Chemistry 380.37 Fall 2015 Dr. Jean M. Standard August 19, 2015 Assignment 1: Molecular Mechanics (PART 1 25 points) In this assignment, you will perform some molecular mechanics calculations using the Avogadro software package. One of the objectives of this assignment is to explore the ability of molecular mechanics force fields to adequately represent the energies of molecules as their geometries are varied. Another objective is to learn how to extract information about force field parameters from calculations. In addition, the use of Avogadro to build simple organic molecules and perform equilibrium geometry and energy calculations will be illustrated. THIS PORTION OF ASSIGNMENT 1 IS DUE WEDNESDAY, AUGUST 26, 2015. Using the Avogadro Software Package The computer program that you will use for these molecular mechanics simulations is a software package called called Avogadro. You will be able to access Avogadro on the Macintosh computers located in Julian Hall Room 216. Alternately, since Avogadro is freely available and includes the molecular mechanics routines as a built-in feature, you may choose to download Avogadro to your personal computer. The software package is available for Windows, Macintosh, and Linux platforms. Please see Appendix 1 for details on downloading the software package. To use Avogadro on the Macs in JH 216, log in using your ULID and password. The Avogadro software package may be started by clicking on its icon in the Dock. PART A (7 points) Conformations of 2,3-dimethylbutane How many stable conformers are there of 2,3-dimethylbutane? Draw sketches (by hand) of each of the stable conformers Newman projections probably would be best. Which of the conformers do you expect to have the lowest energy? Why? Provide some physical explanation as to your predicted energy ordering. Next, build all the predicted stable conformers of 2,3-dimethylbutane using the Avogadro package (see Appendix 2 for a tutorial on building organic molecules). Determine the equilibrium geometries of each of the conformers using the MMFF94 Molecular Mechanics force field (see Appendix 3 for instructions on performing molecular mechanics calculations). Record the total energy of each one in kcal/mol. Discuss whether or not the results agree with your qualitative predictions. PART B (7 points) - Equilibrium Geometry of Biphenyl and Substituted Biphenyl What is the equilibrium torsional angle of biphenyl? To find out, first build the biphenyl molecule using Avogadro. biphenyl
2 The torsional angle in question is for rotation about the central C-C bond. In order to build biphenyl, it is helpful to start with pre-built benzene rings available in the Avogadro library. To locate the fragment library, select "Build Insert Fragment". Open the aromatics folder, select benzene, and then click "Insert Fragment". At this point a benzene molecule should appear in the display window highlighted in blue. Use the mouse buttons to translate and rotate the molecule into a suitable position to form biphenyl; then insert a second benzene fragment and orient it appropriately. The last step is to use the Drawing Tool to connect the two benzene rings to form biphenyl. To do this, select the Drawing Tool, make sure that the element selected is Carbon, and make sure to click ON the button to "Adjust Hydrogens". Then use the mouse to draw a bond from one benzene ring to the other as shown above in the sketch of biphenyl. Once you have built the biphenyl molecule, perform a calculation to determine its equilibrium geometry using the MMFF94 force field. Measure the torsional (dihedral) angle (use the Measure Tool, ; see Appendix 4 for additional information on measurement). With the torsional angle displayed, repeat the selection of "Extensions Optimize Geometry" until the torsional angle stops varying this is the final result. Report the calculated value of the torsional angle of biphenyl. Does the result of your molecular mechanics calculation agree with the experimental result of 45 degrees? If four methyl groups are placed in the ortho positions on each of the phenyl rings, how do you expect the equilibrium torsional angle to be affected? Explain, and then verify with a calculation: build the tetramethyl substituted compound and perform a calculation of its equilibrium geometry using Avogadro and the MMFF94 force field (check for convergence in the same way you did for biphenyl). Report the equilibrium torsional angle and compare with your expectations. PART C (11 points) - Determination of Force Field Parameters In this part of the assignment, you will vary the bond length and bond angle of a simple molecule and use the energies to extract the force constants for bond stretching and angle bending for the MMFF94 force field. Determination of Stretching Force Constant 1. Build and determine the equilibrium geometry of the water molecule using the MMFF94 force field. Measure and record the total energy in kcal/mol and the equilibrium bond length in Å. 2. The next step is to vary the O-H bond distance for one of the bonds from 0.85 to 1.15 Å in 7 steps (0.05 Å increments). To do this, follow the instructions in Appendix 4 to use the Bond Manipulation tool,, to adjust the bond length of one of the O-H bonds to each of the suggested values (the other O-H bond distance and bond angle should not be changed). Then, compute single point energies for each bond length and record these values in kj/mol (see Appendix 3 for instructions on computing single point energies); these energies must be converted into kcal/mol in step 3. 