Chemistry 363 RWQ 11/04 Spring 010 JMS/DLC 3/09 Polyatomic Molecular Vibrations: An Experimental/ Computational Study of Acid Rain Precursors Experimental Objectives: Computational molecular modeling studies will be performed in order to predict the fundamental vibrational frequencies for the gas phase triatomic molecules water and sulfur dioxide. The fundamental vibrational frequencies of the molecules will be determined from infrared vibrational spectra. Vibrational force constants for stretching and bending vibrations will be calculated from the experimental results. In addition, complexes involving water and sulfur trioxide as acid rain precursors will be investigated using molecular modeling. SECTION 1: THEORETICAL BACKGROUND Review: Diatomic Molecular Vibrations In the experiment on the infrared spectroscopy of HCl and DCl, the vibration-rotation spectra of diatomic molecules were investigated. The simplest picture of the vibrations of a diatomic molecule is the harmonic oscillator. In the harmonic oscillator approximation, the potential energy for vibrations is V( r) = 1 k ( r r e), (1) where r is the bond length, r e is the equilibrium bond length, and k is the force constant. Solving the Schrödinger equation for this potential leads to quantized energy levels for vibrational motion. The quantized energy levels are E v = hν 0 ( v + 1 ), v = 0,1,K. () In Eq. (), h is Planck's constant, ν 0 is the harmonic vibrational frequency, and v is the vibrational quantum number. The harmonic vibrational frequency ν 0 is related to the force constant through the relation ν 0 = 1 k π µ 1/. (3) The reduced mass µ in Eq. (3) is defined by µ = m A m B m A + m B, (4) where m A and m B are the masses of the two atoms which comprise the diatomic molecule.
Molecular Vibrations of ABA Triatomic Molecules The description of the vibrational motion of a polyatomic molecule is similar to that for a diatomic molecule. However, polyatomic molecules possess more than one vibrational mode. A nonlinear polyatomic molecule with N atoms possesses 3N-6 vibrational modes. In this experiment, the focus will be on study of the vibrational modes of symmetric ABA triatomic molecules. The ABA triatomic molecule has 3 vibrational modes. In order to describe the vibrational motion, it is customary to define internal coordinates for the molecule, as shown in Figure 1. B r 1 r A α Figure 1. Internal coordinates for an ABA triatomic molecule. In Fig. 1, the coordinates r 1 and r correspond to the instantaneous AB bond lengths and the coordinate α corresponds to the instantaneous ABA bond angle. Using the harmonic approximation, the potential energy in internal coordinates for the ABA triatomic molecule is given by V( r 1, r, α) = 1 f r( r 1 r e) + 1 f r( r r e) + 1 f α r e ( α α e ). (5) In Eq. (5), f r and f α are the force constants for bond stretching and angle bending, respectively. Because of the symmetry of the ABA triatomic, the force constant f r is the same for both bonds, as is the equilibrium bond length r e. The equilibrium ABA angle is denoted by α e. Note that because of the factor r e included in the last term, the units of the stretching and bending force constants are identical; for example, typical units for the force constants are Nm -1. Eq. (5) represents a simplification of the potential energy function; in addition to neglect of anharmonic correction terms, coupling terms between the two bonds and between the bonds and the angle have been neglected. This leads to a simplified analysis of the spectrum. Because of the symmetry of the ABA triatomic molecule, it is convenient to convert the potential energy from the bond displacement and angle displacement coordinates given in Eq. (5) to symmetry coordinates. The three symmetry coordinates are denoted S 1, S, and S 3. The symmetry coordinates are composed of linear combinations of the bond and angle displacements, given by A S 1 = 1 r [ ( 1 r e ) + ( r r e )] S = α α e S 3 = 1 [( r 1 r e ) ( r r e )]. (6)
