Stabilized jellium: Structureless pseudopotential model for the cohesive and surface properties of metals

Abstract

The ions in a simple metal act on the valence electrons via a pseudopotential. The long-range part is represented by the electrostatic potential from the positive background of the jellium model. The short-range part can be simulated by a constant (over the interior of the metal), chosen to stabilize the metal at its observed bulk valence-electron density. In this structureless pseudopotential model, the bulk properties of a metal depend only upon valence z and bulk density parameter ${\mathit{r}}_{\mathit{s}}$, while the surface properties depend upon ${\mathit{r}}_{\mathit{s}}$ alone (an experimental trend heretofore not understood). These properties are calculated in closed analytic form, and the anomalies of the jellium model (negative surface energy for ${\mathit{r}}_{\mathit{s}}$\ensuremath{\approxeq}2; negative bulk modulus for ${\mathit{r}}_{\mathit{s}}$\ensuremath{\approxeq}6) are found to be rectified. The new model, perhaps the simplest one viable for all ${\mathit{r}}_{\mathit{s}}$, may also be used to study interfaces, metallic clusters, vacancies, electromagnetic response, etc. A variant of the model, which simulates the effects of atomic corrugation, predicts the crystal face dependence of surface properties. This dependence is strong for the electron-density profile, but not for the surface energy, work function, and distance from the centroid of excess charge to the first lattice plane. Results are presented for metallic hydrogen as well as for Al, Pb, Zn, Mg, Ca, Li, Sr, Ba, Na, K, Rb, and Cs.