Collisional broadening and line intensities in the pure rotational spectrum of PH3

JOURNAL

OF MOLECULAR

SPECTROSCOPY

131,66-76 (1988)

Collisional Broadening and Line Intensities in the Pure Rotational Spectrum of PH3 M. SERGENT-ROZEY,

NGUYEN-VAN-THANH,

I. ROSSI, N. LACOME, AND

A. LEVY

Laboratoired’hfrarouge, associPau CNRS, Bat. 350, Universite’de Paris-&d, 91405 Orsay Cedex, France The HZ- and He-broadened widths have been measured at room temperature for seven pure rotational lines of phosphine in the spectral range lo-80 cm-‘. With the available resolution of the instrument (=0.060 cm-‘) the K structure of lines was not resolved. The retrieval of linewidths was carried out, on the assumption of identical linewidths for the J + 1 K components within a given multiplet J + 1 + J. The results obtained are in good agreement with the previous determination reported by H. M. Pickett, R. L. Poynter, and E. A. Cohen for the 1 + 0 line (J. Quant. Spectrosc.Radiat. Transfer 26, 197- 198 ( 1981)). The linestrengths were also determined for five of the lines under study. The measured values compare well with the calculated ones, derived by using the recommended value of the dipole moment for PH3, Jo = 0.574 D. 0 1988 Academic Press, Inc.

1. INTRODUCTION

In the past 10 years, infrared measurements have provided a considerable amount of information about the gaseous composition of the Jovian atmosphere. It is now recognized that far-infrared and submillimeter spectroscopy can also produce valuable data on the chemical composition of the atmosphere of outer planets. Both techniques could, therefore, be of use for studying spatial and temporal variations of concentration for some nonuniformly mixed minor species. In particular, systematic investigation of their vertical and horizontal distribution is expected to be of help in gaining better knowledge of the general circulation and of the main chemical processes taking place in the atmospheres of giant planets ( 1). One such minor component is phosphine which is known to be present on Jupiter (2). Recently, evidence has been given for the presence of PH3 also on Saturn (3). Among the missions of planetary interest that are planned for the next decade, the near-infrared mapping spectrometer (NIMS) experiment (4) is intended to perform a global mapping of the Jovian atmosphere in the range 0.7-5.2 pm. Similarly, the project FIRST, currently considered by the European Spatial Agency, is designed to operate in the submillimeter range 100 pm-1 mm (loo-10 cm-‘). It is therefore important to make accurate spectral parameters available for all of the molecules expected to be observed or suspected to be present. Regarding PH3 specifically, while the positions of the pure rotational lines are well known ( 5-8)) data for linestrengths are much fewer in number ( 9-Z 1) , and only two linewidth measurements are available from the literature (12, 13). The aim of the present work is, thus, to investigate broadening of the pure rotational lines of PHS by 0022-2852188 $3.00 Copyrip0 1988 by Academic

66 Press, Inc.

All rights of reproduction in any fOn31reserved.

PH3 PURE ROTATIONAL

the two major Jovian components high-resolution conditions.

SPECTRUM

67

H2 and He in view of future observations under

II. EXPERIMENTAL

DETAILS

All spectra were recorded with the laboratory-built FIR Fourier transform spectrometer which has been described elsewhere ( 14, IS). The optical arrangement adopted in the present work is shown in Fig. 1. The detector-a composite doped Ge bolometer operating at 4 K (15)-is located outside the interferometer housing, and a CaF2-cooled filter is used for rejecting higher frequencies. The optical cell consists of a 70-cm-long, 16-mm-i.d., stainless steel light pipe closed with quartz windows. It is devised so that one end is inside the interferometer housing, and the other end is inside a small evacuated tank directly connected to the detector. Thus the whole optical path is under vacuum. The beam emerging from the absorption cell travels through a reflecting cone and then through a short light pipe which directs it onto the detector. The optical aperture of the system is f /2.5. Owing to this geometry, the extreme rays of the incident beam make an angle of 11’ with the optical axis of the cell. This results in a possible increase in the absorbing pathlength 1 of at most 2%. This value will be adopted hereafter as the magnitude of the error interval on 1, when measuring line intensities. For the present experiments, a 37-pm-thick beam splitter was used, which allowed measurements in the spectral range lo-80 cm-‘. Since the B rotational constant of PH3 is -4.45 cm-‘, we were able to study seven lines J + 1 + J for J values ranging from 1 to 7. Only the first line 1 + 0 was not obtainable. The temperature of the cell was controlled with a platinum sonde and it was observed that, throughout the duration of each run, the thermal stability was better than 1 K. The pressure of samples was measured with two capacitance gauges, operating in the

FIG. 1. Optical scheme of the experimental device.

