Ab initio UHF calculations have been carried out for naked transition metal-methylene ions. The low-spin open-shell states are found to be the ground states of these ions, in accord with the GVB-CI results. The low-spin transition metal-methylene ions are regarded as direct exchange-coupled systems formed from high-spin transition metal ions and the triplet monocentric diradical. The direct exchange couplings between these species can be described on the basis of the Heisenberg model. The CASSCF calculations using UHF natural orbitals (UNOs) have been carried out for low-spin states, showing that UNOs and their occupation numbers are good trials. However, they provide poor binding energies for the transition metal-carbon double bonds and indicate the necessity for dynamical correlation corrections. The approximate spin-projected UHF Møller-Plesset and UHF coupled-cluster methods provide reasonable binding energies for the transition metal-methylene ions, which are close to those of modified coupled-pair functional (CPF) and average CPF methods.
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