Energy-Only Construction of a Symmetry-Adapted Quasi-Diabatic Hamiltonian for the Two Lowest States of Na

Abstract

Nonadiabatic dynamics of Na3 are strongly influenced by an E′ Jahn-Teller conical intersection seam at D3h geometries. Here, we construct a D3h symmetry-adapted two-state quasi-diabatic Hamiltonian for Na3 from ab initio adiabatic energies alone. Fundamental invariants and symmetry-covariant basis functions impose permutation symmetry and the symmetry-required conical intersection structure, while three scalar fundamental invariant neural-network functions describe the coordinate dependence of the Hamiltonian elements. The resulting quasi-diabatic matrix elements are smooth, and diagonalization reproduces the ab initio ground-and excited-state energies with rootmean-square errors of 4.6 × 10-5 and 1.5 × 10-4 eV, respectively. The fitted quasidiabatic potential energy matrix is applied to Na + Na2(v = 0, j = 0) quantum scattering. Comparison with adiabatic calculations shows that the geometric phase (GP) substantially modifies the resonance structure, while the remaining differences suggest a role for excited-state participation in the reaction dynamics. This work provides an energy-only route to quasi-diabatic Hamiltonians that incorporate molecular symmetry for nonadiabatic dynamics in metal trimers.