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, He2, LiH, and Be.