Elementary Bonding Theory

In the spirit of elementary bonding theories, we expect that the dominant contributions to h,(A) come only from the first summation, consisting (for an s/p-block atom) simply of the four contributions (s, px, pv, p-) from the valence shell. At this level, the hybrid can be written simply as (dropping the atom label throughout)... 

Gray, H. B. (1965). Electrons and Chemical Bonding. Benjamin, New York. An elementary presentation of bonding theory that is both readable and well illustrated. 

As predicted by elementary hybrid bonding theory, the multiple bonds of the chemist s Lewis-structure diagram are usually found to correspond to two distinct types of NBOs (1) sigma-type, having exact or approximate cylindrical symmetry about the bond axis (as discussed in Sections 3.2.5-3.2.7), and (2) pi-type, having a nodal mirror plane passing through the nuclei 44... 

We would also like to mention here another important point. Since the Hiickel and topological matrices are closely related for a particular conjugated molecule, all properties of a molecule (i.e. energy, MOs, bond orders, charge densities) which may be derived from the topological matrix by mathematical treatment must be dependent on the molecular topology 23>. This may be one reason why the predictive power of elementary Hiickel theory is in many cases (e.g. for alternant hydrocarbons) as good as that of any more elaborate approach 58>. 

Another rather interesting relation between the resonance theory and elementary MO theory was established by Ham and Ruedenberg 107>. Let Pp be the Pauling bond-order matrix known from resonance theory 179>. If the adjacency matrix of the -th Kekute graph is Aj, then... 

The formulas of the chemical compounds are no accident. There is an NaCl, but no NaCl2 there is a Cap2, but no CaF. On the other hand, certain pairs of elements form two, or even more, different compounds, e.g. C]u20, CuO N2O, NO, NO2. In the case of ionic compounds the relative number of positive and negative ions in a formula is governed simply by the rule of electrical neutrality. In covalent compounds, or within polyatomic ions (like NO ), structures are formed by covalent bonds (i.e., electron sharing). A hierarchy of covalent bonding theories exists, of which the simplest, the drawing of Lewis structures, is emphasized in this and in most elementary texts. 

Gas molecules can react only when they come close enough to one another for direct energy exchange that can lead to bond breaking. From elementary kinetic theory, the frequency of collisions per unit volume of gas of molecules of type i of mass w, with molecules of type j of mass mj is (Benson, 1976)... 

For CO, its HOMO is the lone pair 5 o orbital and its LUMOs are the unoccupied 2 JT orbitals. Elementary chemical bonding theory describes the interaction with a molecule as CO only through chemical bonding contributions through its HOMO and LUMOs. We will see that this is a rather approximate view of the surface chemical bond, because of the important hybridization that occurs in the adsorbing molecule. 

Another useful notion is the so-called generalized bond index Kab referred to the given atoms A and B. According to [36], in case of CIS excited states, Kab, more exactly, Kab[C1S], turns out to be connected with CT numbers Ia b and some additional quantities. Before giving expressions applicable also to RPA and related models, we briefiy clarify the meaning of the generalized bond index. Even within the elementary MO theory, such as the tt-electron model, the corresponding quantity, that is /sT,uy[MO], is not the same as the usual bond order Instead, the squared bond order makes its appearance, namely, by definition the orbital index... 

The Hiickel 4A + 2 rule was derived for monocyclic tt systems from elementary molecular orbital theory, whereas simple valence bond theory finds rings with 4A tt electrons to be no less stable. [34, p. 33] It has long been known that real molecules lie somewhere between the two extremes. [35]... 

The advantages of VB theory are formal as well as conceptualJ In a formal sense, we start with a set of VB Configuration Wavefunctions (CW s), constructed from a set of nonorthogonal Atomic Orbitals (AO s), which ultimately yield the proper electronic states with no constraints placed on the way in which the CW s are combined to form these various electronic states. In a conceptural sense, we can define elementary bonds, "lone" electrons, and vacant orbitals (or holes) so that their interaction can be conveniently studied. 

Interatomic interaction entails the interference of extranuclear electronic waves. Constructive interference must occur at specific interatomic distances, which should correlate with the notion of bond order, numerically related to the golden ratio. The feasibility of modeling chemical interaction by elementary number theory is foreseen. 

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