document: For decades, vibronic coupling models [1–4] have served as bridges connecting nuclear dynamics studies with the static studies of electronic structure calculations [5]. The vibronic coupling model is a simple polynomial expansion of diabatic potential energy surfaces and couplings. The expansion coefficients are chosen so that the eigenvalues of the potential operator map on to the adiabatic potential surfaces. This diabatisation by ansatz circumvents many of the problems of describing non-adiabatic systems. It is also the inspiration for a diabatisation scheme that is used in modern, direct-dynamic methods that include non-adiabatic effects [6]. For a model Hamiltonian to correctly approximate the eigenvectors of the true Hamiltonian it has to span the totally symmetric irreducible representation (IrRep) of the point groups the molecule belongs to, at the appropriate symmetric geometries [7]. In recent times, many articles have demonstrated the advantages of using symmetry when constructing analytic model potentials [8–12], most often in the context of permutation-inversion groups [13].
doc_bio_tags: O O B I I O O O O O O B I I O O O O O B I I O O B I I O O O B I O B I I I I I O B I O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O B I O O O O O O O B I O O O O O O O B I B O O O O O O O O O O O B I O O O O O O O O O O O O O O O B I I O O O O O O O O O O
extractive_keyphrases: analytic model potentials diabatic potential energy surfaces and couplings diabatisation electronic structure calculations expansion coefficients irreducible representation irrep model hamiltonian nuclear dynamics studies polynomial expansion symmetric geometries true hamiltonian vibronic coupling model vibronic coupling models
abstractive_keyphrases: diabatisation scheme direct-dynamic methods non-adiabatic systems permutation-inversion groups