MCAT Organic Chemistry Review

Bonding

3.2 Molecular Orbitals

When two atomic orbitals combine, they form molecular orbitals. Molecular orbitals are obtained mathematically by adding or subtracting the wave functions of the atomic orbitals. While the mathematics of combining wave functions is outside the scope of the MCAT, some questions may ask for the visualization of molecular orbitals, as shown in Figure 3.2. If the signs of the wave functions are the same, a lower-energy (more stable) bonding orbital is produced. If the signs are different, a higher-energy (less stable) antibonding orbital is produced.

Figure 3.2. Molecular Orbitals Molecular orbitals can be bonding or antibonding, depending on the signs of the atomic orbitals used to form them; head-to-head or tail-to-tail overlap of atomic orbitals results in a σ bond.

σ AND π BONDS

When a molecular orbital is formed by head-to-head or tail-to-tail overlap, as in Figure 3.2, the resulting bond is called a sigma (σ) bond. All single bonds are σ bonds, accommodating two electrons.

KEY CONCEPT

Sigma (σ) bonds are formed by head-to-head or tail-to-tail overlap of atomic orbitals. These bonds are by far the most common in organic compounds and on the MCAT.

When two p-orbitals line up in a parallel (side-by-side) fashion, their electron clouds overlap, and a bonding molecular orbital, called a pi (π) bond, is formed. This is demonstrated in Figure 3.3. One π bond on top of an existing σ bond is a double bond. A σ bond and two π bonds form atriple bond. Unlike single bonds, which allow free rotation of atoms around the bond axis, double and triple bonds hinder rotation and, in effect, lock the atoms into position.

Figure 3.3. Pi (π) Bond Electron density exists above and below the plane of the molecule, restricting rotation about a double bond.

It is important to remember that a π bond cannot exist independently of a σ bond. Only after the formation of a σ bond will the p-orbitals of adjacent carbons be parallel and in position to form the π bond. The more bonds that are formed between atoms, the shorter the overall bond length. Therefore, a double bond is shorter than a single bond, and a triple bond is shorter than a double bond. Shorter bonds hold atoms more closely together and are stronger than longer bonds; shorter bonds require more energy to break.

While double bonds are stronger than single bonds overall, individual π bonds are weaker than σ bonds. Therefore, it is possible to break only one of the bonds in a double bond, leaving a single bond intact. This happens often in organic chemistry, such as when cistrans isomers are interconverted between conformations. Breaking a single bond requires far more energy.

KEY CONCEPT

A double bond consists of both a σ bond and a π bond; a triple bond consists of a σ bond and two π bonds. π bonds are weaker than σ bonds, but the strength is additive, making double and triple bonds stronger overall than single bonds.

As discussed previously, double and triple bonds do not freely rotate like single bonds. As such, double bonds in compounds make for stiffer molecules. Partial double-bond character in structures with resonance also restricts free rotation, resulting in more rigid structures. Proteins exhibit this kind of limited rotation because there is resonance in the amide linkages between adjacent amino acids.

MCAT Concept Check 3.2:

Before you move on, assess your understanding of the material with these questions.

1.    Which is more stable: a bonding orbital or an antibonding orbital? Which has higher energy?

·        More stable:

·        Higher energy:

2.    What differences would be observed in a molecule containing a double bond compared to the same molecule containing only single bonds?

3.    Rank the following orbitals in decreasing order of strength: σ bond, π bond, double bond, triple bond.