On the Kohn--Sham density response in a localized basis set

Details On the Kohn--Sham density response in a localized basis set On the Kohn--Sham density response in a localized basis set

2009-04-24

arxiv.org/abs/0904.3834v2

J. Chem. Phys. 131, 044103 (2009)

Physics

Condensed Matter

Other Condensed Matter

20 pages, 11 figures

Scientific paper

10.1063/1.3179755

We construct the Kohn--Sham density response function $\chi_{0}$ in a previously described basis of the space of orbital products. The calculational complexity of our construction is $O(N^{2}N_{\omega})$ for a molecule of $N$ atoms and in a spectroscopic window of $N_{\omega}$ frequency points. As a first application, we use $\chi_{0}$ to calculate molecular spectra from the Petersilka--Gossmann--Gross equation. With $\chi_{0}$ as input, we obtain correct spectra with an extra computational effort that grows also as $O(N^2 N_{\omega})$ and, therefore, less steeply in $N$ than the $O(N^{3})$ complexity of solving Casida's equations. Our construction should be useful for the study of excitons in molecular physics and in related areas where $\chi_{0}$ is a crucial ingredient.

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