Absolute line intensities and broadening coefficients for the ν11 band of allene

J. Quant.

Spxtrosc.

Pergamon

Radiat. Transfer Vol. 58. No. 2, pp. 145-149. 1997 1‘ 1997 Elsevier Science Ltd. All rights reserved

Pnnted in Great Britain

PII: S0022-4073(97)00043-5

ABSOLUTE LINE COEFFICIENTS

0022-4073197

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INTENSITIES AND BROADENING FOR THE v,, BAND OF ALLENE

J. MARCOS SIROTA,“? DENNIS C. REUTERb and JOAN FRYE’ ,‘Department of Physics, University of Maryland Baltimore County, 1000 Hilltop Circle, Baltimore. MD 21250, U.S.A., hPlanetary Systems Branch, NASA Goddard Space Flight Center. Code 693. Greenbelt, MD 20771, U.S.A. and “Department of Chemistry, Howard University,

Washington. DC 20059, U.S.A. (Received

9 Drcemher

1996)

strengths for the v,, band of allene (352.636 cm ‘) have been measured using tunable diode laser spectroscopy. The dipole moment and band strengths have been derived, and pressure broadening coefficients for self and N2 broadening were determined at temperatures representative of Titan’s atmosphere (160-190 K). The absolute value for the dipole moment is 0.1093 debye giving a band intensity of 26.29 cm-* atm-’ (300 K). This band strength is about 6% lower than that inferred from the low resolution measurements performed by Koga et a1,14which is the only previous strength measurement for this band. ,c 1997 Elsevier Science Ltd Abstract-Line

1. INTRODUCTION

The infrared spectrum of allene (H,C=C=CH,) has been extensively studied, primarily because of its interesting symmetry (DZdgroup) and because of the effects of Coriolis-type interactions on its energy levels. However, there are few measurements of absolute transition strengths for its various infrared bands. This molecule is particularly important for planetary astronomy, since its existence in the atmosphere of Titan has been predicted at a mixing ratio of 5 x 10e9 by photochemical models’ and and at a mixing ratio of 7 x 10e9 by plasma discharge experiment?. Allene was not detected on Titan by the Voyager IRIS instrument 3, but an upper limit for its mixing ratio of 5 x lo-’ was determined,4 based on that spectrometer’s sensitivity. In the near future, two space platforms equipped with instruments of higher spectral resolution will be able to measure this species on Titan at much lower abundances.4 The short wavelength/long wavelength spectrometer aboard the Infrared Space Observatory, and the composite infrared spectrometer (CIRS) aboard Cassini will both be capable of recording allene spectra at a resolution about 10 times hi’gher than that of the IRIS spectrometer aboard Voyager. The observation of allene spectra on Titan is thus very likely. The v,, band in the 340-360 cm-’ region is the optimal band to observe since there is no interference from other species, while other bands, such as vgand vIOare in the same spectral region as ethane lines. Furthermore, allene is expected to be found in a region of the atmosphere where the temperatures are from 150 to 200 K, so the Planck function radiances argue for longer wavelength observations. Accurate laboratory values for v,, intensities are required to interpret these observations. In this paper we present intensity measurements for eight lines of the v,, fundamental, as well as preliminary coefficients for self- and N,-pressure broadening. All measurements were performed at temperatures between 160 and 190 K, which is the relevant temperature range for those altitudes were the highest thermal radiance from this species is predicted.’ These temperatures also reduced the number of hot band transitions, and simplified the spectrum. 2. EXPERIMENTAL

CONDITIONS

The measurements were performed using a tunable laser spectrometer optimized for long wavelength operation.5 The infrared source was a lead salt semiconductor laser. The laser current tTo

whom all correspondence should be addressed. 145

J. Marcos Sirota et al

146

was modulated with a ramp waveform at 40 Hz, generating a periodic laser frequency sweep. The allene gas, with a manufacturer specified purity greater than 97%, was contained in a 30 cm brass cell. The cell was enclosed in a vacuum container and was cooled by a Sterling-cycle cryocooler. The cryocooler was turned-off during measurements to reduce temperature gradients, while the large mass of the cell kept the temperature nearly constant during a whole set of measurements. The temperature was monitored at three points along the wall of the cell. These three values did not differ by more than 2.0 K for any of the measurements. The average of these values was used as the gas temperature in the analysis. The pressure in the cell was measured with a capacitive type manometer. After passing through the cell the beam was focused onto a blocked impurity band Sb-doped silicon detector working at LHe temperature.s This detector provided high signal to noise ratios with short integration times, which minimized the effect of diode laser frequency drift. The signal was recorded in a signal averager board installed in a PC-type computer. Averages of about 256 scans were taken. Details of the experimental system can be found in Ref. 5. 3. DATA

