Hybrid orbitals in carbon

We start this section with a word of caution. Students frequently find hybridization a rather difficult concept to understand and appreciate. However, there is no particular reason why this should be so. 

Chemistry is an experimental science, and to rationalize our observations we gradually develop and invoke a number of rules and principles. Theories may have to change as scientific data increase, and as old principles cease to explain the facts. All of the foregoing description of atomic and molecular orbitals is a hypothesis for atomic and molecular structure supported by experimental data. So far, the description meets most of our needs and provides a good rationalization of chemical behaviour. However, it falls short in certain ways, and we have to invoke a further modification to explain the facts. Here are three observations based upon sound experimental evidence, which are not accommodated by the above description of bonding  

None of these observations follows immediately from the electronic configuration of carbon 

which shows that carbon has two unpaired electrons, each in a 2p orbital. From our study of bonding so far, we might predict that carbon will be able to bond to two other atoms, i.e. it should be divalent, though this would not lead to an octet of electrons. Carbon is usually tetravalent and bonds to up to four other atoms. Therefore, we need to modify the model to explain this behaviour. This modification is hybridization. 

However, this does not explain why methane is tetrahedral and has four equivalent bonds. The bond that utilizes the 2s electron would surely be different from those that involve 2p electrons, and the geometry of the molecule should somehow reflect 

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PROBLEM Write the expressions for an orthonormal set of the three sp hybrid orbitals in carbonate ion, all exactly equivalent, lying in the xy plane with one orbital pointing along the x axis. Use the 2s and 2p subshells. 

Figpre 2.16 Schematic diagram that shows the formation of sp hybrid orbitals in carbon, (a) Promotion of a 2s electron to a 2p state (b) this promoted electron in a 2p state (c) three 2sp orbitals that form by mixing the single 2s orbital with two 2p orbitals—the 2p orbital remains unhybridized. 

Section 2 7 The carbon-carbon bond in ethane is a a bond in which an sp hybrid orbital one carbon overlaps with an sp hybrid orbital of the other... 

In addition to its three sp hybrid orbitals each carbon has a half filled 2p orbital that can participate m tt bonding Figure >b shows the continuous rr system that encompasses all of the carbons that result from overlap of these 2p orbitals The six tt electrons of benzene are delocalized over all six carbons... 

FIGURE 14 3 (a) The unshared electron pair occupies an sp hybridized orbital in dichlorocarbene There are no electrons in the unhybridized p orbital (b) An electrostatic potential map of dichlorocarbene shows negative charge is concentrated in the region of the unshared pair and positive charge above and below the carbon... 

Section 2.6 Bonding in methane is most often described by an orbital hybridization model, which is a modified for m of valence bond theory. Four equivalent sp hybrid orbitals of carbon are generated by mixing the 2s, 2p 2py, and 2p orbitals. Overlap of each half-filled sp hybrid orbital with a half-filled hydrogen I5 orbital gives a a bond. 

When we discussed sp3 hybrid orbitals in Section 1.6, we said that the four valence-shell atomic orbitals of carbon combine to form four equivalent sp3 hybrids. Imagine instead that the 2s orbital combines with only two of the three available 2p orbitals. Three sp2 hybrid orbitals result, and one 2p orbital remains unchanged- The three sp2 orbitals lie in a plane at angles of 120° to one another, with the remaining p orbital perpendicular to the sp2 plane, as shown in Figure 1.13. 

FIGURE 3.14 Each C H bond in methane is formed by the pairing of an electron in a hydrogen U-orbital and an electron in one of the four sp hybrid orbitals of carbon. Therefore, valence-bond theory predicts four equivalent cr-bonds in a tetrahedral arrangement, which is consistent with experimental results. 

All the atoms of butadiene lie in a plane defined by the s p hybrid orbitals. Each carbon atom has one remaining p orbital that points perpendicular to the plane, in perfect position for side-by-side overlap. Figure 10-42 shows that all four p orbitals interact to form four delocalized molecular orbitals two are bonding MOs and two are antibonding. The four remaining valence electrons fill the orbitals, leaving the two p orbitals empty. 

It will thus be apparent why the use of hybrid orbitals, e.g. sp3 hybrid orbitals in the combination of one carbon and four hydrogen atoms to form methane, results in the formation of stronger bonds. 

Figure 5 Energy changes during the formation of the sp3 hybrid orbitals in a carbon atom.

Hybridisation is the process of mixing atomic orbitals within an atom to generate a set of new atomic orbitals called hybrid orbitals. In the case of a carbon atom, the one 2s orbital can mix with the three 2p orbitals to form four hybrid orbitals known as sp hybrid orbitals. 

The sp hybrid orbitals of carbon were considered as a mix of the 2s orbital with three 2p orbitals. To provide a model for ethylene, we now need to consider hybrid orbitals that are a mix of the 2s orbital with two 2p orbitals, giving three equivalent sp orhitals. In this case, we use just three orbitals to create three new hybrid orbitals. Accordingly, we find that the energy level associated with an sp orbital will be below that of the sp orbital this time, we have mixed just two high-energy p orbitals with the lower energy orbital (Figure 2.13). The... 

Before we move on from the hybrid orbitals of carbon, we should take a look at the electronic structure of important reactive species that will figure prominently in our consideration of chemical reactions. First, let us consider carbanions and carbocations. We shall consider the simplest examples, the methyl anion CHs and the methyl cation CH3+, though these are not going to be typical of the carbanions and carbocations we shall be meeting, in that they lack features to enhance their stability and utility. 

The platinum(II)-ylide bond involves donation of a pair of electrons in a formally sp3 hybrid orbital on carbon to an empty orbital on platinum(II). The short bond lengths and XPES spectroscopy suggest some multiple bond character. 

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