Generalized Gradient Approximation Made Simple.

@article{Perdew1996GeneralizedGA,
  title={Generalized Gradient Approximation Made Simple.},
  author={Perdew and Burke and Ernzerhof},
  journal={Physical review letters},
  year={1996},
  volume={77 18},
  pages={
          3865-3868
        }
}
Generalized gradient approximations (GGA’s) for the exchange-correlation energy improve upon the local spin density (LSD) description of atoms, molecules, and solids. We present a simple derivation of a simple GGA, in which all parameters (other than those in LSD) are fundamental constants. Only general features of the detailed construction underlying the Perdew-Wang 1991 (PW91) GGA are invoked. Improvements over PW91 include an accurate description of the linear response of the uniform… 

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References

SHOWING 1-10 OF 13 REFERENCES

ElectronicStructureof Solids‘91, edited Í by : P

  • Ziescheand H. Eschrig(AkademieVerlag, Berlin,
  • 1991

J. Comput. Chem

  • J. Comput. Chem
  • 1997

Phys. Rev. Lett. Phys. Rev. Lett

  • Phys. Rev. Lett. Phys. Rev. Lett
  • 1993

Geometriesof NO, ClB and PC

  • Chem. Soc. 101,
  • 1979

Phys. Rev. B

  • Phys. Rev. B
  • 1994

Mol. Phys

  • Mol. Phys
  • 1996

Permanent address: Department of Chemistry

  • Permanent address: Department of Chemistry

J. Chem. Phys

  • J. Chem. Phys
  • 1994