On the attraction between linear chain molecules and the many-body problem

The van der Waals energy between two identical parallel chains of harmonic oscillators, varying between two and twenty polarizable units on both chains, is analyzed in some detail. The treatment takes account of nonadditive many-body interactions to all orders within the dipolar approximation, and includes the major contributions from dipole–quadrupole and quadrupole–quadrupole couplings. It is shown that for large interchain separations the many-body effects play an important role, but at short distances the exact energy is very nearly the same as the pairwise additive energy, provided the latter is calculated on the basis of the unperturbed polarizability units. The apparent absence of nonadditive forces at short distances is shown to result largely from cancellation of three- and four-body forces; at large separations the four-body forces dominate the three-body. It is concluded that simple limiting formulas designed for large separations or their macroscopic analogs give results which are much too large when applied to Drude chains at equilibrium distances, and it is suggested that great caution ought to be exercised in applying such formulas to real molecular systems.

The contributions from dipole-quadrupole and quadrupole-quadrupole couplings are found to be small for the cases considered.