Linear augmented-Slater-type-orbital method for electronic-structure calculations. III. Structural and cohesive energies of the 5d elements Lu–Au

The linear augmented-Slater-type-orbital method is applied to the electronic band structures of the 5d transition metals Lu through Au. Scalar relativistic, muffin-tin potential, and local density calculations are performed for each metal in both the fcc and bcc structures. Special sets of k points are used and the variation in crystal total energy as a function of mesh density (≊10 to ≊110 points in 1/48th of the Brillouin zone) are studied, and it is found that the total energy usually converges to ≊1 millihartree when ≊30 k points are used. Cohesive energies are calculated (the hcp metals are taken to be fcc for this purpose). A cohesive energy is the difference in energy between the crystal and the free atom in its ground state; local density theory, as applied to the free atom, is usually appropriate to the average of a number of multiplet levels. For those cases where the promotion energy to this average can be estimated, the resulting cohesive energies are in accord with experiment. The fcc-bcc structural energy differences, taken as the difference in two total energies, are also calculated. These agree with experiment as to which structure is the more stable. There are no observed values for these differences but they are markedly greater in the middle of the 5d row than the generally accepted values, obtained in the course of constructing phase diagrams for alloys using regular solution theory. The present results suggest that these constructs should be reexamined. The s, p, and d orbital character of the occupied electron levels is also examined using a Mulliken population analysis, and the more standard analysis where the charge density, within a Wigner-Seitz sphere, is decomposed into l components. The Mulliken analysis indicates somewhat greater d occupancy. More notably it indicates much less s and more p character than the Wigner-Seitz cell analysis does for all the metals except for Au.