Diode Laser Spectroscopy in the 9.8-μm ν14Band of Benzene

JOURNAL OF MOLECULAR SPECTROSCOPY ARTICLE NO.

184, 434–441 (1997)

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Diode Laser Spectroscopy in the 9.8-mm n14 Band of Benzene I. Experiment, Data Treatment, and Results for Line Intensities J. Waschull, Y. Heiner, B. Sumpf, and H.-D. Kronfeldt Optisches Institut der Technischen Universita¨t Berlin, Sekretariat PN 0-1, Hardenbergstr. 36, 10623 Berlin, Germany Received March 28, 1997

High-resolution diode laser spectroscopy was applied to measure absolute line intensities in the 9.8-mm n14 band of benzene 12C6H6 . A new data treatment had to be developed to derive single line parameters from the strongly overlapped lines. This procedure includes a self-deconvolution and an adapted fit technique for complete pressure series. The obtained data set contains absolute line intensities of 73 lines between 1017.31 and 1045.85 cm01 with 9 £ J 9 £ 66 and 1 £ K 9 £ 66. These results for individual lines formed the basis for the calculation of the vibrational bandstrength S 0V of the n14 band considering l-type resonance. In contrast to previous values derived from bandshape integration the deduced value of S 0V Å (17.0 { 1.4) cm02 /atm at 295 K is not affected by difference band lines. q 1997 Academic Press INTRODUCTION

Up to now the knowledge on vibrational–rotational line parameters of the n14 band of benzene (Herzberg notation) covers only line positions. PlıB va and Johns (1) applied a Fourier transform spectrometer while Junttila et al. (2) used a molecular-beam optothermal technique to investigate this band of 12C6H6 . Considering the whole infrared absorption spectrum of benzene single line parameters other than positions are only known from Dang-Nhu et al. (3). They gave absolute line intensities of 30 P-branch lines of the n4 band near 15 mm determined by diode laser spectroscopy. Subsequently they used these results to deduce the vibrational bandstrength of the n4 band. Moreover, Dang-Nhu and PlıB va (4) published a procedure to calculate line intensities for all infrared active fundamentals of benzene. The reason for the lack of experimental data is the high line density in the benzene fundamentals which is enlarged by difference bands such as n14 / n20 0 n20 in the case of the n14 band. But the exact knowledge of line parameters is necessary for the application of high-resolution spectroscopic methods for the benzene detection in gas mixtures. In that connection the n14 band is of special importance because it is the only infrared active fundamental of benzene which is rather free from atmospheric interference. Furthermore, line intensity values of single lines enable the calculation of vibrational bandstrengths free from the influence of difference bands or combination bands. Such experimental bandstrengths are very useful as critical tests for force field calculations for the benzene molecule (5–7). In this paper we present our experimental setup and the new developed data treatment which enabled us to measure single line parameters to specify our results for absolute line

intensities and to interpret the data considering the l-type resonance for perpendicular bands: Thus we are able to give the first value of the vibrational bandstrength of the n14 band which does not include the absorption caused by difference bands. This value is compared to bandstrengths from bandshape integration. The second part of this paper will contain the experimental results for benzene self-broadening coefficients at different temperatures, their interpretation in the frame of the Anderson–Tsao–Curnutte theory (ATC), and benzene–air and benzene–noble gas broadening coefficients. The data given here actualize some of our preliminary data (8–11) and extend them substantially. THEORY

The absorbance A( nI ) is calculated from the measured spectrum I( nI ) according to Lambert–Beer’s law A( nI ) Å 0ln

Å Lrppart

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[1]

where I0 ( nI ) designates an empty-cell measurement. L and ppart are the optical pathlength and the partial pressure of the absorbing gas, respectively. The spectrum A( nI ) is treated as a superposition of single lines i at the position nI 0 with a line intensity S and the lineshape function f which is presumed to be a Voigt profile and therefore characterized by the Doppler width DnI D and the Lorentzian width DnI L (both HWHM). The latter is connected to the broadening coefficient g and the total cell pressure ptot by

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∑ Si rfi ( nI 0 nI 0,i , DnI D,i , DnI L,i ), i

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I( nI ) I0 ( nI )

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DIODE LASER SPECTROSCOPY IN THE n14 BAND OF BENZENE—LINE INTENSITIES

DnI L Å gr ptot .

