Trends in the properties and structures of the simple metals from a universal local pseudopotential

The properties of simple metals are fixed primarily by the equilibrium average valence-electron density parameter ${r}_{s},$ and secondarily by the valence z. The simplest level of theory that can account quantitatively for these trends invokes a ``universal'' local electron-ion pseudopotential, defined for each pair ${(r}_{s},z)$ and treated as a second-order perturbation. We construct this pseudopotential from two conditions: (1) The total energy should minimize at the equilibrium Wigner-Seitz radius ${z}^{1/3}{r}_{s}.$ (2) The bulk modulus should equal the realistic ${r}_{s}$-dependent prediction of the stabilized jellium model with effective valence ${z}^{*}=1.$ These conditions can be satisfied by an analytic local pseudopotential depending upon two parameters other than z; we show that the choice of the two-parameter form (evanescent core vs Heine-Abarenkov) is not important. Our universal local pseudopotential is applied to calculate realistic bulk binding energies, pressure derivatives of bulk moduli, Voigt shear moduli, and interstitial electron numbers, revealing their trends as functions of ${r}_{s}$ and z. Equilibrium crystal structures are mapped in the ${r}_{s}\ensuremath{-}z$ plane, where the Hume-Rothery rules for substitutional alloys are manifest. The effect of pressure on crystal structure is also examined.