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Pressure broadening and shifting parameters for the spectral lines in the first overtone vibration–rotation bands of HBr and HI in mixtures with rare gases
Journal of Molecular Spectroscopy 253 (2009) 20–24
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Pressure broadening and shifting parameters for the spectral lines in the first overtone vibration–rotation bands of HBr and HI in mixtures with rare gases A.V. Domanskaya a,*, M.O. Bulanin a, K. Kerl b, C. Maul b a b
Department of Physics, St. Petersburg University, 2, Ulianovskaya Street, Peterhof, 198504 St. Petersburg, Russian Federation Institut für Physikalische und Theoretische Chemie der Technischen Unversität Braunschweig, D-38106 Braunschweig, Germany
a r t i c l e
i n f o
Article history: Received 29 July 2008 In revised form 24 September 2008 Available online 2 October 2008 Keywords: Infrared spectra Diatomic molecules Pressure broadening Pressure shift
a b s t r a c t We present experimental data on the previously unknown line broadening and shifting coefficients in the (2 0) overtone vibration–rotation bands of the HBr and HI molecules in mixtures with several rare gases. The vibrational dependence of the isotropic and anisotropic components of the binary interaction potential is probed by separating the measured line shifts into parts symmetric and asymmetric in the line number m and by comparing with the previously published similar data for the fundamental bands of the same molecules. It is shown that the line shifts are dominated by the vibrational dependence of the isotropic potential. A linear correlation is found between the asymptotic values of the symmetric shifts in the overtone bands for all HX–Rg (X = F, Cl, Br, I) pairs and the respective C6 long-range potential energy constants. Line broadening parameters in the overtone band of pure HBr are also reported. Ó 2008 Elsevier Inc. All rights reserved.
1. Introduction We recently reported comprehensive data on the pressure broadening and shifting coefficients for the spectral lines in the fundamental (1 0) vibration–rotation absorption bands of the HBr and HI molecules in mixtures with the rare gas (Rg) perturbers [1]. Similar data are reported here on the spectral line parameters in the (2 0) first vibrational overtone bands of the same molecules obtained using a high-resolution FTIR spectroscopic technique. Pressure broadening and shifting parameters of the spectral lines in the vibrational overtone bands are useful for testing performance of various model intermolecular interaction potential energy surfaces and of their dependence on the vibrational states of interacting species, including semi-empirical model potentials deduced from numerous studies of the rotationally resolved spectra of different van der Waals complexes. Comparison of our experimental results with the available information for other hydrogen halides allows reveal how the vibration–rotation spectra of different HX (X = F, Cl, Br, I) molecules respond to interactions with the identical environments. To the best of our knowledge, there were no previous measurements of the spectral line parameters in the overtone bands of HBr and HI perturbed by collisions with the Rg-atoms. In contrast, many studies had been reported earlier (some presented in a graphical format only [2]) on the spectral effects due to interactions with the Rg-perturbers observed in the overtone bands of * Corresponding author. Fax: + 7 812 428 72 40. E-mail address: [email protected] (A.V. Domanskaya). 0022-2852/$ - see front matter Ó 2008 Elsevier Inc. All rights reserved. doi:10.1016/j.jms.2008.09.010
the HF and HCl molecules. Wiggins et al. [3] tabulated line widths and shifts in mixtures of HF with Ar, Kr, and Xe measured with a grating spectrometer. Chou et al. [4] reported data for the P2(3) and P2(6) HF lines in He and Ar perturbers using a diode laser spectroscopy, Grigoriev et al. [5] determined line parameters for HF in a bath of Ar by a high-resolution FTIR technique. The collision-induced effects in the spectra of HF–Ar gas mixtures were also studied in other works [6–9]. Collisional line parameters in several HCl–Rg systems measured with a grating spectrometer were tabulated by Rank et al. [10–12]. The line widths and shifts for HCl in Ar and Xe perturbers were later determined using a SISAM interferometric spectrometer [13–15], showing a reasonably good overall agreement with the former results of Rank et al. More recent data on the parameters of many lines for HCl in a bath of Ar obtained by the FTIR technique were reported by Boulet et al. [16]. Some general conclusions based on these earlier observations are noteworthy. In the range of pressures (or densities) studied so far, the line shifts and widths were found to be linear in buffer gas pressures, indicating the binary nature of interactions. The line shifts tend to approach more or less stable asymptotic values with the increasing rotational quantum numbers J of the initial quantum states and usually appear to be nearly twice as great in the (2 0) bands compared to those observed in the (1 0) bands. The behavior of the overtone line widths in the HX–Rg systems (for X = F, Cl) is less straightforward, though the higher-J lines also tend to be broader than in the fundamental HX bands. The line shapes, when corrected for the finite instrument resolution and – whenever necessary – for the Doppler broadening, commonly appear adequately described by the Lorentzian profiles at higher
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buffer gas pressures. Weak line asymmetries were observed in the HF–Ar mixtures [5–8], more pronounced in the overtone than in the fundamental spectral bands [8]. On the other hand, no noticeable line asymmetries were detected in the spectra of the HCl–Ar system [16]. We report here the vibration–rotation overtone line shifts and broadenings of HBr and HI diluted with rare gases. It also deemed necessary to measure the self-perturbed line parameters in pure gaseous HBr.
