Determination of the Line-Shift and Line-Broadening Coefficients in the ν3 Band of NO2 Perturbed by O2, N2, H2, D2, and CO2

Journal of Molecular Spectroscopy 198, 18 –26 (1999) Article ID jmsp.1999.7912, available online at http://www.idealibrary.com on

Determination of the Line-Shift and Line-Broadening Coefficients in the n 3 Band of NO 2 Perturbed by O 2, N 2, H 2, D 2, and CO 2 S. Bouazza,* A. Kissel,† B. Sumpf,† ,1 and H.-D. Kronfeldt† *De´partement de Physique, Faculte´ des Sciences, B.P. 1039, 51687 Reims Cedex 2, France; and †Optisches Institut der Technischen Universita¨t Berlin, Sekretariat PN 0-1, Hardenbergstr. 36, 10623 Berlin, Germany Received December 14, 1999; in revised form June 22, 1999

A high-resolution three-channel diode-laser spectrometer was used to record a large number of spectra with 14N 16O 2 and foreign gas pressures ranging from 0.1 to 0.4 and 20 to 150 Torr, respectively, at room temperature. The 6.2-mm region corresponding to the n 3 band of NO 2 was analyzed and the broadening and shift coefficients were derived in the case of collisions between NO 2 and H 2, D 2, O 2, N 2, CO 2, and SO 2 for 13 lines with 18 # N0 # 38 and 1 # K0a # 5. This experimental study confirms general trends. The broadening coefficients decrease with an increase of the rotational quantum number N0 whereas the absolute values of the line-shift coefficient increase with increasing N0. In the case of the studied diatomic perturbers the size of the broadening coefficients corresponds to the size of the quadrupole moments. The only collision partner with nonvanishing dipole moment, SO 2, shows the largest broadening effect as expected. All shift coefficients are negative for the lines under study. © 1999 Academic Press Key Words: collisional lineshift; collisional linewidth; diode-laser absorption spectroscopy

n 3 band. The latter is widely used for measurements of atmospheric nitrogen dioxide concentrations in airborne experiments (balloon or satellite) (19). Another advantage of investigating strong n 3 band lines when measuring broadening or shift coefficients is the possibility of using only a very small amount of NO 2 (less than 0.5 Torr in a Herriott multipass absorption cell with a path length of 4.7 m and a volume of only 180 mL (20)). Under these conditions the influence of the self-shift and the self-broadening effects is insignificant. Until recently, no information was available concerning lineshift effects for NO 2 because of its relatively crowded spectrum. Shift coefficients in the case of collision with noble gases were published for seven lines of NO 2 by Sumpf et al. (21) and Bouazza et al. (22). Extending these experiments toward collisions with diatomic and triatomic perturbers in the present work line-broadening coefficients of NO 2 perturbed with H 2, D 2, CO 2, and in selected cases SO 2, and moreover line-shift coefficients for N 2, O 2, H 2, D 2, CO 2, and SO 2, were measured for at least 13 lines at room temperature under laboratory conditions for the first time.

INTRODUCTION

The atmospheric important pollutant NO 2 was investigated extensively in the microwave, the infrared, and the visible regions (1–3). During these last years considerable concern was focused on precise experiments and calculations on line positions and intensities, leading for instance to the determination of accurate spin–rotation ground state levels since this molecule exhibits an unpaired electron. Nevertheless, we can recognize that only a few line-broadening measurements were achieved so far in comparison to other molecules like H 2O, CH 4, and O 3, where precise line-shift data are known (4 –7) or like CO, CO 2, SO 2, and O 3, where broadening coefficients and line mixing have been the subject of numerous studies (8 –15). Pressure shift and pressure broadening are important for providing information concerning intermolecular interactions (16). Furthermore they can help to analyze the Earth or planetary atmospheres. The interest in these data is increasing rapidly at the end of this century: some examples of measuring NO 2 concentrations in the atmosphere are given in Refs. (17, 18). Line intensity and line broadening data are required with high accuracy for quantitative spectroscopic studies on atmospheric constituents. Experimentally, it is easier to deduce precisely these parameters using strong lines. Under this aspect the most preferable absorption region in the case of NO 2 is located around 6.2 mm which corresponds to the strongest rotational–vibrational infrared band of this molecule, i.e., the

MATERIALS AND METHODS

The two-channel setup (23–26) previously used was extended to a three channel system as presented in Fig. 1 in order to determine line-shift coefficients. The diode laser is placed within a helium-flow cryostat Oxford CF 1104 and is excited with rectangular current pulses. The laser beam is focused by a mirror system containing off-axis elliptical and parabolic

1

Present address: Elight Laser Systems GmbH, Warthestr. 21, 14513 Teltow, Germany. 18 0022-2852/99 $30.00 Copyright © 1999 by Academic Press All rights of reproduction in any form reserved.

