Perturbation of the Jahn-Teller effect by partial isotopic substitution: multi-mode vibronic coupling in the X ²E_1g and B ²E_2g states of 1,4-C₆H₄D⁺₂

The effect of partial isotopic substitution on Jahn-Teller spectra is systematically analyzed, taking the X ²E_1g and B ²E_2g degenerate electronic states of the benzene cation as representative examples. The electronic-vibrational coupling constants for the X and B states of 1,4-C₆H₄D⁺₂ are derived from existing ab initio beyond-Hartree-Fock energy gradients with respect to symmetry coordinates of C₆H₆, using the C₆H₆ → C₆H₄D₂ normal-mode scrambling matrix derived from the harmonic force field of benzene. The vibronic dynamics in the X and B states of 1,4-C₆H₄D⁺₂ is treated with the inclusion of up to five nonseparable degrees of freedom. The model spectra reveal a variety of isotopic substitution effects on Jahn-Teller spectra, such as the lifting of Jahn-Teller degeneracies, the breaking of Jahn-Teller selection rules associated with the conservation of vibronic angular momentum, as well as the nonseparability of Jahn-Teller active and progression-forming vibrational modes in systems of reduced nuclear symmetry. It is demonstrated that the consistent inclusion of all active vibrational degrees of freedom is essential for the prediction of isotopically induced line-splitting effects in Jahn-Teller spectra. For the X ²E_1g and B ²E_2g states of 1,4-C₆H₄D⁺₂ a splitting of the origin line of the order to 10 and 100 cm^-1, respectively, is predicted.