  We present an extension of our one-body M{\o}ller-Plesset second-order
perturbation (OBMP2) method for open-shell systems. We derived the OBMP2
Hamiltonian through the canonical transformation followed by the cumulant
approximation to reduce many-body operators into one-body ones. The resulting
Hamiltonian consists of an uncorrelated Fock (unperturbed Hamiltonian) and a
one-body correlation potential (perturbed Hamiltonian) composed of only double
excitations. Molecular orbitals and associated energy levels are then relaxed
via self-consistency, similar to Hartree-Fock, in the presence of the
correlation at the MP2 level. We demonstrate the OBMP2 performance by
considering two examples well known for requiring orbital optimization: bond
breaking and isotropic hyperfine coupling constants. In contrast to
non-iterative MP2, we show that OBMP2 can yield a smooth transition through the
unrestriction point and accurately predict isotropic hyperfine coupling
constants.
