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309 ͑1996͒. 54 16 539 GENERALIZED GRADIENT APPROXIMATION FOR THE
- Publisher
- American Physical Society (APS)
- Copyright
- Copyright © 1996 The American Physical Society
- ISSN
- 1095-3795
- DOI
- 10.1103/PhysRevB.54.16533
- Publisher site
- See Article on Publisher Site
Abstract
We construct a generalized gradient approximation (GGA) for the density n xc ( r , r + u ) at position r + u of the exchange-correlation hole surrounding an electron at r , or more precisely for its system and spherical average 〈 n xc ( u )〉=(4π ) - 1 ∫ d Ω u N - 1 ∫ d 3 r n ( r ) n xc ( r , r + u ). Starting from the second-order density gradient expansion, which involves the local spin densities n ↑ ( r ), n ↓ ( r ) and their gradients ∇ n ↑ ( r ),∇ n ↓ ( r ), we cut off the spurious large- u contributions to restore those exact conditions on the hole that the local spin density (LSD) approximation respects. Our GGA hole recovers the Perdew-Wang 1991 and Perdew-Burke-Ernzerhof GGA’s for the exchange-correlation energy, which therefore respect the same powerful hole constraints as LSD. When applied to real systems, our hole model provides a more detailed test of these energy functionals, and also predicts the observable electron-electron structure factor. © 1996 The American Physical Society.
Journal
Physical Review B – American Physical Society (APS)
Published: Dec 15, 1996