Absorption Spectrum Of Carbon Dioxide Research Articles

The first observation of the 12C16O2 absorption bands near 660 nm

The absorption spectra of carbon dioxide were recorded in the region from 15,000 to 15,300 cm−1, using a Bruker IFS 125 HR Fourier transform spectrometer and a 30 m multipass cell with the White type optical system. The recording was performed at a spectral resolution of 0.044 – 0.050 cm−1, room temperature, a path length of 1057.95 m and pressures of 185 and 362 mbar. Utilization of a LED as a light source provided a sensitivity (noise equivalent absorption) at the level of kν = 1.23 × 10-10 cm−1 and allowed detection of a number of lines of two 3005i − 00001 (i = 2,3) bands and several lines of the 60031 – 00001 band of 12C16O2 with the intensity values down to 10-30 cm−1/(molecule cm−2) at 296 K. These bands were observed for the first time. The uncertainty of the line position measurements was estimated to be about 0.005 cm−1 for the unblended lines with a high signal-to-noise ratio. The uncertainties of the retrieved line intensities for the strongest unblended lines are at the level of 15 %. The spectroscopic constants for observed bands were fitted to the observed line positions. The vibrational transition dipole moments squared of these bands were fitted to the observed line intensities. The measured line positions were compared to those from the HITRAN2020 database and to those predicted with the global effective Hamiltonian. The measured line intensities were compared to the values from the HITRAN2020 database and from the Ames2021 line list.

The absorption bands of 12C16O2 near 718 nm

The absorption spectra of carbon dioxide were recorded in the region from 13,500 to 14,200 cm−1, using a Bruker IFS 125 HR Fourier transform spectrometer and a 30 m multipass cell with the White type optical system. The recording was performed at spectral resolution of 0.03–0.04 cm−1, room temperature, path length of 1057.95 m and at three pressures of 252, 403 and 582 mbar. The achieved sensitivity (noise equivalent absorption) at the level of kν = 6 × 10−10 cm−1 allowed detection of a number of lines of three 2005i - 00001 (i = 1,2,3) bands of 12C16O2 with the intensity values down to 10−29 cm−1/(molecule cm−2) at 296 K. The 20053–00001 band was observed for the first time. The line intensities for all bands were measured for the first time. The uncertainty of the line position measurements was estimated to be about 0.007 cm−1 for the unblended lines with a high value of the signal-to-noise ratio. The uncertainties of the retrieved line intensities for the strongest unblended lines are on the level of 10%. The spectroscopic constants for the three observed bands were fitted to the observed line positions. The vibrational transition dipole moments squared of these bands were fitted to the observed line intensities. A comparison of the measured line positions to those from the HITRAN2020 database was done. Finally a comparison of the measured line intensities to those contained in the HITRAN2020 database as well as in the new version of the Ames line list was also given.

Applying an in-situ calibration method of spectral line shape to determine flame temperature of methane and ethylene spherically expanding flames

Spectral line shape caused by the collision between probing molecules and surrounding species is an important parameter that affects the accuracy of combustion diagnostics. Here, we report an in-situ calibration method of the pressure broadening coefficients using spherically expanding flames over continuously increasing flame pressure. A desirable isothermal condition is produced in the spherical expanding flame with unity Lewis number, in which the thermal and molecular diffusions are balanced during flame propagation. Laminar burning velocities and Markstein length of methane-air and ethylene-air flames are measured to understand their thermodynamic and transport properties. Mid-infrared absorption spectra of carbon dioxide at 4.2 µm are recorded from 0.3 atm to 5 atm in a single run of the experiment. Pressure broadening parameters are extracted using an empirical fitting procedure. After extending to wide ranges of flame conditions, the flame temperatures of the methane-air and ethylene-air flames are correctly determined using the in-situ-determined line shape parameters. The flame temperature deviation from adiabatic flame temperature is imperceptible in the weakly stretched quasi-steady spherically expanding flames. Such unity Lewis number spherical expanding flames are proven to be near-ideal reactors for spectroscopic calibration in combustion diagnostics.

Rotational Dependence of Line Halfwidth for the Fundamental Band 0 0 0 11–0 0 0 01 of CO2 Confined in Nanoporous Aerogel: New Measurements

The absorption spectra of carbon dioxide confined in an aerogel sample with pore sizes of 60 nm have been recorded at room temperature in the 2250–2400 cm−1 region using a Bruker IFS 125HR FTIR spectrometer. Parameters of spectral lines of CO2 are derived; their dependences on rotational quantum numbers are shown. The results are compared with data available in literature.

