70th ISMS Vibration-Rotation Analysis of the 13 CO 2 Asymmetric Stretch Fundamental Band in Ambient Air for the Physical Chemistry Teaching Laboratory David A. Dolson and Catherine B. Anders Department of Chemistry Wright State University Dayton, Ohio

70th ISMS Perspective Acquisition and analysis of infrared vibration-rotation spectra in the physical chemistry teaching laboratory supports the (an)harmonic oscillator, (non)rigid rotor and molecular spectroscopy lecture topics. Historically, students have acquired and analyzed the HCl 1-0 spectrum.   2-0 overtone   DCl   35 Cl/ 37 Cl isotopomer resolution Laboratory instructors with spectroscopic interests have offered numerous variations of analysis methods and choices of molecules for study. The work presented here follows in that path and offers an experiment to students with no sample preparation and a tractable element of realism in making line assignments.

70th ISMS Giles Henderson, EIU Chemistry, 1975 C 2 H 2 /C 2 D From my instruction slides on using the Nicolet iS50 FTIR: “The background spectrum is marked by atmospheric H 2 O and CO 2 bands.” Inspirations

70th ISMS CO 2 has three vibrations (1388 cm -1 1 sym. stretch; 667 cm -1 2 bend; 2349 cm -1 3 asym. stretch) CO 2 3 asymmetric stretch band is one of strongest of small molecules   001 band (001 ← 000, using v 1 v 2 v 3 notation)   Ubiquitous interference in IR  400 ppm   1.1% natural abundance of 13 C C-13 CO 2 also is readily observable in the FTIR background spectra of ambient air 13 CO band P-branch is nearly completely free of overlapping lines of significant intensity = easily assigned by students. 13 CO band R-branch lines are strongly overlapped by 12 CO 2 P-branch lines = more challenging assignments, but tractable. What do we know ?

70th ISMS First measurements in the 13 CO 2 3 band were made in infrared spectra of the atmosphere, motivated by “the existence of a weak absorption maximum with resolvable rotation lines on the low frequency side” of the CO 2 3 band. What else do we know ?

70th ISMS Early work was marked by calibration and assignment errors,...   Nielsen, Phys. Rev. 1938, 53,   Nielsen & Yao, Phys. Rev. 1945, 68,   Plyler et al, JRNBS 1955, 55, but recovery was successful.   Plyler et al, JRNBS 1960, 64A,   Oberly et al, J. Mol. Spectrosc. 1968, 25, **   Devi et al, J. Mol. Spectrosc. 1978, 70, **   ** from the K. N. Rao group (OSU)   Guelachvili, J. Mol. Spectrosc. 1980, 79,   Bailly & Rossetti, J. Mol. Spectrosc. 1984, 105, From a rocky start...

70th ISMS The Unpurged Background Spectrum

70th ISMS  band; P and R branches (selection rule  J = ±1) D  h point group   even/odd J levels of 000 CO 2 have different statistical weights   I = 0 for 16 O (in both isotopomers of CO 2 )   Even J (sym): (I+1)·(2I+1) = 1   Odd J (asym): (I)·(2I+1) = 0   Odd J levels of 000 CO 2 are missing 001 CO 2 spectra have only even P/R branch lines   P(2), P(4), P(6) · · · and R(0), R(2), R(4) · · ·   Adjacent line separation  4B   P(2) – R(0) separation  6B Rotational Structure in the Unpurged Background Spectrum

70th ISMS CO 2 P-branch lines are readily assigned (next slide for details) 13 CO 2 R-branch lines are overlapped by the more intense 12 CO 2 P- branch. This provides an element of realism: the challenge to find and assign spectral lines when overlapped with other spectra.   13 CO 2 R-branch lines may be “followed” into the 12 CO 2 P- branch.   13 CO 2 R-branch lines may be predicted from a fit of P-branch lines and found by searching near predicted positions.   13 CO 2 R-branch lines may be added to the P-branch lines for an improved fit of spectroscopic constants to all of the measured line positions. Assigning P-Branch Lines in the Unpurged Background Spectrum

70th ISMS 2015 Follow the P-branch lines to higher frequency to find P(2) as the last line before the “gap”.   Highest intensity is P(16) Similarity to rotational structure of 12 CO 2 band center 10 Assigning P-Branch Lines in the Unpurged Background Spectrum

70th ISMS Assigning P-Branch Lines in the Unpurged Background Spectrum (0.5 cm -1 )

70th ISMS Analysis of P-Branch Line Positions (0.5 cm -1 )

70th ISMS Assigning R-Branch Lines in the Unpurged Background Spectrum (0.125 cm -1 )

70th ISMS Analysis of Combined P/R-Branch Line Positions cm -1

70th ISMS 2015 Pertinent equations for O=C=O structure: R C = 0 because distances are measured from com to each atom 13 CO 2 and 12 CO 2 have the same B 000 values and same C=O bond length. 15 C=O Bond Length Determination

70th ISMS 2015 R 000 for vibrational ground state from B 000 From 0.5 cm -1 resolution spectra   (4) pm - P quad fit (N=24, 0.020/0.045 cm -1 avg/max resid)   (4) pm - P/R cubic fit (N=34, 0.027/0.092 cm -1 resids) From cm -1 resolution spectra   (2) pm - P quad fit (N=25, 0.003/0.008 cm -1 resids)   (7) pm - P/R cubic fit (N=41, 0.005/0.023 cm -1 resids) Literature value R C=O = (1) pm   Bailly, D.; Rossetti, C. J. Mol. Spectrosc. 1984, 105, Combined P/R fits improved R C=O at both resolutions. 16 C=O Bond Length Determination

70th ISMS 2015 This experiment with 13 CO 2 provides results similar to that from analysis of the 12 CO 2 spectrum, but also offers a realistic challenge for making line assignments in the 13 CO 2 R-branch. – –Gonzalez-Gaitano, G.; Isasi, J. R. Chem. Educator [Online] 2001, 6, – –Ogren, P. J. J. Chem. Educ. 2002, 79, No sample is required, and safety issues are minimized. Thank you to Prof. Ioana Sizemore for release time for C. B. Anders to pursue this project with me. Published as Dolson, D. A.; Anders, C. B. Chem. Educator [Online] 2015, 20, Closing Remarks