Perspective: Fundamental aspects of time-dependent density functional theory

Area of Science:

• Computational Chemistry
• Quantum Physics
• Materials Science

Background:

• Time-dependent density functional theory (TDDFT) has been foundational for electronic spectra and dynamics calculations for over three decades.
• TDDFT has broad applications in chemistry, biology, solid-state physics, and materials science.

Purpose of the Study:

• To review the historical developments of TDDFT.
• To discuss current challenges and recent progress in TDDFT functionals.
• To speculate on future research directions for enhancing TDDFT accuracy.

Main Methods:

• Review of foundational theorems and theoretical advancements in TDDFT.
• Analysis of current state-of-the-art TDDFT functionals.
• Exploration of potential future approximations and methodologies.

Main Results:

• TDDFT has profoundly impacted computational studies in various scientific disciplines.
• Significant progress has been made in understanding the fundamental aspects of TDDFT functionals.
• Current challenges remain in achieving higher accuracy for approximations.

Conclusions:

• TDDFT is a vital and evolving theory with a rich history.
• Continued research is necessary to address existing challenges and improve functional accuracy.
• Future directions aim to enhance the predictive power of TDDFT for complex systems.