# Franck-Condon factors by counting perfect matchings of graphs with loops.

@article{Quesada2019FranckCondonFB, title={Franck-Condon factors by counting perfect matchings of graphs with loops.}, author={Nicol{\'a}s Quesada}, journal={The Journal of chemical physics}, year={2019}, volume={150 16}, pages={ 164113 } }

We show that the Franck-Condon Factor (FCF) associated with a transition between initial and final vibrational states in two different potential energy surfaces, having N and M vibrational quanta, respectively, is equivalent to calculating the number of perfect matchings of a weighted graph with loops that has P = N + M vertices. This last quantity is the loop hafnian of the (symmetric) adjacency matrix of the graph which can be calculated in O(P32P/2) steps. In the limit of small numbers of… Expand

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