# Thermal Density Functional Theory: Time-Dependent Linear Response and Approximate Functionals from the Fluctuation-Dissipation Theorem

## Abstract

We present that the van Leeuwen proof of linear-response time-dependent density functional theory (TDDFT) is generalized to thermal ensembles. This allows generalization to finite temperatures of the Gross-Kohn relation, the exchange-correlation kernel of TDDFT, and fluctuation dissipation theorem for DFT. Finally, this produces a natural method for generating new thermal exchange-correlation approximations.

- Authors:

- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Univ. of California, Berkeley, CA (United States). Department of Chemistry
- Univ. of California, Irvine, CA (United States). Dept. of Physics and Astronomy
- Univ. of California, Irvine, CA (United States). Dept. of Chemistry and Dept. of Physics and Astronomy

- Publication Date:

- Research Org.:
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1389980

- Alternate Identifier(s):
- OSTI ID: 1256152

- Report Number(s):
- LLNL-JRNL-689945

Journal ID: ISSN 0031-9007; PRLTAO

- Grant/Contract Number:
- AC52-07NA27344; FG02-97ER25308

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Physical Review Letters

- Additional Journal Information:
- Journal Volume: 116; Journal Issue: 23; Journal ID: ISSN 0031-9007

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

### Citation Formats

```
Pribram-Jones, Aurora, Grabowski, Paul E., and Burke, Kieron.
```*Thermal Density Functional Theory: Time-Dependent Linear Response and Approximate Functionals from the Fluctuation-Dissipation Theorem*. United States: N. p., 2016.
Web. doi:10.1103/PhysRevLett.116.233001.

```
Pribram-Jones, Aurora, Grabowski, Paul E., & Burke, Kieron.
```*Thermal Density Functional Theory: Time-Dependent Linear Response and Approximate Functionals from the Fluctuation-Dissipation Theorem*. United States. doi:10.1103/PhysRevLett.116.233001.

```
Pribram-Jones, Aurora, Grabowski, Paul E., and Burke, Kieron. Wed .
"Thermal Density Functional Theory: Time-Dependent Linear Response and Approximate Functionals from the Fluctuation-Dissipation Theorem". United States.
doi:10.1103/PhysRevLett.116.233001. https://www.osti.gov/servlets/purl/1389980.
```

```
@article{osti_1389980,
```

title = {Thermal Density Functional Theory: Time-Dependent Linear Response and Approximate Functionals from the Fluctuation-Dissipation Theorem},

author = {Pribram-Jones, Aurora and Grabowski, Paul E. and Burke, Kieron},

abstractNote = {We present that the van Leeuwen proof of linear-response time-dependent density functional theory (TDDFT) is generalized to thermal ensembles. This allows generalization to finite temperatures of the Gross-Kohn relation, the exchange-correlation kernel of TDDFT, and fluctuation dissipation theorem for DFT. Finally, this produces a natural method for generating new thermal exchange-correlation approximations.},

doi = {10.1103/PhysRevLett.116.233001},

journal = {Physical Review Letters},

number = 23,

volume = 116,

place = {United States},

year = {Wed Jun 08 00:00:00 EDT 2016},

month = {Wed Jun 08 00:00:00 EDT 2016}

}

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Cited by: 10 works

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Works referenced in this record:

##
Self-Consistent Equations Including Exchange and Correlation Effects

journal, November 1965

- Kohn, W.; Sham, L. J.
- Physical Review, Vol. 140, Issue 4A, p. A1133-A1138