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Vibration-Rotation Analysis of the 13CO2 Asymmetric Stretch Fundamental Band in Ambient Air for the Physical Chemistry

Teaching Laboratory

David A. Dolson and Catherine B. AndersDepartment of ChemistryWright State University

Dayton, Ohio

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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 35Cl/37Cl 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.

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Giles Henderson, EIU Chemistry, 1975 C2H2/C2D2 1+3

From my instruction slides on using the Nicolet iS50 FTIR:“The background spectrum is marked by atmospheric H2O and CO2 bands.”

Inspirations

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CO2 has three vibrations (1388 cm-1 1 sym. stretch; 667 cm-1 2 bend; 2349 cm-1 3 asym. stretch)

CO2 3 asymmetric stretch band is one of strongest of small molecules

001 band (001 ← 000, using v1 v2 v3 notation) Ubiquitous interference in IR spectra @ 400 ppm 1.1% natural abundance of 13C

C-13 CO2 also is readily observable in the FTIR background spectra of ambient air

13CO2 001 band P-branch is nearly completely free of overlapping lines of significant intensity = easily assigned by students.

13CO2 001 band R-branch lines are strongly overlapped by 12CO2 P-branch lines = more challenging assignments, but tractable.

What do we know ?

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First measurements in the 13CO2 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 CO2 3 band.

What else do we know ?

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Early work was marked by calibration and assignment errors, . . . Nielsen, Phys. Rev. 1938, 53, 983-985. Nielsen & Yao, Phys. Rev. 1945, 68, 173-180. Plyler et al, JRNBS 1955, 55, 183-189.

. . . but recovery was successful. Plyler et al, JRNBS 1960, 64A, 29-48. Oberly et al, J. Mol. Spectrosc. 1968, 25, 138-165. ** Devi et al, J. Mol. Spectrosc. 1978, 70, 160-162. ** ** from the K. N. Rao group (OSU) Guelachvili, J. Mol. Spectrosc. 1980, 79, 72-83. Bailly & Rossetti, J. Mol. Spectrosc. 1984, 105, 229-245.

From a rocky start . . .

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The Unpurged Background Spectrum

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band; P and R branches (selection rule J = ±1) Dh point group

even/odd J levels of 000 CO2 have different statistical weights

I = 0 for 16O (in both isotopomers of CO2)

Even J (sym): (I+1)·(2I+1) = 1 Odd J (asym): (I)·(2I+1) = 0 Odd J levels of 000 CO2 are missing

001 CO2 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

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13CO2 P-branch lines are readily assigned (next slide for details) 13CO2 R-branch lines are overlapped by the more intense 12CO2 P-branch.

This provides an element of realism: the challenge to find and assign spectral lines when overlapped with other spectra.

13CO2 R-branch lines may be “followed” into the 12CO2 P-branch.

13CO2 R-branch lines may be predicted from a fit of P-branch lines and found by searching near predicted positions.

13CO2 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

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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 12CO2 band center

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Assigning P-Branch Lines in the Unpurged Background Spectrum

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

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

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

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Analysis of Combined P/R-Branch Line Positions

0.125 cm-1

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Pertinent equations for O=C=O structure:

RC = 0 because distances are measured from com to each atom

13CO2 and 12CO2 have the same B000 values and same C=O

bond length.

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C=O Bond Length Determination

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R000 for vibrational ground state from B000 From 0.5 cm-1 resolution spectra

116.32(4) pm - P quad fit (N=24, 0.020/0.045 cm-1 avg/max resid) 116.23(4) pm - P/R cubic fit (N=34, 0.027/0.092 cm-1 resids)

From 0.125 cm-1 resolution spectra 116.11(2) pm - P quad fit (N=25, 0.003/0.008 cm-1 resids) 116.199(7) pm - P/R cubic fit (N=41, 0.005/0.023 cm-1 resids)

Literature value RC=O = 116.2058(1) pm Bailly, D.; Rossetti, C. J. Mol. Spectrosc. 1984, 105, 229-245.

Combined P/R fits improved RC=O at both resolutions.

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C=O Bond Length Determination

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This experiment with 13CO2 provides results similar to that from

analysis of the 12CO2 spectrum, but also offers a realistic

challenge for making line assignments in the 13CO2 R-branch.– Gonzalez-Gaitano, G.; Isasi, J. R. Chem. Educator [Online] 2001, 6,

362-364.– Ogren, P. J. J. Chem. Educ. 2002, 79, 117-119.

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, 53-59.

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Closing Remarks