Relativistic coupled-cluster and density-functional studies of argon at high pressure

Abstract

The equation of state $P(V,T)$ for solid argon is determined by the calculation of accurate static and vibrational terms in the free energy. The static component comes from a quantum theoretical many-body expansion summing over all energetic contributions from two-, three-, and four-body fragments treated with relativistic coupled cluster theory, while the lattice vibrations are described at an anharmonic level including two- and three-body forces as well as temperature effects. The dynamic part is calculated within the Debye and Einstein approximation, as well as by a more accurate phonon treatment where the vibrational motions in the lattice are coupled. Our results are in good agreement with room-temperature high-pressure experimental data up to $\ensuremath{\sim}20$ GPa. In the 20--100 GPa pressure range, however, we see considerable deviations between experiment and theory, perhaps indicating missing four-body contributions (beyond the quadruple dipole terms included here), missing five and higher-body effects, and the need to go beyond the coupled cluster singles-doubles with perturbative triples treatment in such higher-body forces. This contrasts with the results for solid neon, where excellent agreement has been achieved taking only two- and three-body forces into account [P. Schwerdtfeger and A. Hermann, Phys. Rev. B 80, 064106 (2009)]. We demonstrate that the phase transition from fcc to hcp cannot account for the large discrepancies observed. Density functional calculations give very mixed results in the high-pressure region, but some functionals such as optB88-vdW (proposed by Lundqvist and co-workers) describe the many-body forces in argon reasonably well over the range of pressures investigated. Theoretical investigations of the heavier rare gas solids reaching experimental accuracy in the high-pressure regime therefore remain a significant challenge.