2. Experimental The experimental procedure being practically the same as was used in our previous studies needs not be detailed here again. Briefly, the spectra in the range of the hydrogen halide overtone bands were recorded with a Bruker 120HR FTIR instrument, equipped with a CaF2/Si beam splitter, a cooled InSb detector, appropriate band-pass filters, and operated at the 0.005– 0.06 cm1 spectral resolutions, depending on the perturbing gas pressures (0.1–0.5 bar for pure HBr gas, up to about 5 bar for the HBr–Rg, and 4 bar for the HI–Rg gas mixtures). Altogether over 50 different combinations of the absorbing/buffer gas samples were measured. Two stainless steel high-pressure gas cells were used of 19.8 and 107 cm-long optical paths, protected inside by a fluorinated polymer coating in order to prevent corrosion and decomposition of hydrogen halides. Sub-atmospheric pressures of HBr and HI were measured with MKS Baratron capacitance gauges, higher pressures of the perturbing gases were measured with Bourdon mechanical manometers. Further details can be found in [1,17]. Our measurements were carried out at (28 ± 1) °C. 3. Results and discussion The experimental conditions chosen did not require introducing any statistically significant corrections to the measured line parameters. To account for the self-induced contributions due to the hydrogen halide species present in gas mixtures, we used the previously reported results on the line parameters in pure HI [18] and the data obtained here for the neat HBr presented below. Some weak suggestions of an asymmetry in the line wings were noted in the spectra of HBr–Xe system, but these were too small for an accurate determination. In the range of the sample pressures used in this work, the spectral line shapes appeared to be adequately described by the Lorentzian profiles. Both the Doppler broadening and hyperfine line structures did not affect the values of the shifting and broadening coefficients for the overtone lines of HBr and HI determined from the slopes of the respective line parameters by linear plots versus foreign gas pressures.
Fig. 1. Spectral line profiles of the isotopic doublet P2(7) in neat H81,79Br at three gas pressures.
Table 1 Measured self-broadening coefficients c (in 103 cm1 atm1) for the (2 lines of HBr averaged over the H79Br and H81Br isotopomers
0) band
m
c(m)
m
c(m)
10 9 8 7 6 5 4 3 2 1
65(3) 79(1) 85(1) 98(1) 110(1) 123(1) 131(1) 131(2) 131(2) 137(2)
1 2 3 4 5 6 7 8 9
126(1) 128(2) 129(2) 123(2) 120(2) 112(1) 101(2) 85a 79a
Standard deviations are shown in parentheses. a Assumed.
and R2(7) H79Br transitions, obtained at lower pressures and by an entirely different spectroscopic technique. The line widths tabulated by Rao and Lindquist [20] and based on earlier isotopically unresolved estimates appear to be incorrect. For jmj P 4, selfbroadening of the HBr lines can be approximated by a linear relation c(m) = 0.173(5) 10.7(2) 103jmj in 103 cm1 atm1 units, which is about five times more strongly jmj-dependent compared 0) HI self-broadened lines [18,21]. with c(m) for the (2 3.2. Line broadening in HX–Rg (X = F, Cl, Br, I)
3.1. Line broadening in neat HBr No differences were found between the line parameters for the H81Br and H79Br molecules at their natural abundances (49.5% and 50.5%, respectively). All the numerical data presented below were averaged over both isotopomers. We did not detect any reliably measurable self-induced line shifts in the (2 0) HBr band, as Fig. 1 illustrates for the P2(7) transition at three gas pressures, where, for clarity, the peak intensities of each isotopic component were normalized to unity. The measured self-broadening coefficients, c(m) (the line numbers are m = J + 1 in the R-branch and m = J in the P-branch), are collected in Table 1. Since the line widths tend to be practically identical at larger jmj numbers, the values for the two last R-branch lines were assumed to be the same as the corresponding ones in the P-branch. Our results are within 10% in agreement with the data of Chou et al. [19] for the P2(2)
We start by briefly describing the available information on the first overtone bands of hydrogen halides in HF–Rg and HCl–Rg mixtures. Older results on the line widths in HF–Ar reported by Wiggins et al. [3] mostly exceed by 15–30% more recent determinations [5] which, in turn, are in an excellent agreement with the high-resolution laser spectroscopy data for a couple of the P2 lines [4]. Comparison of the line shape parameters in the (0 0) pure rotational, (1 0) fundamental, and (2 0) overtone bands of HF in a bath of Ar reveals a significant enhancement of broadening, by more than a factor of two at higher jmj values, with the increase of the upper vibrational quantum state t [5]. Experimental data were adequately reproduced by theoretical calculations [5,7,9] based on a semi-empirical interaction potential derived from analysis of the spectra of HF–Ar van der Waals complexes [22]. Some asymmetry of the c(m) coefficients was noted at higher jmj, show-
