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

## 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 judiciously modified DFT (jmDFT) approach, wherein corrections are constructed from few-parameter, low-order functional forms that fit the shape of semi-local DFT errors. Here we select one such physically intuitive form and incorporate it self-consistently to correct semi-local DFT. We demonstrate on model systems that jmDFT represents the first easy-to-implement, no-overhead approach to recovering the flat plane from semi-local DFT.

- Authors:

- Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)

- Publication Date:

- Research Org.:
- Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC)

- OSTI Identifier:
- 1511169

- Alternate Identifier(s):
- OSTI ID: 1409703

- Grant/Contract Number:
- SC0018096

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Journal of Chemical Physics

- Additional Journal Information:
- Journal Volume: 147; Journal Issue: 19; Journal ID: ISSN 0021-9606

- Publisher:
- American Institute of Physics (AIP)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 74 ATOMIC AND MOLECULAR PHYSICS

### Citation Formats

```
Bajaj, Akash, Janet, Jon Paul, and Kulik, Heather J. Communication: Recovering the flat-plane condition in electronic structure theory at semi-local DFT cost. United States: N. p., 2017.
Web. doi:10.1063/1.5008981.
```

```
Bajaj, Akash, Janet, Jon Paul, & Kulik, Heather J. Communication: Recovering the flat-plane condition in electronic structure theory at semi-local DFT cost. United States. doi:10.1063/1.5008981.
```

```
Bajaj, Akash, Janet, Jon Paul, and Kulik, Heather J. Tue .
"Communication: Recovering the flat-plane condition in electronic structure theory at semi-local DFT cost". United States. doi:10.1063/1.5008981. https://www.osti.gov/servlets/purl/1511169.
```

```
@article{osti_1511169,
```

title = {Communication: Recovering the flat-plane condition in electronic structure theory at semi-local DFT cost},

author = {Bajaj, Akash and Janet, Jon Paul and Kulik, Heather J.},

abstractNote = {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 judiciously modified DFT (jmDFT) approach, wherein corrections are constructed from few-parameter, low-order functional forms that fit the shape of semi-local DFT errors. Here we select one such physically intuitive form and incorporate it self-consistently to correct semi-local DFT. We demonstrate on model systems that jmDFT represents the first easy-to-implement, no-overhead approach to recovering the flat plane from semi-local DFT.},

doi = {10.1063/1.5008981},

journal = {Journal of Chemical Physics},

number = 19,

volume = 147,

place = {United States},

year = {2017},

month = {11}

}

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Web of Science

Works referenced in this record:

##
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- Giannozzi, Paolo; Baroni, Stefano; Bonini, Nicola
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