Can classical marcus theory describe hole transfer in polyethylene?

Recently, hole mobilities in polyethylene (PE) oligomers has been investigated by means of Marcus theory. Although it is well known that Marcus theory is successfully applied to various organic semiconductors, strictly speaking, charge transfer in organic molecules requires quantum mechanical treatment to account for quantum nuclear tunneling between vibrational levels. We evaluate hole transfer rates between PE oligomers by Fermi's golden rule (FGR) rate expression and by classical Marcus rate expression at various temperature and energetic disorder. The results indicate that Marcus theory can be a good approximation for describing hole transfer between long polyethylene chain with small reorganization energy or in highly energetically disordered system. However, hole hopping rate between C
₁₀
H
₂₂
molecules computed by Marcus theory was roughly 100 times smaller than that computed through FGR rate expression. High-temperature approximation must be applied with caution especially for quantitative evaluation of hole transfer rates in PE.