# Violation of the zero-force theorem in the time-dependent Krieger-Li-Iafrate approximation

## Abstract

We demonstrate that the time-dependent Krieger-Li-Iafrate approximation in combination with the exchange-only functional violates the zero-force theorem. By analyzing the time-dependent dipole moment of Na{sub 5} and Na{sub 9}{sup +}, we furthermore show that this can lead to an unphysical self-excitation of the system depending on the system properties and the excitation strength. Analytical aspects, especially the connection between the zero-force theorem and the generalized-translation invariance of the potential, are discussed.

- Authors:

- Physikalisches Institut, Universitaet Bayreuth, D-95440 Bayreuth (Germany)
- (Netherlands)
- (Germany)

- Publication Date:

- OSTI Identifier:
- 20982438

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. A; Journal Volume: 75; Journal Issue: 5; Other Information: DOI: 10.1103/PhysRevA.75.050501; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 74 ATOMIC AND MOLECULAR PHYSICS; APPROXIMATIONS; CATIONS; DENSITY FUNCTIONAL METHOD; DIPOLE MOMENTS; EXCITATION; HEAVY IONS; POTENTIALS; SODIUM; TIME DEPENDENCE

### Citation Formats

```
Mundt, Michael, Kuemmel, Stephan, Leeuwen, Robert van, Reinhard, Paul-Gerhard, University of Groningen, Theoretical Chemistry, Zernike Institute for Advanced Materials, 9747AG, Nijenborgh 4, Groningen, and Institut fuer Theoretische Physik II, Universitaet Erlangen-Nuernberg, Staudtstrasse 7, D-91058 Erlangen.
```*Violation of the zero-force theorem in the time-dependent Krieger-Li-Iafrate approximation*. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVA.75.050501.

```
Mundt, Michael, Kuemmel, Stephan, Leeuwen, Robert van, Reinhard, Paul-Gerhard, University of Groningen, Theoretical Chemistry, Zernike Institute for Advanced Materials, 9747AG, Nijenborgh 4, Groningen, & Institut fuer Theoretische Physik II, Universitaet Erlangen-Nuernberg, Staudtstrasse 7, D-91058 Erlangen.
```*Violation of the zero-force theorem in the time-dependent Krieger-Li-Iafrate approximation*. United States. doi:10.1103/PHYSREVA.75.050501.

```
Mundt, Michael, Kuemmel, Stephan, Leeuwen, Robert van, Reinhard, Paul-Gerhard, University of Groningen, Theoretical Chemistry, Zernike Institute for Advanced Materials, 9747AG, Nijenborgh 4, Groningen, and Institut fuer Theoretische Physik II, Universitaet Erlangen-Nuernberg, Staudtstrasse 7, D-91058 Erlangen. Tue .
"Violation of the zero-force theorem in the time-dependent Krieger-Li-Iafrate approximation". United States.
doi:10.1103/PHYSREVA.75.050501.
```

```
@article{osti_20982438,
```

title = {Violation of the zero-force theorem in the time-dependent Krieger-Li-Iafrate approximation},

author = {Mundt, Michael and Kuemmel, Stephan and Leeuwen, Robert van and Reinhard, Paul-Gerhard and University of Groningen, Theoretical Chemistry, Zernike Institute for Advanced Materials, 9747AG, Nijenborgh 4, Groningen and Institut fuer Theoretische Physik II, Universitaet Erlangen-Nuernberg, Staudtstrasse 7, D-91058 Erlangen},

abstractNote = {We demonstrate that the time-dependent Krieger-Li-Iafrate approximation in combination with the exchange-only functional violates the zero-force theorem. By analyzing the time-dependent dipole moment of Na{sub 5} and Na{sub 9}{sup +}, we furthermore show that this can lead to an unphysical self-excitation of the system depending on the system properties and the excitation strength. Analytical aspects, especially the connection between the zero-force theorem and the generalized-translation invariance of the potential, are discussed.},

doi = {10.1103/PHYSREVA.75.050501},

journal = {Physical Review. A},

number = 5,

volume = 75,

place = {United States},

year = {Tue May 15 00:00:00 EDT 2007},

month = {Tue May 15 00:00:00 EDT 2007}

}

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