The symmetry coordinates are related to the normal modes of vibration of an ABA triatomic molecule. From Eq. (6), S 1 is related to the symmetric stretching mode, S is the bending mode, and S 3 is related to the antisymmetric stretching mode. Solution of the Schrödinger equation for the potential energy in Eq. (5) leads to quantized energy levels for the three vibrational modes of the ABA triatomic molecule. In the harmonic approximation, these energy levels have the form 3 E v1 v v 3 = hν 0i ( v i + 1 ). (7) In Eq. (7), the vibrational quantum numbers for the three modes are v 1, v, and v 3. The harmonic vibrational frequencies for each of the three vibrational modes are ν 0i for i = 1,, and 3, for the symmetric stretch, bend, and antisymmetric stretch, respectively. Because the form of the kinetic energy for an ABA triatomic molecule is more complicated than that of a simple diatomic molecule, the relation between the harmonic frequencies and force constants is not so simple as that given in Eq. (3). However, a set of equations which relate the harmonic frequencies to the force constants may be derived [1]. These equations are i =1 3 4π 1 ν 3 = fr + m A sin α e (8) m B 1 ( ) = f r 4π ν 1 +ν + m A cos α e + f α 1 + m B m A sin α e (9) m B 16π 4 ν 1 ν f = r f α 1 + m A m A m B (10) These equations may be used to calculate the force constants f r and f α from the experimental harmonic vibrational frequencies. In this experiment, the gas phase infrared spectra of the ABA triatomic molecules H O and SO will be obtained. The harmonic vibrational frequencies extracted from the spectra will be used to determine the force constants for the stretching and bending motion. Molecular Modeling of Triatomic Vibrational Motion In this experiment, vibrational frequencies and thermodynamic information will be computed for H O and SO using the Spartan molecular modeling program. The information obtained from Spartan will be used to assign the vibrational modes and compare the harmonic frequencies with those determined from the infrared spectra.
Molecular Modeling of Acid Rain Precursors The triatomic molecules H O and SO play key roles in the formation of acid rain. Emissions of air pollutants such as sulfur dioxide and nitrogen oxides into the atmosphere are the primary cause of acid rain []. In North America, more than 90% of the emissions are of human origin, mostly from burning of fossil fuels. An annual total of nearly 0 million tons of these pollutants are emitted into the atmosphere [3]. Sulfur and nitrogen oxides burned in midwestern power plants drift eastward and fall to earth as acid rain in the eastern United States, Canada and Europe. Not only does acid rain cause damage to man-made structures, it leads to the acidification of natural lakes and streams. Despite reductions in sulfur emissions since 1995, many lakes in New York have continued to acidify [4]. Many fish species are not able to survive acidified conditions. Acid rain also causes damage to trees and other vegetation, particularly at higher altitudes. Throughout the Appalachian Mountains, forests consisting mostly of spruce trees have been severely affected by acid rain which weakens the trees and strips nutrients from the soil. Sulfur dioxide, SO, produced from the burning of fossil fuels is converted in the atmosphere into sulfuric acid, H SO 4, one of the principal components of acid rain. A series of chemical reaction steps has been proposed for this conversion [5]. These steps are SO + OH HOSO (11) HOSO + O SO 3 + O H (1) SO 3 + H O H SO 4. (13) In Eqs. (11) and (1), sulfur dioxide is oxidized to sulfur trioxide. Eq. (13), involving the conversion of sulfur trioxide to sulfuric acid by reaction with water, is thought to proceed through an intermediate complex, SO 3 -H O. The existence of the SO 3 -H O complex in the gas phase has been confirmed via a microwave spectroscopy experiment [6]. 4 H H 103 o 93 o O O S.43 Å O O Figure. Structure of gas-phase SO 3 -H O complex from microwave spectroscopy [6]. In this experiment, molecular modeling studies will be performed in order to investigate the acid rain precursor complex, SO 3 -H O, including determination of the binding energy of the complex. In addition, the rearrangement of the SO 3 -H O complex to sulfuric acid will be studied and the activation energy for the rearrangement process will be calculated.
