# 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…

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## 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.