Conventional bonding

Once the BEs and SBEs have been decided upon, the normal functioning of the MM program causes each bond to be multiplied by the number of times it appears in the computed molecule to find its contribution to the total bond enthalpy. In ethylene, 26.43 + 4(—4.59) = 8.07kcalmol . In Eile Segment 5-1, this sum is denoted BE. This whole procedure is essentially a conventional bond energy calculation. 

Zavarin, E., Activation of wood surface and non-conventional bonding. In Rowell, J. (Ed.), The Chemistry of Solid Wood, Chapter 10. Advances in Chemistry Series, American Chemical Society, Washington, DC, 1984, pp. 349-400. 

Figure Three represernarions of the structure of Cm- (a) normal ball-and-stick model (b) the polyhedron derived by truncating the 12 vertices of an icosahedron to form 12 symmetrically separated pentagonal faces (c) a conventional bonding model.

Li, J. and Carr, P. W., Retention characteristics of polybutadiene-coated zirconia and comparison to conventional bonded phases, Anal. Chem., 68(17), 2857,... 

Figure 4.10 AX4, AX3E, and AX2E2 molecules (a) tangent sphere models or domain models with spherical domains B is a bonding pair and E is a lone pair and (b) conventional bond line structures.

The network of bond paths for a molecule is called its molecular graph. It is identical with the network of lines generated by linking together all pairs of atoms that are believed to be bonded to one another according to conventional bonding ideas such as Lewis structures. A bond path can therefore be taken as the AIM definition of a bond. 

We now compare how the atoms in a molecule and the bonds between them are defined in the AIM theory and in conventional bonding models. 

There is no clear rigorous definition of an atom in a molecule in conventional bonding models. In the Lewis model an atom in a molecule is defined as consisting of its core (nucleus and inner-shell electrons) and the valence shell electrons. But some of the valence shell electrons of each atom are considered to be shared with another atom, and how these electrons should be partitioned between the two atoms so as to describe the atoms as they exist in the molecule is not defined. 

Perhaps the most depressing fact associated with the consequences of the above division is the lack of consistency often found in treatments of compounds which are essentially isostructural. Take, for instance, the different descriptions of the bonding situation in B2H6 on the one hand, and the isostructural (e.g. AI2CI6) molecules on the other while the latter may be treated by the conventional bonding principles expressed in Hyps. III.l to III.5, the treatment of the former (in terms of 3-centre bonds) breaks with Hyps. III.l to III.4. A similar conclusion is in fact reached in the majority of abnormal cases. Other simple examples are provided by the alkali-metal hydrides (with NaCl-type structure), CuH (with ZnS-wurtzite type structure), etc. These examples are typical in that it is only when a scarcity of electrons and/or orbitals enforces a search for extraordinary bonding principles that Hyps. III.l to III.4 are reluctantly (partly or completely) replaced by alter-... 

One of the most conspicuous differences between computational results is in the degree to which a normal H—Si chemical bond is formed. In the local-density pseudopotential calculations, the Si—H separation is about 1.6 A. This is much larger than the predictions of MNDO, Hartree-Fock, or PRDDO calculations, which are much closer to the molecular Si—H distance. It is not clear at this point whether the H—Si bond is, in fact, weaker than a conventional bond when in this configuration and therefore is overestimated by the Hartree-Fock-like calculations, or whether the strength is being underestimated in the local-density calculations. 

Nevertheless, the data in Table 3.5 reveal an important difference between classical hydrogen bonding and dihydrogen bonds. In fact, since in O- - -H conventional bonds the electrostatic component is followed by charge transfer energy while the polarization contribntion iipL is very small, classical hydrogen bonds can be formulated as... 

By using the conventional bond formula (V) for the metal butadiene moiety, we may describe this cyclo-addition process as an orbitally allowed 7r2, + 7r2a + a2, pericyclic reaction (160). (See Fig. 15 for an illustration of the topology of the orbital interactions.)... 

The determinant (= total molecular wavefunction T) just described will lead to (remainder of Section 5.2) n occupied, and a number of unoccupied, component spatial molecular orbitals i//. These orbitals i// from the straightforward Slater determinant are called canonical (in mathematics the word means in simplest or standard form ) molecular orbitals. Since each occupied spatial ip can be thought of as a region of space which accommodates a pair of electrons, we might expect that when the shapes of these orbitals are displayed ( visualized Section 5.5.6) each one would look like a bond or a lone pair. However, this is often not the case for example, we do not find that one of the canonical MOs of water connects the O with one H, and another canonical MO connects the O with another H. Instead most of these MOs are spread over much of a molecule, i.e. delocalized (lone pairs, unlike conventional bonds, do tend to stand out). However, it is possible to combine the canonical MOs to get localized MOs which look like our conventional bonds and lone pairs. This is done by using the columns (or rows) of the Slater T to create a T with modified columns (or rows) if a column/row of a determinant is multiplied by k and added to another column/row, the determinant remains kD (Section 4.3.3). We see that if this is applied to the Slater determinant with k = 1, we will get a new determinant corresponding to exactly the same total wavefunction, i.e. to the same molecule, but built up from different component occupied MOs i//. The new T and the new i// s are no less or more correct than the previous ones, but by appropriate manipulation of the columns/rows the i// s can be made to correspond to our ideas of bonds and lone pairs. These localized MOs are sometimes useful. 

That molecules do have definite bonds, and that these tend to correspond in direction and number to the conventional bonds of simple valence theory, is indicated by the quantum theory of atoms-in-molecules (AIM, or QTAIM) [2], This is based on an analysis of the variation of electron density in molecules. 

Provocative experimental evidence, at variance with conventional theory, is provided by the estimates of molecular diameters for diatomic molecules. Bonding theory requires the concentration of valence densities between the nuclei to increase as a function of bond order, in agreement with observed bond lengths (1.097, 1.208, 0.741 A) and force constants (22.95, 11.77, 5.75 Ncm-1) of the species N=N, 0=0 and H-H respectively. Molecular diameters can be measured by a variety of techniques based on gas viscosity, heat conductivity, diffusion and van der Waals equation of state. The results are in excellent agreement at values of 3.75, 3.61 and 2.72 A, for N2, O2 and H2, respectively. Conventional bonding theory cannot account for these results. 

One of the exceptions, that offers an alternative to the conventional bond diagrams is the density domain approach [4,5] to chemical bonding. This approach is based on the following observation for a given molecule with a specified nuclear configuration K, the infinite family (DD(a,K) of density domains for the range (0, amax] of density thresholds,... 

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