Treatment of semicore states in the linearized augmented-plane-wave method and other linearized electronic-structure methods.

the orthogonality of the valence and core states can be violated if there are semicore states which leak out of the muffin-tin sphere. The only way to avoid the breakdown of the orthogonality is to include these semicore states as valence states. Singh ' recently proposed two ways to do this. In his first proposal he includes, in addition to the usual ul and i I radial basis functions at the valence reference energy, the same set of functions at a semicore reference energy. The expansion coefficients of these four basis functions are determined by matching the value and the first three radial derivatives of each l,I component at the surface of the sphere. Because the plane-wave expansion of the interstitial region must now also converge to the correct second and third derivatives on the surface of the muffintin sphere, more plane waves are required to satisfy these additional requirements and the plane-wave energy cutoff goes up. His second proposal does not suffer from this disadvantage. As an additional radial basis function in the muffin-tin sphere he includes a function that has zero value and slope on the surface of the sphere and therefore does not directly couple to the plane waves. Because the expansion coefficient of this third function is not determined by the plane waves, one has, in addition to the plane-wave expansion coefficients cK, additional variational coefficients, which make programming somewhat more difficult. %'e will now show that the standard linearized augmented-plane-wave (LAPW) method with only two radial functions gives accurate results for atoms containing semicore states if the muffin-tin sphere is smaller than usual and if appropriate radial basis functions are chosen, which can describe both valence and semicore states.