Exploring non-adiabatic approximations to the exchange-correlation functional of TDDFT

Abstract

A decomposition of the exact exchange-correlation potential of time-dependent density functional theory into an interaction component and a kinetic component offers a new starting point for non- adiabatic approximations. The components are expressed in terms of the exchange-correlation hole and the difference between the one-body density matrix of the interacting and Kohn-Sham systems, which must be approximated in terms of quantities accessible from the Kohn-Sham evolution. We explore several preliminary approximations, evaluate their fulfillment of known exact conditions, and test their performance on simple model systems for which available exact solutions indicate the significance of going beyond the adiabatic approximation.

arXiv comment16 pages, 10 figures

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• Accurate Relativistic Real-Time Time-Dependent Density Functional Theory for Valence and Core Attosecond Transient Absorption Spectroscopy
• Propagation of maximally localized Wannier functions in real-time TDDFT
• A reformulation of time-dependent Kohn-Sham theory in terms of the second time derivative of the density
• Nonlocal and nonadiabatic Pauli potential for time-dependent orbital-free density functional theory
• The Exact Exchange-Correlation Potential in Time-Dependent Density Functional Theory: Choreographing Electrons with Steps and Peaks
• Exchange energies with forces in density-functional theory
• Exact time-dependent density functional theory for non-perturbative dynamics of helium atom
• Excitonic effects in time-dependent density functional theory from zeros of the density response
• Real-time ab initio simulation of inelastic electron scattering using the exact, density functional, and alternative approaches
• Impact of free electron degeneracy on collisional rates in plasmas
• Strengths and limitations of the adiabatic exact-exchange kernel for total energy calculations
• Local-density correlation functional from the force-balance equation