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Communication: Two types of flat-planes conditions in density functional theory

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Abstract
Using results from atomic spectroscopy, we show that there are two types of flat-planes conditions. The first type of flat-planes condition occurs when the energy as a function of the number of electrons of each spin, Nα and Nβ, has a derivative discontinuity on a line segment where the number of electrons, Nα + Nβ, is an integer. The second type of flat-planes condition occurs when the energy has a derivative discontinuity on a line segment where the spin polarization, Nα – Nβ, is an integer, but does not have a discontinuity associated with an integer number of electrons. Type 2 flat planes are rare—we observed just 15 type 2 flat-planes conditions out of the 4884 cases we tested—but their mere existence has implications for the design of exchange-correlation energy density functionals. To facilitate the development of functionals that have the correct behavior with respect to both fractional number of electrons and fractional spin polarization, we present a dataset for the chromium atom and its ions that can be used to test new functionals.
Keywords
APPROXIMATIONS, SYMMETRY, CR

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Chicago
Yang, Xiaotian Derrick, Anand HG Patel, Ramón Alain Miranda-Quintana, Farnaz Heidar Zadeh, Cristina E González-Espinoza, and Paul W Ayers. 2016. “Communication: Two Types of Flat-planes Conditions in Density Functional Theory.” Journal of Chemical Physics 145 (3).
APA
Yang, X. D., Patel, A. H., Miranda-Quintana, R. A., Heidar Zadeh, F., González-Espinoza, C. E., & Ayers, P. W. (2016). Communication: Two types of flat-planes conditions in density functional theory. JOURNAL OF CHEMICAL PHYSICS, 145(3).
Vancouver
1.
Yang XD, Patel AH, Miranda-Quintana RA, Heidar Zadeh F, González-Espinoza CE, Ayers PW. Communication: Two types of flat-planes conditions in density functional theory. JOURNAL OF CHEMICAL PHYSICS. 2016;145(3).
MLA
Yang, Xiaotian Derrick, Anand HG Patel, Ramón Alain Miranda-Quintana, et al. “Communication: Two Types of Flat-planes Conditions in Density Functional Theory.” JOURNAL OF CHEMICAL PHYSICS 145.3 (2016): n. pag. Print.
@article{8532317,
  abstract     = {Using results from atomic spectroscopy, we show that there are two types of flat-planes conditions. The first type of flat-planes condition occurs when the energy as a function of the number of electrons of each spin, N\ensuremath{\alpha} and N\ensuremath{\beta}, has a derivative discontinuity on a line segment where the number of electrons, N\ensuremath{\alpha} + N\ensuremath{\beta}, is an integer. The second type of flat-planes condition occurs when the energy has a derivative discontinuity on a line segment where the spin polarization, N\ensuremath{\alpha} -- N\ensuremath{\beta}, is an integer, but does not have a discontinuity associated with an integer number of electrons. Type 2 flat planes are rare---we observed just 15 type 2 flat-planes conditions out of the 4884 cases we tested---but their mere existence has implications for the design of exchange-correlation energy density functionals. To facilitate the development of functionals that have the correct behavior with respect to both fractional number of electrons and fractional spin polarization, we present a dataset for the chromium atom and its ions that can be used to test new functionals.},
  articleno    = {031102},
  author       = {Yang, Xiaotian Derrick and Patel, Anand HG and Miranda-Quintana, Ram{\'o}n Alain and Heidar Zadeh, Farnaz and Gonz{\'a}lez-Espinoza, Cristina E and Ayers, Paul W},
  issn         = {0021-9606},
  journal      = {JOURNAL OF CHEMICAL PHYSICS},
  keyword      = {APPROXIMATIONS,SYMMETRY,CR},
  language     = {eng},
  number       = {3},
  pages        = {4},
  title        = {Communication: Two types of flat-planes conditions in density functional theory},
  url          = {http://dx.doi.org/10.1063/1.4958636},
  volume       = {145},
  year         = {2016},
}

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