Ethane hybrid atomic orbitals

Ethylene is a planar molecule, as the structural representations of Figure 1.24 indicate. Because sp hybridization is associated with a tetrahedral geometry at carbon, it is not appropriate for ethylene, which has a trigonal planar geometry at both of its carbons. The hybridization scheme is determined by the number of atoms to which the carbon is directly attached. In ethane, four atoms are attached to carbon by a bonds, and so four equivalent sp hybrid orbitals are required. In ethylene, three atoms are attached to each carbon, so three equivalent hybrid orbitals are required. As shown in Figure 1.25, these three orbitals are generated by mixing the carbon 2s orbital with two of the 2p orbitals and are called sp hybrid orbitals. One of the 2p orbitals is left unhybridized. 

In a molecule such as ethane H C-CH, each carbon atom has four sp hybrids. Between the two carbon nuclei, there is a localized molecular orbital built up from two hybrids, one for each carbon atom, and pointing at one another. The alignment of the hybrid axes gives the most stable system. Indeed the orbital overlap is maximum and therefore the interaction between atomic orbitals is the strongest The corresponding energy is the highest in absolute... 

Here, the bonding between carbon atoms is briefly reviewed fuller accounts can be found in many standard chemistry textbooks, e.g., [1]. The carbon atom [ground state electronic configuration (ls )(2s 2px2py)] can form sp sp and sp hybrid bonds as a result of promotion and hybridisation. There are four equivalent 2sp hybrid orbitals that are tetrahedrally oriented about the carbon atom and can form four equivalent tetrahedral a bonds by overlap with orbitals of other atoms. An example is the molecule ethane, CjH, where a Csp -Csp (or C-C) a bond is formed between two C atoms by overlap of sp orbitals, and three Csp -Hls a bonds are formed on each C atom. Fig. 1, Al. 

The same kind of orbital hybridization that accounts for the methane structure also accounts for the bonding together of carbon atoms into chains and rings to make possible many millions of organic compounds. Ethane, C2H6, is the simplest molecule containing a carbon-carbon bond. 

Figure 1.17 The hypothetical formation of the bonding molecular orbitals of ethane from two sp -hybridized carbon atoms and six hydrogen atoms. All of the bonds are sigma bonds. (Antibonding sigma molecular orbitals — are called a orbitals — are formed in each instance as well, but for simplicity these are not shown.)... 

We have already explained. In terms of hybridisation, how a carbon atom can form four sp hybrid orbitals (see p. 47). We can apply this concept to explain the bonding in alkanes. Ethane is taken as an example of a typical alkane. The four sp hybrid orbitals on each carbon atom will overlap end-on with four other orbitals three hydrogen Is orbitals and one sp hybrid orbital on the other carbon atom. Four cr bonds will be formed and they will adopt a tetrahedral arrangement. This is illustrated for ethane in the diagram. 

Because they have no ionic states, the previous covalent-only results have too high a kinetic energy contribution, as discussed in Chapter 2. Adding all possible ionic states would lead to the very large number of basis functions quoted in the first paragraph of the discussion of ethane. We will consider the following physical arguments that may be used to limit the number of ionic state functions. This will all be done in the context of hybrid orbitals on the C atoms. 

FIGURE 3.18 The valence-bond description of the bonding in an ethane molecule, CjHf,. Only two of the bonds are shown in terms of their boundary surfaces. Each pair of neighboring atoms is linked by a cr-bond formed by the pairing of electrons in either Hls-orbitals or C2sp3 hybrid orbitals. All the bond angles are close to 109.5° (the tetrahedral angle). 

The three-dimensional structure of ethane, C2H6, has the shape of two tetrahedra joined together. Each carbon atom is sp3 hybridized, with four sigma bonds formed by the four sp3 hybrid orbitals. Dashed lines represent bonds that go away from the viewer, wedges represent bonds that come out toward the viewer, and other bond lines are in the plane of the page. All the bond angles are close to 109.5°. 

In ethane (CH3—CH3), both carbon atoms are sp3 hybridized and tetrahedral. Ethane looks like two methane molecules that have each had a hydrogen plucked off (to form a methyl group) and are joined by overlap of their sp3 orbitals (Figure 2-20). 

Each of the carbon-hydrogen sigma bonds is formed by overlap of an sp2 hybrid orbital on carbon with the Is orbital of a hydrogen atom. The C—H bond length in ethylene (1.08 A) is slightly shorter than the C—H bond in ethane (1.09 A) because the sp2 orbital in ethylene has more s character (one-third, v) than an sp3 orbital (one-fourth, v). The s orbital is closer to the nucleus than the p orbital, contributing to shorter bonds. 

The simplest member of the saturated hydrocarbons, which are also called the alkanes, is methane (CH4). As discussed in Section 14.1, methane has a tetrahedral structure and can be described in terms of a carbon atom using an sp-J hybrid set of orbitals to bond to the four hydrogen atoms (see Fig. 22.1). The next alkane, the one containing two carbon atoms, is ethane (C2H6), as shown in Fig. 22.2. Each carbon in ethane is surrounded by four atoms and thus adopts a tetrahedral arrangement and sp3 hybridization, as predicted by the localized electron model. 

All of the bonds in ethane are a bonds. The C-H bonds are formed from the overlap of one of the three sp hybrid orbitals on each carbon atom with the Is orbital on hydrogen. The C-C bond is formed from the overlap of an sp hybrid orbital on each carbon atom. 

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