Classification of Bonds

Bond types for which there are less than four independent observations are omitted from Tables A.l and A.2 (but each individual observation is given in the fuller versions of these tables [9, 10]). In all other cases, the following statistics were generated by the program STATS. 

The statistics chosen for tabulation effectively describe the distribution of bond lengths in each case. For a symmetrical normal distribution the mean (d) will be approximately equal to the median (w) the lower and upper quartiles will be 

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This classification of bonds allowed the application of logistic regression analysis (LoRA), which proved of particular benefit for arriving at a function quantifying chemical reactivity. In this method, the binary classification (breakable or non-breakable, represented by 1/0, respectively) is taken as an initial probability P0, which is modelled by the following functional dependence (Eqs. 7 and 8) where f is a linear function, and x. are the parameters considered to be relevant to the problem. The coefficients c. are determined to maximize the fit of the calculated probability of breaking (P) as closely as possible to the initial classification (P0). 

Sanderson, R. T. 1951. An interpretation of bond lengths and classification of bonds. Science 114 670-672 1976. Chemical Bonds and Bond Energy, 2nd edn. New York Academic Press. 

The method applied to the problem of chemical reactivity translates into the following. A data set of molecules is chosen and bonds in these molecules are selected and specified either breakable or non-breakable (Pq = 0/1). Then, the physicochemical parameters deemed important for the reactivity of the bonds under investigation are calculated and used as variables x. in Equation 6. LoRA is applied to model the initial classification of bonds into breakable or non-breakable classes. 

Beyond the gel point, the bonds Issuing from a monomer unit can have finite or Infinite continuation. If the continuation Is finite, the Issuing subtree Is also only finite If the continuation Is Infinite, the unit Is bound via this bond to the "infinite" gel. The classification of bonds with respect to whether they have finite or Infinite continuation enables a relatively detailed statistical description of the gel structure. The probability of finite continuation of a bond Is called the extinction probability. The extinction probability Is obtained In a simple way from the distribution of units In generation g>0. This distribution Is obtained from the distribution of units In the root g-0 (for more details see Ref. 6). 

The topological analysis of the density leads to a powerful classification of bonding based on the electron density. It is discussed in the final sections of this chapter. 

Classification of Bonds Based on the Topology of the Electron Density... 

The classification of bonds as single, double or triple is not always clear-cut. For example, the Si-F bond may have some double-bond character, depending on the extent of overlap between empty silicon 3d orbitals and filled F 2p orbitals, and this will vary from one situation to another. The large range quoted for the C(sp2)-C(sp2) bond energy reflects the variable amount of p -pn overlap which may be present. 

The bonds formed between germanium and elements of Group VA can be divided into two categories those in which the element is bonded via a covalent bond and others in which a Lewis acid-Lewis base interaction between the two elements results in coordinate bond formation. The same classification of bond types is also appropriate when discussing organogermanium derivatives of Groups VIA and VII A. 

Although the above classification of bonding is very useful, it must be stressed that it is not rigid and that there is a continuous gradation from one type to another. To understand this, it is necessary to examine the electronic description in more detail. 

Sanderson, R.T. (1951). An Interpretation of Bond Lengths and a Classification of Bonds. Science, 114,670-672. 

Bianchi et al. present a concise pictorial summary of the QTAIM characterisation and classification of bonding interactions in the conclusion of their paper about the electron density of Mn2(CO)io [114]. Figure 2 is an adaptation (with modifications) of their scheme. The classification is to be taken as a general guide since exceptions and special cases do arise as one attempts to draw a correspondence between classical bonding descriptors (ionic, covalent, etc.) and quantum mechanical quantities. 

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