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The flat plane condition is the union of two exact constraints in electronicstructure theory: i) energetic piecewise linearity with fractional electronremoval or addition and ii) invariant energetics with change in electron spinin a half filled orbital. Semi-local density functional theory (DFT) fails torecover the flat plane, exhibiting convex fractional charge errors (FCE) andconcave fractional spin errors (FSE) that are related to delocalization andstatic correlation errors. We previously showed that DFT+U eliminates FCE butnow demonstrate that, like other widely employed corrections (i.e., HartreeFock exchange), it worsens FSE. To find an alternative strategy, we examine theshape of semi-local DFT deviations from the exact flat plane, and we find thisshape to be remarkably consistent across ions and molecules. We introduce thejmDFT approach, wherein corrections are constructed from few-parameter, low-order, functional forms that fit the shape of semi-local DFT errors. We selectone such physically intuitive form and incorporate it self-consistently tocorrect semi-local DFT. We demonstrate on model systems that this jmDFTapproach represents the first easy-to-implement, no-overhead approach torecovering the flat plane from semi-local DFT.

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