[2]

For the presented experiments holds ppart Å ptot . According to (4) is it possible to calculate benzene line intensities using S Å S 0V enI 0 ( nV ZR ) 01[1 0 exp( 0hc nI 0 /kBT )]

[3]

1 exp( 0hcE0 /kBT )F » FR … 2 ,

where the symbols have the following meanings: c, h, and kB are the universal constants the speed of light, Planck’s constant, and Boltzmann’s constant, respectively, e is the nuclear spin statistical weight (4), nV is the band center (2), ZR is the rotational partition function (4), F is the Herman– Wallis factor, and » FR … 2 is the Ho¨nl–London factor (4). The references give the sources of the values we used for our calculations. F was set to unity, we calculated the ground state energy level E0 with the spectroscopic constants from (2) and the formula given in (4), and for the calculation of the transition frequency nI 0 we applied the Hamiltonian matrix from (1) with the spectroscopic constants determined in (2). The estimation of the vibrational bandstrength S 0V was one of the aims of this work. For the evaluation of the fit results, which is part of our data treatment, we made use of the dependence of the line intensity on the temperature T. Considering the temperature dependencies explicitly given in (4) we found the relation S(T 1 ) T 2rZV (T 2 )rZR (T 2 )r[1 0 exp( 0hc nI 0 /kBT 1 )] Å S(T 2 ) T 1rZV (T 1 )rZR (T 1 )r[1 0 exp( 0hc nI 0 /kBT 2 )]

F S

1 exp 0

E0 kB

1 1 0 T1 T2

DG

[4]

for the line intensities (given in temperature-dependent units like [cm02 /atm]) at temperatures T 1 and T 2 . The introduction of the vibrational partition function ZV (4) refers to the temperature dependence of the vibrational bandstrength. EXPERIMENT

The benzene spectra were recorded with a self-built diode laser spectrometer (Fig. 1). The diode laser is excited with rectangular current pulses. The monochromator serves for mode selection. The main components like cryostat, monochromator, detectors, and sampling oscilloscopes are specified in (8). The signal-to-noise ratio of the single shot spectra was approximately 120. The principle of the Herriott cell is demonstrated in (12). For our experiments it was equipped with a heating device and adjusted to an optical pathlength of L Å (480 { 2) cm. Room temperature was supervised with a mercury thermometer and was kept at (295 { 0.5) K. The temperature inside the heated cell could

be stabilized to {1 K. The confocal e´talon had a free spectral range of approximately 0.01 cm01 . The reference cell turned out to be necessary for three reasons: the calibration of the confocal e´talon, the absolute wavenumber scaling which is prerequisite for the assignment of the benzene lines, and to estimate the influence of the finite spectral resolution power of the spectrometer which was dominated by the laser emission linewidth. For the first two points we made use of the OCS (carbonyl sulfide) calibration tables in (13). The last will be explained in the next section. The benzene samples (Merck) applied for the experiments were specified with a purity better than 99.7%. For the gas sample we assume that the isotopic abundance is natural (fraction of 12C6H6 : 93.43% (4)). The pressure of the sample was measured by means of a Leybold CM100 with an accuracy of 0.5% of reading. To determine self-broadening coefficients and line intensities we recorded spectral sections of approximately 0.05 to 0.06 cm01 at 6 to 7 different benzene partial pressures varying between about 0.4 and 1.5 Torr. The pressure range is restricted by the increasing line overlapping. All measurements were carried out at 295 and 344 K sample temperature. DATA TREATMENT

