Angular forces in group-VI transition metals: Application to W(100)

Quantum-mechanical analysis based on a tight-binding model is used to generate a functional form for angular forces in transition metals. Using a moment analysis, an expression is derived that includes angular forces via both explicit many-body interaction terms and a matrix description of a site's local environment. A fit based on this analysis, with only four fitting parameters, is used to treat Cr, Mo, and W. Calibration results for vacancy-formation energies and structural-energy differences are in excellent agreement with experiment and ab initio values. Application to the W(100) surface yields a physical picture of the c(2\ifmmode\times\else\texttimes\fi{}2) reconstruction based on enhanced surface bond-strengthening effects. Agreement with ab initio results for the reconstruction amplitude and energy is obtained for reasonable values of the parameters, although both of these quantities depend on the cutoff radius.