Vibronic interactions symmetric perturbations

Table 3 shows the nonadiabatic levels of B2 symmetry and their absorption intensities between 16000 and 16300 cm l. The equilibrium symmetric-stretch and bending coordinates of the electronic species are different by about 6 and 24%, respectively [17], whereas the antisymmetric stretch is equal. Therefore, the conical intersection preferably couples a2B2(vi,v2,0) combination states with their X Ai partners, but this interaction is perturbed by the A B2 antisymmetric-stretch species. Above 15000 cm l, the nonadiabatic intensity distribution is thus modulated by the maxima due to n> states with large A B2 symmetric stretch-bending character, whereas A B2 pure overtones are much weaker (e.g. bands 409 and 415 of Table 3). As the energy increases, these vibronic interactions give rise to a more and more irregular spectrum.

Consider the APES of a two-level system with the ground state 1 and excited state 2 and an energy gap A between them, which interact (mix) under the symmetrized nuclear displacement Qr- Using perturbation theory with respect to the linear vibronic coupling term (dH/dQr)o Qr we easily obtain [1] that the primary curvature (the curvature without vibronic coupling) of the ground state K, ... 

Since the vibronic couphng contributions to e hamiltonian are one-electron operators, as are the ligand field operators Vlf, the calculation of perturbation energies is relatively simple. We start by considering d-orbital levels which are subject to a first order coupling perturbation due to the interaction with a totally symmetric vibrational mode ci with the atoms moving along the coordinate Si. 

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