Methane, bonding molecular orbitals

Fig. 1.20. Atomic orbital combinations giving rise to bonding molecular orbitals for methane.

Now we can consider the bonding in methane. Using orbital overlap as in the hydrogen molecule as a model, each sp orbital of carbon can now overlap with a 1 orbital of a hydrogen atom, generating a bonding molecular orbital, i.e. a ct bond. Four such... 

Figure 6. Representations for the bonding molecular orbitals in methane.

We must now address a fundamental question. Are there C-H bonds in methane The answer from MO theory is clearly no. Population of the four bonding molecular orbitals with four pairs of electrons leads to a bonding interaction among the carbon atom and all of the hydrogen atoms (not just between carbon and the individual hydrogens). Thus, we should say that there is bonding in MO theory, but there are not distinct bonds formed by separate electron pairs localized between two atoms. 

If, in our imagination, we visualize the hypothetical formation of methane from an ijs -hybridized carbon atom and four hydrogen atoms, the process might be like that shown in Fig. 1.14. For simplicity we show only the formation of the bonding molecular orbital for each carbon-hydrogen bond. We see that an ry) -hybridized carbon gives a tetrahedral structure for methane, and one with four equivalent C—H bonds. 

FIGURE 1.14 The hypothetical formation of methane from an sp -hybrldlzed oarbon atom and four hydrogen atoms. In orbital hybridization we combine orbitals, not electrons. The electrons can then be placed In the hybrid orbitals as necessary for bond formation, but always In accordanoe with the Pauli principle of no more than two eleotrons (with opposite spin) in each orbital. In this illustration we have placed one electron in each of the hybrid carbon orbitals. In addition, we have shown only the bonding molecular orbital of each C—H bond because these are the orbitals that contain the electrons in the lowest energy state of the molecule. 

The bond angles at the carbon atoms of ethane, and of all alkanes, are also tetrahedral like those in methane. A satisfactory model for ethane can be provided by ry) -hybridized carbon atoms. Figure 1.19 shows how we might imagine the bonding molecular orbitals of an ethane molecule being constructed from two ry) -hybridized carbon atoms and six hydrogen atoms. 

As soon as one of the four hydrogens surrounding the central carbon in methane is replaced with another atom, pure tetrahedral symmetry is lost. We might well anticipate that one of the four s- hybrid orbitals of carbon could overlap in a stabilizing way with any atom X offering an electron in any atomic orbital (Fig. 2.11). For maximum stabilization, we want to fill the new, bonding molecular orbital created from this overlap, which requires two, and only two, electrons. 

Atomic Structure The Nucleus Atomic Structure Orbitals 4 Atomic Structure Electron Configurations 6 Development of Chemical Bonding Theory 7 The Nature of Chemical Bonds Valence Bond Theory sp Hybrid Orbitals and the Structure of Methane 12 sp Hybrid Orbitals and the Structure of Ethane 13 sp2 Hybrid Orbitals and the Structure of Ethylene 14 sp Hybrid Orbitals and the Structure of Acetylene 17 Hybridization of Nitrogen, Oxygen, Phosphorus, and Sulfur 18 The Nature of Chemical Bonds Molecular Orbital Theory 20 Drawing Chemical Structures 21 Summary 24... 

Hence we have two molecular orbitals, one along the line of centres, the other as two sausage-like clouds, called the n orbital or n bond (and the two electrons in it, the n electrons). The double bond is shorter than a single C—C bond because of the double overlap but the n electron cloud is easily attacked by other atoms, hence the reactivity of ethene compared with methane or ethane. 

For a molecule as simple as Fl2, it is hard to see much difference between the valence bond and molecular orbital methods. The most important differences appear- in molecules with more than two atoms. In those cases, the valence bond method continues to view a molecule as a collection of bonds between connected atoms. The molecular- orbital method, however, leads to a picture in which the sane electron can be associated with many, or even all, of the atoms in a molecule. We ll have more to say about the similarities and differences in valence bond and molecular- orbital theory as we continue to develop their principles, beginning with the simplest alkanes methane, ethane, and propane. 

The development of molecular orbital theory (MO theory) in the late 1920s overcame these difficulties. It explains why the electron pair is so important for bond formation and predicts that oxygen is paramagnetic. It accommodates electron-deficient compounds such as the boranes just as naturally as it deals with methane and water. Furthermore, molecular orbital theory can be extended to account for the structures and properties of metals and semiconductors. It can also be used to account for the electronic spectra of molecules, which arise when an electron makes a transition from an occupied molecular orbital to a vacant molecular orbital. 

Herzberg (Nobel prize for Chemistry, 1971) commented on the two distinct photoionizations from methane that this observation illustrates the rather drastic nature of the approximation made in the valence bond treatment of CH4, in which the 2s and 2p electrons of the carbon atom are considered as degenerate and where this degeneracy is used to form tetrahedral orbitals representing mixtures of 2s and 2p atomic orbitals. The molecular orbital treatment does not have this difficulty". 

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