3. Make two graphs of your results using Microsoft Excel or another spreadsheet package. The first graph should include the energy on the y-axis in kcal/mol and the bond displacement on the x-axis. The bond displacement is defined as the difference between the bond length and its equilibrium value; the bond displacement is negative when the bond is compressed and positive when the bond is stretched. To determine the stretching force constant for the O-H bond, a second graph should be created with the energy in kcal/mol again placed on the y-axis, but this time the square of the bond displacement is placed on the x-axis. The slope of the line is related to the O-H stretching force constant (refer to class notes for an equation). Calculate the stretching force constant and report its value in units of kcal mol 1 Å 2. Include a table of your data and both graphs when you turn in your assignment.
3 4. Using the relationship between the harmonic frequency ν o and the force constant k, ν o = 1/ 2 1 $ k ' & ), 2π % µ ( determine the harmonic frequency in s 1 corresponding to the stretching force constant that you calculated in step 3. The quantity µ is referred to as the reduced mass and is defined in terms of the masses of the atoms in the bond. For an A-B bond, the reduced mass is µ = m A m B m A + m B. Note that the masses in this equation refer to the mass of a single atom of A or B, not the molar mass. Finally, convert the result to units of cm 1 and discuss whether or not this value is what you would expect for the typical IR stretching frequency of an O-H group. Determination of Bending Force Constant 1. Starting from scratch, build and determine the equilibrium geometry of a new copy of the water molecule using the MMFF94 force field. Measure and record the total energy in kcal/mol and the equilibrium bond angle in degrees. 2. The next step is to vary the H-O-H bond angle from 90 to 120 degrees in 7 steps (5 degree increments). To do this, follow the instructions in Appendix 4 to use the Bond Manipulation tool,, to adjust the bond angle to each of the suggested values (the O-H bond distances should not be changed). Compute single point energies for each bond angle and record these values in kj/mol (see Appendix 3 for instructions on computing single point energies). 3. Follow a similar procedure to that described above for the stretching force constant to make graphs of your results and calculate the H-O-H bending force constant. Report the value that you obtained for the bending force constant in kcal mol 1 deg 2 and include a table of your data and the two graphs when you turn in your assignment.
4 Appendix 1: Downloading the Avogadro Software Package to a Personal Computer The Avogadro software package is freely available for the Mac, Linux, and Windows platforms. If you would like to download Avogadro for personal use, go to this web site: http://avogadro.cc/wiki/main_page. Click on the link that says "Get Avogadro". The site should automatically detect your operating system and provide the appropriate version of Avogadro, so make sure to download it from a computer using the same operating system on which you wish to install the package. Appendix 2: Building Simple Organic Molecules with Avogadro To demonstrate how to build simple organic molecules, n-butane will be used as an example. When you start the Avogadro software package, you should see a window similar to the one shown in Figure A1 on your screen. Figure A1. The main Avogadro window. The Avogadro window that you see may have a black background. If you would like to change the background color, you may do so by selecting "View Set Background Color. " In addition, if the "Settings" area on the left side of the window does not appear, you may toggle it on by clicking on the "Tool Settings" button. To construct an initial structure for the n-butane molecule, click on the Drawing Tool,. Set the Element to Carbon, Bond Order to Single, and make sure that "Adjust Hydrogens" is NOT selected. Then, click with the left mouse button in the Avogadro window and a single carbon atom should be displayed. Next, click three additional times in the window to place three more carbon atoms in an arrangement that resembles the carbon backbone of the anti form of n-butane, as illustrated in Figure A2. NOTE: if you make a mistake during the building process, you can erase it by using keyboard sequence Cmd-Z on Macintosh (or Ctrl-Z on Windows).
