# What drives vibrational cooling in an excited stated?

As we excite a molecule from its ground state, $$S_{0,v=0}$$, to some excited state in a higher vibrational state, i.e. $$S_{1,v'=3}$$, what drives vibrational cooling within that excited state manifold (such as $$S_{1,v'=0} \leftarrow S_{1,v'=3}$$?) This is a fast process, typically on the order of hundreds of femtoseconds, and it occurs prior to any photorelaxation (as per Kasha's rule). Due to the vibrational density of states being quite high near the first excited state, is it the anharmonic coupling to these states that drives vibrational cooling? Furthermore, is there a quantum mechanistic/mathematical way of depicting the probability/rate of this process (as in, what would the relevant perturbation term $$\hat{H}{'}$$ for dealing with this problem in the context of Fermi's golden rule)?

• Where are you, in a condensed phase or in a dilute gas? A compact lattice has no space for local vibrations. – Karl Jun 25 '19 at 22:20
• Good point - I guess the form of vibrational cooling depends on the nature of the state. I'm more interested in the condensed phase, where solvent/bath interactions or possible. My interest mainly lies in the crystalline phase. – kalle Jun 25 '19 at 23:29