1. Line-shapes and intensities of carbon monoxide transitions in the (3 → 0) band
Z. Reed,* O. Polyansky,† J. Hodges*
* National Institute of Standards and Technology
† University College of London

2. Carbon monoxide Line Shapes and Intensities
Carbon monoxide is present in the planetary atmospheres of most planets in this solar system and is a useful probe of atmospheric dynamics
CO is an excellent test case for lineshape modeling
CO can readily be modeled theoretically, presenting a possible approach to link optical measurements to the SI without the use of artifact gas standards

3. Previous Work
Extensive study has been performed on self-, nitrogen-, and air-broadened CO in the 1→0, 2→0, and 3→0 bands [1]
Intensities of the 3→0 band have been previously determined [1-3]
Systematic variation from the Voight profile has been revealed, along with deviations from HITRAN2012 line intensities and a dependence on chosen line shape model
[1] Mondelain, D., et al., Broadband and highly sensitive comb-assisted cavity ring down spectroscopy of CO near 1.57 μm with sub-MHz frequency accuracy. Journal of Quantitative Spectroscopy and Radiative Transfer, : p
[2] Wójtewicz, S., et al., Low pressure line-shape study of self-broadened CO transitions in the (3←0) band. Journal of Quantitative Spectroscopy and Radiative Transfer, : p
[3] Henningsen, J., et al., The 0 → 3 Overtone Band of CO: Precise Linestrengths and Broadening Parameters. Journal of Molecular Spectroscopy, (2): p

4. Frequency Stabilized Cavity Ringdown Spectroscopy (FS-CRDS) at NIST Gaithersburg
reference laser cw
probe laser
cavity stabilization servo
pzt
optical resonator
decay signal
(a)
(b)
time
stabilized comb of
resonant frequencies n
FSR
= 108 MHz
absorption spectrum
I = I0 exp-(t/t) + const
frequency
time
1/(c t) = a0 + a(n)
Hodges, J.T., et al, Rev. Sci. Instrum., 2005, 76, 2

5. Linking measured line parameters to the SI
Gas-filled, length-stabilized ring-down cavity
I2-stabilized
HeNe laser (10 kHz)
Probe Laser
Optical Frequency Comb Cs
Clock
Probe laser servo
Primary Pressure Standards
Primary Temperature
Standards
Calibrated Thermometers (PRT)
Calibrated Manometers (SRT)
Cavity length
servo
1/(c t) = a0 + a(n)
time
frequency

6. Measurement of Line Intensity (S) and Absorber Concentration (n)
S = ∫ a(n)dn /{ n ∫g(n)dn} = A/n
line profile
(unity area)
fitted spectrum area
measured
absorption coefficient
Once the intrinsic property S is known, then
n = A/S

7. Hartmann-Tran Line Profile
Includes mechanisms for collisional narrowing, speed dependent narrowing and shifting, and correlation between velocity- and phase- changing collisions
Average broadening
Γ 𝟎
Speed dependent broadening
Γ 𝟐
Average shifting
Δ 𝟎
Speed dependent shifting
Δ 𝟐
Collisional narrowing
ω 𝒘𝒄
Correlation η

8. HTP Profile reduces to:
Voight profile (VP) when Γ 𝟐 , Δ 𝟐 , ω 𝒘𝒄 , η = 0
Nelkin-Ghatak (NGP) when Γ 𝟐 , Δ 𝟐 , η = 0
Speed-dependent VP when ω 𝒘𝒄 , η = 0
Quadratic speed dependent NGP when ω 𝑒𝑓𝑓 ,
η = 0
Where ω 𝑒𝑓𝑓 = 𝑘 𝐵 𝑇 𝑚 𝑎 𝐷
absorber mass mass diffusion coefficient
Quadratic approximation
to speed dependence
Complex, normalized
narrowing frequency
Complex profile
Mechanisms: 1) collisional narrowing (hard-collision model), 2) speed-dependent broadening and shifting,
3) partial correlations between velocity-changing and dephasing collisions

9. Line Profiles
Measured and fit results of the N2-broadened 13CO transition P3, measured at a total pressure of kPa and 296K
Upper panel, measured (symbols) and fit (line) absorption spectrum
Lower panes show fit residuals and QF values for individual profiles

