The electronic adiabatic-to-diabatic transformation matrix and the irreducible representation of the rotation group

In this publication we consider the electronically multi-fold degeneracy with the aim of revealing the connection between the adiabatic-to-diabatic transformation matrices and Wigner's irreducible representation of the rotation group. To form the connection we constructed simplified models of two, three and four states, all (electronically) degenerate at a single point, and we employed the relevant non-adiabatic coupling matrices. We found that once these matrices are properly quantized (Baer, M. Chem. Phys. 259,123,2000) the adiabatic-to-diabatic transformation matrices and Wigner's dj-rotation matrices are related via a similarity transformation.