Exact electrostatic interactions, computed using Eq. ( ) without any multipole approximation, are attractive in the typical range of intermolecular π-stacking separations (3.4-3.8 Å), and they are attractive also in the edge-to-face (C-H• • • π) configuration also. This has implications for understanding πstacking, as discussed in Section 3.3. For now, we simply note that an atom-centered multipole approximation [Fig. 21(a)] to E elst , which should converge faster than the single-center expansion in Eq. ( ), nevertheless does not agree with exact calculations for the cofacial arrangement until the face-to-face separation R is much larger than typical π-stacking distances. A leading-order approximation, using only the molecular quadrupole moments of the two benzene monomers, does not agree with exact electrostatics until even larger face-to-face separations [Fig. ]. At typical π-stacking separations, such as R = 3.35 Å for graphene 201 or R = 3.4 Å for the parallel-displaced benzene dimer, 195 exact electrostatics is attractive but these multipolar approximations are repulsive. This breakdown in multipolar approximations is sometimes ascribed to charge penetration effects, meaning that multipole approximations no longer describe E elst when ρ A (r) and ρ B (r) interpenetrate. Another interesting example of this effect can be found in the corannulene dimer, (C 20 H 10 ) 2 . The corannulene monomer consists of six hexagonal rings surrounding a central pentagonal ring, the latter of which lends curvature to the structure, which has been called a "buckybowl". This and other concave hydrocarbons form concentric stacks in the solid state, and in fact a five-member ring is not required to induce curvature. The π-electron density at the bottom of these buckybowls must be compensated by electropositive terminal C-H bonds, as it is in benzene as well but the buckybowls break planar symmetry and may develop dipole moments. These range from µ = 2.07 D in C 20 H 10 , based on a gas-phase measurement, 209 to µ > 10 D in larger buckybowls, based on calculations, in what has been called "flexo-electric" π-stacking. The implication is that the driving force for this solid-state stacking phenomenon is to align the dipole moments of the monomers. In view of exact electrostatic calculations for (C 6 H 6 ) 2 , however, this hypothesis should be regarded with suspicion.