Shape bonding models

We saw in the last chapter how covalent bonds between atoms are described, and we looked at the valence bond model, which uses hybrid orbitals to account for the observed shapes of organic molecules. Before going on to a systematic study of organic chemistry, however, we still need to review a few fundamental topics. In particular, we need to look more closely at how electrons are distributed in covalent bonds and at some of the consequences that arise when the electrons in a bond are not shared equally between atoms. 

We cannot generate a tetrahedron by simple overlap of atomic orbitals, because atomic orbitals do not point toward the comers of a tetrahedron. In this section, we present a modification of the localized bond model that accounts for tetrahedral geometry and several other common molecular shapes. 

FIGURE 7-2 Three ways to represent the two stereoisomers of glyc-eraldehyde. The stereoisomers are mirror images of each other. Ball-and-stick models show the actual configuration of molecules. By convention, in Fischer projection formulas, horizontal bonds project out of the plane of the paper, toward the reader vertical bonds project behind the plane of the paper, away from the reader. Recall (see Fig. 1-17) that in perspective formulas, solid wedge-shaped bonds point toward the reader, dashed wedges point away. 

R. F. C url, R. F. Smalley, and 11. W. Kroto were awarded the Nobel prize m chemistry in 199fe for the discovery of the soccer ball-shaped molecule C, . The enthalpy of combustion of (J o is 25 937 kj-mol 1 and its enthalpy of sublimation is +233 kj-mol 1 There are 90 bonds in of which 60 are single and 30 are double bonds. is like benzene in that it has a set of multiple bonds for which resonance structures may be drawn, (a) Determine the enthalpy of formation of Cfj) from its enthalpy of combustion, (h) Calculate the expected enthalpy of formation of from bond enthalpies, assuming the bonds to be isolated double and single bonds, (c) Is CMI more or less stable than predicted on the basis of the isolated bond model ... 

The electron-dot structures described in Sections 7.6 and 7.7 provide a simple way to predict the distribution of valence electrons in a molecule, and the VSEPR model discussed in Section 7.9 provides a simple way to predict molecular shapes. Neither model, however, says anything about the detailed electronic nature of covalent bonds. To describe bonding, a quantum mechanical model called valence bond theory has been developed. 

The VSEPR model works at its best in rationalizing ground state stereochemistry but does not attempt to indicate a more precise electron distribution. The molecular orbital theory based on 3s and 3p orbitals only is also compatible with a relative weakening of the axial bonds. Use of a simple Hiickel MO model, which considers only CT orbitals in the valence shell and totally neglects explicit electron repulsions can be invoked to interpret the same experimental results. It was demonstrated that the electron-rich three-center bonding model could explain the trends observed in five-coordinate speciesVarious MO models of electronic structure have been proposed to predict the shapes and other properties of non-transition element... 

The weak bond model is useful because the distribution of formation energies can be evaluated from the known valence band and defect density of states distributions. Fig. 6.12 illustrates the distribution of formation energies, N iU). The shape is that of the valence band edge given in Fig. 3.16 and the position of the chemical potential of the defects coincides with the energy of the neutral defect gap state. Fig. 6.12 also shows that in equilibrium virtually all the band tail states which are deeper than convert into defects, while a temperatiue-dependent fraction of the states above convert. 

Fig. 6.12. The distribution of formation energies according to the weak bond model. The shape is proportional to the valence band density of states.

The weak bond model assumes a non-equilibrium distribution of weak bonds arising from the disorder of the a-Si H network. It has been proposed that the shapes of the band tails are themselves a consequence of thermal equilibrium of the structure (Bar-Yam, Adler and Joannopoulos 1986). The formation energy of a tail state is assumed proportional to the difference in the one-electron energies, so that the energy, required to create a band tail state of energy Ey from the valence band mobility edge is... 

A straight bond formalism for this compound would require the iridium atom to be related to a hypothetical T-shaped three-coordinate system (just as, on a straight bond model, the cobalt atom in solid Co2(CO)g is to a square pyramidal d system). No such systems are known or expected. 

What does a water molecule look like It isn t possible to see a single molecule, but in Chapter 4, you used a covalent bonding model to explain how two hydrogen atoms and one oxygen atom bond together to form the water molecule. Does this model teU anything about the shape of the molecule It s important to find out because the bonding patterns and the shapes of all molecules have a lot to do with their properties. 

A simple covalent cr-bonding model employing five d orbitals and the next available s and three p orbitals, with appropriate hybridization to match a particular shape, allows a limited interpretation of bonding in coordination complexes. 

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