Perturbation Analysis of Three- and Four-Atom Exchange Interactions in a Gaussian Effective-Electron Model

Abstract

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 fee 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.

Validity of the three‐center, four‐electron model for stability of rare gas halides on the basis of exchange perturbation theory

“…I t is interesting to remark that for this configuration, interactions between three and four fluorine atoms do not cancel, the four-atom contribution being an order of magnitude smaller than both the superexchange and the three-atom interactions. Again, this observation agrees with earlier results [ 8 ] .…”

“…The four-atom cluster, however, yields an attractive contribution which practically cancels the three-atom repulsion. This peculiarity for the square arrangement was already observed in earlier work on the stability of rare gas crystals [8]. For the binding energy of the tetrafluorides, we are then left with superexchange contributions for units XFF separately, plus indirect exchange interactions involving the xenon atom and three and four fluorine atoms.…”

Three-body Effects in Calcium(II)-ammonia Solutions: Molecular Dynamics Simulations

“…In 1962, in order to simplify the calculation of many-body exchange effects, Jansen [2] introduced the Gaussian effective electron model and found that first-order three-body exchange effects for the rare gases could change the exchange energies by as much as 20% of the two-body exchange energies. Furthermore, Lombardi and Jansen [3] also extended the approach to four-body interactions and found that these effects were negligible for most geometries of interest. These observations have been illustrated for a monatomic gas [4] and numerous cases of ions in aqueous solution [5][6][7][8].…”

On the exchange repulsion between beryllium atoms

“…Nevertheless, these investigations proved to be helpful in the explanation of the rare-gas crystal paradox [7]. They also allowed one to explain the greater stabilization and shortening of the hydrogen bonds in ice [8].…”

“…They also allowed one to explain the greater stabilization and shortening of the hydrogen bonds in ice [8]. Unfortunately, most of the existing attempts to assess non-additive effects are based on approximate methods; for example, on the effective electron model [7]. Therefore, it would be very illuminating to compare these results with those one obtains Downloaded by [McGill University Library] at 05:03 17 October 2012 with the exact methods.…”