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Extension of many-body theory and approximate density functionals to fractional charges and fractional spins.

Publication ,  Journal Article
Yang, W; Mori-Sánchez, P; Cohen, AJ
Published in: The Journal of chemical physics
September 2013

The exact conditions for density functionals and density matrix functionals in terms of fractional charges and fractional spins are known, and their violation in commonly used functionals has been shown to be the root of many major failures in practical applications. However, approximate functionals are designed for physical systems with integer charges and spins, not in terms of the fractional variables. Here we develop a general framework for extending approximate density functionals and many-electron theory to fractional-charge and fractional-spin systems. Our development allows for the fractional extension of any approximate theory that is a functional of G(0), the one-electron Green's function of the non-interacting reference system. The extension to fractional charge and fractional spin systems is based on the ensemble average of the basic variable, G(0). We demonstrate the fractional extension for the following theories: (1) any explicit functional of the one-electron density, such as the local density approximation and generalized gradient approximations; (2) any explicit functional of the one-electron density matrix of the non-interacting reference system, such as the exact exchange functional (or Hartree-Fock theory) and hybrid functionals; (3) many-body perturbation theory; and (4) random-phase approximations. A general rule for such an extension has also been derived through scaling the orbitals and should be useful for functionals where the link to the Green's function is not obvious. The development thus enables the examination of approximate theories against known exact conditions on the fractional variables and the analysis of their failures in chemical and physical applications in terms of violations of exact conditions of the energy functionals. The present work should facilitate the calculation of chemical potentials and fundamental bandgaps with approximate functionals and many-electron theories through the energy derivatives with respect to the fractional charge. It should play an important role in developing accurate approximate density functionals and many-body theory.

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Published In

The Journal of chemical physics

DOI

EISSN

1089-7690

ISSN

0021-9606

Publication Date

September 2013

Volume

139

Issue

10

Start / End Page

104114

Related Subject Headings

  • Chemical Physics
  • 51 Physical sciences
  • 40 Engineering
  • 34 Chemical sciences
  • 09 Engineering
  • 03 Chemical Sciences
  • 02 Physical Sciences
 

Citation

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Yang, W., Mori-Sánchez, P., & Cohen, A. J. (2013). Extension of many-body theory and approximate density functionals to fractional charges and fractional spins. The Journal of Chemical Physics, 139(10), 104114. https://doi.org/10.1063/1.4817183
Yang, Weitao, Paula Mori-Sánchez, and Aron J. Cohen. “Extension of many-body theory and approximate density functionals to fractional charges and fractional spins.The Journal of Chemical Physics 139, no. 10 (September 2013): 104114. https://doi.org/10.1063/1.4817183.
Yang W, Mori-Sánchez P, Cohen AJ. Extension of many-body theory and approximate density functionals to fractional charges and fractional spins. The Journal of chemical physics. 2013 Sep;139(10):104114.
Yang, Weitao, et al. “Extension of many-body theory and approximate density functionals to fractional charges and fractional spins.The Journal of Chemical Physics, vol. 139, no. 10, Sept. 2013, p. 104114. Epmc, doi:10.1063/1.4817183.
Yang W, Mori-Sánchez P, Cohen AJ. Extension of many-body theory and approximate density functionals to fractional charges and fractional spins. The Journal of chemical physics. 2013 Sep;139(10):104114.

Published In

The Journal of chemical physics

DOI

EISSN

1089-7690

ISSN

0021-9606

Publication Date

September 2013

Volume

139

Issue

10

Start / End Page

104114

Related Subject Headings

  • Chemical Physics
  • 51 Physical sciences
  • 40 Engineering
  • 34 Chemical sciences
  • 09 Engineering
  • 03 Chemical Sciences
  • 02 Physical Sciences