In this section, we compared the performance of three different SAPT variants: XSAPT, SAPT0(HF), and SAPT0(KS), using either MBD or else ai D3 to replace second-order dispersion (eq. 3) in each case. The purpose of these tests are to examine the importance of the self-consistent XPol charge embedding that is used in XSAPT + MBD, thus the two SAPT0 variants do not include such an embedding. The SAPT0(HF) + MBD method consists of a standard HF-based SAPT0 calculation but with a modified dispersion term, while SAPT0(KS) + MBD uses GDD-tuned LRC-ωPBE in place of HF theory for the monomer wave functions and is therefore similar to XSAPT + MBD except that the self-consistent embedding is omitted. 4.6.1. Total Interaction Energies. Error statistics for the SAPT0(HF) + MBD and SAPT0(KS) + MBD methods, as applied to the S66 dimers data set, are provided in Tables and, respectively, which should be compared to the statistics for XSAPT + MBD that are listed in Table . SAPT0(HF) + MBD is clearly less accurate than either of the approaches based on LRC-ωPBE for the monomers, with MAEs that are consistently 1.0-1.5 kcal/mol larger. (This is analyzed in terms of energy components in Section 4 .6 .2.) Statistically speaking, the performance of SAPT0(KS) + MBD and XSAPT + MBD is about the same for these dimers, which by definition do not experience many-body polarization. This demonstrates that the charge-embedding procedure does not improve the quality of the zeroth-order reference state small dimers in any way that is statistically meaningful.