Measurements and empirical modeling of pure CO 2 absorption in the 2.3- m region at room temperature: far wings, allowed and collision-induced bands

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1 Measurements and empirical modeling of pure CO 2 absorption in the 2.3- m region at room temperature: far wings, allowed and collision-induced bands M. V. Tonkov, N. N. Filippov, V. V. Bertsev, J. P. Bouanich, Nguyen Van-Thanh, C. Brodbeck, J. M. Hartmann, C. Boulet, F. Thibault, and R. Le Doucen Measurements of pure CO 2 absorption in the 2.3- m region are presented. The cm 1 range has been investigated at room temperature for pressures in the atm range by using long optical paths. Phenomena that contribute to absorption are listed and analyzed, including the contribution of far line wings as well as those of the central region of both allowed and collision-induced absorption bands. The presence of simultaneous transitions is also discussed. Simple and practical approaches are proposed for the modeling of absorption, which include a line-shape correction factor that extends to approximately 600 cm 1 from line centers. Key words: CO 2 infrared spectra, induced band, far wings Optical Society of America 1. Introduction The anomalous brightness of the nightside of Venus in the atmospheric window near 2.3 m is well known. 1,2 Radiation in this spectral region originates from low altitude layers and is due mostly to CO 2, which is the major constituent of the atmosphere. Its intensity is strongly underestimated by computations made with Lorentzian line shapes. Unfortunately, the mechanisms involved in radiation absorption emission in this spectral range are not clear and result from several phenomena. These in- M. V. Tonkov, N. N. Filippov, and V. V. Bertsev are with the Institute of Physics, St. Petersburg University, Peterhof, St. Petersburg, Russian Federation. J. P. Bouanich, N. Van- Thanh, C. Brodbeck, J. M. Hartmann, and C. Boulet are with the Laboratoire de Physique Moléculaire et Applications, Laboratoire associé aux Universités de Paris-Sud et Pierre et Marie Curie, Centre National de la Recherche Scientifique, Unité Propre de Recherche 136, Université Paris-Sud, Campus d Orsay, Bâtiment 350, Orsay cedex, France. F. Thibault and R. Le Doucen are with the Département de Physique Atomique et Moléculaire, Centre National de la Recherche Scientifique, Unité de Recherche Associée 1203, Université de Rennes I, Campus de Beaulieu, Rennes cedex, France. Received 22 May 1995; revised manuscript received 2 February $ Optical Society of America clude the breakdown of the Lorentz shape in the line wings, absorption by weak overtone and hot allowed dipolar transitions of CO 2, as well as significant contributions of collision-induced absorption. Because of the large amount of computational time required by remote-sensing spectra inversion, simple approaches must be used for the modeling of absorption. We present a study of the different processes that contribute to absorption by pure CO 2 in the 2.3- m region when large absorber amounts are considered. The CO 2 spectrum in this region has a great absorption coefficient variation approximately 4 orders of magnitude and results from various types of spectral feature allowed and induced bands, band wings that have to be studied with various resolutions. It was therefore necessary to combine the efforts of different research groups having a variety of experimental setups. The absorption by relatively small path lengths was measured in Orsay, the allowed bands in the cm 1 region were studied in Rennes, and the weak bands in the cm 1 region were investigated using the multipass cell in St. Petersburg. We present the synthesis of all the experiments conducted by these groups and we provide data on absorption by pure CO 2 in the cm 1 range. The measurements were done at room temperature by using long optical paths and high pressures, raising the effective gas abundance to 10 km 20 August 1996 Vol. 35, No. 24 APPLIED OPTICS 4863

