So how is non-radiative decay possible? I showed the conical intersections of cytosine some time ago. These geometries, where the first excited and ground state are of the same energy, exist. But the chance of exactly reaching one is zero (since they are only an N-2 dimensional hyperline in the N-dimensional space of geometries of a molecule).
The point is that the picture of isolated electronic states breaks down, i.e. the Born-Oppenheimer approximation. In solid state chemistry that is what they call electron-phonon-coupling.
If you consider the nuclei in terms of an external perturbation, you can take at look at the adiabatic theorem: If nuclear motion is fast and there are close lying electronic states, the states will mix. You get the fast nuclear motion from the excitation energy. About close lying states: Typically all the excited states are close and the molecule quickly reaches S1 if it was initially excited to a higher state (Kasha's rule). If there are suitable intersections to the ground state it can even relax completely.
For doing molecular dynamics you need the energy of your electronic state Ψi as always. But you also need couplings to the other states:
They are called the non-adiabatic coupling vectors and give the major post Born-Oppenheimer contributions.
Here is a little dynamics movie. This is a test MCSCF run on cytosine. The electronic structure is from the Columbus program and the non-adiabatic surface-hopping dynamics are with Newton-X (both from our group actually).
The idea of surface-hopping is that we still want to have a classical trajectory as a basis, but post Born-Oppenheimer corrections are introduced through jumping in between states. Here you can see the cytosine molecule with color coded electronic states: green S1, orange S2. You see how the molecule jumps into the second excited state intermediately and then stays in the first excited state. There is a lot of motion because of the high excess energy.
There is no decay to the ground state in these 341 fs simulated. It should happen soon after or tanning would be extremely dangerous. But the time simulated is still rather short, it is for example a ten-thousandth of the typical fluorescence life-time.
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