Other dispersion corrections use the self-consistent field (SCF) electron density to obtain in situ ("atoms-in-molecules") C 6 , C 8 , . . . coefficients that reflect the manner in which an atom is both confined and polarized by its environment. The exchange dipole moment (XDM) model of Becke and Johnson is one such approach, as is the Tkatchenko-Scheffler (TS) model, sometimes called "vdW-TS". Both methods incorporate what Dobson has dubbed "type A" dispersion nonadditivity, meaning that free-atom C n coefficients are modified by the molecular environment. Separate from that effect, Dobson designates "type B" nonadditivity to reflect the fact that atom-atom dispersion interactions are screened by the presence of polarizable centers on other atoms. These effects become larger with molecular size, leading to a breakdown in the pairwise atom-atom approximation. To correct for this, explicit three-body dispersion corrections can be added, typically of the Axilrod-Teller-Muto "triple-dipole" variety, which is the leading three-body dispersion correction from third-order perturbation theory. Alternatively, implicit nonadditivity can be incorporated by means of a density-dependent many-body dispersion (MBD) model, as pioneered by Tkatchenko and co-workers. For density-based dispersion corrections, it is important to choose a (mostly) dispersion-free XC functional, lest there be substantial doublecounting, and to balance the range of the semilocal functional against that of the dispersion correction. The culmination of sundry efforts to incorporate dispersion into DFT can be seen in Fig. for two archetypal dispersion-bound systems, namely, a rare-gas dimer (Kr 2 ) and the face-to-face or "sandwich" configuration of (C 6 H 6 ) 2 , which is a typical example of a π-stacking interaction. Figure (a) juxtaposes potential energy curves for the latter, computed using a variety of dispersion corrections applied to the Perdew-Burke-Ernzerhof (PBE) functional, a semilocal generalized gradient approximation (GGA). In the absence of any ad hoc dispersion correction, this functional affords a potential energy profile that is strictly repulsive, and in that way it is representative of the early 21st-century state of affairs with regard to nonbonded interactions in DFT. Meanwhile, the addition of various dispersion corrections affords a reasonably accurate potential energy curve, as compared to a benchmark calculation at the CCSD(T) level. (For a recent review of ab initio benchmarks for noncovalent systems, see Patkowski. ) Interaction energies for the benzene dimer obtained using these dispersion-corrected PBE methods (PBE+D3, PBE+MBD, or PBE+XDM) lie in the range 1.5-1.9 kcal/mol, as compared to a complete basis-set (CBS) CCSD(T) benchmark value of 1.7 kcal/mol. Equilibrium separations (in the D 6h geometry) range from 3.9-4.0 Å for dispersion-corrected PBE methods, as compared to the CCSD(T)/CBS value of 3.9 Å.