Electron-pair bonds INDEX

Note that the bond order index defined by Mayer accounts for the covalent contribution to the bond (this is why of late it is often mentioned as shared electron pair density index, SEDI). As such, the index cannot be expected to produce the integer values corresponding to the Lewis picture if a bond has a significant ionic contribution. The bond order index defined in this way measures the degree of correlation of the fluctuation of electron densities on the two atoms in question [7]. 

Hence, it is clear that fundamentally and operationally the physico-chemical process of protonatirMi can be linked to the above akin descriptors — the ionization process, the hardness, softness, electronegativity and electrophilicity. Recently, we (Islam et al. 2010, 2011a, b Ghosh et al. 2011a) have published good number of papers where we have discussed that the three descriptors, the electronegativity, the hardness and the electrophilicity index of atoms and molecules are fundamentally qualitative per se and operationally the same. All three represent the attraction of screened nuclei towards the electron pair/bond. Thus, we can safely and reasonably conclude that the proton affinity and the three descriptors have inverse relationship. 

For a classical covalent bond, the basin is disynaptic, its population is close to 2.0, and the variance (and covariance) is significantly smaller than the population, while a classical ionic bond like NaCl has rally core and monosynaptic basins [9, 16, 53]. Scheme 2 summarizes these features, which defines only two electron-pair bond families, either covalent or ionic, in the original ELF formulations. Any bond with very different values, for the basin population and the corresponding fluctuation index, will not qualify as either covalent or ionic. However, as will be shown immediately, CSB possesses unique ELF characteristics, which foretell the repulsive (or slightly attractive) covalent density. 

FHaya et al. 89) introduced an information index e, called electropy, based on the assumption that the molecule forms a finite space which is divided into several partial bond spaces according to the electronic pairings in the molecule. The electropy, e, is viewed as a measure of the degree of freedom of choice for electrons in occupying different partial spaces in during the process of molecular formation. 

Of the many empirical polarity parameters or indexes that have been proposed, only a few remain viable, in the sense that they are currently more or less widely used to describe the polarity of solvents for various purposes. Some such parameters that are commonly used describe better other, more specific, properties than polarity e.g., hydrogen bond or electron-pair donation ability. Thus, only two polarity parameters have been employed in recent years Dimroth and Reichardt s A T(30) (Dimroth et al. 

This polarity index measures the intermolecular attraction between a solute and a solvent, whereas the Hildebrand solubility parameter is defined for pure solvent. For example, ether is not very polar and has a Hildebrand value of 7.4—about the same as hexane, which has a value of 7.3. However, ether can accept protons in the form of hydrogen bonds to its nonbonding electron pairs, and consequently its polarity index is 2.8 compared to 0.1 for hexane. 

Therefore, the electron probability is not scattered by the lone-pair hybrids. As a result such decoupled subchannels hn = h° representing two lone pairs of oxygen atom in H20 or a single nonbonding electron pair of nitrogen in NH3, introduce the exactly vanishing contributions to both bond components and hence to the overall bond index of these molecules in OCT. 

Bond order A theoretical index of the degree of bonding between two atoms relative to that for a normal single bond, that is, one localized electron pair. In valence bond theory it is expressed by the weighted average of the bond numbers between the respective atoms in the contributing structures. By this criterion each C—C bond in benzene has a bond order of 1.5. 

The bond order traditionally means the number of electron pairs shared between two bonded atoms. The sharing of eleetrons between any two atoms in a molecule is measured by the deloealisation index 8 A,B). This index is the magnitude of the exchange of the eleetrons in the basin of atom A with those in the basin of atom [111] ... 

It systems of cychc polyenes [22,23]. One finds here both charge-density-wave RHF solutions, where the bond indexes are alternant (one strong bond (2i, 2i+i) between two weak bonds (2i-i, 2i) and (2i+l, 2i+2) and spin-density-wave UHF solutions where the electrons are spin-alternant (one a electron on atom 2i surrounded by two pelectrons on atoms 2i l). The first one does not "dissociate" properly (when t/u tends to zero), since it remains half neutral and half ionic but it reduces the weight of the most irrelevant VB situations with respect to their importance in the symmetry-adapted solution. The charge-density-wave solution tends to localize the electrons by (a,P)pairs on the "strong bonds", each one supporting a localized MO... 

TABLE 3.9 Indexes of Solvent Solvation Ability Polarity and Ji, Electron Pair Donicity, DN and /, Hydrogen Bond Donicity, AA and a, and the Softness Parameter, /t... 

We have already seen that J informs us of the overall atomic excitation within a cycloalkane and this is why it correlates with both strain and CH bond length (Table 2). However, there can be no correlation between J and CC bond lengths. The latter depend on the number of bonding electron pairs in S,Tg, not on T. Hence, it is the index V, not J, that informs us about the variation of CC bond lengths. Experimental results are in agreement with expectations (Table 2). However, while J often correlates with strain and carbon acidity in cycloalkanes, there is simply no reason to assume that this will always be true. An example will serve to illustrate this point. 

There have been many attempts to build a link between modern electronic structure calculations and various intuitive models of chemical bonding. Among the concepts that proved to be especially useful in this respect is the idea of bond order and/or the bond index as a theoretical counterpart of the classical concept of bond multiplicity that reflects the number of shared electron pairs involved according to Lewis model in the bonding between the given pair of atoms. There is a plethora of various definitions of bond order but of speeial relevance for our purposes is the so-called Wiberg-Mayer bond order defined by eqn (l)... 

The bond order, as a delocalisation index, measures the number of electron pairs shared between topological atom A and B. This index can be linked to the fluctuation of the electron population, denoted N, in both atoms. 

Secondary bond A bond with a smaller than average valence, formed by an atom with one or more stereoactive lone pairs of electrons Surface instability index The root mean squared deviation of the bond valence sum from the atomic valence averaged over the atoms forming the surface of a solid... 

As has just been described, when a covalent bond forms between two atoms, there is no reason to assume that the pair of electrons is shared equally between the atoms. What is needed is some sort of way to provide a relative index of the ability of an atom to attract electrons. Linus Pauling developed an approach to this problem by describing a property now known as the electronegativity of an atom. This property gives a measure of the tendency of an atom in a molecule to attract electrons. Pauling devised a way to give numerical values to describe this property that makes use of the fact that the covalent bonds between atoms of different electronegativity are more stable than if they were purely... 

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