Assignment 2: Conformation Searching (50 points)

Transcription

1 Chemistry Fall 2015 Dr. Jean M. Standard September 16, 2015 Assignment 2: Conformation Searching (50 points) In this assignment, you will use the Spartan software package to investigate some conformation searching techniques. The objective of conformation searching is to locate the global minimum and low-energy local minima on a molecular potential energy surface. While you will use molecular mechanics force fields to determine the energies of molecules in this study, conformation searching techniques can be employed with any methods that determine molecular energies, including quantum mechanics. THIS ASSIGNMENT IS DUE WEDNESDAY, SEPTEMBER 30, INSTRUCTIONS FOR RUNNING THE SPARTAN SOFTWARE PACKAGE Starting X11 In order to access the Linux workstations to run the Spartan software packages, you must run a software package on the Mac called X11. To start the X11 application, click on the "X" icon in the Dock on the Mac desktop. A single white window should appear on the screen; this is called an "xterm" window, or simply a terminal window. Logging on to the Linux Computers To log on to the Linux computer to which you have been assigned, type the following command in the xterm window: ssh Y compchem@hostname.che.ilstu.edu Here, "ssh" stands for secure shell; this application provides a secure connection to the remote Linux workstation. Also, hostname is the name of the Linux computer to which you have been assigned. The password is "modeling". Enter the password as prompted. Once you have done this, you are connected to the Linux computer. Starting the Spartan Program To start the Spartan program, type "spartan" in the xterm window and hit the return key. A window for the Spartan software package should appear on your screen.

2 2 PART A (12 points) Conformations of n-butanol One of the most important methods for finding the stable conformations of a relatively small molecule is the systematic search. In class, we discussed examples of systematic searching for n-alkanes such as n-pentane. In this part of the assignment, you will carry out a systematic search of a straight chain alcohol, n-butanol. Procedure 1. You will first need to build an initial structure for n-butanol. From the "File" menu, select "New". Construct the n-butanol molecule, save it, and return to the main work area. 2. Next, you will obtain an equilibrium geometry and energy for one of the stable conformations of n-butanol. Select "Calculations" from the "Setup" menu. The task is equilibrium geometry, the model is Molecular Mechanics, and the Force Field is MMFF. Then, click "Save". Next, under the "Setup" menu, select "Submit". Your calculation should complete in a few seconds. Report the energy of the equilibrium structure (in kcal/mol). You can obtain the (gas phase) energy by selecting "Display" "Properties". 3. Measure andreport the equilibrium torsional angles for the stable conformation of n-butanol that you built. To do this, select "Measure" "Dihedral", and click on four atoms in order to select them. Make sure to measure all the significant torsional angles, which include the C1-C2-C3-C4, C2-C3-C4-O, and C3-C4-O-H angles, as shown in the sketch below. C 1 C 2 C 3 C 4 O skeleton of n-butanol H 4. Next, you will carry out a systematic conformation search to find low energy stable conformers of n-butanol by varying the C1-C2-C3-C4, C2-C3-C4-O and C3-C4-O-H dihedral angles. To do this, select "Build Alter Conformation" from the main Spartan window. Click "Systematic" on the panel that opens to choose the systematic conformer search. Then, select the C1-C2-C3-C4 dihedral angle by clicking on the C2-C3 bond. Set the "Fold Rotation" in the box to the right to 6 (this increments the dihedral angle by 360º/6 = 60º). Next, select the C2-C3-C4-O dihedral angle by clicking on the C3-C4 bond and set the "Fold Rotation" to 6. Finally, select the C3-C4-O-H dihedral angle by clicking on the C4-O bond and set the "Fold Rotation" to 6. This will lead to 6 6 6=216 initial structures that will be optimized in the search. Exit the conformer search by selecting "File Return to Main" from the conformer search window. To set up the calculation, select "Setup Calculations". The task is "Conformer Distribution", the model is "Molecular Mechanics", and the force field is MMFF. Then, click on "Save" and to run the calculation, select "Setup Submit" from the top of the main Spartan window. The calculation takes a few minutes. When the calculations are complete, select "Display Spreadsheet". List the values of the C1-C2-C3-C4, C2- C3-C4-O, and C3-C4-O-H dihedral angles in the spreadsheet by selecting "Geometry Measure Dihedral" from the main menu. Click on the C1-C2-C3-C4 atoms, and then click on the post button. Repeat for the C2- C3-C4-O atoms, and then click on the post button. Finally, repeat for the C3-C4-O-H atoms, and then click on the post button. Once the measure dihedral window is closed, all the dihedral angles will be posted to the spreadsheet.

