Temperature-Dependent Line Shift and Broadening of CO Infrared Transitions

Temperature-Dependent Line Shift and Broadeningof 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 Koln, D-50937 Koln, 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 transitionsR(18) andR(20) of the COfundamental band, perturbed by Ar, N2, O2, and H2, have been measured with high frequency accuracy and at temperaturesbetween 160 and 270 K in steps of 20 K. A wavelength stabilized tunable diode laser spectrometer has been combined witha low temperature long path cell of 134 m absorption length and 1 m basis length. For all measurements the CO pressure wasbelow 0.1 mbar to avoid self-shift and self-broadening. In case of line broadening the temperature dependence is quite wellreproduced by an exponential relation,b(T) 5 b(T0)(T/T0)2n. For all foreign gases, the exponentn has been obtained(0.53 # n # 0.71) and avalue for air has been calculated from the weighted mean values of N2 and O2. Within the errorlimits the magnitudes of all shifts decrease with increasing temperatures, but there is no exponential behavior of the shift versustemperature. The line broadening and shift for CO with Ar and the broadening of CO by N2 and O2 have been compared tocalculations from the semi-classical theory of Robert and Bonamy. Sufficient agreement has been achieved for the linebroadening, 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 mo-lecular transitions in the gas phase are of significant interest inmodeling atmospheric conditions and for radiative transfercalculations in climate models (1). A large amount of labora-tory data of increasing precision has been assembled over thepast two decades. Most of the publications concern the effectof spectral line broadenings, but the evaluation of the muchsmaller effect of lineshifting has become the focus of the latesthigh-precision measurements with tunable diode laser spec-trometers (see e.g.,2–4). The temperature dependence of botheffects lacks laboratory data, especially for low temperatures.Smith and Devi (5, 6) have published a large number oftemperature-dependent shift data of ozone and methane mea-sured by Fourier Transform Spectroscopy (FT), but a compar-ison of FT data with tunable diode laser spectra by Yamadaetal. (7) has brought the quality of lineshift measurements by FTspectrometer into question.

Although a simple power law has been found for the tem-perature-dependent line broadening, the situation for the tem-perature-dependent shifts is more difficult, as discussed bySmith et al. (5). Aside from the prominent role of CO inplanetary atmospheres (8), especially of the Earth’s atmo-sphere (9), its low sublimation temperature makes it ideallysuited for studying low-temperature effects. Recent measure-

ments of CO line profiles have been published by Dugganet al.(10) and Henryet al. (11), where pressure-induced line nar-rowing has been observed. The temperature dependence of COline broadening has been studied by several authors (12–14),but to our knowledge only few measurements of temperature-dependent lineshifts of CO have been published. Bouanich (15)investigated the 2–0 overtone band of CO, Nakazawa andTanaka theR-branch of the CO–X fundamental band (X 5CO, N2, O2, and CO2) (16), while Beakyet al. measured thepure rotational lines 14 0 and 24 1 at temperatures between1 and 600 K (17). Theoretical calculations of the temperature-dependent 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 calculationsare based on an earlier semi-classical theory (20), the accuracyof which has been proven for various molecular systems overa wide temperature range (14, 18, 21–28). Indeed, most paperswere devoted to the linewidth data analysis from room tem-perature up to 3500 K in connection with combustion applica-tions (18, 29, 30), but very few measurements of CO concernthe lineshifts.

In this paper we publish the first temperature-dependentlineshift measurements in the fundamental band of CO. Wealso give the coefficientsn for the temperature dependence ofthe broadening parameters. The results for CO perturbed by Ar,N2, and O2 will be compared to calculations based on asemi-classical theory.

1 To whom correspondence should be addressed at I. Physikalisches Institut,Universitat zu Koln, Zulpicher Str. 77, D-50937 Ko¨ln, Germany.

JOURNAL OF MOLECULAR SPECTROSCOPY192,268–276 (1998)ARTICLE NO. MS987694

2680022-2852/98 $25.00Copyright © 1998 by Academic PressAll rights of reproduction in any form reserved.