LINE-SHIFT AND LINE BROADENING IN THE n 3 BAND OF NO 2

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FIG. 1. Experimental setup of the three-channel diode–laser spectrometer. OAP, - off-axis parabolic mirror; BS, beam splitter; SM, spherical mirror; D, HgCdTe photodiode.

mirrors into a monochromator Jobin Yvon HR 250 for mode separation. After mode selection the laser beam was divided by dielectric beam splitters into three rays. The beam splitters are wedged and have a reflectivity of 50% and a transmission of 50%. The line-shifts were measured by comparing the line positions in the sample channels at high total pressures up to 150 Torr with the line positions in the reference channel at low NO 2 pressures. The Herriott cell mentioned above was used as a sample cell, whereas a linear cell of 1.5-m path length was implemented as a reference cell. In the third channel, the calibration channel, a self-built air-spaced confocal e´talon with a free spectral range of 0.01 cm 21 was inserted for relative wavenumber calibration. For all channels the signals were detected with HgCdTe photodiodes, amplified, detected in two synchronized digital storage oscilloscopes (Philips PM 3320 A), and read out via an IEEE 488 interface into an IBM compatible computer. The diode–laser cooler has a temperature stability of about 10 22 K. To reach a stability suitable for high-resolution spectroscopy a passive stabilization method was developed as described by Sumpf et al. (27) and Waschull et al. (28). Using this method the individual shots were accumulated corresponding to the maximum of a pronounced absorption line. Moreover, a linearization procedure was applied to every single-shot spectrum before accumulation, i.e., the measured time equidistant points were transformed into wavenumber equidistant points by applying the e´talon fringes measured simultaneously. Typically, 30 single laser shots were digitized and accumulated

in order to improve the signal-to-noise ratio. The capabilities of this method are described in more detail by Waschull et al. (29) in the case of benzene. Especially the data treatment, particularly when the lines are overlapped, and the estimation of the confidence intervals for the line parameters are given in the mentioned paper. A wavenumber resolution of about 5 3 10 24 cm 21 and a sensitivity of about 10 23 was achieved with the experimental setup. The measured spectra in the reference and the sample channel were fitted simultaneously within one step. The advantage

FIG. 2. Result of a Voigt fit of reference (bottom line, p NO2 5 2.6 Torr, L 5 1.5 m) and sample channel (upper line, p total 5 88.2 Torr, L 5 4.7 m) for the NO 2 doublet at 1581.077 cm 21. F, experimental data; —, fitted Voigt profile.

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TABLE 1 Broadening Coefficients g for Unresolved n 3 Band NO 2 Doublets and Collisions with Di- and Triatomic Gases Together with Their Line Position n˜ 0 a and the Rotational Quantum Numbers N(, K(a, and K(c in the Ground State

a

1, doublet component.

of this data treatment is that the more pronounced line positions of weaker lines at low pressure in the reference channel can be used to avoid uncertainties in fitting the high pressure spec-

trum, where the weaker lines are not clearly observable. An example of such a fit of the unresolved doublet line with ground state rotational quantum numbers (30, 3, 31) at

TABLE 2 Shift Coefficients d for Unresolved n 3 Band NO 2 Doublets and Collisions with Di- and Triatomic Gases Together with Their Line Position n˜ 0 a and the Rotational Quantum Numbers Numbers N(, K(a, and K(c in the Ground State

a

1, doublet component.

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FIG. 3. Dependence of the broadening coefficients g NO2 -perturber for different molecular collisional partners. (A) N 2: F, experimental data this work; E, Pustogov et al. (31); 3, Malathy-Devi et al. (34); p, Goyette et al. (35). (B) O 2: F, experimental data this work; p, Goyette et al. (35). (C) air: F, experimental data this work; —, HITRAN 1996 data (36). (D) H 2: F, experimental data this work. (E) D 2: F, experimental data this work. (F) CO 2: F, experimental data this work.

