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

Xiaotian Derrick Yang; Anand H G Patel; Ramón Alain Miranda-Quintana; Farnaz Heidar-Zadeh; Cristina E González-Espinoza; Paul W Ayers

doi:10.1063/1.4958636

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

J Chem Phys. 2016 Jul 21;145(3):031102. doi: 10.1063/1.4958636.

Authors

Xiaotian Derrick Yang¹, Anand H G Patel¹, Ramón Alain Miranda-Quintana¹, Farnaz Heidar-Zadeh¹, Cristina E González-Espinoza¹, Paul W Ayers¹

Affiliation

¹ Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario LBS 4M1, Canada.

PMID: 27448863
DOI: 10.1063/1.4958636

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.