ANALYSIS

Data were obtained for scans comprising two or three lines, for several regions in the 359 to 361 cm-’ range. At least five different pressures were recorded per group. The data were then analyzed by a least squares fit of the line profiles to a Voigt function.6 The line intensity and the Voigt width are determined in the fit. Allene belongs to the D,, symmetry group. The Hamiltonian parameters for the ground state (Al-type symmetry) have been determined by Heglund et alE’ using combination differences. The v,, state, (the C=C=C bending mode, E-type symmetry) has been studied by Pliva et al* who determined the terms of the Hamiltonian, including both l-type interactions typical of symmetric top molecules and those particular to molecules with four-fold symmetry. We used these Hamiltonians for our analyisis. Assignment was facilitated by the availability of the FTS spectrum recorded by Pliva et al.* The line intensity S, is related to the vibrational band intensity Sv byY

and the band intensity can be expressed as a function of the vibrational transition dipole moment,

s

1

87+LIT0 Y! v w( - EdkT) rt_,,,, . QV

’ - 3hc p0 T '

(2)

vi is the transition frequency, vO,is the band center frequency, g,, is the nuclear spin factor. Qc. and Q, are the vibrational and rotational partition functions, respectively, E,and Ev the rotational and vibrational energy of the lower state, respectively, yi is the isotopic abundance (here 0.967) K.AK is the line strength or Honl-London factor. Since all transitions and L,, the Loschmidt number. LJ., measured in this work are RR type lines, this factor is’” L,cAK

J.AJ

=

(J + K + l)(J + K + 2) J+

1

(3)

for all K, except K = 0,where a factor of 2 should be included due to the intensity perturbation appearing for the l-type doubled K’ = + 1, I = + 1 upper state for perpendicular transitions in a symmetric top.” Examination of the eigenvectors of the Hamiltonians indicated that, for the transitions studied here, the I-type perturbations for K # 0 did not cause significant mixing between K and K f 2 levels, so the rigid rotor expression given in Eq. (3) was sufficient to describe the transition moments. The nuclear spin weights are 3 and 7 for J odd and even respectively for K = 0,12 and 6 and 10 for K odd and even (K # 0) respectively. Qv was calculated using the harmonic oscillator approximation. Qr was determined by direct summation, including spin and

Allene-vll absolute intensities

147

/-type degeneracies. Qf was also evaluated using the rigid rotor approximation, and accounting for spin and I-type degeneracies. I3 A difference lower than 0.2% was found between the direct summation values and the classical expression values for temperatures between 150 and 300 K.

360.5

361.0

I I I

~____-__-__-___~__--__-__-__-i I

1.2

I

I

r

5

)

’

I

’

10

’

-I

t

-0.2

I 360.74

a

I

,,I,,

, 360.75

,

, 360.76

,

,

, 360.77

,

,

,

,

1

360.78

Frequency Fig. 1. Example of measured transmittance spectra. Circles are data points, and the line is the least squares fit to a Voigt profile. The residual is shown magnified by a factor of 5. The upper insert shows a section of the FTS spectrum obtained by Pliva et al.’

148

J. Marcos Sirota et al

Therefore a T’” dependence is quite accurate to calculate Q, in that temperature range, using as reference the value for 300 K given in Table 2. Eq. (1) and Eq. (2) may be combined as S, = X(~,J,0%,,

f

(4)

where all the factors in X are previously known molecular or physical constants. The squared dipole moment was determined by a least-squares fitting using Eq. (4) and then the band intensity was calculated using Eq. (2). 4.

RESULTS

An example of a measured transmittance spectra, and the corresponding Voigt profile fitting are shown in Fig. 1. The same spectral region is shown for the FTS scan obtained by Phva et al. In this case, the higher resolution obtained by TDL spectroscopy permitted the assignment and measurement of lines which were completely blended in the FTS spectra of Ref. 8, but which were correctly identified as two transitions and assigned to the same peak in that work. Here the 0.002 cm -’ separation can be clearly seen, which agrees with the results from the Hamiltonian diagonalization. All the line intensity data are shown in Fig. 2, as well as the least squares fit. The observed line intensities, reduced to a single temperature and averaged, and the calculated values are shown in Table 1. The fitting yielded a value of 0.1093 debye for the transition dipole moment, and a 300 K band intensity of 26.29 cm -* atm - ’ for v,,. This last value may be compared to the broad band measurement performed by Koga et aLi which is the only available strength measurement for this band. We must estimate the fraction of their value corresponding to the fundamental, since their measurements, which were made at a pressure of 11 atm and with a resolution of 1 cm -I, included hot band transitions. In order to extract a value for the dipole moment, we applied a harmonic oscillator approximation (It,, _ , = nri_,,), and used Eq. (1) expanding the total strength as the sum of that for the fundamental plus the first four excited states. We may neglect higher states for the purpose of this comparison. In this way, we obtain a value of 0.1125 debye for the absolute value of the dipole moment from their measurements, which yields a value of 27.88 cm -’ atm ’ for the band intensity of the fundamental transition. These values are listed in Table 2. 5. COLLISIONAL

BROADENING

A series of measurements were performed to determine the pressure broadening coefficient for self- and N,-broadening at temperatures relevant to the spectral observations of allene in Titan’s atmosphere. These measurements are very preliminary, since only one line was studied, and no temperature dependence was determined. However, we report them here to aid in modelling IS0 0.16 r

f@ 0 0

5:1036

I

I

I

I

I

I

6 x 1O36

7 x 1036

8 x 10'6

9 x IO'6

I x 103'

I.1x IO"

X W,

J, 'U

Fig. 2. Measured line intensities (circles) and least squares fit to expression (4) (line).

