High-Accuracy CO(2) Line Intensities Determined from Theory and Experiment

Effect of Non-Markovian Collisions on Measured Integrated Line Shapes of CO

Using cavity ring-down spectroscopy to probe R-branch transitions of CO in N_{2}, we show that the spectral core of the line shapes associated with the first few rotational quantum numbers, J, can be accurately modeled using a sophisticated line profile, provided that a pressure-dependent line area is introduced. This correction vanishes as J increases and is always negligible in CO-He mixtures. The results are supported by molecular dynamics simulations attributing the effect to non-Markovian behavior of collisions at short times. This work has large implications because corrections must be considered for accurate determinations of integrated line intensities, and for spectroscopic databases and radiative transfer codes used for climate predictions and remote sensing.

Ames-2021 CO2 Dipole Moment Surface and IR Line Lists: Toward 0.1% Uncertainty for CO2 IR Intensities

A highly accurate CO₂ ab initio dipole moment surface (DMS), Ames-2021, is reported along with ¹²C¹⁶O₂ infrared (IR) intensity comparisons approaching a 1-4‰ level of agreement and uncertainty. The Ames-2021 DMS was accurately fitted from CCSD(T) finite-field dipoles computed with the aug-cc-pVXZ (X = T, Q, 5) basis for C atom and the d-aug-cc-pVXZ (X = T, Q, 5) basis for O atoms, and extrapolated to the one particle basis set limit. Fitting σ_rms is 3.8 × 10^-7 au for 4443 geometries below 15 000 cm^-1. The corresponding IR intensity, S_Ames-2021, are computed using the Ames-2 potential energy surface (PES), which is the best PES available for CO₂. Compared to high accuracy IR studies for 2001i-00001 and 3001i-00001 bands, S_Ames-2021 matches NIST experiment-based intensities [S_NIST-HIT16 or S_HIT20] to -1.0 ± 1.3‰, or matches DLR experiment-based intensities [S_{DLR-HIT16/UCL/Ames}] to 1.9 ± 3.7‰. This indicates the systematic deviations and uncertainties have been significantly reduced in S_Ames-2021. The S_UCL2015 (or S_HITRAN2016) have larger deviations (vs S_DLR) and uncertainties (vs S_DLR, S_NIST) which are attributed to the less accurate Ames-1 PES adopted in UCL-296 line list calculation. The S_Ames-2021 intensity of ¹²C¹⁶O₂ and ¹³C¹⁶O₂ is utilized to derive new absolute ¹³C/¹²C ratios for Vienna PeeDee Belemnite (VPDB) with uncertainty reduced by ¹/₃ or ²/₃. Further evaluation of S_Ames-2021 intensities are carried out on those CO₂ bands discussed in the HITRAN2020 update paper. Consistent improvements and better accuracies are found in band-by-band analysis, except for those bands strongly affected by Coriolis couplings, or very weak bands measured with relatively larger experimental uncertainties. The Ames-2021 296 K IR line lists are generated for 13 CO₂ isotopologues, with 18 000 cm^-1 and S_296 K > 1 × 10^-31 cm/molecule cutoff and then combined with CDSD line positions (except ¹⁴C¹⁶O₂). The Ames-2021 DMS and 296 K IR line lists represent a major improvement over previous CO₂ theoretical IR intensity studies, including Ames-2016, UCL-296, and recent UCL DMS 2021 update. A real 1 permille level of agreement and uncertainty will definitely require both more accurate PES and more accurate DMS.

Subpromille Measurements and Calculations of CO (3-0) Overtone Line Intensities

Intensities of lines in the near-infrared second overtone band (3-0) of ^{12}C^{16}O are measured and calculated to an unprecedented degree of precision and accuracy. Agreement between theory and experiment to better than 1‰ is demonstrated by results from two laboratories involving two independent absorption- and dispersion-based cavity-enhanced techniques. Similarly, independent Fourier transform spectroscopy measurements of stronger lines in this band yield mutual agreement and consistency with theory at the 1‰ level. This set of highly accurate intensities can provide an intrinsic reference for reducing biases in future measurements of spectroscopic peak areas.