1581.077 cm 21 from the n 3 band is shown in Fig. 2 (line positions marked with arrows). The two doublet components were fitted with individual line strengths and positions, but with identical broadening and shift values. Moreover, two weak lines were taken into account. These lines were assumed to have individual line positions, strengths, and widths but no shifts. For all lines the Doppler width was fixed to the theoretical value. The line profiles were approximated with a Voigt profile. For the numerical calculation of the Voigt profile the algorithm of Humlı´cek (32) was used. The fit was carried out by applying evolution strategies as described by Heiner et al. (33). As a result of the fit to Voigt profiles the line-shift was calculated by comparing the positions of absorption lines in the reference channel at low pressure and the positions of the same lines at higher pressures in the sample channel. By plotting the measured line-shift (in the pressure range up to 150 Torr,

typically between 5 z 10 24 and 2 z 10 23 cm 21) versus the total pressure the line-shift coefficient was determined. For the measurements commercially available NO 2 (99.8%), N 2 (99.999%), O 2 (99.998%), H 2 (99.999%), D 2 (99.7%), SO 2 (99.9%), and CO 2 (99.995%) were used. Usually, about 0.5 Torr NO 2 was filled into the reference cell and in the sample cell. In the latter one the perturber is added in five steps up to total pressures of 150 Torr. The pressure was measured with a Capacitron gauge (Leybold) with an uncertainty of about 0.5% of the measured pressure. RESULTS AND DISCUSSION

The new experimental data for the n 3 band are compiled in Table 1 and 2. For 13 NO 2 lines under study the broadening coefficients g (10 23 cm 21/atm) and shift coefficients d (10 23 cm 21/atm) for collisions between NO 2 and O 2, N 2, H 2, D 2, CO 2, and SO 2 were determined.

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decrease of the broadening coefficient with increasing N0 can be stated. The oxygen broadening coefficients are plotted versus N0 in Fig. 3B. Here the data given by Goyette et al. (35) are inserted, too. As before no differences are significant. A weak decrease could be supposed. Based on the measured O 2 and N 2 data air-broadening coefficients (Fig. 3C) were calculated using the well-known formula

gNO22air 5 0.79 z g NO22N2 1 0.21 z gNO22O2 . The averaging of all our data results in a value of (68.5 6 5.1) z 10 23 cm 21/atm which is in excellent agreement with the HITRAN 1996 database (36) (67.0 z 10 23 cm 21/atm). The relatively large uncertainty is originated in the quantum number dependence within the broadening. In Figs. 3D–F the H 2, the D 2, and the CO 2 broadening data are shown. Within the measured data and quantum number

FIG. 4. (A) Dependence of the N 2 shift coefficients d NO2 -N2 on the rotational quantum number N0. (B) Dependence of the N 2 shift coefficients d NO2 -N2 on the rotational quantum number K0a F, experimental data this work.

Figure 3 illustrates the quantum number dependence g (N0) for six different perturbers (N 2, O 2, air, H 2, D 2, and CO 2). Figures 4–9 show the quantum number dependence d (N0, K0a) for collisions with N 2, O 2, H 2, D 2, CO 2, and SO 2. Whereas for the broadening data due to the absence of any K0a dependence only the dependence on the rotational quantum number N0 is shown, each figure for the shift coefficients contains an individual plot for the N0 and K0a dependencies. For the individual data points the uncertainties are given as error bars. In the case of the broadening data for the majority of lines the size of the error bars is below the size of the symbols and therefore not visible. In Fig. 3A the nitrogen-broadening data are compared with previously measured values by Malathy-Devy et al. (34), Pustogov et al. (31), and Goyette et al. (35). Within the uncertainties no significant difference had to be stated. As expected no simple quantum number dependence is observed. Taking into account only the data point originated in this paper, a slight

FIG. 5. (A) Dependence of the O 2 shift coefficients d NO2 -O2 on the rotational quantum number N0. (B) Dependence of the O 2-shift coefficients d NO2 -O2 on the rotational quantum number K0a F, experimental data this work.

