The Jahn-Teller plus pseudo-Jahn-Teller vibronic problem in the C3 radical and its topological implications

The combined Jahn-Teller plus pseudo-Jahn-Teller [(E'+A1')⊗e'] problem is discussed for the tricarbon radical (C3) by means of ab initio calculations at the multireference configuration interaction level of theory. For the (1)E' electronic state arising from a e'(2) valence configuration, three additional symmetry-equivalent C2v seams are found to lie in close proximity to the D3h symmetry-required seam over the entire range of the breathing coordinate here considered. As the perimeter of the molecule increases, the C2v disjoint seams approach the D3h one almost linearly and ultimately coalesce with it at Q1 = 5.005 a0, thence forming an intersection node or confluence. By further increasing the size of the molecular triangle, the C2v seams get rotated by ±π in the g-h plane. A three-state vibronic Hamiltonian is also proposed to model locally the title system and shown to accurately mimic the calculated data over the region close to the minimum energy crossing point. No net geometric phase effect is observed when the associated electronic wave functions are adiabatically transported along closed paths encircling the four singularity points. For all paths enclosing the intersection node, the sign reversal criterion is shown to be not fulfilled, even for infinitesimal loops. The results so obtained are expected to be valid for other ring systems experiencing similar topological attributes.