A rigorous perturbation theory is proposed, which has the same second order energy as the spin-component-scaled Møller–Plesset second order (SCS-MP2) method of Grimme [J. Chem. Phys. 118, 9095 (2003)]. This upgrades SCS-MP2 to a systematically improvable, true wave-function-based method. The perturbation theory is defined by an unperturbed Hamiltonian, , that contains the ordinary Fock operator and spin operators that act either on the occupied or the virtual orbital spaces. Two choices for are discussed and the importance of a spin-pure is underlined. Like the SCS-MP2 approach, the theory contains two parameters ( and ) that scale the opposite-spin and the same-spin contributions to the second order perturbation energy. It is shown that these parameters can be determined from theoretical considerations by a Feenberg scaling approach or a fit of the wave functions from the perturbation theory to the exact one from a full configuration interaction calculation. The parameters and are found to be optimal for a reasonable test set of molecules. The meaning of these parameters and the consequences following from a well defined improved MP method are discussed.
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