If quantum mechanical calculations for conformation energy are not accurate (as seen through JMol's errors), how can we find the true energy? Molecular mechanics can calculate the energies of different conformations by treating the molecule as a mechanical entity. It uses Hooke's law to describe bonds as springs and calculate the "strain energy" associated with different molecular shapes. This manner of calculation can also be much easier than complicated quantum mechanical equations.
This frame shows a graph of the energy of ethane as a function of the torsional angle between the two carbons, from 0 to 360 degrees. Newman projections of the ethane molecule corresponding to the angles measured are shown at the bottom. This graph shows that the staggered conformations at 60°, 180°, and 300° give identical energy minima at 0 kcal/mol. This makes sense, since all of the hydrogens are identical, and placing them as far apart from each other as possible minimizes repulsion. The maximum energy, which occurs at the eclipsed conformations (0°, 120°, 240°), is 3 kcal/mol. Thus, would take the same amount of energy to get over each barrier to the well next to it.
This frame has a graph of the energy of butane as a function of the torsional angle between the central carbons, from 0 to 360 degrees. Newman projections are again shown at bottom. Here, the graph demonstrates that the gauche formations, with 60 degrees between the two CH3 groups, provide local minima of energy at 0.9 kcal/mol because they separate the two methyl groups without overlapping them with any hydrogens. The global minimum occurs in the anti conformation, where the CH3 groups are as far from each other as possible. Meanwhile, the conformations with a 120 degree angle between CH3 groups occupy local maximums at 3.4 kcal/mol, and the global maximum occurs when these groups have no angular separation, at 4.4 kcal/mol. This difference goes along with the prediction that a methyl and a hydrogen, being smaller, would repel each other less than would two methyls. Because of the difference in the energy of the wells at 60 and 300 compared to the well at 180, it is easier to move from them to the middle, lower energy well (it would happen at a faster rate, too). As seen in Slide 11 (Mol4D_-_Butane), one would be unable to measure the rate of going over the barrier at 0 or 360 because it is easier to go in the opposite direction.
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