Automatic Generation of Even-Tempered Auxiliary Basis Sets with Shared Exponents for Density Fitting

A new algorithm for the automatic generation of auxiliary basis sets for the variational density fitting (DF) of two-electron Coulomb repulsion and Fock exchange energies is presented. It generates even-tempered primitive Hermite Gaussian auxiliary basis sets with shared exponents according to the underlying orbital basis set. To this end, the auxiliary basis sets, denoted GEN-X2, GEN-X3 and GEN-X4, span the product space of the primary orbital basis set for each element. The accuracy of the GEN-Xn (n = 2, 3 and 4) auxiliary basis sets was tested with the DZVP, 6-31G** and def2-TZVPP orbital basis sets for elements from H to Kr employing a large set of small molecules representing (nearly) each element in its common oxidation states. DF errors below 1 kcal/mol were reached for all systems. Whereas this fitting precision is reached in DF PBE calculations already with the smallest GEN-X2 auxiliary basis set for all test systems corresponding DF Hartree-Fock calculations require GEN-X3 and GEN-X4 for molecules containing second and third row elements (including transition metals), respectively. Most satisfying, in all cases the DF error signs reflect the theoretical variational bounds of the Coulomb and Fock fitting. The computational efficiency of the GEN-Xn auxiliary basis sets was benchmarked by single-point energy calculations of hydrogen saturated MFI zeolite cutouts with up to 1408 atoms.