ERROR BOUNDS TO EXPECTATION VALUES OF ONE-ELECTRON OPERATORS USING HARTREE-FOCK WAVEFUNCTIONS

The properties of Hartree-Fock wavefunctions are used to derive a number of new expressions for upper and lower bounds to the true expectation value of an arbitrary one-electron operator. These expressions depend on the prior knowledge of upper and lower bounds to the overlap between the Hartree-Fock and true wavefunctions. A new extrapolation method is presented to obtain accurate bounds to these overlaps. A critical study is made of the effectiveness and accuracy of these new error bounds as applied to the systems He, H2, LiH, and Be.