# Derivative couplings between TDDFT excited states obtained by direct differentiation in the Tamm-Dancoff approximation

## Abstract

Working within the Tamm-Dancoff approximation, we calculate the derivative couplings between time-dependent density-functional theory excited states by assuming that the Kohn-Sham superposition of singly excited determinants represents a true electronic wavefunction. All Pulay terms are included in our derivative coupling expression. The reasonability of our approach can be established by noting that, for closely separated electronic states in the infinite basis limit, our final expression agrees exactly with the Chernyak-Mukamel expression (with transition densities from response theory). Finally, we also validate our approach empirically by analyzing the behavior of the derivative couplings around the T{sub 1}/T{sub 2} conical intersection of benzaldehyde.

- Authors:

- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104 (United States)
- Q-Chem, Inc., 6601 Owens Drive, Suite 105, Pleasanton, California 94588 (United States)

- Publication Date:

- OSTI Identifier:
- 22308575

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Chemical Physics; Journal Volume: 141; Journal Issue: 2; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 74 ATOMIC AND MOLECULAR PHYSICS; 37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; APPROXIMATIONS; BENZALDEHYDE; COUPLINGS; DENSITY FUNCTIONAL METHOD; EXCITED STATES; WAVE FUNCTIONS

### Citation Formats

```
Ou, Qi, Fatehi, Shervin, Alguire, Ethan, Subotnik, Joseph E., E-mail: subotnik@sas.upenn.edu, and Shao, Yihan.
```*Derivative couplings between TDDFT excited states obtained by direct differentiation in the Tamm-Dancoff approximation*. United States: N. p., 2014.
Web. doi:10.1063/1.4887256.

```
Ou, Qi, Fatehi, Shervin, Alguire, Ethan, Subotnik, Joseph E., E-mail: subotnik@sas.upenn.edu, & Shao, Yihan.
```*Derivative couplings between TDDFT excited states obtained by direct differentiation in the Tamm-Dancoff approximation*. United States. doi:10.1063/1.4887256.

```
Ou, Qi, Fatehi, Shervin, Alguire, Ethan, Subotnik, Joseph E., E-mail: subotnik@sas.upenn.edu, and Shao, Yihan. Mon .
"Derivative couplings between TDDFT excited states obtained by direct differentiation in the Tamm-Dancoff approximation". United States.
doi:10.1063/1.4887256.
```

```
@article{osti_22308575,
```

title = {Derivative couplings between TDDFT excited states obtained by direct differentiation in the Tamm-Dancoff approximation},

author = {Ou, Qi and Fatehi, Shervin and Alguire, Ethan and Subotnik, Joseph E., E-mail: subotnik@sas.upenn.edu and Shao, Yihan},

abstractNote = {Working within the Tamm-Dancoff approximation, we calculate the derivative couplings between time-dependent density-functional theory excited states by assuming that the Kohn-Sham superposition of singly excited determinants represents a true electronic wavefunction. All Pulay terms are included in our derivative coupling expression. The reasonability of our approach can be established by noting that, for closely separated electronic states in the infinite basis limit, our final expression agrees exactly with the Chernyak-Mukamel expression (with transition densities from response theory). Finally, we also validate our approach empirically by analyzing the behavior of the derivative couplings around the T{sub 1}/T{sub 2} conical intersection of benzaldehyde.},

doi = {10.1063/1.4887256},

journal = {Journal of Chemical Physics},

number = 2,

volume = 141,

place = {United States},

year = {Mon Jul 14 00:00:00 EDT 2014},

month = {Mon Jul 14 00:00:00 EDT 2014}

}