Chapter

Density Functional Theory I

Volume 180 of the series Topics in Current Chemistry pp 1-30

Date:

Density functionals: Where do they come from, why do they work?

  • Matthias ErnzerhofAffiliated withDepartment of Physics and Quantum Theory Group, Tulane University
  • , John P. PerdewAffiliated withDepartment of Physics and Quantum Theory Group, Tulane University
  • , Kieron BurkeAffiliated withDepartment of Physics and Quantum Theory Group, Tulane University

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Abstract

Gradient-corrected or semi-local functionals (GGA's) have achieved the accuracy required to make density functional theory a useful tool in quantum chemistry. We show that local (LSD) and semi-local functionals work because they usefully model the exchange-correlation hole around an average electron, rather than by yielding accurate results at all electron positions. We discuss the system-averaged hole at small interelectronic separations, where such functionals are extremely accurate, and at large interelectronic separations, where the local approximation is incorrect for finite systems. We argue that the “on-top” hole density provides the missing link between real atoms and molecules and the uniform electron gas. We show how exchange-correlation potentials can be related to energies. We also discuss how the degree of nonlocality, i.e., the error made by LSD, is related to the spatial extent of the hole. Decomposing the energy by coupling-constant and spin, we find that the deeper the on-top hole is, the smaller the error in the local approximation to the energy. We use this insight to demonstrate that Hartree-Fock hybrid functionals do not consistently improve on GGA. A different hybrid invokes wavefunction methods for exchange and parallel-spin correlation, but we show that configuration interaction wavefunction calculations with limited basis sets for the Ne atom make the same relative errors in the antiparallel- and parallel-spin correlation energies, despite the lack of a Coulomb cusp in the parallel-spin correlation hole. Finally, we review a recent reinterpretation of spin density functional theory, which is preferable to the standard interpretation in certain cases of extreme nonlocality.