SECTION. EXPERIMENTAL AND COMPUTATIONAL PROCEDURES 5 A. Molecular modeling of water and sulfur dioxide In this section, Linux workstations in the computational lab (SLB60) will be utilized to carry out molecular modeling simulations of water and sulfur dioxide using the Spartan program. To begin the molecular modeling studies, follow the instructions provided by the instructor or TA to log on to one of the Linux workstations. First use the Spartan program to build the water and sulfur dioxide molecules. Perform equilibrium geometry and vibrational frequency calculations on the two molecules. In this case, select Setup in the main Spartan menu. Then select Calculations. The task is Equilibrium Geometry. Use the Hartree-Fock model and the 6-31G* basis set for the calculations. Note: for the vibrational frequency calculation, click on the "Frequencies" and "Thermodynamics" buttons in the Setup window. When the calculations are complete, record the electronic energy and zero-point vibrational energy in kcal/mol for each of the molecules. The electronic energy may be obtained by selecting "Display Properties". The electronic energy is listed as "Energy gas" in atomic units [1 a.u. = 67.51 kcal/mol]. The zero-point vibrational energy can be found by selecting "Display Output", switching to Verbose Output, and looking near the bottom of the listing. Measure the equilibrium bond lengths and bond angles. Record the vibrational frequencies in wavenumbers. The vibrational frequencies are obtained by selecting "Display Vibrations". View the animation of each vibration to assign the symmetric stretching, bending, and antisymmetric stretching modes. B. Molecular modeling of acid rain precursors 1. Calculation of sulfur trioxide Before beginning calculations on the acid rain precursor molecule, the sulfur trioxide molecule must be built and optimized. Use the Spartan program to build the sulfur trioxide molecule. Perform an equilibrium geometry and vibrational frequency calculation of the molecule using the Hartree-Fock model and the 6-31G* basis set. When the calculation is complete, check that all frequencies (Display Frequencies) are positive. Then record the electronic energy, zero-point vibrational energy (in kcal/mol) and geometrical parameters.. Calculation of the acid rain precursor complex To form an initial structure for the SO 3 -H O complex, open the water and sulfur trioxide molecules on the screen (make sure no other molecules are open). Try to orient the two monomers so that they crudely form the expected structure for the complex (see Figure ). The right mouse button is used to translate the selected molecule, while the middle mouse button is used for rotation. To move the two monomers as a unit, you can use Control-Right Mouse for translation and Control-Middle Mouse for rotation. Once you have the monomers arranged in approximately the correct orientation, use "File Merge As" to combine them into one molecular complex. In the window that pops up, give the complex a new name and click on the "Merge As" button. Perform an equilibrium geometry and vibrational frequency calculation of the molecular complex. Use the Hartree-Fock model and the 6-31G* basis set.
When the calculation is complete, record the electronic energy and zero-point vibrational energy in kcal/mol for the molecular complex. In addition, measure and record the geometrical parameters for the complex, such as bond lengths and bond angles. 6 3. Calculation of the sulfuric acid product The next step is calculation of the product. The SO 3 -H O complex can rearrange to form sulfuric acid, H SO 4. Use Spartan to build the sulfuric acid molecule. Perform an equilibrium geometry and vibrational frequency calculation of sulfuric acid using the Hartree- Fock model and the 6-31G* basis set. If you obtain an imaginary frequency, you must rearrange the initial geometry. Usually positioning the O-H bonds so that they point away from each other is sufficient. After rearranging the molecule, run the calculation one more time. Once the calculation is complete, record the electronic energy and zero-point vibrational energy (in kcal/mol) for the product. Measure and record the geometrical parameters of sulfuric acid. 4. Calculation of the transition state The final step in the calculations involves determination of the transition state for the rearrangement of the SO 3 -H O complex into H SO 4. To build the transition state, open the SO 3 -H O complex. Modify the geometry in a rational way such that it resembles the possible transition state of the reaction. In order to do this, shorten the S-OH bond, change the S-O-H angle (< 80 o ) and elongate one of the O-H bonds. Save the file giving it a different name. Select Setup from the main menu, then Calculations. The task must be changed to Transition State Geometry. The model is Hartree-Fock and 6-31G* is the basis set. Make sure to run a frequency calculation. Once the calculation is complete, check the vibrational frequencies. For a transition state, there should be one negative or imaginary frequency and the rest will all be positive. Record the electronic energy and zero-point vibrational energy in kcal/mol for the product. Measure and record geometrical parameters for the transition state. C. Experimental infrared spectra of water and sulfur dioxide 1. Infrared spectrum of water The first step is to obtain the infrared spectrum of water. Since water vapor is always present in the atmosphere, the spectrum may be taken by running a spectrum of the air in the sample chamber. Make sure that the sample chamber is open while the water vapor spectrum is recorded. Record the spectrum in a similar way you recorded the HCl/DCl spectrum.. Infrared spectrum of sulfur dioxide The next step in the experiment is to obtain the infrared spectrum of sulfur dioxide. The procedure is much the same as that followed in the HCl/DCl experiment. Use the vacuum line to evacuate the IR cell. Remember not to touch the cell windows when handling the IR cell. Remove the IR cell from the vacuum line and place the evacuated IR cell in the sample chamber of the FTIR spectrometer. After purging the sample chamber with nitrogen for a few minutes, record the background spectrum of the empty cell. Return to the vacuum manifold and attach the IR cell to the line. Fill the IR cell with approximately 15-0 torr of sulfur dioxide gas from the storage bulb.
