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Density fitting (DF), also known as the resolution of the identity (RI), is awidely used technique in quantum chemical calculations with various types ofatomic basis sets - Gaussian-type orbitals, Slater-type orbitals, as well asnumerical atomic orbitals - to speed up density functional, Hartree-Fock, andpost-Hartree-Fock calculations. Traditionally, custom auxiliary basis sets arehand-optimized for each orbital basis set; however, some automatic schemes havealso been suggested. In this work, we propose a simple yet numerically stableautomated scheme for forming auxiliary basis sets with the help of a pivotedCholesky decomposition, which is applicable to any type of atomic basisfunction. We exemplify the scheme with proof-of-concept calculations withGaussian basis sets and show that the proposed approach leads to negligibleDF/RI errors in Hartree-Fock (HF) and second-order M{\o}ller-Plesset (MP2)total energies of the non-multireference part of the W4-17 test set when usedwith orbital basis sets of at least polarized triple-$\zeta$ quality. Theresults are promising for future applications employing Slater-type orbitals ornumerical atomic orbitals, as well as schemes based on the use of local fittingapproaches. Global fitting approaches can also be used, in which case thehigh-angular-momentum functions produced by the present scheme can be truncatedto minimize the computational cost.

Straightforward and accurate automatic auxiliary basis set generation for molecular calculations with atomic orbital basis sets