General SCF operator satisfying correct variational condition

Abstract

We have shown that the correct variational equations for the general SCF orbitals are ${\mathrm{[F}}_i{\mathrm{-\Sigma }}_j{\mathrm{\hspace{0.17em}|\psi }}_j{\mathrm{〉\hspace{0.17em}〈\; \psi }}_j{\mathrm{\hspace{0.17em}|G}}_{\mathrm{ji}}{\mathrm{]\hspace{0.17em}|\psi }}_i\text{〉=0}$ , where $G_{\mathrm{ji}}{\mathrm{=\lambda }}_{\mathrm{ji}}{F}_j{\text{+(1−λ}}_{\mathrm{ji}}{\mathrm{)F}}_i{\mathrm{;\hspace{0.17em}\lambda }}_{\mathrm{ji}}\text{≠ 0}$ and how these may be combined into simple eigenvalue problems. In the course of discussions, we re‐examined whether the coupling operators suggested previously are based on the correct variational conditions.