Computational Molecular Modeling Exercises

1. Use VSEPR to predict the electron geometry of the O-atom in anisole.  From that electron domain geometry, predict the molecular geometry (including C–O–C bond angle), hybridization of the O-atom, and the hybridization of each O-atom lone pair.  Remember that the idealized bond angles for an sp³-hybridized atom are 109.5 °, 120 ° for an sp² hybrid, and 180 ° for an sp hybrid. (2 pts)
2. Draw the important resonance structures of anisole by delocalizing one of the O-atom lone pairs over the aromatic ring.Use proper resonance arrows between your structures and include a resonance hybrid. (1 pt)

1. In the Coordinate Scan output, click on the film strip icon () in the Coordinate Scan table to view an animation of the C_ipso–O bond rotation explored in this exercise.  You should observe the -180 – 180 ° rotation of the C_ortho–C_ipso–O–C_methyl fragment described by the dihedral angle and the associated energy value in Hartrees displayed in the lower left corner of the molecule viewer.

2. Click the magnifying glass () at the top of the coordinate scan table to view a potential energy (Hartrees) plot of the -180 – 180 ° rotation of the methoxy substituent.

3. To view this graph in a more useful manner, export the coordinates and energies of the scan by clicking the floppy disk icon () in the same table.  This will export a comma separated values file (.csv), which can be opened using Excel or another spreadsheet program.  Convert the units from Hartrees/particle to kcal/mol using the conversion factor 1 Hartree/particle = 627.509 kcal/mol.  In cell C2, enter the formula, “=B2*627.509”.  Fill this formula down the column to convert all energy values.

4. Convert all of these B3LYP energy values to relative B3LYP energy values by following the steps below.  Find the lowest energy value in column C, which will be associated with the most stable conformer.  Note that these are negative values, so the value with the largest magnitude is the lowest value.  Note the cell containing the lowest value (referred to here as C#).  In cell D2, enter the formula, “=C2-$C$#”, using the appropriate row number in place of #.  Fill this formula to all cells in the column.  This is now a column of relative B3LYP energies, rather than B3LYP energies.  Relative energies are the energy value of a given structure compared to the structure with the lowest energy.  Thus, the lowest energy conformation will have a relative energy of 0.0, while other conformations will have positive energy values, allowing easy visual comparison of energies.

   1. To generate the plot of energies as a function of C–C–O–C dihedral angle, highlight the cells containing angles (A2 – A44) and the cells with the corresponding relative energies (D2 – D44).  Most systems will allow you to do this by highlighting the angles, then holding down the CTRL key, and selecting the relative energy cells.

   2. If using a recent version of Excel, go to the INSERT tab and click the symbol depicting a scatter plot.  From the dropdown menu, select “Scatter with Smooth Lines and Markers”. 
      
      If using Google Sheets, you may either press the Chart button () or go the Insert menu and select “Chart”.
      
      If using another spreadsheet program, the procedure will be similar, but you may need to find how to insert scatter plots.

5. Place the -180 – 180 ° plot in your laboratory notebook.  Label both axes, as well as each energy minimum and each energy maximum with the C–C–O–C dihedral angle and relative energy (kcal/mol).  Additionally, label each energy maximum with a double dagger (‡), indicating that it is a transition state.  It may be useful to draw or print yourself images clearly depicting the different conformations.  (1 pt)

6. The geometries of the minimum and maximum energy structures have been optimized and the resulting jobs (Opt + Vib Freq or TS Opt + Vib Freq) are provided for you on the website.  Click the image with the corresponding dihedral angle to view the optimized structure and related information.  Use these jobs to generate a table like the one below summarizing the key points of the coordinate scan following the directions listed in 6a – 6d.  Report all values to two decimal points.  (1 pt)

   C-C-O-C Angle (º)	negative vibrational frequency (cm-1)	RB3LYP Energy (Hartree/Particle)	RB3LYP Energy (kcal/mol)	Relative Energy (kcal/mol)

   1. For each conformation, provide the calculated energy in Hartrees/particle (labeled “RB3LYP Energy”), available in the Overview Table, as depicted below.
      

   2. Convertthis calculated energy to kcal/mol using the conversion factor, 1 Hartree/particle = 627.509 kcal/mol, as above.

   3. Onceall of the calculated energies are filled out, determine the relative energy by first determining the lowest kcal/mol energy value (remember that they are negative) and then subtracting it from each of the calculated energy (kcal/mol) values.

