March's Advanced Organic Chemistry: Reactions, Mechanisms, and Structure, 7th Edition (2013)

Chapter 1. Localized Chemical Bonding

1.D. Multiple Bonds

If ethylene (H₂C=CH₂) is examined in terms of the MO concepts discussed so far, each carbon has three σ bonds, one to each of the three atoms. Therefore, sp² orbitals are used to form those three bonds. These sp² orbitals arise from hybridization of the 2s¹, 2p_x¹, and 2p_y¹ electrons after promotion of electrons (Sec. 1.C). In general, any carbon atom that is bonded to only three different atoms uses sp² orbitals for this bonding. The three σ bonds of ethylene are one to each of two hydrogen atoms and one to the other carbon. Each carbon therefore has another electron in the 2p_z orbital that is perpendicular to the plane of the sp² orbitals. The two parallel 2p_z orbitals, one on each of the two adjacent carbon atoms, can overlap sideways to generate a bonding and an antibonding orbital (Fig. 1.5). In the ground state, both electrons go into the bonding orbital and the antibonding orbital remains vacant. In other words, a new bond is formed, but it is formed by sideways overlap of adjacent p orbitals rather than direct overlap of σ orbitals. Molecular orbitals formed by the overlap of atomic orbitals whose axes are parallel are called π orbitals if they are bonding and π∗ if they are antibonding.

Fig. 1.5 (a) Overlapping p orbitals form a π and a π∗ orbital. The σ orbitals are shown in (a). The π orbitals are shown in (b) as the highest occupied molecular orbital (HOMO) (on the left) and the LUMO. In (c), the electron potential map of ethylene shows the concentration of electron density above and below the plane of the atoms, consistent with a π bond.

In this picture of ethylene, there are two bonds connecting the adjacent carbon atoms, but the two orbitals that make up the double bond are not equivalent.⁸ This means that the two bonds are different one from the other. The σ orbital is ellipsoidal and symmetrical about the C–C axis, and this is the familiar σ bond. The π orbital is in the shape of two ellipsoids, one above the plane and one below, and forms the second bond, a π bond. The plane itself represents a node for the π orbital. In order for the p orbitals to maintain maximum overlap, they must be parallel. Since both a σ bond and the π bond connect the two carbon atoms, free rotation is not possible about the double bond. In other words, the two p orbitals would have to reduce their overlap to allow one H–C–H plane to rotate with respect to the other (i.e., the π bond would have to disappear). With two sp² hybrid carbon atoms in ethylene, the six atoms associated with the double bond (H₂C=CH₂) are in a plane with angles that should be ~120°. Double bonds are shorter than the corresponding single bonds because maximum stability is obtained when the p orbitals overlap as much as possible (see Sec. 1.J). Double bonds between carbon and oxygen (C=O) or nitrogen (C=N) similarly consist of one σ and one π orbital.

When carbon is connected to another carbon atom by a triple bond, as in acetylene (HCCH), each carbon is connected to only two other atoms by a σ bond, and hence uses sp hybridization. This fact requires that the four atoms of acetylene (2H and 2C) are in a straight line (Fig. 1.6).⁹ Each carbon has two p orbitals remaining, with one electron in each. These orbitals are perpendicular to each other and also to the C–C axis. They overlap in the manner shown in Fig. 1.7 to form two π orbitals. A triple bond is thus composed of one σ and two π orbitals. Triple bonds between carbon and nitrogen can be represented in a similar manner, CN.

Fig. 1.6 The σ orbitals of acetylene.

Fig. 1.7 (a) The electron density map of acetylene. Note the concentration of electron density along a line between the nuclei of each atom, consistent with overlap of σ orbitals in a triple bond. (b) Electron potential map of acetylene showing the concentration of electron density between the carbon atoms, consistent with two orthogonal π bonds.

For most organic molecules, double and triple bonds typically involve the first-row elements carbon, nitrogen, and oxygen.¹⁰ Second-row elements tend to form weaker π bonds than do the first-row elements,¹¹ so multiple bonds are less common and compounds containing them are generally less stable.¹² Compounds with C=S bonds are known, for example, and C=S compounds are generally much less stable than the corresponding C=O compounds (however, see pπ–dπ bonding in Sec. 2.H). Stable compounds with Si=C and Si=Si bonds are rare, but examples have been reported,¹³ including a pair of cis and trans Si=Si isomers.¹⁴

There is at least one report of a so-called two-electron, four-center C–C bond for the dimer of tetracyanoethylene.¹⁵ While such multi-center bonding is not formally an example of the multiple bonding described in this section, it constitutes a different type of bonding when compared to the simple C–C bonds described earlier.