Projected States of Open Shell Molecules: The Pi-Electron States of the Cyclopentadienyl Cation

Wavefunctions of pure spin and spatial symmetry were projected from the unrestricted pi‐electron wavefunction of the cyclopentadienyl cation. Since the M=1 triplet functions for this molecule are forced eigenfunctions of S² and the molecular symmetry operators, the calculations were carried out using a broken symmetry M=0 function for the starting point of the semiempirical unrestricted treatment. This procedure has the advantage of providing an unrestricted wavefunction for the lowest singlet state along with the unrestricted triplet wavefunction. The energy lowering produced by the unrestricted treatment followed by projection, as compared to that found using the molecular orbitals determined by symmetry, was greatest for the $E_2\prime$ singlet state. The energy lowering produced by projecting the $A_2\prime$ spatial component of the triplet was as great as the energy lowering produced by spin projection. The major results were only slightly affected by varying the semiempirical parameters by a fraction of their initial values. The $A_2\prime$ triplet was the lowest energy state for all of the values used for these parameters.