2 Table 1. Experimental Apparatus Group Apparatus St. Petersburg Rennes Orsay Spectrometer Grating at first order Fourier transform Fourier transform Grating at first order Bruker HR120 Bruker IFS 66V Ge low-pass filter cm 1 filter No filter Ge low-pass filter 3.0-cm 1 resolution 0.1-cm 1 resolution 0.5-cm 1 resolution 4.0-cm 1 resolution Source Halogen tungsten lamp Halogen tungsten lamp Glow bar Glow bar Detector Room temperature PbS Liquid nitrogen InSb Liquid nitrogen InSb Liquid nitrogen InSb Cell 4-m-long multipass 2-m-long multipass 3-m-long single pass 7-cm-long single pass m paths 120-m paths 3-m paths 7-cm paths Stainless steel Stainless steel Stainless steel Titanium CaF 2 windows CaF 2 windows Sapphire windows Sapphire windows Temperatures Stabilized 1 K Stabilized 0.5 K Stabilized 1 K Stabilized 1 K K range 297-K range K range 292-K Pressures Bourdon manometer Bourdon and transducer Piezoresistive transducer Sedeme transducer 0.1-atm precision 0.1-atm precision 0.3-atm precision 0.1-atm precision atm range 1 22-atm range atm range atm range Studied region cm cm cm cm 1 atm. The contributions of far wings of the 1 3 band as well as those of bands centered within the studied wave-number range are analyzed. It is shown that absorption results from the usual allowed bands as well as collision-induced vibrational transitions including a simultaneous transition. Simple empirical approaches are proposed to model the different contributions to the spectra. It is shown that the central region of allowed bands can be computed by using spectroscopic data from databases 3,4 or using molecular constants from Ref. 5. Integrated band intensities are measured from the present data and a simple band-shape model was used for collision-induced contributions. Finally, we propose an empirical correction to the Lorentz line shape that enables computation of line wings to approximately 600 cm 1 from line center. The remainder of the paper is divided into two parts. In Section 2 we describe the experimental details and data reduction procedures. In Section 3 we have organized the presentation of data into three parts devoted, respectively, to contributions of farwing line shape, allowed transitions located in the spectral region, and collision-induced bands. 2. Experiments A. Setups and Data Analysis Measurements of pure CO 2 absorption in the 2.3- m region have been made by three different groups using a variety of experimental setups. The main characteristics of the apparatus are described in Table 1. The data of different sources were used in the spectral shape analysis of various regions. The studies of the 1 3 band wing shape in the cm 1 region were based mainly on the Orsay data. The allowed bands centered between 3950 and 4050 cm 1 were studied using the Rennes data obtained at higher resolution. The weak bands within the cm 1 range were registered by the St. Petersburg group since the other measurements in this region were invalid because of the too weak absorption for the path lengths used. Purity of the CO 2 gas used is important because the effective gas content reached 10 km atm. The gas used in Orsay was supplied by Alphagaz with a stated purity of %. In the Rennes experiments the gas was supplied by Prodair Airproducts with a stated purity of %. In both cases, the main impurities a few ppm 10 6 were water and hydrocarbons C n H m. The most difficult experiment was done with a density of 20.1 amagats in the St. Petersburg multipass cell with an optical path length of 482 m. Since traces of CO, CH 4,H 2 O, and N 2 O were detected in the original gas sample, an additional gas purification was performed by using chemical KOH, P 2 O 5 and physical from a gas-mask capsule absorbants. Unfortunately, we are not sure that the traces of N 2 O were removed completely since the 2 3 band of N 2 O and the band of CO 2 are located in the same frequency range and have a similar shape. The other impurities were absent from the spectrum after three days of purification. In all cases the absorption coefficient, n CO2 at wave number and CO 2 density n CO2 was obtained from two experiments, i.e.,, n CO2 1 d ln I, n CO 2 I, 0, (1) where d is the path length and I, n CO2 and I, 0 are the intensities that were measured with the gas sample and an empty cell, respectively. The density of CO 2 in amagats 1 amagat mol cm 3 was deduced from the measured temperature and pressure of the gas sample by using the data of Ref. 6. B. Data Intercomparisons and Checks Since data on CO 2 absorption was provided by various groups, intercomparisons between the different 4864 APPLIED OPTICS Vol. 35, No August 1996

