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The time-dependent density functional theory (TDDFT) and the many-body perturbation method (GW@BSE) are considered as the two most popular and successful methods to describe the excited-stated properties of materials. In fact, both methods have been reviewed in this classical paper published in the Review of Morden Physics. From that almost twenty years have passed. What are the recent developments of TDDFT? What's the most popular and successful package that implements TDDFT? And what're the main challenges to realize the simulation of real materials with TDDFT?

Disclaimer: According to the one-topic-per-answer, a twin question related to the GW@BSE method is asked in another post. But any comparisons between both methods in recent developments are welcome.

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Time-dependent density functional theory (TDDFT) has indeed seen significant developments since its review in the classical paper you mentioned. One of the recent advancements in TDDFT is:

  1. Nonlinear Response Functions
  • In the context of Time-Dependent Density Functional Theory (TDDFT), Nonlinear response functions refer to the exploration of phenomena beyond linear response properties. While traditional TDDFT focuses on linear response, there has been increasing interest in investigating nonlinear optical processes and strong light-matter interactions using TDDFT. This extension allows for the study of phenomena such as harmonic generation, two-photon absorption, and higher-order nonlinear optics. Nonlinear TDDFT has been applied to gain insights into materials with significant light-matter interactions. For example, a study https://doi.org/10.1063/1.4867271 published by Federico Zahariev and Mark S. Gordon. in the Journal of Chemical Phyiscs (2014) titled "Nonlinear response time-dependent density functional theory combined with the effective fragment potential method" investigated the calculattio of the two-photon absorption cross section and incorporated solvent effects via the EFP method. The nonlinear-response TDDFT/EFP method was shown to be able to make correct qualitative predictions for both gas phase values and aqueous solvent shifts of several important nonlinear properties. The package that was used in this study was GAMESS.

Among the challenges in realizing the simulation of real materials with TDDFT, strongly correlated systems is challenging.

  • Strongly correlated systems pose a challenge for TDDFT due to the intricate electron-electron interactions involved. Examples of such systems include transition metal complexes and strongly correlated materials, where the standard TDDFT approach may not be sufficient to capture their properties accurately. To address the treatment of strongly correlated systems within TDDFT, researchers have explored advanced theoretical approaches, such as the combination of TDDFT with dynamical mean-field theory (DMFT). This hybrid approach aims to incorporate the effects of strong electron-electron correlations, which are crucial for accurately describing the electronic structure and excited states of these systems. A study https://doi.org/10.1103/PhysRevLett.106.116401 published by Daniel Karlsson et al. in Physical Review Letters (2011) titled "Time-Dependent Density-Functional Theory Meets Dynamical Mean-Field Theory: Real-Time Dynamics for the 3D Hubbard Model". The authors proposed a new class of exchange-correlation potentials for a static and time-dependent density-functional theory of strongly correlated systems in three-dimensions Those studies exemplify the ongoing efforts to develop theoretical approaches that extend TDDFT to treat strongly correlated systems accurately. The combination of TDDFT with advanced methods like DMFT offers a promising avenue for understanding the electronic structure and excited states of materials with strong electron-electron correlations.

Regarding the most popular and successful package that implements TDDFT, there are several widely used software packages available, each with its own strengths and capabilities. Some of the popular packages include:

  • Gaussian: Widely used computational chemistry software that offers TD-DFT functionality. It provides a comprehensive suite of methods for studying excited-state properties, including UV/Vis spectra, fluorescence, and excited-state dynamics. Gaussian is known for its versatility and extensive user community.
  • GPAW: GPAW (Generalized Projector Augmented Wave) is a popular electronic structure code that implements TDDFT. It is known for its efficiency and scalability, making it suitable for large-scale simulations.
  • NWChem: NWChem is a computational chemistry package that includes TDDFT functionality. It offers a wide range of methods, including both TDDFT and GW calculations, making it versatile for studying excited-state properties.
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  • $\begingroup$ I gave you +1, but I encourage you though to look at some of our other questions with the one-topic-per-answer tag, such as this one. Notice how all the answers go into detail about one topic? With the way that you have written this answer, it leaves not much room nor motivation for others to write an answer because it looks like all that there is to be said, has been mentioned already. Instead, do you think you can pick one of these recent developments, and go into the amount of detail that we see for example in the above link? Thanks! $\endgroup$
    – Nike Dattani - No Free Time
    Commented Nov 7, 2023 at 3:52
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    $\begingroup$ I got your point, I will modify the answer $\endgroup$
    – Jaafar Mehrez
    Commented Nov 7, 2023 at 4:46

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