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

TL;DR

This paper compares two non-adiabatic extensions of TDDFT, C-TDDFT and L-TDDFT, analyzing their effectiveness in modeling dynamic electron behavior beyond the adiabatic local-density approximation.

Contribution

It provides a detailed comparison and analysis of C-TDDFT and L-TDDFT, highlighting their differences and applicability in modeling non-adiabatic electron dynamics.

Findings

Non-adiabatic effects are significant during large density deformations.

C-TDDFT and L-TDDFT show qualitative and quantitative differences.

ALDA breaks down under rapid, large deformations.

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.