Generalization of localized perturbation theory, which results with a method able to span the spin space correctly, is presented. This generalization is achieved by using a multiconfigurational (MC) wave function as the reference. This is the most comprehensive expansion used within MC-LMP2 approach to date, with, however, low computational cost [computational scaling with system size (N) of the new method is O(N-3)]. Recently, we have reported the successful Jaguar2 (J2) model for calculating atomization energies. Within the MC-LMP2 framework, the J2 model for calculating heats of formation is based on the generalized valence bond-perfect pairing (GVB-PP) wave function. The J2 model was applied only to closed shell cases because of the perfect pairing (PP) restriction in the reference function. In order to describe other systems, the PP restriction needs to be lifted. This work describes efforts in that direction. The PP restriction can be lifted by a restricted configuration interaction (RCI) procedure applied to the GVB-PP wave function. In this paper, the equations describing the application of LMP2 theory to self-consistent RCI wave function are derived and explained. The RCI wave function is a "true" MC expansion as opposed to the GVB-PP, which uses only a single spin eigenfunction (SEF). We also present the self-consistent (SC) optimization of the RCI wave function. The SC-RCI-LMP2 is the first MC-LMP2 method where the spin space is spanned in the reference. This is important for describing the nondynamical correlation (near degeneracy) effects associated, for example, with bond breaking processes. The SC-RCI-LMP2 is an efficient method applicable to large systems; it is shown to reproduce the potential energy surfaces calculated by the complete active space-second order perturbation (CAS-SCF-PT2) method. This is demonstrated, for the first time, on some widely used test cases.