Analysis of measured high-resolution doublet rovibronic spectra and related line lists of CH and OH

Detailed understanding of the energy-level structure of the quantum states as well as of the rovibronic spectra of the ethylidyne (CH) and the hydroxyl (OH) radicals is mandatory for a...

Correcting photodetector nonlinearity in dual-comb interferometry

Photodetector nonlinearity, the main limiting factor in terms of optical power in the detection chain, is corrected to improve the signal-to-noise ratio of a short-time measurement in dual-comb spectroscopy. An iterative correction algorithm minimizing out-of-band spectral artifacts based on nonlinearity correction methods used in classical Fourier-transform spectrometers is presented. The exactitude of the nonlinearity correction is validated using a low power linear measurement. Spectroscopic lines of H¹²CN are provided and the increase in absorption depth of 24% caused by the saturation of the detector is corrected yielding residuals limited by the measurement noise.

Linear Probing of Molecules at Micrometric Distances from a Surface with Sub-Doppler Frequency Resolution

We report on precision spectroscopy of subwavelength confined molecular gases. This was obtained by rovibrational selective reflection of NH_{3} and SF_{6} gases using a quantum cascade laser at λ≈10.6  μm. Our technique probes molecules at micrometric distances (≈λ/2π) from the window of a macroscopic cell with submegahertz resolution, allowing molecule-surface interaction spectroscopy. We exploit the linearity and high resolution of our technique to gain novel spectroscopic information on the SF_{6} greenhouse gas, useful for enriching molecular databases. The natural extension of our work to thin cells will allow compact frequency references and improved measurements of the Casimir-Polder interaction with molecules.

Absolute 13C/12C Isotope Amount Ratio for Vienna Pee Dee Belemnite from Infrared Absorption Spectroscopy

Measurements of isotope ratios are predominantly made with reference to standard specimens that have been characterized in the past. In the 1950s, the carbon isotope ratio was referenced to a belemnite sample collected by Heinz Lowenstam and Harold Urey¹ in South Carolina's Pee Dee region. Due to the exhaustion of the sample since then, reference materials that are traceable to the original artefact are used to define the Vienna Pee Dee Belemnite (VPDB) scale for stable carbon isotope analysis². However, these reference materials have also become exhausted or proven to exhibit unstable composition over time³, mirroring issues with the international prototype of the kilogram that led to a revised International System of Units⁴. A campaign to elucidate the stable carbon isotope ratio of VPDB is underway⁵, but independent measurement techniques are required to support it. Here we report an accurate value for the stable carbon isotope ratio inferred from infrared absorption spectroscopy, fulfilling the promise of this fundamentally accurate approach⁶. Our results agree with a value recently derived from mass spectrometry⁵, and therefore advance the prospects of SI-traceable isotope analysis. Further, our calibration-free method could improve mass balance calculations and enhance isotopic tracer studies in CO₂ source apportionment.

Raman Laser Spectrometer: Application to 12C/13C Isotope Identification in CH4 and CO2 Greenhouse Gases

A compact Raman laser gas spectrometer is developed. It comprises a high-power green laser at 532.123 nm as an excitation source and a specially designed gas cell with an internal volume of less than 0.6 cm3 that can withstand gas pressures up to 100 atm. The resolution of the spectrometer is ~1 cm−1. The Raman spectra of chemically pure isotopically enriched carbon dioxide (12CO2, 13CO2) and methane (12CH4, 13CH4) gases are studied. The expected limit of detection (LOD) is less than 100 ppm for the isotopologues of CO2 and less than 25 ppm for those of CH4 (at a gas pressure of 50 atm.), making the developed spectrometer promising for studying the sources of emissions of greenhouse gases by resolving their isotopologue composition. We also show the suitability of the spectrometer for Raman spectroscopy of human exhalation.

