Density functional theory is straying from the path toward the exact functional

  title={Density functional theory is straying from the path toward the exact functional},
  author={Michael G. Medvedev and Ivan S. Bushmarinov and Jianwei Sun and John P. Perdew and Konstantin A. Lyssenko},
  pages={49 - 52}
Whither the density in DFT calculations? The continuing development of density functional theory (DFT) has greatly expanded the size and complexity of molecules amenable to computationally tractable simulation. The conventional metric of success for new functionals has been the accuracy of their calculated energies. Medvedev et al. examined how well these functionals calculate electron density across a series of neutral and cationic atoms (see the Perspective by Hammes-Schiffer). Although… 

Electron Density Errors and Density-Driven Exchange-Correlation Energy Errors in Approximate Density Functional Calculations.

A molecular test set with chemically relevant densities is constructed and the performance of several density functional approximations including the less-investigated double hybrids are analyzed, seeking for a rationale behind the global hybrid or double hybrid methods from the density's point of view.

Improving Results by Improving Densities: Density-Corrected Density Functional Theory.

Density functional theory (DFT) calculations have become widespread in both chemistry and materials, because they usually provide useful accuracy at much lower computational cost than

Density functional orbitals in quantum Monte Carlo: The importance of accurate densities.

It is found that the accuracy of the density is a strong indicator of the quality of the many-body nodal surface produced by a determinant of the corresponding Kohn-Sham orbitals, and suggests that prioritizing accurate densities in the future development of DFAs would also contribute to the continued improvement of DMC.

Introductory lecture: when the density of the noninteracting reference system is not the density of the physical system in density functional theory.

This work develops the expressions for the electron density so defined through the linear response for general DFAs, demonstrates the results for orbital functionals and for many-body perturbation theory within the second-order and the random-phase approximation, and explores the connections to developments in DFT.

Density functional analysis: The theory of density-corrected DFT.

This paper provides the formal theoretical framework and assumptions for the analysis of any functional minimization with an approximate functional, and generalizes DC-DFT to allow comparison of any two functionals, not just comparison with the exact functional.

Exact exchange-correlation potentials from ground-state electron densities

This work presents a numerically robust and accurate scheme to evaluate the exact exchange-correlation potentials from correlated ab-initio densities, and proposes an approach for an accurate solution to the inverse DFT problem.

Self-Consistent Density-Functional Embedding: A Novel Approach for Density-Functional Approximations

In the present work, we introduce a self-consistent density-functional embedding technique, which leaves the realm of standard energy-functional approaches in density functional theory and targets

Orbital-free density functional theory correctly models quantum dots when asymptotics, nonlocality, and nonhomogeneity are accounted for

Million-atom quantum simulations are in principle feasible with Orbital-Free Density Functional Theory (OF-DFT) because the algorithms only require simple functional minimizations with respect to the

Machine learning accurate exchange and correlation functionals of the electronic density

This work proposes a framework to create density functionals using supervised machine learning, termed NeuralXC, designed to lift the accuracy of baseline functionals towards that provided by more accurate methods while maintaining their efficiency.

Ab initio construction of the energy density functional for electron systems with the functional-renormalization-group-aided density functional theory

We show an $\textit{ab initio}$ construction of the energy density functional (EDF) for electron systems using the functional renormalization group. The correlation energies of the homogeneous



The densities produced by the density functional theory: comparison to full configuration interaction.

It is reasoned how functionals such as B3LYP, despite being quite average for density, could still be very successful in predicting thermodynamic properties by reasoning how CCSD theory itself starts to break down.

Semilocal density functional obeying a strongly tightened bound for exchange

This article presents a realistic “meta-GGA made very simple” (MGGA-MVS) for exchange that respects this optimal bound on the exchange energy, which no previous beyond-LSDA approximation satisfies.

Density functionals with broad applicability in chemistry.

This Account compared the performance of the M06-class functionals and one M05-class functional (M05-2X) to that of some popular functionals for diverse databases and their performance on several difficult cases.

Simple tests for density functional methods

The analysis of the exact KS potential at the bond critical point of the dissociating H 2 molecule shows that, for this property, the second order Moller]Plesset perturbation theory yields a better potential than the density functionals studied in this article.

Quest for a universal density functional: the accuracy of density functionals across a broad spectrum of databases in chemistry and physics

  • R. PeveratiD. Truhlar
  • Chemistry
    Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
  • 2014
A set of databases of reference data for a variety of energetic and structural properties in chemistry and physics is developed, and two wave function methods and 77 density functionals are tested in a consistent way across this same broad set of data.

An extended hybrid density functional (X3LYP) with improved descriptions of nonbond interactions and thermodynamic properties of molecular systems.

The form for the exact exchange energy density for a density that decays with Gaussian-type behavior at long range is derived and the X3LYP extended functional is proposed, which significantly enlarges the field of applications for density functional theory.

A density difference based analysis of orbital-dependent exchange-correlation functionals

We present a density difference based analysis for a range of orbital-dependent Kohn–Sham functionals. Results for atoms, some members of the neon isoelectronic series and small molecules are

Accurate first-principles structures and energies of diversely bonded systems from an efficient density functional.

It is shown that the recently developed non-empirical strongly constrained and appropriately normed SCAN meta-generalized gradient approximation (meta-GGA) within the density functional theory framework predicts accurate geometries and energies of diversely bonded molecules and materials.

Universal variational functionals of electron densities, first-order density matrices, and natural spin-orbitals and solution of the v-representability problem.

  • M. Levy
  • Chemistry
    Proceedings of the National Academy of Sciences of the United States of America
  • 1979
The v-representability problem, which is especially severe for trial first-order density matrices, has been solved and universal variational functionals in Hartree-Fock and other restricted wavefunction theories are presented.

Atoms, molecules, solids, and surfaces: Applications of the generalized gradient approximation for exchange and correlation.

A way is found to visualize and understand the nonlocality of exchange and correlation, its origins, and its physical effects as well as significant interconfigurational and interterm errors remain.