PERTURBATION ANALYSIS OF 3- AND 4-ATOM EXCHANGE INTERACTIONS IN A GAUSSIAN EFFECTIVE-ELECTRON MODEL

An analysis of three- and four-atom interactions of exchange type in first and second orders of perturbation theory is presented, on the basis of an effective-electron model with a Gaussian distribution of charge. The results are then applied to a determination of the three- and four-atom components of the crystal energy for close-packed rare-gas solids. It is found that both the three- and four-atom interactions favor a fcc crystal structure. The magnitude of the four-atom energy relative to the three-atom component for a given atomic species and a given crystalline configuration is essentially a function only of the ratio between the second- and first-order pair interactions for nearest neighbors in the solid. For the most probable range of values of this ratio, the four-atom crystal energy is relatively unimportant. The sum of three- and four-atom crystal energies is found to vary little with the ratio. Calculated values for the stacking-fault energy in solid argon and xenon agree reasonably well with those obtained from observations on thin films of these solids. © 1968 The American Physical Society.