# Prescription for the design and selection of density functional approximations: more constraint satisfaction with fewer fits.

@article{Perdew2005PrescriptionFT, title={Prescription for the design and selection of density functional approximations: more constraint satisfaction with fewer fits.}, author={John P. Perdew and Adrienn Ruzsinszky and Jianmin Tao and Viktor N. Staroverov and Gustavo E. Scuseria and G{\'a}bor I. Csonka}, journal={The Journal of chemical physics}, year={2005}, volume={123 6}, pages={ 62201 } }

We present the case for the nonempirical construction of density functional approximations for the exchange-correlation energy by the traditional method of "constraint satisfaction" without fitting to data sets, and present evidence that this approach has been successful on the first three rungs of "Jacob's ladder" of density functional approximations [local spin-density approximation (LSD), generalized gradient approximation (GGA), and meta-GGA]. We expect that this approach will also prove…

## Figures from this paper

## 701 Citations

Construction of a generalized gradient approximation by restoring the density-gradient expansion and enforcing a tight Lieb-Oxford bound.

- ChemistryThe Journal of chemical physics
- 2008

A new GGA is constructed that has no empirical parameters, that satisfies one more exact constraint than PBEsol, and that performs 20% better for the lattice constants of 18 previously studied solids, although it does not improve on PBE solids for molecular atomization energies (a property that neither functional was designed for).

Density-functional expansion methods: evaluation of LDA, GGA, and meta-GGA functionals and different integral approximations.

- Materials ScienceThe Journal of chemical physics
- 2010

The results suggest that the origin of the short-range repulsive potential within self-consistent charge density-functional tight-binding methods mainly arises from the approximations made to the first-order matrix elements.

Hyper-generalized-gradient functionals constructed from the Lieb-Oxford bound: implementation via local hybrids and thermochemical assessment.

- PhysicsThe Journal of chemical physics
- 2012

OC-lh correlation with exact exchange yields rather accurate energy barriers for chemical reactions, and the importance of near-self-consistency for fully nonlocal functionals is discussed.

A computationally efficient double hybrid density functional based on the random phase approximation.

- ChemistryPhysical chemistry chemical physics : PCCP
- 2016

Structural optimizations of small molecules with PWRB95 indicate an accurate description of bond distances superior to that provided by TPSS-D3, PBE0- D3, or other RPA type methods.

Self-consistent implementation of meta-GGA functionals for the ONETEP linear-scaling electronic structure package.

- Computer ScienceThe Journal of chemical physics
- 2016

This paper lays out the theoretical innovations necessary to implement τ-dependent meta-GGA functionals within ONETEP's linear-scaling formalism, and presents the outcome of self-consistent meta- GGA calculations on amyloid fibrils of increasing size, up to tens of thousands of atoms.

Performance of a nonempirical meta-generalized gradient approximation density functional for excitation energies.

- Chemistry, PhysicsThe Journal of chemical physics
- 2008

It is confirmed that TPSS is indeed a reliable nonhybrid universal functional which can serve as the starting point from which higher-level approximations can be constructed and the systematic underestimate of the low-lying vertical excitation energies of molecules with time-dependent density functionals within the adiabatic approximation suggests that further improvement can be made with nonadiabatic corrections.

Analytic derivatives for perturbatively corrected "double hybrid" density functionals: theory, implementation, and applications.

- ChemistryThe Journal of chemical physics
- 2007

The results reveal that the B2-PLYP functional provides excellent molecular geometries that are superior compared to those from standard DFT and MP2.

Simple Modifications of the SCAN Meta-Generalized Gradient Approximation Functional.

- PhysicsJournal of chemical theory and computation
- 2018

It is concluded that the SCAN meta-generalized gradient approximation density functional can be modified to separately reproduce the exchange and correlation energies of the helium atom by locally releasing the strongly tightened lower bound for the exchange energy density in single-orbital regions, but this leads to an unbalanced improvement in the single- orbital electron densities.

Nonempirical density functionals investigated for jellium: Spin polarized surfaces, spherical clusters, and bulk linear response

- Physics
- 2008

Earlier tests show that the Tao-Perdew-Staroverov-Scuseria (TPSS) nonempirical meta-generalized gradient approximation (meta-GGA) for the exchange-correlation energy yields more accurate surface…

Functional derivatives of meta-generalized gradient approximation (meta-GGA) type exchange-correlation density functionals.

- ChemistryThe Journal of chemical physics
- 2013

The TDDFT working equations for meta-GGA density functionals are presented here for the first time, together with the technical details of their computer implementation.

## References

SHOWING 1-10 OF 111 REFERENCES

Tests of a ladder of density functionals for bulk solids and surfaces

- Physics
- 2004

The local spin-density approximation (LSDA) and the generalized gradient approximation (GGA) of Perdew, Burke, and Ernzerhof (PBE) are fully non-empirical realizations of the first two rungs of…

Meta-generalized gradient approximation: explanation of a realistic nonempirical density functional.

- PhysicsThe Journal of chemical physics
- 2004

It is suggested that satisfaction of additional exact constraints on higher rungs of a ladder of density functional approximations can lead to further progress in the meta-GGA.

Generalized Gradient Approximation Made Simple.

- ChemistryPhysical review letters
- 1996

A simple derivation of a simple GGA is presented, in which all parameters (other than those in LSD) are fundamental constants, and only general features of the detailed construction underlying the Perdew-Wang 1991 (PW91) GGA are invoked.

Simple tests for density functional methods

- ChemistryJ. Comput. Chem.
- 1997

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.

Evaluating density functional performance for the quasi-two-dimensional electron gas

- Physics
- 2000

The exchange-correlation energy Exc is a significant part of the total energy of the quasi-two-dimensional electron gas. We investigate the performance of three-dimensional density functionals Exc [n…

Density functional for short-range correlation: Accuracy of the random-phase approximation for isoelectronic energy changes

- Physics
- 2000

Within a density-functional context, the random-phase approximation ~RPA! for the correlation energy makes a short-range error that is well suited for correction by a local spin density or…

Climbing the density functional ladder: nonempirical meta-generalized gradient approximation designed for molecules and solids.

- PhysicsPhysical review letters
- 2003

This work constructs a meta-GGA density functional for the exchange-correlation energy that satisfies exact constraints without empirical parameters, and describes both molecules and solids with high accuracy, as shown by extensive numerical tests.

Assessment of the Perdew–Burke–Ernzerhof exchange-correlation functional

- Chemistry
- 1999

In order to discriminate between approximations to the exchange-correlation energy EXC[ρ↑,ρ↓], we employ the criterion of whether the functional is fitted to a certain experimental data set or if it…

Size-Consistency, Self-Interaction Correction, and Derivative Discontinuity in Density Functional Theory

- Chemistry
- 1990

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

- PhysicsPhysical review. B, Condensed matter
- 1992

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.