Chem 2302 Organic IR Winter 2012
Infrared Stretching Modes of Common Organic Molecules Introduction The infrared (IR) vibrational spectra of polyatomic molecules reflect complicated motions. These molecules have 3n-­‐6 normal modes of vibration, where n is the number of constituent atoms in the molecule. Each of these modes involves concerted and approximately harmonic motion of some or all of the atoms in the molecule. A rigorous model used to predict the frequency of these vibrations must take into account the masses of all the atoms in the molecule, the force constants associated with each possible stretch, bend, twist and deformation of the molecular framework, and the interactions between these motions. Such a model is mathematically complex. Fortunately, most normal vibrational modes of bond stretching primarily involve the motion of only two atoms. For example, a carbonyl stretching mode primarily involves the motion of the C and O atoms. Since the other atoms in the molecules remain almost motionless, vibrations for a particular functional group give rise to IR absorptions that fall within a certain narrow range of wavenumber (cm-­‐1) values. For example the carbonyl stretch for acyclic ketones is usually a strong band in the 1700-­‐1730 cm-­‐1 range. Knowing the wavenumber ranges associated with the functional groups (sometimes called "characteristic group frequencies") allows the prediction of functional groups present in a molecule by simply “eyeballing” its IR spectrum. It is possible to model the stretching mode of various functional groups using a diatomic species comprised of the two atoms after which the mode is named (i.e. C-­‐H stretch is modelled by a diatomic C-­‐H molecule). This approach requires that the diatomic species have the same bond order as the bond in question. The problem can be treated with the known solution to the quantum harmonic oscillator model. This model will only work for stretching vibrational modes since other modes (like bending) involve the motion of more than two atoms. The harmonic oscillator model is the simplest model for a vibrating diatomic molecule consisting of two atoms having masses 𝑚𝑚 and 𝑚𝑚 . The allowed energy levels, 𝐸𝐸 (𝜐𝜐), for a harmonic oscillator are 𝐸𝐸(𝜐𝜐) = ℎ𝜈𝜈 𝜐𝜐 +
1
, 𝜐𝜐 = 0, 1, 2, 3, … 2
Equation 1 where ℎ is Plank’s constant, 𝜈𝜈 is the vibrational frequency and , and 𝜐𝜐 is the vibrational quantum number. The fundamental vibrational transition energy is given by the following expression Page 1 of 6 Chem 2302 Organic IR 𝜈𝜈 =
Winter 2012
1
𝑘𝑘
2𝜋𝜋𝜋𝜋 𝜇𝜇
Equation 2 where c is the speed of light (in cm/s), 𝑘𝑘 is the force constant and 𝜇𝜇 is the reduced mass, which is given by 𝜇𝜇 =
. Note that using units of cm/s for 𝑐𝑐 will yield 𝜈𝜈 in units called wavenumbers (cm-­‐1), which are the conventional units to report infrared absorptions. Extension of this model to polyatomic molecules can be made if we assume that the portion of the molecule involved in the stretching motion is similar in behaviour to a diatomic molecule consisting of the two atoms after which the mode is named. With this assumption, the only variable remaining in equation 2 is the force constant, which essentially is a measure of bond strength. Covalently bound molecules consisting of C, H, O and N atoms form a family of compounds having similar bond strengths. Thus, bond dissociation energies for covalent bonds in typical organic compounds usually fall in the range of 300 – 400 kJ/mol and have force constants of 500 – 700 N/m. The model can be further generalized by invoking the following rule: “the force constant for a given type of bond stretch is proportional to the bond order for that bond”. Therefore, the force constant for a given type of single bond stretching mode will double if the bond order is two and will triple if the bond order is three. An equation can now be written for the prediction of the wavenumber of absorptions associated with all stretching modes of CHON molecules, irrespective of bond order, using an effective single-­‐bond force constant, 𝑘𝑘 : 𝜈𝜈 =
𝛼𝛼𝑘𝑘
1
𝜇𝜇
2𝜋𝜋𝜋𝜋
Equation 3 where 𝛼𝛼 is the order of the bond in question. Values of 𝑘𝑘 will be calculated for many functional groups appearing in the molecules for which IR spectra are obtained. The best value of 𝑘𝑘 is given by: 𝑘𝑘 = 𝛽𝛽 𝑘𝑘 Equation 4 where 𝛽𝛽 is a “refinement constant”. It will be determined from the slope of a 𝜈𝜈 vs. 𝜈𝜈 plot. 𝜈𝜈 𝑘𝑘 = 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 ×𝜈𝜈 Equation 5 Note that forcing the line to pass through the origin is implied by the form of equation 5. The equation for the best value of the effective force constant, 𝑘𝑘 , is by definition: Page 2 of 6 Chem 2302 Organic IR Winter 2012
