MOLECULAR MODELLING EXERCISES CHAPTER 17 Exercise 17.6 Conformational analysis of n-butane Introduction Figure 1 Butane Me Me In this exercise, we will consider the possible stable conformations of butane (Fig. 1) in part A. In part B, we will create a plot of steric energy versus bond rotation around the central C-C bond (see Introduction to Medicinal Chemistry, section 17.8.3) The Tasks Part A Construct the anti-conformation of butane and energy minimise the structure. Identify the stable conformations for butane and calculate their steric energies using molecular mechanics. Prepare a spreadsheet which includes steric energy, the torsion angles for the four carbon atoms, the relative energy and the Boltzmann distribution. Identify the proportion of molecules in each of the conformations. Part B Build another molecule of butane in a new file. Create 36 conformers resulting from 10 o rotations around the central C-C bond. Calculate the energies of these conformations using molecular mechanics. Open a spreadsheet and add the torsion angle, energy, relative energy and Boltzmann distribution as above. Identify the percentage of molecules in the most stable conformations. Plot the data showing dihedral angle on the X-axis and relative Energy on the y-axis. Identify the conformations corresponding to energy peaks and energy troughs. A detailed set of procedures is given below, but you may wish to tackle the exercise yourself before following them.
PROCEDURES The following procedures are written for the Apple Mac version of Spartan 10 (version 1.0.1). Mouse operations will vary for Windows users. Modifications of the procedures may also be required for other versions of Spartan. You are advised to familiarize yourself with basic Spartan procedures described in the file Spartan Introduction before attempting any of the exercises. Part A 1. Construct the anti-conformation of butane (Figs. 1 & 2) and energy minimise the structure by clicking the icon. Figure 2 The anti-conformation of butane 2. Choose Set Torsions from the Geometry Menu. You will see a yellow collar appear on the central bond (Fig. 3). On the bottom right hand of the window, you will see the number of conformations that have been generated by the default rotation of this bond (Conformers = 3). Figure 3 Yellow collar showing the rotatable bond used to generate different conformations. 3. Click on the following symbols at the bottom right of the window to view the three different conformations. 4. Now click on the downward facing arrow to the right of the above symbols. You will be asked if you wish to Generate a List? Click on OK. The three conformations are now on three windows within the same file. You can view each of them by clicking on the following symbols which are now on the bottom left hand side of the window. 5. We will now calculate the steric energies of these conformations. Choose Calculations from the Set Up menu to provide you with a Calculations dialogue window. From the drop down menus at the top, select Energy at the Ground state with Molecular Mechanics using MMFF. Butane is uncharged, so the Total Charge should be left as Neutral and the Multiplicity left as Singlet. Click on Submit. A message will ask you what name you want to save the
file as and where you want to save it. Once you have completed that, click on Save. A message will now appear telling you that the job has started. After a few seconds a second message should appear telling you that the task has been completed. Click on the OK button. Although you only have one of the conformations visible on screen, the energies of all three conformations have been calculated. In order to view the results of these calculations, we now need to open up a spreadsheet for the file. 6. Choose Spreadsheet from the Display menu. The spreadsheet will indicate the three conformations as M0001, M0002 and M0003. You can rename these if you wish by double clicking on the label and typing in your own labels. Each label has a small box to the left. The box coloured blue indicates the conformation that is visible on the window. Click on each of the labels (not the boxes) to view each of the conformations in turn. 7. Click on the Add button at the bottom of the spreadsheet. Another dialogue window will be revealed with a list of properties. Click on E and click on OK. The steric energies for the three conformations will now appear on the spreadsheet. 8. We will now add the torsion angle (dihedral angle) for each conformation into the spreadsheet. Choose Measure Dihedral from the Geometry menu. Click on each of the carbon atoms. The torsion angle for the visible conformation will appear at the bottom right hand side of the window. Now click on the red P on the yellow background that is to the right of this. You will now find that the dihedral angles for all three conformations are entered onto the spreadsheet. 9. Click on the Add button on the Spreadsheet to re-open the list of properties. Click on rel.e, then click OK. The energy differences between the conformations are now displayed on the spreadsheet. You should find that the most stable conformation has a dihedral angle of 180 o (the anticonformation). The other two conformations (gauche conformations) have dihedral angles of +60 and -60 o, with identical steric energies. 10. Since the central C-C bond of butane is freely rotatable, the gauche and anti conformations are all present, but one would expect more molecules to be in the anticonformation than the gauche conformation since the former is more stable. One can calculate relative populations of these conformations by a Boltzmann distribution. Click on the Add button at the bottom of the spreadsheet to bring up the list of properties. Click on Boltzmann Distribution, then click on OK. The Boltzmann distribution will now be added to the spreadsheet indicating that 0.938 (93.8%) of the anti-conformation is preferred to the two gauche conformations in the ratio 93.8:6.2.
Part B Conformational Analysis of butane Build another molecule of butane in a new file and energy minimize the structure. Choose Set Torsions from the Geometry menu. At the bottom right you will see that three stable conformations are identified as before. It would be tempting to think that these are the only possible conformations for the molecule. To assess whether this is the case, we are going to generate a series of less stable conformations and calculate their steric energies. Click on the middle C-C bond with the yellow collar round it. At the bottom right, the number 3 will appear in the small window next to Fold. You can enter the number of conformations that you wish to enter. Enter 36 and either click in the main window or press the return key on your keypad. The central bond marked in yellow has now been rotated to generate 36 conformations. This has been done by systematically rotating the bond by 10 o intervals. Create a list of these conformations as described in Part A, section 4. Calculate the energies of these conformations as described in part A, section 5, and save the file as butane part B. Open the spreadsheet and add the torsion angle (select C-C-C-C), energy, relative energy and Boltzmann distribution as in part A. You should find that the most frequent conformation has a torsion angle for C-C-C-C of 180 o. However, there are significant populations of conformations with other dihedral angles. Indeed the Boltzmann distribution indicates that about a third of the molecules are in the most stable conformation at any one time. You can plot this data to get a more visual representation of the results. Choose Plots from the Display menu. This gives you a window where you can choose what properties should be chosen for the x- and y-axes of a plot. Select Dihedral angle for the X-axis and relative Energy for the y-axis. Click on Create Plot. A plot will now appear which plots the energy of each conformation with increasing dihedral angle. If the plot looks distorted, choose Properties from the Display menu. Click on the line of the plot and a window should come up allowing you to modify the plot. Choose Fourier LSQ from the Fit menu. Each data point on the plot corresponds to one of the generated conformations. If you click on a data point, the relevant conformation will appear. You can rotate this to study it. Click on the highest energy conformation. By rotating the conformation that comes up, you should identify that it corresponds to a fully eclipsed conformation (Fig. 4B). Click on the most stable conformation and this should correspond to a fully staggered conformation (Fig. 4A).
Figure 4 Plot of dihedral angle versus relative energy (A) Most stable conformation visible. B) Least stable conformation visible To conclude, butane can undergo free rotation around the central C-C bond. The most stable conformation is the fully staggered conformation, but it would be wrong to think that the vast majority of ethane molecules are in this conformation at any one time.