Journal of Molecular Spectroscopy 297 (2014) 58–61

Contents lists available at ScienceDirect

Journal of Molecular Spectroscopy

journal homepage: www.elsevier .com/locate / jms

H2 line mixing coefficients in the m2 and m4 bands of PH3

http://dx.doi.org/10.1016/j.jms.2014.01.0030022-2852/� 2014 Elsevier Inc. All rights reserved.

⇑ Corresponding author.E-mail address: sfjamel1@yahoo.fr (J. Salem).

Jamel Salem a,⇑, Ghislain Blanquet b, Muriel Lepère b, Hassen Aroui a

a Laboratoire de Dynamique Moléculaire et Matériaux Photoniques, Université de Tunis, Ecole Nationale Supérieure d’Ingénieurs de Tunis, 5 Avenue Taha Hussein, 1008 Tunis, Tunisiab Laboratoire Lasers et Spectroscopies, Research Center in Physics of Matter and Radiation, University of Namur, 61, rue de Bruxelles, B-5000 Namur, Belgium

a r t i c l e i n f o

Article history:Received 23 May 2013In revised form 2 January 2014Available online 27 January 2014

Keywords:Diode-laser spectrometerPhosphineHydrogèneLine mixing

a b s t r a c t

Using a tunable diode-laser spectrometer, we measured the H2 line mixing coefficients for 32 lines in them2 and m4 bands of phosphine (PH3) at room temperature. These lines are located in the spectral rangefrom 1016 to 1106 cm�1. The pressure line mixing parameters have been obtained by fitting themeasured line shapes using a multi-pressure fitting procedure that accounts for the apparatus functionas well as the Doppler and collisional effects. The variation of these parameters with the rotationaland vibrational quantum numbers is discussed.

� 2014 Elsevier Inc. All rights reserved.

1. Introduction

The PH3 molecule is the subject of large spectroscopic interestsfor different reasons. On one hand, study of the phosphine spectrais important for some astrophysical applications. For example,phosphine was detected in the atmospheres of the giant planetsSaturn and Jupiter [1–5]. On the other hand, the PH3 molecule isof interest from a purely theoretical point of view because it isone of the lightest pyramidal molecules. As a consequence, numer-ous spectroscopic effects and peculiarities that are inherent inpyramidal molecules should be particularly pronounced in thespectra of phosphine.

Recently, improved spectroscopic parameters of PH3 have beendetermined for its ground vibrational state [6], using very accuraterotational transition frequencies combined with previous data[7–9].

Previously, He-, Ar- and self-broadening coefficients of individ-ual lines in the m2 and m4 bands of phosphine have beendetermined at room temperature [10,11].

H2- and N2-broadening coefficients have also been determinedfor individual lines in the m2 and m4 bands at room [12,13] andlow temperatures [14,15]. From these results, the temperaturedependencies of collisional broadening coefficients have beendetermined for H2–PH3 [14] and N2–PH3 [15] mixtures.

In this paper, we present the first study of the H2 line mixingparameters at room temperature for 6 doublets and 20 individuallines in the m2 and m4 bands of the PH3 molecule. The measure-

ments were carried out using a tunable diode laser spectrometer.The determination of line mixing coefficients was performed usinga nonlinear least squares multi-pressure fitting procedure of theexperimental spectra.

2. Experimental and fitting procedures

2.1. Experiment

The spectra of PH3 mixed with H2 were recorded using an im-proved Laser Analytics (LS3 model) tunable diode-laser spectrom-eter that was reported previously [16,17]. The resulting spectrawere averaged over 100 scans to increase the signal to noise ratio(better than 1000). The measurement of the line mixing parameterrequired 8 different records: the laser emission profile withoutabsorption; the line broadened by four different perturber gaspressures with the same quantity of PH3; the effective Doppler linerecorded at room temperature with very low pressure of pure PH3

in order to determine the apparatus function; the saturated PH3

line from which the 0% transmission is deduced; and finally, thefringe pattern obtained by introducing a confocal etalon with a freespectral range of 0.007958 cm�1 in the laser beam. These differentspectra are illustrated in Fig. 1 for the RR(4,3) doublet of the m4

band of PH3 diluted in H2 at room temperature.The introduction of the confocal etalon allowed the extraction

of a relative wavenumber calibration. This etalon had 0.25 m be-tween mirrors and was used in passive mode. The interfringe spac-ing was 0.007958 cm�1. The etalon fringe pattern provided a checkof the laser mode quality for correction of the slightly nonlineartuning of the diode-laser. Furthermore, it aided in linearization of

