a) What is the statement of the Born-Oppenheimer approximation?
According to the Born-Oppenheimer approximation, the electronic motion and the nuclear motion can be separated, i.e., the positions of the atoms, and thus bond lengths, do not change while ionization takes place.
b) What is the statement of the Franck-Condon principle?
The Franck-Condon principle states that the probability for an electronic transition is highest where the electronic wave functions of both ground state and ionized state have their maxima.
c) Can you explain the difference between vertical and adiabatic ionization?
According to the Franck-Condon principle, a ground state neutral is most probably converted into a vibrationally excited molecular ion. This process is represented by a vertical line in the diagram (hence the name). The counterpart of vertical ionization is a process where ionization of the neutral in its vibrational ground state would yield the radical ion also in its vibrational ground state; this is termed adiabatic ionization.