Adiabatic BO approximation

For the description of a vibronic transition both electronic and nuclear coordinates must be taken into account. In the adiabatic BO approximation, the complete wave function can be separated into the product... 

It is evident that the approximation is expected to work well in situations (such as that near to equilibrium distances in Fig. 1.2) in which the electronic wave-functions are slowly changing functions of the nuclear coordinates, but to be much less valid when (as in the region of the crossing dashed lines of Fig. 1.2) the electronic wavefunctions change abruptly with nuclear motion. In the latter case, there may be some dynamic tendency for the states to preserve their electronic identity instead of following the changes predicted by the adiabatic BO approximation. 

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