Lattice structure of mercury: Influence of electronic correlation

Abstract

Mercury condenses at $233\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ into the rhombohedral structure with an angle of 70.53\ifmmode^\circ\else\textdegree\fi{}. Theoretical predictions of this structure are difficult. While a Hartree-Fock treatment yields no binding at all, density-functional theory (DFT) approaches with gradient-corrected functionals predict a structure with a significantly too large lattice constant and an orthorhombic angle of about 60\ifmmode^\circ\else\textdegree\fi{}, which corresponds to an fcc structure. Surprisingly, the use of the simple local density approximation (LDA) functional yields the correct structure and lattice constants in very good agreement with experiment; relativistic effects are shown to be essential for reaching this agreement. In addition to DFT results, we present a wave-function-based correlation treatment of mercury and discuss in detail the effects of electron correlation on the lattice parameters of mercury including $d$-shell correlation and the influence of three-body terms in the many-body decomposition of the interatomic correlation energy. The lattice parameters obtained with this scheme at the coupled cluster level of theory agree within 1.5% with the experimental values. We further present the bulk modulus calculated within the wave-function approach, and compare to LDA and experimental values.