500 1000 15000

1000

2000

3000

Point number

(6): 43.80 mbar(5): 36.27(4): 29.33(3): 20.89

8

7

21

0.007958 cm-1

Tran

smitt

ance

Fig. 1. Example of spectra recorded for the RR(4,3) doublet at room temperature inthe region of the m4 band of PH3 diluted in H2. (1) diode-laser emission profile, (2)record of low-pressure lines of pure PH3 used to determine the apparatus function(Doppler line), (3–6) records of the broadened lines at different pressures of H2, (7)confocal etalon fringe pattern, and (8) 0% transmission level.

1174.62 1174.64 1174.66 1174.68

0.0

0.4

0.8

1.2

___ Measured

. Calc With line mixing

. Calc Without line mixing

. Meas-Calc: With

. Meas-Calc: Without

36.27 mbar 20.89

Tra

nsm

itta

nce

Wavenumber σ (cm-1)

Fig. 2. Graphical demonstration of line mixing obtained by the multi-spectrum fitsof PH3 diluted by 20.89 and 36.27 mbar of H2 for the RR(4,3) doublet of the m4 bandof PH3. (—). ( ) and ( ) are measured and calculated spectra with (Y – 0) andwithout (Y = 0) line mixing, respectively. Residuals (measured minus calculated) areshown with (Y – 0) ( ) and without (Y = 0) ( ) line mixing.

J. Salem et al. / Journal of Molecular Spectroscopy 297 (2014) 58–61 59

the spectra with a constant step of 0.000121 cm�1. All spectra werelinearized using the cubic splines techniques [18].

The phosphine sample with a stated purity of 99.999% was sup-plied by Union Carbide, while hydrogen with a purity of 99.99%was supplied by Air Liquide. The gas mixtures were contained ina multipass White-type cell with an absorption length of 20.17 mfor the PH3 doublet lines and 12.17 m for the other lines.

The pressures were measured using two Baratron gauges with afull scale of 1.2 and 120 mbar with an accuracy of 5 � 10�4 and2 � 10�2 mbar, respectively.

For each doublet recorded, the partial pressure of PH3 was keptconstant, ranging from 0.0046 mbar to 0.1874 mbar, while the H2

pressures were varied between 15 and 45 mbar. This pressureregion was chosen because at a relative ‘‘low’’ pressure(15–45 mbar) the line mixing effect is small. For the other recordedfeatures, the partial pressure of PH3 was kept constant, rangingfrom 0.0136 mbar to 0.34 mbar, while the H2 pressures variedbetween 20 and 80 mbar.

2.2. Fitting procedure

The experimental absorbance a(r) at wavenumber r is ob-tained through the Beer–Lambert law,

ItðrÞI0ðrÞ

¼ e�aðrÞ ð1Þ

I0(r) and It(r) are the transmitted intensities measured with the cellunder vacuum and filled with the gas sample, respectively. The po-sition of the baseline I0(r), was systematically readjusted to mini-mize the discrepancies between the calculated and observedlineshapes.

The analyses of the spectra were performed by taking into ac-count interference effects. For transitions with small rotational en-ergy separation or when the gas pressure increases, the linesoverlap and rotational energy exchanges can mix these lines. Thismixing has the effect of transferring populations between energylevels. This is true provided that appropriate collisional selectionrules allow such transfers. In such conditions, because of this linemixing effect [19], the usual Lorentz line profile can no longer cor-rectly reproduces the experimental spectra. Within the impact the-ory of the spectral shape, the collisional absorption coefficient a(r)can be written as [19,20]

aðrÞ ¼ PPH3

pX

lines k

SkPYkðr� rkÞ þ Pck

ðr� rkÞ2 þ ðPckÞ2 ð2Þ

where k represents the line viJiKi ? vf JfKf0, Sk its intensity; rk itswavenumber; ck its half-width; and Yk its interference parameterwhich is related to the off-diagonal elements of the relaxationmatrix.

The spectra were analyzed using the nonlinear least squaresfitting procedures with the following theoretical expression sC(r)for the transmission and the collisional absorption coefficient fromEq. (2).

sCðrÞ ¼Z þ1

�1FAppðr� r0Þ

� exp �lZ þ1

�1aDopðr0 � r00Þaðr00Þdr00

� �dr0 ð3Þ

where aDop is the Doppler profile, FApp is the apparatus function witha Gaussian shape, and l is the cell length. The collisional parametersfor a given temperature have been deduced from a nonlinear leastsquares multi-pressure fitting in which all spectra at variouspressures are successively adjusted using Eqs. (2) and (3).

