The transfer of energy between electrons and ions in solids

Abstract

In this review we consider those processes in condensed matter that involve the irreversible flow of energy between electrons and nuclei that follows from a system being taken out of equilibrium. We survey some of the more important experimental phenomena associated with these processes, followed by a number of theoretical techniques for studying them. The techniques considered are those that can be applied to systems containing many nonequivalent atoms. They include both perturbative approaches (Fermi's Golden Rule and nonequilibrium Green's functions) and molecular dynamics based (the Ehrenfest approximation, surface hopping, semi-classical Gaussian wavefunction methods and correlated electron-ion dynamics). These methods are described and characterized, with indications of their relative merits.

Inelastic transport theory from first principles: Methodology and application to nanoscale devices

“…The Hamiltonian ͑1͒ naturally arises from the adiabatic approximation of Born-Oppenheimer in which the time scales of electronic and vibrational dynamics are separated. 12 Since the electrons move on a much shorter timescale than the heavy nuclei, the adiabatic approximation states that the electronic Hamiltonian depends parametrically on the nuclear coordinates, i.e., that Ĥ e = Ĥ e ͑Q͒, where Q ϵ R − R 0 is a displacement variable around the equilibrium configuration R 0 . Next, limiting ourselves to small displacements we can expand the electronic Hamiltonian to lowest order in Q…”

“…The interaction between electrons and nuclear vibrations plays an important role for the electron transport at the nanometer scale, 11,12 and is being addressed experimentally in ultimate atomic-sized systems. [13][14][15][16][17][18][19] Effects on the electronic current due to energy dissipation from electron-phonon ͑e-ph͒ interactions are relevant, not only because they affect device characteristics, induce chemical reactions, 20 and ultimately control the stability; these may also be used for spectroscopy to deduce structural information-such as the bonding configuration in a nanoscale junction-which is typically not accessible by other techniques simultaneously with transport measurements.…”

Calculation of non-adiabatic coupling vectors in a local-orbital basis set

“…Although this approach is very useful and has been widely employed to a large variety of systems, there are many important problems in physics, chemistry, biology, etc., that require to go beyond the adiabatic approximation (e.g., see Refs. [3][4][5][6]. Some illustrative examples are: photochemical processes in biology and chemistry (photosynthesis, photocatalysis, etc.…”

Exact Factorization of the Time-Dependent Electron-Nuclear Wave Function

“…To make numerical calculations feasible, the description usually involves approximations such as classical dynamics for nuclei with electron-nuclear coupling provided by Ehrenfest dynamics or surfacehopping [1], or even just static nuclei [2]. Quantum features of the nuclear dynamics (e.g., zero-point energies, tunneling, and interference) are included approximately in some methods [3,4], while numerically exact solutions of the time-dependent Schrödinger equation (TDSE) for the coupled system of electrons and nuclei have been given for very small systems like H + 2 [5]. Clearly, the full electron-nuclear wavefunction contains the complete information on the system, but it lacks the intuitive picture that potential energy surfaces (PES) can provide.…”