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I am trying to create a crude electron-hopping model to study conductivity in a biological wire composed of discrete sites. The model is pretty simple: imagine a line composed of sites. Electrons can hop from site to site with probabilities that depend on the free energy difference between those sites.

All these free energies were obtained numerically for the case where only one electron is in the system. Now I am considering the scenario where two electrons are in adjacent sites, and Coulomb repulsion would push them apart, changing their probability of hopping.

My question is how to add this extra Coulomb interaction to the free energy directly. I imagine that the internal energy and also the Hamiltonian change by a simple addition of a term, but I could not yet figure out how to account for an extra entropic difference that would be involved. Since I have the free energies obtained numerically for the case without this extra interaction, I wouldn't know how to decompose this back to a partition function so that it could be recalculated.

Thanks!

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# I Including Coulomb interaction in a free energy calculation

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