The parameters deduced from the fits for a line k are Pck, rk, Sk,and PYk. Two examples of a multi-pressure fit, in the case of theRR(4,3) doublet for PH3 broadened by H2 at 298 K, are shown inFig. 2 for the two pressures 20.89 and 36.27 mbar.

The slopes of the straight lines obtained from the unconstrainedlinear least squares procedures give the line mixing parameter Y(atm�1). A typical plot of PY versus the pressure P of hydrogen isshown in Fig. 3 for the A1 and A2 components of the RR(4,3)doublets of PH3 at the temperature of 298 K. This figure illustratesthe linear dependence of the PY values with the pressure of theperturber. As expected, the line shape model of Eq. (2) is demon-strated to be well adapted to our experimental conditions.

3. Results and discussion

The measured line mixing parameters are presented in Table 1and Fig. 4 along with the experimental errors. They are derivedfrom the multi-pressure fitting procedure, accounting for the appa-ratus function as well as the Doppler and collisional effects.

Table 1 illustrates the dependencies of Y on the J and K quantumnumbers for 32 lines of the six branches considered in the m2 andm4 bands of PH3.

For some manifolds pertaining to the branches of the m2 band, Yappears to increase with K quantum number for a given value of J.

0.020 0.025 0.030 0.035 0.040 0.045

-0.02

-0.01

0.00

0.01

0.02

××

×

×

ο

ο ο

ο

RR (4,3,A2)

RR(4,3,A1)

PY

(x 1

0-3)

P (atm)

Fig. 3. Pressure variations of the line mixing parameter PY of the RR(4,3) doublet ofthe m4 band of PH3. The A1 and A2 components of the doublet have opposite signs ofline mixing parameter.

Table 1H2 line mixing parameters Y (atm�1) for PH3 at T = 298 K in some branches of the m2

and m4 bands as a function of the J and K quantum numbers. The values given inparenthesis correspond to the estimated uncertainties expressed as one standarddeviation.

Transition Wavenumber m0 (cm�1) Band Y (10�3 atm�1)

QR(2,0) 1016.7311 m2 �0.889 ± 0.017QR(2,1) 1016.9293 m2 �0.034 ± 0.001QR(4,4) 1034.5644 m2 �0.268 ± 0.011QR(6,6) 1051.7724 m2 �0.082 ± 0.010QR(7,0) 1051.4496 m2 0.106 ± 0.024QR(7,1) 1051.6224 m2 2.460 ± 0.005QR(7,2) 1052.1428 m2 0.644 ± 0.419QR(7,5) 1055.8929 m2 0.208 ± 0.122QR(8,6) 1063.8745 m2 1.660 ± 0.170QR(9,0) 1063.6111 m2 0.373 ± 0.132QR(9,1) 1063.7716 m2 0.485 ± 0.231QR(9,9) 1077.8521 m2 0.180 ± 0.028QR(10,2) 1070.0241 m2 �0.099 ± 0.064QR(15,8) 1104.5940 m2 �0.053 ± 0.018PP(5,2) 1073.5258 m4 �0.265 ± 0.002PP(7,4) 1051.8799 m4 0.368 ± 0.121RP(6,1) 1074.0873 m4 �0.055 ± 0.005RP(7,0) 1066.6132 m4 0.079 ± 0.016RP(10,1) 1048.1455 m4 �0.169 ± 0.034PQ(7,7) 1105.0196 m4 �0.158 ± 0.166RR(4,3,A1) 1174.6263 m4 0.449 ± 0.026RR(4,3,A2) 1174.6453 m4 �0.574 ± 0.086PP(6,3, A1) 1062.3592 m4 0.023 ± 0.023PP(6,3, A2) 1062.7064 m4 �0.206 ± 0.046QR(7,3, A1) 1053.0157 m2 1.180 ± 0.450QR(7,3, A2) 1053.0211 m2 �1.390 ± 0.240QR(8,3, A1) 1059.1402 m2 0.318 ± 0.066QR(8,3, A2) 1059.1499 m2 �0.333 ± 0.053QR(9,3, A1) 1065.0593 m2 0.291 ± 0.028QR(9,3, A2) 1065.0756 m2 �0.507 ± 0.065QR(9,6, A1) 1139.8726 m2 0.936 ± 0.132QR(9,6, A2) 1139.8801 m2 �0.945 ± 0.075

2 4 6 8 10 12 14 16

-1,5

-1,0

-0,5

0,0

0,5

1,0

1,5

2,0

2,5

3,0

ν2ν4

Y(10-3 atm

-1)

J

Fig. 4. Measured H2 line mixing coefficients of PH3 at 298 K in the m2 and m4 bandsas a function of J quantum number.