Optical-Optical Double-Resonance Absorption Spectroscopy of Molecules with Kilohertz Accuracy

Selective pumping and probing of highly excited states of molecules are essential in various studies but are also challenging because of high density of states, weak transition moments, and lack of precise spectroscopy data. We develop a comb-locked cavity-assisted double-resonance spectroscopy (COCA-DR) method for precision measurements using low-power continuous-wave lasers. A high-finesse cavity locked with an optical frequency comb is used to enhance both the pumping power and the probing sensitivity. As a demonstration, Doppler-free stepwise two-photon absorption spectra of CO₂ were recorded by using two milliwatt diode lasers (1.60 and 1.67 μm), and the rotation energies in a highly excited state (CO-stretching quanta = 8) were determined with an unprecedented accuracy of a few kilohertz.

Cavity ring-down spectroscopy based on a comb-locked optical parametric oscillator source

Spectroscopy of molecules in the mid-infrared (MIR) region has important applications in various fields, such as astronomical observation, environmental detection, and fundamental physics. However, compared to that in the near-infrared, precision spectroscopy in the MIR is often limited by the light source and has not shown full potential in sensitivity. Here we report a cavity ring-down spectroscopy system using a tunable narrow-linewidth optical parametric oscillator, which fulfills the requirement of high sensitivity and high precision in the MIR region. The Lamb-dip spectrum of the N₂O molecule at 2.7 μm was measured as a demonstration of spectroscopy in the MIR with kilohertz accuracy.

A well-isolated vibrational state of CO2verified by near-infrared saturated spectroscopy with kHz accuracy

Quantitative determination of atmospheric CO₂concentration by remote sensing relies on accurate line parameters.

Cavity ring-down spectroscopy of CO2 near λ = 2.06 μm: Accurate transition intensities for the Orbiting Carbon Observatory-2 (OCO-2) "strong band"

The λ = 2.06 μm absorption band of CO₂ is widely used for the remote sensing of atmospheric carbon dioxide, making it relevant to many important top-down measurements of carbon flux. The forward models used in the retrieval algorithms employed in these measurements require increasingly accurate line intensity and line shape data from which absorption cross-sections can be computed. To overcome accuracy limitations of existing line lists, we used frequency-stabilized cavity ring-down spectroscopy to measure 39 transitions in the ¹²C¹⁶O₂ absorption band. The line intensities were measured with an estimated relative combined standard uncertainty of u _r = 0.08 %. We predicted the J-dependence of the measured intensities using two theoretical models: a one-dimensional spectroscopic model with Herman-Wallis rotation-vibration corrections, and a line-by-line ab initio dipole moment surface model [Zak et al. JQSRT 2016;177:31-42]. For the second approach, we fit only a single factor to rescale the theoretical integrated band intensity to be consistent with the measured intensities. We find that the latter approach yields an equally adequate representation of the fitted J-dependent intensity data and provides the most physically general representation of the results. Our recommended value for the integrated band intensity equal to 7.183 × 10^-21 cm molecule^-1 ± 6 × 10^-24 cm molecule^-1 is based on the rescaled ab initio model and corresponds to a fitted scale factor of 1.0069 ± 0.0002. Comparisons of literature intensity values to our results reveal systematic deviations ranging from -1.16 % to +0.33 %.

Comb-locked cavity ring-down spectroscopy with variable temperature

Temperature dependence of molecular absorption line shape is important information for spectroscopic studies and applications. In this work, we report a comb-locked cavity ring-down spectrometer employing a cryogenic cooler to perform absorption spectroscopy measurements at temperatures between 40 K and 300 K. As a demonstration, we recorded the spectrum of the R(0) line in the (2-0) band of HD at 46 K. The temperature was also confirmed by the Doppler width of the HD line. Spectra of CH₄ near 1.394 μm were also recorded in a wide temperature range of 70-300 K. Lower-state energies of methane lines were analyzed by fitting these spectra, which can be directly compared with the HITRAN and TheoReTS databases. Considerable deviations were observed, indicating the need to investigate the assignments of the methane lines in this region.

