Diastereomers of Butane

William Bloemeke and Jamie McCormick

Purpose of the Project
Scientific Background
Computational Approach
Results
References

Purpose of the Project

In researching the diastereomers of butane we propose to find the heats of formation for the various isomers and to compare them to each other. In this process we attempted to discover which isomers have the lowest heats of formation and thusly which isomers butane has a tendency towards forming.

Scientific Background

Butane is a four-carbon organic molecule, connected only by single bonds. In the geometry of this molecule, there are various possibilities for the construction, while still yielding the same empirical formula. These possibilities are known as isomers. Due to the different constructions of these isomers, they each have different chemical properties. There are several different types of isomers though. The first is Constitutional isomers. They differ in the construction and connection of the atoms. The second type of isomers are called stereoisomer. These isomers differ in the disposition of the atoms in space, not in the construction of the molecule. Stereoisomers are divided into to sections. The first is enantiomers, which are isomers that are arranged in a mirror image of each other. The second is diastereomers, which are not arranged as mirror images of each other. There are a few prefixes used to represent the arrangement of the atoms within a diastereomer. The prefix cis- denotes that a carbon chain has two of the same functional group or the same atom coming off the chain on the same side. Trans- shows that the two functional groups are on opposite sides of the molecule. The prefix anti- tells that two funtional groups make a perfect 180 degree dihedral angle in the molecule. The prefix gauche- denotes that the functional groups make neither a 0 nor a 180 degree angle, they make an odd, or skew, angle. The heat of formation for a molecule shows the energy released or absorbed when that molecule is formed. When any isomer of butane is formed from solid carbon and hydrogen gas, a certain amount of energy is released in the form of heat. The different isomers release different amounts of energy when they are formed. The most stable isomers release more energy when they are formed; the less stable isomers release less energy. The reason for these isomers being less stable is that after they release energy, they still have a good deal stored inside them, whereas the more stable isomers have less energy stored in them. These various energy states are directly related to the dihedral angle of each molecule. The dihedral angle is the angle formed by all four cabon atoms in butane. Three of these carbons form one straight line, and the bond to the fourth forms the dihedral angle with that line. The difference in these angles affects the energy of the molecule by causing interference in the molecular orbitals of the electrons. Two molecular orbitals that are in direct conflict with each other can cause tension in the molecule, which is represented as energy. In the most stable isomers, the molecular orbitals are in the least conflict with each other, and thus the molecule can exist as its lowest enery state.

Computational Approach

The molecules were first built using MacSpartan's builder. Each molecule's dihedral angle was constrained to the appropriate degree and was then minimized to find it's proper geometry. Once each molecule had been minimized, each was geometrically optimized using the semi-empirical method with the AM1 basis set. This level of theory was chosen so that the data could be compared to the data from a 3-21G ab initio method found in a text book. This level of theory was also much less computationally expensive than the ab initio. AM1 rather than AM1-SM2 was chosen for this research, because butane exists mainly in a gaseous state and is infrequently used in a solvent. Data for the heats of formation were taken from the results of these geometric optimizations. The graphical representation of that data was then made using Microsoft Excel. From this graph and data, we determined which isomers of butane were the most stable. We then set about to compare these isomers to each other. Using the MacSpartan viewer we computed the Highest Occupied Molecular Orbitals (HOMOs). Rationalizing that these outermost electrons are the ones that affect each other the most within a molecule, we searched for patterns in the HOMOs of the various isomers. From manipulating the molecules to view them at a more desirable angle, we were able to discover what interactions the molecular orbitals made with each other, and how this affected the structure of the molecule and the stability of the isomer.

Results

After computing the heats of formation for the various isomers, the numbers were graphed using Microsoft Excel. This graph allowed us to see where the maxima were for the most stable isomers of butane.

This graph and chart clearly show that there are peaks in the stability of butane isomers that are directly related to the angle of the dihedral. It is clear that there are peaks at 60 degrees and at 180 degrees. These isomers will hereafter be named, respectively, as gauche-butane and anti-butane. There is another gauche-butane isomer that occurs near 300 degrees in the dihedral. In actuality, this isomer is the same as the 60 degree gauche-butane, and thus has the same heat of formation. Simple addition shows that the anti-butane isomer is approximately 0.8kcal/mol more stable than gauche-butane. Using this knowledge, we labeled anti-butane and gauche-butane as the two most stable isomers and then compared them to the less stable isomers. Based on the knowledge that the outermost electrons in the molecular orbitals affect the stability of the molecule, we used the HOMO function of MacSpartan to view the orbitals of these outermost electrons.

The upper graphic is a MacSpartan representation of the anti-butane isomer with the HOMOs. The lower graphic depicts a cis-butene isomer, with the dihedral angle constrained at 0 degrees. The blue areas represent an electron rich orbital, while the red areas represent an electron poor orbital. In the upper, stable isomer, the orbitals that surround the methyl groups are extremely removed from each other. The orbitals are staggered throughout the entire molecule, resulting in low conflict between the like-orbitals. In the lower isomer, the methyl groups are in very close proximity to each other, and, by looking at the graph above, it can be seen that this isomer is one of the most unstable possible. From this, we concluded that the interaction between the orbitals of the methyl groups is more important in calculating the intereaction of the orbitals of the methyl group and the CH bond group. From other isomers that space and time do not permit us to show here, we concluded that the interaction of electron-rich orbitals is more important in the stability of the molecule than the interation of electron-poor orbitals. The gauche-butane isomer had interaction between the red areas but not during the blue, and when the opposite was true, the energy was much higher.

References

Parker, Sybyl P.,ed. Physical Chemistry Source Book. New York: McGraw-Hill Book Co.,1988.

Hehre, Burke, Shusterman, Pietro. Experiments in Computational Organic Chemistry. Irvine: Wavefunction, Inc., 1993.

Hehre, Shusterman, Huang. A Laboratory Book of Computational Organic Chemistry. Irvine: Wavefunction, Inc., 1996.

Gotwals, Bob. "Personal Conversations" Computational Chemistry. 11-15 Aug., 1997.