Non-adiabatic electron dynamics in time-dependent density-functional theory

Abstract

Time-dependent density-functional theory (TDDFT) treats dynamical exchange and correlation (xc) via a single-particle potential, Vxc(r,t), defined as a nonlocal functional of the density n(r',t'). The popular adiabatic local-density approximation (ALDA) for Vxc(r,t) uses only densities at the same space-time point (r,t). To go beyond the ALDA, two local approximations have been proposed based on quantum hydrodynamics and elasticity theory: (a) using the current as basic variable (C-TDDFT) [G. Vignale, C. A. Ullrich, and S. Conti, Phys. Rev. Lett. 79, 4878 (1997)], (b) working in a co-moving Lagrangian reference frame (L-TDDFT) [I. V. Tokatly, Phys. Rev. B 71, 165105 (2005)]. This paper illustrates, compares, and analyzes both non-adiabatic theories for simple time-dependent model densities in the linear and nonlinear regime, for a broad range of time and frequency scales. C- and L-TDDFT are identical in certain limits, but in general exhibit qualitative and quantitative differences in their respective treatment of elastic and dissipative electron dynamics. In situations where the electronic density rapidly undergoes large deformations, it is found that non-adiabatic effects can become significant, causing the ALDA to break down.

15 pages, 15 figures

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• A brief compendium of time-dependent density-functional theory
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• Real-time electron dynamics with exact-exchange time-dependent density-functional theory
• Time-dependent V-representability on lattice systems
• Density-driven correlations in many-electron ensembles: theory and application for excited states
• Time-dependent deformation functional theory
• Understanding real-time time-dependent density-functional theory simulations of ultrafast laser-induced dynamics in organic molecules
• Adiabatic approximation in time-dependent reduced-density-matrix functional theory
• Non-Adiabatic Approximations in Time-Dependent Density Functional Theory: Progress and Prospects
• Perspective: How to overcome dynamical density functional theory
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• Some open questions in TDDFT: Clues from Lattice Models and Kadanoff-Baym Dynamics
• Noether-Constrained Correlations in Equilibrium Liquids
• Physical signatures of discontinuities of the time-dependent exchange-correlation potential
• Force balance in thermal quantum many-body systems from Noether's theorem
• The generator coordinate method in time-dependent density-functional theory: memory made simple
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• Excitonic effects in time-dependent density functional theory from zeros of the density response
• Nonadiabatic time-dependent density-functional theory at the cost of adiabatic local density approximation
• Electronic excited states in deep variational Monte Carlo