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

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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.