Intermolecular interaction energies by topologically partitioned electric properties .2. Dispersion energies in one-centre and multicentre multipole expansions

Multicentre multipole expansions in principle should allow one to solve the 'shape' convergence problem arising in the calculation of long-range interaction energies between large non-spherical molecules via point-multipole expansions. In part I of this series (1996, Molec. Phys., 88, 69) it was shown that this indeed is the case for first-order electrostatic and second-order induction energies when employing distributed multipole moments and static polarizabilities generated from the topological partitioning of the molecular volume as provided by Bader's 'atoms-in-molecules' theory. Their generalization to frequency-dependent, topologically partitioned polarizabilities is used in the present contribution to compare the convergence behaviour of one-centre and multicentre multipole expansions of the second-order dispersion energy for homomolecular dimers of the water, carbon monoxide, cyanogen and urea molecules. The findings are similar to those for the induction energy; the radial 'extension' convergence problem, which already exists for point-multipole expanded interaction energies between atoms, necessarily persists, but the angular convergence problems linked to the shape of the interacting molecules can successfully be treated by multicentre multipole expansions of the dispersion energy.