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A generalized quantum master equation approach is introduced to describe electron transfer in molecular junctions that spans both the off-resonant (tunneling) and resonant (hopping) transport regimes. The model builds on prior insights from scattering theory but is not limited to a certain parameter range with regard to the strength of the molecule–electrode coupling. The framework is used to study the simplest case of energy and charge transfer between the molecule and the electrodes for a single site noninteracting Anderson model in the limit of symmetric and asymmetric coupling between the molecule and the electrodes. In the limit of elastic transport, the Landauer result is recovered for the current by invoking a single active electron Ansatz and a binary collision approximation for the memory kernel. Inelastic transport is considered by allowing the excitation of electron–hole pairs in the electrodes in tandem with charge transport. In the case of low bias voltages where the Fermi levels of the electrodes remain below the molecular state, it is shown that the current arises from tunneling and the molecule remains neutral. However, once the threshold is reached for aligning the fermi level of one electrode with the molecular orbital, a small amount of charge transfer occurs with a negligible amount of hopping current. While inelasticity in the current has a minimal impact on the shape of the current–voltage curve in the case of symmetric electrode coupling, the results for a slight asymmetry in coupling demonstrate complete charge transfer and a significant drop in current. These results provide encouraging confirmation that the framework can describe charge transport across a wide range of electrode–molecule coupling and provide a unique perspective for developing new master equation treatments for energy and charge transport in molecular junctions. An extension of this work to account for inelastic scattering from electron–vibrational coupling at the molecule is straightforward and will be the subject of subsequent work.
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Hypothetical Efficiency of Electrical to Mechanical Energy Transfer during Individual Stochastic Molecular Switching Events
There are now many examples of single molecule rotors, motors, and switches in the literature that, when driven by photons, electrons, or chemical reactions, exhibit well-defined motions. As a step toward using these single molecule devices to perform useful functions, one must understand how they interact with their environment and quantify their ability to perform work on it. Using a single molecule rotary switch, we examine the transfer of electrical energy, delivered via electron tunneling, to mechanical motion and measure the forces the switch experiences with a noncontact q-plus atomic force microscope. Action spectra reveal that the molecular switch has two stable states and can be excited resonantly between them at a bias of 100 mV via a one-electron inelastic tunneling process which corresponds to an energy input of 16 zJ. While the electrically induced switching events are stochastic and no net work is done on the cantilever, by measuring the forces between the molecular switch and the AFM cantilever, we can derive the maximum hypothetical work the switch could perform during a single switching event, which is ∼55 meV, equal to 8.9 zJ, which translates to a hypothetical efficiency of ∼55% per individual inelastic tunneling electron-induced switching event. When considering the total electrical energy input, this drops to 1 × 10–7% due to elastic tunneling events that dominate the tunneling current. However, this approach constitutes a general method for quantifying and comparing the energy input and output of molecular-mechanical devices.
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- PAR ID:
- 10197577
- Date Published:
- Journal Name:
- ACS Nano
- ISSN:
- 1936-0851
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1021/acsnano.0c04082