𝜈𝜈 𝑘𝑘 = 1.0 ×𝜈𝜈 Equation 6 Dividing equation 5 by equation 6, on substitution of equation 2 for 𝜈𝜈 , yields an expression relating 𝛽𝛽 to the slope of the 𝜈𝜈 vs. 𝜈𝜈 plot 𝜈𝜈 𝑘𝑘
𝜈𝜈 𝑘𝑘
=
𝛼𝛼𝑘𝑘
1
2𝜋𝜋𝜋𝜋
𝜇𝜇
𝛽𝛽𝛽𝛽𝑘𝑘
1
2𝜋𝜋𝜋𝜋
𝜇𝜇
=
1
= 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 𝛽𝛽
Equation 7 Thus, 𝛽𝛽 =
1
𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 Equation 8 Experimental Procedure The infrared spectra of acetone, acetonitrile, butanamine, cyclohexene, and propanol will be measured using the attenuated total reflectance (ATR) module of the Bruker Alpha IR spectrometer located in C-­‐3041. This instrument is new and very expensive (even though it’s very small). Please treat it with care! 1. The IR spectrometer’s computer must be booted into Windows XP. If Windows 7 is running, restart the computer and choose Windows XP when the operating system choices screen appears. Log on to XP using the account named Nick. The password is bruker. 2. On the desktop, double-­‐click on the OPUS icon and login using the account named Chem. 2302 student using the password physchem. 3. If the green light on the instrument is blinking it is on standby mode. Press the (very) small green button on the back of the instrument to turn it on. The instrument will take approximately 7 minutes to warm up. During this time the status light in the bottom right corner of the OPUS window will be yellow. The instrument is ready when the OPUS status light turns green. 4. The ATR module will be used to obtain spectra, however, the standard sample holder is most likely installed. Consult an instructor who will explain how install the ATR module. Immediately after it is installed, the instrument will run a module test. Please wait until OPUS reports that the test is complete (lower right corner) before proceeding. Page 3 of 6 Chem 2302 Organic IR Winter 2012
5. Setup the experiment parameters by clicking on... The arrow next to the Measurement button on the toolbar Setup “Measurement” Check Signal tab **Wait for peak to appear** Save Peak Position Advanced tab Load Organic IR Experiment.xpm OPEN Save and Exit 6. Click the Measurement button on the tool bar and type the sample name (i.e. acetone) and form (i.e. liquid) 7. Without anything on the ATR’s small diamond crystal, click Start Background Measurement. The number of scans that the instrument has completed is shown in the status bar on the bottom of the screen. 8. When “No active task” appears in the status bar, use a small dropping pipette to place a few drops of the organic liquid to be analyzed on the diamond crystal. Click Start Sample Measurement. 9. When “No active task” appears in the status bar, use a Kimwipe to remove the organic liquid from the diamond crystal. Rinse the crystal with ethanol and remove it with another Kim-­‐wipe. 10. Zoom in on the area of interest in the spectrum, if necessary. 11. Click the black arrow next to the Peak Picking button and select Interactive Peak Picking. Drag the box in the middle of the spectra so that the desired peaks are labeled with the wavenumber of their maxima. 12. Make sure save changes, print, unload and measure next sample are checked under the Report tab of the side bar and click Go. 13. Repeat steps 8 – 12 for each additional organic liquid to be studied. 14. If you need to open any of the spectra again you will find the files in the following folder: D:\Documents and Settings\Nick\My Documents\My IR Spectra\chemistry 2302 student\<Today`s Date>\ Page 4 of 6 Chem 2302 Organic IR Winter 2012
Results You will follow the following steps to develop a model for predicting absorption wavenumbers for functional groups in covalently bonded organic molecules: Experiment Analyze Calculate • Measure IR spectra of common organic molecles • Print spectra • Iden�fy all stretching modes • Record peak absorp�on wavenumbers • Effec�ve single-­‐bond force constants for "diatomic molecules" • Average Predict Op�mize Check / Test • Use average effec�ve force constant to predict absorp�on wavenumbers for all diatomic func�onal groups • Plot predicted vs observed wavenumbers • regression analysis to determine slope of best-­‐fit line • Calc op�mized value of force constant • Re-­‐plot graph and check that slope is very close to 1 Extrapolate Using a table of group frequencies (see handout provided to you during the experiment) identify, directly on your spectral printouts, the absorptions corresponding to all stretching vibrations of your molecules. This should include