Existence of the Cs-symmetric planar confluence in penta-atomic molecules (N = 5)

Determine whether any real penta-atomic molecules exhibit the predicted Cs-symmetric planar confluence of conical intersection seams that arises near planar configurations when the doubly-degenerate lowest electronic eigenspace transforms as A′ ⊕ A″ (Example 3, Case (ii)). This aims to confirm the branching behavior derived for N = 5 in the equivariant transversality analysis of the Born–Oppenheimer electronic Hamiltonian.

Background

The authors study planar (but noncolinear) molecular configurations with reflection symmetry Cs and analyze degeneracies of the Born–Oppenheimer electronic Hamiltonian using equivariant transversality. They decompose the nuclear vibrational modes into A′ and A″ representations and examine cases depending on the representation type of the degenerate electronic eigenspace.

For Case (ii) with A′ ⊕ A″, they derive explicit forms of the degeneracy set F−1(0). For N = 4, the resulting confluence has been observed in HNCO; however, for N = 5 the predicted confluence has not been found in any real molecule, despite the expectation that it should occur generically in penta-atomic systems.