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The use of the linear combination of atomic orbitals method for excited states involves products of orbitals that are known to be linearly dependent. We identify a basis in the space of orbital products that is local for orbitals of finite support and with a residual error that vanishes exponentially with its dimension. As an application of our previously reported technique we compute the Kohn–Sham density response function  $\chi _{0} $  for a molecule consisting of  N  atoms in  $N^{2} N_{\omega } $  operations, with  $N_{\omega } $  the number of frequency points. We test our construction of  $\chi _{0} $  by computing molecular spectra directly from the equations of Petersilka–Gossmann–Gross in  $N^{2} N_{\omega } $  operations rather than from Casida's equations which takes  $N^{3} $  operations. We consider the good agreement with previously calculated molecular spectra as a validation of our construction of  $\chi _{0} $ . Ongoing work indicates that our method is well suited for the computation of the  GW  self‐energy  $\Sigma = {\rm i}GW$  and we expect it to be useful in the analysis of exitonic effects in molecules.

Fast construction of the Kohn–Sham response function for molecules