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The anisotropy of the zinc and cadmium hexagonal close-packed (hcp) lattices
is an anomaly amongst the elemental metals. Of those that crystallise in
the hcp structure, even including high-pressure phases, none deviate from
the ideal close-packed ratio of the lattice parameters c/a = 1.63 by more
than 4%, except Zn, Cd, and the high-pressure hcp phase of Hg.
In Zn and Cd the hcp lattice is distorted by having much too large ratios of
c/a, which results in a layered structure where the bonds in the hexagonal
plane are length a and the bonds between planes are around 10% longer. Thus
instead of the normal hcp environment in which each atom has 12 nearest
neighbours, in these layered structures each atom has only 6 nearest
neighbours, sitting in the hexagonal close-packed plane, and 6 next nearest
neighbours positioned above and below the hexagonal plane.
DFT calcuations using the local density approximation, GGA functionals or
hybrid functionals have been unable to correctly describe this structure,
and so we have performed CCSD(T) calcuations within the recently developed
method of increments for metals.
The method of increments is a general scheme for the ab initio calculation
of large and periodic systems [1]. It has been applied to a number of
systems including van der Waals crystals, insulators and most recently,
metals. In particular, the cohesive energy, lattice parameters and bulk
modulus of solid mercury in the rhombohedral structure have been calculated
in very good agreement with experiment for the first time [2].
Using a general many-body expansion for the binding energy, in the case of
metals we restrict this expansion to the correlation energy only, and
perform a Hartree-Fock calculation in the periodic solid. Thus the
long-range part of the metallic binding is included at the mean-field level,
while the correlation energy, which is known to be short range, is
calculated in an expansion in terms of localised orbitals.
We will discuss new developments of the method with reference to
calculations of the structure of the anisotropic hcp metals Zn and Cd.
[1] B. Paulus, Phys. Rep. 421, 1 (2006). [2] N. Gaston, B. Paulus, K. Rosciszewski, P. Schwerdtfeger and H. Stoll, Phys. Rev. B 74, 094102 (2006). |
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