Temperature-Dependent Line Shift and Broadening of CO Infrared Transitions

JOURNAL OF MOLECULAR SPECTROSCOPY ARTICLE NO.

192, 268 –276 (1998)

MS987694

Temperature-Dependent Line Shift and Broadening of CO Infrared Transitions T. Drascher,* T. F. Giesen,*,1 T. Y. Wang,* N. Schmu¨cker,* R. Schieder,* G. Winnewisser,* P. Joubert,† and J. Bonamy† *I. Physikalisches Institut, Universita¨t zu Ko¨ln, D-50937 Ko¨ln, Germany; and †Laboratoire de Physique Mole´culaire, UMR CNRS 6624, Faculte´ des Sciences et des Techniques, 25030 Besanc¸on Cedex, France Received April 16, 1998; in revised form August 1, 1998

The temperature dependence of lineshift and broadening of the rovibrational transitions R(18) and R(20) of the CO fundamental band, perturbed by Ar, N2, O2, and H2, have been measured with high frequency accuracy and at temperatures between 160 and 270 K in steps of 20 K. A wavelength stabilized tunable diode laser spectrometer has been combined with a low temperature long path cell of 134 m absorption length and 1 m basis length. For all measurements the CO pressure was below 0.1 mbar to avoid self-shift and self-broadening. In case of line broadening the temperature dependence is quite well reproduced by an exponential relation, b(T) 5 b(T 0 )(T/T 0 ) 2n . For all foreign gases, the exponent n has been obtained (0.53 # n # 0.71) and a value for air has been calculated from the weighted mean values of N2 and O2. Within the error limits the magnitudes of all shifts decrease with increasing temperatures, but there is no exponential behavior of the shift versus temperature. The line broadening and shift for CO with Ar and the broadening of CO by N2 and O2 have been compared to calculations from the semi-classical theory of Robert and Bonamy. Sufficient agreement has been achieved for the line broadening, while the calculated shifts are for all temperatures larger than the measured values. © 1998 Academic Press I. INTRODUCTION

The pressure effects of lineshifting and broadening of molecular transitions in the gas phase are of significant interest in modeling atmospheric conditions and for radiative transfer calculations in climate models (1). A large amount of laboratory data of increasing precision has been assembled over the past two decades. Most of the publications concern the effect of spectral line broadenings, but the evaluation of the much smaller effect of lineshifting has become the focus of the latest high-precision measurements with tunable diode laser spectrometers (see e.g., 2– 4). The temperature dependence of both effects lacks laboratory data, especially for low temperatures. Smith and Devi (5, 6) have published a large number of temperature-dependent shift data of ozone and methane measured by Fourier Transform Spectroscopy (FT), but a comparison of FT data with tunable diode laser spectra by Yamada et al. (7) has brought the quality of lineshift measurements by FT spectrometer into question. Although a simple power law has been found for the temperature-dependent line broadening, the situation for the temperature-dependent shifts is more difficult, as discussed by Smith et al. (5). Aside from the prominent role of CO in planetary atmospheres (8), especially of the Earth’s atmosphere (9), its low sublimation temperature makes it ideally suited for studying low-temperature effects. Recent measure1

To whom correspondence should be addressed at I. Physikalisches Institut, Universita¨t zu Ko¨ln, Zu¨lpicher Str. 77, D-50937 Ko¨ln, Germany.

ments of CO line profiles have been published by Duggan et al. (10) and Henry et al. (11), where pressure-induced line narrowing has been observed. The temperature dependence of CO line broadening has been studied by several authors (12–14), but to our knowledge only few measurements of temperaturedependent lineshifts of CO have been published. Bouanich (15) investigated the 2– 0 overtone band of CO, Nakazawa and Tanaka the R-branch of the CO–X fundamental band (X 5 CO, N2, O2, and CO2) (16), while Beaky et al. measured the pure rotational lines 1 4 0 and 2 4 1 at temperatures between 1 and 600 K (17). Theoretical calculations of the temperaturedependent broadening of CO perturbed by Ar, N2, O2, and CO2 as well as self-broadening have been published by Bonamy (18) et al. and Bouanich and Blanquet (19). These calculations are based on an earlier semi-classical theory (20), the accuracy of which has been proven for various molecular systems over a wide temperature range (14, 18, 21–28). Indeed, most papers were devoted to the linewidth data analysis from room temperature up to 3500 K in connection with combustion applications (18, 29, 30), but very few measurements of CO concern the lineshifts. In this paper we publish the first temperature-dependent lineshift measurements in the fundamental band of CO. We also give the coefficients n for the temperature dependence of the broadening parameters. The results for CO perturbed by Ar, N2, and O2 will be compared to calculations based on a semi-classical theory.

