Electron localization-delocalization transitions in dissociation of the C4- anion: a large-D analysis

We present a study, employing high level ab initio methods, of electron localization-delocalization transitions along the dissociation path of the C4- anion to C2 and C2-. We find that at the equilibrium geometry, the symmetrical and nonsymmetrical configurations of the linear C4- anion are almost isoenergetic. However, along a collinear dissociation path, the dipole moment drops abruptly to zero when the separation between the two middle carbon nuclei reaches about R = 2.15 angstroms. The dipole moment remains zero until about R = 2.78 angstroms, and then continuously increases as dissociation proceeds. This behavior is analogous to critical phenomena: The abrupt drop to zero of the dipole moment resembles a first-order phase transition, the later steady rise resembles a continuous phase transition. We show that a simple sub-Hamiltonian model, corresponding to the large-dimension limit for an electron in the field of four collinear carbon atoms, exhibits both kinds of phase transitions along the dissociation path.