Two carbons, with sp3 hybrid orbitals, may form a sigma bond between them with an overlap of an sp3 orbital from each carbon.  The carbons, and the other atoms attached to the carbon, are not in fixed positions; they are relatively free to rotateabout the sigma bond connecting the two carbon atoms. These different arrangements formed by rotations about a single bond are called conformations.  Molecules do not stay in one conformation; they are constantly rotating through all the possible conformations.

        For the two-carbon alkane, ethane (C₂H₆), there are an infinite number of conformations possible, because the angle between the hydrogen atoms on the first and second carbon atoms can take on an infinite number of values.  However, not all the conformations have the same energy.  Certain conformations have higher or lower energy depending upon the position of the hydrogen atoms on the first carbon atom with respect to the hydrogen atoms on the second carbon atom.  The energies of the conformations vary as ethane rotates due to a resistance to rotation, called torsional strain.  The energies of the various conformations are given with respect to the lowest energy conformer.
 

1,2-difluoroethane Data:

         For this project, the various conformations of 1,2-difluoroethane were examined.  In this compound, there is a fluorine atom attached to each of the carbon atoms.  These fluorine atoms cause an additional strain in the molecule.  Steric strain is the interference between two atoms or groups that are so close together that their electron clouds experience a strong repulsion.  When the two fluorine atoms are far apart, there is minimal steric strain in the molecule, but the closer they come to one another, the more steric strain involved and the higher the energy of the molecule.  The lowest energy conformation is the one with the fluorine atoms as far from each other as possible while also keeping the hydrogen atoms at a great distance, as well.  The energy of this conformer is theoretically calculated.  Then carbon-2 is rotated 60^o to a new conformer; the energy of this next conformer is determined.  The difluoroethane is rotated, at 60^o intervals, throughout a complete 360^o cycle.

         The energies for the various conformations were calculated by using a program called GAMESS VERSION = 25 MAR 2000, from Iowa State University.  GAMESS, short for The General Atomic and Molecular Electronic Structure System, is a general ab initio quantum chemistry package.  It optimizes molecular geometries using the energy gradient, in terms if Cartesian coordinates.  It also searches for potential energy surface saddle and computes energy hessians.  (For more information on this program, click here.  To return, use the Back Button on your browser.)

 The data for the various conformations of 1,2-diflouroethane is as follows:
 

Angle of rotation	0o	60o	120o	180o	240o	300o	360o
Angle between F	180o	120o	60o	0o	120o	60o	180o
Energy  (kcal/mol)	0	1.38	0.63	5.08	0.63	1.38	0

The energy is actually the energy difference from the reference lowest energy conformer.
The angle of rotation is the angle through which the original molecule has rotated.

The energy difference is lowest when the two fluorine atoms are as far apart as possible, see Figure 1.  Here, the F-C-C-F angle is 180^o.  In this conformation there is minimal steric strain caused by the two fluorine atoms and therefore it has the least energy of all the conformers.  This is called the anti conformation.

The energy difference is highest when the F-C-C-F angle is 0^o, see Figure 4.  This conformation exhibits maximum steric strain because of the closeness of the two fluorine atoms; and the most strain means the highest energy exists in this conformer.  This is called a totally eclipsed conformation.

Rotation of 120^o and rotation of 240^o produces two conformations that have the same the energy.  See Figure 3 and Figure 5.  In these, the F-C-C-F angle is 60^o, and there is some steric strain that causes this small amount of energy in these molecules.   These are gauche conformations.

Rotation of 60^o and rotation of 300^o also produces two conformations that have the same energy.  See Figure 2 and Figure 6.  In these, the F-C-C-F angle is 120^o.  Now since the fluorine atoms are farther apart than in the two cases of 120^o and 240^o rotation, it is curious that the energy is higher.  This is explained by looking at the figures and seeing that these are eclipsed conformations.  Although, they are not totally eclipsed, the fluorine is aligned with the hydrogen atoms; so the F-C-C-H angle is 0^o.  This steric strain in this conformation exists between the fluorine and the hydrogen and causes the energy to be higher in these eclipsed conformations than in the gauche conformations.

A 360^o rotation will produce an anti conformation like the initial molecule of the discussion.  See Figure 1.
 

Comparison of the Energies of the Conformations of 1,2-difluoroethane and Butane

        The energies of butane may be compared to those of 1,2-difluoroethane by looking at the sigma bond between carbon-2 and carbon-3 and determining the energy as the C2-C3 bond undergoes rotation.  While the 1,2-difluoroethane has a fluorine attached to each carbon atom, the C2 and C3 each have a methyl group attached.  There is a similarity between the energies of the conformations of 1,2-difluoroethane and butane throughout a 360^o rotation.  According to the information in Organic Chemistry, Fourth Edition by L. G. Wade Jr., the energy values for the rotation of butane about the C2-C3 bond are as follows:
 

Angle of rotation	0o	60o	120o	180o	240o	300o	360o
Angle between CH3	180o	120o	60o	0o	120o	60o	180o
Energy  (kcal/mol)	0	3.6	0.9	-5	0.9	3.6	0

 The energy is actually the energy difference from the reference lowest energy conformer
 The angle of rotation is the angle through which the original molecule has rotated.

Compare the two sets of data:

For a larger version of the graph, click here.

         Notice that the energies of the two compounds follow a similar pattern.  The anti conformation is lowest in energy and the totally eclipsed conformation has the highest energy.  The most striking difference is the energy difference between the other eclipsed conformation with a CH3-C-C-CH3 angle of 120^o.  (See figure to the right.)  The energy of this conformation of 1,2-difluoroethane is 1.38 kcal/mol while the energy of this conformation of butane is 3.6 kcal/mole, more than 2.5 times larger.  The questions seems to be: why is there such a large difference between these energies?  The difference comes about because of the size of the substituents.  The fluorine is much smaller than the methyl group.  So there will be greater steric strain caused by the two methyl groups than by the two fluorines.  Greater steric strain leads to molecule having a greater energy.  In the case of butane in the eclipsed form,  the hydrogen is interacting with the methyl group to a much greater extent than the hydrogen interacting with the fluorine causing such a great difference in the energies.

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