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literature. This fact can be deduced from the uncertainty in the underground, but agree to these data within their confidence intervals. The measurements can be compared to theoretical works published by Tejwani (37) and Tejwani and Yeung (38). Based on the Anderson–Tsao–Curnutte theory they calculated linebroadening coefficients for collisions with NO 2, N 2, and O 2. Whereas in the first paper Tejwani took into account only the dipole– dipole interaction in the case of self-broadening and the dipole– quadrupole interaction for nitrogen broadening but calculated data for individual lines, averaged values for nitrogen, oxygen, air, and self-broadening coefficients were given in the latter paper taking into account the dipole– dipole, dipole– quadrupole, quadrupole– dipole, and quadrupole– quadrupole interaction for the self-broadening and the dipole– quadrupole and quadrupole– quadrupole interaction for the N 2, air, and O 2 broadening. For the A-type n 3 band Tejwani and Yeung (38) calculated an averaged value for the nitrogen broadening of 80.6 z 10 23

FIG. 6. (A) Dependence of the H 2 shift coefficients d NO2 -H2 on the rotational quantum number N0. (B) Dependence of the H 2 shift coefficients d NO2 -H2 on the rotational quantum number K0a F, experimental data this work.

range no significant trend is visible, one can maybe suppose a weak decrease of the broadening data with increasing rotational quantum number. Up to now these experiments present the first data for collisions between NO 2 and these molecules. Additionally shift coefficients were measured for the perturbers mentioned above for the first time. In all experiments (Fig. 4, N 2; Fig. 5, O 2; Fig. 6, H 2; Fig. 7, D 2; Fig. 8, CO 2; and Fig. 9, SO 2) the absolute size of the shift increases with increasing N0, but no K0a trend is observable. In all cases the shift is negative. Besides these systematic investigations, self-broadening coefficients of NO 2 taking into account the presence of N 2O 4 (30) were determined for three Q-branch lines where doublet components are clearly resolved (Table 3). Due to an extremely structured background caused by several neighbored lines the data have large confidence intervals (up to 7 z 10 23 cm 21/atm) compared to data published previously by Pustogov et al. (smaller than 1 z 10 23 cm 21/atm) (31) and Malathy-Devy et al. (34). The absolute data are slightly larger compared to the

FIG. 7. (A) Dependence of the D 2 shift coefficients d NO2 -D2 on the rotational quantum number N0.(B) Dependence of the D 2 shift coefficients d NO2 -D2 on the rotational quantum number K0a F, experimental data this work.

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FIG. 8. (A) Dependence of the CO 2 shift coefficients d NO2 -CO2 on the rotational quantum number N0. (B) Dependence of the CO 2 shift coefficients d NO2 -CO2 on the rotational quantum number K0a F, experimental data this work.

cm 21/atm which is larger than our averaged value of (70 6 5) z 10 23 cm 21/atm. The given B-type band value of 68.2 z 10 23 cm 21/atm is much closer to our experimental data. One reason for this effect could be the overestimation of the vibrational dependence in the work of Tejwani which was found for SO 2 in previous measurements by Sumpf (39). Here the experimental data for A-type bands follow even the predictions by Tejwani (40) for B-type bands in the rotation quantum number dependence. Applying this knowledge to the data of NO 2 self-broadening the experimental data from our group (this work and Ref. (31)) with an average value of (96 6 14) z 10 23 cm 21/atm is again closer to the B-type predictions by Tejwani of 102.5 z 10 23 cm 21/atm than to the A-type value of 116.5 z 10 23 cm 21/atm. Larger deviations had to be stated for O 2 broadening. Here our averaged value is (61 6 4) z 10 23 cm 21/atm, whereas Tejwani predicts 45.2 z 10 23 cm 21/atm for A-type bands and 39.0 z 10 23 cm 21/atm for B-type bands. This was already observed by Goyette et al. (35). The comparison with air-broad-

FIG. 9. (A) Dependence of the SO 2 shift coefficients d NO2 -SO2 on the rotational quantum number N0. (B) Dependence of the SO 2 shift coefficients d NO2 -SO2 on the rotational quantum number K0a F, experimental data this work.

ening prediction could not be successful due to the mentioned deviations, although our data of (69 6 5) z 10 23 cm 21/atm is close to the prediction of 62 z 10 23 cm 21/atm for B-type bands and 73.1 z 10 23 cm 21/atm for A-type bands due to the agreement in the case of the nitrogen broadening. As found by Pustogov et al. (31), Malathy-Devi et al. (34), and Gianfrani et al. (41), the broadening coefficient for colli-