Allene-e,, absolute Table J’

K’

9 13 15 I7 I5 8 I’) 17 *From

I. Observed

and calculated line intensities J”

5 3 2 I 3 7

8 I2 14 16 14 7

I

18

2

I6

K”

149

intensities

for RR transitions

v,*

S, cobs)

359.2260 359.4504 359.5392 359.5460 360.6803 360.7504 360.7726 360.7746

0.1001 0.1205 0.0645 0.1520 0.1029 0.0754 0.1315 0.0617

in the vII band of H,C=C=CHI. S,

(talc)

IO-Cl (%)

0.0809

19.1 6.2

0.1134 0.0653 0.1350 0.1228 0.0652 0.1338 0.0661

1.2 11.2 19.3 13.4 1.7 7.1

T (KJ 189.5 175.2 175.2 175.2 171.0 171.0 171.0 171.0

Ref. 8.

Table 2. Transition

dipole

moment,

band strength,

and broadening This

Dipole moment (abs. value) [debye] Band strength (cm _ ’ atm _ ‘) @ 300 K Self-broadening coefficient (cm _ ‘/atm) (measured for “R,(8) @ I89 K) N,-broadening coefficient (cm _ ‘/atm) (measured for R&(8) @ 189 K)

coefficients.

work

0.1093(20) 26.29(49) 0.0856( 17) 0.0903(18)

Others 0.1125 2188

Qv (300 K) = 1.6203, QR (300 K) = I.3155 x IO’. “Ref. 14. see text.

and CIRS observations. A broadening study involving many lines and including temperature dependence is currently in progress. Since these measurements were carried out in the same 30 cm coolable cell used for the intensity experiments, the maximum pressure for self broadening measurements was limited by saturation. Nitrogen broadening was determined using Nz pressures up to 70 Torr. A self-broadening coefficient of 0.0856 cm-‘/atm and a N,-broadening coefficient of 0.0903 cm ‘/atm were measured for the 359.2260 cm I RR4(8) line at 189 K. These vaiues are also listed in Table 2. Acknowledgrmenrs-This of NASA under RTOP

work was supported in part by the Planetary Atmospheres Program of the Solar System Division 154-50-80. We thank Dr J. Pliva for making available to us the original FTS spectrum.

REFERENCES I. Yung, Y. L., Allen, M. and Pinto, J. P., App. J. Supp. Ser.,

1984, 55, 465-506.

2. Reid Thompson, W., Henry, T. J., Schwartz, J. M., Kare, B. N. and Sagan, C., Icarus, 1991, 90, 57-73. 3. Coustenis, A., Bezard, B. and Gautier, D., Icarus, 1989, 80, 54-76. 4. 5.

6. I. 8. 9. 10. 1I. 12. 13. 14.

Coustenis, A., Encrenaz, Th., Bezard, B., Rjoraker, B., Graner, G., Dang-Nhu, M. and Arie, E., Icarus, 1993, 102, 24&260. Sirota, J. M., Reuter, D. C. and Mumma, M. J., Appl. Opt., 1993, 32, 2117-2121. Weber, M., FTSFIT and TDLFIT routines, private communication. Hegelund, F., Anderssen, N. and Koivusaari, M., J. Mol. Spec., 1991, 149, 305-313. Pliva, J. and Kaupinnen, J., J. Mol. Spec., 1985, 111, 93-101. Smith, M. A. H., Fridovich, B. and Rao, K. N., Molecular Spectrosopy: Modern Research, III, Chap. 3, ed. K. N. Rao. Academic Press, New York, 1985. Allen, H. C. and Cross, P. C., Mole&w Vib-rotors. Wiley, New York, 1963. Di Lam-o, C. and Mills, I. M., J. Mol. Spec., 1966, 21, 386-413. Weber, A., J. Chem. Phys., 1980, 73, 3952-3972. Herzberg, G., In Moiecular Spectra and Molecular Structure, IZ. Infrared and Raman Spectra of Polyatomic Molecules. Van Nostrand, New York, 1956. Koga, Y., Kondo, S., Nakanaga, T. and Saeki, S., J. Chem. Ph_rs., 1971, 71, 2404-2411.