Surface hopping with a manifold of electronic states. III. Transients, broadening, and the Marcus picture

Abstract

In a previous paper [Dou et al., J. Chem. Phys. 142, 084110 (2015)], we have introduced a surface hopping (SH) approach to deal with the Anderson-Holstein model. Here, we address some interesting aspects that have not been discussed previously, including transient phenomena and extensions to arbitrary impurity-bath couplings. In particular, in this paper we show that the SH approach captures phonon coherence beyond the secular approximation, and that SH rates agree with Marcus theory at steady state. Finally, we show that, in cases where the electronic tunneling rate depends on nuclear position, a straightforward use of Marcus theory rates yields a useful starting point for capturing level broadening. For a simple such model, we find I-V curves that exhibit negative differential resistance.

Full counting statistics of vibrationally assisted electronic conduction: Transport and fluctuations of thermoelectric efficiency

“…The celebrated Anderson-Holstein model, with a single electronic orbital coupled to a local phonon mode, exposes an intricate interplay between the electronic and nuclear degrees of freedom. The model has been extensively studied to reveal the behavior of the current and its fluctuations in different regimes of electron-phonon coupling, see for example [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30] . An extension of the Anderson-Holstein model with a secondary phonon bath was examined in many studies, see e.g.…”

Lindblad equation and its semiclassical limit of the Anderson-Holstein model

“…Using the wide band approximation, the hopping rate could be explicitly computed using Franck-Condon factors [18,36].…”

“…The semiclassical limit of the Redfield equation, known as the classical master equation (CME), has been considered in [5], which also proposed a numerical method based on surface hopping. The CME perspective has then been used to study various physical aspects of Anderson-Holstein model, e.g., broadening, Marcus rate [17][18][19]. In all these works, the focus has been on Redfield equation (or Redfield generator).…”

“…Anderson-Holstein model, since introduced, has been widely studied using various theoretical and numerical approaches, for instance, the Green's function approach [6,7], equation-of-motion method [8,9], quantum Monte Carlo method [10], semi-classical approximation [11,12], non-crossing approximation [13] and by using quantum master equations [5,[14][15][16][17][18][19]. In the perspective of quantum master equation, which is mostly related to the current work, the quantum master equation in Redfield flavor for Anderson-Holstein model has been derived in [14][15][16].…”

Reconciling perturbative approaches in phonon-assisted transport junctions

“…Nuclear motion in conducting molecules and the surroundings governs effects such as local heating of the junction, which may lead to instabilities 11 , and incoherent tunnelling processes, responsible for the development of ohmic conduction 12 . These effects can be captured within simple models: The celebrated Anderson-Holstein model includes a single electronic site embedded between metals, further coupled to a single vibration, or a harmonic bath [13][14][15][16][17][18][19][20][21][22][23][24][25][26] . A different class of problems, relevant as well to photovoltaic devices 27 , concerns donor-acceptor type molecular systems, with two electronic sites coupled to molecular vibrations 11,[28][29][30][31][32][33][34] .…”