Franck-Condon considerations

The Frank-Condon principle states that electronic transitions take place in times that are very short compared to the time required for the nuclei to move significantly. Because of this, care must be taken to ensure that the calculations actually do reflect what is wanted.

Examples of various phenomena which can be studied are:

If the purpose of a calculation is to predict the energy of photoexcitation, then the ground-state should first be optimized. Once this is done, then a C.I. calculation can be carried out using 1SCF. With the appropriate keywords (MECI C.I.=n etc.), the energy of photoexcitation to the various states can be predicted.

A more expensive, but more rigorous, calculation would be to optimize the geometry using all the C.I. keywords. This is unlikely to change the results significantly, however.

If the excited state has a sufficiently long lifetime, so that the geometry can relax, then if the system returns to the ground state by emission of a photon, the energy of the emitted photon will be less (it will be red-shifted) than that of the exciting photon. To do such a calculation, proceed as follows: In order for fluorescence to occur, the photoemission probability must be quite large, so only transitions of the same spin are allowed. For example, if the ground state is S0, then the fluorescing state would be S1.
If the photoemission probability is very low, then the lifetime of the excited state can be very long (sometimes minutes). Such states can become populated by S $_1 \rightarrow $ T1 intersystem crossing. Of course, the geometry of the system will relax before the photoemission occurs.
Indirect emission
If the system relaxes from the excited electronic, ground vibrational state to the ground electronic, ground vibrational state, then a more complicated calculation is called for. The steps of such a calculation are:
An excimer is a pair of molecules, one of which is in an electronic excited state. Such systems are usually stabilized relative to the isolated systems. Optimization of the geometries of such systems is difficult. Suggestions on how to improve this type of calculation would be appreciated.