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Communication: Two types of flat-planes conditions in density functional theory
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, Yu. Ralchenko
, J. Reader
, and NIST ASD Team
, NIST Atomic Spectra Database (version 5.3), National Institute of Standards and Technology, Gaithersburg, MD, 2015, available online at http://physics.nist.gov/asd
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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
α and N
β, has a derivative discontinuity on a line segment where the number of electrons,
α + N
β, 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,
α – N
β, 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.
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