Auxiliary Basis Sets for Density Fitting in Explicitly Correlated Calculations: The Atoms H–Ar

Auxiliary basis sets specifically matched to the correlation consistent cc- pVnZ-F12 and cc-pCVnZ-F12 orbital basis sets for the elements H−Ar have been optimized at the density-fitted second-order Møller−Plesset perturbation theory level of theory for use in explicitly correlated (F12) methods, which utilize density fitting for the evaluation of two-electron integrals. Calculations of the correlation energy for a test set of small to medium sized molecules indicate that the density fitting error when using these auxiliary sets is 2 to 3 orders of magnitude smaller than the F12 orbital basis set incompleteness error. The error introduced by the use of these fitting sets within the resolution-of-the-identity approximation of the many-electron integrals arising in F12 theory has also been assessed and is demonstrated to be negligible and well-controlled. General guidelines are proposed for the optimization of density fitting auxiliary basis sets for use with F12 methods for other elements.