Force and total-energy calculations for a spatially compact adsorbate on an extended, metallic crystal surface

Abstract

A first-principles, scattering-theory formalism is presented for the calculation of the energy of, and forces on, a spatially localized group of atoms in proximity to a metallic crystalline surface. A formula is derived for the adsorption energy which is rapidly convergent both with respect to the size of the matrix equations that must be solved and the number of mesh points required in the numerical computation of the matrix elements of the electron-electron potential. The force formula, following the method of Pulay, guarantees the tangency of the calculated force to the adsorption-energy surface if both are calculated using accurate solutions to the local-density-functional energy-minimization problem. The force formula thereby provides a useful internal consistency check on the calculations as well as a rapid means of finding adsorption equilibrium geometries, vibrational force constants, etc. Results of implementing the formalism are reported for the case of a single Al atom adsorbed on a two-layer Al(001) film, highlighting the close agreement of the calculated values of adsorption energy and the force on the adsorbed Al.