Hellmann–Feynman Theorem for Multiconfiguration Self-Consistent Field Theory and Correlation Energy

The Hellmann–Feynman theorem for the multiconfiguration self-consistent field (MC SCF) theory is derived. This theorem is general enough to be applied to both open- and closed-shell systems. In conjunction of this result with Sinanoǧlu's many-electron theory of atoms and molecules using the multi-configuration general restricted Hartree–Fock (GRHF) method, an expression for the change of correlation energies is obtained. It is shown that the correlation energies should be nearly constant with respect to the change of any one-electron parameter, which is independent of symmetry and exclusion effects, of the zeroth-order Hamiltonian. This result justifies the following: (1) The dynamical correlation energies of isoelectronic atomic systems are nearly constant. (2) The potential-energy surface of a molecule determined from the GRHF approximation should be parallel to the actual potential-energy surface.