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HF-DFT, the practice of evaluating approximate density functionals on Hartree-Fock densities, has long been used in testing density functional approximations. Density-corrected DFT (DC-DFT) is a general theoretical framework for identifying…

Time-dependent density functional theory continues to draw a large number of users in a wide range of fields exploring myriad applications involving electronic spectra and dynamics. Although in principle exact, the predictivity of the…

We develop an ensemble density functional theory for the fractional quantum Hall effect using a local density approximation. Model calculations for edge reconstructions of a spin-polarized quantum dot give results in good agreement with…

Usually, density functional models are considered approximations to density functional theory, However, there is no systematic connection between the two, and this can make us doubt about a linkage. This attitude can be further enforced by…

When developing and assessing density functional theory methods, a finite basis set is usually employed. In most cases, however, the issue of basis set dependency is neglected. Here, we assess several basis sets and functionals. In…

Rigorous mathematical foundations of density functional theory are revisited, with some use of infinitesimal (nonstandard) methods. A thorough treatment is given of basic properties of internal energy and ground-state energy functionals…

The effective action for the charge density and the photon field is proposed as a generalization of the density functional. A simple definition is given for the density functional, as the functional Legendre transform of the generator…

In electron density functional theory formal properties of density functionals play an important role in constructing and testing approximate functionals. In this paper it is shown that a set of density functionals satisfy an equation that…

An extremely easy method for accurately calculating the adiabatic connection of density functional theory is presented, and its accuracy tested on both Hooke's atom and the He atom. The method is easy because calculations are needed only…

Many-electron systems at substantial finite temperatures and densities present a major challenge to density functional theory. Very little is known about the free-energy behavior over the temperature range of interest, for example, in the…

Fundamentals of energy density functional in nuclear physics are presented. Much attention is paid to a mathematically rigorous treatment of deriving the energy density functional. The specific features of the density functional used in…

Density-functional theory is used to study the electronic structure of quantum dots in a magnetic field. New series of magic numbers are found for the total angular momentum of electrons. The empirical formula for the plateau width is…

Density functional theory together with the Kohn-Sham scheme represent an efficient framework to recover the ground state density and energy of a many-body quantum system from an auxiliary ``non-interacting'' system (one-body with a local…

To speak about fundamental measure theory obliges to mention dimensional crossover. This feature, inherent to the systems themselves, was incorporated in the theory almost from the beginning. Although at first it was thought to be a…

The many-body problem can in general not be solved exactly, and one of the most prominent approximations is to build perturbation expansions. A huge variety of expansions is possible, which differ by the quantity to be expanded, the…

We argue in favour of developing a comprehensive dynamical theory for rationalizing, predicting, designing, and machine learning nonequilibrium phenomena that occur in soft matter. To give guidance for navigating the theoretical and…

A recently developed viewpoint on the fundamentals of density-functional theory for finite interacting spin-lattice systems that centers around the notion of degeneracy regions is presented. It allows for an entirely geometrical description…

In principle, density functional theory yields the correct ground-state densities and energies of electronic systems under the action of a static external potential. However, traditional approximations fail to include Van der Waals energies…

Understanding the thermodynamic properties of many-body quantum systems and their emergence from microscopic laws is a topic of great significance due to its profound fundamental implications and extensive practical applications. Recent…

As density functional theory conventionally assumes that the density of a chosen model system (e.g., the Kohn-Sham system) is the same as the exact one, one might expect that approximations to the exact density introduce supplementary…