   4. Identify the lowest energy vibrational mode for each structure (the first one in the Vibrational Modes list).  A negative value indicates that this structure is a transition state.  Provide the negative frequency value (cm^-1) for each molecule that has one and describe the molecular motion in your laboratory notebook.  To view the motion, click on the animation icon ().
      

7. Examine the Natural Bond Orbitals (NBO) output for the lowest-energy conformation(s).  Using the Molecular Orbitals list, view each orbital by clicking on the associated magnifying glass symbol ( ).  Starting from the highest energy occupied molecular orbital (HOMO), work your way to lower energy molecular orbitals until you find π₁, the lowest energy π-symmetry orbital.  Place an image of this orbital in your lab notebook and describe which atoms participate in conjugation.  (1 pt)

8. To understand the stability of the low energy conformation, investigate the geometry and hybridization of the O-atom and its lone pairs.

   1. Review your answer to pre-lab question one concerning the VSEPR-based prediction of the electron geometry and molecular geometry of the O-atom in anisole.

   2. Use the NBO computational output to view the Natural Hybrid Orbitals description and image of each O-atom lone pair.  Find the O-atom lone pairs (LP(1)O2 and LP(2)O2) and the O-atom bonding pairs (BD(1)O2(C1) and BD(1)O2(C3)) in the Natural Hybrid Orbitals list.  Using page 7 as a reference, include an image of each lone pair and state the hybridization of each in your lab notebook using standard sp^x notation.  (1 pt)

   3. Click the selection tool (), then click sequentially on the atoms defining the C–O–C bond angle.  Provide the measured angle (given in blue at the bottom left corner of the molecule viewer window) in your laboratory notebook.

   4. Basedupon all of the information available, state the approximate hybridization of the O-atom in anisole and justify your reasoning.  Make specific reference to the validity of the VSEPR prediction.  (2 pts)

   5. Explain how the O-atom lone pair hybridization relates to the conjugated π system of anisole.  Include important molecular orbital depictions and/or resonance structures.  (2 pts)

9. ​Directly compare the lowest energy and highest energy conformations of anisole.  State which isomer has:

   • the highest steric strain based upon measured atomic distances

   • the most effective π-conjugation based upon its lone pair hybridizations and orientations

Based upon your answer, state whether steric strain or π-conjugation is most important in determining the most stable conformation of anisole.  (2 pts)

10. Enjoy the quotation at the bottom of the WebMO output.  Gaussian 09 provides a quotation at the end of each job.  :)

1. Draw the important resonance structures for each of the molecules above.  (4 pts)
2. Using your resonance structures from the previous question, classify each substituent as π-electron-donating or π-electron-withdrawing with respect to the aromatic ring.  Using your knowledge (or a table) of electronegativities, predict whether each group is σ-electron-donating or σ-electron-withdrawing with respect to the aromatic ring.  Complete the table below.

1. Usingthe NBO output for each of the molecules, find “Electrostatic Potential” in the Molecular Orbitals list.  Click the magnifying glass () icon to view the electrostatic potential map, which is a way of visualizing electron distribution in the molecule.  The Options box is on the left-hand side of the screen.  Uncheck “Auto scale range” and set the values to range from -0.05 to 0.05.  If you get a screen capture image of each electrostatic potential map, you can paste them into Word, Powerpoint, Excel, Paint, etc. and compare side-by-side.
2. Click theglass icon at the top of the Natural Population Analysis (NPA) table to view the NPA charges on the atoms.  Label an image of each molecule in your lab notebook with the NPA charges.  Using this information, fill in the table on the next page.  Where two ¹H-NMR equivalent atoms bear different charges, average the two values.  (3 pts)

   

   	Benzene
   	Charge	1H-atom NMR shift (ppm)*
   Cipso	-0.243	7.33
   Cortho	-0.243	7.33
   Cmeta	-0.243	7.33
   Cpara	-0.243	7.33

    

   		Aniline
   	Charge	Charge relative to benzene	1H-atom NMR shift (ppm)*	1H atom NMR shift* relative to benzene (ppm)
   Cipso			-
   Cortho			6.64
   Cmeta			7.12
   Cpara			6.73
   	Styrene
   	Charge	Charge relative to benzene	1H-atom NMR shift (ppm)*	1H atom NMR shift* relative to benzene (ppm)
   Cipso			-
   Cortho			7.41
   Cmeta			7.32
   Cpara			7.25
   	Benzoic Acid
   	Charge	Charge relative to benzene	1H-atom NMR shift (ppm)*	1H atom NMR shift* relative to benzene (ppm)
   Cipso			-
   Cortho			8.15
   Cmeta			7.49
   Cpara			7.63

