Transferability of atomic properties

The study of the molar volumes of the normal hydrocarbons provided the earliest example of the additivity of group properties (Kopp 1855). The experimentally determined heats of formation for the same homologous series of molecules, CH3(CH2)mCH3, also obey a group additivity scheme (Franklin 1949 Prosen 1946 Benson 1968 Pittam and Pilcher 1972). It is possible to fit the experimental heats of formation for this series, beginning with m = 0, with the expression, 

The distributions of charge for molecules in this series are illustrated in Fig. 1.1 in terms of an outer envelope of the charge density p and, specifically for the five- and six-carbon members, in Fig. 6.9 in the form of contour maps of p. The latter maps show the bond paths linking the nuclei and indicate the intersection of the interatomic surfaces with the plane of the diagram. The intersection of these same surfaces with the density envelopes are shown in Fig. 1.1 and they define the methyl and methylene groups as envisaged by chemists and as defined by theory. The diagrams show qualitatively what the atomic properties will demonstrate quantitatively, that the methyl and 

Relative properties of methyl and methylene groups in normal hydrocarbons 

The additivity of the energy in the w-alkanes is obtained in spite of small differences in group properties, differences which necessarily result from a change in the nature of the bonded neighbour. Thus, there are two kinds of methyl groups the one unique to ethane and the transferable methyl group which is bonded to a methylene group. There are three kinds of methylene 

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Bader, R. F. W., Becker, P. (1988). Transferability of atomic properties and the theorem of Hohenberg and Kohn. Chem. Phys. Lett. 148,452 58. 

Energy of an Atom in a Molecule and Transferability of Atomic Properties... 

These are three examples of the use of atomic properties to obtain quantitative structure-activity relationships (QSAR) or structure-function relationships. One should bear in mind that all properties have an atomic basis, making a multitude of new relationships possible. The atomic contribution to the polarizability, for example, is definable and shown to be transferable [26-28], offering the possibility of improving the use of an electrostatic potential map from zero- to first-order estimates of energies of interaction. 

Tab. 7.1 Comparison of atomic properties for the maximal transferable group in morphine and PEO. ... 

Similarity between quantum systems, such as atoms and molecules, plays a very important role throughout chemistry. Probably the best example is the ubiquitously known periodic system of the elements. In this system, elements are arranged both horizontally and vertically in such a way that in both directions, elements have a high similarity to their neighbors. Another closely related idea is that of transferability. In chemistry, one speaks of transferability of an entity when its properties remain similar between different situations. An example is the transferability of the properties of a functional group between one molecule and another. The main motto of using similarity in chemistry is the assumption that similar molecules have similar properties. 

It is well known, as it has been previously commented, that chemists rely quite often on the concept of transferability of the properties of atoms or functional groups between different molecules. In this context, a molecular fragment is more transferable if it is more similar to the same fragment in a different molecule. 

Other than in polymer matrix composites, the chemical reaction between elements of constituents takes place in different ways. Reaction occurs to form a new compound(s) at the interface region in MMCs, particularly those manufactured by a molten metal infiltration process. Reaction involves transfer of atoms from one or both of the constituents to the reaction site near the interface and these transfer processes are diffusion controlled. Depending on the composite constituents, the atoms of the fiber surface diffuse through the reaction site, (for example, in the boron fiber-titanium matrix system, this causes a significant volume contraction due to void formation in the center of the fiber or at the fiber-compound interface (Blackburn et al., 1966)), or the matrix atoms diffuse through the reaction product. Continued reaction to form a new compound at the interface region is generally harmful to the mechanical properties of composites. 

The issue of transferability of atomic charge models between conformations has been more vigorously discussed in the last decade. Most force fields assume that the charge distribution associated with each atom is independent of conformation. However, it has been noted that potential derived atomic charges do vary with the conformation of the molecule used to derive them and that these variations have a significant effect on computed properties such as the free energy of hydration of alcohols. 

It is the use of zero-flux surfaces for the topological definition of atoms or functional grouping of atoms in molecules that maximizes the extent of transferability of their properties between systems. 

The starting point for the kinetic theory of dilute mono-atomic gases is the Boltzmann equation determining the evolution of the distribution function in time and space. The formulation of the collision term is restricted to gases that are sufficiently dilute so that only binary collisions need to be taken into account. It is also required that the molecular dimensions are small in comparison with the mean distance between the molecules, hence the transfer of molecular properties is solely regarded as a consequence of the free motion of molecules between collisions. 

To control the properties of the fabricated thin films, it is necessary to operate under vacnnm to minimize the interaction between residnal gases and the surface of growing films. The thin films can be obtained in the crystalline or amorphous state by controlling the concentration of the vapor. The process of the film formation by this method involves the following three stages (1) evaporation or sublimation of the charge to form vapor, (2) transfer of atoms or molecnles from evaporation source to the substrate, and (3) condensation of vapor on the snbstrate. 

A specific subset of the broader class of thermodynamic LFERs is known under the acronym LSER, linear solvation energy relationships. The LSER paradigm invokes explicitly the processes in which the solute transfer between two phases takes place and evolved from the work of Abraham (7,10), who built on the pioneer work of Hammet and later on Kamlet and Taft (11,12), enabling the extension of LFER from the realm of atomic properties to the realm of intermolecular interactions. 

On the other hand, it is at the limit of near-perfect transferability of group properties as exhibited by the alkanes that one can detrmine whether or not a proposed theory meets the requirements of experiment, for at this limit one may experimentally determine to high precision the properties of atoms in molecules via their additive contributions. By demonstrating that the atoms defined by quantum mechanics account for and recover the experimentally measured properties of atoms in molecules, one establishes that the atoms of theory are the atoms of chemistry. There is no test of theory other than the demonstration that it predicts what can be measured. 

It has also been shown that in the atomic regions the virial theorem holds [27, 33]. That is why Bader s partitioning of the electron density is often cited as the virial partitioning method [35, 36]. Bader s theory leads to an unequivocal formulation of the transferability idea the ensemble of atomic properties, in particular the contribution of an atom to the total energy, may be the same in different molecules, provided the charge density of the atomic region is identical [27]. The chemical bonds can be identified with the paths of maximal electron density, which interconnect the various nuclei. This point and several other chemical applications of Bader s theory have been recently reviewed by Wiberg [37]. 

In this chapter, we have dealt with radiative transfer of atoms and molecules between different energy states rather extensively. However, transitions can also be induced by collisions. Extensive information on the static and dynamic properties of atoms and molecules can be obtained from collision physics. Although this book is centred on the spectroscopy of atoms and molecules, the importance of collisional physics should be clearly pointed out. For studies of these aspects the reader is referred to [4.32-37]. 

The surface relaxation effects do not affect the second-order magnetic properties of AIMs such as magnetic susceptibility and chemical shielding. The transferability of these properties provides a theoretical basis for the empirical Pascal rules. A Hilbert space approach to the partitioning of magnetic susceptibility into atomic contributions has also been proposed. ... 

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