# Real time propagation of the exact two component time-dependent density functional theory

## Abstract

We report the development of a real time propagation method for solving the time-dependent relativistic exact two-component density functional theory equations (RT-X2C-TDDFT). The method is fundamentally non-perturbative and may be employed to study nonlinear responses for heavy elements which require a relativistic Hamiltonian. Here, we apply the method to several group 12 atoms as well as heavy-element hydrides, comparing with the extensive theoretical and experimental studies on this system, which demonstrates the correctness of our approach. Because the exact two-component Hamiltonian contains spin-orbit operators, the method is able to describe the non-zero transition moment of otherwise spin-forbidden processes in non-relativistic theory. Furthermore, the two-component approach is more cost effective than the full four-component approach, with similar accuracy. The RT-X2C-TDDFT will be useful in future studies of systems containing heavy elements interacting with strong external fields.

- Authors:

- Univ. of Washington, Seattle, WA (United States). Dept. of Chemistry

- Publication Date:

- Research Org.:
- Univ. of Washington, Seattle, WA (United States)

- Sponsoring Org.:
- USDOE; National Science Foundation (NSF)

- OSTI Identifier:
- 1467884

- Alternate Identifier(s):
- OSTI ID: 1324365

- Grant/Contract Number:
- SC0006863

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Journal of Chemical Physics

- Additional Journal Information:
- Journal Volume: 145; Journal Issue: 10; Journal ID: ISSN 0021-9606

- Publisher:
- American Institute of Physics (AIP)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY

### Citation Formats

```
Goings, Joshua J., Kasper, Joseph M., Egidi, Franco, Sun, Shichao, and Li, Xiaosong.
```*Real time propagation of the exact two component time-dependent density functional theory*. United States: N. p., 2016.
Web. doi:10.1063/1.4962422.

```
Goings, Joshua J., Kasper, Joseph M., Egidi, Franco, Sun, Shichao, & Li, Xiaosong.
```*Real time propagation of the exact two component time-dependent density functional theory*. United States. doi:10.1063/1.4962422.

```
Goings, Joshua J., Kasper, Joseph M., Egidi, Franco, Sun, Shichao, and Li, Xiaosong. Tue .
"Real time propagation of the exact two component time-dependent density functional theory". United States.
doi:10.1063/1.4962422. https://www.osti.gov/servlets/purl/1467884.
```

```
@article{osti_1467884,
```

title = {Real time propagation of the exact two component time-dependent density functional theory},

author = {Goings, Joshua J. and Kasper, Joseph M. and Egidi, Franco and Sun, Shichao and Li, Xiaosong},

abstractNote = {We report the development of a real time propagation method for solving the time-dependent relativistic exact two-component density functional theory equations (RT-X2C-TDDFT). The method is fundamentally non-perturbative and may be employed to study nonlinear responses for heavy elements which require a relativistic Hamiltonian. Here, we apply the method to several group 12 atoms as well as heavy-element hydrides, comparing with the extensive theoretical and experimental studies on this system, which demonstrates the correctness of our approach. Because the exact two-component Hamiltonian contains spin-orbit operators, the method is able to describe the non-zero transition moment of otherwise spin-forbidden processes in non-relativistic theory. Furthermore, the two-component approach is more cost effective than the full four-component approach, with similar accuracy. The RT-X2C-TDDFT will be useful in future studies of systems containing heavy elements interacting with strong external fields.},

doi = {10.1063/1.4962422},

journal = {Journal of Chemical Physics},

number = 10,

volume = 145,

place = {United States},

year = {Tue Sep 13 00:00:00 EDT 2016},

month = {Tue Sep 13 00:00:00 EDT 2016}

}

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