268 0022-2852/98 $25.00 Copyright © 1998 by Academic Press All rights of reproduction in any form reserved.

CO TEMPERATURE EFFECTS

FIG. 1.

The cryo-system with the 134-m multipass cell and the temperature control system.

II. EXPERIMENT

A frequency-stabilized tunable diode laser spectrometer with a shock-isolated cold head (2) has been combined with a low-temperature multiple traversal cell of 134 m path length and 1 m basis length. The optical design is similar to a Herriott-type cell (31). Figure 1 shows the cryo-system with the multipass cell. Cooled by vaporized nitrogen, the temperature can be varied continuously between 160 K and room temperature. A control unit keeps the cell at a constant temperature within 60.3 K. The temperature distribution along the cell is monitored by eight sensors, and deviations

FIG. 2.

269

from the set-point are minimized by regulating the flux of the coolant and the current of a heating element. The multipass cell (see Fig. 2) is made of Pyrex glass to handle also aggressive gases and to minimize the deposition of water vapor and other contaminations on the walls. We used PTFE-O-rings (Advanced) for the vacuum sealings, which are specified to work in the temperature range between 70 and 500 K. The design of the multipass optics requires a precise distance of the two spherical mirrors. Therefore, the entire optics is mounted on quartz rods inside the cell to minimize thermal contractions.

The design of the multipass cell with 1 m basis length and 134 m absorption length.

Copyright © 1998 by Academic Press

270

DRASCHER ET AL.

FIG. 3. Lorentzian line widths (HWHM) of the R(18) transition of CO at several pressures of O2 and at different temperatures. At each temperature the broadening parameter b O2 is calculated by a least squares fit to the line widths.

The pressure in the cell can be varied between 0 and 1000 mbar and is measured by a Baratron pressure gauge for the 0–1 mbar regime with 0.1% precision and a Piezovac gauge for pressures up to 1 bar with 2% uncertainty. The combination of a cryo-system and a long path cell allows us to measure the temperature dependence of line profiles with great accuracy, and an exact simulation of the temperature and pressure conditions of the Earth’s atmosphere up to 80 km of altitude is possible. The absorption signal is detected by a photo-voltaic HgCdTe detector, and the output voltage is converted to a corresponding frequency by a voltage-controlled oscillator (VCO). The VCO frequency is evaluated by fast digital counters and the result is read into a PC. This gives the lineshape in the zeroth derivative. The digitized storage procedure is free of any memory effect caused by the time constants of analog devices. III. MEASUREMENT AND DATA REDUCTION

The foreign gas pressure effects of the R(18) and R(20) rovibrational transitions of CO at 2209.5083 and 2215.7044 cm21 have been studied with Ar, N2, O2, and H2 as perturbers in the pressure range between 0 and 450 mbar and for temperatures between 160 and 270 K. The CO pressure was less than 0.1 mbar to avoid the disturbing effects of self-broadening and self-shift. Each transition was measured at six to seven different temperature values; at each temperature the lineprofile, and the lineposition relative to a N2O reference line were measured at 5 to 6 pressure values and averaged over 100 single scans to reduce the noise on the signal. A fast computer algorithm (32) fitted a generalized

