Localized bond analog

Physical adsorption (physisorption) occurs when an adsorptive comes into contact with a solid surface (the sorbent) [1]. These interactions are unspecific and similar to the forces that lead to the non-ideal behavior of a gas (condensation, van der Waals interactions). They include all interactive and repulsive forces (e.g., London dispersion forces and short range intermolecular repulsion) that cannot be ascribed to localized bonding. In analogy to the attractive forces in real gases, physical adsorption may be understood as an increase of concentration at the gas-solid or gas-liquid interface imder the influence of integrated van der Waals forces. Various specific interactions (e.g., dipole-induced interactions) exist when either the sorbate or the sorbent are polar, but these interactions are usually also summarized under physisorption unless a directed chemical bond is formed. 

Tetrahedron. Sn2Bi2" and Pb2Sb2 with (2)(2) + (2)(3) -h 2 = 12 skeletal electrons for localized bonds along the edges of the tetrahedron analogous to organic tetrahedrane derivatives R4C4. 

In this connection it is also possible to remark that the conjugated skeletons could, of course, also be described by molecular orbitals, e.g. of the HMO type, but for the sake of maximal simplicity we prefer here a qualitative description in terms of localized bonds. Some more complicated examples, for which the delocalized description in terms of molecular orbitals is required are discussed in detail in the study [14]. After having specified the structure of the reacting molecules, the next procedure is completely analogous to the previous case and consists in the construction of assigning tables for both alternative reaction mechanisms. Thus, e.g., in the case of comotatory cyclization, the corresponding assignment has the form (24) (only the orbitals on the reaction centers are involved for brevity). 

The localized bond model for acetylene is precisely analogous to that for ethylene. The n MOs y + 2) and (z + Z2) survive as before. Each carbon atom has two AOs left over. We combine them into a pair of sp hybrids, s xj and (S2 X2) (Fig. 1.35a), pointing in opposite directions along the x axis. These hybrid AOs are used to form localized CH bonds to the hydrogen atoms, and a localized CC a bond. 

Fig. 32. Analogy between local bond flaws and cracks in metallic skins.

Specialized orbitals tailored for analysis of phenomena such as bonding in molecular clusters and electron excitations are obtained by maximization of suitably chosen functionals. The so-called pseudo-Wannier orbitals are produced by a procedure that maximizes similarities between one-electron wavefunc-tions localized within analogous units of a given molecular cluster. These orbitals reveal terminal-group effects in linear polymers and provide systematic schemes for partitioning of the total energy and one-electron properties of finite clusters. 

Several methods of quantitative description of molecular structure based on the concepts of valence bond theory have been developed. These methods employ orbitals similar to localized valence bond orbitals, but permitting modest delocalization. These orbitals allow many fewer structures to be considered and remove the need for incorporating many ionic structures, in agreement with chemical intuition. To date, these methods have not been as widely applied in organic chemistry as MO calculations. They have, however, been successfully applied to fundamental structural issues. For example, successful quantitative treatments of the structure and energy of benzene and its heterocyclic analogs have been developed. It remains to be seen whether computations based on DFT and modem valence bond theory will come to rival the widely used MO programs in analysis and interpretation of stmcture and reactivity. 

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