# First-order derivative couplings between excited states from adiabatic TDDFT response theory

## Abstract

We present a complete derivation of derivative couplings between excited states in the framework of adiabatic time-dependent density functional response theory. Explicit working equations are given and the resulting derivative couplings are compared with derivative couplings from a pseudo-wavefunction ansatz. For degenerate excited states, i.e., close to a conical intersection (CI), the two approaches are identical apart from an antisymmetric overlap term. However, if the difference between two excitation energies equals another excitation energy, the couplings from response theory exhibit an unphysical divergence. This spurious behavior is a result of the adiabatic or static kernel approximation of time-dependent density functional theory leading to an incorrect analytical structure of the quadratic response function. Numerical examples for couplings close to a CI and for well-separated electronic states are given.

- Authors:

- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104 (United States)
- Department of Chemistry, University of California, Irvine, 1102 Natural Sciences II, Irvine, California 92697-2025 (United States)

- Publication Date:

- OSTI Identifier:
- 22416099

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Chemical Physics; Journal Volume: 142; Journal Issue: 6; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; ADIABATIC APPROXIMATION; COMPARATIVE EVALUATIONS; DENSITY FUNCTIONAL METHOD; EQUATIONS; EXCITATION; EXCITED STATES; KERNELS; RESPONSE FUNCTIONS; TIME DEPENDENCE; WAVE FUNCTIONS

### Citation Formats

```
Ou, Qi, Subotnik, Joseph E., E-mail: subotnik@sas.upenn.edu, Bellchambers, Gregory D., and Furche, Filipp, E-mail: filipp.furche@uci.edu.
```*First-order derivative couplings between excited states from adiabatic TDDFT response theory*. United States: N. p., 2015.
Web. doi:10.1063/1.4906941.

```
Ou, Qi, Subotnik, Joseph E., E-mail: subotnik@sas.upenn.edu, Bellchambers, Gregory D., & Furche, Filipp, E-mail: filipp.furche@uci.edu.
```*First-order derivative couplings between excited states from adiabatic TDDFT response theory*. United States. doi:10.1063/1.4906941.

```
Ou, Qi, Subotnik, Joseph E., E-mail: subotnik@sas.upenn.edu, Bellchambers, Gregory D., and Furche, Filipp, E-mail: filipp.furche@uci.edu. Sat .
"First-order derivative couplings between excited states from adiabatic TDDFT response theory". United States.
doi:10.1063/1.4906941.
```

```
@article{osti_22416099,
```

title = {First-order derivative couplings between excited states from adiabatic TDDFT response theory},

author = {Ou, Qi and Subotnik, Joseph E., E-mail: subotnik@sas.upenn.edu and Bellchambers, Gregory D. and Furche, Filipp, E-mail: filipp.furche@uci.edu},

abstractNote = {We present a complete derivation of derivative couplings between excited states in the framework of adiabatic time-dependent density functional response theory. Explicit working equations are given and the resulting derivative couplings are compared with derivative couplings from a pseudo-wavefunction ansatz. For degenerate excited states, i.e., close to a conical intersection (CI), the two approaches are identical apart from an antisymmetric overlap term. However, if the difference between two excitation energies equals another excitation energy, the couplings from response theory exhibit an unphysical divergence. This spurious behavior is a result of the adiabatic or static kernel approximation of time-dependent density functional theory leading to an incorrect analytical structure of the quadratic response function. Numerical examples for couplings close to a CI and for well-separated electronic states are given.},

doi = {10.1063/1.4906941},

journal = {Journal of Chemical Physics},

number = 6,

volume = 142,

place = {United States},

year = {Sat Feb 14 00:00:00 EST 2015},

month = {Sat Feb 14 00:00:00 EST 2015}

}