Molecular models are useful for examining steric interactions but do not give quantitative information about steric energy. A more complete approach to understanding spatial relationships and stereochemistry is to combine molecular models with computer based molecular mechanics calculations.
The total steric energy for the optimized geometry of a molecule is perhaps the most widely used piece of information obtained from a molecular mechanics calculation. The absolute value for the steric energy varies from program to program and is of little or no use; however, the relative size of individual interactions (compression, bending, stretch-bend, torsional) that compose the total steric energy can be helpful in identifying specific sites and types of strain. In general, however, it is most informative to compare steric energies and establish the relative stabilities of structural isomers, stereoisomers, and rotomers in staggered conformations.
The molecular mechanics force field is a computational model for describing the potential energy surface for all the possible movements of atoms within a molecule. In some respects, it is similar to the familiar hand-held molecular models, but it is much more sophisticated. Force fields have been parameterized, or fit, to give excellent geometries, relative conformational energies, heats of formation, crystal packing arrangements, and even transition state structures and reactivities.
The major distinction between the molecular mechanics method used in this experiment and quantum mechanics is that molecular mechanics does not consider the electrons in the molecule explicitly. Molecular mechanics treats the atoms and their associated electrons as units interconnected by the potential functions that we have described. On the other hand, quantum mechanics is very much concerned with the three dimensional distribution of electrons around the nuclei. With molecular mechanics, steric hindrance, conformation, bond angle deformation, etc., can be addressed in a quantitative manner. This approach supplants many of the hand-waving arguments based upon hand-held models that one typically finds in the classroom.
Because small changes in structure can lead to large changes in total energy, calculations to determine optimum geometry are iterative. The energy and its first derivative with respect to all geometrical coordinates are calculated for the starting geometry, and this information is then used to project a new geometry. The process needs to continue until the optimized geometry (with the lowest energy) is reached. Geometry optimization does not guarantee that the final structure has a lower energy than any other structure of the same molecular formula. All that it guarantees is a local minimum, that is, a geometry with an energy lower than that of any similar geometry.
Your task in this exercise is to determine the relative concentrations of the two chair conformers of cis-1-bromo-2-methylcyclohexane and one other disubstituted cyclohexane of your choosing.
Part One
Start Spartan. Open a new file in order to begin building your molecule. Choose cyclohexane from the rings drop-down menu. Add the substituents by using the buttons on the panel at the right. When you are finished building the molecule, click on the "V" button at the top of the screen. This step will move you into the part of the program where you can carry out calculations.
Under the "Setup" menu, choose Calculations. Use the menu boxes to do an equilibrium geometry calculation using a molecular mechanics calculation with the MMFF force field option. When you submit the calculation, you'll be asked to save the file. You should save it to your network space or a thumb drive. The calculation will not take much time. When it finishes, you should look at the results by choosing Output (under the "Display" menu). Record the energy from the final cycle shown. The numerical value is reported without units. The units are kcal/mol.
Repeat the building and calculation process, changing the substituents so that those which were axial become equatorial and vice versa.
Part Two
Repeat the entire process, using a 1,3 or 1,4 disubstituted cyclohexane of your choice.
Determine ΔG for the "reaction" of flipping between the two chair conformers of cis-1-bromo-2-methylcyclohexane that you built. Determine the equilibrium constant K using equation 1. Assume that T is room temperature, 25 oC or 298 K.
ΔG = -RT ln K (1)
R = 8.315 J/mol K = 34.76 cal/mol K
Finally, determine the percent composition of the sample from the equilibrium constant you found. Be aware that the Spartan results are reported in kcal. You will need to pay attention to units, converting between kcal and Joules.
Repeat these steps for the second disubstituted compound that you chose.