Lattice structure of mercury: Influence of electronic correlation

Abstract

Mercury condenses at 233K into the rhombohedral structure with an angle of 70.53o . Theoretical predictions of this structure are difficult. While a Hartree-Fock treatment yields no binding at all, density-functional (DFT) approaches with gradient-corrected functionals predict a structure with a significantly too large lattice constant and an orthorhombic angle of about 60 o , which corresponds to an fcc structure. Surprisingly, the use of the simple 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 wavefunction-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, CCSD(T), agree within 1.5% with the experimental values. We further present the bulk modulus calculated within the wavefunction approach, and compare to LDA and experimental values.

Error estimates for density-functional theory predictions of surface energy and work function

“…This explains why materials in the right part of the d block suffer from worse surface energy predictions within PBE, as the correlation energy offers a large contribution to the total energy for these materials. This is for example apparent from the extreme case of Hg [81]. In the case of the p metals, the overestimation of the exchange energy also corrects for the absence of dispersion contributions.…”

Cluster melting: new, limiting, and liminal phenomena

“…Such studies -including also photoabsortion spectra -have been able to demonstrate the likely coexistence of isomers at finite temperature as well [26]. A similar comparison of theory and experiment has been used to deduce the structures of metal cluster based on trapped ion electron diffraction [27,28].…”

“…of small mercury clusters [46,47] demonstrate a non-monotonic evolution of the melting temperature with size, due to the complex change of electronic structure from a noble gas-like van der Waals system, towards a metallic state as the s-p gap closes [32].…”

“…In the first case, depending on the sophistication of the potential used, the consequences of electronic structure are treated indirectly -to the extent that a lead nanoparticle will behave differently than, say, an aluminium one. However, care should be taken in the use of such potentials outside their range of applicability: in particular, at sizes small enough that the structures known for the extended bulk are no longer favoured or where even the nature of atomic bonding can change, as is known for example in mercury clusters [31,32].…”

Ab initio Correlation Calculations for the Lattice Structures of Zn, Cd and Hg

“…There is no tabulated experimental value of c/a for mercury. An optimisation of the hcp lattice for Hg, performed with LDA which is the only density functional to find the rhombohedral structure as the minimum and therefore describe mercury approximately correctly (see [6]), finds an optimum value of c/a = 1.41. This would correspond to a structure with weakly bound hexagonal planes with strong binding between layers.…”