Generating symmetry-adapted bases for non-Abelian point groups to be used in vibronic coupling Hamiltonians

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Colleges, School and Institutes


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∞h (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∞h 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.


Original languageEnglish
Pages (from-to)125-134
JournalChemical Physics
Early online date7 Aug 2015
Publication statusPublished - 16 Oct 2015


  • Vibronic coupling, Symmetry-adapted basis, Acetylene spectrum, Singlet excited states, Renner–Teller, Pseudo Jahn–Teller