Global and local curvature in density functional theory
Name
726430_1_merged_1468501285.pdf
Size
2.58 MB
Format
Adobe PDF
Checksum (MD5)
bacd7bdca92ca6095582d58e96f65cdc
Author(s)
Zhao, Qing
Ioannidis, Efthymios Ioannis
Kulik, Heather Janine
Date Issued
August 2016
Journal
The Journal of Chemical Physics
Publisher
American Institute of Physics (AIP)
Citation
Zhao, Qing, Efthymios I. Ioannidis, and Heather J. Kulik. “Global and Local Curvature in Density Functional Theory.” The Journal of Chemical Physics 145.5 (2016): 054109.
Version
Author's final manuscript
Abstract
Piecewise linearity of the energy with respect to fractional electron removal or addition is a requirement of an electronic structure method that necessitates the presence of a derivative discontinuity at integer electron occupation. Semi-local exchange-correlation (xc) approximations within density functional theory (DFT) fail to reproduce this behavior, giving rise to deviations from linearity with a convex global curvature that is evidence of many-electron, self-interaction error and electron delocalization. Popular functional tuning strategies focus on reproducing piecewise linearity, especially to improve predictions of optical properties. In a divergent approach, Hubbard U-augmented DFT (i.e., DFT+U) treats self-interaction errors by reducing the local curvature of the energy with respect to electron removal or addition from one localized subshell to the surrounding system. Although it has been suggested that DFT+U should simultaneously alleviate global and local curvature in the atomic limit, no detailed study on real systems has been carried out to probe the validity of this statement. In this work, we show when DFT+U should minimize deviations from linearity and demonstrate that a “+U” correction will never worsen the deviation from linearity of the underlying xc approximation. However, we explain varying degrees of efficiency of the approach over 27 octahedral transition metal complexes with respect to transition metal (Sc–Cu) and ligand strength (CO, NH3, and H2O) and investigate select pathological cases where the delocalization error is invisible to DFT+U within an atomic projection framework. Finally, we demonstrate that the global and local curvatures represent different quantities that show opposing behavior with increasing ligand field strength, and we identify where these two may still coincide.
MIT Department
Massachusetts Institute of Technology. Department of Chemical Engineering
Massachusetts Institute of Technology. Department of Mechanical Engineering
Sloan School of Management
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1063/1.4959882
