## Representing the thermal state in time-dependent density functional theory

## Abstract

Classical molecular dynamics (MD) provides a powerful and widely used approach to determining thermodynamic properties by integrating the classical equations of motion of a system of atoms. Time-Dependent Density Functional Theory (TDDFT) provides a powerful and increasingly useful approach to integrating the quantum equations of motion for a system of electrons. TDDFT efficiently captures the unitary evolution of a many-electron state by mapping the system into a fictitious non-interacting system. In analogy to MD, one could imagine obtaining the thermodynamic properties of an electronic system from a TDDFT simulation in which the electrons are excited from their ground state by a time-dependent potential and then allowed to evolve freely in time while statistical data are captured from periodic snapshots of the system. For a variety of systems (e.g., many metals), the electrons reach an effective state of internal equilibrium due to electron-electron interactions on a time scale that is short compared to electron-phonon equilibration. During the initial time-evolution of such systems following electronic excitation, electron-phonon interactions should be negligible, and therefore, TDDFT should successfully capture the internal thermalization of the electrons. However, it is unclear how TDDFT represents the resulting thermal state. In particular, the thermal state is usually representedmore »

- Authors:

- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
- Samsung Semiconductor, Inc., Austin, TX (United States). Advanced Logic Lab,

- Publication Date:

- Research Org.:
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA)

- OSTI Identifier:
- 1110660

- Report Number(s):
- SAND-2013-7774J

Journal ID: ISSN 0021-9606; JCPSA6; 474165

- Grant/Contract Number:
- AC04-94AL85000

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Journal of Chemical Physics

- Additional Journal Information:
- Journal Volume: 142; Journal Issue: 20; Journal ID: ISSN 0021-9606

- Publisher:
- American Institute of Physics (AIP)

- Country of Publication:
- United States

- Language:
- English

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

### Citation Formats

```
Modine, N. A., and Hatcher, R. M.. Representing the thermal state in time-dependent density functional theory. United States: N. p., 2015.
Web. doi:10.1063/1.4921690.
```

```
Modine, N. A., & Hatcher, R. M.. Representing the thermal state in time-dependent density functional theory. United States. doi:10.1063/1.4921690.
```

```
Modine, N. A., and Hatcher, R. M.. Thu .
"Representing the thermal state in time-dependent density functional theory". United States. doi:10.1063/1.4921690. https://www.osti.gov/servlets/purl/1110660.
```

```
@article{osti_1110660,
```

title = {Representing the thermal state in time-dependent density functional theory},

author = {Modine, N. A. and Hatcher, R. M.},

abstractNote = {Classical molecular dynamics (MD) provides a powerful and widely used approach to determining thermodynamic properties by integrating the classical equations of motion of a system of atoms. Time-Dependent Density Functional Theory (TDDFT) provides a powerful and increasingly useful approach to integrating the quantum equations of motion for a system of electrons. TDDFT efficiently captures the unitary evolution of a many-electron state by mapping the system into a fictitious non-interacting system. In analogy to MD, one could imagine obtaining the thermodynamic properties of an electronic system from a TDDFT simulation in which the electrons are excited from their ground state by a time-dependent potential and then allowed to evolve freely in time while statistical data are captured from periodic snapshots of the system. For a variety of systems (e.g., many metals), the electrons reach an effective state of internal equilibrium due to electron-electron interactions on a time scale that is short compared to electron-phonon equilibration. During the initial time-evolution of such systems following electronic excitation, electron-phonon interactions should be negligible, and therefore, TDDFT should successfully capture the internal thermalization of the electrons. However, it is unclear how TDDFT represents the resulting thermal state. In particular, the thermal state is usually represented in quantum statistical mechanics as a mixed state, while the occupations of the TDDFT wave functions are fixed by the initial state in TDDFT. Two key questions involve (1) reformulating quantum statistical mechanics so that thermodynamic expectations can be obtained as an unweighted average over a set of many-body pure states and (2) constructing a family of non-interacting (single determinant) TDDFT states that approximate the required many-body states for the canonical ensemble. In Section II, we will address these questions by first demonstrating that thermodynamic expectations can be evaluated by averaging over certain many-body pure states, which we will call thermal states, and then constructing TDDFT states that approximate these thermal states. In Section III, we will present some numerical tests of the resulting theory, and in Section IV, we will summarize our main results and discuss some possible future directions for this work.},

doi = {10.1063/1.4921690},

journal = {Journal of Chemical Physics},

number = 20,

volume = 142,

place = {United States},

year = {2015},

month = {5}

}

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