### Gradient corrections to the exchange-correlation free energy

We develop the first-order gradient correction to the exchange-correlation free energy of the homogeneous electron gas for use in finite-temperature density functional calculations. Based on this, we propose and implement a simple temperature-dependent extension for functionals beyond the local density approximation. These finite-temperature functionals show improvement over zero-temperature functionals, as compared to path-integral Monte Carlo calculations for deuterium equations of state, and perform without computational cost increase compared to zero-temperature functionals and so should be used for finite-temperature calculations. Furthermore, while the present functionals are valid at all temperatures including zero, non-negligible difference with zero-temperature functionals begins at temperatures above 10 000 K.

- Publication Date:

- Report Number(s):
- LA-UR-14-26354

Journal ID: ISSN 1098-0121; PRBMDO

- Grant/Contract Number:
- AC52-06NA25396

- Type:
- Accepted Manuscript

- Journal Name:
- Physical Review. B, Condensed Matter and Materials Physics

- Additional Journal Information:
- Journal Volume: 90; Journal Issue: 15; Journal ID: ISSN 1098-0121

- Publisher:
- American Physical Society (APS)

- Research Org:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

- Sponsoring Org:
- USDOE

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 74 ATOMIC AND MOLECULAR PHYSICS; 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; 36 MATERIALS SCIENCE; 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; density functional theory; exchange-correlation; warm dense matter

- OSTI Identifier:
- 1246924

- Alternate Identifier(s):
- OSTI ID: 1180836

```
Sjostrom, Travis, and Daligault, Jerome.
```*Gradient corrections to the exchange-correlation free energy*. United States: N. p.,
Web. doi:10.1103/PhysRevB.90.155109.

```
Sjostrom, Travis, & Daligault, Jerome.
```*Gradient corrections to the exchange-correlation free energy*. United States. doi:10.1103/PhysRevB.90.155109.

```
Sjostrom, Travis, and Daligault, Jerome. 2014.
"Gradient corrections to the exchange-correlation free energy". United States.
doi:10.1103/PhysRevB.90.155109. https://www.osti.gov/servlets/purl/1246924.
```

```
@article{osti_1246924,
```

title = {Gradient corrections to the exchange-correlation free energy},

author = {Sjostrom, Travis and Daligault, Jerome},

abstractNote = {We develop the first-order gradient correction to the exchange-correlation free energy of the homogeneous electron gas for use in finite-temperature density functional calculations. Based on this, we propose and implement a simple temperature-dependent extension for functionals beyond the local density approximation. These finite-temperature functionals show improvement over zero-temperature functionals, as compared to path-integral Monte Carlo calculations for deuterium equations of state, and perform without computational cost increase compared to zero-temperature functionals and so should be used for finite-temperature calculations. Furthermore, while the present functionals are valid at all temperatures including zero, non-negligible difference with zero-temperature functionals begins at temperatures above 10 000 K.},

doi = {10.1103/PhysRevB.90.155109},

journal = {Physical Review. B, Condensed Matter and Materials Physics},

number = 15,

volume = 90,

place = {United States},

year = {2014},

month = {10}

}