Comb-assisted, Pound-Drever-Hall locked cavity ring-down spectrometer for high-performance retrieval of transition parameters

Fast and high-performance cavity ring-down spectrometer (CRDS) is highly desired to precisely extract spectral parameters. In this paper, we present our comb-assisted Pound-Drever-Hall (PDH) locked CRDS setup, aiming to retrieve molecular parameters. In the setup, a dynamic feedback is used to keep the tight PDH locking even under strong absorption in the spectral measurement. PDH light and probing light enter the ring-down cavity simultaneously under orthogonal polarization, which enables a fast acquisition of ring-down events without interrupting PDH locking. Ultra-stable cavity temperature is realized, which has an accuracy below 0.5 mK in 27 minutes. The optical frequency comb (OFC) system is developed to rapidly and automatically measure the frequency axis with a relatively wide beat-note range. The minimum detectable absorption coefficient and noise-equivalent absorption coefficient (NEA) are 7.6×10^-12cm^-1 and 5.3×10^-12cm^-1Hz^-1/2, respectively. The spectrometer is implemented to measure CO₂ transition and extract line parameters. The uncertainty for line position is evaluated to be 120 kHz. An accuracy of 0.31% for line intensity is beneficial to the precise determination of CO₂ content for the purpose of environment protection and other applications.

Twenty-Five-Fold Reduction in Measurement Uncertainty for a Molecular Line Intensity

To accurately attribute sources and sinks of molecules like CO_{2}, remote sensing missions require line intensities (S) with relative uncertainties u_{r}(S)<0.1%. However, discrepancies in S of ≈1% are common when comparing different experiments, thus limiting their potential impact. Here we report a cavity ring-down spectroscopy multi-instrument comparison which revealed that the hardware used to digitize analog ring-down signals caused variability in spectral integrals which yield S. Our refined approach improved measurement accuracy 25-fold, resulting in u_{r}(S)=0.06%.

High-accuracy and wide dynamic range frequency-based dispersion spectroscopy in an optical cavity

A spectroscopic method free from systematic errors is desired for many challenging applications of gas detection. Although existing cavity-enhanced techniques exhibit very high precision, their accuracy strongly depends on propagation of the light amplitude through an optical system and its detection. Here, we demonstrate that the frequency-based molecular dispersion spectroscopy, involving sub-Hz-level precision in frequency measurements of optical cavity resonances, leads to sub-per-mille accuracy and a wide dynamic range, both previously unattainable by any other spectroscopic technique. The method offers great sensitivity of 5×10^-11 cm^-1, high speed, limited only by the fundamental response time of the cavity, and traceability of both axes of the spectrum to the primary frequency standard. All these features are necessary for convenient realization of comprehensive molecular spectroscopy from Doppler up to collisional regime without changing the spectroscopic method and modification of the experimental setup. Moreover, the presented approach does not require linear, high-bandwidth nor phase-sensitive detectors and can be directly implemented in existing cavity-enhanced spectrometers utilizing either continuous-wave or coherent broadband radiation. We experimentally prove the predominance of frequency-based spectroscopy over intensity-based one. Our results motivate replacement of intensity-based absorption spectroscopy with a pure frequency-based dispersion one in applications where the highest accuracy is required.

Discovery of New Lines in the R9 Multiplet of the 2v_{3} Band of ^{12}CH_{4}

We present the first results for resolving methane (CH_{4}) line transition frequencies down to the kilohertz level for overlapping lines using comb-linked cavity ring-down spectroscopy, while most available laboratory measurements, having resolution at the megahertz level, cannot separate merged lines. To demonstrate the technique, Lamb-dip spectra and linear-absorption spectra were used to identify overlapped lines of vibration-rotation spectra in the R9 multiplet of the 2v_{3} band. Three new weak lines were found for the first time. The experimental methods are extensible to other important bands of CH_{4} and many other gas-phase molecules, and should provide a more detailed understanding of molecular structure and line parameters for future high-precision studies.

A variationally computed room temperature line list for AsH3

Calculations are reported on the rotation–vibration energy levels of the arsine molecule with associated transition intensities.

