Spin-rovibronic wavefunction

As discussed in Section 8.2.1, when nonadiabatic couplings cannot be neglected, the BO approximation is not reliable and coupled electronic states must be considered simultaneously with their interactions. For small systems, several full-dimensional approaches based on the vibronic or spin-rovibronic wavefunctions and taking into account simultaneously at least two electronic states have been developed [2, 100-104]. To quote some examples, the full vibronic Hamiltonians have been derived and employed for linear tetra-atomic molecules showing Renner-Teller interactions [103] or CXaY-like molecules of Csv symmetry showing Jahn-Teller interactions [104]. In the following, we will present the computational approaches based on the full rovibronic Carter-Handy Hamiltonian [100], developed for triatomic molecules and expressed in internal coordinates, which allows us to take into account up to three interacting electronic states [2, 100, 101]. 

Figure 8.14 Total spin-rovibronic wavefunctions represented by plots of vibrational parts corresponding to two interacting electronic states. Shown are the cuts of the pure vibrational part along two internal coordinates, bending (x axis) and X Y stretching (y axis), with the /fnx kept at the equilibrium value. Positive and negative lobes ate ploted with continuous and dashed lines, respectively. The two electronic components (A and A") are plotted in adjacent panels with contributions from each electronic state to the total wavefrmction shown in the upper right corner of each panel.

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