Abstract
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.
Highlights
Vibronic coupling models [1,2,3,4] have served as bridges connecting nuclear dynamics studies with the static studies of electronic structure calculations [5]
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]
Many articles have demonstrated the advantages of using symmetry when constructing analytic model potentials [8,9,10,11,12], most often in the context of permutation-inversion groups [13]
Summary
Vibronic coupling models [1,2,3,4] have served as bridges connecting nuclear dynamics studies with the static studies of electronic structure calculations [5]. A textbook example are the linear terms in the E e Jahn–Teller diabatic model describing E degenerate states with a branching space along e degenerate modes The symmetry of this system dictates that the linear coupling and gradient should share the same coefficient, correctly resulting in the well-known ‘‘mexican hat” adiabatic potential. We present approaches for generating such diabatic matrices that form bases for totally symmetric IrReps, starting from functions representing electronic states and nuclear coordinates which transform as known IrReps of the group for which the matrix representations for the operations are known. To generate the D1h Hamiltonian, we followed a similar approach to Viel and Eisfeld [16], who generated matrices up to sixth order for E e Jahn–Teller Hamiltonians They used them to fit to the 2E0 anharmonic surfaces along twofold e0 stretches of NO3 obtained from ab initio MR-SDCI calculations. This is a well known method for generating symmetry-adapted functions and only briefly presented here
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