Practical implementation and remaining problems for the film linearized muffin-tin orbital calculation of surface electronic structure.

Abstract

We describe the details of implementation of the film linearized muffin-tin orbital method of Krakauer and Cooper [Phys. Rev. B 16, 605 (1977)] for slab geometries. Using the constrained wave functions as described by Krakauer and Cooper, we get consistently good results except for the work function. We describe an alternate method that we have also implemented to improve the work function. This discards the plane-wave orbitals while striving to improve the quality of the basis functions for describing the vacuum behavior without increase in matrix sizes. We find the quality of results poorer; therefore, in Appendix A, we suggest a way of increasing the variational freedom by removing the constraint on the plane-wave orbitals. We report on our investigations on the stability of the results with respect to variations in the most sensitive energy parameters that appear in the theory, and the effect on the results of various shaping approximations on the charge density and on the potential. We find that because of the small matrix sizes, diagonalization times are an insignificant portion of the total running time for a complete iteration. This total time per iteration is only slightly faster (by a factor of 1.6) than a corresponding linearized augmented-plane-wave iteration. However, because the small matrix sizes imply memory requirements which are smaller than those of other methods currently in use, systems with a greater number of atoms in the unit cell may be studied (for a given computer) than with those methods.