Approximate spin projection of three-component UHF wavefunctions: The states of the pentachlorocyclopentadienyl cation and the croconate dianion, C5O52−

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Abstract
The approximate spin projection method of Amos et al. is extended to handle UHF wavefunctions having three significant components of differing multiplicity. An expression is given for the energy after single annihilation which differs from that of Amos and Hall. The new expression reproduces the results obtained from a previous exact calculation for which the weights and energies of the components are known. The extended approximate projection method is applied to the pi-electron UHF wavefunctions for the ground states of the pentachlorocyclopentadienyl cation and the croconate dianion, C5O52−. The results indicate a triplet ground state for the former and a singlet ground state for the latter, in agreement with experimental ESR susceptibility measurements for these molecular ions. C5Cl5+ cannot be treated by restricted Hartree-Fock theory due to its open-shell ground state. Incorrect results are obtained for the croconate dianion if restricted Hartree-Fock theory and singly excited configuration interactions are utilized.