60 J. Salem et al. / Journal of Molecular Spectroscopy 297 (2014) 58–61

For example, as shown by this table and Fig. 4, the Y value of theQR(9,6,A1) transition, which is equal to 0.936 atm�1, is greater thanthe value of Y for the QR(9,3, A2) transition, which is 0.291 atm�1.This behavior can be explained in part by the decrease in the split-ting of the doublets, Dr = r0l � r0k, where r0l and r0k are theunperturbed wavenumbers of the l and k transitions. Then thistable illustrates the large amount of coupling processes for doubletswith small splitting Dr. This may be easily understood because inEq. (2), the line mixing parameter Y is inversely proportional toDr as illustrated by the following equation [21–23]:

Yk ¼ 2Xl – k

dl

dk

Wlk

r0l � r0k; ð4Þ

where dk and dl are the dipole moment reduced matrix elements ofthe two lines and Wlk is their line mixing coefficient.

However, there are several exceptions to this behavior. Exami-nation of Table 1 shows that the Y value of the QR(7,5) line is smal-ler than the value of the QR(7,2) line.

As can be observed in Table 1, numerous A1 and A2 componentsof the doublets in the m2 and m4 bands have opposite signs of Y.

Fig. 4 is a plot of Y value in atm�1, versus J for all lines ofbranches of the two bands studied. The horizontal line indicatesa line mixing parameter of zero. As observed in this Figure and inTable 1, the line mixing parameters are both positive and negativeand do not reveal any systematic dependencies on J. Table 1 showsthat about half of the lines have a positive value for Y.

We note that the splitting, Dr, could be large enough to containlines other than those pertaining to the doublet of interest. There-fore, the line mixing processes can occur not only between the twocomponents of the doublets but also between more than two tran-sitions provided that the selection rules are valid.

Compared to other molecules, such as the NH3 studied in Ref.[24] using a Fourier transform spectrometer and a multi-pressurefitting procedure, the line mixing parameters studied here aresmall with absolutes value ranging from about 0.023 � 10�3 atm�1

to 2.46 � 10�3 atm�1.The mean absolute value of the line mixing parameter

Ym = (0.611 ± 0.107) � 10�3 atm�1 for the m2 band is greater thanthat of the m4 band, which is Ym = (0.235 ± 0.052) � 10�3 atm�1.Therefore, the H2 line mixing effect seems to be more pronouncedin the m2 band than in the m4 band.

4. Estimated errors

The experimental errors reported in Table 1, estimated as onestandard deviation derived from the linear fit, vary widely depend-ing on the quality of the spectral lines.

This table reveals that the line mixing parameters are moreaccurate in the m4 band than in the m2 band. The mean value ofaccuracy is about 16% for the m4 band and 23% for the m2 band.

The main sources of uncertainties in the Y values arise from thebaseline location, the sample pressure, the temperature, theabsorption path length, the nonlinear tuning of the laser, the over-lapping with neighboring lines, the line shape model used in themulti-pressure procedure, and the signal to noise ratio of the dif-ferent spectra.

J. Salem et al. / Journal of Molecular Spectroscopy 297 (2014) 58–61 61

We note that for some lines, the line mixing parameter accura-cies can reach values greater than 50%, or are of the same order ofmagnitude as the parameter itself. This makes them difficult tomeasure reliably.

5. Conclusion

With a high resolution tunable diode laser spectrometer and amulti-pressure fitting technique, we have obtained line mixingparameters for 32 selected lines in 6 branches of the m2 and m4

bands of PH3 at T = 298 K. The analyses of the recorded spectrawere made with and without taking into account line mixingeffects.

The estimated errors vary widely depending on the quality ofthe spectral lines with a better accuracy for the isolated lines withlarge intensity. On the average, the accuracies of the measure-ments are estimated to be 16% and 23% for the m2 and m4 bands,respectively.

