How does the Born-Oppenheimer approximation break down

1 How does the Born Oppenheimer approximation break down  

In cases where the Born-Oppenheimer perturbation theory of Eq. (2.36) is not valid, mainly as a result of the degenerate situation among the static electronic states, quantum mechanical mixing among them through the nuclear kinetic operator becomes significant. Consequently nonadiabatic 

To be a little more precise about the notion of quantum entanglement, it should be noted that even a single term in the Born-Huang expansion such as x(R) R) in Eq- (5-1) has already, at least to some extent, taken into account quantum entanglement through the functional form of the electronic wavefunction. This is made clearer if we formally expand it into independent basis functions as 

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