Orthogonality to Lower States and the Hartree—Fock Method

Abstract

By a simple adaptation of a theorem regarding quadratic forms it is shown that imposition of the stationary-energy requirement on Rayleigh—Ritz, and in certain cases Hartree—Fock trial functions, has the effect of constraining the trial function to be orthogonal to lower-state functions which are ``most effective'' in raising the higher-state energy, rather than to the exact wavefunctions of the lower states. Hence these methods lead to energy overestimates arising both from improper orthogonalization and from limited flexibility of trial function. He 1s2s 1S was calculated by use of expansion-type Hartree—Fock trial functions which were constrained to be orthogonal to various approximate forms of the 1s21S function, including a ``most effective'' one. The energy overestimate arising from improper orthogonalization was small compared with that resulting from limited flexibility of trial function.