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TABLE 3 Self-broadening Coefficients g NO2 -NO2 in the n 3 Band NO 2

LINE-SHIFT AND LINE BROADENING IN THE n 3 BAND OF NO 2

TABLE 4 Dipole Momentum m, Quadrupole Momentum U, and Dipole Polarizability a Values in the Ground State for Molecules Used as Collisional Partners in This Work (44)

sions between NO 2 and NO 2 is larger than for the collision with N 2 and O 2. This is expected since both N 2 and O 2 molecules do not have a permanent dipole moment in contrast to NO 2. This could be illustrated using the NO 2–SO 2 broadening data. Here, the influence of the dipole momentum of SO 2 which is significantly larger compared to NO 2 itself causes a larger NO 2–SO 2 broadening coefficient of (114 6 16) z 10 23 cm 21/atm compared to (96 6 14) z 10 23 cm 21/atm for the self-broadening of NO 2 (for the dipole m and quadrupole momentum data Q, see Table 4). Comparing the broadening in the case of dominant quadrupole momentum, i.e., collision with O 2, N 2, CO 2, H 2, and D 2, one had to distinguish between the heavier molecules (O 2, N 2, and CO 2) and the very light molecules (H 2 and D 2). In the case of O 2, N 2, and CO 2 the size of the averaged broadening coefficient is proportional to the size of the quadrupole momentum. O 2 with the smallest quadrupole momentum Q had the smallest broadening coefficient, whereas CO 2 with the largest Q exhibits the largest g. The influence of the velocity of the perturber molecules can be illustrated directly by analyzing the collisions with H 2 and D 2, which have approximately the same quadrupole momentum. The light H 2 causes a larger broadening effect than D 2 due to the higher speed. The results for the shift coefficients for collision between NO 2 and the partners cited above, i.e., O 2, N 2, H 2, D 2, CO 2, and SO 2, are totally new and will be the subject of theoretical studies. Difficulties are expected due to the complexity of the problem when taking into account all contributions of higher order interactions. First attempts to calculate line-shifts were carried out by Ponomarev et al. (42). Whereas the linewidths show an overall decrease with increasing of rotational quantum numbers, almost identical behavior for P- and R-branches, and quasi-independence on the vibrational quantum number as a general trend, the characteristics for shifts could be different. For the majority of lines for all perturbers nonvanishing line-shifts were measured and all shift coefficients are negative. In most cases the absolute values of line-shift coefficients increase when the rotational quantum number increases. The shift magnitude given in Table

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2 is within the uncertainties quite the same for all perturbers except SO 2. The polarization interaction contributes mainly (about 90%) into the shift magnitude (43). We inserted the dipole polarizability values in the ground state for the concerned molecules in Table 4. One can notice that these values are very close to each other except for CO 2 and particularly SO 2. In our previous work (22) based on experimental data for collisions between NO 2 and noble gases the magnitudes of mean polarizability of NO 2 in (001) vibrational state (3.10 6 0.15) Å 3 and z components of the polarizability tensor in (000) and (001) states which are, respectively, a zz (000) 5 (2.1 6 0.2) Å 3 and a zz(001) 5 (2.15 6 0.20) Å 3, were determined. We hope to redefine these parameters using the new values for collisions also with molecular perturbers as given in Table 1 and Table 2 in the near future. CONCLUSION

In this paper our systematic studies concerning NO 2 and different molecular perturbers are completed by measuring broadening and shift for collisions with NO 2, SO 2, N 2, O 2, H 2, D 2, and CO 2. The broadening data for collisions with NO 2, N 2, and O 2 show an excellent agreement with previous measurements and calculations by different authors. The broadening data for other collision partners and the shift data at all are the first report of experimental data. These data could be the basis for additional comparisons between theoretical models and the available measurements. This would be necessary to determine the interaction parameters and empirical corrections which will give the best overall agreement more precisely. These comparisons should include a wider range of N0 and K0a and different vibrational bands, including self-broadening, temperature dependence, and maybe differences between the two doublet components. This will be the subject of a forthcoming paper. ACKNOWLEDGMENTS The authors thank Y. Heiner for the helpful discussions. B.S. acknowledges the support of the Deutsche Forschungsgemeinschaft.

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