SERGENT-ROZEY

68

ET AL.

range 0- 10 Torr (for the partial pressure of PHs) and 0- 1000 Torr (for the total pressure), respectively. The accuracy of pressure measurements (including uncertainties in the calibration of the electronic device, thermal drifts, etc.) was estimated to be =I%. Due to the wide variation of relative intensities of the observed lines, the pressures of PH3 ranged from 39 Torr, for the 2 + 1 line, to 0.8 Torr, for the 8 + 7 line. For each line under study several spectra were taken with pressures of the perturber gas (H2 or He) ranging from 200 to 700 Torr. The gases were provided by “1’Air Liquide.” The stated purity of PH3 was 99.998% and it was used without any additional treatment. High-purity (99.9999%) hydrogen and helium were used, with a stated amount of residual water vapor less than a fraction of a part per million. In practice, no parasitic Hz0 lines were detectable in our spectra. III. MEASUREMENT

METHOD AND DATA REDUCTION

1. Instrument Function All data were taken in the form of transmittance profiles, calculated by ratioing the spectrum of each sample, and a background recorded with the pure perturber gas under the same conditions of path length and total pressure. Two runs were averaged for each background and spectrum. The spectra were calculated from single-sided interferograms with a maximum path difference of 18 cm. A triangular function was used for apodization. The instrumental function was determined experimentally by recording transmittance spectra of several weak rotational lines of CO, under a few Torr of pressure, so that the intrinsic widths of lines would be significantly smaller than the expected instrumental width. The effective shape and width of the apparatus function were taken to be the ones obtained by averaging (after normalization) the various line profiles so recorded. The corresponding resolution was found to be equal to 0.060 cm-‘.

2. Measurement Method The principle of the method consists in computing correspondence tables allowing retrieval of the collisional width y (and the strength S) of a given line from the knowledge of two “apparent” parameters measured on the recorded profile: the peak transmittance Tabs and the half-width w at half-maximum. The tables are built up by generating synthetic lines of given y and S values and convolving the corresponding profile (generally assumed to be Voigt shaped) with the instrument function. The apparent quantities w and Tabsare easily determined from the resulting contour. Then, by varying the set of initial “true” parameters y and S, all the range of obtainable values for w and TO, can be covered. All details are given in a previous paper (16). The method was first applied to study spectra consisting of isolated lines of N20 ( 17, 18). It was subsequently extended to the case of doublets of known unequal intensities of HCl (1.5). In the present work, the procedure is generalized for the processing of multiplets. Let a rotational transition J + 1 + J be investigated. The synthetic lines used for generating the tables will accordingly consist of J + 1 K components. Since the Doppler

PH, PURE ROTATIONAL

SPECTRUM

69

broadening is quite negligible here (7~ G 10m4cm-’ at 296 K and u < 100 cm-‘), each of the components is given a Iorentz profile. This profile is defined by three spectral parameters, -the

spectral position a(J, K)

-the

collisional width y (J, K)

-the

intensity S( J, K) = S. f(J, 1y),

where S denotes the total intensity of the multiplet and f( J, K), the distribution of relative intensities of the K components. This distribution function is normalized, so that ;: f(J, K) = 1. K=O

For each one of the multiplets under study f( J, K) was determined once and for all by calculating the intensity of each component S(J, K) and the total linestrength

S(J) S(J) = C S(J, K) K

and by tabulatingf( J, K) = S( J, K)/S( J) as a function of K. Two additional assumptions are then made: (i) within a given multiplet, the halfwidth y (J, K) of the various K components are given identical values of y(J), and (ii) the individual absorption coefficients of components are assumed to be strictly additive (no account is thus taken of possible line-mixing effects). Under these assumptions, the true absorption coefficient of the J + 1 + J synthetic line which is expressed as k(u)

=

;;

S(J,

K=O

=

Y(J>

[u-

K)

u(J, K)12 + r’(J, K)

can be rewritten as

cJ [u-

s.r(J)

k(u) = -

lr

Kd,

f(J, K) 4J, K)12 + r2(J)

