Density fitting with auxiliary basis sets from Cholesky decompositions

Recent progress in the use of Cholesky decomposition techniques within the density fitting approximation of two-electron integrals is reviewed with emphasis on the theoretical background. Special attention is paid to the fact that errors due to the density fitting approximation can be controlled by constructing auxiliary basis sets by means of Cholesky decomposition of either the entire or certain subblocks of the molecular two-electron integral matrix. Finally, the prospects of trivial linear-scaling calculation of fitting coefficients in the Cholesky decomposition-based density fitting scheme are outlined