Download Project 1: Infrared Spectra of Volcanic Plumes

Chemistry 362
Spring 2017
Dr. Jean M. Standard
February 17, 2017
Project 1: Infrared Spectra of Volcanic Plumes
In this project, you will carry out some quantum mechanical calculations for a variety of diatomic and polyatomic
molecules. This involves determining the equilibrium geometry of each molecule and then the vibrational
frequencies. The molecules that you will study are related to a topic from the chemical literature on remote infrared
spectroscopy for the study of volcanic plumes.
The computer program that you will use for these simulations is a software package called Gaussian for the
quantum mechanical calculations and a software package called Avogadro for visualization. You will be able to
access Gaussian and Avogadro in the computer lab located in Julian Hall Room 216. Please note that the computers
in the JH 216 are usually available at any time during the day; however, they are occasionally reserved for classes as
noted on the schedule posted on the door.
This project requires you to complete calculations for a number of molecules using the Avogadro/Gaussian software
packages. You may use any of the Macintosh computers in JH 216 to access the Avogadro/Gaussian programs
(instructions are provided later in this handout). In fact, you can use one Macintosh for one part of the project, and
another Macintosh for another part of the project since none of the data is stored on the Macs. All the calculations
actually will be carried out on Linux workstations that you will connect to from the Macintosh computers.
This portion of the project is worth 19 points and is due on Friday, March 3, 2017.
[Note that 6 points out of the total of 25 points for this project have already been awarded based on the introductory
assignment that you completed during the first week of classes.]
THEORETICAL BACKGROUND
Introduction
Quantum chemistry is the study of molecular structure, bonding, dynamics, interactions, and reactions via quantum
mechanics. Because of the complexity of the equations involved, it is feasible to apply quantum mechanics to only
the simplest of molecular systems without the aid of computational methods. In this project, the Gaussian software
package (Gaussian, Inc.) will be demonstrated as a tool for quantum chemical calculations with the Avogadro
software package for visualization.
In order to apply quantum mechanics to a molecule, we must solve the Schrödinger equation, Hˆ ψ = Eψ , for the
system. The Hamiltonian operator Hˆ is the sum of the kinetic energy and potential energy operators, and E is the
2
energy of the molecule. The wavefunction ψ contains all the information about the system. For example, ψ (or
ψ *ψ if ψ is complex) is the total electron density of the molecule.
€
€
€
€ as the hydrogen atom, the Schrödinger equation cannot be solved
For all but the simplest systems, such
exactly. In
€
€ quantum chemistry, two assumptions are generally made to enable us to find approximate solutions of the
Schrödinger equation. The first is that if we are interested in the electron density of a molecule (which tells about
bonding and potential reactive sites, among other things), then we can consider that the nuclei are fixed. This
assumption is called the Born-Oppenheimer approximation, and it works because the electrons are much lighter (and
faster) than the nuclei.
A second assumption that is generally made in quantum chemistry is that the molecular orbitals are made up of
linear combinations of atomic orbitals (the familiar s, p, d, and f-type atomic orbitals). For example, we can take the
two 1s atomic orbitals on two hydrogen atoms and combine them in two ways to obtain a bonding orbital and an
antibonding orbital for the H2 molecule:
ψ MO ( bonding) = ψ1sA + ψ1sB
ψ MO ( antibonding) = ψ1sA − ψ1sB .
Here, A and B are labels that denote the orbitals located on the two different hydrogen atoms. For most of the
project, you will employ a quantum
mechanical technique called density functional theory (and in specific, the
€
B3LYP model). This method is one of the most common approaches employed today to solve the Schrödinger
equation, and represents a good balance between accuracy and calculation time.
Geometry Optimization
One of the major uses of quantum calculations is to determine the equilibrium structure of a molecule. For H2, for
example, we can vary the bond distance (R) between the two H atoms and calculate the energy E by solving the
Schrödinger equation. If we plot E versus R, we get a curve similar to the one shown in Figure 1.
