A general strategy for the calculation of energy differences between states of different total spin is proposed. The procedure goes through the definition of a minimal model space and a set of energy-difference contributing determinants is established through the second-order development of the corresponding Hamiltonian in the framework of the quasidegenerate perturbation theory. The forementioned determinants are treated variationally in a so-called differential configuration interaction (CI). Several test calculations for simple model Li clusters have been carried out, and the results of the differential CI compare favorably with those of the exact solution in the full CI procedure.