Symmetric Nonlocal Weighted Density Approximations from the Exchange-Correlation Hole of the Uniform Electron Gas Academic Article uri icon

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  • Nonlocal exchange-correlation energy functionals are constructed using the accurate model exchange-correlation hole for the uniform electron gas developed by Gori-Giorgi and Perdew. The exchange-correlation hole is constrained to be symmetric and normalized, so the resulting functionals can be viewed as symmetrized versions of the weighted density approximation; we call them two-point weighted density approximations. Even without optimization of parameters or functional forms, the exchange-correlation energies for small molecules are competitive with those of the best generalized gradient approximation functionals. Two-point weighted density approximations seem to be an interesting new direction for functional development. A more general version of the conditions that define the energy for fractional electron number and fractional spin are presented. These "generalized flat-planes" conditions are closely linked to the normalization of the spin-resolved exchange-correlation hole at noninteger electron number. This and many other properties of the exact exchange-correlation functional can be imposed straightforwardly and directly in symmetrized weighted density approximation.


  • Cuevas-Saavedra, Rogelio
  • Chakraborty, Debajit
  • Rabi, Sandra
  • Cárdenas, Carlos
  • Ayers, Paul

publication date

  • November 13, 2012