Highly excited vibrational levels of methane up to 10 300 cm-1: Comparative study of variational methods

In this work, we report calculated vibrational energy levels of the methane molecule up to 10 300 cm^-1. Two potential energy surfaces constructed in quite different coordinate systems with different analytical representations are employed in order to evaluate the uncertainty of vibrational predictions. To calculate methane energy levels, we used two independent techniques of the variational method. One method uses an exact kinetic energy operator in internal curvilinear coordinates. Another one uses an expansion of Eckart-Watson nuclear motion Hamiltonian in rectilinear normal coordinates. In the Icosad range (up to five vibrational quanta bands-below 7800 cm^-1), the RMS standard deviations between calculated and observed energy levels were 0.22 cm^-1 and 0.41 cm^-1 for these two quite different approaches. For experimentally well-known 3v₃ sub-levels, the calculation accuracy is estimated to be ∼1 cm^-1. In the Triacontad range (7660-9188 cm^-1), the average error of the calculation is about 0.5 cm^-1. The accuracy and convergence issues for higher energy ranges are discussed.

Precision spectroscopy of H13CN using a free-running, all-fiber dual electro-optic frequency comb system

We demonstrate the precision molecular spectroscopy of H¹³CN using a free-running, all-fiber dual electro-optic frequency comb system. Successive interferograms, acquired at a rate of Δf_rep=1  MHz, were phase-corrected in post-processing, averaged, and normalized to yield the complex transmission spectrum of several transitions within the 2ν₁H¹³CN band centered near λ=1545  nm. With spectral signal-to-noise ratios as high as 326:1 achieved in 2 ms of integration time, we report accurate measurements of H¹³CN transition intensities which will aid in the study of extreme astrophysical environments.

High-accuracy water potential energy surface for the calculation of infrared spectra

Transition intensities for small molecules such as water and CO₂ can now be computed with such high accuracy that they are being used to systematically replace measurements in standard databases. These calculations use high-accuracy ab initio dipole moment surfaces and wave functions from spectroscopically determined potential energy surfaces (PESs). Here, an extra high-accuracy PES of the water molecule (H₂¹⁶O) is produced starting from an ab initio PES which is then refined to empirical rovibrational energy levels. Variational nuclear motion calculations using this PES reproduce the fitted energy levels with a standard deviation of 0.011 cm^-1, approximately three times their stated uncertainty. The use of wave functions computed with this refined PES is found to improve the predicted transition intensities for selected (problematic) transitions. A new room temperature line list for H₂¹⁶O is presented. It is suggested that the associated set of line intensities is the most accurate available to date for this species.This article is part of the theme issue 'Modern theoretical chemistry'.

High-accuracy 12C16O2 line intensities in the 2 μm wavelength region measured by frequency-stabilized cavity ring-down spectroscopy

Reported here are highly accurate, experimentally measured ro-vibrational transition intensities for the R-branch of the (20012) - (00001) ¹²C¹⁶O₂ band near λ = 2 μm. Measurements were performed by a frequency-stabilized cavity ring-down spectroscopy (FS-CRDS) instrument designed to achieve precision molecular spectroscopy in this important region of the infrared. Through careful control and traceable characterization of CO₂ sample conditions, and through high-fidelity measurements spanning several months in time, we achieve relative standard uncertainties for the reported transition intensities between 0.15 % and 0.46 %. Such high accuracy spectroscopy is shown to provide a stringent test of calculated potential energy and ab initio dipole moment surfaces, and therefore transition intensities calculated from first principles.

Optical Measurement of Radiocarbon below Unity Fraction Modern by Linear Absorption Spectroscopy

High-precision measurements of radiocarbon (¹⁴C) near or below a fraction modern ¹⁴C of 1 (F¹⁴C ≤ 1) are challenging and costly. An accurate, ultrasensitive linear absorption approach to detecting ¹⁴C would provide a simple and robust benchtop alternative to off-site accelerator mass spectrometry facilities. Here we report the quantitative measurement of ¹⁴C in gas-phase samples of CO₂ with F¹⁴C < 1 using cavity ring-down spectroscopy in the linear absorption regime. Repeated analysis of CO₂ derived from the combustion of either biogenic or petrogenic sources revealed a robust ability to differentiate samples with F¹⁴C < 1. With a combined uncertainty of ¹⁴C/¹²C = 130 fmol/mol (F¹⁴C = 0.11), initial performance of the calibration-free instrument is sufficient to investigate a variety of applications in radiocarbon measurement science including the study of biofuels and bioplastics, illicitly traded specimens, bomb dating, and atmospheric transport.

