Fast construction of the Kohn-Sham response function for molecules

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 (NN omega)-N-2, 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 (NN omega)-N-2 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 = iGW and we expect it to be useful in the analysis of exitonic effects in molecules. (C) 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim