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Density Functional Theory (DFT) is widely used for atomistic simulations. However, its reach stays limited due to several limitations such as lack of accurate exchange-correlation functional, requirement of costly O(N 3) diagonalization…

The exact-exchange relativistic density functional theory (Ex-RDFT) of atomic nuclei has been solved in three-dimensional lattice space for the first time. The exchange energy is treated within the framework of the orbital-dependent…

Ensemble density functional theory (EDFT) is a promising alternative to time-dependent density functional theory for computing electronic excitation energies. Using coordinate scaling, we prove several fundamental exact conditions in EDFT…

Kohn-Sham density functional theory (DFT) is the workhorse of quantum chemistry, offering an attractive balance between accuracy and computational cost. Although exact in principle, DFT in practice relies on an approximation to the unknown…

The dynamical mean field theory (DMFT) has become a standard technique for the study of strongly correlated models and materials overcoming some of the limitations of density functional approaches based on local approximations. An important…

This chapter presents the development of a density functional theory (DFT)-based method for accurate, reliable treatment of various resonances in atoms. Many of these are known to be notorious for their strong correlation, proximity to more…

Effective field theory (EFT) methods are applied to density functional theory (DFT) as part of a program to systematically go beyond mean-field approaches to medium and heavy nuclei. A system of fermions with short-range, natural…

Density functional theory (DFT) became a universal approach to compute ground-state and excited configurations of many-electron systems held together by an external one-body potential in condensed-matter, atomic, and molecular physics. At…

In the realm of quantum chemistry, the accurate prediction of electronic structure and properties of nanostructures remains a formidable challenge. Density Functional Theory (DFT) and Density Matrix Renormalization Group (DMRG) have emerged…

The extension of the density functional theory (DFT) to include pairing correlations without formal violation of the particle-number conservation condition is described. This version of the theory can be considered as a foundation of the…

Recently, Tao and Mo proposed an accurate meta-generalized gradient approximation for the exchange-correlation energy. The exchange part is derived from the density matrix expansion, while the correlation part is obtained by improving the…

DFT calculations have become widespread in both chemistry and materials, because they usually provide useful accuracy at much lower computational cost than wavefunction-based methods. All practical DFT calculations require an approximation…

Improving the predictive capability of molecular properties in ab initio simulations is essential for advanced material discovery. Despite recent progress making use of machine learning, utilizing deep neural networks to improve quantum…

The self consistent version of the density functional theory (DFT) is presented, which allows to calculate the ground state and dynamic properties of finite multi-electron systems such as atoms, molecules and clusters. The exact functional…

Density functional theory is the workhorse of modern electronic structure calculations, with wide-ranging applications in chemistry, physics, materials science, and machine learning. At its heart lies the exchange-correlation functional, a…

Based on recent progress on fermionic exchange symmetry we propose a way to develop new functionals for reduced density matrix functional theory. For some settings with an odd number of electrons, by assuming saturation of the inequalities…

Subsystem Density-Functional Theory (DFT) is an emerging technique for calculating the electronic structure of complex molecular and condensed phase systems. In this topical review, we focus on some recent advances in this field related to…

Density functional theory (DFT) is an exact alternative formulation of quantum mechanics, in which it is possible to calculate the total energy, the spin and the charge density of many-electron systems in the ground state. In practice, it…

Density functional theory (DFT) is an indispensable ab initio method in both quantum chemistry and condensed matter physics. Based on recent advancements in reduced density matrix functional theory (RDMFT), a variant of DFT that is believed…

Recently, an approximate theoretical framework was introduced, called local reduced density matrix functional theory (local-RDMFT), where functionals of the one-body reduced density matrix (1-RDM) are minimized under the additional…