Each recording of a spectrum consists of 30 single shots which were accumulated by a specific procedure to improve the signal-to-noise ratio. This procedure is described in detail in (8) and (11). As part of the accumulation procedure the time equidistant measured points of the spectrum were transformed into a wavenumber equidistant scale with the help of the measured e´talon fringes. This is necessary due to the nonlinear wavenumber tuning of the laser during the current pulse. Empty cell measurements I0 ( nI ) and recordings of the signal of the unexposed detector were used to calculate the absorbance A( nI ) from the absorption spectra I( nI ). The spectra at this stage of treatment consist of 512 data points with individual values for their confidence interval at a relative wavenumber scale. The signal-to-noise ratio is approximately 650. Simultaneous measurements of benzene spectra and exactly known OCS spectra (13) enabled the conversion from the relative to an absolute wavenumber scale. The assignment of the lines was carried out by the comparison of specially recorded survey spectra (Fig. 2A) to synthesized spectra (Fig. 2B). The synthesized spectra were calculated from line position and relative intensity data provided by PlıB va (14), who recalculated the spectrum of the n14 band using the Hamiltonian matrix from (1) and the spectroscopic constants from (2). Moreover, Fig. 2 illustrates the influence of difference band lines since it can be assumed that Fig. 2B contains all significant n14 fundamental lines.

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FIG. 1. Experimental set-up. ms, mirror system. The depicted nonplanar mirrors are off-axis parabolic mirrors.

At that point of the data analysis the strong overlap of benzene lines even with Doppler-dominated linewidths leads to considerable difficulties. The lines of interest have to be treated together with its spectral neighborhood with the consequence that a lot of strongly correlated parameters (position, intensity, and Doppler and Lorentzian widths for every line) have to be determined. To overcome this problem we developed the following procedure consisting of self-

deconvolution, serial fit, and fit valuation by temperature dependent intensity change. The starting point of the line-parameter analysis was a Fourier self-deconvolution of the spectrum with the lowest cell pressure (and thus nearly Doppler-shaped spectral lines). The basic ideas of this technique which we implemented in an interactive program (written for Mathcad 3.1, MathSoft. Inc.) are given in (15) and (16). Using the theo-

FIG. 2. Comparison of experimental (A) and theoretical (B) spectra. Theoretical spectrum calculated with Doppler profiles with the data from ( 14); the relative intensities of the lines are comparable only within each single spectrum.

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FIG. 3. Self-deconvolution (solid line) of a benzene spectrum (dotted line, ptot Å 0.616 Torr, L Å 480 cm). The ordinate refers to the measured spectrum, the arrow marks a line the existence of which was revealed by the application of the self-deconvolution, and the vertical lines confine the section for the parameter fit (see Fig. 4).

retical Doppler width and an appropriate Lorentzian linewidth, this procedure reduces the Voigt linewidth by a factor of up to 1.6 depending on the signal-to-noise ratio and the number of data points given per line. These linewidth-reduced spectra were very helpful (and mostly necessary) for the determination of the number of lines which has to be included into the line-parameter fit. Figure 3 gives an example where the dotted line represents the experimental spectrum and the solid line gives the result of the self-deconvolution. The arrow marks a line the existence of which was only revealed by the application of the self-deconvolution. The vertical lines confine the spectral section chosen for the parameter fit. The labels with the meaning DK D JK 0 (J 9 ) mark the strong lines of the n14 band in this section. The core of the parameter analysis of the spectra is the fit of Voigt profiles to all lines and to all spectra of a pressure series simultaneously by means of evolution strategies. The employment of stochastic evolution strategies instead of the common deterministic Levenberg–Marquardt algorithm is motivated by the smaller sensitivity to the choice of initial fit parameters and its feasibility to leave local minima of the parameter space. Both features are explained in detail in (11). For the Voigt profile we used the analytical representation given by HumlıB cek (17). The simultaneous fit of spectra measured at different pressures allows a drastic reduction of the ratio of free spectral parameters in relation to the number of measured data points. This leads to a higher accuracy of the estimated parameters. Basic aspects of this method are pointed out in (18) as

well. To determine benzene line parameters the following parameter reductions proved to be practicable: • fit of gi to the whole pressure series instead of DnI L,i to each line of interest separately for every measured spectrum at a given pressure, • instead of fitting the line integral si Å LrppartrSi for each line at every ppart we determined its slope LrSi for the whole pressure series, • calculation of one common broadening coefficient for all weak difference band lines which overlap the lines of interest, • keep the Doppler width fixed at its theoretical value for all lines of the related spectrum, • only one set of relative line positions is fitted to the whole pressure series; neglecting line shift and narrowing effects finds its justification in the smallness of the measured pressure interval.

