On the Spin-Coupled description of the pi system of the cyclopentadienyl anion

It is well-known that the Spin-Coupled (SC) description of the cyclopentadienyl anion is problematic. A converged six electrons in six orbitals SC calculation on this anion break the D_5h electron density spatial symmetry by approximately localizing two of the six pi singly-occupied orbitals over one carbon. A complete active space valence bond (CASVB) calculation for the same six pi electrons in six orbitals does not break symmetry, yielding five equivalent pi orbitals over the five carbons and one pi orbital with high amplitude along the C₅ molecular rotation axis. A Spin-Coupled calculation comprising six electrons in five orbitals, SC(6,5), yields five equivalent non-orthogonal pi orbitals over the carbons with “1.2” (6/5) electron occupancy each. In this paper, these different solutions are contrasted with one generated by the present author in which five spatially different but equivalent configurations of a perfect-pairing symmetry broken solution are put together in a multi-configuration Spin-Coupled calculation of six electrons in 30 orbitals. It is concluded that, in spite of the computational complexity of this calculation, its result is qualitatively more akin to a valence bond-like description of the resonant pi system of the cyclopentadienyl anion.