1. Expanded Choices for Vibration-Rotation Spectroscopy in the Physical Chemistry Teaching Laboratory Joel R. Schmitz and David A. Dolson Department of Chemistry Wright State University Dayton, OH

2. Traditional Vibration-Rotation Spectrum Experiment in the Teaching Laboratory  Quantum mechanical and spectroscopy theory is reinforced to third year Physical Chemistry students in the laboratory through laboratory experience with vibration-rotation spectroscopy.  Stafford et al. 1 introduced vibration-rotation spectroscopy of HCl vapor in teaching laboratories in 1963.  With time, many other molecular choices were demonstrated in the chemical education literature.  Gaseous hydrogen chloride (HCl) has remained the common molecule of choice due to its simple synthesis or availability, simple & resolvable P/R branch structure, isotopic variance, and strong infrared (IR) spectrum. 1. Stafford, F. et al., J. Chem. Educ. 1963,40, 245-249.

3. Figure 1. Fundamental vibrational band 2 with rotational branches of HCl at 2860 cm -1. 2. Schwenz, R. et al., J. Chem. Educ., 1999, 76, 1302-1307.

4. Selected Literature  Various analysis methods (difference methods, polynomial fits, multiple linear and nonlinear regressions, global analysis with multiple isotopomers) have been suggested by Schwenz et al. 2, Iannone 3, and Tellinghuisen 4.  Deuteration methods for HCl/DCl & HBr/DBr preparation have been suggested by Rieck et al 5, Ganapathisubramani 6 and Lehmann et al 7. 1.Stafford, F. et al., J. Chem. Educ. 1963,40, 245-249. 2.Schwenz, R. et al., J. Chem. Educ. 1999, 76, 1302-1307. 3.Iannone, M., J. Chem. Educ. 1998, 75, 1188-1189. 4.Tellinghuisen, J. J. Chem. Educ. 2005, 82, 150-156. 5.Rieck, D. F., J. Chem. Educ. 1989, 66, 682. 6.Ganapathisubramani, N. J. Chem. Educ. 1993, 70, 1035. 7.Lehmann, E. et al., J. Chem. Educ. 2010, 87, 1402.

5. Improved Instrumental Resolution Offers New Choices for Molecular Samples  Choices include other linear molecules: HBr/DBr, HCN/DCN, C 2 H 2 /C 2 D 2, CO, CO 2, OCS and N 2 O...  HCl/DCl and HBr/DBr 1-0 & 2-0 vibration-rotation spectra (without halogen isotope resolution) can be obtained with 2 cm -1 resolution.  Increasingly improved instrumental resolution (to 0.25 and 0.125 cm -1 ) is becoming available to academic teaching laboratories, which is sufficient to resolve H 79 Br/D 79 Br vibration-rotation lines.  Many 13 CO and 13 CO 2 lines may be resolved in fundamental IR spectra of natural abundance gas samples with resolutions of 0.5 cm -1 and better. (RC09 - Dolson & Anders)  Vibration-rotation lines of O 13 CS/O 12 CS may be resolved in the fundamental C=O stretching band of a natural abundance gas sample with a resolution of 0.125 cm -1

6. Sample Preparation

7. Figure 2. HBr fundamental band.Figure 3. HBr overtone band.

8. Figure 4. Isotopic splitting of the R(1) peak of the HBr fundamental at 0.125 cm -1 resolution. Figure 5. Isotopic splitting of the R(1) peak of the HBr fundamental at 0.25 cm -1 resolution.

9. Figure 6. DBr fundamental band.Figure 7. DBr overtone band.

10. Data Analysis 8. Dunham, J.L., Phys. Rev. 1932, 41, 721-731.

11. Dunham Coefficient ParameterValue (cm -1 ) Literature Value 9 (cm -1 ) Y 10 ωeωe 2649.39(2)2649.3698(88) -Y 20 ωexeωexe 45.55(1)45.5795(70) Y 01 BeBe 8.4643(1)8.464877(37) -Y 11 αeαe 0.23257(8)0.233254 (88) -Y 02 DeDe 3.434(5) x 10 -4 3.4579(18) x 10 -4 Y 12 βeβe 3.4(2) x 10 -6 3.99 (24)x 10 -6 Table 1. Vibration-rotational constants for H 81 Br. 9. Stocker & Goldman, J. Quant. Spectrosc. and Radiat. Transfer 1976, 16, 335-346. Average Residual: 0.0085 cm -1 Maximum Residual: 0.0410 cm -1

12. Determination of CO Vibration-Rotation Constants 10. Mina-Camilde, N. et al., J. Chem. Educ. 1996, 73, 804-807.

13. Figure 6. 12 CO fundamental band. Figure 7. 12 CO overtone band.

14. Figure 8. Expanded view of CO fundamental P-branch to show 13 CO lines.

15. Dunham Coefficient Parameter Value (cm -1 ) Literature Value 11 (cm -1 ) Y 10 ωeωe 2169.745(5)2169.812670(13) -Y 20 ωexeωexe 13.237(2)13.28787634(774) Y 01 BeBe 1.93134(7)1.931280985(18) -Y 11 αeαe 1.7505(3) x 10 -2 1.75043923(130) x 10 -2 -Y 02 DeDe 6.14(5) x 10 -6 6.121615183(892) x 10 -6 Table 2. Vibration-rotational constants for 12 C 16 O. 11. Farrenq et al., J. Mol, Spectrosc. 1991, 149, 375-390. Average Residual: 0.009 cm -1 Maximum Residual: 0.066 cm -1

16. Conclusions  Infrared vibration-rotation spectroscopy is used in the teaching laboratory to reinforce fundamental quantum concepts and spectroscopic theory.  Typically HCl/DCl is the chosen molecule for experiments, but higher resolution makes other options available.  HBr/DBr and CO were synthesized and the vibration-rotation constants for the various isotopomers were determined through non-linear regressions in terms of Dunham coefficients.  Experimentally determined spectroscopic constants are in satisfactory agreement with literature values.  Laboratory instructors have more choices of molecules to conduct vibration-rotation spectroscopy, as instrument resolution permits. ( 12/13 C isotopomers of CO, CO 2, OCS; 79/81 Br isotopomers of HBr/DBr)

18. Vibration-Rotation Analysis by Polynomial Fit of Frequency (cm -1 ) vs. m Plots  = 0 + (B+B  ) m + (B-B  ) m 2 – 4·D m 3  m = - J  for P-branch lines  m = J  +1 for R-branch lines  0 is the band center  B v = B e -  e (v+½) + · · ·  Examine residuals after cubic fit to determine if a quartic fit is warranted – redefines quadratic and cubic coefficients.  D v = D e -  e (v+½) + · · · Herzberg vol I, Eq III-139