As additional free parameters for each spectrum we introduced a wavenumber-independent absorbance which is due to very weak and unresolvable difference band lines as well as one parameter per spectrum which adjusts shifts of the relative wavenumber scales of the spectra. The number of free spectral parameters could be reduced by the abovementioned steps down to about 20% compared to the full set of four parameters for every line (depending on the specific spectral section) without changes of the underlying model (1, 2). To consider the resolving power of the spectrometer we

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FIG. 4. Result of the serial Voigt-profile fit of the confined section of Fig. 3. The spectra are shifted for clearance, and the error bars of the data points are results of the accumulation procedure; for details concerning the free parameters see the text.

measured self-broadening pressure series of isolated OCS lines. Keeping the Doppler width at its theoretical value, we determined the Lorentzian width by means of a Voigt-profile fit and draw it versus the OCS pressure. The extrapolation of the linear regression to pressure zero gave the segment of the ordinate c which quantifies the influence of the spectrometer on the line-parameter determination. Depending on the particular laser mode, we found c values from 0.017 1 10 03 to 0.078 1 10 03 cm01 (HWHM). These values became part of the benzene line analysis by changing the linewidth formula [2] to DnI L Å gr ptot / c.

[5]

If the shape of the laser emission line is expected to be Lorentzian and additional broadening effects caused by the time constant of the detector – amplifier system can be ruled out ( to be sure about this we performed additional experiments ) , the c values can be interpreted as emission linewidth and with that as spectral resolution power of the spectrometer. The result of the pressure series fit to the spectral section of Fig. 3 is shown in Fig. 4. Ten Voigt profiles were fitted to a spectral section of about 16 1 10 03 cm01 . For the six spectra we applied 34 parameters: 10 line positions, 10 slopes of the line integrals, 2 individual broadening coefficients for the strong lines of the n14 band, 1 common broadening coefficient for 8 weak lines, 6 wavenumber-independent absorbances, and 5 shift corrections.

For all parameters we give 68.3% confidence intervals. The basics of these confidence estimations can be found in (19) and their application to our problem is pointed out in (11). But self-deconvolution and pressure-series fit cannot totally remove any doubt about the number of lines which have to be included into the fit. Thus every additional Voigt profile decreases, as a rule, the deviations between fit result and experiment. Therefore we were looking for an additional criterion to evaluate our fit results. The temperature-dependent change of the line intensity provides such a criterion. For that reason we repeated the measurements with gas samples heated to 344 K and compared the experimental data to the ratios Si (295K)/Si (344K) calculated according to [4]. The results of the measurements for a certain line were ignored for the following discussion if the deviation between experimental and theoretical ratio exceeded 5%. RESULTS AND DISCUSSION

To investigate quantum number dependencies of the line parameters we made efforts to treat benzene lines within extended quantum number intervals. From the P branch we measured 52 lines between 1017.31 and 1031.22 cm01 and quantum number regions of 1 £ K 9 £ 66 and 19 £ J 9 £ 66. The R branch was investigated between 1041.81 and 1045.85 cm01 . From that we give data of lines with ground state quantum numbers 1 £ K 9 £ 23 and 9 £ J 9 £ 23. The individual line intensities Si at 295 K and their confidence intervals dSi are summarized in Table 1. The values refer to

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TABLE 1 List of the Experimental Absolute Line Intensities and Its Confidence Intervals as well as the Deduced Vibrational Band Intensities with and without Consideration of the l-Type Resonance

Note. The intensities listed in this table refer to an abundance of 100% 12C6H6 .

