No Access Submitted: 23 July 2018 Accepted: 27 September 2018 Published Online: 19 October 2018
J. Chem. Phys. 149, 154112 (2018); https://doi.org/10.1063/1.5049537
Charge transport through molecular junctions is often described either as a purely coherent or a purely classical phenomenon, and described using the Landauer–Büttiker formalism or Marcus theory (MT), respectively. Using a generalised quantum master equation, we here derive an expression for current through a molecular junction modelled as a single electronic level coupled with a collection of thermalised vibrational modes. We demonstrate that the aforementioned theoretical approaches can be viewed as two limiting cases of this more general expression and present a series of approximations of this result valid at higher temperatures. We find that MT is often insufficient in describing the molecular charge transport characteristics and gives rise to a number of artefacts, especially at lower temperatures. Alternative expressions, retaining its mathematical simplicity, but rectifying those shortcomings, are suggested. In particular, we show how lifetime broadening can be consistently incorporated into MT, and we derive a low-temperature correction to the semi-classical Marcus hopping rates. Our results are applied to examples building on phenomenological as well as microscopically motivated electron-vibrational coupling. We expect them to be particularly useful in experimental studies of charge transport through single-molecule junctions as well as self-assembled monolayers.
The authors thank James Thomas and Bart Limburg for useful discussions and Núria Aliaga-Alcalde and co-workers for providing us with the results of the DFT calculations from Ref. 1515. E. Burzurí, J. O. Island, R. Díaz-Torres, A. Fursina, A. González-Campo, O. Roubeau, S. J. Teat, N. Aliaga-Alcalde, E. Ruiz, and H. S. van der Zant, ACS Nano 10, 2521 (2016). https://doi.org/10.1021/acsnano.5b07382. J.K.S. thanks the Clarendon Fund, Hertford College, and EPSRC for financial support. E.M.G. acknowledges funding from the Royal Society of Edinburgh and the Scottish Government, and J.A.M. acknowledges funding from the Royal Academy of Engineering. This project was supported by a grant from the John Templeton Foundation. The opinions expressed in this publication are those of the authors and do not necessarily reflect the views of the John Templeton Foundation.
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