1. Communication: Two types of flat-planes conditions in density functional theory.
- Author
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Xiaotian Derrick Yang, Patel, Anand H. G., Miranda-Quintana, Ramón Alain, Heidar-Zadeh, Farnaz, González-Espinoza, Cristina E., and Ayers, Paul W.
- Subjects
DENSITY functional theory ,ATOMIC spectroscopy ,ELECTRONS ,LEPTONS (Nuclear physics) ,SPIN polarization - 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
α 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. [ABSTRACT FROM AUTHOR]- Published
- 2016
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