Adiabatic assumption failure

Several explanations have been given for this result. One possibility is the failure of the adiabatic assumption in this ionization process a transition state is generated that may not be a combination of the initial and final states, but may include mixing in of an excited state structure. This idea will reappear in the following pages. 

Assuming that the diabatic space can be truncated to the same size as the adiabatic space, Eqs. (64) and (65) clearly define the relationship between the two representations, and methods have been developed to obtain the tians-formation matrices directly. These include the line integral method of Baer [53,54] and the block diagonalization method of Pacher et al. [179]. Failure of the truncation assumption, however, leads to possibly important nonremovable derivative couplings remaining in the diabatic basis [55,182]. 

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