Ro-vibronic transition intensities for triatomic molecules from the exact kinetic energy operator; electronic spectrum for the C̃ 1B2 ← X̃ 1A1 transition in SO2

A procedure for calculating ro-vibronic transition intensities for triatomic molecules within the Born-Oppenheimer approximation is reported. Ro-vibrational energy levels and wavefunctions are obtained with the DVR3D suite, which solves the nuclear motion problem with an exact kinetic energy operator. Absolute transition intensities are calculated both with the Franck-Condon approximation and with a full transition dipole moment surface. The theoretical scheme is tested on C̃ ¹B₂ ← X̃ ¹A₁ ro-vibronic transitions of SO₂. Ab initio potential energy and dipole moment surfaces are generated for this purpose. The calculated ro-vibronic transition intensities and cross sections are compared with the available experimental and theoretical data.

Accurate frequency referencing for fieldable dual-comb spectroscopy

We describe a dual-comb spectrometer that can operate independently of laboratory-based rf and optical frequency references but is nevertheless capable of ultra-high spectral resolution, high SNR, and frequency-accurate spectral measurements. The instrument is based on a "bootstrapped" frequency referencing scheme in which short-term optical phase coherence between combs is attained by referencing each to a free-running diode laser, whilst high frequency resolution and long-term accuracy is derived from a stable quartz oscillator. The sensitivity, stability and accuracy of this spectrometer were characterized using a multipass cell. We demonstrate comb-resolved spectra spanning from 140 THz (2.14 µm, 4670 cm^-1) to 184 THz (1.63 µm, 6140 cm^-1) in the near infrared with a frequency sampling of 200 MHz (0.0067 cm^-1) and ~1 MHz frequency accuracy. High resolution spectra of water and carbon dioxide transitions at 1.77 µm, 1.96 µm and 2.06 µm show that the molecular transmission acquired with this system operating in the field-mode did not deviate from those measured when it was referenced to a maser and cavity-stabilized laser to within 5.6 × 10^-4. When optimized for carbon dioxide quantification at 1.60 µm, a sensitivity of 2.8 ppm-km at 1 s integration time, improving to 0.10 ppm-km at 13 minutes of integration time was achieved.

Precise methane absorption measurements in the 1.64 μm spectral region for the MERLIN mission

In this article we describe a high-precision laboratory measurement targeting the R(6) manifold of the 2ν₃ band of ¹²CH₄. Accurate physical models of this absorption spectrum will be required by the Franco-German, Methane Remote Sensing LIDAR (MERLIN) space mission for retrievals of atmospheric methane. The analysis uses the Hartmann-Tran profile for modeling line shape and also includes line-mixing effects. To this end, six high-resolution and high signal-to-noise absorption spectra of air-broadened methane were recorded using a frequency-stabilized cavity ring-down spectroscopy apparatus. Sample conditions corresponded to room temperature and spanned total sample pressures of 40 hPa - 1013 hPa with methane molar fractions between 1 μmol mol^-1 and 12 μmol mol^-1. All spectroscopic model parameters were simultaneously adjusted in a multispectrum nonlinear least-squares fit to the six measured spectra. Comparison of the fitted model to the measured spectra reveals the ability to calculate the room-temperature, methane absorption coefficient to better than 0.1% at the on-line position of the MERLIN mission. This is the first time that such fidelity has been reached in modeling methane absorption in the investigated spectral region, fulfilling the accuracy requirements of the MERLIN mission. We also found excellent agreement when comparing the present results with measurements obtained over different pressure conditions and using other laboratory techniques. Finally, we also evaluated the impact of these new spectral parameters on atmospheric transmissions spectra calculations.