Energy-Minimum Principle for Hartree—Fock Calculations of Certain Excited Atomic States

An energy-minimum principle, 〈E〉≥Eexact, for Hartree—Fock calculations of atomic states not the lowest of a given symmetry, is shown to hold under conditions which are satisfied for a large number of optical states, without the necessity of constraining the trial function to be orthogonal to wavefunctions of lower states of the same symmetry. The principle follows from application of a theorem by MacDonald and by Hylleraas and Undheim to an expansion-type Hartree—Fock procedure in which the radial function of the excited electron is expanded in a fixed basis set while all other orbitals are assumed fixed.