Voigt profile (33) to the data and gave the pressure-induced Lorentzian half-width and the line center frequency relative to the reference line. The uncertainty of the baseline profile can have a marked effect on the determination of the linewidth and the line center, as has been discussed by Schmu¨cker et al. recently (33). To minimize these errors a frequency range of 8–10 times the linewidth has been measured, and a third order polynomial has been fitted to the baseline. The line profile algorithm allows the simultaneous fit of the Doppler and Lorentz width. A decreasing Doppler width at increasing pressures has been observed for most of the measurements, indicating the effect of pressure-induced line narrowing (34). At a fixed temperature, the Lorentzian linewidth gL(p, Tconst) and the lineshift d(p, Tconst) are linear functions of the pressure. Figures 3 and 4 show the line broadening (HWHM) and shifting of the CO R(18) transition perturbed by O2 as a function of pressure at three different temperatures. The largest effect of line broadening and shifting was found at the lowest temperatures. In all cases the line center was shifted to lower frequencies, indicated by negative shift values. The error bars are three times the standard deviation s of the fit. From each set of pressures the shift and broadening parameters a(Tconst) and b(Tconst) are obtained for a constant temperature by a least squares fit procedure.

g L~ p, T const! 5 b~T const! z p; d ~ p, T const! 5 a~T const! z p,

where p is the pressure in bar.

Copyright © 1998 by Academic Press

[1]

271

CO TEMPERATURE EFFECTS

FIG. 4. Shift of the CO R(18) line center at different pressures of O2. The shift parameter a(T) has been calculated from a least squares fit analysis of the shift data.

IV. RESULTS

Table 1 shows the shift and broadening parameters (HWHM) of the CO transitions R(18) and R(20) for various temperatures with argon as foreign gas. In Table 2 the temperaturedependent parameters for CO with N2 are given, and Table 3 contains all results for the R(18) transition perturbed by O2 and H2. The line-broadening parameters decrease with increasing temperatures. The broadening coefficients depend exponentially on the temperature and are given by b~T! 5 b~T 0! z

SD T T0

2n

,

[2]

TABLE 1 Broadening (HWHM) and Shift Parameters of CO R(18) and R(20) with Ar as Foreign Gas

where T 0 is a reference temperature, which was in each case the lowest temperature value of the plot. The exponent n has been determined by a least squares fit procedure applied to a log/log-plot of the measured broadening parameters versus temperature. All exponents for the R(18) and R(20) transitions for different foreign gases are given in Table 4. The calculated values in Table 4 have been determined from the calculated broadening coefficients. Figure 5 is a plot of all measured broadening coefficients versus temperature. For the R(18) transition the temperature dependence of CO perturbed by air is calculated by the weighted means of the measured values for N2 and O2 via b air~T const! 5 0.78 z b N2~T const! 1 0.22 z b O2~T const!.

[3]

Figure 6 shows all lineshift parameters, whose magnitude is decreasing with increasing temperatures. In all cases the broadening and shift parameters do not significantly differ between the two rotational quantum numbers of R(18) and R(20), but they exhibit a clear dependence on the perturbing gas, which can partly be explained by their different relative velocities due to their different masses. The largest line broadening was observed for CO perturbed by H2, whereas the smallest broadening effect was obtained for Ar: b H2 $ b N2 $ b O2 $ b Ar.

Copyright © 1998 by Academic Press

[4]

272

DRASCHER ET AL.

TABLE 2 Broadening (HWHM) and Shift Parameters of CO R(18) and R(20) with N2 as Foreign Gas

CO–O2 stystem. For H2 as perturber, the validity is questionable in this temperature range (rotational constant ' 60 cm21), so that the calculations have not been done for this system. The anisotropic intermolecular potential used in the calculations of line broadening and lineshifting coefficients is an atom– atom pairwise additive Lennard–Jones potential (20), supplemented for CO–N2 by electrostatic dipole-quadrupole and quadrupole-quadrupole interactions. The resulting potential is V5

O @~d /r ij

12 1i,2j

6 ! 2 ~e ij/r 1i,2j !# 1 V m1Q2 1 V Q1Q2,

[6]

i, j

For the shift parameters a the inverse relation holds true; large shift parameters were found for collisions of CO with Ar but small effects for CO diluted in H2. a H2 # a N2,a O2 # a Ar.

