The mean field configuration interaction (MFCI) method is a variational approximation method, which has been developed to solve the Schrödinger equation for molecular vibrations (VMFCI), for electrons (EMFCI), or for both: Electron-Nucleus MFCI. 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. These two approaches can be merged in a unified method, the perturbative ansatz at order more than one, giving a more general ``effective field'' (EF) than the order one ``mean field''. EF arising from the vibrational motion of semi-rigid molecules have proved useful to compute acurate rotational spectra at moderate computational cost. In the present paper, we argue that EF can also be taken advantage of to deal with systems presenting large amplitude motion such as HOOH and/or a large number of degrees of freedom such as naphtalene.