an abundance of 100% 12C6H6 . The given line positions are the theoretical ones already used for the assignment (14). In column 8 of Table 1 we notice the vibrational bandstrengths S 0V,i which follow from the application of [3] to the corresponding experimental line intensity. The results of this calculation are plotted in Fig. 5 dependent on the quantum number K *. To keep this figure clear we renounce the error bars. A systematic deviation from the expected S 0V value for all measured lines reveals the distinction of lines with DK Å /1 ( j ) and DK Å 01 ( h ). Decreasing K * leads to a seeming increase in the vibrational bandstrength for lines with DK Å 01 and to a diminution of S 0V for transitions with DK Å /1. The reason for the depicted behavior is the influence of the l-type resonance in that perpendicular band on the line intensities. By considering the off-diagonal elements of the Hamiltonian matrix which describe the coupling of the inter-

acting states this behavior becomes plausible: according to (1) the quantum number dependence of the off-diagonal elements is given as {[J * (J * / 1) 0 K * (K * 0 1)] 1 [J * (J * / 1) 0 (K * 0 1)(K * 0 2)]} 1 / 2 .

Consequently, a smaller K * causes a stronger interaction of the corresponding l Å /1 and l Å 01 levels at a given J *. For a quantitative inclusion of that effect in the determination of the vibrational bandstrength we follow the explanations of Cartwright and Mills (20). If we designate the ground state wavefunction as C9 and the pair of the perturbed interacting final states as C */ and C *0 , É» C9ÉmP ÉC */ …É2 Å a 2 M 21 / b 2 M 22 / 2abM1 M2

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[6]

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[7]

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FIG. 5. Vibrational band intensities calculated according to [3] from the experimental absolute line intensities dependent on K * ; DK Å /1 ( j ), DK Å 01 ( h ).

and É» C9ÉmP ÉC *0 …É2 Å b 2 M 21 / a 2 M 22 0 2abM1 M2

[8]

hold for the squared transition moments which are proportional to the line intensity. Formula [7] is valid for DK Å 01 transitions and [8] for DK Å /1 in the case of the n14 band of benzene. The definition of the eigenvectors a and b only includes the elements of the Hamiltonian matrix (1) and is given in Appendix 2 in (20). M1 and M2 are the

transition moments between C9 and the unperturbed interacting final states. Their squares are given by the Ho¨nl– London factors. For the determination of the vibrational band intensity we calculated the quotient r which has to be multiplied to the right side of [3] to consider the l-type resonance:

rÅ

É» C9ÉmP ÉC */ …É2 É» C9ÉmP ÉC *0 …É2 , resp. r Å . [9] M 21 M 22

FIG. 6. Vibrational band intensities as shown in Fig. 5 but calculated with additional consideration of the l-type resonance; DK Å /1 ( j ), DK Å 01 ( h ).

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DIODE LASER SPECTROSCOPY IN THE n14 BAND OF BENZENE—LINE INTENSITIES

TABLE 2 List of Experimental Values of the Integrated Band Intensity of the n14 Band of Benzene and Comparision to the Vibrational Band Intensity of This Work

441

of the intensity of the n14 band. The second is that combination bands (mostly n18 / n20 at 1006 cm01 with approximately 2% of the intensity of the n14 band (7)) or other fundamentals can be neglected in the spectral region of that band. ACKNOWLEDGMENTS The authors thank J. PlıB va for providing the complete data set of calculated line positions and relative strengths of the n14 band of benzene. Y.H. and J.W. thank the Deutsche Bundesstiftung Umwelt for a grant; B.S. was supported by the Deutsche Forschungsgemeinschaft.

REFERENCES

The values of r are given in column 9 of Table 1 for the measured lines. Column 10 contains the vibrational band intensity calculated from every line with regard to the l-type 0 resonance, now denoted as S V,i * . The effect of that correction becomes clear in comparison of Fig. 6 to Fig. 5. The ordinates of both are drawn in the same scale. 0 Averaging S V,i * results in S 0V Å ( 17.0 { 1.4 ) cm02 / atm at 295 K. With that we give the first experimental value for the vibrational band intensity of the n14 band of benzene which is not affected by difference band transitions. To compare our result to integrated measurements which were carried out according to SB Å

