An atom-atom partitioning of the electrostatic energy between unperturbed molecules is proposed on the basis of the topology of the electron density. Atom-atom contributions to the electrostatic energy are computed exactly, i.e., via a novel six-dimensional integration over two atomic basins, and by means of the spherical tensor multipole expansion, up to total interaction rank L = l(A) + l(B) + I = 6. The convergence behavior of the topological multipole expansion is compared with that using distributed multipole analysis (DMA) multipole moments for a set of van der Waals complexes at the B3LYP/6-311+G(2d,p) level. Within the context of the Buckingham-Fowler model it is shown that the topological and DMA multipole moments converge to a very similar interaction energy and geometry (average absolute discrepancy of 1.3 kJ/mol and 1.3 degrees, respectively) and are both in good to excellent agreement with supermolecule calculations.