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ing broader R1 than P1 lines in the (1 0) HF–Rg bands [3,5,9], however, this asymmetry becomes reversed in the (2 0) HF–Rg bands [3]. Among investigations of the HCl–Rg systems, best studied are the spectra of the HCl–Ar mixtures. The previously published data are in a satisfactory agreement with the latest results of Boulet et al. [16], showing an increase of c(m) with t, though the effect is smaller than in HF–Ar, about 25–30% on the average for the higher-jmj lines. In HCl–Kr, a twofold increase of high-jmj line widths was reported by Rank et al. [11] on going from the (1 0) to (2 0) transitions. Two sets of data for HCl–Xe [11,13] are in a rather poor mutual agreement in regard of absolute c(m) values, however, both indicate a strong enhancement in the overtone line broadening, by at least a factor of two. No noticeable P/R line broadening asymmetries were observed in HCl–Rg mixtures. In contrast, we found almost the same line broadening in the (2 0) and (1 0) bands of HBr diluted by He, Ar, and Kr, only marginally larger in the P2-branches. A stronger t-dependence exists in HBr–Xe. Comparison of the broadening parameters for two gas mixtures is presented in Fig. 2. Finally, practically no t-dependence was detected beyond the combined error margins for the HI–Rg mixtures. The appearance of shoulders on the c(m) plots near jmj 4 observed before in HBr–Xe and HI–Xe [1] was con-
firmed, being somewhat more distinct in the harmonic bands. The line broadening coefficients c = c(m) measured in HBr–Rg and HI–Rg systems are listed in Tables 2 and 3. 3.3. Line shifting in HX–Rg (X = Br, I) The best way of comparing collision-induced spectral line shifts, d = d(m), is to present them in two parts, namely, the part symmetric in the line number, dS(m) = (1/2)[d(m) + d(m)], and the part asymmetric in the line number, dA(m) = (1/2)[d(m) d(m)]. The symmetric part is determined by the isotropic component of the intermolecular interaction potential, while the asymmetric part depends on the anisotropy of interaction, provided the anisotropic component of the potential is t-independent and perturbs only the rotational eigenstates of molecules [23]. Usually dS(m) functions with increasing tend to approach some asymptotic values dlim S jmj, although the number of lines measured in the overtone bands was sometimes insufficient to reach the asymptote. For example, small blue shifts have been determined for only a pair of lines in HF–He; for P2(6), d(6) = +10.4(0.4) 103 cm1 atm1 [4]. The line shift coefficients d = d(m) measured in HBr–Rg and HI– Rg are collected in Tables 2 and 3, symmetric and asymmetric shifts are plotted in Figs. 3 and 4. In HBr–He, the shifts were too small for reliable determination. Comparison of the values of dlim S for the (2 0) and (1 0) bands in the same foreign gases shows that the asymptotic shifts in the overtone are indeed nearly twice those in the fundamentals. The profile of the weakly m-dependent dS(m) function for HI–Ne closely mimics one observed in the fundamental and varies in a narrow range of dS = ±5 103 cm1 atm1. Shoulders visible in the c(m) plot (Fig. 2b) are clearly reproduced in the dS(m) function for HI–Xe. Of course, the asymmetric shifts are much smaller in magnitude (except for the m = ±1 lines) and consequently have larger relative experimental uncertainties that mask whatever small differences in the dA(m) shifts are there due to different perturbers, or the vibrational excitation effects. Worth mentioning probably is only the HBr–Xe pair, for which the potential anisotropy appears to be the weakest among other systems with heavier foreign gases. Next we consider the available results for other hydrogen halides. Data of Refs. [3,5] for HF–Ar are in a satisfactory mutual agreement at ¼ 50ð2Þ 103 cm1 atm1 . The shifts mealarge jmj and yield dlim S ¼ 62ð3Þ 103 cm1 atm1 , smaller sured in HF–Kr suggest dlim S shifts in HF–Xe listed with uncertain experimental errors are unlikely [3]. Overtone line shifts for HCl in mixtures with He, Ar, Kr, and Xe have been tabulated by Rank et al. [11,12] at 300 and 900 °C. In He, all the lines experience blue shifts with a weak mdependence, of about d +10(3) 103 cm1 atm1 on the average. Combined results for HCl–Ar [11,12,16] are consistent with ¼ 30ð3Þ 103 cm1 atm1 . Only high-temperature numeridlim S cal data were published for HCl–Kr [12], but it was noted that the temperature effect on shifts is small. The asymptotic shift is ¼ 42ð2Þ 103 cm1 atm1 in this case. In the two room temdlim S perature studies of HCl–Xe [11,13], the asymptotic shifts have not been quite reached, however, more extensive data of Rank et al. ¼ 78 103 cm1 atm1 as a lower estimate. [11] suggest dlim S Earlier we demonstrated existence of a linear correlation befor the (1 0) bands of all hydrogen hatween the values of dlim S lides perturbed by rare gases and the mixed long-range potential energy constants C6(HX–Rg) [1]. A similar correlation holds for the (2 0) bands as well, as Fig. 5 shows.
4. Concluding remarks Fig. 2. Comparison of the line broadening coefficients c(m) in the (1 (2 0) bands of HBr in mixtures with argon (a) and xenon (b).
