A Theory of the Local Chemical Bond

In other words, the basis set and the corresponding fermion operators are partitioned into different subspaces and the expansion coefficients are strictly localized on one of these subspaces. The wave function  

Assume the existence of a local subset of basis orbitals assigned to each two-electron chemical bond of the molecule. Such basis orbitals can be constructed from local atomic hybrids or off-centered bond functions, for example. We do not discuss the actual choice of the basis set here supposing only that each basis function is uniquely assigned to one of the chemical bonds of the molecule. The term chemical bond is used here in a broad sense it refers to two-center bonds as well as other two-electron fragments (inner shells, lone pairs) of the system. 

The most general local wave function for the bond i, expanded in the corresponding subset, is given by Eq. (16.28), in which a is a creation operator creating an electron on the basis orbital x, p 6 i. In order to derive the local equations for determining the optimum values of the expansion coefficients we have to analyze the structure of the Hamiltonian. The analysis should be performed in terms of the basis orbitals x which form a nonorthogonal set. Hence, the Hamiltonian is written as  

Since each basis function x is assigned to a particular bond, any summation over basis orbitals can be formally substituted by a summation over bonds i and 

This operator is considered as the Hamiltonian for the bond i. Apart from overlap effects reflected by the biorthogonal integral list, it describes an isolated bond. The next three terms of the total Hamiltonian in Eq. (16.32) describe interbond interactions. The expressions of these interaction Hamiltonians can be obtained by the partitioning of the summation labels according to Eq. (16.31). The pairwise interaction operator H after simple algebraic manipulations can be given in the following compact form  

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The physics community has developed a theoretical description of the surface chemical bond, which borrows from scattering theory [13, 14). The Newns-Anderson description of the surface chemical bond is that of a scattering resonance of colliding conduction electrons [15, 16). These theories have been essential for the development of a detailed understanding of the compromise between localization of electrons in a surface bond versus delocahzation of the valence electrons in the metal. 

Information theory has been shown to provide a novel and attractive perspective on the entropic origins of the chemical bond. It also offers a complementary outlook on the transformation of the electronic information content in the elementary chemical reactions. In this short overview, we have first introduced the key IT concepts and techniques to be used in such a complementary analysis of electron distributions in molecular systems. They have been subsequently applied to explore the bonding pattern in typical molecules in terms of the information distribution, the bond localization/multiphcity, and its ionic/covalent composition. The use of the information densities as local probes of electronic distributions in molecules has been advocated and the importance of the nonadditive entropy/information measures in extracting subtle changes due to the bond formation has been stressed. The use of the CG density, of the nonadditive Fisher information (electronic kinetic energy) in the AO resolution, as an efficient localization probe of the direct chemical bonds has been validated. 

Gas phase transition metal cluster chemistry lies along critical connecting paths between different fields of chemistry and physics. For example, from the physicist s point of view, studies of clusters as they grow into metals will present new tests of the theory of metals. Questions like How itinerant are the bonding electrons in these systems and Is there a metal to non-metal phase transition as a function of size are frequently addressed. On the other hand from a chemist point of view very similar questions are asked but using different terminology How localized is the surface chemical bond and What is the difference between surface chemistry and small cluster chemistry Cluster science is filling the void between these different perspectives with a new set of materials and measurements of physical and chemical properties. 

It is essential to have tools that allow studies of the electronic structure of adsorbates in a molecular orbital picture. In the following, we will demonstrate how we can use X-ray and electron spectroscopies together with Density Functional Theory (DFT) calculations to obtain an understanding of the local electronic structure and chemical bonding of adsorbates on metal surfaces. The goal is to use molecular orbital theory and relate the chemical bond formation to perturbations of the orbital structure of the free molecule. This chapter is complementary to Chapter 4, which... 

According to Pauling [6-9], valence bond theory can also be used to describe metallic systems. At a first glance, this seems to be contradictory, since VB deals with localized chemical bonds and a metallic bond is thought of as completely delocalized. Pauling s argument is that the metal atoms in the crystal have an available orbital to receive an extra electron and thus form an extra covalent bond, through a mechanism he called unsynchronized resonance. 

According to localized orbital theories of the chemical bond, during the rotation the system must pass through a structure with no overlap between p(Si) and s(H) orbitals. 

The Mills-Nixon hypothesis had, as its foundation, certain differences in the chemical behaviour of indan (3) and tetralin (4) from which a localization of the aromatic 7r-bonds was predicted to occur in the direction depicted by la rather lb. The original experimental evidence upon which the effect was based was shown to be erroneous, but calculations at various levels of theory indicated that aromatic bond localization should exist and become more pronounced as the size of the annelated ring decreases In essence one can recognize that the structure of benzene has a symmetry such that both Kekule structures must contribute equally. With Q tetralin (4) (and the lower homologues) no such symmetry requirement exists and ring annelation could induce bond length alternation within the arene nucleus. As the strain imposed by the fused ring increases, the Mills-Nixon effect should increase. The hypothesis has been the subject of considerable discussion and the controversy is far from settled. 

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