Broken-atomic-bond model

Simple criteria for surface segregation in alloys (relative melting points, enthalpies of sublimation, metal atom radii, surface free energies of the pure metals) all indicate that surface segregation of titanium should occur on Pt/Ti alloys in vacuo. However, this is inadequate because of the large departures from ideality in Pt/Ti alloys. Analysis (11) of a broken bond model of the system, especially with the use of data directly determined with Pt/Ti alloys, gives a more reliable result. 

Although the discussion on the broken bond model has been mainly focused on pure metallic surfaces, the extension can be easily made simply by replacing the binding energy term Ej, in Eq. (1) with the interaction energies among different atoms in the case of metallic alloys [15-17]. However, in the case of ceramic materials the... 

Figure 14.12 Vaporization and surface tension y both involve breaking bonds, modelled through the quantity u AA- The slope of y x area (liquid metals. Source redrawn from SH Overbury, PA Bertrand and GA Somorjai, Chem Rev 75, S47-560 (1975). 

As reactants transfonn to products in a chemical reaction, reactant bonds are broken and refomied for the products. Different theoretical models are used to describe this process ranging from time-dependent classical or quantum dynamics [1,2], in which the motions of individual atoms are propagated, to models based on the postidates of statistical mechanics [3], The validity of the latter models depends on whether statistical mechanical treatments represent the actual nature of the atomic motions during the chemical reaction. Such a statistical mechanical description has been widely used in imimolecular kinetics [4] and appears to be an accurate model for many reactions. It is particularly instructive to discuss statistical models for unimolecular reactions, since the model may be fomuilated at the elementary microcanonical level and then averaged to obtain the canonical model. 

The representation of an essentially infinite framework by a finite SCF treated cluster of atoms, (with or without point-ions), inevitably leads to the problem of how to truncate the model-molecule . Previous attempts at this have included using hydrogen atoms l and ghost atoms . Other possibilities include leaving the electron from the broken bond in an open shell, or closing this shell to form an ionic cluster. A series of calculations were performed to test which was the host physically realistic, and computationally viable, solution to this problem for this system. 

The main handicap of MD is the knowledge of the function [/( ). There are some systems where reliable approximations to the true (7( r, ) are available. This is, for example, the case of ionic oxides. (7( rJ) is in such a case made of coulombic (pairwise) interactions and short-range terms. A second example is a closed-shell molecular system. In this case the interaction potentials are separated into intraatomic and interatomic parts. A third type of physical system for which suitable approaches to [/( r, ) exist are the transition metals and their alloys. To this class of models belong the glue model and the embedded atom method. Systems where chemical bonds of molecules are broken or created are much more difficult to describe, since the only way to get a proper description of a reaction all the way between reactant and products would be to solve the quantum-mechanical problem at each step of the reaction. 

Fig. 41. Crystal structure of the f-imidazolium dihydrate associate 1,) (O atoms dotted, N atoms hatched) showing intra-associate H-bonds (broken lines) and the resulting coinciding atomic sites from the fitting experiment with SGPA (bold dots). A position marked indicates the translated OlO from the anion. An expected atomic position of the Or atom of Seri 95 (not considered as a part of the modelling experiment) is indicated merely to show the resulting would-be position executing the same transformation as for the seven fitted atoms. Only relevant H atoms are shown...

Consideration of the feasibility of these shifts as concerted processes, i.e. via cyclic transition states, requires as usual a consideration of the symmetry of the orbitals involved. A model related to the transition state can be constructed by the device of assuming that the C—H a bond that is migrating can be broken down into a hydrogen Is orbital and a carbon 2p orbital. For the case where x = 1 in (36), the T.S. can then be considered as being made up from a pentadienyl radical (38), with a hydrogen atom (one electron in a Is orbital) migrating between the terminal carbon atoms of its Site system (i.e. a 6e system overall is involved) ... 

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