II. EXPERIMENT

A frequency-stabilized tunable diode laser spectrometerwith a shock-isolated cold head (2) has been combined witha low-temperature multiple traversal cell of 134 m pathlength and 1 m basis length. The optical design is similar toa Herriott-type cell (31). Figure 1 shows the cryo-systemwith the multipass cell. Cooled by vaporized nitrogen, thetemperature can be varied continuously between 160 K androom temperature. A control unit keeps the cell at a constanttemperature within60.3 K. The temperature distributionalong the cell is monitored by eight sensors, and deviations

from the set-point are minimized by regulating the flux ofthe coolant and the current of a heating element. The multi-pass cell (see Fig. 2) is made of Pyrex glass to handle alsoaggressive gases and to minimize the deposition of watervapor and other contaminations on the walls. We usedPTFE-O-rings (Advanced) for the vacuum sealings, whichare specified to work in the temperature range between 70and 500 K. The design of the multipass optics requires aprecise distance of the two spherical mirrors. Therefore, theentire optics is mounted on quartz rods inside the cell tominimize thermal contractions.

FIG. 1. The cryo-system with the 134-m multipass cell and the temperature control system.

FIG. 2. The design of the multipass cell with 1 m basis length and 134 m absorption length.

269CO TEMPERATURE EFFECTS

Copyright © 1998 by Academic Press

The pressure in the cell can be varied between 0 and 1000 mbarand is measured by a Baratron pressure gauge for the 0–1 mbarregime with 0.1% precision and a Piezovac gauge for pressures upto 1 bar with 2% uncertainty. The combination of a cryo-systemand a long path cell allows us to measure the temperature depen-dence of line profiles with great accuracy, and an exact simulationof the temperature and pressure conditions of the Earth’s atmo-sphere up to 80 km of altitude is possible.

The absorption signal is detected by a photo-voltaic HgCdTedetector, and the output voltage is converted to a correspondingfrequency by a voltage-controlled oscillator (VCO). The VCOfrequency is evaluated by fast digital counters and the result isread into a PC. This gives the lineshape in the zeroth deriva-tive. The digitized storage procedure is free of any memoryeffect caused by the time constants of analog devices.

III. MEASUREMENT AND DATA REDUCTION

The foreign gas pressure effects of theR(18) andR(20) rovi-brational transitions of CO at 2209.5083 and 2215.7044 cm21

have been studied with Ar, N2, O2, and H2 as perturbers in thepressure range between 0 and 450 mbar and for temperaturesbetween 160 and 270 K. The CO pressure was less than 0.1 mbarto avoid the disturbing effects of self-broadening and self-shift.Each transition was measured at six to seven different temperaturevalues; at each temperature the lineprofile, and the linepositionrelative to a N2O reference line were measured at 5 to 6 pressurevalues and averaged over 100 single scans to reduce the noise onthe signal. A fast computer algorithm (32) fitted a generalized

Voigt profile (33) to the data and gave the pressure-inducedLorentzian half-width and the line center frequency relative to thereference line. The uncertainty of the baseline profile can have amarked effect on the determination of the linewidth and the linecenter, as has been discussed by Schmu¨cker et al. recently (33).To minimize these errors a frequency range of 8–10 times thelinewidth has been measured, and a third order polynomial hasbeen fitted to the baseline. The line profile algorithm allows thesimultaneous fit of the Doppler and Lorentz width. A decreasingDoppler width at increasing pressures has been observed for mostof the measurements, indicating the effect of pressure-induced linenarrowing (34). At a fixed temperature, the Lorentzian linewidthgL(p, Tconst) and the lineshiftd(p, Tconst) are linear functions of thepressure. Figures 3 and 4 show the line broadening (HWHM) andshifting of the COR(18) transition perturbed by O2 as a functionof pressure at three different temperatures. The largest effect ofline 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 timesthe standard deviations of the fit. From each set of pressures theshift and broadening parametersa(Tconst) and b(Tconst) are ob-tained for a constant temperature by a least squares fit procedure.

gL~ p, Tconst! 5 b~Tconst! z p;

d~ p, Tconst! 5 a~Tconst! z p,[1]

wherep is the pressure in bar.

FIG. 3. Lorentzian line widths (HWHM) of theR(18) transition of CO at several pressures of O2 and at different temperatures. At each temperature thebroadening parameterbO2

is calculated by a least squares fit to the line widths.

