Application of Method for Rapid Convergence of Lattice Sums of Pseudopotential Calculation of Formation Energy of Vacancy in Metals

A method for rapid convergence of lattice sums is applied to calculate the structural part, E VS , of the formation energy of a vacancy in metals by using Faber's formula. Pair potentials discussed here are those derived from parameterized pseudopotentials screened by various dielectric functions. The method proves useful for this calculation; an error due to convergence is reduced so that numerical differentiation in Faber's formula is performed accurately. Present result of the calculation for E VS is compared with results by Minchin et al. , Popovic et al. , and Ho. The comparison shows that errors in the calculations of E VS by these authors often exceed relaxation energies. The present method shows that E VS depends largely on the lattice size and on the form of the pseudopotential. Thus the calculation of E VS gives a method for reasonable choice of the potential form.