10. Line Profiles Line Mixing α(ν)=A{Re I (ν- ν0) + Y Im(I (ν- ν0)) }
Where A = fitted area
Y= dimensionless line mixing term
Re(I) = real component
Im (I)= imaginary component
Measured and fit results of the N2-broadened 13CO transition P3, measured at a total pressure of kPa and 296K
Upper panel, measured (symbols) and fit (line) absorption spectrum
Lower panes show fit residuals and QF values for individual profiles

11. Fitted Area Dependence
Relative fitted area of N2-broadened 13CO transition P3 measured at a total pressure of kPa and 296K, as a function of varying line profiles.
Voight profile systematically underestimates line area

12. Line Intensity Determination
Once the intrinsic property S is known, then
n = A/S
n must be known to determine S
NIST CO in N2 standard prepared via gravimetric weighing method
%± CO in N2

13. Line Intensity Determination
Linear fit of fitted line areas of N2-broadened 13CO transition P3 measured at 296K at pressures ranging from 50 torr to 350 torr. Spectra are fitted with SDNGP profile with line mixing. GP
SDNGP
SDNGP+LM
S (cm-1/( molec. cm-2)
1.0146E-25
1.0151E-25
1.0153E-25
Uncertainty (%)
0.031
0.010
0.0083

14. Measurement repeatability
Transition
Transition no.
S (NIST)
(cm-1/( molec. cm-2)
uncertainty (%)
12C16O   P26 1
1.161E-25
0.043
12C16O   P27 2
7.239E-26
0.054
12C16O   P28 3
4.416E-26
0.12
13C16O   P1 4
3.77E-26
0.14
13C16O   P2 5
7.20E-26
0.10
13C16O   P3 6
1.013E-25
0.29
13C16O   R0 7
3.972E-26
0.23
12C18O R4 8
3.26E-26
0.19
Normalized line strengths determined via repeated experiment (symbols). Error bar represent individual fit uncertainty
Calculated line strengths and combined uncertainty

15. Comparison to Literature and Theory
Isotope
Transition
Wojtewicz1
% diff w.r.t NIST
HITRAN
Ab initio
12C16O
P26
-0.34
-0.13
P27
-2.51
-0.67
-0.06
P28
-3.06
-0.58
0.05
13C16O P1
-1.25
10.61 P2
-1.71
10.44 P3
-0.49
10.89 R0
9.44
12C18O R4
3.28
All electron MRCI calculations with highest available basis set in MOLPRO
Aug-cc-pCV6Z results are extrapolated to complete basis set limit
First and second order relativistic corrections and adiabatic corrections included
[1] Wójtewicz, S., et al., Low pressure line-shape study of self-broadened CO transitions in the (3←0) band. JQSRT, : p
[2] A. A. Kyuberis, L. Lodi, V. Ebert, N. F. Zobov, J. Tennyson, O. L. Polyansky

16. Error Budget NIST uncertainties (not including fit) Isotope Transition
Intensity
Uncertainty
(cm-1/
(molec. cm-2) %
12C16O
P26
1.16E-25
0.043
P27
7.24E-26
0.054
P28
4.42E-26
0.12
13C16O P1
3.77E-26
0.14 P2
7.20E-26
0.1 P3
1.01E-25
0.29 R0
3.97E-26
0.23
12C18O R4
3.26E-26
0.19
NIST uncertainties (not including fit)
unc. (%)
unc2
pressure
5.00E-03
2.50E-05
composition
7.93E-03
6.28E-05
isotopic composition
1.00E-02
1.00E-04
Temperature
5.00E-02
2.50E-03
Pressure zero drift
2.00E-03
4.00E-06
combined (%)

17. Conclusions
Line strengths of selected 12C16O, 13C16O, and 12C18O transitions in the (3 → 0) band measured at highest precision to date
Calculated line strengths vary significantly from HITRAN and previous literature values, but compare well to ab initio calculations
Link to SI and theoretical line strengths demonstrates possible route to artifact-free determination of molecular concentrations, including isotope ratios
Funding: NIST Greenhouse Gas Measurements and Climate Research Program