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

Abstract

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.

20 pages, 11 figures

References in corpus (6)

• Selfconsistent order-N density-functional calculations for very large systems
• Van der Waals Energies in Density Functional Theory
• Turbo charging time-dependent density-functional theory with Lanczos chains
• Adiabatic-connection fluctuation-dissipation density-functional theory based on range separation
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Cited by in corpus (6)

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• First-principles GW calculations for fullerenes, porphyrins, phtalocyanine, and other molecules of interest for organic photovoltaic applications
• Fully self-consistent $GW$ and quasi-particle self-consistent $GW$ for molecules
• An O(N^3) implementation of Hedin's GW approximation for molecules
• Optical response of silver clusters and their hollow shells from Linear-Response TDDFT
• Fast construction of the Kohn--Sham response function for molecules