Rotational Dependence of Line Half-width for 0 0 0 11–0 0 0 01 Fundamental Band of CO2 Confined in Aerogel Nanopores

The absorption spectrum of carbon dioxide confined in aerogel has been measured in the 2250–2400 cm–1 region for the first time with the use of a Bruker IFS 125HR FTIR spectrometer. The dependence of CO2 half-widths on rotational quantum numbers was studied and compared with literature data.

Temperature dependence of line parameters of near studied by tunable diode laser spectroscopy**Project supported by the Young Scientists Fund of the National Natural Science Foundation of China (Grant Nos. 41205021 and 61701006), the Youth Innovation Promotion Association of the Chinese Academy of Sciences (Grant No. 2015264), and the Scientific Research Foundation of the Higher Education Institutions of Anhui Province, China

The absorption spectrum of carbon dioxide at has been recorded at sample temperatures between 218.0 K and room temperature, by using a high-resolution tunable diode laser absorption spectrometer (TDLAS) combined with a temperature controlled cryogenically cooled absorption cell. The self-, N2-, and air-broadening coefficients for nine transitions of belonging to the band in the 4987 cm−1–4998 cm−1 region have been measured at different temperatures. From these measurements, we have further determined the temperature dependence exponents of the pressure-broadening coefficients. To the best of our knowledge, the temperature dependence parameters of the collisional broadening coefficients are reported experimentally for the first time for these nine transitions. The measured halfwidth coefficients and the air temperature dependence exponents of these transitions are compared with the available values reported in the literature and HITRAN 2012 database. Agreements and discrepancies are also discussed.

The rotational–translational spectra of N2 and CO2 and their mixtures with argon

Rotational–translational absorption spectra of carbon dioxide, nitrogen and their mixtures with argon in the wavelength range 20–190 cm–1 induced by pair collisions of molecules are obtained and analyzed. It is shown that, in contrast to absorption in noble gas mixtures, terahertz spectra of N2 a CO2 are mainly caused by quadrupole interactions, The role of the overlapping mechanism in the formation of these spectra was estimated, and the quadrupole moments of the N2 and CO2 molecules, equal to 1.5–1.7∙10–26 CGSE and 4.25∙10–26 CGS, respectively, were determined from the integrated intensity of the recorded spectra.

Experimental study of carbon dioxide spectroscopic parameters around 2.0 µm region for combustion diagnostic applications

The high-resolution absorption spectra of carbon dioxide were measured at sample temperatures in the range of 296–800 K. The measurements were performed based on direct laser absorption spectroscopy using a tunable diode laser combined with a home-made heated static cell. Line strengths, self-broadening coefficients and their temperature dependences of five selected strong lines belonging to the 20012←00001 band of carbon dioxide near 2.0 µm were inferred from these measured spectra. To the best of our knowledge, this is the first study that measures the line parameters for the five selected strong CO2 lines at elevated temperature. The measured line strengths and self-broadening coefficients of these lines are compared with the available values listed in HITRAN/HITEMP database. The temperature dependence exponents of self-broadening coefficients are compared with theoretical calculations and values inferred from HITEMP2010. Agreements and discrepancies are discussed.

Measurements of the CO2 line parameters in the 10000–10300 cm−1 region

The absorption spectra of carbon dioxide have been recorded in the near infrared region from 10,000 to 10,300cm-1, using the Bruker IFS 125HR Fourier transform spectrometer and a 30m multipass cell with the White type optical system. The spectra were recorded at a spectral resolution of 0.03cm−1, room temperature, a path length of 953.6m and at two pressures of 294 and 523mbar. The achieved sensitivity (noise equivalent absorption) at the level of kν=1.38×10−10cm−1 allowed detection of a number of new transitions with the intensity values down to 10–29cm/molecule at 296K. Two bands 60014-00001 and 60015-00001 of 12C16O2 were detected for the first time. The line positions and intensities of these bands were determined using the Voigt profile as a line shape. The uncertainty of the line position determination was estimated to be about 0.003cm-1 for the unblended lines with a high value of the signal-to-noise ratio. The uncertainty of the line intensity determination varies from 4% to 40% depending on the strength of the line and the extent of the line overlapping. The measured line intensities of the 60014-00001 and 60015-00001 bands together with those published earlier for the ΔP=15 series of transitions were used to fit the effective dipole moment parameters of this series. Here P=2V1+V2+3V3 is the polyad number (Vi (i=1,2,3) are the harmonic oscillators quantum numbers). The fitted parameters reproduce the measured line intensities within their experimental uncertainties. Using the effective Hamiltonian parameters published earlier and the fitted effective dipole moment parameters the line positions and intensities of the 6001i-00001 (i=1,2,3,4,5,6,7) bands have been calculated. A comparison of the measured line positions and intensities to those contained in the new version (huang.seti.org) AMES line list as well as in the High-T line list are given.