0) and
We reported here for the first time the experimental data on the line broadening and shifting coefficients for the lines in the
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A.V. Domanskaya et al. / Journal of Molecular Spectroscopy 253 (2009) 20–24 Table 2 Measured pressure shifting and broadening coefficients (in 103 cm1 atm1) for the (2 m
10 9 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9
0) HBr band lines in mixtures with rare gases
c(m)
d(m) Ar
Kr
Xe
He
Ar
Kr
Xe
13.6(2) 14.6(2) 16.1(2) 17.1(1) 18.0(2) 18.3(1) 17.8(2) 15.45(7) 12.8(1) 10.1(2) 2.3(2) 8.9(2) 11.8(1) 13.7(1) 15.3(2) 15.9(2) 15.8(4) 16.1(3) 14.8(9)
25.4(3) 26.9(6) 26.9(4) 27.0(2) 26.0(3) 24.9(3) 20.3(4) 15.9(4) 15.3(2) 9.7(8) 4.1(5) 10.9(1) 11.3(5) 16.0(4) 21.6(5) 25.3(7) 26.6(8) 26.3(7) 27(1)
43.8(4) 44.0(4) 41.2(4) 38.1(3) 33.7(4) 27.5(4) 19.4(3) 18.1(2) 13.0(2) 15.7(3) 7.0(2) 12.7(1) 16.2(1) 18.6(3) 25.9(3) 32.7(5) 38.1(5) 42.3(6) 42(1)
24(1) 25.2(6) 26.6(8) 27.5(7) 27.4(7) 28.3(8) 28.1(9) 28(1) 28(1) 32(1) 33.0(7) 29.3(9) 29.7(7) 27(1) 28.1(9) 27.0(9) 26.0(9) 25(1) 23(2)
18(1) 19.9(7) 22.5(6) 26.7(6) 31.0(5) 35.9(6) 40.1(5) 43.3(6) 46.2(7) 62.9(9) 62(1) 44.1(6) 42.4(5) 36.8(8) 33.9(7) 28.2(9) 25.6(9) 20.1(6) 19(2)
17(2) 22(2) 22(1) 26(1) 32(4) 39(4) 45(3) 48(1) 47(3) 53(3) 60(5) 45(3) 46(3) 38(1) 34(2) 29(4) 28(6) 14(6) 14(6)
34(2) 36(1) 38(1) 42(1) 47(1) 52(2) 53(1) 49(1) 55(1) 63(1) 57(1) 46(1) 47(1) 42(1) 44(1) 41(1) 42(2) 36(2) 33(5)
Standard deviations are shown in parentheses.
Table 3 Measured pressure shifting and broadening coefficients (in 103 cm1 atm1) for the (2 0) HI band lines in mixtures with rare gases m
11 10 9 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9 10 11 12 13
c(m)
d(m) Ne
Ar
Xe
Ne
Ar
Xe
4.36(9) 3.5(2) 2.1(2) 0.80(8) 0.7(2) 1.9(1) 3.3(1) 4.0(1) 4.0(1) 2.8(2) 4.3(2) 0.85(7) 2.4(1) 2.4(2) 1.7(2) 0.8(2) 0.4(1) 0.9(1) 2.1(1) 3.3(1) 4.7(2) 5.85(9) 6.7(1) 7.7(2)
8(1) 8.6(9) 9.6(5) 11.8(2) 13.5(3) 14.0(2) 14.6(4) 14.7(1) 11.81(7) 10.9(6) 9(1) 0.3(2) 7.9(3) 8.4(1) 10.0(2) 11.0(2) 11.63(3) 11.4(2) 10.44(3) 9.2(2) 8.0(1) 6.1(1) 4.8(5) 2.9(8)
31(1) 33.6(6) 33.5(5) 33.2(3) 32.2(3) 29.3(4) 23.6(5) 20.5(4) 20.3(3) 12.6(3) 18.7(5) 7.7(3) 8.3(4) 17.4(4) 17.1(4) 19.2(4) 25.4(4) 29.1(6) 30.8(5) 32.2(6) 32.9(6) 31.9(9) 31.4(8) 31.6(7)
15.9(9) 16.3(5) 18.8(3) 21.1(2) 23.5(6) 26(1) 27.3(5) 28.7(6) 30.2(8) 31.8(7) 33.5(5) 32.9(3) 30.9(4) 29.3(5) 27(1) 26(1) 21.3(9) 19.4(8) 18.4(7) 18.0(7) 17.1(7) 16.2(5) 15.3(6) 14.3(4)
18(1) 21(2) 22.2(8) 25(1) 28.5(5) 31.8(5) 35.8(3) 39.9(7) 41.1(9) 44(1) 61(2) 62(2) 46(2) 42(2) 36(1) 32(1) 30(2) 29(3) 25(2) 23(2) 21(2) 20(2) 17(2) 15(1)
24(1) 28.3(9) 30.0(5) 32(2) 36(2) 42(3) 48(2) 45(3) 49(2) 55(2) 62(2) 57.1(4) 48.9(5) 48.4(9) 47(2) 45(2) 42(1) 37.8(7) 33(1) 31(1) 27.0(9) 23(1) 22.1(8) 20.6(5)
Standard deviations are shown in parentheses.
