Drude-Model Calculation of Dispersion Forces. II. The Linear Lattice

The London-van der Waals cohesive energy of a linear lattice is calculated in the dipole-dipole approximation, including all orders of perturbation. This result is obtained by applying the Born-von Kármán method to the electronic motions, using a model which represents each molecule as an isotropic harmonic dipole-oscillator. The dispersion interaction energy of the lattice is expanded in powers of the parameter α/a3 (where α is the molecular polarizability and a the nearest neighbor distance), and is computed up to the eighth order. For values of α/a3 appropriate to actual molecular crystals, the main contribution to the energy comes from the second order. Among the higher order terms, the third order is always important, but for α/a3≥0.06, contributes less than one-half of the total correction to the second-order energy.