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Charge transport through molecular junctions is often described either as apurely coherent or a purely classical phenomenon, and described using theLandauer-B\"uttiker formalism or Marcus theory, respectively. Using ageneralised quantum master equation, we here derive an expression for currentthrough a molecular junction modelled as a single electronic level coupled to acollection of thermalised vibrational modes. We demonstrate that theaforementioned theoretical approaches can be viewed as two limiting cases ofthis more general expression, and present a series of approximations of thisresult valid at higher temperatures. We find that Marcus theory is ofteninsufficient in describing the molecular charge transport characteristics andgives rise to a number of artefacts, especially at lower temperatures.Alternative expressions, retaining its mathematical simplicity but rectifyingthose shortcomings, are suggested. In particular, we show how lifetimebroadening can be consistently incorporated into Marcus theory, and we derive alow-temperature correction to the semi-classical Marcus hopping rates. Ourresults are applied to examples building on phenomenological as well asmicroscopically-motivated electron-vibrational coupling. We expect them to beparticularly useful in experimental studies of charge transport throughsingle-molecule junctions as well as self-assembled monolayers.

Beyond Marcus theory and the Landauer-B\"uttiker approach in molecular junctions: A unified framework