For almost all lines and pressures considered in this work, itwas shown that the first-order Rosenkranz absorption coefficienttaking into account line mixing effects is adequate to extract withsufficient accuracy the line mixing parameters of PH3.

The Y values are rather small and are more bipolar for the sixisolated doublets than those of the 20 individual lines of the m2

and m4 bands. No significant branch and rotational dependenciesare observed, except for the A1 and A2 components of the doubletsin the two bands for which the line mixing parameter appears toincrease with the K quantum number.

Furthermore, a rather small vibrational effect has been identi-fied, especially when the mean values of the results of the twobands are compared, but with no evidence of systematic differ-ences between the individual transitions with the same rotationalquantum numbers.

Finally, these first results about the line mixing in the m2 and m4

bands of PH3 need to be improved by performing new measure-

ments using other experimental setups for several branches inother vibrational states of this molecule.

References

[1] S.T. Ridgway, L. Wallace, G.R. Smith, Astrophys. J. 207 (1976) 1002.[2] R.A. Hanel, B.J. Conrath, F.M. Flasar, V.G. Kunde, P. Lowman, W. Maguire, J.C.

Pearl, J.A. Pirraglia, R. Samuelson, Science 204 (1979) 972.[3] V.G. Kunde, R.A. Hanel, W. Maguire, D. Gautier, J.-P. Baluteau, A. Marten, A.

Chedin, N. Husson, Astrophys. J. 240 (1982) 327.[4] H.P. Larson, U. Fink, H.A. Smith, D. Scott Davies, Astrophys. J. 240 (1980) 327.[5] R.W. Lovejoy, R. Schaeffer, D.L. Frasco, C.C. Chackerian, R.W. Boese, J. Mol.

Spectrosc. 109 (1985) 246.[6] S.P. Müller Holger, J. Quant. Spectrosc. Radiat. Transfer 130 (2013) 335.[7] P.B. Davies, R.M. Neumann, S.C. Wofsy, W. Klemperer, J. Chem. Phys. 55 (1971)

3564.[8] L. Fusina, M. Carlotti, J. Mol. Spectrosc. 130 (1988) 371.[9] G. Cazzoli, C. Puzzarini, J. Mol. Spectrosc. 239 (2006) 64.

[10] J. Salem, J.P. Bouanich, J. Walrand, H. Aroui, G. Blanquet, J. Mol. Spectrosc. 232(2005) 247.

[11] J. Salem, H. Aroui, J.P. Bouanich, J. Walrand, G. Blanquet, J. Mol. Spectrosc. 225(2004) 174.

[12] J.P. Bouanich, J. Salem, H. Aroui, J. Walrand, G. Blanquet, J. Quant. Spectrosc.Radiat. Transf. 84 (2004) 195.

[13] J.P. Bouanich, J. Walrand, G. Blanquet, J. Mol. Spectrosc. 232 (2005) 40.[14] J. Salem, J.P. Bouanich, J. Walrand, H. Aroui, G. Blanquet, J. Mol. Spectrosc. 228

(2004) 23.[15] J.P. Bouanich, G. Blanquet, J. Mol. Spectrosc. 241 (2007) 186.[16] M. Lepère, G. Blanquet, J. Walrand, J.P. Bouanich, J. Mol. Spectrosc. 180 (1996)

218.[17] L. Fissiaux, G. Blanquet, M. Lepère, J. Quant. Spectrosc. Radiat. Transf. 113

(2012) 1233.[18] W.H. Press, B.P. Flannery, S.A. Tendolsky, W.T. Vetterling, Numerical Recipes-

Tha Art of Scientific Computing (FORTRAN version), Cambridge Univ. Press,Cambridge, 1992.

[19] A. Levy, N. Lacome, C. Chackerian Jr., Academic Press Inc., New York, 1992. pp.261–337.

[20] P.W. Rosenkranz, IEEE Trans. Antenn. Propag. 23 (1975) 498–506.[21] F. Thibault, J. Boissoles, R. Le Doucen, R. Farrenq, M. Morillon-Chapey, C.

Boulet, J. Chem. Phys. 97 (1992) 4623.[22] G. Gentry, L. Larrabee Strow, J. Chem. Phys. 86 (1987) 5722.[23] A.S. Pine, J. Quant. Spectrosc. Radiat. Transf. 57 (1997) 157.[24] H. Aroui, H. Laribi, J. Orphal, P. Chelin, J. Quant. Spectrosc. Radiat. Transf. 110

(2009) 2037.