The Role of Exact Conditions in TDDFT

TL;DR

This chapter discusses the importance of exact conditions in time-dependent density functional theory (TDDFT), highlighting their role in developing reliable approximations like ALDA and the challenges in extending beyond them.

Contribution

It emphasizes the significance of exact conditions in TDDFT and analyzes their influence on the development of approximations such as ALDA.

Findings

LDA's reliability is due to exact conditions it satisfies

ALDA plays a similar role in TDDFT as LDA does in ground-state DFT

Extending beyond ALDA with nonlocality in time remains challenging

Abstract

This chapter is devoted to exact conditions in time-dependent density functional theory. Many conditions have been derived for the exact ground-state density functional, and several have played crucial roles in the construction of popular approximations. We believe that the reliability of the most fundamental approximation of any density functional theory, the local density approximation (LDA), is due to the exact conditions that it satisfies. Improved approximations should satisfy at least those conditions that LDA satisfies, plus others. (Which others is part of the art of functional approximation). In the time-dependent case, as we shall see, the adiabatic LDA (ALDA) plays the same role as LDA in the ground-state case, as it satisfies many exact conditions. But we do not have a generally applicable improvement beyond ALDA that includes nonlocality in time. For TDDFT, we have a surfeit of exact conditions, but that only makes finding those that are useful to impose an even more demanding task.