# Linear optical response of finite systems using multishift linear system solvers

## Abstract

We discuss the application of multishift linear system solvers to linear-response time-dependent density functional theory. Using this technique the complete frequency-dependent electronic density response of finite systems to an external perturbation can be calculated at the cost of a single solution of a linear system via conjugate gradients. We show that multishift time-dependent density functional theory yields excitation energies and oscillator strengths in perfect agreement with the standard diagonalization of the response matrix (Casida's method), while being computationally advantageous. We present test calculations for benzene, porphin, and chlorophyll molecules. We argue that multishift solvers may find broad applicability in the context of excited-state calculations within density-functional theory and beyond.

- Authors:

- Department of Materials, University of Oxford, Oxford OX1 3PH (United Kingdom)

- Publication Date:

- OSTI Identifier:
- 22419920

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Chemical Physics; Journal Volume: 141; Journal Issue: 4; Other Information: (c) 2014 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; BENZENE; CHLOROPHYLL; DENSITY; DENSITY FUNCTIONAL METHOD; EXCITATION; EXCITED STATES; MOLECULES; OSCILLATOR STRENGTHS; SOLUTIONS; TIME DEPENDENCE

### Citation Formats

```
Hübener, Hannes, and Giustino, Feliciano.
```*Linear optical response of finite systems using multishift linear system solvers*. United States: N. p., 2014.
Web. doi:10.1063/1.4890736.

```
Hübener, Hannes, & Giustino, Feliciano.
```*Linear optical response of finite systems using multishift linear system solvers*. United States. doi:10.1063/1.4890736.

```
Hübener, Hannes, and Giustino, Feliciano. Mon .
"Linear optical response of finite systems using multishift linear system solvers". United States.
doi:10.1063/1.4890736.
```

```
@article{osti_22419920,
```

title = {Linear optical response of finite systems using multishift linear system solvers},

author = {Hübener, Hannes and Giustino, Feliciano},

abstractNote = {We discuss the application of multishift linear system solvers to linear-response time-dependent density functional theory. Using this technique the complete frequency-dependent electronic density response of finite systems to an external perturbation can be calculated at the cost of a single solution of a linear system via conjugate gradients. We show that multishift time-dependent density functional theory yields excitation energies and oscillator strengths in perfect agreement with the standard diagonalization of the response matrix (Casida's method), while being computationally advantageous. We present test calculations for benzene, porphin, and chlorophyll molecules. We argue that multishift solvers may find broad applicability in the context of excited-state calculations within density-functional theory and beyond.},

doi = {10.1063/1.4890736},

journal = {Journal of Chemical Physics},

number = 4,

volume = 141,

place = {United States},

year = {Mon Jul 28 00:00:00 EDT 2014},

month = {Mon Jul 28 00:00:00 EDT 2014}

}