Non-Hermitian representations in localized orbital theories

Abstract

We consider a non‐Hermitian version of Adams' localized orbital equations which is directly analogous to the conventional pseudopotential equation of Austin, Heine, and Sham. This allows the use of the familiar ``pseudizing'' arguments in localized orbital theories and also permits a simple discussion of the relationship between Adams' theory and Anderson's self‐consistent pseudopotential theory of localized orbitals. A study of the differences in the Hermitian and non‐Hermitian representations shows that the non‐Hermitian localized orbital equation has additional localization of the left (adjoint) eigenfunction which may have advantages in practical calculations. An analysis of the secular equation method of going from the localized orbitals to the total system's wavefunction suggests that a non‐Hermitian representation again has additional local properties which could prove useful in interpreting and extending semiempirical parameterization methods such as the Hückel theory.