Measurement of absorption spectrum around 1.572 μm

Differential absorption lidar (DIAL) is widely accepted as a most promising remote sensing technique for measuring the atmospheric CO2, and has been built in many countries to study the global climate change and carbon cycle. However, the imperfect information about CO2 spectrum leads to evident errors in estimating some parameters (such as the absorption cross sections, the broadening coefficients, the optical depth, etc.) which are the critical parameters in retrieving processes of a DIAL, and will eventually result in unacceptable errors of XCO2 retrievals. Coping with that problem, a self-built constant temperature differential absorption spectroscopy system has been set up which can be used to accurately measure the absorption spectrum of carbon dioxide in the band of 1.57 μm.#br#On that basis, the absorption spectra of the pure carbon dioxide are measured respectively at the temperatures from 230 K to 320 K and the pressures from 20 kPa to 100 kPa by the highprecision oscilloscope and wavelength meter. A series of optical depths at absorption peak is respectively calculated at different temperatures and the results show that the optical depth linearly and monotonically changes while the temperature increases from 230 K to 320 K. At the same time, the relations between the corresponding absorption cross sections and temperature are analyzed, showing that the absorption cross sections first increases and then decreases with temperature increasing. The self-broadening coefficients are inferred from the spectral data at the same temperature and different pressures, and the temperature-dependent exponent is calculated. Furthermore, the air-broadening coefficients are calculated by carbon dioxide absorption spectrum data from different mixing ratios and its temperature-dependent exponent is obtained. The temperature-dependent exponent of self-broadening coefficient is 0.644 and the temperature-dependent exponent of air-broadening coefficient is 0.764, which are almost the same as the data in the high-resolution transmission molecular absorption database (HITRAN). The numerical calculation formulae of optical depth and absorption cross section are verified through these results.#br#Those parameters supplement the widely-used HITRAN database. Moreover, quantitative analysis is conducted to explore the influences of temperature and pressure on CO2 spectrum, thereby establishing a function for modeling the differential absorption optical depth and the absorption cross-section. The above results have already been used in China's CO2-DIAL and lay a foundation of accurate retrieval. It is believed that other similar CO2-DIAL of which operating wavelength is around 1.572 μm would also benefit from those newly measured parameters.

Photochemistry of carbon dioxide from first principles: Application to photoabsorption of hot CO2

This paper analyzes the temperature dependence of the absorption spectrum of carbon dioxide in the wavelength range λ≤250nm by means of a first principles model. The model combines the high level ab initio potential energy surfaces of four excited electronic states and their coordinate dependent transition dipole moment vectors with quantum mechanical calculations of the photodissociation dynamics and the absorption spectra corresponding to excitations from many initial rovibrational states of the parent CO2. The calculations demonstrate that photodynamics from first principles can be realized for CO2 with high accuracy: The absorption cross section can be reliably calculated for λ≤250nm and T≤2500K and used for modeling the one-step photolytic reduction of CO2 to CO. An ab initio-based estimate of the contribution of low lying triplet states to the optical absorption of hot CO2 is also given.

JARZENIOWY PROMIENNIK CO[sub]2[/sub

The paper presents the physical basis of the constructed model of the fluorescent emitter of CO2 emitting infrared radiation with frequencies exactly coinciding with the absorption spectrum of carbon dioxide. This study describes the basic model and given a physical interpretation of the results. Attention is paid on the properties of the emitted radiation by the device and the ability to use the device in various fields.