   * ¹H-NMR shift in CDCl₃

   Charge relative to benzene

   =

   [Charge on substituted aromatic ring C-atom]

   -

   [Charge on corresponding benzene C-atom]

    

   1H-atom NMR shift relative to benzene

   =

   [1H-atom NMR shift of substituted aromatic ring]

   -

   [1H-atom NMR shift of benzene]

3. Use the equations above the calculate the difference in charge between corresponding C-atoms in benzene and each substituted aromatic ring, as well as the corresponding difference in ¹H-NMR chemical shifts.  State the relationship between the charge difference at each position and the ¹H-atom chemical shift difference.
4. Using your resonance structures from the prelab and NPA charges, briefly describe how each substituent affects the charge distribution on the C-atoms in the ring and how this influences the ¹H-NMR chemical shifts.  (2 pts)
5. Use the Molecular Orbitals list to find and view the highest energy occupied molecular orbital (HOMO) and the lowest energy unoccupied molecular orbital (LUMO) for each molecule.  Place an image of each of these orbitals in your lab notebook.  These are the frontier molecular orbitals, which are involved in chemical reactions.  If the molecule acts as an electron-donor, the HOMO of the molecule is involved.  If the molecule acts as an electron-acceptor, the LUMO is involved.  (2 pts)
6. Using the NBO and geometry optimization calculations of aniline, assess the hybridization of the nitrogen atom and its lone pair, in a manner similar to anisole in the previous exercise.  Summarize each item below in your laboratory notebook.  (1 pt)
   • ​​Provide the ideal VSEPR-predicted electron/molecular geometries (including H–N–H bond angle) and associated hybridization of an N-atom with one lone pair and three bond pairs of electrons.
   • Measure the B3LYP-optimized H–N–H bond angle.
   • Measure the B3LYP-optimized H–N–C bond angles.
   • Measurethe B3LYP-optimized C–C–N–H dihedral angle.
   • Obtain the NBO calculated Natural Hybrid Orbital N-atom lone pair hybridization.
7. Briefly rationalize the difference between the N-atom lone pair and atomic hybridizations predicted by VSEPR and the NBO data.  (2 pts)

1. Estimate the pKa of protonated phenol and protonated aniline (shown below).  State which of the molecules is a stronger acid.  (3 pts)  A simple pKa table is provided.

1. Determine the relative energy of each of the protonated 4-aminophenols using their calculated MP2 energies.  Set the lowest energy isomer to a relative energy of 0.0 kcal/mol.
2. Based on the relative energies calculated above, draw the appropriate structure on the lines in the energy diagram below and fill in the appropriate relative energy in the open box.  The more basic atom is thermodynamically more favorable (i.e.  has a smaller ΔE_rxn) to protonate.  State which atom of 4-aminophenol is more basic.  (2 pts)
   
3. Use the pK_a values for a protonated phenol and for a protonated aryl amine (protonated aniline) from the prelab question as estimates of the corresponding acidities in 4-aminophenol.  Explain whether or not your calculation from part one is consistent with these pK_a values.  The diagram above should also be helpful in answering this question.  (1 pt)
4. An interesting structural change occurs to the N-atom of 4-aminophenol when the O-atom is protonated.  Measure the dihedral angle (Θ_C-C-N-H) in both 4-aminophenol and O-protonated 4-aminophenol.  Use the NBO calculation to determine the hybridization of the N-atom lone pair in each molecule.  Include an image of each of these two lone pair orbitals in your answer to the question.  Rationalize the geometry change of the N-atom and the change in lone pair hybridization upon protonation of the O-atom.  (2 pts)
5. Similarly to 4-aminophenol, there are two different atoms that can be protonated in formamide.  As above, determine the relative energy of each protonated formamide using their calculated MP2 energies.  Set the lowest energy isomer to a relative energy of 0.0 kcal/mol.  State which atom of formamide is more basic.  (2 pts)
6. Rationalize the relative basicity of the N-atom and O-atom in formamide using the π-symmetry molecular orbitals of formamide, O-protonated formamide, and N-protonated formamide.  Include an image of the π₁ orbital of each molecule in your explanation.  (3 pts)