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M(o)ller-Plesset perturbation theory (MP)[1] is widely used to deal with the closed-shell problems.However,the UMP series[2] is not successful for open-shell problems because of its slow convergence due to the spin contamination of the perturbation wavefunctions.A novel single reference perturbation theory131 has been developed for these problems.In the theory the zero-th Hamiltonian is a sum of one-particle operator which is implicitly defined.When the operator acts on a ROHF or CASSCF orbital the resultant eigenvalue is the orbitals corresponding orbital energy coming from the ROHF or CASSCF calculation.Numerical tests with molecules HF,F2 and N2 with stretched bonds demonstrate that the first three-order energies calculated with the present theory are all size extensive.