E
R
Figure 1. A sketch of energy versus bond distance for a diatomic molecule.
The minimum energy in the plot corresponds to the equilibrium structure. The process of finding the geometry
corresponding to the minimum energy is called geometry optimization. The same approach can be used to
determine the equilibrium structure of a polyatomic molecule except that the curve will be multidimensional,
depending upon all the coordinates in the molecule.
Molecular Vibrations
Though quantum calculations may be used to determine a wide variety of molecular properties, one of the most
useful molecular properties is the set of harmonic frequencies of vibration. Vibrational motion in molecular systems
is an important tool for structural and functional group identification from infrared and Raman spectroscopy.
Vibrational motion is related to the motion of the nuclei in the molecule, and for a nonlinear polyatomic molecule
containing N atoms, there are 3N-6 molecular vibrations (3N-5 for a linear molecule).
The frequencies of the vibrations are related to the curvature of the energy vs. coordinate plot. For our example of
H2 discussed above, the harmonic frequency of vibration ( ν 0 ) is given by
1/ 2
1 $k'
ν0 =
& ) ,
2π % µ (
€
where µ is the reduced mass and k is related to the second derivative of the energy E at the minimum ( R = Ro ),
€
k =
€
d 2E
dR 2
.
R =R o
€
2
3
USING THE COMPUTERS AND THE AVOGADRO SOFTWARE PACKAGE
This section contains instructions for logging in to the Macintosh computers in JH 216 and accessing the Linux
computers on which the calculations will be performed. In addition, it provides instructions on how to start the
Avogadro software package. The use of the Gaussian software package will be described later.
Logging In
To log in to one of the Macintosh computers in JH 216, enter your ISU ULID and password.
Starting X11
In order to access the Linux workstations to run the Avogadro/Gaussian software packages, you must run a software
package on the Mac called X11. To start the X11 application, find it in the Applications and then Utilities folder;
then double click to start the application. 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
Each person will be assigned one of the six available Linux computers to use for the project. To log on to the Linux
computer to which you were assigned, type the following command in the xterm window:
ssh –Y [email protected]
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 were assigned (options: frodo, samwise, gandalf,
aragorn, legolas, gimli). The password is "wavefun". Enter the password as prompted. Once you have done this,
you are connected to the Linux computer.
Starting the Avogadro Program
To start the Avogadro program, type "avogadro" in the xterm window and hit the return key. A window for the
Avogadro software package should appear on your screen. At this point, you are ready to begin the project.
PROJECT 1 PROCEDURE: Infrared Spectra of Volcano Eruptions
This project illustrates the role of computational chemistry as an analysis tool. Suppose that you are a scientist who
is interested in studying volcano eruptions. You wish to determine the composition of the gases that are venting
from a crater, for example. How do you do it? It is obviously not very safe to get close enough to the crater to bring
a spectrometer to the site and perform measurements. Likewise, it is not particularly easy (or smart) to go to the site
and collect samples of gas to be analyzed after returning to the laboratory. After the spectra are obtained, they must
be analyzed. This can be done either by comparing the spectra to experimental spectra of known compounds, or by
comparing the experimental spectra to values obtained from calculations, or by a combination of both approaches.
There are a variety of approaches to study gases venting from a volcano during and after an eruption. Popocatepetl,
shown in Figure 2, is a volcano located in Mexico that stands 13,776 ft above the surrounding basin. The name
Popocatepetl, meaning "Smoking Mountain," was given to the volcano by the Aztecs, and suggests that the volcano
has long been active. Accurate knowledge of the activity of this volcano reaches back to the first days of Spanish
conquest. Popocatepetl has erupted dozens of times, with more recent activity starting in 1994 after being dormant
for nearly 50 years; the volcano has since continued its activity to the present day. A 1998 article in Nature by S. P.
