Calculation of Molecular Properties with Limited-Basis Hartree—Fock Functions

The use of the limited-basis (Roothaan) approximation to Hartree—Fock functions and its implications for the accuracy of calculations on one-electron operators are discussed. Only for the true Hartree—Fock function does Brillouin's theorem guarantee second-order errors for expectation values of these operators. The mean square deviation of one Roothaan function from a second with an incremented basis set provides a measure of how closely the true Hartree—Fock function is being approached. Expectation values of one-electron operators reflect this as well, but it is shown that the improvement or lowering of energy on addition of functions to the basis is much less suitable.