Choice between the Diabatic and Adiabatic Models

If the approximate deperturbed potential curves cross, they are diabatic curves. One can assume an interaction matrix element given by Eq. (3.3.5) and carry out a complete deperturbation. 

The choice of an adiabatic picture leads to difficulties when one of the potentials has a double minimum (see Fig. 3.5). The vibrational level separations of such a curve do not vary smoothly with vibrational quantum number, as do the levels of a single minimum potential. In the separate potential wells (below the barrier), the levels approximately follow two different smooth curves. However, above the potential barrier the separation between consecutive energy levels oscillates. The same pattern of behavior is found for the rotational constants below and above the potential barrier. In addition, the rotational levels above the barrier do not vary as BVJ(J + 1). An adiabatic deperturbation of the (E,F+G,K) states of H2 has been possible (Dressier et al., 1979) only because the adiabatic curves were known from very precise ab initio calculations. 

If the approximate deperturbed curves do not cross or have similar spectroscopic constants, the most convenient starting point is an adiabatic approach. Two situations must be considered  

The adiabatic curves result from an apparently avoided crossing. This means that the diabatic curves belong to very different electronic configurations. The coupling matrix element, We(R), can be assumed to have a Lorentzian shape [Eq. (3.3.14)]. This is the situation for the G and I states of SiO. 

The vibrational eigenstates of neither the diabatic nor the adiabatic potential curve exactly represent the observed levels. Interaction matrix elements between these zero-order levels (eigenstates of either diabatic or adiabatic potentials) 

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