Love and coworkers [S. P. Love, F. Goff, D. Counce, C. Siebe, and H. Delgado, Nature 396, 563-567 (1998)]
describes an approach employed to study the eruption of Popocatepetl using remote infrared spectroscopy.
4
Figure 2. Popocatepetl volcano.
Major volcanic eruptions have the capability of emitting large amounts of ash and hot gases into the atmosphere.
Another article by von Glasow and coworkers published in Chemical Geology in 2009 describes in detail some of
the atmospheric impacts of volcanic eruptions [R. von Glasow, N. Bobrowski, C. Kern, Chem. Geol. 263, 131-142
(2009)].
To complete the project, please read the articles, perform the calculations, and respond to the questions that are
posed below. Some of the questions are general and do not require the results of the Avogadro/Gaussian
calculations. You may find the answers to many of the general questions in the Nature and Chemical Geology
articles; however, some of the questions will require you to find the answers on the internet. The parts of the project
that involve direct use of the Avogadro/Gaussian software packages are marked with asterisks.
1. Volcanoes and Volcanic Gases (4 points)
1a. Popocatepetl is a type of volcano known as a stratovolcano. What exactly is a stratovolcano?
1b. Are stratovolcanoes common or not? Explain. Are there any other stratovolcanoes in North America? If so,
provide two or three names and locations of North American stratovolcanoes (besides Popocatepetl) and
whether or not they have experienced "recent" activity (last 30 years).
1c. Provide a list of the gases from the volcanic eruption that have been observed in the spectra shown in the Nature
article. Are there other gases that are typically emitted in significant amounts during a volcanic eruption that
are not shown in the spectra provided in the Nature article? List them.
1d. A striking example of the impact of volcanic eruptions on atmospheric chemistry was observed with the 1991
eruption of Mount Pinatubo in the Phillipines. What impact did this eruption have on the global surface
temperature in the year or two following the eruption? What was the cause of this perturbation in global surface
temperature?
2. Vibrations and Infrared Spectra of HF and HCl (4 points)
*2a. The first molecule that you will perform calculations on using the Avogadro/Gaussian software packages is
hydrogen fluoride, HF. Following the instructions above to start the Avogadro software package should lead to
a window similar to the one shown in Figure 3 appearing on your screen.
Figure 3. 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 HF molecule, click on the Drawing Tool,
. Set the Element to
Fluorine, Bond Order to Single, and make sure that "Adjust Hydrogens" is selected. Then, click with the left
mouse button in the Avogadro window and the HF molecule should be displayed in a manner similar to that
shown in Figure 4.
Figure 4. The initial structure of the HF molecule.
5
6
The next step is to perform a quantum mechanical calculation of the HF molecule using the Gaussian software
package. The equilibrium geometry and vibrational frequencies of the molecule will be determined. From the
Avogadro menus at the top of the window, select "Extensions → Gaussian". You should see a popup window
similar to that shown in Figure 5.
Figure 5. Setting up a Gaussian calculation.
Make sure that the following settings are entered for the calculation:
Calculation: Frequencies
Processors: 2
Theory: B3LYP
Basis: 6-31G(d)
Charge: 0
Multiplicity: 1
Once the settings are correct, click "Compute". You will be prompted to enter a filename. Use the filename 'hfXYZ.com', where 'XYZ' corresponds to your initials. After the filename is entered, click "Save". The
calculation will begin and you should see a popup window appear that says "Running Gaussian calculation...".
When the popup window disappears, your calculation of the HF molecule should be complete. The results from
the completed calculation should then load automatically into the Avogadro window.
Since HF is a diatomic molecule, it possesses only a single vibrational frequency. The vibrational frequencies
should be listed under the heading "Vibrations" to the right of the Avogadro molecular display. The single
vibrational frequency should be reported in cm–1 along with the predicted IR intensity of the peak. Record the
frequency value in cm–1.
7
*2b. Repeat the procedure outlined in step 2a to use Avogadro to construct the HCl molecule and carry out a
Gaussian calculation of the vibrational frequency of the HCl molecule. (You may open a new builder window
in Avogadro by selecting "File → New".)
