1 Molecular Calculations Lab: Some guideline given at the bottom of page 3. 1. Use the semi-empirical AM1 method to calculate ΔH f for the compound you used in the heat of combustion experiment. Be sure to select equilibrium geometry for the calculation. Record the value and decide if it is more appropriate for the gas phase or for the solid (condensed) phase. Look up the enthalpy of sublimation for your compound and use that to find ΔH f for the other phase. Compare your results with literature values for both enthalpies of formation. Compound: AM1 ΔH f = phase: Literature value ΔH sub : Source: Based on AM1 ΔH f & ΔH sub, ΔH f = phase: Literature values: ΔH f, gas = % error Source: ΔH f, solid = % error For comparison, your experimental value was ΔH f = phase: 2. Diatomic Molecules Pick one of the following molecules: { C 2, N 2, O 2, F 2, }. Inform your instructor of your choice before starting the calculation. For each of the following calculations select equilibrium geometry, and calculate the bond length, energy, and vibrational frequency for the singlet and triplet state of your molecule. The vibrational frequencies should be different for each type of calculation. If all are the same, it is probably a software error; if this occurs, obtain the vibrational frequency from the bottom of the output, not from the vibration menu. Find literature values for the bond lengths, vibrational frequency (compute the fundamental frequency, v = 0 to v = 1, using ω e, ω e x e, and ω e y e, if given), and the relative energy of the state compared to the ground state. Values for ν f, T e, ω e, ω e x e, and ω e y e should be in cm -1. Literature vibrational energy levels in the NIST Webbook are given by the formula: G( ) = e ( + ½) - ex e ( + ½) 2 + ey e ( + ½) 3 4 + ez e ( + ½).. Molecule: Singlet r e energy ν f semi-empirical PM3 Hartree-Fock 3-21G (*) Hartree-Fock 6-31G * Literature: T e = Source: ω e = ω e x e = ω e y e =
Molecule: Triplet r e energy ν f 2 semi-empirical PM3 Hartree-Fock 3-21G (*) Hartree-Fock 6-31G * Literature: T e = Source: ω e = ω e x e = ω e y e = Which is more stable, the singlet or triplet? Does the ground-state assignment agree with the literature? PM3 ; 3-21G (*) ; 6-31G (*). How did the bond lengths compare with the literature value? Singlet: semi-empirical PM3 % error Hartree-Fock 3-21G (*) % error Hartree-Fock 6-31G * % error Triplet semi-empirical PM3 % error Hartree-Fock 3-21G (*) % error Hartree-Fock 6-31G * % error Comment on the agreement. Did the errors appear systematic (ie, all too large or too small)? How did the vibrational frequencies compare with the literature value? Singlet: semi-empirical PM3 % error Hartree-Fock 3-21G (*) % error Hartree-Fock 6-31G * % error Triplet semi-empirical PM3 % error Hartree-Fock 3-21G (*) % error Hartree-Fock 6-31G * % error Comment on the agreement. Did the errors appear systematic?
Using the Hartree-Fock 6-31G * basis set, calculate the orbital energy and surfaces for the first ten molecular orbitals of the ground state. Classify each as σ or π ( and g or u if appropriate), and as antibonding, bonding, or nonbonding. Indicate which is the HOMO and which the LUMO. Orbital Energy Symmetry Bonding Classification 1 2 3 4 5 6 7 8 9 10 The HOMO is The LUMO is Which, if any, are degenerate? 3 Note: Record bond lengths (Å) to three places after the decimal, Bond angles ( ) to two places after the decimal, Frequencies (ν, cm -1 ) to two places after the decimal, Energies in kcal/mol to two or three places after the decimal, Energies in kj/mol to two or three places after the decimal, Energies in hartrees (au) to five places after the decimal. Links for comparison with experimental values: 1. NIST Webbook: http://webbook.nist.gov/chemistry/ Search using either the formula or name. Data of interest: Thermodynamic data for gas or condensed phase Phase change data Vibrational and electronic energy levels Constants for diatomic molecules Note: Energy level are arranged according to energy, with the ground state at the bottom. Check to see if the state is a singlet, triplet, etc. T e indicates separation (in cm -1 ) from the ground state. 2. Computational Chemistry Comparison and Benchmark Data: http://srdata.nist.gov/cccbdb/ Select 3. Links to all experimental and all calculated data for one species Type in the desired species and enter Click on x under experimental for vibrations (or elsewhere) and joyfully browse