1 ppartrL

*

band

ln(I/I0 )d nI ,

[10]

we make use of the approximation S 0V É SB /ZV

[11]

given in (4). Table 2 summarizes integrated band intensities known from the literature and gives their conversion to S 0V values at 295 K. The vibrational band intensities which are calculated according to [11] agree quite well with the experimental determined value of this work. There are two reasons that the approximation [11] holds so strong for the n14 band of benzene. The first is that the difference bands which superimpose the fundamental band are infrared active, above all the n14 / n20 0 n20 band with approximately 29%

1. J. PlıB va and J. W. C. Johns, J. Mol. Spectrosc. 107, 318–323 (1984). 2. M.-L. Junttila, J. L. Domenech, G. T. Fraser, and A. S. Pine, J. Mol. Spectrosc. 147, 513–520 (1991). 3. M. Dang-Nhu, G. Blanquet, J. Walrand, and F. Raulin, J. Mol. Spectrosc. 134, 237–239 (1989). 4. M. Dang-Nhu and J. PlıB va, J. Mol. Spectrosc. 138, 423–429 (1989). 5. M. Akiyama, J. Mol. Spectrosc. 93, 154–163 (1982). 6. L. Goodman, A. G. Ozkabak, and K. B. Wiberg, J. Chem. Phys. 91, 2069–2080 (1989). 7. P. E. Maslen, N. C. Handy, R. D. Amos, and D. Jayatilaka, J. Chem. Phys. 97, 4233–4254 (1992). 8. B. Sumpf, Y. Heiner, Ka. Herrmann, F. Ku¨hnemann, V. Pustogov, and J. Waschull, in ‘‘Proceedings of the International Conference on LASERS’93,’’ pp. 297–304. STS Press, McLean, VA, 1994. 9. J. Waschull, B. Sumpf, Y. Heiner, V. V. Pustogov, and H.-D. Kronfeldt, Ber. Bunsenges. Phys. Chem. 99, 381–383 (1995). 10. J. Waschull, B. Sumpf, Y. Heiner, and H.-D. Kronfeldt, Infrared Phys. Technol. 37, 193–198 (1996). 11. Y. Heiner, O. Stier, V. Tu¨rck, J. Waschull, B. Sumpf, and A. Ostermeier, J. Quant. Spectrosc. Radiat. Transfer 56, 769–782 (1996). 12. H.-D. Kronfeldt and J. Berger, Proc. SPIE 1780, 650–656 (1992). 13. A. G. Maki and J. S. Wells, ‘‘Wavenumber Calibration Tables from Heterodyne Frequency Measurements,’’ NIST Special Publication 821. National Institute of Standards and Technology, 1991. 14. J. PlıB va, private communication. 15. J. PlıB va, A. S. Pine, and P. D. Willson, Appl. Opt. 19, 1833–1837 (1980). 16. J. K. Kauppinen, D. J. Moffatt, H. H. Mantsch, and D. G. Cameron, Appl. Spectrosc. 35, 271–276 (1981). 17. J. HumlıB cek, J. Quant. Spectrosc. Radiat. Transfer 27, 437–444 (1982). 18. D. C. Benner, C. P. Rinsland, V. Malathy Devi, M. A. H. Smith, and D. Atkins, J. Quant. Spectrosc. Radiat. Transfer 53, 705–721 (1995). 19. W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, ‘‘Numerical Recipes in C,’’ 2nd ed., Cambridge Univ. Press, Cambridge, UK, 1992. 20. G. J. Cartwright and I. M. Mills, J. Mol. Spectrosc. 34, 415–439 (1970). 21. H. Spedding and D. H. Whiffen, Proc. R. Soc. London Ser. A, 238, 245–255 (1956). 22. J. Overend and M. J. Youngquist, unpublished work. [cited in J. Overend, ‘‘Quantitative Intensity Studies and Dipol Moment Derivatives’’ in ‘‘Infra-red Spectroscopy and Molecular Structure’’ (M. Davies, Ed.). Elsevier Publishing Company, Amsterdam, 1963] 23. F. Raulin, private communication. [Cited in 4]

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