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ENERGY OF ETHANE & BUTANE'S CONFORMERS

Introduction
Ethane and Butane Graphs
Ethane and Butane Excel Data
Discussion/ Comparison

Introduction: Energy of Ethane and Butane Conformers

The conformers of ethane and butane have varying steric energies depending upon the relative position of the bonds in the molecule and the interactions that occur between them.  The purpose of this exercise was to model various conformers in Chem3D (by changing the dihedral bond angle in 15 degree increments), and then use the Molecular Mechanics (MM2) feature of Chem3D to calculate various energies using classical mechanical approximations.  The minimum energy conformer for both ethane and butane, the anti-staggered conformer with a dihedral bond angle of 180 degrees, was obtained by manually adjusting the molecule and then using the 'Minimize Energy' feature.  The following energies were recorded and graphed using Excel:

1) TORSIONAL ENERGY--energy from the ROTATION of a bond away from its optimal position (anti, staggered conformer)
2) 1,4-VAN DER WAAL'S ENERGY--energy from the STERIC REPULSION of nonbonded atoms on adjacent carbons
3) non-1,4-VAN DER WAAL'S ENERGY--other STERIC REPULSIONS or ATTRACTIVE INSTANTANEOUS DIPOLES within the molecule
4) TOTAL STERIC ENERGY--the sum energy associated with a particular molecular conformer (from bending, stretching, torsion, and vanderwaals interactions)

Graphs: Click on a chart for a closer view.

energy of ethane conformers graphenergy of butane conformers graph



Discussion/ comparison:

ETHANE
An analysis of the total energy of ethane's conformers shows a cyclic cosine-like wave.  The groups on the two carbons are all hydrogens and therefore all equivalent.  The highest  energy conformer, the eclipsed conformer, maximizes the repulsions between the C-H bonds on one carbon and the C-H bonds of the adjacent carbon, resulting in an energy of 3.5803 kcal/ mol.  The staggered conformer has a minimum steric energy of 0.818 kcal/ mol because it minimizes the repulsions aforementioned.  As the dihedral angle increases, the molecule oscillates from the eclipsed (high energy) conformer to the staggered (low energy) conformer every 60 degrees.

BUTANE
An analysis of the total energy of butane's conformers shows a more complex wave because the groups on C2 and C3 are not all equivalent (as in ethane); C2 and C3 have 2 H's and 1 CH3 (methyl) group attached to them.  There are, therefore, two types of eclipsed conformations corresponding to the global maximum (10.212 kcal/ mol) and the local maxima (5.6321 kcal/ mol).  The highest energy eclipsed conformation results when the bond and steric repulsions are maximized by eclipsing the two larger methyl groups--at 0 and 360 degrees.  The lower energy eclipsed conformation results when the two methyl groups are eclipsed with hydrogens--at 120 and 240 degrees.  The global minimum (2.1735 kcal/ mol), which occurs at 180 degrees, corresponds to the anti-staggered conformer that places the methyl groups as far as possible from each other to minimizes the repulsions aforementioned.  The local minima (3.4145 kcal/ mol) in butane occur at 75 and 285 degrees. 

COMPARISON

1) TORSIONAL ENERGY--The torsional energy for both ethane and butane is about the same in scale, however butane's torsional energy at 60 and 300 degrees does not reach zero, as it does in ethane, because the methyl groups still sterically interact with each other, increasing energy. 

2) 1,4-VAN DER WAAL'S ENERGY--The 1,4-van der Waal's energy for ethane and butane is the same in pattern, but has a higher magnitude in butane because of the larger relative size of C1 and C4 as compared to H atoms.  The larger size of the C atoms increases the steric repulsion.

3) non-1,4-VAN DER WAAL'S ENERGY--The ethane molecule has 0 non-1,4-vdw energy.  Butane's non-1,4-vdw energy between 75 and 285 degrees is slightly negative, with local minima at 90 and 270 degrees, indicating a weak, attractive, energy-lowering interaction.  The contribution of the non-1,4-vdw energy shifts the local minima from the expected 60 and 300 degrees to 75 and 285 degrees; the C-H bond on C1 and the C-H bond on C4 repulse each other more strongly at 60 and 300 degrees than at 75 and 285.  It should be noted that in this model of butane, only the C2-C3 bond is rotated but the C1-C2 and C3-C4 bond are held stationary.

4) TOTAL STERIC ENERGY--See ethane and butane discussion above.