Statistical atom model

The reliability of initial equations and regulations was proved with numerous calculations and comparisons. In particular, it was shown [8] that PE-parameter numerically equals the energy of valence electrons in a statistical atom model and is a direct characteristic of electron density in the atom at the given distance from the nucleus. 

EXPLORING THE ORBITAL DECOMPOSITION OF THE KINETIC THEORY WITH STATISTICAL ATOMIC MODELS... 

TerwiUiger, T. C. (2003c). Improving macromolecular atomic models at moderate resolution by automated iterative model building, statistical density modification and refinement. Acta Crystallogr. D 59,1174 1182. 

Many years ago, Lacher (17) explained the P-C-T data shown in Figure 1 with a statistical mechanical model, a model that has formed the basis of subsequent treatments of nonstoichiometry in other systems as well. With the assumption that the hydrogen atoms are localized to each site, the resulting partial configurational entropy is given by... 

The calculation of entropies for gaseous species generally requires detailed knowledge of geometry, bond distances and vibrational frequencies. We have developed a statistical mechanical model which allows an estimation of the entropy of an unknown molecule using as input only the atomic masses and Interatomic distances. Details of the development of the model have been given in previous publications (4). A brief summary of the important assumptions and equations is given below. 

The last topic to comment is the difference between the optimum compositions in Ru of the Pt-Ru alloys for the oxidation of CO (50 at.% Ru) and methanol (10-20 at.% Ru). Gasteiger et al. " proposed an explanation based on a statistical modelization of the surface of an alloy containing x at.% Ru. The stmctural atomic model proposed by these authors needs a maximum number of 3-fold platinum sites for the adsorption of the CH3OH molecule, and adjacent to 1 Ru atom to adsorb the OH species. This would correspond to a surface with 8-14 at.% Ru depending on the orientation of the low index single crystal planes, 8% for (111), 10% for (100)... 

The discussion in this chapter has focused on the properties of liquids at interfaces. A related area of contemporary research is the study of solid gas interface. The solid surface is quite different in that atomic or molecular components of a solid are relatively motionless compared to those of liquid. For this reason it is easier to define a plane associated with a well-defined solid surface. The approach to studying adsorption on solids has been more molecular with the development of sophisticated statistical mechanical models. On the other hand, the study of liquid I gas and liquid liquid interfaces has been much more macroscopic in approach with a firm connection to classical thermodynamics. As the understanding of liquids has improved at the molecular level using contemporary statistical mechanical tools, these methods are being applied now to fluids at interfaces. 

A related but somewhat more fundamental question concerns the underlying thermodynamic basis of the transition. Specifically, we need to know whether it is sufficient to understand the behavior of simplest atomic models to explain the thermodynamic aspects of the phenomenon (as is the case, e.g., for the equilibrium melting and freezing transitions. If so, it would be possible for computer simulation experiments of sufficient accuracy to provide the basis for a molecular level statistical mechanical account of all aspects of the glass transition. 

---