The duhka of DFT: a noble path to better functionals via a point electron approximation for the exchange–correlation hole†,‡

Dylan Jayatilaka; Amir Karton

doi:10.1071/CH21332

RESEARCH ARTICLE (Open Access)

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The duhka of DFT: a noble path to better functionals via a point electron approximation for the exchange–correlation hole^†^,^‡

Dylan Jayatilaka ^A ^* and Amir Karton

^A ^*

+ Author Affiliations

- Author Affiliations

^A School of Molecular Sciences, The University of Western Australia, Perth, WA 6009, Australia.

^* Correspondence to: dylan.jayatilaka@uwa.edu.au

Handling Editor: Curt Wentrup

Australian Journal of Chemistry 75(11) 888-892 https://doi.org/10.1071/CH21332
Submitted: 14 December 2021 Accepted: 17 January 2022 Published: 28 March 2022

© 2022 The Author(s) (or their employer(s)). Published by CSIRO Publishing. This is an open access article distributed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND)

Abstract

Density functional theory (DFT) is currently experiencing a golden age. The past two decades witnessed remarkable advances in the general applicability of density functionals in the top rungs of Jacob’s Ladder. Nevertheless, Jacob’s Ladder may have reached its highest rung in terms of dependencies on occupied (rung four) and unoccupied orbitals (rung five). Moreover, the fifth rung is associated with a computational cost far greater than the lower rungs. Another limitation is that each rung includes dozens of different functionals, and at present, there is no clear pathway for systematic improvements within each rung of the ladder. This highlight provides an overview of the exchange–correlation (XC) hole and how it could be used in developing new density functionals. We begin with a brief overview of the current status and challenges in developing better density functionals, followed by the intimate relationship between the XC functional and hole. We present a conceptually simple and computationally economical method for calculating the XC hole and how this method could offer new directions in developing better exchange–correlation functionals.

Keywords: density functional theory, electron correlation, exchange correlation energy, exchange correlation functional, exchange correlation hole, Jacob’s Ladder, pair correlation function.

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