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

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

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, 2015. 154: p. 35-43 [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, 2013. 130: p. 191-200. [3] Henningsen, J., et al., The 0 → 3 Overtone Band of CO: Precise Linestrengths and Broadening Parameters. Journal of Molecular Spectroscopy, 1999. 193(2): p. 354-362.

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

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

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

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

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

Line Profiles Measured and fit results of the N2-broadened 13CO transition P3, measured at a total pressure of 13.33 kPa and 296K Upper panel, measured (symbols) and fit (line) absorption spectrum Lower panes show fit residuals and QF values for individual profiles

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 13.33 kPa and 296K Upper panel, measured (symbols) and fit (line) absorption spectrum Lower panes show fit residuals and QF values for individual profiles

Fitted Area Dependence Relative fitted area of N2-broadened 13CO transition P3 measured at a total pressure of 13.33 kPa and 296K, as a function of varying line profiles. Voight profile systematically underestimates line area

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 11.9858%±0.00095 CO in N2

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

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

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, 2013. 130: p. 191-200. [2] A. A. Kyuberis, L. Lodi, V. Ebert, N. F. Zobov, J. Tennyson, O. L. Polyansky

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 (%) 0.05188

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