(2)

thus yielding a transmission profile: T(u) = exp[-k(u).I]. This profile, characterized by the “true” parameters S(J) and y(J) , is then convolved with the instrument function. Due to the respective values of the collisional widths y(J) considered here and of the breadth of the instrument function, the convolution resulted in a blurring out of the K structure. A single-peaked contour is thus obtained, from which the values of w and Tabsare easily derived. The process is then repeated by considering a new set of initial parameters S(J) and y(J). In the present study, the wavenumbers of the rotational lines were accurately calculated from the set of rotational constants given by Tarrago et al. ( 29) for the ground

SERGENT-ROZEY

70

ET AL.

vibrational state. The calculation of line intensities was performed from the basic relations reported in Ref. (20). The detailed form for all practical calculations is given below in Section IV-2. IV. RESULTS

AND DISCUSSION

1. Linewidth Measurements Seven rotational lines were investigated, from J = 1 to J = 7. For each of them, several pressures of the broadening species X ( =H2 or He) were used, with a given pressure (a few Torr) of the active gas PH3. The linewidth observed for a given sample can be expressed as Y=

T~V’H~-PH~).PO’H~)

+

(3)

r”U’H3-OpW,

where r”( PH3-PH3) and r”( PH3-X) are the self- and foreign gas-broadening coefficients of phosphine, respectively. The former have not been measured thus far, except for the 1 + 0 line studied by Pickett et al. (13). We did not attempt to extract, from the least-squares fit of our experimental data, these parameters along with the HZand He-broadening coefficients. Even by assuming, for all of the considered lines, a self-broadening coefficient equal to that observed for the 1 + 0 line, the magnitude of the term y”(PH3-PH3) - p(PH3) would amount to less than 2 X 10e3 cm-’ for a pressure of phosphine as large as 10 Torr. Due to the small magnitude of this contribution, the fit could not determine it reliably. We therefore constrained this parameter to a fixed value, as follows. y may be written as

~“U’&-PW

p(PH3)

Y~U-‘H~-X)

1

or Y=

r”(PH3-X)[~W)

(4)

+ w~W’H3)1,

where CQ denotes the relative broadening ability of phosphine as compared to the perturber. An experimental value of ax can be derived for the 1 +- 0 line from the work of Pickett et al. ( 13)) who measured the self-, Hz, and He broadening. One then obtains

Y~U’H~-PW= Y~U-‘H~-&) * l

ffH2 =

T~V’H~-PW=

28

(YHe= T”(PH3-He)

2

51

*

*

We then make the additional assumption that Q is independent of the rotational quantum number J, so that we can use the above two values for all of the presently investigated lines. Such an assumption does not seem unreasonable: recently we observed in an investigation of Nz and O2 broadening of CO, lines in the 10.4~pm laser transition (21) that the relative broadening remained nearly constant all over the range of J up to J = 40. Thus, we can write y = y”(PH3-X).

p*,

(5)

PH,

PURE

ROTATIONAL

71

SPECTRUM

where p* is an “effective” total pressure defined by P* = P(X) + ax.

(6)

PV'H,).

The observed widths y(T), measured at temperature T, are then reduced to the reference temperature To, assuming the usual temperature dependence relationship:

y(T) = r(To)*(TolT)“.

(7)

Here To is taken to be 296 K. Experimental values of the temperature exponent n for PH3-Hz were recently determined, in a high-resolution investigation of the vibrationrotation spectrum of PH3 near 5 pm (22). Averaged values 12= 0.70 for PH3-H2 and n = 0.44 for PH3-He were obtained. We assume here that these values still hold for the pure rotational spectrum. A least-squares fit of the values y ( TO)vs effective pressures p* to a straight line passing through the origin immediately yields r”( PH3-X). Figure 2 gives a visualization of such a fit for the 6 + 5 line and shows the typical scatter of the data for both PHJ-HZ and PH3-He. Table I summarizes the results obtained for the broadening coefficients y ‘( PH,X) and the standard deviations u. In most cases, 0 remains smaller than 1.5-2%. If one adopts 3a as a magnitude of the experimental error, Ay would be ~5%. Taking into account uncertainties arising from pressure, temperature, and path length measurements, a reasonable estimate of the total error can be taken to be =7%. The present results are in good agreement with those reported by Pickett et al. (13) for the 1 + 0 line, as shown in Fig. 3, which gives a plot of y”(PH3-X) vs the rotational quantum number J. In the case of PH3-Hz, the measurement of Pickett (J = 0) is very closely fitted by the “curve” obtained from the present data (J = 1 to J = 7 ) . For PH3-He their value would suggest a slight decrease of y ’ for J = 0. But the deviation remains within the limits of experimental errors. Obviously the presently measured broadening coefficients are, for each value of J, averaged parameters, since a possible K dependence of the broadening was ignored. This is partly justified by the recent high-resolution investigation of PH3 in the near infrared. From the preliminary results (22) it appears that for low values of J, observed in several transitions (2~2, 2uq, and vz + vq), the individual widths of the different K

0

200

FIG.2. Hz- and He-broadened

400

600

600

widths of the 6 + 5 line versus the “effective”

pressure p*.

