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Recovering the flat-plane condition in electronic structure theory at semi-local DFT cost
Materials Science · Submitted 6 Oct 2017
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim 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.
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The abstract, sentence by sentence
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.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | 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. | background 1.00 | 0.11 | 0.04 | asserted 1.00 |
| s1 | 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. | background 0.96 | 0.15 | 0.04 | asserted 1.00 |
| s2 | 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. | result 0.54 | 0.77 | 0.07 | asserted 1.00 |
| s3 | 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. | result 0.73 | 0.95 | 0.04 | asserted 1.00 |
| s4 | 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. | method 0.72 | 0.90 | 0.11 | asserted 1.00 |
| s5 | We select one such physically intuitive form and incorporate it self-consistently to correct semi-local DFT. | method 0.94 | 0.93 | 0.09 | asserted 0.97 |
| s6 | 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. | result 0.80 | 0.94 | 0.83 | asserted 1.00 |
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Original 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.
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