Drude-Model Calculation of Dispersion Forces. III. The Fourth-Order Contribution

Abstract

The results of part I are applied in calculating the fourth-order dipole-dipole contribution to the dispersion interaction energy of a system containing N identical spherical molecules. This contribution to the energy consists of pair terms proportional to Rij-12, triplet terms proportional to (RijRjk)-6, and quadruplet terms proportional to (RijRjkRklRli)-3, where Rij is the separation of the ith and jth molecules. The expression for the fourth-order energy is summed approximately over the face-centered-cubic lattice. The result is E(4) ≃—100NV(α/R03)4, where α is the polarizability and V the characteristic dispersion energy of the molecules, R0 is the nearest-neighbor distance in the lattice, and N is the number of molecules in the crystal. The triplet terms are responsible for the main contribution to this sum. The fourth-order dipole-dipole dispersion energy of the lattice is negative and comparable in magnitude with the positive triple-dipole energy computed by Axilrod and others, in cases where the latter contribution is substantial.