5 Figure A2. Constructing the carbon backbone of the n-butane molecule. The next step is to create the carbon-carbon bonds. Using the Drawing Tool, connect the carbon atoms by drawing line segments to connect them, as shown in Figure A3. Figure A3. Creating the carbon-carbon bonds for the n-butane molecule. The final step in creating an initial structure of the n-butane molecule is to add the hydrogen atoms. To do this, select "Build Add Hydrogens" from the menu at the top of the screen. Your final creation should appear similar to that shown in Figure A4.
6 Figure A4. The completed initial structure of the n-butane molecule. Appendix 3: Performing Molecular Mechanics Calculations with Avogadro In order to perform a molecular mechanics calculation, a force field must be selected. Avogadro has a number of force fields available, including MMFF94 (a force field primarily useful for organic and biological molecules) and UFF (a multi-purpose force field that spans the periodic table). To designate the force field to be used, select "Extensions Molecular Mechanics Setup Force Field" from the menu at the top of the screen. The force field may then be selected from the pull-down menu in the window that pops up. For organic molecules, select MMFF94 as the force field to be used. There are two basic types of molecular mechanics calculations that may be performed using Avogadro: single point energy calculations and geometry optimization calculations. A single point energy calculation determines the energy of the current geometry of the molecule as specified in the current display window. No adjustments in bond lengths, bond angles, or other geometrical parameters are made. To perform a single point energy calculation, select "Extensions Molecular Mechanics Calculate Energy" from the menu at the top of the screen. The energy of the molecule will be displayed in kj/mol. To redisplay the current energy, you may also click on the "Messages" tab at the bottom of the screen; the Total Energy listed there is the same as was displayed by the Calculate Energy command, except the result is listed in kcal/mol instead of kj/mol. A geometry optimization calculation begins by determining the energy of the current geometry of the molecule. Then the calculation continues by varying the geometrical parameters and recalculating the energy until a minimum in the energy is achieved. The geometry at the minimum energy is said to be the optimized geometry or a stable structure. To perform a geometry optimization calculation, select "Extensions Optimize Geometry" from the menu at the top of the screen. The energy of the optimized structure may be viewed by clicking on the "Messages" tab at the bottom of the screen; the final energy shown is in kcal/mol. You should always make sure that the geometry optimization is complete by repeating the calculation and making sure that the final energy is converged to 0.01 kcal/mol.
7 Appendix 4: Measuring and Adjusting Geometrical Parameters with Avogadro It is sometimes useful to be able to measure and also change the bond lengths, bond angles, and torsional angles of a molecular structure using Avogadro. MEASURING GEOMETRICAL PARAMETERS To measure geometrical parameters, use the Measure Tool,. Clicking with the left mouse button on two atoms will display the distance between them. Clicking on three atoms in sequence will display distances 1-2 and 2-3 along with angle 1-2-3. Finally, clicking on four atoms in sequence will display the associated distances and angles as well as the dihedral (or torsional) angle 1-2-3-4. ADJUSTING GEOMETRICAL PARAMETERS To make adjustments to geometrical parameters, use the Bond Manipulation tool,. To adjust a bond length, left click on the bond to select it (a plane will be displayed that contains the bond). Then, right click on one of the atoms and drag the mouse to change the bond length (the value is displayed at the bottom of the screen). To adjust a bond angle, left click on one of the bonds that comprises the bond angle to select it and move the mouse so that the plane that appears is rotated into the plane of the display. This is illustrated in Figure A5 for the water molecule. Then, left click and drag the mouse to change the bond angle. Figure A5. Preparing to adjust the bond angle using the Bond Manipulation tool.