3 Fig. 1. Experimental room temperature pure CO 2 absorption coefficients for a density of 20 amagats: curve, Rennes spectrum; E, St. Petersburg spectrum. results enabled a test of experimental procedures. This was done in two ways. When measurements had been made under the same conditions, n CO2 by different groups, direct comparison of absorption coefficients was possible. An example is plotted in Fig. 1 where spectra recorded in St. Petersburg and Rennes are compared. The agreement is satisfactory in the range in which absorption coefficients were measured with precision. In spectral regions that are sufficiently far away from allowed bands of significant contribution, the absorption results from far wings and collision-induced transitions. It is thus proportional to the square of the CO 2 density. In these regions, one can extract the normalized absorption coefficient B 0 cm 1 amagat 2 : B 0 1 n CO2 2, n CO 2. (2) This quantity enables comparison of experimental results obtained for different densities. The plot of Fig. 2 demonstrates the consistency of the experiments. Fig. 3. Experimental room temperature pure CO 2 absorption coefficient for a density of 20 amagats showing some of the contributions: a, far wing; b, allowed bands; c, collision-induced absorption bands. 3. Analysis of Absorption Figure 3 presents a typical spectrum in the cm 1 range. The different contributions to absorption that can be seen clearly are the following: a The smooth baseline is due mainly to the far wings of the intense C 16 O 2 band that is centered on the low-frequency side of the considered spectral range. This contribution increases with the square of the CO 2 density. Features that stick out from this baseline are due to local absorption transitions that are of different types, distinguishable through their dependences on density. b Dipole allowed absorption bands whose integrated intensities increase linearly with density; the structure centered near 4020 cm 1, for example, corresponds to the R branch of the band of 12 C 16 O 2. c Collision-induced absorption bands whose magnitudes increase as the square of density; the band centered near 4063 cm 1 was observed previously 7,8 and corresponds to the 12 C 16 O II vibrational transition. These different contributions to the overall absorption coefficient are analyzed and modeled hereafter. A. Far-Wing Contributions It is well known that absorption by far wings of CO 2 absorption lines is strongly sub-lorentzian. 7 This behavior results from the combined influences of line mixing and finite duration of collision. 9,10 Theoretical approaches for direct computations 9 12 require significant computer time, and their accuracies are still insufficient for practical applications. Since the latter require precise, low computer cost, and easy to implement modeling of line-wing absorption, empirical corrections to the Lorentz shape are generally used; the absorption coefficient for pure CO 2 can then be written as Fig. 2. Experimental room temperature pure CO 2 normalized absorption coefficients: }, Orsay-2 values; curve, Orsay-1 values; F, St. Petersburg values;, values from Burch et al. 7 S wing 2, T, n CO2 n CO2 s l l lines l l l T, l. 2 (3) 20 August 1996 Vol. 35, No. 24 APPLIED OPTICS 4865

4 Fig. 4. Room temperature pure CO 2 absorption coefficients for a density of 20 amagats: E, experimental values; computed values accounting for allowed HITRAN-92 and induced transitions with the factor from dashed curve, Ref m region ; solid curve, Ref m region. Fig. 5. Room temperature pure CO 2 absorption coefficients for a density of 20 amagats: E, experimental values; solid curve, computed values accounting for allowed and induced transitions with the factor of Table 2; dashed curve, computed contribution of the far wings of the 1 3 band. The spectroscopic data l, S l, s l, which are the position, intensity, and self-broadening coefficient of line l, were taken from the HITRAN-92 database. 3 The line-shape correction factor is considered independent of the transition but depends on both temperature and collision partner CO 2 in the present case. A large set of factors has been proposed for pure CO 2 line wings. 