Towards a highly efficient theoretical treatment of Jahn-Teller effects in molecular spectra: The $1A2$ and $2A2$ electronic states of the ethoxy radical

Nonadiabatic effects in the two lowest electronic states of the ethoxy radical, the $1A2$ and $2A2$ states, are considered, using multireference configuration interaction (MRCI) wave functions comprised of over $15×106$ configuration state functions. The lowest point on the seam of conical intersection is located. Using this point as the origin, a quasidiabatic Hamiltonian suitable for use in a multimode vibronic coupling treatment of the coupled $1A2$ and $2A2$ electronic states is determined. The Hamiltonian includes all contributions from all internal coordinates through second order in displacements from the origin and is comprised of over 500 parameters. By using the average energy gradient, the energy difference gradients, and the derivative couplings, all of which are obtained at little additional cost once the requisite eigenstates are known, the second order Hamiltonian is determined from MRCI calculations at only 35 nuclear configurations. This is essentially the same number of points required to obtain the frequencies for the ground state equilibrium structure using centered differences of gradients. The diabatic Hamiltonian provides a good description of the seam space, the $(Nint−2)$-dimensional space of conical intersection points, continuously connected to the minimum energy crossing point, enabling, for the first time, an analysis of the changes in the branching plane induced by seam curvature in the full seam space. Comparing the diabatic representation and MRCI results we find a good agreement for the ground state equilibrium structure, $Req(1A2)$⁠, as well as the ground state energy and vertical excitation energy. In good agreement with the available experimental data are the ground state equilibrium structure and the excitation energy to the $AA2$ state, predicted here to involve a cone state level. Agreement between the harmonic frequencies at $Req(1A2)$ computed from the MRCI wave function and from the diabatic Hamiltonian is excellent for all but the three lowest energy normal modes where significant deviations are observed indicating the need for selected cubic and/or quartic terms. For the low-lying vibrational levels, the diabatic representation can be used to partition the normal modes into two groups, those that involve inter(diabatic) state coupling and those that are spectators as far as nonadiabatic effects are concerned. The spin-orbit coupling interaction is determined using the Breit-Pauli approximation and its incorporation into the diabatic Hamiltonian is discussed.