270 DRASCHER ET AL.


IV. RESULTS

Table 1 shows the shift and broadening parameters (HWHM)of the CO transitionsR(18) andR(20) for various tempera-tures with argon as foreign gas. In Table 2 the temperature-dependent parameters for CO with N2 are given, and Table 3contains all results for theR(18) transition perturbed by O2and H2. The line-broadening parameters decrease with increas-ing temperatures. The broadening coefficients depend expo-nentially on the temperature and are given by

b~T! 5 b~T0! z S T

T0D2n

, [2]

whereT0 is a reference temperature, which was in each casethe lowest temperature value of the plot.

The exponentn has been determined by a least squares fitprocedure applied to a log/log-plot of the measured broadeningparameters versus temperature. All exponents for theR(18)andR(20) transitions for different foreign gases are given inTable 4. The calculated values in Table 4 have been deter-mined from the calculated broadening coefficients. Figure 5 isa plot of all measured broadening coefficients versus temper-ature. For theR(18) transition the temperature dependence ofCO perturbed by air is calculated by the weighted means of themeasured values for N2 and O2 via

bair~Tconst! 5 0.78 z bN2~Tconst! 1 0.22 z bO2~Tconst!. [3]

Figure 6 shows all lineshift parameters, whose magnitude isdecreasing with increasing temperatures.

In all cases the broadening and shift parameters do notsignificantly differ between the two rotational quantum num-bers ofR(18) andR(20), butthey exhibit a clear dependenceon the perturbing gas, which can partly be explained by theirdifferent relative velocities due to their different masses. Thelargest line broadening was observed for CO perturbed by H2,whereas the smallest broadening effect was obtained for Ar:

bH2 $ bN2 $ bO2 $ bAr. [4]

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

TABLE 1Broadening (HWHM) and Shift Parameters of CO R(18)

and R(20) with Ar as Foreign Gas



For the shift parametersa the inverse relation holds true; largeshift parameters were found for collisions of CO with Ar butsmall effects for CO diluted in H2.

aH2 # aN2,aO2 # aAr. [5]

Because CO perturbed by argon exhibits a small broadeningbut a large lineshift effect, the evaluation of the temperature-dependent shift is most reliable for these measurements, and acomparison to calculated values by the high level semi-classi-cal collision theory of Robert and Bonamy is most revealing.

V. SEMI-CLASSICAL CALCULATION

Calculations within the semi-classical model are valid if theenergy defects due to collisions are small compared tokT. This isthe case when the rotational constants of the molecules are small.Thus, the calulations have been done for the CO–N2 and the

CO–O2 stystem. For H2 as perturber, the validity is questionablein this temperature range (rotational constant' 60 cm21), so thatthe calculations have not been done for this system.

The anisotropic intermolecular potential used in the calcula-tions of line broadening and lineshifting coefficients is an atom–atom pairwise additive Lennard–Jones potential (20), supple-mented for CO–N2 by electrostatic dipole-quadrupole andquadrupole-quadrupole interactions. The resulting potential is

V 5 Oi, j

@~dij/r 1i,2j12 ! 2 ~eij/r 1i,2j

6 !# 1 Vm1Q2 1 VQ1Q2, [6]

wheredij and eij are the atomic pair energy parameters be-tween thei th atom of molecule 1 and thej th of molecule 2,r1i ,2j is the distance between these two atoms,m1 is the dipolarmoment of CO, andQ1 andQ2 are the quadrupolar momentsof both molecule.

The classical trajectory is approximated by a straight line,tangential to the real trajectory at the distance of closest ap-proachrc and with apparentrelative velocityv9c defined byBonamyet al. (18).

By using a Lennard–Jones isotropic potentialViso with char-acteristic parameterse ands fitted to the angular average of theatom-atom potential, the conservation of angular momentumand energy leads to

b 5 r cF1 22Viso~r c!

mv2 G 1/ 2

, [7]

v9c 5 vF1 28e

mv2 H5Ss

r cD 12

2 2Ss

r cD 6JG 1/ 2

, [8]

and

r ~t! 5 @r c2 1 v9c

2t2#1/ 2. [9]

TABLE 2Broadening (HWHM) and Shift Parameters of CO R(18)

and R(20) with N2 as Foreign Gas

TABLE 3Broadening and Shift Parameters of CO R(18)

with O2 and H2 as Foreign Gases

TABLE 4The 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 theweighted values of N2 and O2.