first vibrational overtone bands of HBr and HI diluted in several rare gases. These data may serve for parameterization of the model intermolecular interaction potentials. Collision-induced line shifts in the vibration–rotation bands provide information on the differences between the interaction potentials of molecules in different combining vibrational states. Separation of the shifts measured in the fundamentals and overtones into symmetric and asymmetric parts allows probing the vibrational dependence of the isotropic and anisotropic components of the potential. We confirmed that the vibrational dependence of the asymmetric shifts is significantly weaker than that for the sym-
Fig. 3. Symmetric dS(m) (a) and asymmetric dA(m) (b) shift coefficients of HBr lines in rare gases.
metric ones. It follows that the observed line shifts are indeed dominated by the vibrational dependence of the isotropic component of the potential. Variations of the line broadening param-
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eters for hydrogen halides in the baths of the monoatomic buffer gases appear to be comparably sensitive to both vibrational and rotational relaxation processes. The previously reported P/R line broadening asymmetry in the fundamental band of HF mixed with monoatomic buffers and later suggested to be caused by the vibration–rotation coupling effect upon the interaction potentials [9] might be explained by a particularly slow vibrational relaxation in the HF-containing systems [25]. No such band line-broadening asymmetries were observed in our studies of the spectra of HBr–Rg and HI–Rg systems.
Acknowledgments The authors are grateful to Dr. H. Franz for preparing pure sample of hydrogen iodide. This work was supported by Deutsche Forschungsgemeinschaft (DFG).
References
Fig. 4. Symmetric dS(m) (a) and asymmetric dA(m) (b) shift coefficients of HI lines in rare gases.
Fig. 5. Correlation between asymptotic symmetric line shifts dlim in the overtone S bands of HI, HBr, HCl, and HF as functions of the mixed C6(HX–Rg) potential energy constants. The values of C6 in atomic units taken from Murdachaew et al. [24].
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Pressure broadening and shifting parameters for the spectral lines in the first overtone vibration–rotation bands of HBr and HI in mixtures with rare gases A.V. Domanskaya a,*, M.O. Bulanin a, K. Kerl b, C. Maul b a b
Department of Physics, St. Petersburg University, 2, Ulianovskaya Street, Peterhof, 198504 St. Petersburg, Russian Federation Institut für Physikalische und Theoretische Chemie der Technischen Unversität Braunschweig, D-38106 Braunschweig, Germany
a r t i c l e
i n f o
Article history: Received 29 July 2008 In revised form 24 September 2008 Available online 2 October 2008 Keywords: Infrared spectra Diatomic molecules Pressure broadening Pressure shift
a b s t r a c t We present experimental data on the previously unknown line broadening and shifting coefficients in the (2 0) overtone vibration–rotation bands of the HBr and HI molecules in mixtures with several rare gases. The vibrational dependence of the isotropic and anisotropic components of the binary interaction potential is probed by separating the measured line shifts into parts symmetric and asymmetric in the line number m and by comparing with the previously published similar data for the fundamental bands of the same molecules. It is shown that the line shifts are dominated by the vibrational dependence of the isotropic potential. A linear correlation is found between the asymptotic values of the symmetric shifts in the overtone bands for all HX–Rg (X = F, Cl, Br, I) pairs and the respective C6 long-range potential energy constants. Line broadening parameters in the overtone band of pure HBr are also reported. Ó 2008 Elsevier Inc. All rights reserved.
1. Introduction We recently reported comprehensive data on the pressure broadening and shifting coefficients for the spectral lines in the fundamental (1 0) vibration–rotation absorption bands of the HBr and HI molecules in mixtures with the rare gas (Rg) perturbers [1]. Similar data are reported here on the spectral line parameters in the (2 0) first vibrational overtone bands of the same molecules obtained using a high-resolution FTIR spectroscopic technique. Pressure broadening and shifting parameters of the spectral lines in the vibrational overtone bands are useful for testing performance of various model intermolecular interaction potential energy surfaces and of their dependence on the vibrational states of interacting species, including semi-empirical model potentials deduced from numerous studies of the rotationally resolved spectra of different van der Waals complexes. Comparison of our experimental results with the available information for other hydrogen halides allows reveal how the vibration–rotation spectra of different HX (X = F, Cl, Br, I) molecules respond to interactions with the identical environments. To the best of our knowledge, there were no previous measurements of the spectral line parameters in the overtone bands of HBr and HI perturbed by collisions with the Rg-atoms. In contrast, many studies had been reported earlier (some presented in a graphical format only [2]) on the spectral effects due to interactions with the Rg-perturbers observed in the overtone bands of * Corresponding author. Fax: + 7 812 428 72 40. E-mail address: [email protected] (A.V. Domanskaya). 0022-2852/$ - see front matter Ó 2008 Elsevier Inc. All rights reserved. doi:10.1016/j.jms.2008.09.010