2c. Look up literature values of the vibrational frequencies of the HF and HCl molecules. The literature values that
you are looking for are called the harmonic vibrational frequencies. Good places to find these include your
textbook and the NIST web site (webbook.nist.gov). Please see Dr. Standard if you need assistance in finding
the literature values.
Compare the literature values for the HF and HCl frequencies to your calculated frequencies. Report the
percent differences.
2d. In Figures 2a and 2b of the Nature article, a progression of many peaks is seen in the infrared spectra for both
HCl and HF. Explain qualitatively what types of energy level transitions lead to the progression of peaks.
[Hint: read the figure caption.]
2e. For HCl in Figure 2a of the Nature article, a doublet-like structure is observed in the progression of peaks.
Explain the origin of the "doublet" structure. [Hint: read the figure caption.]
3. Vibrations and Infrared Spectrum of Sulfur Dioxide
*3a. Start the Avogadro program and build the SO2 molecule. An easy way to do this is to click on the Drawing
Tool. Select Element: Sulfur, Bond Order: Single, and make sure this time to uncheck "Adjust Hydrogens".
Click with your mouse in the drawing window to place a single sulfur atom. Then switch the element to oxygen
and place two oxygen atoms on the screen in a nonlinear arrangement in the order O-S-O as shown in Figure 6.
Figure 6. Placement of sulfur and oxygen atoms on the screen to form the beginnings of the SO2 molecule.
Now, use the mouse to draw bonds between the sulfur and oxygen atoms in order to complete the construction
of the SO2 molecule. A double bond may be included by clicking on a single bond once it is drawn in. When
finished, your structure should look similar to that shown in Figure 7.
8
Figure 7. Completed drawing of the SO2 molecule.
Next, perform a quantum mechanical calculation of the SO2 molecule using the Gaussian software package.
The equilibrium geometry and vibrational frequencies of the molecule will be determined. From the Avogadro
menus at the top of the window, select "Extensions → Gaussian". Use the same settings as in step 2a and
Figure 5:
Calculation: Frequencies
Processors: 2
Theory: B3LYP
Basis: 6-31G(d)
Charge: 0
Multiplicity: 1
Once the settings are correct, click "Compute". You will be prompted to enter a filename. Use the filename
'so2-XYZ.com', where 'XYZ' corresponds to your initials. After the filename is entered, click "Save". The
calculation will begin and you should see a popup window appear that says "Running Gaussian calculation…".
When the popup window disappears, your calculation of the SO2 molecule should be complete. The results
from the completed calculation should then load automatically into the Avogadro window.
*3b. Since sulfur dioxide is a nonlinear molecule, you should expect 3N-6 vibrational frequencies, where N is the
number of atoms in the molecule. The vibrational frequencies should be listed under the heading "Vibrations"
to the right of the Avogadro molecular display.
Record the vibrational frequencies in cm–1. To display an animation of a particular vibrational mode, click on
the row corresponding to the vibrational frequency that you want to view, and then click the "Start Animation"
button. You may need to rotate the molecule on the screen to get a better visual idea of the vibrational motion.
A molecule may be rotated using the left mouse button if the Navigation Tool
is selected.
Provide a short description and sketch the type of vibration that you observe for each frequency. For example,
you might list symmetric or antisymmetric S-O stretch or O-S-O bend.
3c. Explain which of the vibrations of SO2 are expected to be infrared active and why. A molecular vibration will
be infrared active if the vibration involves a change in the dipole moment of the molecule. See your textbook
for more information on infrared activity.
9
3d. From the Nature article, report the positions in wavenumbers of the vibrational bands that are observed for SO2
in the volcanic spectra. Note that there is more than one observed band for SO2 – make sure that you refer to
both Figures 1 and 2 in the article. Compare these to your calculated values from the Gaussian program. To
which vibrational modes might the experimental bands correspond? Explain.