7,13 18 Except for the research of Burch et al. 7 who have investigated various spectral regions, all the other studies refer to the 3 band. On the other hand, the only factor for pure CO 2 and temperatures in the K range is, to our knowledge, that of Ref. 13, which was deduced from measurements beyond the 3 bandhead. In Fig. 4 we plotted a comparison between the present experimental results and predictions using the factors of Refs. 7 and 13. The methods that were used to account for allowed and induced bands are discussed below. Figure 4 shows that line-wing contributions are underestimated when we use a factor adapted to the 4- m region 13 ; this is consistent with the results of Figs. 13 and 14 of Ref. 7, which indicate that line wings in the 3 band are more sub- Lorentzian than those of the 1 3 band. The agreement obtained with Burch s factor 7 is much better although absorption in the far wing seems slightly overestimated. To correct some of the discrepancies we have derived a new factor, which is described in Table 2, for the 2.3- m spectral region. The accuracy of the fit is shown in Fig. 5. These computations show that Table 2. Parameters of the Factor Fitted from the Current Experiments T 296 K cm exp exp exp most of the far-wing contributions in the cm 1 region result from lines of the 1 3 I,II bands that are centered 3,5 near 3700 and 3600 cm 1. The factor deduced from the present experiments thus extends to approximately 600 cm 1 from line centers. We emphasize that this factor is empirical and it probably corrects for a number of small local contributions weak allowed bands, collision-induced absorption, simultaneous transitions, dimers,... that have not been accounted for in the computations. B. Allowed Bands Located in the Spectral Region Molecular spectroscopic databases 3,4 provide spectroscopic information on the lines centered in this wavenumber range whereas Ref. 5 describes the main bands. Because of the moderate densities involved by the present experiments, use of the modified Lorentzian shape of Ref. 19 generally enables accurate prediction of absorption coefficients in the central region of absorption bands. The prediction is more questionable for Q-branches in which line-mixing effects are significant due to the small spacing between lines; nevertheless such regions are quite narrow and errors in the computations have little consequences, considering the aim of this study. We have thus computed the absorption coefficients by using the following expression: 1 n Lor CO2 S l T n cor, n CO2 lines s CO2 l T l l 2 n s CO2 l T 2 cor l, n CO2. (4) The spectroscopic data l, S l, s l, which are the position, intensity, and self-broadening coefficient of line l, were again taken from the HITRAN-92 database. 3 The correction function cor was computed following Ref. 19 by using the corrective factor of Table 2. Note that cor is equal to the sub-lorentzian factor in the far wing but the intensity removed from the wing is transferred to the central part of each line 4866 APPLIED OPTICS Vol. 35, No August 1996

5 Fig. 6. Room temperature pure CO 2 absorption coefficients for a density of amagats: solid curve, experimental absorption Rennes data corrected for far wings difference between the experimental data and that calculated according to Eq. 3. Computed contributions of local allowed transitions: dot dash curve, HITRAN-92 database; dashed curve, HITRAN-95 database. Fig. 7. Room temperature pure CO 2 absorption coefficients for a density of 20 amagats: F, experimental values; solid curve, computed values accounting for allowed and induced transitions with the optimized factor of Table 2 and the HITEMP database; dashed curve, computed contribution of the far wings of allowed bands centered outside the considered spectral region. The lower plot gives the relative difference between observed and computed spectra. such that the line intensity is conserved. Nevertheless, at the considered density, the Lorentzian shape is quite accurate and corrections remain small see, for example, Ref. 20. When compared with experimental values corrected from far-wing and collision-induced contributions the computed absorption by local allowed transitions is in reasonable agreement with experiment with few exceptions. For example, HITRAN-92 does not enable correct modeling of absorption in the band near 4005 cm 1 probably owing to an error in the Herman Wallis factor. Therefore, thanks to L. Rothman, this part of the database has been replaced by the 1995 HITRAN version that will soon be available, leading to a reasonable agreement with experiment as it appears from Fig. 6. Similarly, the 2 3 band of 16 O 13 