To determine the optimal natural auxiliary function (NAF) threshold, we plotted the C K-edge IP value corresponding to the cyanide carbon atom of CH3CN in SS-FNO-IP-EOM-CCSD* at different NAF thresholds while keeping SS-FNO threshold at 10 -4 . We have used even-tempered natural auxiliary functions automatically generated from the orbital basis set in PySCF, resulting in 1002 auxiliary basis functions for CH3CN. Our result shows that using an NAF truncation threshold of 10 -2 leads to an error of less than 0.0001 eV in Figure and retains half the dimension of the auxiliary basis functions. This suggests that the use of NAFs can effectively reduce the computational cost of density-fitting-based EOM calculations without any significant error. Interestingly, both the corrected and uncorrected versions showed almost similar performance, and the default of 10 -2 was used for the subsequent calculations.