Density functional theory: foundations, challenges, and new horizons in the quantum mechanics of atoms, molecules, and solids - Barbosa, Matheus; Villegas-Lelovsky, Leonardo; Torres, Alberto; Barros de Oliveira, Alan; Souza, Amaury; R. L. Galvao, Breno; R. Rocha, Alexandre; S. C. Mazzoni, Mário; Matos, Matheus (Cadernos de Astronomia, 2025)
On the centennial of quantum mechanics, this work provides a comprehensive review of the theoretical foundations, current challenges, and emerging frontiers in many-body quantum theory, with particular emphasis on Density Functional Theory (DFT), the GW approximation, and their applications in fields such as astronomy and in novel methodologies grounded in Machine Learning (ML) and evolutionary algorithms. By surveying these diverse applications, from astrophysical systems to artificial intelligence, we underscore the inherently interdisciplinary character of this sixty-year-old framework, which continues to be indispensable for advancing our understanding of the properties of matter and for driving technological innovation.
Keywords: Density Functional Theory; Electronic Structure; Condensed Matter Physics; Hohenberg-Kohn Theorem; Machine learning; evolutionary algorithms