Scaling lengths of elemental metals

The average interstitial electron densities n of the elemental alkali, nobl e, and transition metals were computed as a function of the lattice spacing using a scalar-relativistic total-energy band-structure code. The calculat ions showed that the average interstitial electron density varied exponenti ally as exp(-a/L-D), where a measures the lattice spacing in terms of the e quivalent Wigner-Seitz radius. In principle, the value of L-D could be cons idered to be a new characteristic length for the metals-a density length sc ale. However, we found that L-D is very nearly proportional to the energy l ength scale L-E that enters into the definition of the universal bonding en ergy relations, i.e., L(E)similar to 0.85L(D). Two consequences of this app roximate equality are described. First, the normalized cohesive energy can be usefully approximated by a universal function of the normalized intersti tial density. Second, the bulk moduli of the elemental metals can be approx imately determined from the Wigner-Seitz radius, the bonding valence, and t he density length scale. [S0163-1829(98)04244-1].