Bond equalization

For a bond between two atoms of the same element assign the elec trons in the bond equally... 

The bond orders in the polymethine chain are equalized in the ground and excited states. If Tg = 45°, the bond equalization is maximum. This is the ideal polymethine state (1) of the polymethine chain. Any deviation from this state (ie, Oq is greater than or less than 45°) causes the bond to alternate from the polymethine chain center to its ends. The alternation ampHtude is found to be proportional to the absolute value 45° — 4>g. ... 

Here are the salient features from a typical Gaussian98 run on ethene at the HF/6-311G level of theory, using the Z-matrix option (Figure 14.3). I have forced D2h symmetry by setting all the C-H bonds equal, all HCC bond angles equal and all azimuthal angles equal. 

The concept of mesohydric tautomerism was advanced by Hunter and his associates in a series of papers which appeared between 1940 and 1950 (e.g., references 15 and 16). This concept was based on the fact that in all cases where the mobile hydrogen atom would be bonded to oxygen, sulfur, or nitrogen atoms in both possible tautomers, the individual forms had not been isolated. It was further established that many of these compounds were associated both in the liquid state and in solution, and it was concluded that the individual tautomers did not exist. The actual molecules were thought to be intermolec-ularly hydrogen-bonded, the mobile hydrogen atom being bonded equally to both of the hetero atoms. This concept has been useful and has led to clarification of the tautomerism which occurs in solids and... 

An example of quantum mechanical schemes is the oldest and most widely used Mulliken population analysis [1], which simply divides the part of the electron density localized between two atoms, the overlap population that identifies a bond, equally between the two atoms of a bond. Alternatively, empirical methods to allocate atomic charges to directly bonded atoms in a reasonable way use appropriate rules which combine the atomic electronegativities with experimental structural information on the bonds linking the atoms of interest. A widely used approach included in many programs is the Gasteiger-Hiickel scheme [1]. 

The question of electronic conductivity in the polyphosphazenes inevitably raises questions regarding the electronic structure of the phosphazene linkage.7-12 This matter has been the subject of controversy in the literature, but experimentally the situation is now well known.4,13 In spite of the fact that the phosphazene backbone is fully conjugated, bond equalized and possesses bond lengths which are indicative of partial double bond character, the evidence suggests that these are localized systems. 

On first consideration it may be concluded that if suitable crystals are available X-ray crystallography is the ideal method to decide unambiguously if a candidate compound is, in fact, homoaromatic (Childs et at., 1986a). The bond equalization and planarization associated with homoaromaticity should be readily detected by this means. However, the degree of bond equalization and the size of the homoconjugation gap necessary for homoaromaticity are open to debate (vide infra) (Childs et al., 1986a Haddon, 1988a). In addition, for systems capable of fluxional behaviour, dynamic or static disorder may lead to erroneous conclusions in the interpretation of the X-ray data (see Jackman et al., 1989). In suitable cases very careful X-ray studies can probably avoid this confusion (Dunitz et al., 1988). 

By contrast, the Dewar resonance energy represents solely the contribution coming from the cyclic electron (bond) delocalization since the model reference structure is represented not by a system of isolated 7r-bonds, but by a hypothetical cyclic polyene with the number of tr- and tr-bonds equal to that in a given molecule. Making use of the additivity of bond energies in acyclic polyenes (65JA692), one may calculate the total energy... 

Aromatic cyclic 7r-electron delocalization does indeed stabilize the planar structure with bond equalization (84ZOR897)—the problem is that, in addition to that effect, there may exist some others that may eventually overshadow it. Thus, the foregoing warrants the conclusion that the preference of a planar or nonplanar geometry of heterocycle depends on a number of factors including aromaticity (antiaromaticity), which may not even be the most important. In any case, this factor should not be disregarded if one wishes to obtain a correct overall energy balance. For example, aromaticity is reflected in the values of inversion barriers. Thus, for antiaromatic 2-azirine the nitrogen inversion barrier is, as was mentioned earlier, 37.7 kcal/mol, whereas in the case of its saturated... 

The first case is the copolymerization of monomer A with diene BB where all the double bonds (i.e., the A double bond and both B double bonds) have the same reactivity. Methyl methacrylate-ethylene glycol dimethacrylate (EGDM), vinyl acetate-divinyl adipate (DVA), and styrene-p- or m-divinylbenzene (DVB) are examples of this type of copolymerization system [Landin and Macosko, 1988 Li et al., 1989 Storey, 1965 Ulbrich et al., 1977]. Since r = Yi, Fi = f and the extent of reaction p of A double bonds equals that of B double bonds. There are p[A] reacted A double bonds, p[B] reacted B double bonds, and p2[BB] reacted BB monomer units. [A] and [B] are the concentrations of A and B double bonds,... 

We may calculate the electric dipole moment expected for the water molecule with inclusion of the doubly ionic structure and with neglect of it. By using the O—H interatomic distance 0.965 A. and H—O—H bond angle 104.5°, we find that the calculated values of the dipole moment are 2.21 D with inclusion of the doubly ionic structure and 1.36 D with its neglect. The experimental value, 1.86 D, lies between these values it corresponds to inclusion of the doubly ionic structure to such an extent as to make the partial ionic character of each bond equal to 33 percent rather than 39 percent. 

Clearly a quantum chemical calculation of the energy surface for this reaction would have to be based on a multiconfigurational wave function, with four active orbitals, the k orbitals of the two ethene molecules, and four active electrons. However, a complication appears cyclobutane is a quadratic molecule with all four carbon-carbon bonds equal. Our wave function does not have this property. The CC bonds between atoms A and B are treated using... 

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