Approximating infinite-k representations: surface relaxations and work functions of Al(001) and Be(0001)

Abstract

Self-consistent techniques, such as the linearized augmented plane wave (LAPW) and surface embedding Green function (SEGF) methods, frequently yield calculated quantities which show damped oscillatory behaviour as a function of the number of special k-points. In the present work, the oscillatory dependence has been fitted to a damped harmonic oscillator in order to approximate the value corresponding to an infinite number of k-points in the Brillouin zone. The asymptotic value, amplitude, frequency, and phase are determined as functions of the damping constant by matching the value and derivative of the damped harmonic oscillator at consecutive turning points. It is shown that the asymptotic value of the damped oscillator may fall within the rms error of the asymptotic value of the fitting function. Results are reported for the surface relaxations and work functions of Al(001) and Be(0001).