Measurements of CO2 line parameters in the 9250–9500 cm−1 and 10,700–10,860 cm−1 regions

The absorption spectra of carbon dioxide have been recorded in two wavenumber ranges 9250–9500cm−1 and 10,700–10,860cm−1 of the near infrared region using a Bruker IFS 125HR Fourier transform spectrometer and a 30m multipass cell with the White type optical system. The spectra were recorded at spectral resolution of 0.03cm−1, room temperature, path length of 726.7m and at four pressures ranging from 187 to 674mbar. The achieved sensitivity (noise equivalent absorption) at the level of kν=7.2×10−10cm−1 allowed detection of numerous new transitions with intensity values down to 5×10−29cm/molecule. The respective measurement time is about 20h. The multispectrum fittings with the Voigt profile were performed to retrieve the line positions and intensities of 12 observed bands. Three hot bands of 12C16O2 in the 9250–9500cm−1 region were detected for the first time. The line intensities of 30032−00001 and 30033−00001 bands of 12C16O2 and of 20032−00001 band of 16O12C18O were measured for the first time.The uncertainty of the line position determination is estimated to be about 0.001cm−1 for the unblended lines with high value of signal-to-noise ratio. The uncertainty of the line intensity determination varies from 5% to 40% depending on the line strength and on extent of line overlapping. The measured line intensities of 30032−00001 and 30033−00001 bands together with those published for the 00051−00001 band were used to fit the effective dipole moment parameters of 12C16O2 for the ΔP=15 series of transitions, where P=2V1+V2+3V3 is a polyad number (Vi (i=1,2,3) are vibrational quantum numbers). The fitted parameters reproduce the measured line intensities within experimental uncertainties. Comparison of the measured line positions and intensities to those contained in HITRAN, GEISA, CDSD and AMES line lists is given.

Measurements of 12C16O2 line parameters in the 8790–8860, 9340–9650 and 11,430–11,505 cm−1 wavenumber regions by means of Fourier transform spectroscopy

Absorption spectra of carbon dioxide, 12C16O2, have been studied in the three wavenumber ranges (8790–8860, 9340–9650 and 11,430–11,505cm−1) of the near infrared region using spectrophotometric complex of V.E. Zuev Institute of Atmospheric Optics based on an Bruker IFS 125 HR and a 30m multipass cell with the White type optical system. The spectra were recorded at spectral resolution of 0.015cm−1, path length of 613.82m and at pressure range from 209 to 400mbar. The multispectrum fittings with the Voigt profile were performed to retrieve the line positions and intensities of eight bands 5001r−00001 (r=3, 4), 2003r−00001 (r=1,2,3) 2113r−01101 (r=1,2) and 00051−00001. The uncertainty of the line position determination is estimated to be about 0.001cm−1. The absolute accuracy of the line intensity measurement is 5% for 5001r−00001 (r=3,4) bands, 3% for 2003r−00001 (r=1,2,3) bands, 10% for 00051−00001 band and 15% for 2113r−01101 (r=1,2) bands. The measured line intensities were used to fit the effective dipole moment parameters of 12C16O2. The fitted parameters reproduce the measured line intensities within their experimental uncertainties. A comparison of measured positions and intensities with those contained in HITRAN, CDSD, AMES-296, and High-T databases is presented and discussed.

Air pressure broadening and shifting of high- J lines of (00011) ← (00001) band of 12C 16O 2

The absorption spectra of carbon dioxide (isotope 626, natural abundance in air, ambient temperature) have been studied at total pressures 68–570 Torr with spectral resolution 0.003–0.005 cm −1. The spectra were measured in the spectral domain of 2273–2393 cm −1 by FTIR spectrometer Bruker IFS 125 HR equipped with White-type multipass cell (6.4–41.6 m) and with a cell having 10 cm optical path length. Pressure broadening and shift coefficients were obtained from a series of spectra by means of a nonlinear least-squares spectral fitting technique for the lines of the (00011)←(00001) band with rotational quantum number up to J=82. For fitting of the individual line shapes, we used the Voigt profile with pre-calculated Doppler broadening parameter. The experimental pressure broadening and shift coefficients are compared with the values available in spectroscopic databases HITRAN 2008 and Carbon Dioxide Spectroscopic Databank (CDSD-296) and with other experimental values reported in the literature.

