Electronic structure off-shell metals

Free-electron theory to first order in an empty-core pseudopotential, with radius determined spectroscopically, is found to predict successfully equilibrium spacings and bulk moduli for the rare-earth metals. This provides also a simple two-body interaction, second order in the same pseudopotential, for calculating other elastic and vibrational properties. For the light actinides a tight-binding $f$-band theory is formulated, leading to interatomic matrix elements of the form $V_{\mathrm{ffm}}=\frac{{\eta }_{\mathrm{ffm}}{\hslash }^2{r_f}^5}{m{d}^7}$. Coefficients ${\eta }_{\mathrm{ffm}}$ are derived and $r_f$ values fit for the light actinides. Spin-orbit coupling is included and a bandwidth obtained from a second-moment analysis to be used with the Friedel model for the density of states in the calculation of energetics. It is found necessary to include also the next-order correction to the interatomic interactions, a repulsion proportional to $\frac{{\hslash }^2{r}_f^{10}}{m{d}^{12}}$ which, though small, is significant for the bulk modulus. With the use of pseudopotential core radii fit to the equilibrium spacing, the bulk moduli and thermal-expansion coefficients are predicted. All contributions can be written as two-body interactions, but adjustment is needed before using them to calculate properties. Inclusion of intra-atomic exchange fails to predict localization for americium.