Complex Beyond Born–Oppenheimer Theory: A New Perspective on the Jahn–Teller Distortion Phenomenon

The first-principles-based diabatization formalism of adiabatic potential energy surfaces (PESs) and nonadiabatic coupling terms (NACTs) vis-á-vis its applications in several molecular species of spectroscopic interest, triatomic reactive scattering processes, as well as unit cells of solid crystals are mainly associated with "real" adiabatic PESs, NACTs, and adiabatic-to-diabatic transformation (ADT) matrices. Nevertheless, these three properties (adiabatic PESs, NACTs, and ADT matrices) often appear as complex (both real and imaginary parts) quantities for three types of molecular species/processes/phenomena, namely, (a) resonance states calculated with the complex absorbing potential method (where adiabatic PESs contain imaginary terms), (b) spin-orbit matrix elements (often possess imaginary components), and (c) complex mixing of electronic states through nuclear coordinates in the Jahn-Teller (JT) distortion phenomenon (ADT matrix becomes complex). In other words, the development of complex diabatization is indeed necessary for "true" generalization of beyond Born-Oppenheimer (BBO) theory. The present work is mainly focused on the formulation of the Complex BBO (CBBO) methodology only for case 'c', as illustrated above, and the workability of such an approach has been explored for benzene radical cation (C₆H₆⁺), where the mixing angles between electronic states contain both real and imaginary parts, leading to complex ADT vis-á-vis diabatic PESs matrices.