is the electrostatic potential generated by the function pair µν at the point R b , the location of nucleus b ∈ B. The integral that is implicit in Eq. ( ) is over the electron coordinate r and the second term in Eq. ( ), involving (Φ b ) µν , comes from the electrostatic interaction between ρ A (r) and the embedding charges {q b } on monomers B = A. The final term in Eq. ( ) includes the response of the embedding charges to changes in the fragment wavefunctions (∂q a /∂P A µν ), and ensures that the converged XPol energy is variational. The embedding potential E embed is a straightforward sum of interactions between point charges q a ∈ A and monomer densities ρ B (r), along with interactions between the charges and the nuclei, and ∂E embed /∂q a is easy to evaluate. In contrast, the derivative ∂q a /P A µν depends on how the embedding charges {q a } are determined from the SCF wavefunction for monomer A. Mulliken charges are used in the original XPol method but we find them to be unstable when extended basis sets are used, as are Löwdin charges. A physically appealing choice are "ChElPG" charges derived from the molecular electrostatic potential, 118 which are the atomic charges that best reproduce the SCF electrostatic potential near the vdW surface of the molecule. The requisite derivatives ∂q a /P A µν are complicated but they have been implemented. In recent work, however, we have taken the q a from "Charge Model 5" (CM5), 120 which is an empirical modification of the Hirshfeld scheme, 121 which is designed to reproduce molecular dipole moments. This model avoids some significant computational overhead associated with evaluating ∂q a /P A µν for ChElPG charges, as illustrated by timing data in Fig. for a C 60 -buckycatcher complex where the time to compute the derivatives ∂q a /P µν is reduced from 16.7 h (ChElPG) to 2.0 h (CM5). The former value represents about 35% of the total cost of the XSAPT calculation whereas the cost to differentiate the CM5 is close to negligible, resembling the cost to evaluate E xc on the DFT quadrature grid.