  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.
