skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: A many-body states picture of electronic friction: The case of multiple orbitals and multiple electronic states

Abstract

We present a very general form of electronic friction as present when a molecule with multiple orbitals hybridizes with a metal electrode. To develop this picture of friction, we embed the quantum-classical Liouville equation (QCLE) within a classical master equation (CME). Thus, this article extends our previous work analyzing the case of one electronic level, as we may now treat the case of multiple levels and many electronic molecular states. We show that, in the adiabatic limit, where electron transitions are much faster than nuclear motion, the QCLE-CME reduces to a Fokker-Planck equation, such that nuclei feel an average force as well as friction and a random force—as caused by their interaction with the metallic electrons. Finally, we show numerically and analytically that our frictional results agree with other published results calculated using non-equilibrium Green’s functions. Numerical recipes for solving this QCLE-CME will be provided in a subsequent paper.

Authors:
;  [1]
  1. Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104 (United States)
Publication Date:
OSTI Identifier:
22679016
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Chemical Physics; Journal Volume: 145; Journal Issue: 5; Other Information: (c) 2016 Author(s); Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; BOLTZMANN-VLASOV EQUATION; ELECTRONIC STRUCTURE; EXPERIMENTAL DATA; FOKKER-PLANCK EQUATION

Citation Formats

Dou, Wenjie, and Subotnik, Joseph E. A many-body states picture of electronic friction: The case of multiple orbitals and multiple electronic states. United States: N. p., 2016. Web. doi:10.1063/1.4959604.
Dou, Wenjie, & Subotnik, Joseph E. A many-body states picture of electronic friction: The case of multiple orbitals and multiple electronic states. United States. doi:10.1063/1.4959604.
Dou, Wenjie, and Subotnik, Joseph E. Sun . "A many-body states picture of electronic friction: The case of multiple orbitals and multiple electronic states". United States. doi:10.1063/1.4959604.
@article{osti_22679016,
title = {A many-body states picture of electronic friction: The case of multiple orbitals and multiple electronic states},
author = {Dou, Wenjie and Subotnik, Joseph E.},
abstractNote = {We present a very general form of electronic friction as present when a molecule with multiple orbitals hybridizes with a metal electrode. To develop this picture of friction, we embed the quantum-classical Liouville equation (QCLE) within a classical master equation (CME). Thus, this article extends our previous work analyzing the case of one electronic level, as we may now treat the case of multiple levels and many electronic molecular states. We show that, in the adiabatic limit, where electron transitions are much faster than nuclear motion, the QCLE-CME reduces to a Fokker-Planck equation, such that nuclei feel an average force as well as friction and a random force—as caused by their interaction with the metallic electrons. Finally, we show numerically and analytically that our frictional results agree with other published results calculated using non-equilibrium Green’s functions. Numerical recipes for solving this QCLE-CME will be provided in a subsequent paper.},
doi = {10.1063/1.4959604},
journal = {Journal of Chemical Physics},
number = 5,
volume = 145,
place = {United States},
year = {Sun Aug 07 00:00:00 EDT 2016},
month = {Sun Aug 07 00:00:00 EDT 2016}
}
  • The results for the spectrum of bound states and of solitons first deduced by Dashen, Hasslacher, and Neveu for a model of interacting fermions by techniques of functional integration are obtained here by methods based on Heisenberg field mechanics analogous to those applied previously to models of self-interacting bosons. The method of solution is suggested by a simplified physical picture of the bound states: These are computed in a Hartree approximation in which the self-consistent potential is a sum of contributions from the fermions (and antifermions) occupying orbitals in the conventional many-body picture and from the vacuum fluctuations of single-closed-loopmore » type. In the same approximation the self-consistent field generated by the heavy soliton is a result of the vacuum fluctuations alone. As the main new technical contribution, we deduce and solve directly equations determining the self-consistent fields as well as the amplitudes (''wave functions'') from which these are constructed. We comment on the degeneracy of the heavy soliton state. (AIP)« less
  • Energies of the ground and a number of even- and odd-parity excited states of multi-valence-electron ions have been computed by a computational method in the framework of relativistic multireference many-body perturbation theory. Relativistic multireference perturbation calculations are reported for the ground and over 80 low-lying odd- and even-parity excited states of siliconlike argon (Ar{sup 4+}) and aluminumlike iron (Fe{sup 13+}) to demonstrate the unprecedented accuracy of the method. The theory deviates from experiment by less than 0.2% for all but a few excited levels in siliconlike argon. For the more highly ionized aluminumlike iron, the deviations are reduced to withinmore » 0.06%. Theoretical magnetic dipole and electric quadrupole transition rates of the lowest-lying {sup 2}P{sub 3/2}{sup o} state of aluminumlike Fe and Mn are evaluated, and lifetimes are compared with a recent ion trap experiment.« less
  • The performance of the quasi-degenerate many-body perturbation theory up to the third order is investigated for the ground state, five excited states, and the first quintet of a simple four-electron H{sub 4} model system consisting of two stretched hydrogen molecules, in which the degree of quasi-degeneracy can be continuously varied from a nondegenerate to a full degenerate situation. We employ a DZP basis set. The effect of intruder states is considered and a comparison with other multireference correlation techniques is also provided. Finally a criterion for the model space to be quasi-degenerate will be reformulated and generalized. 50 refs., 6more » figs., 14 tabs.« less
  • We investigate a simple surface hopping (SH) approach for modeling a single impurity level coupled to a single phonon and an electronic (metal) bath (i.e., the Anderson-Holstein model). The phonon degree of freedom is treated classically with motion along–and hops between–diabatic potential energy surfaces. The hopping rate is determined by the dynamics of the electronic bath (which are treated implicitly). For the case of one electronic bath, in the limit of small coupling to the bath, SH recovers phonon relaxation to thermal equilibrium and yields the correct impurity electron population (as compared with numerical renormalization group). For the case ofmore » out of equilibrium dynamics, SH current-voltage (I-V) curve is compared with the quantum master equation (QME) over a range of parameters, spanning the quantum region to the classical region. In the limit of large temperature, SH and QME agree. Furthermore, we can show that, in the limit of low temperature, the QME agrees with real-time path integral calculations. As such, the simple procedure described here should be useful in many other contexts.« less