles. However, apart from for 4 He at low temperatures, Bose exchange may be safely neglected for all other inert gas elements because of the large atomic mass [47,52,53,66]. Even in low-temperature helium solids Bose exchange occurs very rarely [56].…”