The multireference, state specific, second-order, Brillouin-Wigner perturbation theory is presented. A posteriori corrections are made which in the case of a single reference function recover the well-known formula of second-order many-body perturbationtheory, i.e. Moller-Plesset 'MP2' theory, and in the multireference case yields a state specific multireference second-order Rayleigh-Schrodinger perturbation theory. Applications to the bond breaking processes in the ground states of the BH and FH molecules are described using basis sets for which the corresponding full configuration interaction calculations are possible. Multireference Brillouin-Wigner coupled cluster calculations, in the CCSD approximation, are presented for these diatomic moleculesusing the same basis sets.