title: Communication: Two types of flat-planes conditions in density functional theory.
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.
authors.affiliation: Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario LBS 4M1, Canada.
authors.forename: Xiaotian Derrick
authors.initials: XD
authors.lastname: Yang
authors.affiliation: Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario LBS 4M1, Canada.
authors.forename: Anand H G
authors.initials: AH
authors.lastname: Patel
authors.affiliation: Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario LBS 4M1, Canada.
authors.forename: Ramón Alain
authors.initials: RA
authors.lastname: Miranda-Quintana
authors.affiliation: Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario LBS 4M1, Canada.
authors.forename: Farnaz
authors.initials: F
authors.lastname: Heidar-Zadeh
authors.affiliation: Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario LBS 4M1, Canada.
authors.forename: Cristina E
authors.initials: CE
authors.lastname: González-Espinoza
authors.affiliation: Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario LBS 4M1, Canada.
authors.forename: Paul W
authors.initials: PW
authors.lastname: Ayers