Existence of the D3h A1–A2 confluence in real triatomic molecules

Determine whether any real triatomic molecules with D3h symmetry—i.e., three identical atoms arranged in an equilateral triangular configuration—exhibit the predicted A1–A2 confluence of conical intersection seams that arises when the doubly-degenerate lowest electronic eigenspace transforms as the A1 ⊕ A2 representation of D3h in the Born–Oppenheimer electronic Hamiltonian. This seeks empirical confirmation of the confluence structure derived in the equivariant transversality analysis (Example 2, Case (v)).

Background

The paper analyzes eigenvalue degeneracies of real symmetric matrices under symmetry constraints and applies the theory to the Born–Oppenheimer electronic Hamiltonian of molecules. For triatomics with three identical atoms, the nuclear configuration at an equilateral triangle has D3h symmetry.

In Example 2 (Case (v)), the authors consider the scenario where the doubly-degenerate ground-state eigenspace transforms as A1 ⊕ A2 under D3h. Their equivariant transversality analysis predicts a specific confluence structure: the degeneracy set in parameter space becomes a D3h-invariant union of smooth curves branching from a symmetry-required seam. While related confluences have been observed experimentally or computationally for other representation cases, this particular A1–A2 confluence has not yet been documented in real molecules.