absorptions for C-­‐H, C=C, O-­‐H, N-­‐H, C≡N, C=O and any other stretching modes you can think of for which you have group frequency data. Choose only one C-­‐H stretching mode involving an sp3 carbon and only one involving an sp2 carbon. Note that C-­‐C stretching absorptions tend to be very weak and are normally not observed in IR spectra. • Use op�mized model to predict vibra�onal frequency ofdiatomic func�onal gropus not contained in the molecules studied in this experiment. Use Excel to create a table to organize the data you have gathered. Set up columns for substance name, bond name, bond order, mass of atom1, mass of atom2, observed wavenumber 𝜈𝜈 (of absorption maxima), and literature wavenumber (from group frequency table). For methanol, for example gather data for the absorptions that correspond to the C-­‐H, C-­‐O and O-­‐H bond stretches. In two subsequent columns, calculate the reduced mass, µ, and the force constant K (using equation 2) for each bond. Here we will assume that the quantum-­‐mechanical harmonic oscillator model is followed and that the vibration is associated with a diatomic molecule consisting of the two atoms in question. For example, for a carbonyl stretching mode, assume that the mode is associated with the stretching mode of a C=O molecule. (Note that we must assume bond orders that are inappropriate for a true diatomic molecule, i.e., the diatomic molecule consisting of one C and one O atom is C≡O but we assume it is C=O). Page 5 of 6 Chem 2302 Organic IR Winter 2012
Assuming a linear relationship between bond order and force constant, calculate the effective single-­‐bond force constants, keff, in the next column by dividing the calculated force constants by the bond orders. Now calculate the average value of keff below the generated values in your spreadsheet. Label the next column “predicted wavenumber”. Using your average value of keff, generate predicted vibrational wavenumbers 𝜈𝜈 for all observed modes (using equation 3) for which you have recorded data. Plot a graph of 𝜈𝜈 vs. 𝜈𝜈 . Preform a regression analysis on this data, restricting the line to pass through the origin. The best value of keff will yield a slope of 1, indicating that, on average, 𝜈𝜈 is the same as 𝜈𝜈 . Calculate a value of the refinement constant, 𝛽𝛽 , using equation 8 and then calculate the optimal value of the effective single-­‐bond force constant, kopt, with equation 4. Recalculate the predicted vibrational wavenumbers in a column labeled “optimized wavenumber”, 𝜈𝜈 . Plot a new graph (of 𝜈𝜈 vs. 𝜈𝜈 and show that the slope of the regression analysis is, in fact, very close to 1. You now have a “refined” model with which you can predict vibrational wavenumbers associated with stretching modes of covalently bound molecules containing C, H, O and N atoms. Since this model was developed using molecules containing only the atoms mentioned, you should not expect it to be able to accurately predict vibrational wavenumbers of stretching modes for molecules that are not in this family. To prove this, in a new spreadsheet, use your model to calculate the vibrational wavenumbers associated with stretching modes for the following functional groups (notice that the bolded functional groups ARE in the family of molecules that we have studied): C=S, C=N, P=O, S=O, N=O, S-­‐H, Si-­‐H, C-­‐F, C-­‐Cl, C-­‐Br In the next blank column, tabulate the expected vibrational wavenumbers using group frequency (literature) data and then calculate the percent error for each. Discussion Functional groups within covalently bound molecules can be identified using IR spectroscopy due to the variation in absorptions of these groups. What are the two major factors causing this variation? Compare your optimized predicted wavenumbers (for vibrational modes for which you collected data) to the provided list of group frequencies. What does this indicate about the validity of your model (and the assumptions that were made)? Why is there some discrepancy between your observed wavenumbers and those provided in the table of group frequencies? Comment on the effectiveness of your model when it is used to predict the absorption frequencies of stretching vibrational modes associated with functional groups that are not in the family of groups used to develop your model. How will the force constant for these groups compare to your optimized force constant? References 1. J. Mark Parnis and Matthew G. K. Thompson, Journal of Chemical Education 81 (2004), 1196. 2. Peter Atkins and Julio de Paula, ``Physical Chemistry``, 7th ed., W. H. Freeman and Company, 2002. Page 6 of 6