3 3 To add the conformer energies to the spreadsheet, select "Column Add Rel E gas in kcal/mol" from the spreadsheet window. The relative molecular mechanics energies should be listed in the spreadsheet. Note that these are the energies of optimized structures; thus, they correspond directly to the low energy conformations of n-butanol. There may be duplicates in the list. You can sort these conformers with respect to energy by selecting "Column Sort" with the title of the energy column highlighted. 5. Next, you can export the spreadsheet data from Spartan to a form suitable for importing into Microsoft Excel. To export the spreadsheet data to a file, select "Sheet Export" from the spreadsheet menu. You can then retrieve the data file from the Linux workstation using FTP (file transfer protocol). To do this, quit Spartan and sign out of the Linux computer by typing the "exit" command (don't close the X11 program, though). In the X11 terminal window, type the command: ftp computer.che.ilstu.edu Here "computer" is the name of the Linux workstation that you are using (obi-wan, beckert, etc.). You will then be prompted to enter the username (compchem) and password (modeling). To retrieve the spreadsheet file, type the command: get filename Here, "filename" refers to the name of the spreadsheet data file that you exported from the Spartan program. Finally, exit the FTP program by typing the "quit" command. You can then get the file off the Mac using either a USB flash drive or by ing the file to yourself. Results and Discussion Provide a list in tabular form of the relative energies of all the unique conformations within 2 kcal/mol of the global minimum that you found for n-butanol, along with the values of the C1-C2-C3-C4, C2-C3-C4-O, and C3-C4-O-H dihedral angles for each. Order your table from lowest to highest energy. How many total unique conformers did you find that have relative energies between 0 and 1 kcal/mol? How many total are between 0 and 2 kcal/mol? Considering the total number of conformers between 0 and 1 kcal/mol, what percentage of the total has the fourcarbon backbone oriented in the anti form? What percentage of the total between 0 and 2 kcal/mol has the fourcarbon backbone oriented in the anti form?

4 4 PART B (19 points) Conformations of alanine dipeptide Even though we discussed in class that a systematic search might not be the most efficient method of finding all the conformations of a large biomolecule, this method may be utilized for small biomolecular systems for which computational cost is not a factor. In this part of the assignment, you will carry out a detailed systematic search to find stable low-energy conformations of the biomolecule alanine dipeptide, shown in the figure below. O H CH 3 H C1 C3 N5 H 3 C N2 C4 CH 3 H alanine dipeptide O Procedure 1. Using the Spartan software package, build the alanine dipeptide molecule. Pay particular attention to the stereochemistry of the groups attached to C3 when building this molecule (the CH 3 group is coming out of the paper towards you in the figure above). Also, note that the structure of alanine dipeptide is planar at the two nitrogens because of resonance, so when using the builder to insert the two nitrogens, make sure to use the planar nitrogen in the builder, N. You might also need to rotate around particular bonds to build the correct structure using the space bar/middle mouse button. Optimize the geometry of the initial structure of alanine dipeptide using the MMFF force field. Record the energy and the values of the C1-N2-C3-C4 and N2-C3-C4-N5 dihedral angles shown in the figure. 2. Next, you will carry out a systematic conformation search to find low energy stable conformers of alanine dipeptide by varying the C1-N2-C3-C4 and N2-C3-C4-N5 dihedral angles. To do this, select "Build Alter Conformation " from the main Spartan window. Click "Systematic" on the panel that opens to choose the systematic conformer search. Then, select the C1-N2-C3-C4 dihedral angle by clicking on the N2-C3 bond. Set the "Fold Rotation" in the box to the right to 18 (this increments the dihedral angle by 360º/18 = 20º). Note that to make sure that all the low-energy conformers are found, we are using a very fine grid in dihedral angles for this search. Next, select the N2-C3-C4-N5 dihedral angle by clicking on the C3-C4 bond and set the "Fold Rotation" to 18. This will lead to 18 18=324 initial structures that will be optimized in the search. Exit the conformer search by selecting "File Return to Main" from the conformer search window. To set up the calculation, select "Setup Calculations". The task is "Conformer Distribution" and the force field is MMFF. Then, click on "Save" and to run the calculation, select "Setup Submit" from the top of the main Spartan window. The calculation takes a few minutes. When the calculations are complete, select "Display Spreadsheet". List the values of the C1-N2-C3-C4 and N2-C3-C4-N5 dihedral angles in the spreadsheet by selecting "Geometry Measure Dihedral" from the main menu. Click on the C1-N2-C3-C4 atoms, and then click on the post button. Repeat for the N2-C3-C4-N5 atoms, and then click on the post button. Once the measure dihedral window is closed, all the dihedral angles will be posted to the spreadsheet.

