Dominant density parameters and local pseudopotentials for simple metals

The properties of the simple metals are controlled largely by three density parameters: the equilibrium average valence electron density 3/4\ensuremath{\pi}${\mathit{r}}_{\mathit{s}}^{3}$, the valence z, and the density on the surface of the Wigner-Seitz cell, represented here by the equilibrium number ${\mathit{N}}_{\mathrm{int}}$ of valence electrons in the interstitial region. To demonstrate this fact, and as a refinement of the ``stabilized jellium'' or ``structureless pseudopotential'' model, we propose a structured local electron-ion pseudopotential w(r) which depends upon either ${\mathit{r}}_{\mathit{s}}$ and z (``universal'' choice for ${\mathit{N}}_{\mathrm{i}\mathrm{n}\mathrm{t})}$, or ${\mathit{r}}_{\mathit{s}}$, z, and ${\mathit{N}}_{\mathrm{int}}$ for each metal (``individual'' potential). Calculated binding energies, bulk moduli, and pressure derivatives of bulk moduli, evaluated in second-order perturbation theory, are in good agreement with experiment for 16 simple metals, and the bulk moduli are somewhat better than those calculated from first-principles nonlocal norm-conserving pseudopotentials. Structural energy differences agree with those from a nonlocal pseudopotential calculation for Na, Mg, and Al, but not for Ca and Sr. Our local pseudopotential w(r) is analytic for all r, and displays an exponential decay of the core repulsion as r\ensuremath{\rightarrow}\ensuremath{\infty}. The decay length agrees with that of the highest atomic core orbital of s or p symmetry, corroborating the physical picture behind this ``evanescent core'' form. The Fourier transform or form factor w(Q) is also analytic, and decays rapidly as Q\ensuremath{\rightarrow}\ensuremath{\infty}; its first and only zero ${\mathit{Q}}_{0}$ is close to conventional or empirical values. In comparison with nonlocal pseudopotentials, local ones have the advantages of computational simplicity, physical transparency, and suitability for tests of density functional approximations against more-exact many-body methods.