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. Anders
Department of Chemistry
Wright State University
Dayton, Ohio
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Perspective
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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
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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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Inspirations
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.”
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What do we know ?


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
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C-13 CO2 also is readily observable in the FTIR background
spectra of ambient air
13CO 001 band P-branch is nearly completely free of
2
overlapping lines of significant intensity = easily assigned by
students.
13CO 001 band R-branch lines are strongly overlapped by 12CO
2
2
P-branch lines = more challenging assignments, but tractable.
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What else do we know ?

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.
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From a rocky start . . .
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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.
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. . . but recovery was successful.
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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.
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The Unpurged Background Spectrum
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Rotational Structure in the Unpurged
Background Spectrum
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 band; P and R branches (selection rule J = ±1)
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Dh 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
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Assigning P-Branch Lines in the Unpurged
Background Spectrum
 13CO2
P-branch lines are readily assigned (next slide for details)
 13CO2
R-branch lines are overlapped by the more intense 12CO2 Pbranch. This provides an element of realism: the challenge to find and
assign spectral lines when overlapped with other spectra.

R-branch lines may be “followed” into the 12CO2 Pbranch.
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13CO
2

13CO
2
13CO
2
R-branch lines may be predicted from a fit of P-branch
lines and found by searching near predicted positions.
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.
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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)
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Similarity to rotational structure of 12CO2 band center
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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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C=O Bond Length Determination
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Pertinent equations for O=C=O structure:
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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
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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)
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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)
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Literature value RC=O = 116.2058(1) pm
 Bailly, D.; Rossetti, C. J. Mol. Spectrosc. 1984, 105, 229-245.
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Combined P/R fits improved RC=O at both resolutions.
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Closing Remarks
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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.
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No sample is required, and safety issues are minimized.
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Thank you to Prof. Ioana Sizemore for release time for C. B.
Anders to pursue this project with me.
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Published as Dolson, D. A.; Anders, C. B. Chem. Educator [Online] 2015,
20, 53-59.
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