NON-INTEGER BONDS

In addition to the traditional integer (single, double, triple, and, in inorganic chemistry, quadruple) bonds, some additional bonds having selected standardized bond orders are introduced. Three of these play a major role in establishing a unified system of nomenclature  

Meanwhile, however, a third property of great importance in describing chemical moieties, bond angle [both between three atoms (coplanar) and between four or more atoms (in 3-dimensional space)], is not as amenable to standardization. Nevertheless, because some degree of standardization is better than none, a partial utilization of the system based on G. N. Lewis s description of bonding [2] that defines bond order as one-half the number of electrons in bonding orbitals minus one-half the number of electrons in anti-bonding orbitals has been adopted. 

Pauling [1] advises there is a chemical bond between two atoms or groups of atoms in case that the forces acting between them are such as to lead to the formation of an aggregate with sufficient stability to make it convenient for the chemist to consider it as an independent molecular species . 

Because of the incongruity in the desired extension of bond order (using a discrete variable as the measure for a concept that requires a continuous variable), any nomenclature will have to lump together structures having similar bond orders. Here the heuristics of similar is assumed — with all of the consistency problems that could arise by such an assumption. In the proposed system, 

Note the compatibility of this choice with the Robinson ring indicating a bond and a half between each pair of carbon atoms in benzene. 

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The essence of the resonance concept is partial (non-integer) bond order, intermediate between, e.g., the idealized single- and double-bond patterns in (5.28a). 

One of the most significant changes over existing systems is the introduction of a selective use of non-integer bonds directly into the nomenclature. Not only does such an introduction subsume the underlying concepts sometimes expressed as "half-bond" (3 center 2 electron bond) structures in the boranes, as well as "bond and a half (Robinson) ring structures in aromatic compounds, etc., but also this approach points the way... 

A practice-oriented modification of the latter approach in order to also include the chemistry of molecules with non-integer formal covalent bond orders requires a mathematical device that is capable of taking into account chemical considerations beyond the formal, and of transforming the aforementioned data structures according to chemical reactions. 

The unusual non-integer hybridizations for these lone pairs should not be surprising any combination of hybridization parameters is possible as long as the total s% and p% add to 100 and 300%, respectively (i.e. one s-orbital and three p-orbitals). Such flexible and variable rehybridization in individual orbitals is needed to provide the most stable bonding situation for complex electronic distribution of a non-symmetric molecule. ... 

Figure 5.1 The family of carbon nanostructures. The mark sp" indicates intermediate carbon forms with a non-integer degree of carbon bond hybridization. 

When Pauling turned around the chain in order to form a helix the fact that non-integer number of amino acid units occurred at any given turn gained added significance the intramolecular hydrogen bonds did not link identical parts in the... 

Common examples of systems often mistaken as being aromatic (because of their alternating double and single bonds) are cyclobutadiene and cyclo-octatetraene (shown in Figure 6-9). In the case of cyclobutadiene, 4n + 2 = 4, giving n = 0.5, while for cyclooctatetraene, 4n + 2 = 8, so that n = 1.5. In these two compounds, n is not an integer, so these systems are anti-aromatic (nonaromatic). Anti-aromatic systems (non-Hilckel systems) are less stable than aromatic or normal systems. 

The most revolutionary consequence of the Bohmian interpretation of orbital angular momentum is perhaps the natural interpretation of non-steric molecular barriers to rotation and the nature of multiple bonds. It completely destroys the notion of 7r-bonding and explains the absence of a barrier to rotation in bonds of odd integer order. 

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