C 18 O centered 5 near 4508 cm 1, which is not given in the HITRAN-92 database because of its intensity cutoff, is responsible for some of the observed discrepancy: In order to test the completeness of the HITRAN-92 base for local allowed transitions for the large absorber amounts considered here, we have compared the allowed contributions in the cm 1 region computed with HITRAN-92 and with the HITEMP database. This calculation has been made by Bezard and Drossard within the framework of Ref. 2. Comparison of Figs. 5 and 7 shows that the differences can be significant, as has already been shown in Ref. 2 the arrow in Fig. 7 corresponds to the center of the 2 3 band of 16 O 13 C 18 O. The remaining discrepancies, restricted to the cm 1 spectral region, are due mainly to incorrect modeling of the collision-induced absorption missing bands, wrong shape in the wings of these bands and the far-wing contributions of the I,II,III bands centered beyond 4800 cm 1 as well as neglecting other contributions such as simultaneous transitions. C. Collision-Induced Bands Collision-induced absorption bands of CO 2 in the near IR have been observed previously. 7,8,21 23 In this study the main bands have been identified by their increasing intensity with squared density, elimination of allowed bands, and knowledge of the energies of CO 2 vibrational levels. 5 Their integrated intensities have been estimated by integration of the absorption coefficient after corrections for the baseline that is due to line wings and subtraction of allowed bands. The results obtained, which are given in Table 3, have large uncertainties and should be considered with great caution. Unfortunately, there is, to our knowledge, a lack of data for the intensities of these bands. Table 3 also lists the band centers that are compared with the theoretical predictions deduced from Ref. 5. The calculated transition frequencies for CO 2 are in good accordance with measured ones with one exception: The feature near 4280 cm 1 shows a quadratic dependence on density and thus should be treated as an induced band. It was detected at Table 3. Observed Collision-Induced Bands: Estimated Band Centers and Intensities Upper Level of Vibrational Transitions Calculated Frequency cm 1 Measured Frequency cm 1 Measured Intensity 10 6 cm 2 amagat III II I a II a II I I I I I a The assignment of weak observed structures is doubtful. 20 August 1996 Vol. 35, No. 24 APPLIED OPTICS 4867

6 higher densities both by the St. Petersburg team and in Orsay, but its wave-number center 4278 cm 1 does not coincide with any possible collision-induced transition from the ground state. However, its central wave number is close to that associated with the double transition 1 a I and 2 3 b in molecules a and b at cm 1. The appearance of the Fermi dyad 1 a I,II 2 3 b can be used to explain the great difference in intensities of the components at 4250 and 4383 cm 1 : the observed band at 4383 cm 1 corresponds to the superposition of single and double transitions. This interpretation can be confirmed by the absence of the two bands at 4278 and 4383 cm 1 in the spectra of high density CO 2 Ar mixtures measured in Orsay. For practical applications, modeling of the shape of near-infrared collision absorption bands is required. Introducing the spectral density function the collision-induced absorption CIA coefficient is given by Fig. 8. Optimized normalized spectral density n for the collisioninduced bands as a function of the detuning wave number from the band center. 1 exp hc k CIA, n CO2 n 2 b T CO2 S band T band, T, (5) band 1 exp hc k b T band, T d where S band T is the band intensity, band is the band center see Table 3, and the integral expands over the whole region of significant absorption. In the absence of a simple theoretical model for the computation of the spectral density function, band, T has been obtained using the following procedure: It was first assumed that the normalized line shape is independent of the type of induced vibrational band. This hypothesis seems acceptable for g g bands but is probably less appropriate for g g bands with significantly different structures. Then the central part of 40 cm 1 was deduced from the current observed values of the collision-induced band located around 4063 cm 1. The wings 40 cm 1 were obtained by a shape derived from previous experiments made in the