72

SERGENT-ROZEY

ET AL.

TABLE 1 Hz- and He-Broadened Linewidths of PHp J

r” &W-Hz)

I <- o(a)

111.2 f

v”(pH3-He) 56.1

3.0

f

3.0

2cl

106.7 f

1.8

61.3 f

1.0

3.~2

103.15f

1.7

58.8 f

1.2

4c3

103.0 f

1.1

55.2 f

0.9

5c4

98.4 f

1.3

55.3 f

0.6

6.~5

95.4 f

0.5

51.3 f

0.4

lC6

86.25 f

2.6

46.3 f

0.7

8c7

84.0 f

1.1

41.3 f

2.1

All valueaare expressedin 10-3. cm-l. abn-1 at 296 K. Quoteduncetities me one standarddeviation. (a) Pickettet ol. (Ref.13).

components within a given multiplet remain nearly constant within limits of error. Only for the highest J values (J > 10) was a variation clearly detectable, with the following general trend: for the lower K components of a given multiplet, no significant K variation could be pointed out, while for K approaching J (K = J - 2, J - 1, J) a progressive decrease of r”( J, K) systematically appeared. Consequently, for the range of Jvalues investigated here, the assumption of K-independent broadening coefficients is quite reasonable. An attempt was made to check qualitatively the influence of such a K dependence of the broadening. For two different values of J, synthetic multiplets were generated

A y(lO-”

)

cm-’ atm-’

120 b q

100 -

n

q q

•I

PH3- t-l, q

q

ao-

60-

40

0

.

. I 2

.

. I 4

. .

I 6

PH,- He

J

. 8

FIG. 3. Hz- and He-broadened linewidths versus J (rotational quantum number of the lower state). (Ki,O) Present work; (0, X) Ref. (5).

PHX PURE ROTATIONAL

73

SPECTRUM

with a linewidth distribution simulating the above-described variation vs K. We adopted a constant value y” for 0 c K G J - 2, a value 0.8 - y” for K = J - 1, and 0.5. y” for K = J. It was then found that the retrieved “mean value” of y” is not very sensitive to the introduced Kdependence: the deviation observed does not exceed a few percent. This is not really surprising since the total width is dominated by the lowest K components. Thus the observed width of the broadened J line is only slightly affected by the variation of widths of the higher K components. It is interesting to compare the present results with those obtained in the 5-pm region under high resolution (22). Some of the preliminary results are reported in Table II for QR lines with J varying from 1 to 5. Two main observations can be made. First, there is no significant K dependence of linewidths for these low values of J and second, the “averaged” value for each J compares very favorably with the currently reported far-infrared determinations. 2. Results for Line Intensities The present work was primarily aimed at the investigation of foreign gas-broadening coefficients. Accordingly, the pressures of the optically active species PHx were kept as small as possible in order to minimize self-broadening contributions. As a result, simultaneous derivation of line intensities from the same spectra becomes highly inaccurate. Otherwise, if higher pressures of phosphine would be used, the lack of selfbroadening data (except for 1 + 0 as seen above) would lead to increased uncertainties in the determination of linewidths. As a test of consistency of our measurement method, an attempt was made to extract from the present experiments values of the rotational intensity parameters of PH3. Five lines were studied from 2 + 1 to 6 + 5. For 7 f 6 and 8 + 7, since the pressure of PH3 was exceedingly small, our resulting errors are rather large. The line intensity values So were derived by averaging, for each line, the data obtained for both types of mixtures PHJ-He and PH3-HZ. The results are given in column 2 of Table III. TABLE II K Dependence of the He-Broadened Widths of QR Lines in the 5-pm Region (Preliminary Results) 0

K

2

1

1

3

57.9

56.7

3

57.6

62.1

57.5

4

53.3

-

56.7

55.6

56.7

All values arc

55.4

5

58.2

2

5

4

exprcsstd in10-3. cm-‘.

