9.6: Exercise 3 - Modeling Sulfur Dioxide - Comparing the Results of Different Basis Sets and Calculation Models
- Page ID
- 419803
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Exercise 3 - Modeling Sulfur Dioxide: Comparing the Results of Different Basis Sets and Calculation Models
This experiment is designed to explore the performance of various basis sets, models of Ab initio calculations and Semi Empirical calculations, and Density Functional calculations. The SO2 molecule is used as a model.
- Start a New Build.
- To introduce you to another approach to building a molecule, select the Inorganic tab of the builder.
- Build SO2 as follows: Change the element to sulfur.
Select atom hybridization. Double-click in the working area. Rotate the molecule to make all the bonds visible. Select O from the periodic table
and Select
atom hybridization. Click at the ends of the bonds to S to make
.
Select double bond 
from the Bond Order buttons and double-click on both S–O bonds. Be sure they have changed to double bonds.
- Click the
button to do a quick molecular mechanics minimization of the energy.
- Select Setup, Calculations from the menu. Choose calculate: Equilibrium Geometry with Hartree-Fock, 6-31G*. Total charge should be Neutral, and Unpaired Electrons should be 0. Select compute: IR. Click submit. Save the file when prompted and run the calculation.
- From the Summary section of the Output (Display menu), record the energy of the molecule in your lab notebook. Record the frequencies of the SO2 vibrations from the Raman/IR Table section of the Output Summary in your lab notebook.
- Go to the Display Spectra area and view the calculated IR spectrum as you did for HCl and DCl. Animate the vibrations by highlighting the different frequencies. Assign frequencies as ‘symmetric stretch’, ‘bend’, or ‘asymmetric stretch’.
- Close the spectrum window.
- Measure and record the O–S–O angle and the S–O bond length.
- Return to the calculation setup window and repeat the HF calculation with a 3-21G basis set.
- Submit the calculation. Record and compare your results for frequencies, bond length, and the angle with the previous calculation.
- Repeat again using the STO3G basis set, the Semi-Empirical theories PM3, RM1, and AM1, and the Density Functional theory \( \omega\)B97X-D with 6-31G* basis set. It might be a good idea to Save as each time to save each calculation in a separate file. Or if not, at least save a new file for each calculation model (HF, Semi-Empirical, Density Functional.
If you do not save each calculation under a new filename, the new calculation overwrites the old in the current file.
- Fill out the table of Theories and Basis sets for each combination.
- Compare your results with your experimental (FTIR) data for SO2 (CHEM 310 only), and literature data for frequencies, bond length and bond angle. Which combination of theory and basis set gives the most accurate prediction? Close your molecule.
The NIST CCCBDB database is a good source for literature values for the SO2 molecule.
|
Table for SO2 |
Theory |
Basis set |
S–O bond length(Å) |
Bond Angle, (˚) |
\(nu\)1 |
\(nu\)2 |
\(nu\)3 |
|
Ab initio |
HF |
STO-3G |
|||||
|
HF |
3-21G |
||||||
|
HF |
6-31G* |
||||||
|
Semi-empirical |
PM3 |
N/A |
|||||
|
RM1 |
N/A |
||||||
|
AM1 |
N/A |
||||||
| Density Functional | \(\omega\)B97X-D, 6-31G* | ||||||
|
Your exptl. data |
|||||||
|
Literature data* |
|||||||
| * Reference | |||||||
This section of your lab notebook should include:
- A table that records, for each basis set:
- Calculated energy of SO2
- Frequencies of SO2 oscillations
- Assign each frequency ‘symmetric stretch’, ‘bend’, or ‘asymmetric stretch’. You only have to do this for one basis set.
- S-O bond length
- O-S-O bond angle
- Comparison of calculated results to experimental (CHEM 310 only) and literature values
- Which combination of theory and basis set gives the most accurate prediction?
(See your ELN template for details)