Insights into Current Limitations of Density Functional Theory

  title={Insights into Current Limitations of Density Functional Theory},
  author={Aron J. Cohen and Paula Mori-S{\'a}nchez and Weitao Yang},
  pages={792 - 794}
Density functional theory of electronic structure is widely and successfully applied in simulations throughout engineering and sciences. However, for many predicted properties, there are spectacular failures that can be traced to the delocalization error and static correlation error of commonly used approximations. These errors can be characterized and understood through the perspective of fractional charges and fractional spins introduced recently. Reducing these errors will open new frontiers… 

Density‐Functional Approximations for Exchange and Correlation

Density-functional theory (DFT) is based on two pivotal theorems due to Hohenberg and Kohn [1]. The first theorem states that the ground-state density ρ(r) of a system of electrons uniquely

Replacing hybrid density functional theory: motivation and recent advances.

Six modern attempts to go beyond classical DFT while maintaining hybrid DFT's relatively low computational cost are introduced: DFT+U, self-interaction corrections, localized orbital scaling corrections, local hybrid functionals, real-space nondynamical correlation, and the rung-3.5 approach.

Perspective: Fundamental aspects of time-dependent density functional theory.

  • N. Maitra
  • Physics
    The Journal of chemical physics
  • 2016
This Perspective looks back to some of these developments, reports on some recent progress and current challenges for functionals, and speculates on future directions to improve the accuracy of approximations used in this relatively young theory.

Fragment-based treatment of delocalization and static correlation errors in density-functional theory.

This work demonstrates how these errors, which plague density-functional calculations of bond-stretching processes, can be avoided by employing the alternative framework of partition density- functional theory (PDFT) even using the local density approximation for the fragments.

Unified formulation of fundamental and optical gap problems in density-functional theory for ensembles

Solving the fundamental and optical gap problems, which yield information about charged and neutral excitations in electronic systems, is one of the biggest challenge in density-functional theory

Delocalization error of density-functional approximations: a distinct manifestation in hydrogen molecular chains.

This work demonstrates unambiguously the effect of delocalization error on a series of hydrogen molecular chains and elucidate the underlying relationship between the error magnitude and system geometry.

The self-interaction error and the description of non-dynamic electron correlation in density functional theory

The self-interaction error (SIE) plays a central role in density functional theory (DFT) when carried out with approximate exchange-correlation functionals. Its origin, properties, and consequences

Anomalous scaling and breakdown of conventional density functional theory methods for the description of Mott phenomena and stretched bonds

Density functional theory provides the most widespread framework for the realistic description of the electronic structure of solids, but the description of strongly correlated systems has remained

Electronic responses of long chains to electrostatic fields: Hartree-Fock vs. density-functional theory: a model study.

The response to an electrostatic field is determined through simple model calculations, within both the restricted Hartree-Fock and density functional theory methods, for long, finite as well as

DFT: A Theory Full of Holes?

A rough, quirky overview of both the history and present state of the art of density functional theory focuses on the underlying exact theory, the origin of approximations, and the tension between empirical and nonempirical approaches.



Self-interaction errors in density-functional calculations of electronic transport.

A simple and computationally undemanding atomic self-interaction correction (SIC) opens conduction gaps in I-V characteristics that otherwise are predicted metallic, as in the case of the prototype Au/ditholated-benzene/Au junction.

Localization and delocalization errors in density functional theory and implications for band-gap prediction.

The band-gap problem and other systematic failures of approximate exchange-correlation functionals are explained from an analysis of total energy for fractional charges and identifies the physical nature of the error to be addressed to obtain accurate band gaps from density functional theory.

Density-functional theory of atoms and molecules

Current studies in density functional theory and density matrix functional theory are reviewed, with special attention to the possible applications within chemistry. Topics discussed include the

Exact exchange-correlation treatment of dissociated H(2) in density functional theory.

This work proposes an orbital dependent exchange-correlation functional that yields this exact Kohn-Sham solution and offers an alternative to local-density and generalized gradient approximations and the prospects are indicated for treating with it some outstanding problems in density functional theory.

Many-electron self-interaction error in approximate density functionals.

After identifying the sufficient condition for functionals to be free from SIE, the focus on the symptoms and investigate the performance of most popular functionals, which show that these functionals suffer from many-electron SIE.

Accurate polymer polarizabilities with exact exchange density-functional theory

The long-standing problem of the large overestimation of polymer polarizabilities in density-functional theory is reexamined and largely solved using an exact exchange method. We have built an

Role of the exchange-correlation potential in ab initio electron transport calculations.

The effect of the exchange-correlation potential in ab initio electron transport calculations is investigated by constructing optimized effective potentials using different energy functionals or the

Self-Consistent Equations Including Exchange and Correlation Effects

From a theory of Hohenberg and Kohn, approximation methods for treating an inhomogeneous system of interacting electrons are developed. These methods are exact for systems of slowly varying or high

Self-interaction correction to density-functional approximations for many-electron systems

exchange and correlation, are not. We present two related methods for the self-interaction correction (SIC) of any density functional for the energy; correction of the self-consistent one-electron

Fractional charge perspective on the band gap in density-functional theory

The calculation of the band gap by density-functional theory (DFT) is examined by considering the behavior of the energy as a function of number of electrons. It is explained that the incorrect