272 DRASCHER ET AL.


In these equations,m is the reduced mass of the collidingpartners,b is the impact parameter, andv is the relativevelocity at infinity. The atomic and molecular parameters used

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

FIG. 5. Measured broadening coefficientsb(T) plotted versus temperature. The values for the air broadening ofR(18) arecalculated using the weightedmean of the N2 and O2 data.

FIG. 6. Measured shift parameters plotted versus temperature. The error bars are set to three times the standard deviation of the fit.



formed for CO-Ar, using parameters that give best resultscompared to the measured line broadening.

The expression for the linewidth and lineshift of a transitionconnecting two states labeledi and f is the following:

$gfi 2 idfi%~cm21! 5n

2pc^v@1 2 e2S2,fi~b,v!eihfi~b,v!#&b,v, j2. [10]

In Eq. [10], gfi and dfi are the half-width (HWHM) and theshift of the i 3 f line, respectively,n is the density ofperturbers, and the average is taken over the impact parameterb, the initial relative velocity and the rotational quantum num-ber j2 of the perturber.

The quantityS2,fi(b, v) denotes the second order differen-tial cross section accounting for the anisotropic interaction,andhfi(b, v) is a dephasing contribution which can be writtenas

hfi~b, v! 5 ~S1, f 2 2 S1,i2! 1 ~S92, f 2 2 S92,i2!. [11]

The first order term in Eq. [11] is due to the vibrationaldependence of the isotropic potential, while the secondorder contribution is a rotational phase shift which is relatedto that appearing in the broadening by the usual dispersionrelations (35). For CO-Ar theR(18) andR(20) line broad-

ening and shift coefficients calculated for various tempera-tures are gathered in Table 6; the calculated values for thebroadening due to N2 and O2 are given in Table 7. Alltheoretical results are compared with the experiment. In Fig.7a the calculated and measured broadening parameters forthe R(18) and theR(20) transition with argon as foreign gasare plotted versus temperature. The calculations are basedon two different sets of intermolecular potentials. Figure 7bis a plot of calculated and measured shifts. Figure 8, a and

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

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

TABLE 6Calculated Broadening and Shift Parameters for CO-Ar

with Two Different Sets of Potential Parameters

TABLE 7Calculated Broadening Parameters (HWHM)

for CO-N2 and CO-O2

274 DRASCHER ET AL.


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

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



b shows the calculated and measured broadening coeffi-cients for R(18) and R(20) perturbed by N2, and Fig. 8ccontains the temperature-dependent broadening of theR(18)transition with O2.

VI. DISCUSSION

We have shown that the temperature dependence of both thebroadening and the shift parameters can be measured withsufficient accuracy to verify the validity and quality of moderncollision theories. As Fig. 4 shows, the shift measurements ata particular temperature value have remarkably small errorsthat cannot explain the scattering of the shift parameters plottedversus temperature (see Fig. 6). Although the errors for theshifts are given as three times the standard deviation of the fit,the systematic errors still seem to be underestimated. Insofar aswe have ruled out errors in the acquisition of the data, itappears very likely that an unpredictable source of uncertain-ties is the determination of the baseline. In the data analysisroutine the spectral range of eight times the line width(FWHM) has been taken into account, by fitting a third orderpolynomial to give the most reliable shape of the baseline.

Taking into account the uncertainty connected to the atom-atom potential parameters, the agreement between theory andexperiment is quite good concerning the HWHM.

A systematic deviation from the calculated values has beenfound for both lineshift and broadening. The lineshift valuesare, as usual, less accurate, due to the fact that the shiftcoefficient is more sensitive than the broadening coefficient tothe accuracy of the potential. Moreover, the semi-classicaltheory is basically most appropriate when the collision-inducedchange of energy is small compared tokT, i.e., for low j valuesand for high temperatures. The situation studied here (j 5 19,E/kT 5 0.5; 150 ! T ! 300 K) lies near the limit ofconfidence of the theory. For the CO-Ar system, a new accu-rate potential is now available (36) which would permit im-proved calculations within a quantum mechanical approach.For CO–N2 and CO–O2, however, the semi-classical calcula-tion is the only one possible due to the large number ofcollisional channels concerned.

ACKNOWLEDGMENTS

This work was supported in part by the Deutsche Forschungsgemeinschaftvia Grant SFB 301. The authors thank F. Schmu¨lling for the software packageDADA which was used for data acquisition and data reduction.

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Temperature-Dependent Line Shift and Broadening of CO Infrared Transitions