The conventional analysis of Perdew and Levy, and Sham and Schlüter shows that the functional derivative discontinuity of the exchange-correlation density functional plays a critical role in the correct prediction of bandgaps, or the chemical hardness. In a recent work by the present authors, explicit expressions for bandgap prediction with all common types of exchange-correlation functionals h...

Multi-reference effects can be covered by density functional theory (DFT) either implicitly via the exchange-correlation functional or explicitly via the form of the Kohn-Sham wave function. With the help of the exchange hole it is shown that the self-interaction error of the exchange functional will mimic long-range electron correlation effects if restricted Kohn-Sham theory is used. Functiona...

Most approximate exchange-correlation functionals used within density-functional theory are constructed as the sum of two distinct contributions for exchange and correlation. Separating the exchange component from the entire functional is useful since, for exchange, exact relations exist under uniform density scaling and spin scaling. In the past, accurate exchange-correlation potentials have b...

Natural orbitals (NOs) are central constituents for evaluating correlation energies through efficient approximations. Here, we report the closed-form expression of the NOs of two-electron quantum rings, which are prototypical finite-extension systems and new starting points for the development of exchange-correlation functionals in density functional theory. We also show that the natural occupa...

The ground-state energy, electron density, and related properties of ordinary matter can be computed efficiently when the exchange-correlation energy as a functional of the density is approximated semilocally. We propose the first meta-generalized-gradient approximation (meta-GGA) that is fully constrained, obeying all 17 known exact constraints that a meta-GGA can. It is also exact or nearly e...

The superconducting phase in iron-based high-[Formula: see text] superconductors (FeSC), as in other unconventional superconductors such as the cuprates, neighbors a magnetically ordered one in the phase diagram. This proximity hints at the importance of electron correlation effects in these materials, and Hund's exchange interaction has been suggested to be the dominant correlation effect in F...

We propose the vorticity expansion approximation VEA formulas of the exchange and correlation energy functionals of the current density functional theory CDFT . They have a form of the second-order expansion with respect to the vorticity. Expansion coefficients are determined by requiring them to satisfy exact relations that have been derived from scaling properties of exchange and correlation ...