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The Wiedemann-Franz (WF) law is a fundamental result in solid-state physicsthat relates the thermal and electrical conductivity of a metal. It is derivedfrom the predominant origin of energy conversion in metals: the motion ofquasi-free charge-carrying particles. Here, an equivalent WF relationship isdeveloped for molecular systems in which charge carriers are moving not as freeparticles but instead hop between redox sites. We derive a concise analyticalrelationship between the electrical and thermal conductivity generated byelectron hopping in molecular systems and find that the linear temperaturedependence of their ratio as expressed in the standard WF law is replaced by alinear dependence on the nuclear reorganization energy associated with theelectron hopping process. The robustness of the molecular WF relation isconfirmed by examining the conductance properties of a paradigmatic molecularjunction. This result opens a new way to analyze conductivity in molecularsystems, with possible applications advancing the design of moleculartechnologies that derive their function from electrical and/or thermalconductance.

Wiedemann-Franz Law for Molecular Hopping Transport