Bond counting picture

From this tabulation, it is obvious, that the (111) surface has the lowest surface free energy because it exhibits the smallest number of dangling bonds per unit area. This simple bond counting picture indicates correctly that the minimum energy surface of a covalent diamond structure crystal is the (111) surface and also the natural shape of a diamond crystal. The (111) plane is also the cleavage plane for C, Si, and Ge because the number of broken bonds is minimal as shown in Table 9.4. The dependence of the surface free energy with crystal orientation has... 

The driving force for this process is the dramatic gain in surface energy as shown in Table 9.2, where the estimates are compared with the measured values for low-index Si surfaces Compared with the bond counting picture, a real Si(OOl) surface exhibits a surface free energy that is reduced by 1 eV per (1 x 1) unit cell. 

Table 9.3 Number of broken bonds, unit cell area, and estimated surface energies of truncated bulk SI surfaces in the framework of a bond counting picture.

As second-series transition metals, Ag, Mo, and Y have 5s and 4d valence electrons. All the valence electrons will occupy a composite s-d band, which can accommodate 12 electrons per metal atom. To identify each metal, count the number of 5s and 4d valence electrons and compare that number with the population of bands in pictures (1), (2), and (3) above. The melting point and hardness of a metal is expected to increase as the difference between the number of bonding and antibonding electrons increases. 

Despite the completely different approach to chemical interaction, which has been followed here, the conventional standard symbols which are used to define the connectivity in covalent molecules, can also be applied, without modification, to distinguish between interactions of different order. However, each linkage pictured by formulae such as H3C-CH3, H2C=CH2, HC=CH, represents the sharing of a single pair of electrons with location unspecified. The number of connecting fines only counts bond order and may be established from the classical valence rules, e.g. v(C,N,0,F)=(4,3,2,l). Special symbols are used for non-integral bond orders, as in the symbol for benzene ... 

Benzene has two major resonance structures that contribute equally to the resonance hybrid. These are sometimes called Kekule structures because they were originally postulated by Kekule in 1866. You may also encounter benzene written with a circle inside the six-membered ring rather than the three double bonds. This representation is meant to show that the bonds in benzene are neither double nor single. However, the circle structure makes it difficult to count electrons. This text uses a single Kekule structure to represent benzene or its derivatives. You must recognize that this does not represent the true structure and picture the other resonance structure or call upon the MO model presented in Section 16.3 when needed. 

A central atom is any atom that is bonded to more than one other atom. In some molecules, more than one central atom may be present. In such cases, we determine the arrangement around each in turn, to build up a picture of the overall shape of the entire molecule or ion. We first count the number of regions of high electron density around the central atom, as follows ... 

It is convenient to start the MO analysis from the model [(PH3)3Co(//-X)2-Co(PH3)3], Scheme la, which has a planar M2X2 skeleton. Many pieces of chemical information are obtainable by applying distortional perturbations to the basic MO picture of the latter. In partieular, it may be inferred how the formation of M-M and/or X-X tran.v-annular bonds in either model a or b in Scheme 1 depends on the electron count. Moreover, some hints can be gained about the potential reactivity of these species. 

These are aciually three resonance forms of the protonnted molecule. It may look odd to draw resonance forms where a whole single bond is missing, but such pictures ( no-bond structures") are useful in some cases, provided you recognize that the individual forms are not real and that only the intermediate resonance hybrid really counts. In the case above, the re.sonance hybrid will probably look niorc like the alkyloxoniiim and 3 carbocation stnictures than the 2° carbocation structure (because 2 carbocations arc worse than 3 carbocations). 

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