# 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 Laboratories, Albuquerque, New Mexico 87185-1315 (United States)
- Advanced Logic Lab, Samsung Semiconductor, Inc., Austin, Texas 78754 (United States)

- Publication Date:

- OSTI Identifier:
- 22415864

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Chemical Physics

- Additional Journal Information:
- Journal Volume: 142; Journal Issue: 20; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0021-9606

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; ATOMS; CAPTURE; COMPARATIVE EVALUATIONS; DENSITY FUNCTIONAL METHOD; ELECTRON-ELECTRON COUPLING; ELECTRON-PHONON COUPLING; ELECTRONS; EQUATIONS OF MOTION; EXCITATION; GROUND STATES; MANY-BODY PROBLEM; MIXED STATE; MIXED STATES; MOLECULAR DYNAMICS METHOD; PURE STATES; QUANTUM MECHANICS; THERMALIZATION; THERMODYNAMIC PROPERTIES; TIME DEPENDENCE; WAVE FUNCTIONS

### 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.
```

```
@article{osti_22415864,
```

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 wavefunctions are fixed by the initial state in TDDFT. We work to address this puzzle by (A) reformulating quantum statistical mechanics so that thermodynamic expectations can be obtained as an unweighted average over a set of many-body pure states and (B) constructing a family of non-interacting (single determinant) TDDFT states that approximate the required many-body states for the canonical ensemble.},

doi = {10.1063/1.4921690},

journal = {Journal of Chemical Physics},

issn = {0021-9606},

number = 20,

volume = 142,

place = {United States},

year = {2015},

month = {5}

}