the HF and HCl molecules. Wiggins et al. [3] tabulated line widths and shifts in mixtures of HF with Ar, Kr, and Xe measured with a grating spectrometer. Chou et al. [4] reported data for the P2(3) and P2(6) HF lines in He and Ar perturbers using a diode laser spectroscopy, Grigoriev et al. [5] determined line parameters for HF in a bath of Ar by a high-resolution FTIR technique. The collision-induced effects in the spectra of HF–Ar gas mixtures were also studied in other works [6–9]. Collisional line parameters in several HCl–Rg systems measured with a grating spectrometer were tabulated by Rank et al. [10–12]. The line widths and shifts for HCl in Ar and Xe perturbers were later determined using a SISAM interferometric spectrometer [13–15], showing a reasonably good overall agreement with the former results of Rank et al. More recent data on the parameters of many lines for HCl in a bath of Ar obtained by the FTIR technique were reported by Boulet et al. [16]. Some general conclusions based on these earlier observations are noteworthy. In the range of pressures (or densities) studied so far, the line shifts and widths were found to be linear in buffer gas pressures, indicating the binary nature of interactions. The line shifts tend to approach more or less stable asymptotic values with the increasing rotational quantum numbers J of the initial quantum states and usually appear to be nearly twice as great in the (2 0) bands compared to those observed in the (1 0) bands. The behavior of the overtone line widths in the HX–Rg systems (for X = F, Cl) is less straightforward, though the higher-J lines also tend to be broader than in the fundamental HX bands. The line shapes, when corrected for the finite instrument resolution and – whenever necessary – for the Doppler broadening, commonly appear adequately described by the Lorentzian profiles at higher
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buffer gas pressures. Weak line asymmetries were observed in the HF–Ar mixtures [5–8], more pronounced in the overtone than in the fundamental spectral bands [8]. On the other hand, no noticeable line asymmetries were detected in the spectra of the HCl–Ar system [16]. We report here the vibration–rotation overtone line shifts and broadenings of HBr and HI diluted with rare gases. It also deemed necessary to measure the self-perturbed line parameters in pure gaseous HBr.
2. Experimental The experimental procedure being practically the same as was used in our previous studies needs not be detailed here again. Briefly, the spectra in the range of the hydrogen halide overtone bands were recorded with a Bruker 120HR FTIR instrument, equipped with a CaF2/Si beam splitter, a cooled InSb detector, appropriate band-pass filters, and operated at the 0.005– 0.06 cm1 spectral resolutions, depending on the perturbing gas pressures (0.1–0.5 bar for pure HBr gas, up to about 5 bar for the HBr–Rg, and 4 bar for the HI–Rg gas mixtures). Altogether over 50 different combinations of the absorbing/buffer gas samples were measured. Two stainless steel high-pressure gas cells were used of 19.8 and 107 cm-long optical paths, protected inside by a fluorinated polymer coating in order to prevent corrosion and decomposition of hydrogen halides. Sub-atmospheric pressures of HBr and HI were measured with MKS Baratron capacitance gauges, higher pressures of the perturbing gases were measured with Bourdon mechanical manometers. Further details can be found in [1,17]. Our measurements were carried out at (28 ± 1) °C. 3. Results and discussion The experimental conditions chosen did not require introducing any statistically significant corrections to the measured line parameters. To account for the self-induced contributions due to the hydrogen halide species present in gas mixtures, we used the previously reported results on the line parameters in pure HI [18] and the data obtained here for the neat HBr presented below. Some weak suggestions of an asymmetry in the line wings were noted in the spectra of HBr–Xe system, but these were too small for an accurate determination. In the range of the sample pressures used in this work, the spectral line shapes appeared to be adequately described by the Lorentzian profiles. Both the Doppler broadening and hyperfine line structures did not affect the values of the shifting and broadening coefficients for the overtone lines of HBr and HI determined from the slopes of the respective line parameters by linear plots versus foreign gas pressures.
Fig. 1. Spectral line profiles of the isotopic doublet P2(7) in neat H81,79Br at three gas pressures.
Table 1 Measured self-broadening coefficients c (in 103 cm1 atm1) for the (2 lines of HBr averaged over the H79Br and H81Br isotopomers
0) band
m
c(m)
m
c(m)
10 9 8 7 6 5 4 3 2 1
65(3) 79(1) 85(1) 98(1) 110(1) 123(1) 131(1) 131(2) 131(2) 137(2)
1 2 3 4 5 6 7 8 9
126(1) 128(2) 129(2) 123(2) 120(2) 112(1) 101(2) 85a 79a
Standard deviations are shown in parentheses. a Assumed.
