The parameters ζ λ,A , c 0,λ,A , c 1,λ,A , k 1,A , k 2,A , and k 3,A were optimized variationally, similarly to the first version of q-vSZP. See Ref. 12 for details of the optimization process. An important difference from the first version is the use of reference DFT charges at the ωB97M-V 77 /def2-TZVPPD Hirshfeld 76 level for optimizing the basis set instead of the CEH charges used during application. This has two advantages: First, the optimization process becomes independent of changes in the CEH model, e.g., avoiding re-parameterizations due to changed CEH parameters. Second, since the basis set parameters were optimized with reference DFT charges, rare cases where the CEH charges are qualitatively incorrect do not affect the basis set optimization. The optimization of the q-vSZP for the new elements (lanthanoids,