On the derivation of the Hartree-Fock equations II

Abstract

The UHF equations are derived from the variation principle by using only a single Lagrangian multiplier corresponding to the normalization of the totalN-electron wave function, and by assuming the orthonormality of the one-electron orbitals only after the variation has been performed. It is also shown that if the UHF equations are taken in the form

$$\hat F\psi _m = \sum\limits_k^{5 spins} {\left\langle {\psi _k \left| {\hat F} \right|\psi _m } \right\rangle \psi _k } $$

($\hat F$ being the usual UHF operator), then their solutions are, in all non-singular cases, automatically orthonormalized.

A necessarily convergent procedure for the solution of these equations is discussed.