[5]

Because CO perturbed by argon exhibits a small broadening but a large lineshift effect, the evaluation of the temperaturedependent shift is most reliable for these measurements, and a comparison to calculated values by the high level semi-classical collision theory of Robert and Bonamy is most revealing.

where d ij and e ij are the atomic pair energy parameters between the ith atom of molecule 1 and the jth of molecule 2, r 1i,2j is the distance between these two atoms, m1 is the dipolar moment of CO, and Q 1 and Q 2 are the quadrupolar moments of both molecule. The classical trajectory is approximated by a straight line, tangential to the real trajectory at the distance of closest approach r c and with apparent relative velocity v9c defined by Bonamy et al. (18). By using a Lennard–Jones isotropic potential V iso with characteristic parameters e and s fitted to the angular average of the atom-atom potential, the conservation of angular momentum and energy leads to

F

v9c 5 v 1 2

V. SEMI-CLASSICAL CALCULATION

Calculations within the semi-classical model are valid if the energy defects due to collisions are small compared to kT. This is the case when the rotational constants of the molecules are small. Thus, the calulations have been done for the CO–N2 and the TABLE 3 Broadening and Shift Parameters of CO R(18) with O2 and H2 as Foreign Gases

F

b 5 rc 1 2

2V iso~r c! mv 2

G

1/ 2

,

[7]

H S D S D JG

s 8e 2 5 mv rc

12

22

s rc

6

1/ 2

,

[8]

and r~t! 5 @r 2c 1 v9c2t 2# 1/ 2.

TABLE 4 The Temperature Exponent n for the Broadening Parameters of the CO R(18) and R(20) Transitions with Foreign Gases

Note. The value for air is calculated from the weighted values of N2 and O2.

Copyright © 1998 by Academic Press

[9]

CO TEMPERATURE EFFECTS

273

FIG. 5. Measured broadening coefficients b(T) plotted versus temperature. The values for the air broadening of R(18) are calculated using the weighted mean of the N2 and O2 data.

In these equations, m is the reduced mass of the colliding partners, b is the impact parameter, and v is the relative velocity at infinity. The atomic and molecular parameters used

FIG. 6.

in the calculations are given in Table 5 and Ref. (28). Because some of the atomic parameters are derived within a certain range of values, two different calculations have been per-

Measured shift parameters plotted versus temperature. The error bars are set to three times the standard deviation of the fit.

Copyright © 1998 by Academic Press

274

DRASCHER ET AL.

TABLE 5 Potential Parameters for CO-Ar, CO-N2, and CO-O2

TABLE 6 Calculated Broadening and Shift Parameters for CO-Ar with Two Different Sets of Potential Parameters

* Values that have been fitted to the angle-independent part of the atomatom potential.

formed for CO-Ar, using parameters that give best results compared to the measured line broadening. The expression for the linewidth and lineshift of a transition connecting two states labeled i and f is the following: $ g fi 2 i d fi%~cm 21! 5

n ^v@1 2 e 2S2,fi~b,v!e ihfi~b,v!#& b,v, j2. 2pc

[10]

In Eq. [10], g fi and d fi are the half-width (HWHM) and the shift of the i 3 f line, respectively, n is the density of perturbers, and the average is taken over the impact parameter b, the initial relative velocity and the rotational quantum number j 2 of the perturber. The quantity S2,fi(b, v) denotes the second order differential cross section accounting for the anisotropic interaction, and hfi(b, v) is a dephasing contribution which can be written as

h fi~b, v! 5 ~S 1, f 2 2 S 1,i2! 1 ~S92, f 2 2 S92,i2!.

ening and shift coefficients calculated for various temperatures are gathered in Table 6; the calculated values for the broadening due to N2 and O2 are given in Table 7. All theoretical results are compared with the experiment. In Fig. 7a the calculated and measured broadening parameters for the R(18) and the R(20) transition with argon as foreign gas are plotted versus temperature. The calculations are based on two different sets of intermolecular potentials. Figure 7b is a plot of calculated and measured shifts. Figure 8, a and

TABLE 7 Calculated Broadening Parameters (HWHM) for CO-N2 and CO-O2

[11]

The first order term in Eq. [11] is due to the vibrational dependence of the isotropic potential, while the second order contribution is a rotational phase shift which is related to that appearing in the broadening by the usual dispersion relations (35). For CO-Ar the R(18) and R(20) line broad-

Copyright © 1998 by Academic Press

CO TEMPERATURE EFFECTS

275

FIG. 7. Calculated broadening (a) and shift parameters (b) for the R(18) and R(20) transitions perturbed by Ar. Calculated values are given for the two different sets of potential parameters of Table 5. The measured values are indicated by circles.