7 Remove the IR cell from the vacuum line. Return to the FTIR spectrometer and place the IR cell in the sample chamber. Allow the sample chamber to purge with nitrogen for a few minutes. Record the infrared spectrum of sulfur dioxide. Return to the vacuum manifold and reattach the IR cell to the vacuum line. Evacuate the line, isolate the manifold from the vacuum pump, and then open the stopcocks to the IR cell and the SO storage bulb. Use a dewar filled with liquid nitrogen to recompress the SO gas back into the storage bulb. SECTION 3. CALCULATIONS A. Molecular modeling of water and sulfur dioxide From the molecular modeling studies of the water and sulfur dioxide molecules, calculate adjusted fundamental frequencies for each molecule in wavenumbers. To do this, scale the molecular modeling frequencies by a factor of 0.89. The factor of 0.89 is an empirical scaling factor which adjusts the modeling values to take into account anharmonicity [Ab Initio Molecular Orbital Theory, W. J. Hehre, L. Radom, P. v. R. Schleyer, J. A. Pople, John Wiley & Sons, New York, 1985]. The scaling allows easier comparison of the modeled and experimental frequencies, since the fundamental frequencies obtained in the molecular modeling study were determined using the harmonic oscillator approximation, while the experimental values include anharmonicity. B. Acid rain precursor studies 1. Calculation of the binding energy of the acid rain precursor complex Use the energies from the Spartan calculations to determine the binding energy of the SO 3 H O complex. Consider the formation of the complex from SO 3 and H O, SO 3 + H O SO 3 H O. (14) The energy of this reaction (total energy of products minus total energy of reactants) is the binding energy of the complex. Thus, the binding energy (BE) is given by the equation BE = E T (complex) E T (SO 3 ) E T (H O). (15) In Eq. (15), E T represents the total energy of the molecule, defined as E T = E el + E ZPE, (16) where E el is the electronic energy and E ZPE is the vibrational zero point energy of the molecule. For the formation of a stable molecular complex, the binding energy will be negative, indicating a favorable interaction. The larger the magnitude of the binding energy, the stronger the interaction between the molecules. Calculate and report the binding energy of the SO 3 H O complex in kcal/mol.
. Calculation of the activation energy for rearrangement to sulfuric acid The results of the Spartan calculations should be used to determine the activation energy for rearrangement of the SO 3 -H O complex to H SO 4. The activation energy is the amount of energy that must be added to the system before the reaction will proceed, as illustrated in Figure 3. 8 E SO 3 -H O Transition State Activation Energy H SO 4 Figure 3. Reaction path for rearrangement of SO 3 -H O complex to H SO 4. If the activation energy is too high, the reaction will not occur, or it will only occur very slowly. From Fig. 3, the activation energy E a is the total energy of the transition state minus the total energy of the molecular complex, E a = E T (trans. state) E T (complex). (17) Calculate and report the activation energy for the rearrangement of the SO 3 H O complex to H SO 4 in kcal/mol. C. Experimental infrared spectra of water and sulfur dioxide From your infrared spectra of water and sulfur dioxide, determine the three fundamental harmonic vibrational wavenumbers (ω e values) for each molecule. Recall that the fundamental frequency ω e (in wavenumbers) is related to the harmonic frequency v 0 (in s -1 ) by the formula ω e = v 0 c. (18) If rotational structure is evident in the spectrum of the molecule, follow the procedure described for the secondary diatomic molecule in the HCl/DCl experiment to obtain the fundamental vibrational frequencies. That is, the harmonic frequency can be calculated from the average of the R(0) and P(1) peaks in the spectrum. If no vibration-rotation lines are observed, but the outline of R and P branches can be seen in the spectrum, then the fundamental frequency can be determined as the value of the central band gap in the spectrum. Finally, if no rotational structure is observed, the fundamental frequency can be obtained from the value of the maximum of the absorption peak. Report the fundamental vibrational frequencies for each molecule in wavenumbers. Use the results from the computer simulations to assign the vibrational mode corresponding to each of the experimental vibrational frequencies. In other words, use the computer simulations
