Systematic Analysis of Many-Body Interactions in Molecular Solids

Abstract

In the latter case, we could intercompare 1/TR and 1/TRO and eliminate the common interaction parameter B from them. In this way, Eq. (24) could be tested. This would not only test the present theory, but also Eq. (18), i.e., the theory of the anharmonic relaxation time of local modes. In other cases, a cruder test is possible by taking Ac^B and intercomparing TRO and m>According to the theory of Montroll and Potts, 4 one would expect local vibrational modes to occur at paramagnetic ions which are substitutional impurities and are either of lighter mass than the normal atom at that site, or are bound to the neighboring atoms with forces stronger than the normal forces. If a lighter atom was also more weakly bound, such that the effect of the mass was compensated by weaker bonds, a local mode would not occur. In general, we know little about interatomic forces, but it may be presumed that if the paramagnetic ion is substantially lighter than the parent atom (say half), a local mode will occur, and the present considerations will apply. Unfortunately, none of the paramagnetic ions in various environments, whose spin lattice relaxation has been studied to date, fulfills this * This research has been made possible through the support and sponsorship of the U. S. Department of Army, through its European Research Office.

Many-Body Contribution to Self-Diffusion in Rare-Gas Solids

“…We shall now consider briefly other many-body interactions: four-dipole interactions 26 "" 30 and Jansen three-atom superexchange forces. [31][32][33] We shall find that consideration of these forces greatly improves the agreement between the experimental and calculated vacancy formation energy and between the experimental self-diffusion activatibn energy and that calculated for a divacancy mechanism; these many-body interactions worsen the agreement between the experimental activation energy and that calculated for single vacancies. Jansen 33 has previously pointed out that superexchange forces lower the vacancy formation energy to give reasonable agreement with experiment.…”

“…Jansen 31 pointed out that there is a serious problem in the direct application of the Axilrod-Teller-type multiple-dipole forces to the solid. Axilrod and Teller assumed well-separated atoms with no electron exchange.…”

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

“…This can lead to a serious modification of the simulation models, especially in cases of condensed-phase systems [1 ]. 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.…”

Non-additive three-body interaction energies for H3(quartet spin state)

“…There have been single-Gaussian-orbital effective one-electron model calculations [23] of non-additive interaction energies, and in particular of L, NAK' (1) and ~' NA';' (2) This model corresponds to replacing the Slater ls orbital in the discussion of this paper by its Gaussian analogue O(r) = (fl/nl/2) 3/a exp (-2-lflr2). In the associated calculations of *Z"(I!NA and .~' (2)NA, the range parameter fl was determined by fitting the dipole-dipole dispersion energy, in the effective one-electron Gaussian model, to the 17(2) The attractive part of an empirical potential with "-"NA~' (2) being normalized to *:AOt)' problems with this approach have been discussed in the literature [1,11,24,25] and, at least partly because the values of the range parameters fl are too small, it strongly overestimates the non-additive energies.…”

“…where d, e and f are one of the orbitals a, b or c. Both the symbolic mathematical derivation computer package REDUCE 3 [20] and a hand derivation were employed to obtain the expression for "~NA'(2) The required integrals, for a single Gaussian s orbital, have been investigated and/or used by several workers [21][22][23]; unfortunately there are some errors or other difficulties associated with the results so obtained [1,11,19,24,25]. Most of the integrals in Slater form have not been investigated before and techniques that are reliable for both small and large R are required for the purposes of this work.…”