FIG. 8. Calculated and measured broadening parameters of CO. For the R(18) (a) and R(20) (b) transition perturbed by N2. The R(18) transition perturbed by O2 (c). Circles indicate the calculated values.

Copyright © 1998 by Academic Press

276

DRASCHER ET AL.

b shows the calculated and measured broadening coefficients for R(18) and R(20) perturbed by N2, and Fig. 8c contains the temperature-dependent broadening of the R(18) transition with O2. VI. DISCUSSION

We have shown that the temperature dependence of both the broadening and the shift parameters can be measured with sufficient accuracy to verify the validity and quality of modern collision theories. As Fig. 4 shows, the shift measurements at a particular temperature value have remarkably small errors that cannot explain the scattering of the shift parameters plotted versus temperature (see Fig. 6). Although the errors for the shifts are given as three times the standard deviation of the fit, the systematic errors still seem to be underestimated. Insofar as we have ruled out errors in the acquisition of the data, it appears very likely that an unpredictable source of uncertainties is the determination of the baseline. In the data analysis routine the spectral range of eight times the line width (FWHM) has been taken into account, by fitting a third order polynomial to give the most reliable shape of the baseline. Taking into account the uncertainty connected to the atomatom potential parameters, the agreement between theory and experiment is quite good concerning the HWHM. A systematic deviation from the calculated values has been found for both lineshift and broadening. The lineshift values are, as usual, less accurate, due to the fact that the shift coefficient is more sensitive than the broadening coefficient to the accuracy of the potential. Moreover, the semi-classical theory is basically most appropriate when the collision-induced change of energy is small compared to kT, i.e., for low j values and for high temperatures. The situation studied here ( j 5 19, E/kT 5 0.5; 150 ! T ! 300 K) lies near the limit of confidence of the theory. For the CO-Ar system, a new accurate potential is now available (36) which would permit improved calculations within a quantum mechanical approach. For CO–N2 and CO–O2, however, the semi-classical calculation is the only one possible due to the large number of collisional channels concerned. ACKNOWLEDGMENTS This work was supported in part by the Deutsche Forschungsgemeinschaft via Grant SFB 301. The authors thank F. Schmu¨lling for the software package DADA which was used for data acquisition and data reduction.

REFERENCES 1. K. N. Rao and A. Weber, (eds.), “Spectroscopy of the Earth’s Atmosphere and Interstellar Medium,” Academic, New York, 1992. 2. N. Anselm, K. M. T. Yamada, R. Schieder, and G. Winnewisser, J. Mol. Spectrosc. 161, 284 –296 (1993). 3. F. Raynaud, B. Lemoine, and F. Rohart, J. Mol. Spectrosc. 168, 584 –592 (1994).

