The electronic adiabatic-to-diabatic transformation matrix and the Wigner rotation matrix

In this publication we consider electronically multi-fold degeneracy with the aim of revealing the connection between the adiabatic-to-diabatic transformation (ADT) matrices and Wignerʹs 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 employed the relevant non-adiabatic coupling matrices (NACMs). We found that once these matrices were properly quantized [Chem. Phys. 259, (2000) 123] the ADT matrices and Wignerʹs dj-rotation matrices are related via a similarity transformation.