3. Ozone 4 The bond in O 2 is considered a double bond ( bond order of two ) and has a bond length of 1.21 angstroms. The O-O bond in hydrogen peroxide, H 2 O 2, is considered a single bond and has a bond length of 1.49 angstroms. Harkening back to the glory days of organic chemistry and even general chemistry, write the two major contributing structures for ozone, O 3 : Would you expect ozone to have a dipole moment, since all three atoms are the same? For each contributing structure, write the formal charge above each atom. Using the much-vaunted VSEPR rules, and making no allowance for the greater repulsion due to lone pair electrons as compared to bonding electrons, the ozone bond angle should be ( 90, 109.5, 120, 180 ). If just one contributing structure is considered, one bond should be a single bond and one bond should be a double bond. Using Spartan, construct the ozone molecule with one single bond and one double bond. This is not particularly easy. One possible way is to use the Expert Builder Screen screen, select -O- (bent), then attach the other O as O, and then select = as the bond type to convert one single bond to a double bond. Quit to the main screen and do a MMFF molecular mechanics calculation. Be sure that the symmetry box is not checked. After the calculation measure the calculated bond lengths and the bond angle. MMFF: O=O bond length O-O bond length Bond angle Is one bond length longer than the other or are both about the same? Do molecular mechanics calculations appear to depend on the valence state ascribed to the atom? Do molecular mechanics calculations allow one to compute orbital surfaces? (try and see) Do an PM3 semi-empirical calculation. After the calculation measure the calculated bond lengths and bond angle. PM3: O=O bond length O-O bond length Bond angle Is one bond length longer than the other or are both about the same? Does the molecule appear to have 1 single and 1 double bond, 2 single bonds, 2 double bonds, or two bonds in between a single bond and a double bond? (recall the typical oxygen-oxygen bond lengths given at the top of the page). Check the calculated dipole moment and the electrostatic partial charges on the atoms. Does the molecule have a dipole moment? Do the electrostatic charges agree qualitatively with the formal charges?
Do an 6-31G (*) calculation. After the calculation measure the calculated bond lengths and bond angle. Hartree-Fock 6-31G (*) : O=O bond length O-O bond length Bond angle Is one bond length longer than the other or are both about the same? Does the molecule appear to have 1 single and 1 double bond, 2 single bonds, 2 double bonds, or two bonds in between a single bond and a double bond? (recall the typical oxygen-oxygen bond lengths given at the top of the page). Check the calculated dipole moment and the electrostatic partial charges on the atoms. Does the molecule have dipole moment? Do the electrostatic charges agree qualitatively with the formal charges? Determine surfaces for the LUMO+2 through the HOMO-11 molecular orbitals. Examine each. Do the molecular orbitals tend to be localized or delocalized molecular orbitals? Which ones appear to be π orbitals? Pick out at least two orbitals that are bonding orbitals with respect to the central atom and a terminal atom, including one π orbital. Pick out at least two orbitals that are antibonding orbitals with respect to the central atom and a terminal atom, including one π orbital. Determine the vibrational frequencies. Write down the frequencies for each, and classify each as a bending mode, a symmetric stretch, or an asymmetric stretch. Frequency Classification. 5 Find literature values for the bond length(s), bond angle, dipole moment, and vibrational frequencies. Calculate the % error with respect to the 6-31G (*) calculation, and include in parentheses after the literature value. See http://cccbdb.nist.gov/ (use B3 and internal coordinates to get experimental geometry values) and CRC tables. Bond length(s): Bond angle: Dipole moment: Vibrational frequencies: Literature source(s)
Examples Using the Electrostatic Potential 4. Construct acetic acid CH 3 COOH. You can use the carboxylic acid group if you wish. Go to Surfaces under Setup and add the density with electrostatic potential as the property. Do a Hartree-Fock/6-31G* calculation. Be sure to check the Atomic Charges box. Submit the calculation. CH 3 COOH: atomic charge on H attached to O H attached to C: CH 3 COOH: C=O bond length Å, C-O bond length Å Are both the same length? In general, one would expect that the greater the (positive, negative) charge on the H, the easier to remove a proton (H + ) and the stronger the acid. Which appear to be more acidic H, the H bonded to the O or the H bonded to the C, or both? Display the density with the electrostatic potential displayed, the transparent display works best. The bluer the potential map, the more positive the potential and therefore the more acidic the hydrogen. Which of the H appears to be the more acidic hydrogen? You may wish to change the scale of the potential map; select Display and click on the density/potential map. The electron density is an observable, so this is a more reliable indication of acidity. Save the old calculation in case it is needed again. Then use Save As under File or the computer disk icon to save the file with a new name; just adding anion to the old name will suffice. To construct the anion, click on the + icon to return to the build mode. Using the delete key (the icon looks like an explosion), delete the H and the O- valence for each acid. In the calculation box set the charge to anion or to -1. Be sure the density surface with potential is still selected. Do a Hartree-Fock/6-31G* calculation, then make the following measurements on the anion. CH 3 COO - : C=O bond length Å, C-O bond length Å Are the bond lengths consistent with a single and a double bond? Are both bond lengths about the same? Display the density with potential map. Is the negative charge localized on the O oxygen or evenly over both oxygen atoms? (Use atomic charges to check.) 