Recovering the flat-plane condition in electronic structure theory at semi-local DFT cost

TL;DR

This paper introduces jmDFT, a simple correction method that, at semi-local DFT cost, effectively recovers the flat-plane condition crucial for accurate electronic structure calculations.

Contribution

The paper presents jmDFT, a novel, low-parameter correction approach that restores the flat-plane condition in semi-local DFT, addressing its inherent errors.

Findings

jmDFT accurately corrects flat-plane deviations in model systems.

The shape of DFT errors is consistent across different molecules and ions.

jmDFT is easy to implement with no additional computational overhead.

Abstract

The flat plane condition is the union of two exact constraints in electronic structure theory: i) energetic piecewise linearity with fractional electron removal or addition and ii) invariant energetics with change in electron spin in a half filled orbital. Semi-local density functional theory (DFT) fails to recover the flat plane, exhibiting convex fractional charge errors (FCE) and concave fractional spin errors (FSE) that are related to delocalization and static correlation errors. We previously showed that DFT+U eliminates FCE but now demonstrate that, like other widely employed corrections (i.e., Hartree Fock exchange), it worsens FSE. To find an alternative strategy, we examine the shape of semi-local DFT deviations from the exact flat plane, and we find this shape to be remarkably consistent across ions and molecules. We introduce the jmDFT approach, wherein corrections are constructed from few-parameter, low- order, functional forms that fit the shape of semi-local DFT errors. We select one such physically intuitive form and incorporate it self-consistently to correct semi-local DFT. We demonstrate on model systems that this jmDFT approach represents the first easy-to-implement, no-overhead approach to recovering the flat plane from semi-local DFT.