The precision is about 4 46.

m-l

51.8 54.0

at 296 K.

-

74

SERGENT-ROZEY ET AL. TABLE III Intensities of Pure Rotational Lines of PH3 This work

I

Ref. 5

s’obs

socal

socal

solA

(296 K)

(296 K)

(300 K)

(3O’JK)

lc0

0.00307

0.00301

0.00308

2Cl

0.045 f 0.002

0.0404

0.0395

0.0405

3.~2

0.218 f 0.013

0.1714

0.1679

0.1718

4c3

0.537 f 0.067

0.5125

0.5022

0.5137

5c4

1.05 f 0.15

1.0334

1.0127

1.0360

6.~5

1.66 f 0.21

1.6682

1.6348

1.6723

All valuesareexpressedin cme2.abn-l.

On the other hand, linestrengths can be calculated from the following relation: 8;T.K

=

S( J,

K)

=

!$

No

?+it

g

exp[ _EVyf’] hco(J, kT

K)

IIP ,4

2 (J+

l)‘J+

K2

1

A.

(8)

This relation is easily derived from the general expression given in Ref. (20) for symmetric top molecules. All symbols in Eq. (8) have their usual meaning. For the sake of comparison with our experimental intensity values, the partition function Q(T) has been calculated at 296 K. This was done by using the method proposed by Robiette and Dang Nhu (23). The vibrational contribution is found to be QV= 1.O18 1 and the rotational one, Qrot = 1597.135. A is a numerical factor, which is taken to be equal to 2 for K-value multiples of 3 in order to account for the unresolved splitting of A+/A_ levels and otherwise equal to unity. The permanent dipole moment of phosphine was first derived by Burrus (24) and, later on, accurately remeasured by Davies et al. (25) from Stark spectroscopy data. The so-obtained result ~1= 0.5739 D is now commonly used as the recommended value. From this value of the dipole moment and the rotational constants given in Ref. ( 19)) the line intensities were calculated for J varying from 0 to 5. The results are also given in Table III (column 3), Inspection of this table shows that, for three of the currently measured lines, the experimental intensities agree with the calculated ones to better than a few percent, which we regard as quite satisfactory. For the 2 f 1 line, the difference is =7%, which remains within limits of experimental errors, whereas for 3 + 2, the deviation is nearly 20%. This is an indication that the measured pressure of PH3 probably involved an

PH3 PURE ROTATIONALSPECTRUM

0.

-

0 FIG.

9 2

# 4

I

I

I

,

6

8

10

12

75

J,

4. Experimentaland calculatedline intensitiesat 296K. (El) Calculated,(#) experimental.

important error. (Deviations of similar magnitude were also observed for J = 6 and J = 7 due to the insufficient accuracy on the small pressure of PH3 .) Figure 4 shows the calculated distribution of line intensities at 296 K, up to J = 10. On the whole, the present experimental data correctly fit the curve up to J = 5. A similar calculation has been reported in the JPL catalog (5) by Poynter and Pickett. The corresponding values [given therein in units of cm - ’ / ( molecule - cm -* ) at 300 K] are converted here to cm-* atm-’ and listed in Table III (column 5). Comparison with our calculation (column 4) shows very close agreement. The apparent systematic deviation ( &_/Spresentwork = 1.023 ) is easily accounted for by introducing the vibrational partition function which was neglected by Poynter and Pickett. Therefore, predictive calculations of phosphine absorption can be safely performed henceforth, for the purpose of planetary modeling. The values reported in the GEISA data bank (26) compare less favorably with ours. However, these data are currently being revised and will probably be modified in a future updating of the tape. l

CONCLUSION From the present results, the need for high-resolution measurements clearly appears: first, to determine experimentally the “true” K dependence of linewidths within each J multiplet, and therefore to assess the limits of validity of the assumptions adopted here. This would also help in deriving more accurate line intensity parameters. Lastly, it would also be of importance to investigate the temperature dependence of linewidths, in the temperature range of planetary interest, i.e., down to 150- 100 K. This was done recently for several vibration-rotation lines in the 5-pm region (22). Extension to the pure rotational spectrum would allow us to establish whether linewidth parameters are sensitive to vibrational excitation. ACKNOWLEDGMENTS The authorswouldthankDr. G. Tarragofor helpful discussions and comments, and Dr. Ch. Chackerian, Jr., for reading and improving the manuscript. RECEIVED:

March 24, 1988

SERGENT-ROZEY

76

ET AL.

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