and R2(7) H79Br transitions, obtained at lower pressures and by an entirely different spectroscopic technique. The line widths tabulated by Rao and Lindquist [20] and based on earlier isotopically unresolved estimates appear to be incorrect. For jmj P 4, selfbroadening of the HBr lines can be approximated by a linear relation c(m) = 0.173(5) 10.7(2) 103jmj in 103 cm1 atm1 units, which is about five times more strongly jmj-dependent compared 0) HI self-broadened lines [18,21]. with c(m) for the (2 3.2. Line broadening in HX–Rg (X = F, Cl, Br, I)
3.1. Line broadening in neat HBr No differences were found between the line parameters for the H81Br and H79Br molecules at their natural abundances (49.5% and 50.5%, respectively). All the numerical data presented below were averaged over both isotopomers. We did not detect any reliably measurable self-induced line shifts in the (2 0) HBr band, as Fig. 1 illustrates for the P2(7) transition at three gas pressures, where, for clarity, the peak intensities of each isotopic component were normalized to unity. The measured self-broadening coefficients, c(m) (the line numbers are m = J + 1 in the R-branch and m = J in the P-branch), are collected in Table 1. Since the line widths tend to be practically identical at larger jmj numbers, the values for the two last R-branch lines were assumed to be the same as the corresponding ones in the P-branch. Our results are within 10% in agreement with the data of Chou et al. [19] for the P2(2)
We start by briefly describing the available information on the first overtone bands of hydrogen halides in HF–Rg and HCl–Rg mixtures. Older results on the line widths in HF–Ar reported by Wiggins et al. [3] mostly exceed by 15–30% more recent determinations [5] which, in turn, are in an excellent agreement with the high-resolution laser spectroscopy data for a couple of the P2 lines [4]. Comparison of the line shape parameters in the (0 0) pure rotational, (1 0) fundamental, and (2 0) overtone bands of HF in a bath of Ar reveals a significant enhancement of broadening, by more than a factor of two at higher jmj values, with the increase of the upper vibrational quantum state t [5]. Experimental data were adequately reproduced by theoretical calculations [5,7,9] based on a semi-empirical interaction potential derived from analysis of the spectra of HF–Ar van der Waals complexes [22]. Some asymmetry of the c(m) coefficients was noted at higher jmj, show-
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ing broader R1 than P1 lines in the (1 0) HF–Rg bands [3,5,9], however, this asymmetry becomes reversed in the (2 0) HF–Rg bands [3]. Among investigations of the HCl–Rg systems, best studied are the spectra of the HCl–Ar mixtures. The previously published data are in a satisfactory agreement with the latest results of Boulet et al. [16], showing an increase of c(m) with t, though the effect is smaller than in HF–Ar, about 25–30% on the average for the higher-jmj lines. In HCl–Kr, a twofold increase of high-jmj line widths was reported by Rank et al. [11] on going from the (1 0) to (2 0) transitions. Two sets of data for HCl–Xe [11,13] are in a rather poor mutual agreement in regard of absolute c(m) values, however, both indicate a strong enhancement in the overtone line broadening, by at least a factor of two. No noticeable P/R line broadening asymmetries were observed in HCl–Rg mixtures. In contrast, we found almost the same line broadening in the (2 0) and (1 0) bands of HBr diluted by He, Ar, and Kr, only marginally larger in the P2-branches. A stronger t-dependence exists in HBr–Xe. Comparison of the broadening parameters for two gas mixtures is presented in Fig. 2. Finally, practically no t-dependence was detected beyond the combined error margins for the HI–Rg mixtures. The appearance of shoulders on the c(m) plots near jmj 4 observed before in HBr–Xe and HI–Xe [1] was con-
firmed, being somewhat more distinct in the harmonic bands. The line broadening coefficients c = c(m) measured in HBr–Rg and HI–Rg systems are listed in Tables 2 and 3. 3.3. Line shifting in HX–Rg (X = Br, I) The best way of comparing collision-induced spectral line shifts, d = d(m), is to present them in two parts, namely, the part symmetric in the line number, dS(m) = (1/2)[d(m) + d(m)], and the part asymmetric in the line number, dA(m) = (1/2)[d(m) d(m)]. The symmetric part is determined by the isotropic component of the intermolecular interaction potential, while the asymmetric part depends on the anisotropy of interaction, provided the anisotropic component of the potential is t-independent and perturbs only the rotational eigenstates of molecules [23]. Usually dS(m) functions with increasing tend to approach some asymptotic values dlim S jmj, although the number of lines measured in the overtone bands was sometimes insufficient to reach the asymptote. For example, small blue shifts have been determined for only a pair of lines in HF–He; for P2(6), d(6) = +10.4(0.4) 103 cm1 atm1 [4]. The line shift coefficients d = d(m) measured in HBr–Rg and HI– Rg are collected in Tables 2 and 3, symmetric and asymmetric shifts are plotted in Figs. 3 and 4. In HBr–He, the shifts were too small for reliable determination. Comparison of the values of dlim S for the (2 0) and (1 0) bands in the same foreign gases shows that the asymptotic shifts in the overtone are indeed nearly twice those in the fundamentals. The profile of the weakly m-dependent dS(m) function for HI–Ne closely mimics one observed in the fundamental and varies in a narrow range of dS = ±5 103 cm1 atm1. Shoulders visible in the c(m) plot (Fig. 2b) are clearly reproduced in the dS(m) function for HI–Xe. Of course, the asymmetric shifts are much smaller in magnitude (except for the m = ±1 lines) and consequently have larger relative experimental uncertainties that mask whatever small differences in the dA(m) shifts are there due to different perturbers, or the vibrational excitation effects. Worth mentioning probably is only the HBr–Xe pair, for which the potential anisotropy appears to be the weakest among other systems with heavier foreign gases. Next we consider the available results for other hydrogen halides. Data of Refs. [3,5] for HF–Ar are in a satisfactory mutual agreement at ¼ 50ð2Þ 103 cm1 atm1 . The shifts mealarge jmj and yield dlim S ¼ 62ð3Þ 103 cm1 atm1 , smaller sured in HF–Kr suggest dlim S shifts in HF–Xe listed with uncertain experimental errors are unlikely [3]. Overtone line shifts for HCl in mixtures with He, Ar, Kr, and Xe have been tabulated by Rank et al. [11,12] at 300 and 900 °C. In He, all the lines experience blue shifts with a weak mdependence, of about d +10(3) 103 cm1 atm1 on the average. Combined results for HCl–Ar [11,12,16] are consistent with ¼ 30ð3Þ 103 cm1 atm1 . Only high-temperature numeridlim S cal data were published for HCl–Kr [12], but it was noted that the temperature effect on shifts is small. The asymptotic shift is ¼ 42ð2Þ 103 cm1 atm1 in this case. In the two room temdlim S perature studies of HCl–Xe [11,13], the asymptotic shifts have not been quite reached, however, more extensive data of Rank et al. ¼ 78 103 cm1 atm1 as a lower estimate. [11] suggest dlim S Earlier we demonstrated existence of a linear correlation befor the (1 0) bands of all hydrogen hatween the values of dlim S lides perturbed by rare gases and the mixed long-range potential energy constants C6(HX–Rg) [1]. A similar correlation holds for the (2 0) bands as well, as Fig. 5 shows.