5 5 To add the conformer energies to the spreadsheet, select "Column Add Rel E gas in kcal/mol" from the spreadsheet window. The relative molecular mechanics energies should be listed in the spreadsheet. Note that these are the energies of optimized structures; thus, they correspond directly to the low energy conformations of alanine dipeptide. There may be duplicates in the list. You can sort these conformers with respect to energy by selecting "Column Sort" with the title of the energy column highlighted. 3. Next, you can export the spreadsheet data from Spartan to a form suitable for importing into Microsoft Excel. To export the spreadsheet data to a file, select "Sheet Export" from the spreadsheet menu. You can then retrieve the data file from the Linux workstation using FTP (file transfer protocol) in the same way as described in Part A of this Assignment. Results and Discussion List in tabular form the relative energies of all the distinct conformations that you found for alanine dipeptide along with the values of their C1-N2-C3-C4 and N2-C3-C4-N5 dihedral angles. Order your table from lowest to highest energy. Note or label in some way the conformation corresponding to the initial structure that you created and optimized in step 1 of the Procedure. How many conformers did you find that have relative energies between 0 and 2 kcal/mol? How many total have relative energies between 0 and 5 kcal/mol? Are there any above 5 kcal/mol? Using Boltzmann factors, calculate and list the fractional populations at 300 K of all of your distinct alanine dipeptide conformers. Do you believe that you found all the stable conformers of alanine dipeptide? Explain. Do you expect that the lowest energy conformer you found corresponds to the global minimum? Explain. Compare your conformer search and energies to a literature study of alanine dipeptide that employed quantum mechanical calculations [R. Vargas, J. Garza, B. P. Hay, and D. A. Dixon, J. Phys. Chem. A 2002, 106, ]. Be as specific as possible in your comparisons with the literature study. For example, you might want to include information about the relative energies and numbers of conformers obtained. In addition, you might want to compare the dihedral angles of the various conformers you found to those obtained in the literature study and discuss whether the relative energy ordering of the conformers is the same. [When comparing with the literature study, it is best to focus on the results labeled MP2 or MP2/aug-cc-pVDZ from that work. That corresponds to a high-level quantum mechanical method which is generally very reliable.] It is found that in proteins the C1-N2-C3-C4 and N2-C3-C4-N5 dihedral angles (referred to as Φ and Ψ, respectively) often take only a narrow range of values. A plot with the C1-N2-C3-C4 dihedral angle (Φ) on the x- axis and the N2-C3-C4-N5 dihedral angle (Ψ) on the y-axis is called a Ramachandran plot. Using the data for each of the distinct conformers that you found, make a Ramachandran plot for alanine dipeptide. Note that yours will not look as "nice" as the one in the handout from class because there are many fewer data points. How many of the conformers that you found fall within the two major basins of Φ and Ψ values (see the handout from class). Do any fall within the minor basin? Of the ones that do not fall into the major or minor basins (if any), how many are highenergy conformers?

6 6 PART C (19 points) Conformations of n-hexane In this part of the assignment, you will use another method of conformation searching, the Monte Carlo method. This is one of the methods of choice for larger molecules when systematic searching becomes computationally intractable. You will use this method to locate low energy conformations of n-hexane, with its carbon backbone shown below. Even though this is a relatively small molecule, rotations about three bonds, C2-C3, C3-C4, and C4- C5, lead to significant changes in the carbon skeleton and therefore many different stable conformers. While a systematic search is still possible, an 18-fold rotation will lead to =5832 different initial structures to be optimized. C 1 C 2 C 3 C 4 C 5 C 6 carbon skeleton of n-hexane Procedure 1. Using the Spartan software package, build the n-hexane molecule. Optimize the geometry of the initial structure of n-hexane using the MMFF force field. Record the energy and the values of the C1-C2-C3-C4, C2- C3-C4-C5, and C3-C4-C5-C6 dihedral angles shown in the figure. 2. To set up the Monte Carlo search, select "Build Alter Conformation" from the main Spartan window. Click "Monte Carlo" on the panel that opens to choose the Monte Carlo conformer search. Then, click on the C2-C3, C3-C4, and C4-C5 bonds one at a time to indicate that those bonds will be varied randomly in the Monte Carlo search. Set the "Fold Rotation" in the box to the right to 18 for each dihedral angle (this increments the dihedral angles randomly by 360º/18 = 20º units). Exit the conformer search by selecting "File Return to Main" from the conformer search window. Now, to set up the calculation, select "Setup Calculations". The task is "Conformer Distribution" and the force field is MMFF. Click "Save" and select "Setup Submit" from the top of the main Spartan window to run the calculation. It takes a few minutes for the calculations to complete. When the calculations are complete, select "Display Spreadsheet". List the values of the C1-C2-C3-C4, C2-C3-C4-C5, and C3-C4-C5-C6 dihedral angles in the spreadsheet by selecting "Geometry Measure Dihedral" from the main menu. Click on the post button for each dihedral angle to post these values to the spreadsheet. In addition, measure the end-to-end distance from C1 to C6 by selecting "Geometry Measure Distance" and clicking on C1 and C6. Click the post button again to include this data in the spreadsheet. Finally, to include the relative energies of each conformation in the spreadsheet, select "Column Add Rel E gas in kcal/mol" from the spreadsheet menu. Sort the conformers according to energy. 3. Next, you can export the spreadsheet data from Spartan to a form suitable for importing into Microsoft Excel. To export the spreadsheet data to a file, select "Sheet Export" from the spreadsheet menu. You can then retrieve the data file from the Linux workstation using FTP (file transfer protocol) in the same way as described in Part A of this Assignment.

