Real bonds

Another set of terms considered by Eyring, et al. consisted of structures having a double bond between carbons. These should be expected to be involved to some small extent—small because they have one less real bond. This is essentially invoking hyperconjugation. These authors did not reach a definite conclusion regarding the importance of these structures and decided that they probably would stabilize the eclipsed configuration, which was not known at that time to be the incorrect one. It is still not simple to make a reliable estimate of the importance of this contribution. 

In the pseudobond method of Yang and coworkers [47] a pseudobond is formed with one free-valence atom with an effective core potential (optimized to reproduce the length and strength of the real bond). This core potential can be applied in Hartree-Fock and density functional calculations and is designed to be independent of the choice of the MM force field. 

For convenience and to avoid confusion, we will symbolize a purely covalent bond between A and B centers as A — B, while the notation A—B will be employed for a composite bond wave function like the one displayed in Equation 3.4. In other words, A—B refers to the real bond while A — B designates its covalent component. 

Smaller interatomic separations characteristic for the real bonds correspond to the limit Cm 2> 1 and the ESVs in this limit have the following asymptotic behavior ... 

Three types of adsorption can be considered (i) molecularly chemisorbed, (ii) atomically chemisorbed and (iii) molecularly physisorbed. In the case hydrogen is chemisorbed on platinum, a real bond between Pt and atomic H is formed, i.e. two electrons are located in a bonding orbital between Pt and H or H2. In the case hydrogen is molecularly physisorbed, the interaction between Pt and molecular H2 is electrostatic, i.e. no electrons are shared in a Pt-H bond and no dissociation takes place. 

Bearing in the mind that a real bond should be described by three classical VB structures, we return to the case of benzene. Across the whole history of resonance theory, Kekule structure has been treated as the hypothetical 1,3,5-cyclohexatiene whose double bonds are comparable to ethylene. However, it is clear from the previous paragraph that the n bond in ethylene should be expressed as a sum of three classical VB structures. Furthemore, there are three ji bonds in a Kekule structure. Consequently, from the mathematical point of view, the wave function for a Kekule structure should be expanded by 33=27 classical VB structures as follows ... 

Let us consider the lattice of bonds illustrated in Fig. 4.16. The real bond introduces the interaction wL (with values w or 0), but no diagonal term. In contrast, the effective bond introduces an interaction weff(z) and a bond potential s(z) at the two ends. In the case of a lattice with all bonds equivalent, the effective medium is represented by a single type of bond the Green s function of this medium takes the form... 

Figure 4.16. Scheme of lattice with effective bonds used in HCPA. A bond is characterized by one interaction Weff(z) and one bond potential s(z). Self-consistency is obtained by requiring a zero value of the mean scattering on a real bond (interaction tv, without potential) immersed in the effective medium. 

In addition one can also speak of a free valence (index) or indice de liaison fibre of 0.07 for each corner of the benzene molecule since the para-para bond in the DEWAR-configurations is not a real bond but rather represents two free electrons (with opposite spins) at opposite corners. 

FIGURE 13.15. Libration causing apparent (not real) bond shortening, (a) Because the atom is vibrating but the bond length stays the same, the atom (b) vibrates in an arc (librates) (c). The electron density is interpreted as an ellipsoid (d), but its major axis is displaced as shown in that the bond appears shortened. 

Hyperconjugation of the kind described above is called sacrificial hyperconjugation, since there is one less real bond in structures like II than in I. In contrast, the kind of... 

Laboratory measurements show that most real bonds are neither fully ionic nor fully covalent, but instead possess a mixture of ionic and covalent character. Bonds in which there is a partial transfer of charge are called polar covalent. This section provides an approximate description of the polar covalent bond based on the relative abilities of each atom to attract the electron pair toward its nucleus. This ability is estimated by comparing the electronegativity values for the two atoms. 

The theoretically derived geometry of HCO has been compared to that measured experimentally. The OCH bond angles (128.0" and 127.4", respectively) agree closely whereas r(C—H) is calculated (1.100 A) to be shorter than experimentally determined (1.110 A), the calculated r(C—O) value (1.180 A) is larger than the experimental value (1.171 A). The theoretician finds this latter observation astonishing, and, based on previous correlations between theoretical and experimental bond distances, whould predict a real bond length of 1.195 A, ca. 0.015 A larger than the calculated value. 

Resonance structures are not real bonding depictions O3 does not change back and forth from structure I at one instant to structure II the next. The actual molecule is a resonance hybrid, an average of the resonance forms. 

The r ]ax values from the exponential decay fits to the bond distance-force constant data set maximum distances for real bonding (but not, for example, van der Waals interactions, vide infra). Longer distances would generally be considered nonbonding. The converse of this statement... 

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