Error of Expectation Values from the MC SCF Theory

It is proved that the expectation values of one-electron operators calculated from multiconfiguration self-consistent field (MC SCF) wavefunctions are correct to the order of λ2, when the accuracy of the wavefunctions is correct to the order of λ. By using the formalism of Sinanoğlu's many-electron theory of atoms and molecules, it is further shown that only when the MC SCF wavefunctions include all the nondynamical correlation energies, then the errors of the expectation values for one-electron operators are independent of the specific characters of the operators. This result, in combination with our previous studies of correlation energy of MC SCF theory, suggests a criterion for defining the “best” one-electron model of many-electron atomic and molecular systems.