In contrast to the behavior for IL16 and AHB21, where XSAPT + ai D3 appears to offer clear improvement over the other two +ai D3 methods, results from all three approaches are much more similar for the CHB6 data set; see Table . This data set consists of M + (H 2 O) and M + (C 6 H 6 ) complexes with M = Li, Na, or K. Specifically for the cations, the tuning procedure affords rather large values of ω GDD (Table ): ω GDD = 1.30 a -1 0 , 0.84 a -1 0 , and 0.59 a -1 0 for Li + , Na + , and K + , respectively. The values for Li + and Na + are much larger than the tuned values for small, charge-neutral monomers or anions, and even the value obtained for K + is somewhat larger than what we observe for other systems. The range separation in LRC-ωPBE occurs at a distance of ≈ ω -1 GDD , and that value corresponds to 0.41 Å for Li + , 0.63 Å for Na + , and 0.90 Å for K + . In each case, this is smaller than the van der Waals radius of the cation itself, meaning that for the purpose of intermolecular interactions computations, the XSAPT + ai D3 calculations are using HF theory for the exchange functional. This explains the close similarity with SAPT0(HF) + ai D3. 4.6.2. Energy Components. In order to further investigate these three variants of SAPT and to understand the origins of the differences between them, we wish to examine individual energy components. For this we turn to the S22 data set, for which benchmark energy components are available, computed at the SAPT2+(3)/ aug-cc-pVTZ level. Figure compares benchmarks against the SAPT0(HF) + MBD, SAPT0(KS) + MBD, and XSAPT + MBD methods and Table lists the error statistics in each energy component. These data indicate that the E exch and E ind , for the electrostaticallydominated subset of S22, are responsible for the diminished accuracy of SAPT0(HF) + MBD relative to other methods; these two components exhibit MAEs of 3.6 and 2.0 kcal/mol, respectively, for the subset that includes the hydrogen-bonded dimers.