The generalized mean field configuration interaction method

22 pages+ annexe 71 pagesThe mean field configuration interaction (MFCI) method is a variational approximation method that has been developed to solve the Schrödinger equation for molecular vibrations (VMFCI) and electrons (EMFCI). The Rayleigh-Schrödinger perturbation theory generalized to eigen-operators in non-commutative rings has been proposed to solve the Schrödinger equation for molecular rotation-vibration degrees of freedom. In the present work, the two approaches are merged in a unified method, the perturbative ansatz giving a ''generalized mean field'' for the MFCI approach. At order one of perturbation, the MFCI method is recovered. However, higher orders give more accurate mean fields taking better into account the coupling of the so-called ''active'' and ''spectator'' degrees of freedom (DOF) defined in a MFCI step. The new method has increased flexibility, since not only one can build any hierarchy of partitions of the system DOF as in the MFCI method, but one can also tune up the perturbation order at each MFCI step for each subset of DOF. An illustrative calculation of methane ro-vibrational spectrum is presented