I'm running out of professors to talk to, and I need to clarify a couple of things for the sake of making a realistic model of electron travel through a mesh.
This is about calculations of electron hopping using Marcus theory. The Marcus equation results in a frequency of electron jumps (1/s) worked out by electric coupling of a pair of molecules, the Gibbs free energy, reorganization energy of adjacent particles, ambient temperature and the Dirac constant.
This rate of electron hopping is worked out per bond between molecule n and molecule n+1, for instance. So when an electron is 'sitting' on a molecule, there are several paths (bonds) it could follow, to go to other molecules. We're assuming that the probability of following these paths is based on the rate of hopping worked out per bond.
So when I look at one pair of molecules, a given electron hopping rate (a property of the bond) from n to n+1 should give the the percentage chance to move from n to n+1, and a percentage chance to move from n+1 to n. How can I interpret this rate quantity in order to get these probabilities?