Cholesky decomposition of the atomic two-electron integral matrix has recently been proposed as a procedure for automated generation of auxiliary basis sets for the density fitting approximation [F. Aquilante, J. Chem. Phys. 127, 114107 (2007)]. In order to increase computational performance while maintaining accuracy, we propose here to reduce the number of primitive Gaussian functions of the contracted auxiliary basis functions by means of a second Cholesky decomposition. Test calculations show that this procedure is most beneficial in conjunction with highly contracted atomic orbital basis sets such as atomic natural orbitals, and that the error resulting from the second decomposition is negligible. We also demonstrate theoretically as well as computationally that the locality of the fitting coefficients can be controlled by means of the decomposition threshold even with the long-ranged Coulomb metric. Cholesky decomposition-based auxiliary basis sets are thus ideally suited for local density fitting approximations.
Bibliographical noteFunding Information:
Part of this work was carried out under the HPC-EUROPA project (Grant No. RII3-CT-2003-506079) with the support of the European Community-Research Infrastructure Action of the FP6 “Structuring the European Research Area” Programme. Funding from the Swiss National Science Foundation (SNF) (Grant No. 200020-120007), and Swedish Research Council (VR) are also acknowledged.