7 7 Results and Discussion Include a table of results, listing each distinct conformer, the relative energy, dihedral angles, and C1-C6 distance. Order your table from lowest to highest energy. How many stable conformers of n-hexane are there from your analysis? Do not count duplicate conformers that have the same (or very nearly the same) energies and dihedral angles. Do your results agree with the finding in the figure shown below? Discuss possible reasons why if not. Stable conformations of n-hexane [from Chemical Applications of Molecular Modelling, J. M. Goodman, Royal Society of Chemistry, Cambridge, 1998]. What are the three C-C-C-C dihedral angles of the lowest energy conformer? Does this agree with the figure above and your chemical intuition? Note that the conformers are listed in order of increasing energy from upper left to lower right in the figure, and from left to right across each row. Explain the physical reasons why this conformer is expected to be the lowest in energy. What are the three C-C-C-C dihedral angles of the highest energy conformer that you found? Does this agree with the figure above? Explain the physical reasons why this conformer would be expected to be the highest in energy. Compare and contrast this conformer to the one that you obtained for the global minimum. Is there a correlation between energy of the conformers and end-to-end distance from C1 to C6? Make a plot using Microsoft Excel or some other graphing package with the end-to-end distance on the x-axis and the energy of the conformer on the y-axis. Discuss your findings. Do you think that they will hold for longer alkanes? What about for long alkanes in a polar solvent? Compare the relative energies you obtained for the conformations of n-hexane to the results presented in a literature study that employed high-level quantum mechanical methods [S. Tsuzuki, L. Schafer, H. Goto, E. D. Jemmis, H. Hosoya, K. Siam, K. Tanabe, and E. Osawa, J. Am. Chem. Soc. 1991, 113, ]. In particular, you should make quantitative comparisons between your results and those at the MP4SDQ level presented in Table II of the literature study. Finally, demonstrate the overall correlation between your results and those in the literature study by making a plot in which the relative energy of each conformer in your study is plotted on the x-axis and the relative energy of each conformer from the literature study is plotted on the y-axis. Include a trendline on your graph. The closer this graph is to linearity with a slope =1, the better the agreement between the two studies. Discuss your findings with regard to the correlation.

8 8 APPENDIX: Capturing images from Spartan If you would like to capture images of structures for use in your assignment, the easiest way to do it is to take a screenshot on the Mac. Here are the steps to save images if you desire. 1. Log on to the Linux workstation using the X11 application, and start Spartan. 2. If the background of the Spartan window is not white in color, it is best to change it to white. To do this, from the Spartan logo menu at the top of the screen,, select "Colors". Then click on the button to select white as the background color. Close the color selection window. 3. Open the molecule of which you wish to capture an image. Orient the molecule in the desired fashion using the mouse. 4. Next, use the keystroke combination COMMAND-SHIFT-4. At this point, you should see a crosshair appear in place of the usual cursor. Drag the crosshair to make a box around the region you wish to capture on the screen. The captured selection is saved to the desktop as a screenshot in PNG image format. 5. Additional screen captures of other structures may be performed by repeating steps 2-4. Each image captured will be saved with a different name. You may then copy these files from the desktop onto a flash drive for later use. Example An example image captured from the n-butanol conformer search in Part A is shown below.