The vibronic coupling Hamiltonian is a standard model used to describe the potential energy surfaces of systems in which non-adiabatic coupling is a key feature. This includes Jahn-Teller and Renner-Teller systems. The model approximates diabatic potential energy functions as polynomials expanded about a point of high symmetry. One must ensure the model Hamiltonian belongs to the totally symmetric irreducible representation of this point group. Here, a simple approach is presented to generate functions that form a basis for totally symmetric irreducible representations of non-Abelian groups and apply it to D<inf>∞h</inf> (2D) and O (3D). For the O group, the use of a well known basis-generating operator is also required. The functions generated for D<inf>∞h</inf> are then used to construct a ten state, four coordinate model of acetylene. The calculated absorption spectrum is compared to the experimental spectrum to serve as a validation of the approach.
Robertson, C., & Worth, G. A. (2015). Generating symmetry-adapted bases for non-Abelian point groups to be used in vibronic coupling Hamiltonians. Chemical Physics, 460, 125–134. https://doi.org/10.1016/j.chemphys.2015.07.034