High sensitivity CW-cavity ring down spectroscopy of 12CO 2 near 1.35 μm (II): New observations and line intensities modeling

In a previous contribution [Kassi S, Song KF, Campargue A. High sensitivity CW-cavity ring down spectroscopy of 12CO 2 near 1.35 μm (I): line positions. JQSRT 110 (2009) 1801–1814], the line positions analysis of the high sensitivity absorption spectrum of carbon dioxide has been reported in the 7123–7793 cm −1 region. In this second contribution, the spectral region investigated by CW-cavity ring down spectroscopy has been extended up to 7917 cm −1. It added about 400 lines to our previous list of about 2500 transitions. These additional lines include transitions belonging to six newly observed 12C 16O 2 bands for which we provide the spectroscopic parameters. Over the whole 7123–7917 cm −1 region, the accurate intensities of about 2900 lines belonging to four isotopologues ( 12C 16O 2, 13C 16O 2, 16O 12C 18O and 16O 12C 17O) were retrieved with an average accuracy of 3%. Intensity values range between 1.2×10 −29 and 4.1×10 −25 cm/mol. Compared to the present version of the carbon dioxide spectroscopic databank recently adopted for the HITRAN database, important deviations were evidenced for some weak bands of the main isotopologue. The CW-CRDS intensity data relative to a total of 46 12C 16O 2 bands together with selected intensity information available in the literature for nine bands have been fitted simultaneously using the effective operators approach. The Δ P=11 set of the 12C 16O 2 effective dipole moment parameters has been refined leading to a much better agreement with the measured intensity values. In addition, the Δ P=10 effective dipole moment parameters of the 16O 12C 18O minor isotopologue were determined for the first time. The obtained results will help to improve the carbon dioxide spectroscopic databank (CDSD).

High sensitivity CW-cavity ring down spectroscopy of 12CO 2 near 1.35 μm (I): line positions

The absorption spectrum of carbon dioxide in natural isotopic abundance has been investigated by CW-cavity ring down spectroscopy with a new setup based on fibred distributed feedback (DFB) laser diodes. By using a series of 25 DFB lasers, the CO 2 spectrum was recorded in the 7123–7793 cm −1 region with a typical sensitivity of 3×10 −10 cm −1. A 2125 transitions with intensities as low as 1×10 −29 cm/molecule were detected and assigned to the 1 2C 16O 2, 1 6O 1 2C 1 7O and 1 6O 1 2C 1 8O isotopologues. For comparison, only 357 of them were previously reported from Venus spectra and 344 transitions were included in the 2004 version of the HITRAN database. The band by band analysis has led to the determination of the rovibrational parameters of 28, 2 and 6 bands for the 1 2C 16O 2, 1 6O 1 2C 1 7O and 1 6O 1 2C 1 8O isotopologue, respectively. While the uncertainty on the experimental line positions is on the order of 5×10 −4 cm −1, the average deviation from the 1 2C 16O 2 calculated values provided by the most recent version of the carbon dioxide spectroscopic databank (CDSD) is −2.8×10 −3 cm −1 with an root mean square ( rms) deviation of 3.5×10 −3 cm −1. Maximum deviations in the order of 0.02 and 0.12 cm −1 were evidenced for some bands of the 1 6O 1 2C 1 7O and 1 6O 1 2C 1 8O minor isotopologues. The obtained results improve significantly the previous measurements from Venus spectra and will be valuable to refine the sets of effective Hamiltonian parameters used to generate the CDSD database.

High sensitivity CW-CRDS spectroscopy of 12C 16O 2, 16O 12C 17O and 16O 12C 18O between 5851 and 7045 cm −1: Line positions analysis and critical review of the current databases

The exhaustive line positions analysis of the absorption spectrum of carbon dioxide in natural abundance has been performed on the basis of high sensitivity CW-Cavity Ring Down spectroscopy between 5851 and 7045 cm −1 (1.71–1.42 μm). The achieved sensitivity (noise equivalent absorption α min ∼ 2–5 × 10 −10 cm −1) have allowed the detection of 8293 transitions of the 12C 16O 2, 16O 12C 17O and 16O 12C 18O isotopologues. They belong to a total of 130 bands. Line intensities of the weakest transitions are on the order of 2 × 10 −29 cm/molecule. The rovibrational assignments were performed on the basis of accurate predictions of the effective Hamiltonian model of the respective isotopologues. The band-by-band analysis has allowed deriving accurate spectroscopic parameters of 121 bands from a fit of the measured line positions. A number of resonance interactions were identified. In particular, the first observation of an interpolyad coupling is reported for the 16O 12C 18O isotopologue. The results of the complete line positions analysis are provided as Supplementary material. The obtained experimental dataset which is the most complete in the considered region, has been used for a critical review of the most currently used spectroscopic databases of carbon dioxide: HITRAN, GEISA, HITEMP, and the recent JPL and CDSD databases.