5. Do a semi-empirical Geometry Search PM3 calculation on singlet BeH 2, and calculate the IR, the surfaces LUMO+3, LUMO+2, LUMO+1, LUMO, HOMO, HOMO-1, and density with electrostatic potential. Answer the following about the resulting structure: bond length: Å, H-Be-H bond angle: H f = (units) Examine the electron density with the electrostatic potential map. Describe its appearance. 6 Is the H an acidic hydrogen (δ+) or more like a hydride (H - or δ-)? Explain. Examine the orbital surfaces LUMO+3, LUMO+2, LUMO+1, LUMO, HOMO, HOMO-1. List one that is a π orbital and one that is a σ orbital Are there any that are degenerate? If so, list two degenerate orbitals. List one that is bonding, one that is antibonding, & one nonbonding List the IR frequencies in cm -1 : List any degenerate frequencies(in cm -1 ). & Are there any that would not appear in the IR? If so, list here
6. Conformer Search and Rotation Barrier for Glyoxal Construct glyoxal (ethanedial). Be sure the OCCO dihedral is 0 by selecting the Dihedral icon (next to the angle icon) and clicking on the O, C, C, O in order. The dihedral angle will appear at the bottom on the right. If not 0, type in 0.00 in the box and hit Enter. Put a constraint on the dihedral by either selecting Constrain Dihedral from the Geometry menu or by useing the Constrain Dihedral icon (looks like a dihedral with a lock in the middle, to the right of the measurement icons). Again click on the O, C, C, O in order, then click on the lock icon to the right of the dihedral dialog box at the bottom of the page on the right. The icon should change from an unlocked to a locked. Select Properties from the Display menu and click on the arrow-like constraint marker on the selected dihedral. The Contraint Properties dialog box should appear. Check the Dynamic box. This allows the selection of a range of values for the calculation. The first box should contain 0.00; if not, enter 0 in the box and hit Enter. Then enter 180. in the to box and hit Enter before leaving the box; otherwise the change will not be recorded. Next type 13 in the Steps box and hit Enter to record the change. This permits the calculation for the molecule from a dihedral of 0.00 to 180 in steps of 15 (180 /15 + 1 = 13, the number of steps.) Click on the x to dismiss the box and go to Calculations under Setup. Change the first box from Equilibrium Geometry to Energy Profile and do a Hartree-Fock/6-31G* calculation. Give the calculation the name of your choice. All bond lengths and angles except the constrained dihedral will be optimized at each point, so the calculation may take a few minutes. After completion, Close the molecule an screen to avoid confusion and Open the name.profile1.spartan file, where name is what you named the calculation. The molecule will appear. You can scroll through the 13 molecules using the scroll controls at the bottom of the page on the left. Bring up the Spreadsheet in the Display menu. To add a column to the spreadsheet for the constrained dihedral, click on the Constrain Dihedral icon, then click on the constaint marker in the middle of the dihedral on the molecule, then click on the yellow P symbol which appears at the bottom of the page after the lock icon. The dihedral angles should appear in the column after the label column. Next add energy columns. Click the top of an empty column heading, select add.., and choose what to put in the column. I suggest the relative energy (rel. E) in kcal/mol or kj/mol; add other columns if desired. To print out the spreadsheet, be sure it is active and select Print Spreadsheet under File. Construct a plot be selecting Plots under Display; put the dihedral (the constrain) on the x-axis and the energy on the y-axis. Move the molecule and the spreadsheet off the plot, the spreadsheet can be closed if you have printed it off or have copied the columns. Use the scroll keys at the bottom left to move along the plot; the molecule will change appropriately. To copy the graph, hold down both mouse keys, draw a box around the plot, and use Copy under Edit. Paste in a word document for printing. Enclose a copy with your report. Fill in the table below and answer the questions; barrier refers to the rotation barrier for complete rotation (max min). dihedral 0.0 (s-cis) 15.0 30.0 45.0 60.0 75.0 90.0 energy 7 dihedral 105.0 120.0 135.0 150.0 165.0 180. (s-trans) barrier energy The global minimum occurs at a dihedral angle of. Is there a local minimum as well? If so, the local minimum occurs at a dihedral angle of. There is an activation energy of for going from the local minimum to the global minimum, and the process is exothermic by. Extra Credit: Literature value for rotation barrier: % Error Source:
8 s-cis glyoxal (s-cis ethanedial) s-trans glyoxal (s-trans ethanedial)