Points-on-a-sphere approach

New MM3+-based force fields for (p.3-allyl)palladium and palladium olefin complexes with various co-ligands, which are based on the points-on-a-sphere approach and do not require dummy atoms to define the connectivity, have been developed and validated with experimentally observed and quantum-mechanically computed data[454l... 

Why the VSEPR approach should be so successful has been muchly discussed whether the electron pairs are truly similar in energy and whether they repel by either simple electrostatic forces or by the Pauli Exclusion principle (i5). In his comparison of the VSEPR "points-on-a-sphere" formalism with results of Molecular Orbital computations of potential energy surfaces, Bartell concluded that "the VSEPR model somehow captures the essence of molecular behavior" (76). 

Hard-Sphere Model, in 1973, it was suggested that the ionomer peak is ascribed to the distance between ionic aggregates, with the contrast provided by the difference in the electron density between the ionic aggregates and the hydrocarbon phase (22). The scattering centers are considered to be points on a paracrys-talline lattice. In 1983, a refined model was proposed (23) in this hard-sphere model, the midtiplets have hquid-like order and the distance of closest approach... 

For a typical system size used in simulation, = q and a plot of log (a(q)a(-q)) versus log q should be a straight line with slope 2. The key to this approach is determining the instantaneous surface z = f(s). This can be accomplished by finding the contact points (on a grid) between a probe sphere of a fixed radius and the interfacial molecules " once the set of... 

One final point should be noted. Theoretical discussions of electron transfer processes have focused almost entirely on outer-sphere processes. When we have an inner-sphere mechanism, or sufficient electronic interaction in a dynamically trapped mixed-valence complex to produce a large separation between upper and lower potential surfaces, the usual weak-interaction approach has to be abandoned. Thus a detailed knowledge of a potential surface which is not describable as an intersection surface of perturbed harmonic surfaces, for example, is required. For this purpose, detailed calculations will be required. The theory of these processes will be linked more... 

Stated physically, the critical condition for pyrophoricity under the proposed assumptions is that the heat release of the oxide coat formed on a nascent sphere at the ambient temperature must be sufficient to heat the metal to its vaporization point and supply enough heat to vaporize the remaining metal. In such an approach one must take into account the energy necessary to raise the metal from the ambient temperature to the vaporization temperature. If r is assumed to be the radius of the metal particle and 6 the thickness of the oxide coat [(r - <5) is the pure metal radius], then the critical heat balance for pyrophoricity contains three terms ... 

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