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The systematic underestimation of band gaps is one of the most fundamental challenges in semilocal density functional theory (DFT). In addition to hindering the application of DFT to predicting electronic properties, the band gap problem is…
In electronic structure methods based on the correction of approximate density-functional theory (DFT) for systematic inaccuracies, Hubbard $U$ parameters may be used to quantify and amend the self-interaction errors ascribed to selected…
Semi-local DFT methods exhibit significant errors for the phase diagrams of transition-metal oxides that are caused by an incorrect description of molecular oxygen and the large self-interaction error in materials with strongly localized…
We derive an exact representation of the exchange-correlation energy within density functional theory (DFT) which spawns a class of approximations leading to correct long-range asymptotic behavior. In what amounts to be the simplest…
The band-gap problem and other systematic failures of approximate functionals are explained from an analysis of total energy for fractional charges. The deviation from the correct intrinsic linear behavior in finite systems leads to…
A critical challenge for density functional theory (DFT) in practice is its limited ability to treat static electron correlation, leading to errors in its prediction of charges, multiradicals, and reaction barriers. Recently, we combined…
We propose a method that incorporates explicit derivative discontinuity of the total energy with respect to the number of electrons and treats both delocalization and static correlation effects in density functional calculations. Our…
A systematic comparative study has been performed to better understand DFT$+U$ (density functional theory + $U$) method. We examine the effect of choosing different double counting and exchange-correlation functionals. The calculated energy…
Hubbard-corrected density functional theory, denoted by DFT+U method, was developed to enable correct prediction of insulating properties for strongly-correlated electron systems. UO$_2$ is an example having O-$2p$, U-$6d$, and U-$5f$…
Density functional theory (DFT) is the most promising method for calculating quantum properties of molecules and materials at moderate and large scales. However, commonly used density functional approximations (DFAs) have systematic…
We argue that any general mathematical measure of density error, no matter how reasonable, is too arbitrary to be of universal use. However the energy functional itself provides a universal relevant measure of density errors. For the…
Density functional theory (DFT) is used in thousands of papers each year, yet lack of universality reduces DFT's predictive capacity, and functionals may produce energy-density imbalances. The absolute electronegativity (\chi) and hardness…
Density-functional theory (DFT) has revolutionized computer simulations in chemistry and material science. A faithful implementation of the theory requires self-consistent calculations. However, this effort involves repeatedly diagonalizing…
Practical density functional theory (DFT) owes its success to the groundbreaking work of Kohn and Sham that introduced the exact calculation of the non-interacting kinetic energy of the electrons using an auxiliary mean-field system.…
Density functional theory (DFT) has been widely applied to a variety of realistic materials but often struggles to explain the properties of correlated systems. The DFT + U method, which introduces a Hubbard U correction to the DFT, has…
We develop a generalization of the Kohn-Sham density functional theory (KS-DFT) + Hubbard $U$ (DFT+$U$) method to the excited-state regime. This has the form of Hubbard $U$ corrected linear-response time-dependent DFT, or `TDDFT+$U$'.…
We review the role of self-consistency in density functional theory. We apply a recent analysis to both Kohn-Sham and orbital-free DFT, as well as to Partition-DFT, which generalizes all aspects of standard DFT. In each case, the analysis…
Many-body theories such as dynamical mean field theory (DMFT) have enabled the description of the electron exchange-correlation interactions that are missing in current density functional theory (DFT) calculations. However, there has been…
In their famous paper Kohn and Sham formulated a formally exact density-functional theory (DFT) for the ground-state energy and density of a system of $N$ interacting electrons, albeit limited at the time by certain troubling…
The delocalization error of popular density functional approximations (DFAs) leads to diversified problems in present-day density functional theory calculations. For achieving a universal elimination of delocalization error, we develop a…