Force and virial formula in the linear combination of atomic orbitalsXαmethod and its application to oxygen chemisorption on the Al(111) and Mg(0001) surfaces

An expression for the gradient (with respect to nuclear coordinates) of the electronic total energy is given using the LCAO-$X\alpha$ method and related to the virial. The formulas are extended to the linear combination of plane waves (LCPW) method. Our method is applied to the chemisorption of oxygen on Al(111) and Mg(0001) surfaces. The calculations are performed using O/${\mathrm{Al}}_4$ and ${\mathrm{O}/\mathrm{M}\mathrm{g}}_4$ model clusters with the metal-metal distance equal to the bulk. The calculated forces explain the experiments which report that oxygen is not absorbed below the Al surface but is absorbed below the Mg surface. The difference in the chemisorption processes is due to differences in the strength of the metal-metal bond interaction.