far-infrared region for the pure collision-induced rotational band, 24,25 which is free of any contamination by contributions of allowed transitions. The resulting density function is plotted in Fig. 8. A test of the current approach i.e., Eq. 5, Table 3, and Fig. 8 is presented in Fig. 9. Although the computation accounts for the main features, significant discrepancies remain. They may result from a number of approximations that include large uncertainties on the intensities and shapes that were used for modeling collision-induced absorption. Furthermore it is clear that a number of weak absorption contributions have not been taken into account. For example, the feature indicated by an arrow in Fig. 9 at 4430 cm 1 has to be attributed to an allowed transition because of its density dependence. Its origin is not clear. The rather strong CO 2 band 3 is in this region. However, this explanation remains doubtful since the strong 2 3 band of N 2 O, which may be present as impurity in our samples, is also in this region. Computations with the HITRAN-92 database 3 enabled estimation of the N 2 O amount 0.05% and removal of this absorption. Finally Fig. 10 gives a global idea of the quality of the optimized fit obtained in the spectral region Fig. 9. Room temperature pure CO 2 absorption coefficients for a density of 20 amagats: E, experimental values corrected for local allowed transitions with the HITRAN-92 database; dashed curve, computed contribution of local collision-induced transitions; solid curve, experimental absorption corrected for local allowed and collision-induced transitions difference between the previous two APPLIED OPTICS Vol. 35, No August 1996

7 available part of the 1995 version of HITRAN for CO 2 prior to publication. Fig. 10. Room temperature pure CO 2 absorption coefficients for a density of 20 amagats. Ratio of the experimental to computed absorption with the HITRAN-92 database including all the mechanisms and the optimized factor of Table 2. where the use of the HITRAN-92 database is valid. This fit can be considered reasonable. 4. Conclusion Measurements and analysis of the processes that contribute to radiation absorption in the cm 1 spectral range have been presented. Empirical modelings of the contributions of collision-induced bands and far line wings have been proposed that enable satisfactory agreement with experiments in the cm 1 range at room temperature. Remaining discrepancies result from weak absorption processes allowed, collision-induced bands, simultaneous transitions that have not been accounted for. Nevertheless, the empirical line-shape correction function proposed enables correct modeling of spectra, accounting for line-wing contributions to approximately 600 cm 1 from line centers. This study has been limited to room temperature, whereas modeling of spectra resulting from the deep atmosphere of Venus requires knowledge of the farwing line-shape dependence with temperature in the K range. As high temperature and long path-length measurements are hardly feasible in the laboratories, the following method may be considered: Taking into account recent progress in the theory of far-wing absorption, 9,12,26 29 the calculation of the far-wing line shape for the CO 2 CO 2 system can be developed and compared with an experimental factor at room temperature. Since the formalism can reasonably be used to predict the temperature dependence of the far-wing absorption for various other systems, 12,27 29 it can also be used in a second step to derive the temperature dependence of the factor for CO 2 CO 2. The authors are grateful to P. Drossart and B. Bézard from Observatoire de Meudon for communicating the results they obtained with the HITEMP database. They also thank L. Rothman who made References 1. B. Bézard, C. de Berg, D. Crisp, and J. P. Maillard, The deep atmosphere of Venus revealed by high-resolution nightside spectra, Nature London 345, J. B. Pollack, J. B. Dalton, D. Grinspoon, R. B. Wattson, R. Freedman, D. Crisp, D. A. Allen, B. Bézard, C. de Berg, L. P. Giver, Q. Ma, and R. H. Tipping, Near-infrared light from Venus nightside: a spectroscopic analysis, Icarus 103, L. S. Rothman, R. R. Gamache, R. H. Tipping, C. P. Rinsland, M. A. H. Smith, D. C. Benner, V. Malathy Devi, J. M. Flaud, C. Camy-Peyret, A. Perrin, A. Goldman, S. T. 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