Review of the foundations of time-dependent density-functional theory (TDDFT)

TL;DR

This paper critically examines the theoretical foundations of time-dependent density-functional theory (TDDFT), questioning its claimed rigor and highlighting the lack of solid justification for its validity in describing electron dynamics.

Contribution

The paper provides a detailed critique of TDDFT's foundational assumptions, challenging its status as a formally rigorous approach for electron excitation calculations.

Findings

No valid justification currently exists for TDDFT

Criticism challenges the formal rigor of TDDFT

Expectations of a remedy for TDDFT are unfounded

Abstract

Time-dependent density-functional theory (TDDFT) is deemed to be a formally rigorous way of dealing with the time-evolution of a many-electron system at the level of electron densities rather than the underlying wavefunctions, which in turn provides an, in principle, exact density-based approach to the treatment of electron excitations in atoms and molecules. This claim has not remained unchallenged, and a detailed account of the relevant criticism is given in this paper. In view of our analysis one has to face the conclusion that there is currently no valid justification for TDDFT, and expectations of finding a remedy here are hardly justified.