4. M. Fabian, R. Schieder, K. M. T. Yamada, and G. Winnewisser, J. Mol. Spectrosc. 177, 294 –301 (1996). 5. M. A. H. Smith, C. P. Rinsland, V. M. Devi, D. C. Benner, Spectrochim. Acta 48A, 1257–1272 (1992). 6. V. M. Devi, D. C. Benner, M. A. H. Smith, C. P. Rinsland, J. Quant. Spectrosc. Radiat. Transfer 51, 439 – 465 (1994). 7. K. M. T. Yamada, M. Harter, and T. Giesen, J. Mol. Spectrosc. 157, 84 –94 (1993). 8. D. E. Jennings, J. Quant. Spectrosc. Radiat. Transfer 40, 221–238 (1988). 9. C. P. Rinsland, M. R. Gunson, R. Zander, M. Lopezpuertas, J. Geophys. Res. 97, 20479 –20495 (1992). 10. P. Duggan, P. M. Sinclair, A. D. May, J. R. Drummond, Phys. Rev. A 51, 218 –224 (1995). 11. A. Henry, M. Margottin-Maclou, and A. Valentin, Spectrochim. Acta 52A, 835– 841 (1996). 12. P. Varansi, J. Quant. Spectrosc. Radiat. Transfer 15, 191–196 (1975). 13. J.-P. Bouanich, R. Farrenq, and C. Brodbeck, Can. J. Phys. 61, 192–197 (1983). 14. J.-P. Bouanich, J. Quant. Spectrosc. Radiat. Transfer 31, 561–567 (1984). 15. J.-P. Bouanich, Can. J. Phys. 61, 919 –922 (1983). 16. T. Nakazawa and M. Tanaka, J. Quant. Spectrosc. Radiat. Transfer 28, 409 – 416 (1982); ibid, 471– 480 (1982). 17. M. M. Beaky, T. M. Goyette, and F. De Lucia, J. Chem. Phys. 105, 3994 – 4004 (1996). 18. J. Bonamy, D. Robert, and C. Boulet, J. Quant. Spectrosc. Radiat. Transfer 31, 23–34 (1984). 19. J.-P. Bouanich and G. Blanquet, J. Quant. Spectrosc. Radiat. Transfer 40, 205–220 (1988). 20. D. Robert and J. Bonamy, J. Phys. 10, 923–943 (1979). 21. B. Lavorel, G. Millot, R. Saint-Loup, C. Wenger, H. Berger, J. P. Sala, J. Bonamy, and D. Robert, J. Phys. 47, 417– 425 (1986). 22. J. M. Hartmann, J. Taine, J. Bonamy, B. Labani, and D. Robert, J. Chem. Phys. 86, 144 –156 (1987). 23. B. Labani, J. Bonamy, D. Robert, and J. M. Hartmann, J. Chem. Phys. 87, 2781–2789 (1987). 24. L. Rosenmann, J. M. Hartmann, M. Y. Perrin, and J. Taine, J. Chem. Phys. 88, 2999 –3006 (1988). 25. J. Bonamy, D. Robert, J. M. Hartmann, M. L. Gonze, R. Saint-Loup, and H. Berger, J. Chem. Phys. 91, 5916 –5925 (1989). 26. M. Margottin-Maclou, P. O. Dahoo, A. Henry, A. Valentin, and L. Henry, J. Mol. Spectrosc. 131, 21–35 (1988). 27. J. P. Looney and G. J. Rosasco, J. Chem. Phys. 95, 2379 –2390 (1991). 28. A. Roblin, J. Bonamy, D. Robert, M. Lefebvre, and M. Pealat, J. Phys. 2, 285–294 (1992). 29. G. J. Rosasco, L. A. Rahn, W. S. Hurst, R. E. Palmer, and S. M. Dohne, J. Chem. Phys. 90, 4059 – 4068 (1989). 30. H. S. Lowry and C. J. Fischer, J. Quant. Spectrosc. Radiat. Transfer 27, 585–591 (1982). 31. D. Herriott, H. Kogelnik, and R. Kompfner, Appl. Opt. 3, 523–526 (1964). 32. A. K. Hui, B. H. Armstrong, and A. A. Wray, J. Quant. Spectrosc. Radiat. Transfer 19, 509 –516 (1978). 33. N. Schmu¨cker, Ch. Trojan, T. Giesen, R. Schieder, K. M. T. Yamada, and G. Winnewisser, J. Mol. Spectrosc. 184, 250 –256 (1997). 34. R. H. Dicke, Phys. Rev. 89, 472– 473 (1953). 35. L. Bonamy, J. Bonamy, D. Robert, B. Lavorel, R. Saint-Loup, R. Chaux, J. Santos, and H. Berger, J. Chem. Phys. 89, 5568 –5577 (1988). 36. S. Shin, S. K. Shin, and F. M. Tao, J. Chem. Phys. 104, 183–190 (1996). 37. D. Oobatake and T. Ooi, Prog. Theor. Phys. 48, 2132–2143 (1972). 38. D. E. Stogryn and A. P. Stogryn, Mol. Phys. 11, 371–393 (1966). 39. W. L. Meerts, F. H. de Leeuw and A. Dymanus, Chem. Phys. 22, 319 –328 (1977).

Copyright © 1998 by Academic Press