LON-CAPA MolecularMotions

Molecular Motions I: Free Rotation

Introduction

Until now our view of molecular structure has been a static one. In fact, molcules are anything but static. They move about, they vibrate, they rotate, they spin. Sometimes they invert like an umbrella in the wind!! We will examine molecular vibrations when we discuss infra-red spectroscopy, and we will consider umbrella-like inversions when we study nucleophilic aliphiphatic substitution reactions. In this discussion we will restrict our attention to the type of molecular motion known as free rotation.

Free Rotation

According to valence bond theory, the positions of two atoms that are bonded together is fixed, which is to say that every pair of bonded atoms has a characteristic bond length. As we saw when we discussed the formation of dihydrogen, this length corresponds to the distance between the bonded nuclei at which the Coulombic attractions of those nuclei for the electrons they share are a maximum. At this distance the potential energy of the bonding electrons is a minimum.

According to VSEPR theory, the potential energy of all of the electrons in a molecule is minimized by maximizing the distance between those electrons. This is another manifestation of the version of Coulomb's Law which states that Like charges repel, and the repulsion leads to a more stable system. It's important to remember that VSEPR theory describes the spatial distribution of electrons around a single atom, the so-called central atom. In molecules that contain more than one central atom, VSEPR theory does not describe the positions of the groups attached to one central with respect to those attached to another central atom. Consider ethane, CH₃CH₃, for example. VSEPR theory tells us that each carbon atom should be tetrahedral. But it does not say anything about the positions of the hydrogen atoms on one carbon relative to those on the other. In fact, as the interactive model in Figure 1 can demonstrate, the relative positions of the hydrogens vary.

Figure 1

Ethane: Take It for a Spin

(N.B. You must have the Chem 3D plug-in installed to view this model. To rotate around the C-C bond, first position the molecule so that you can see both carbon atoms. Then shift-click the pointer on each atom. Position the cursor on any atom in the structure while holding down the control key, and click the mouse. A menu will appear: Select Movies, then select Spin Torsional Angles from the Movies sub-menu. The second atom that you selected will begin to spin relative to the first. You may stop the rotation temporarily by holding down the mouse on the green arrow at the bottom of the model window.)

The rotation demonstrated in Figure 1 occurs approximately one million revolutions per second!! That's why it's called free rotation. In fact, this rotation is not free. To understand why it's not free, consider the four views of ethane shown in Figure 2.

Figure 2

Freeze-Frame Views of Free Rotation

The views labeled staggered and eclipsed are called conformations. Figure 3 presents two alternative representations for the front view of the staggered conformation of ethane. These alternatives are self-explanatory.

Figure 3

Different Strokes for Different Folks

Exercise 1 Draw a Newman projection and a sawhorse projection of the eclipsed conformation of ethane.

Exercise 2 If you start with an eclipsed conformation and rotate around the C-C bond of ethane in 20^o increments, how many staggered conformations will you generate by the time you have rotated 360^o?

The red and blue lines in the side views of the conformations shown in Figure 2 measure the distances between a hydrogen atom on one carbon and a hydrogen atom on the other. As you can see, the distance between hydrogens in the staggered conformation is larger than in the eclipsed conformation. This means that the distance between the electron pairs in the corresponding C-H bonds is larger as well. Consequently, electron pair-electron pair repulsions are less in the staggered conformation of ethane than in the eclipsed conformation. This means that the potential energy of the staggered conformation is less than that of the eclipsed conformation. Figure 4 outlines the changes in the potential energy of an ethane molecule during rotation about the C-C bond.

Figure 4

Profiling Free Rotation

The eclipsed conformation has the highest potential energy, while the staggered conformation has the lowest. The difference between the two conformations is 2.8 kcal/mol. This represents a barrier to rotation about the C-C bond, but there is more than enough energy available at room temperature to overcome this barrier, so that the process is described as free rotation.

The angle between a C-H bond on one carbon atom and a C-H bond on the other carbon is called the dihedral angle. In the eclipsed conformation of ethane, the dihedral angles are all 0^o. There are two dihedral angles in the staggered conformation, 60^o and 180^o. These are identified inFigure 5.

Figure 5

Playin' the Angles

Exercise 3 What is the dihedral angle between H_b and H_f in Figure 5? What is the dihedral angle between H_c and H_e in Figure 5?

Exercise 4 Ethyl told Ester that the dihedral angle between H_c and H_b was 120^o. Ester told Ethyl she was a doofus. Who's right? Ethyl Ester

Before we look into free rotation and conformational analysis any further, let's summarize the three different levels at which we have invoked Coulomb's Law in our discussions of molecular structure.

The atoms that make up molecules are held together by chemical bonds, which are the result of increased Coulombic attractions that occur when two atoms share one or more pairs of electrons.
The spatial distribution of atoms around a central atom in a molecule is determined by the Coulombic repulsions that occur between the electrons around the central atom.
When two central atoms are bonded together, the dihedral angles between the substituents attached to those central atoms changes due to free rotation about the bond between them. The conformation of minimum energy is the one in which the Coulombic repulsions between the bonds to substituents on one central atom and those to substituents on the other are minimized.

Now let's apply our analysis to a slightly more complex molecule, butane. An interactive model of this molecule is shown in Figure 6. Study the rotation about the C₂-C₃ bond.

Figure 6

Cranking It Up a Notch

Refer to Figure 7 and answer the following questions.

Figure 7

Conformations of Butane

Exercise 5

a. Which conformation is the least stable?

b. Which conformation is the most stable?

c. Which conformation has the same energy as 2?

d. Which conformation has the same energy as 5?

Exercise 6 Draw a potential energy diagram similar to the one shown in Figure 4 for the free rotation about the C₂-C₃ bond in butane.

Exercise 7 Draw Newman and sawhorse projections of the staggered and eclipsed conformations of butane that are generated by rotation around the C₁-C₂ bond. Draw a potential energy diagram similar to the one shown in Figure 4 for this process.

As the substituents attached to the the atoms at the end of a bond become larger, free rotation becomes more difficult. As the increase in potential energy required to go from one conformation to another becomes larger, the rate of rotation decreases. In such cases the motion is described as restricted rotation. We will look at several situations where restricted rotation is an important consideration in understanding molecular structure and chemical reactivity in Molecular Motions II.