Additives hard-soft concept

The equations 7, 8 and 9 fail to operate when the HOMO - LUMO energy gap becomes too small and do not consider the influence on chemical properties of other orbitals, besides the HOMO and LUMO s. Moreover, it is not possible to study the site selectivity of a chemical species considering only absolute hardness other than space-dependent (local) versions of hardness/softness concepts [5]. Thus in addition to the global definition of r) and S, the local hardness [4] and local softness [5] have been introduced as follows ... 

In addition we will consider the possibility to obtain reliable theoretical information on the preferred attach sites for proton and metal cations and on the potential energy surfaces (PES) that cannot be determined experimentally even with the most modern and sophisticated mass-spectrometric instruments [22,23j. Furthermore, we will propose the way to rationalize some of chemical properties by using the concepts of hardness, softness and other reactivity indices (Fukui functions) for which an exact definition exists only in the framework of DFT 1111. These last fascinating tools can contribute to increase funhemiore the DFT use going in the "core" of molecules to predict and explain basic chemical concepts. 

Apart from the local and global softness (hardness), the concept of group softness (hardness) has been introduced [19], especially for studying the electronic effect of substituents in aromatic compounds [25]. It also applies to solids and can be directly calculated according to the additivity rule for local softness, Eq. (23). Yet another related quantity can be defined, which is useful for understanding observed trends and which has considerable predictive value. 

The Pearson concept can be transferred to metal surfaces. In this case, in addition to the character of the bonding electrons, the crystallographic structure of the metal surface and the surface topography must be taken into account. For cubic close-packed structures the most prominent crystallographic surfaces are the (111), (100), and (110) interfaces. The (111) face is the closest packed structure and has the hardest surface topography followed by the (100) and (110) interfaces (the softest one). The hard-soft character of a polycrystalline... 

Eq. (1) with no obvious advantages for this additional complication since "strength of hardness and strength of softness would have to change in a way contrary to the accepted definition of the words. This equation doesn t correlate our quantitative data, and the HSAB concept as usually applied is not an adequate way to describe intermolecular... 

Condensation polymerization and stepwise addition polymerization are, for example, applied for the preparation of block polyesters. The synthesis concepts are different from those of chain polymerization in that at least one monomer is an oligomer with one or two functional end groups, for example polytetrahy-drofurane with a molecular weight of several hundred and OH-end groups (see Example 3-23). If this oligomer partially replaces butandiol in the condensation polymerization with terephthalic acid (compare examples 4-1 and 4-2), a po-ly(ether ester) is obtained with hard ester segments and soft ether segments and with the properties of a thermoplastic elastomer. 

Thus we can understand easily enough that the reaction between bromine and ethylene giving dibromoethane is exothermic—it replaces one n bond (C=C) with two a bonds (C—Br) at the expense of a weak a bond (Br—Br). However, it is not always obvious how strong the bonds will be when one molecule combines with another to form a single new molecule, or what happens to the energy if we exchange parts of one molecule with parts of another. A useful addition to understanding this sort of problem has been Pearson s concept of hard and soft acids and bases (HSAB). 

As is obvious from the equations, the local and global hardness and softness are structure-dependent properties. For small molecules, one such a structural feature is the molecular size because softness is additive, and because of its dominantly positive character [8], its value is a function of the number of atoms in the molecule. This paraUels our concepts regarding charge delocalization (stabilization) more substituents make it easier. Examples are given later. For infinite crystals however there are other topological parameters to account for. 

According to the proposed mechanism, addition of the silyl-rhodium moiety to the coordinated carbonyl group converts it into the a-siloxyalkyl-rhodium complex (III), which most likely is an equilibrium mixture of complexes Ilk and Iltt. Then, transfer of the hydride ligand in III from the metal center to the alkyl carbon affords the products, IVfl and IV, respectively. The formation of the a-siloxyalkyl-rhodium intermediate is quite probable in view of the well-documented soft-hard conception , and must be characteristic of the ketone hydrosilylation. 

This concept of HSAB can be applied to interpret the difference in the base metals concentrated to different vein-type deposits in Japan (Shikazono and Shimizu 1992).Major vein-type deposits in Japan include precious metal deposits and base metal deposits which is characterized by enrichments of Hg, Te, Se, As, Sb, Cd and T1 in addition to Au and Ag, and Cu, Pb, Zn, Fe, Mn, Ag, Cu, Bi, As, Sb, In, Ga, Sn and W, respectively. This means precious metal and base metal vein-type deposits are characterized by enrichment of soft metals and hard metals, respectively. This difference is consistent with fluid inclusion data showing that Cl of ore fluids responsible for base metal deposits is distinctly higher than that responsible for precious deposits (Shikazono and Shimizu 1992). 

It is shown that Density Functional Theory offers both a conceptual and a computational tool for chemists in relating electronic structure of atoms and molecules to their properties both as isolated systems and upon interaction. The computational performance of DFT in the calculation of typical DFT quantities such as electronegativity and hardness and in the ev uation of atomic electronic affinities and molecular dipole and quadrupole momCTits is assessed. DFT concepts are discussed as such (a non finite difference evaluation of the electronic Fukui function, local softness and its use in similarity analysis of peptideisosteres and the nuclear Fukui function as a indicator of nuclear rearrangemCTits upon reaction) and in the context of principles (EEM, MHP, HSAB) for a variety of reactions involving the influence of solvent on the acidity of alcohols and the addition of HNC to dipolarophiles. 

The excluded volume theory is the most commonly used continuum analytical model of percolation. The excluded volume of an object is defined as the volume around the object into which another identical object cannot enter without contacting the first object as illustrated in Figure 2. ° The principal concept in the excluded volume model is that the percolation threshold of a system is determined by the excluded volume of filler particles, rather than their true volume. This is particularly applicable to asymmetrical, unaligned objects for which the excluded volume can differ significantly from their true volume. Therefore, this model has been applied to describe critical percolation phenomena for a wide variety of filler geometries. In addition, excluded volume arguments provide useful theoretical approximations in many computational stu-dies. Excluded volume solutions were first formulated for soft-core (interpenetrable) fillers, and later extended to core-shell (impenetrable hard-core surrounded by a penetrable shell) fillers. ... 

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