4.
Vibrations and Infrared Spectrum of Silicon Tetrafluoride (4 points)
*4a. Use the Avogadro software package to build a model of the silicon tetrafluoride (SiF4) molecule. This molecule
has a tetrahedral shape like methane. An easy way to do this is to click on the Drawing Tool. Select Element:
Other and choose Silicon from the periodic table, Bond Order: Single, and check "Adjust Hydrogens". Click
with your mouse in the drawing window to place a single silicon atom. The silicon atom should appear with
four hydrogen atoms around it in a tetrahedral arrangement. Switch the element to fluorine and click on each of
the hydrogen atoms to convert them to fluorine atoms. When finished, you should have a structure for SiF4
similar to that shown in Figure 8.
Figure 8. Completed drawing of the SiF4 molecule.
Perform a quantum mechanical calculation of the equilibrium geometry and vibrational frequencies of SiF4
molecule using the Gaussian software package. From the Avogadro menus at the top of the window, select
"Extensions → Gaussian". Use the same settings as in steps 2a & 3a and Figure 5:
Calculation: Frequencies
Processors: 2
Theory: B3LYP
Basis: 6-31G(d)
Charge: 0
Multiplicity: 1
Once the settings are correct, click "Compute". Use the filename 'sif4-XYZ.com'. After the filename is entered,
click "Save". The calculation will begin and you should see a popup window appear that says "Running
Gaussian calculation…". When the popup window disappears, the calculation of the SiF4 molecule should be
complete. The results from the completed calculation should then load automatically into the Avogadro
window.
10
*4b. The vibrational frequencies of SiF4 should be listed under the heading "Vibrations" to the right of the Avogadro
molecular display. Record the vibrational frequencies in cm–1. Because of the tetrahedral symmetry of SiF4,
there will be degeneracies in the vibrational frequencies. Make sure that you note the degeneracy of each of
the vibrations (for example, not degenerate, doubly degenerate, triply degenerate). Assume that two or more
frequency values are degenerate if they are within ~1-2 cm–1 of each other and the intensities are also nearly the
same.
Display each vibration on the screen and provide a short description and sketch of each type of vibration that
you see. It may help to rotate the molecule to better observe the vibrational motion in and out of the plane of
the screen.
When you are finished, select "File → Quit" to close the Avogadro software program. To log off the Linux
workstation, type "exit" in the xterm window. Don't forget to log off the Mac when you are done, too!
4c. Explain which of the vibrations of silicon tetrafluoride are expected to be infrared active and why.
4d. Use the NIST WebBook (webbook.nist.gov) to find an experimental IR spectrum for silicon tetrafluoride in the
gas phase. Make sure you display the spectrum in absorption mode rather than %transmittance. Include a copy
of the spectrum, and assign the major (most intense) peak(s) that you observe in the spectrum by comparing the
peak frequencies to the vibrational frequencies that you calculated for this molecule. Are there IR active modes
that are not observed in the NIST spectrum? Explain.
4e. One of the low intensity peaks in the SiF4 IR spectrum from NIST that appears at about 1200 cm–1 is called a
combination band. A combination band arises from an excitation of two different vibrational modes at once (in
a combination). The frequency of absorption for combination bands is approximately equal to the sum of the
harmonic frequencies for each of the two vibrational modes that are involved in the combination band. From
your calculated vibrational frequencies, list the possible combinations of vibrational modes that could correlate
with the combination band at about 1200 cm–1 in the SiF4 spectrum.
5.
Volcanic Production of Silicon Tetrafluoride (3 points)
5a. What are the melting and boiling points of SiF4? Is there anything unusual about these values? How do the
melting and boiling points of SiF4 compare with those of the carbon analogue, CF4? Discuss.
5b. From the article in Nature, from where does the observed SiF4 found in the volcanic plume originate?
5c. What is the balanced chemical reaction that produces SiF4 in the volcanic plume?