Universal diabatic representation of operators using Cnv/Dnh symmetry. I. General derivation

The diabatic representation of operators of any irreducible representation is derived for the Cnv and the Dnh symmetry groups. Both Jahn–Teller and pseudo Jahn–Teller systems are considered. The resulting compact expressions recover not only expansions of totally symmetric operators like the one needed for potential energy surfaces, but also expansions for dipole, quadrupole, and angular momentum surfaces. The present work also investigates the limitations of the Franck–Condon principle and related approximations for (pseudo) Jahn–Teller systems, using analytical model potentials and dipole transition surfaces. To this end, a prototypical C3v (A + E) ⊗ e system is used as a numerical example to study the effects approximating a dipole transition surface using more approximated expressions has on the simulated absorption spectrum. In addition, relations and selection rules for transition moments are provided, with explicit examples for systems of C3v, C4v, and C5v symmetry. A D6h (E1g + E2g) ⊗ (e1g + e2g) Hamiltonian to second order is also provided as a practical example for how to apply the presented expressions to a more realistic multi-mode system.