A (nearly) complete experimental linelist for 13C 16O 2, 16O 13C 18O, 16O 13C 17O, 13C 18O 2 and 17O 13C 18O by high-sensitivity CW-CRDS spectroscopy between 5851 and 7045 cm −1

An experimental database for the 13C 16O 2, 16O 13C 18O, 16O 13C 17O, 13C 18O 2 and 17O 13C 18O isotopologues of carbon dioxide has been constructed on the basis of the high-sensitivity absorption spectrum of carbon dioxide with 99% enrichment in 13C recorded by CW-cavity ring down spectroscopy (CW-CRDS) between 5851 and 7045 cm −1. As a result of the achieved sensitivity (typical noise equivalent absorption α min ∼2–5×10 −10 cm −1) combined with the high linearity and dynamics (more than four decades) of the CW-CRDS technique, the amount of spectroscopic information contained in these spectra was considerable. A total of 8639 transitions of the 13C 16O 2, 16O 13C 18O, 16O 13C 17O, 13C 18O 2 and 17O 13C 18O isotopologues with line strength as low as 5×10 −29 cm/molecule were assigned. They belong to a total of 150 bands, while less than 20 bands were previously reported by Fourier transform spectroscopy. The excellent agreement between the predictions of the effective operators model and the observations has allowed using an automatic search program to assign the weaker lines observed in the congested spectrum. The spectroscopic parameters of the vibrational upper levels were obtained from a fit of the measured line positions. A number of resonance interactions were observed; in particular, several occurrences of interpolyad anharmonic couplings not included in the polyad model of effective Hamiltonian, were found to affect a few bands of the 16O 13C 18O and 16O 13C 17O isotopologues. In the list of 8639 transitions, which are provided as Supplementary material, line positions are experimental values (typical uncertainty in the order of 1×10 −3 cm −1), while line strengths were calculated at 296 K by using the effective operators approach (typical uncertainty in the order of 5%). In the case of the 13C 16O 2 isotopologue, the reported transitions represent 99.65% of the total absorbance in the region considered.

Comment on “Spectroscopic database of CO 2 line parameters: 4300–7000 cm –1”

The “Spectroscopic database of CO 2 line parameters: 4300–7000 cm –1” constructed by Toth et al., has been considered in relation with our previous and current studies of the absorption spectrum of carbon dioxide (CO 2) by high-sensitivity CW-cavity ring down spectroscopy (CW-CRDS) in the 5850–7000 cm −1 region. Part of the line parameters of the database are based on accurate spectroscopic measurements by Fourier transform spectroscopy (FTS) but Toth et al. have chosen to fix to a very low value (4×10 −30 cm/molecule) the lower intensity cut off. This value which is far below the FTS detection limit has led to long range extrapolations to high J values and to the inclusion of weak unobserved bands which were theoretically predicted. In the 5850–7000 cm −1 region, most of these calculated transitions were previously observed by CW-CRDS. The comparison with the CW-CRDS 13CO 2 spectrum in this region, has evidenced that (i) many weak bands above the intensity cut off are missing; (ii) there are important deviations between the line parameters provided in the database and our previous observations both for line positions (up to 1.7 cm −1) and line intensities (up to a factor 80). Our discussion was limited to the three 13C species ( 13C 16O 2, 16O 13C 18O and 16O 13C 17O) but the conclusions should apply to the other isotopologues in particular 12C 16O 2 and to the full spectral range of the database. Alternatively, the global effective operators models for CO 2 can reproduce satisfactorily all the experimental line positions and line intensities available in the literature. This polyad model, which has been developed for most of the CO 2 isotopologues, constitutes an interesting alternative for the most accurate and complete CO 2 database. In particular, very weak bands, accidental resonances, intensity transfers and extra lines are accurately accounted for and predicted by this polyad model.