An atom-atom partitioning of the electrostatic energy between unperturbed m
olecules 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 analy
sis (DMA) multipole moments for a set of van der Waals complexes at the B3L
YP/6-311+G(2d,p) level. Within the context of the Buckingham-Fowler model i
t is shown that the topological and DMA multipole moments converge to a ver
y 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.