to figure out which frequencies correspond to the symmetric stretch, antisymmetric stretch, and bending modes for both water and sulfur dioxide. Report these assignments along with the numerical values of the frequencies. Convert the fundamental vibrational frequencies of water and sulfur dioxide (in cm -1 ) to harmonic frequencies (in s -1 ) using Eq. (18). For each molecule, use Eqs. (8)-(10) to solve for the force constants f r and f α. Report the force constants for water and sulfur dioxide in units of N/m. SECTION 4. ITEMS TO INCLUDE IN YOUR REPORT Please note that the report is a formal one, consult the handout on writing lab reports for all items that must be included. Abstract Summarize experimental objectives, results and conclusions from your experiment and modeling Introduction Some general background information on acid rain formation and polyatomic molecular vibrations may be useful. Remember to progress from general to specific, include any pertinent equations, and state the goals of the experiment. Experimental and Computational Details Summarize in a narrative style your experimental setting. Include pressure of gas used, spectrometer resolution and range. Also include in the computational details the method used and what type of calculation was carried out. Data and Results Experimental spectra and vibrational frequency assignments must be included, as well as values of the force constants for both water and sulfur dioxide. From the computer simulations, the vibrational frequencies of water sulfur dioxide should be given, along with the geometries of water, sulfur dioxide, and the SO 3 -H O complex. In addition, the electronic and vibrational zeropoint energies of the various species, along with calculated binding and activation energies, should be reported. Discussion Obtain experimental literature values for the equilibrium bond lengths and bond angles of water and sulfur dioxide. Compare to the molecular modeling results. Compare the experimental fundamental vibrational frequencies (in wavenumbers) of water and sulfur dioxide to the scaled values obtained from the molecular modeling study. Also, compare your experimental fundamental vibrational frequencies (in wavenumbers) for water and sulfur dioxide to experimental literature values. Compare your stretching force constants for water and sulfur dioxide to experimental literature values (bending force constants are not easily found). Compare and contrast the stretching force 9
constants for water and sulfur dioxide and relate to bond order. Discuss qualitatively the magnitudes of the stretching and bending force constants for each molecule. 10 Look up information about the experimental gas phase geometry of the SO 3 -H O complex from Ref. [6]. Compare the structure obtained for the SO 3 H O complex from molecular modeling to the experimental gas phase geometry. Compare the calculated binding energy of the SO 3 H O complex to a computational literature value. How does the magnitude of the binding energy compare to the strength of an ordinary covalent chemical bond? Compare the calculated activation energy for the rearrangement of the SO 3 H O complex to H SO 4 to a computational literature value. Discuss the significance of the magnitude of the activation energy. Describe in terms of key changes in atom distances and angles the reaction path for the rearrangement of the SO 3 H O complex to H SO 4. Explain qualitatively the mechanism of the rearrangement. Treatment of Data Sample calculations of the experimental frequencies from R(0) and P(1) lines should be shown. Sample calculations should be given for conversion of frequencies from units of wavenumbers to s -1. Determination of stretching and bending force constants from Eqs. (8)-(10) should be presented. In addition, sample calculations of binding energies and activation energies should be presented. No propagation of error need be included. References [1] G. Herzberg, Molecular Spectra and Molecular Structure II. Infrared and Raman Spectra of Polyatomic Molecules, Van Nostrand, Princeton, NJ, 1945, pp. 168-17. [] M. J. Molina, L. T. Molina, and C. E. Kolb, Ann. Rev. Phys. Chem. 47, 37 (1998). [3] "Environmental Effects of Acid Rain," Acid Rain Program, United States Environmental Protection Agency, http://www.epa.gov/docs/acidrain/effects/envben.html. [4] Chemical and Engineering News, May 3, 1999, p. 31. [5] J. G. Calvert, A. Lazrus, G. L. Kok, B. G. Heikes, J. G. Walega, J. Lind, and C. A. Cantrell, Nature 317, 7 (1985). [6] J. A. Phillips, M. Canagaratna, H. Goodfriend, K. R. Leopold, J. Phys. Chem. 99, 501 (1995). SECTION 6: INSTRUCTIONS FOR OPERATING THE PERKIN ELMER SPECTRUM ONE FTIR SPECTROMETER You will obtain the vibration-rotation spectrum of gas phase molecules using a Perkin Elmer Spectrum One FTlR spectrometer located in SLB 0. Opening the Software Log into the computer using an ADILSTU account. To start up the FTIR software, click on the Start bar, go to All Programs, then PE Applications, double click the Spectrum icon. A window will open indicating what instrument to use, make sure to select the Spectrum One and click OK.
