  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.
