Generalized non-muffin-tin band theory
A new way of applying the non-spherically-symmetric phase-functional method of Williams and van Morgan to the band-structure problem is derived that results in a generalized (non-muffin-tin) Green's-function band theory that is variationally stationary and exact in the single-electron, local-potential approximation. The "near-field" correction, believed to destroy the separability of Green's-function band theories, is implicitly included in the nonspherically-symmetric phase-functional basis. This basis is discussed in some detail as we correct an error in the previous work of Williams and van Morgan. Using this basis to expand the crystal wave function, we obtain an equation that is the most general expression of Green's-function band theory. This equation contains a sum over the structure constants of the Korringa-Kohn-Rostoker method and two "phase functions" (corresponding to the cosine and sine of the nondiagonal partial-wave phase shifts) that are independently calculable; hence the effects of structure and cellular potential completely separate. The variational procedure of Kohn and Rostoker then yields a secular determinant that can be solved for the non-muffin-tin bands and wave functions; the resulting theory is suitable for self-consistent-field applications. © 1983 The American Physical Society.