11 Parameter and Instrument Setup The software may request a background collection; click Cancel because you need to set up the instrument to the conditions required by your experiment. Before any spectral collection you must set the range, resolution and number of scans to be collected. Go to the menu bar and click on Instrument, then Scan. Click Cancel if a window requesting a background collection pops up. A window with different tabs will open. The default tab is Sample. Type the name of the file you will give to the background (bkg) and record some comments (like resolution, sample pressure, etc.). Next select the Scan tab and set the spectrum type to Background (units set automatically to EGY) and the scan number to 16. Next select the Instrument tab and set the resolution to 1.0 cm -1. Click Apply. A background collection window will open. Click Cancel. Collecting a Background and Spectrum To obtain a spectrum of your sample, you must first collect a background spectrum with no sample in the cell, and then collect the spectrum of your sample. The computer will automatically correct and subtract for any background peaks from the spectrum of your sample. The steps for collecting a background and sample spectrum are: 1. With the empty cell positioned in the sample compartment click Scan in the Instrument Setup window that is already open. A window displaying a graph with the background energy spectrum and a scan status bar (indicating number of scans) will be shown. The background spectrum takes a few minutes to complete. The background will be autosaved although if a file with the name you provided is already there a window will pop up. You may overwrite the file. A window will pop up on the screen displaying the background energy spectrum.. In order to collect the sample spectrum, carefully place the gas cell in the FTIR spectrometer sample compartment. Select the Instrument option in the menu. The Instrument Setup window will open. Provide a name for your Sample file and enter some comments. Go to the Scan tab and select the Absorbance units (A). Click Apply, then Scan. A window displaying the FTIR spectrum of the sample and a scan status bar will be shown. If the spectrum is displayed in Transmittance units convert it to Absorbance units by clicking on the icon with the big A. The computer automatically subtracts the background data and adjusts the baseline. When the data collection is complete, you may be asked whether you want to overwrite the file or create a file with a New Name. Provide a New Name (suggested name DCl_HCl.sp) and save your spectrum. Labeling, Printing and Saving the Spectrum 1. First delete the background spectrum from the window. Select the bkg.sp file name at the bottom left of the screen. Then go to the menu bar and click on Edit, then Delete.. Now select the spectrum filename in the bottom left section of the screen. Use the AutoY icon to display the whole spectrum in the screen. Since you have used DCl as the sample, you will have two intense bands. One corresponds to DCl and the other to HCl (which is a contaminant of DCl). First you need to enlarge one of the regions of the spectrum corresponding to the absorption of one of them. In order to do this, depress the left mouse button and draw a rectangle around the region of the spectrum that you would like to enlarge. Then double click in the region you have highlighted to enlarge it to full screen. 3. To label the peaks go to the menu and click on View, then Label Peaks. You can also generate a list of peaks by going to the menu and click on Process, then Peak Table. A new window with a list of peaks will be displayed. Be aware that each band is a doublet due to the natural presence of the less abundant 37 Cl isotope. Thus only labels on the more intense band of each doublet should be used in your report. 4. To print, select the window you want to print and then go to File, then Print. Make sure you select the proper printer (in Print Setup) before you submit your print job. Suggested printer is the one in SLB319. 5. Repeat the procedure above (steps -4) for the other band. 6. Finally save you may want to save your spectrum as a text file (extension.asc) for your records. Go to File, then Save As, there select from the type file, the ascii (*.asc) option, browse to the Folder indicated by the instructor/ta and Save the file. You will be able to open this file in Excel in case you need it when working on your report. Finishing Up On the computer, select Exit or Close from the File menu, this will close the program. Carefully remove the gas cell from the spectrometer. Your instructor will assist you with emptying the cell.