4. Concluding remarks Fig. 2. Comparison of the line broadening coefficients c(m) in the (1 (2 0) bands of HBr in mixtures with argon (a) and xenon (b).
0) and
We reported here for the first time the experimental data on the line broadening and shifting coefficients for the lines in the
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A.V. Domanskaya et al. / Journal of Molecular Spectroscopy 253 (2009) 20–24 Table 2 Measured pressure shifting and broadening coefficients (in 103 cm1 atm1) for the (2 m
10 9 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9
0) HBr band lines in mixtures with rare gases
c(m)
d(m) Ar
Kr
Xe
He
Ar
Kr
Xe
13.6(2) 14.6(2) 16.1(2) 17.1(1) 18.0(2) 18.3(1) 17.8(2) 15.45(7) 12.8(1) 10.1(2) 2.3(2) 8.9(2) 11.8(1) 13.7(1) 15.3(2) 15.9(2) 15.8(4) 16.1(3) 14.8(9)
25.4(3) 26.9(6) 26.9(4) 27.0(2) 26.0(3) 24.9(3) 20.3(4) 15.9(4) 15.3(2) 9.7(8) 4.1(5) 10.9(1) 11.3(5) 16.0(4) 21.6(5) 25.3(7) 26.6(8) 26.3(7) 27(1)
43.8(4) 44.0(4) 41.2(4) 38.1(3) 33.7(4) 27.5(4) 19.4(3) 18.1(2) 13.0(2) 15.7(3) 7.0(2) 12.7(1) 16.2(1) 18.6(3) 25.9(3) 32.7(5) 38.1(5) 42.3(6) 42(1)
24(1) 25.2(6) 26.6(8) 27.5(7) 27.4(7) 28.3(8) 28.1(9) 28(1) 28(1) 32(1) 33.0(7) 29.3(9) 29.7(7) 27(1) 28.1(9) 27.0(9) 26.0(9) 25(1) 23(2)
18(1) 19.9(7) 22.5(6) 26.7(6) 31.0(5) 35.9(6) 40.1(5) 43.3(6) 46.2(7) 62.9(9) 62(1) 44.1(6) 42.4(5) 36.8(8) 33.9(7) 28.2(9) 25.6(9) 20.1(6) 19(2)
17(2) 22(2) 22(1) 26(1) 32(4) 39(4) 45(3) 48(1) 47(3) 53(3) 60(5) 45(3) 46(3) 38(1) 34(2) 29(4) 28(6) 14(6) 14(6)
34(2) 36(1) 38(1) 42(1) 47(1) 52(2) 53(1) 49(1) 55(1) 63(1) 57(1) 46(1) 47(1) 42(1) 44(1) 41(1) 42(2) 36(2) 33(5)
Standard deviations are shown in parentheses.
Table 3 Measured pressure shifting and broadening coefficients (in 103 cm1 atm1) for the (2 0) HI band lines in mixtures with rare gases m
11 10 9 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9 10 11 12 13
c(m)
d(m) Ne
Ar
Xe
Ne
Ar
Xe
4.36(9) 3.5(2) 2.1(2) 0.80(8) 0.7(2) 1.9(1) 3.3(1) 4.0(1) 4.0(1) 2.8(2) 4.3(2) 0.85(7) 2.4(1) 2.4(2) 1.7(2) 0.8(2) 0.4(1) 0.9(1) 2.1(1) 3.3(1) 4.7(2) 5.85(9) 6.7(1) 7.7(2)
8(1) 8.6(9) 9.6(5) 11.8(2) 13.5(3) 14.0(2) 14.6(4) 14.7(1) 11.81(7) 10.9(6) 9(1) 0.3(2) 7.9(3) 8.4(1) 10.0(2) 11.0(2) 11.63(3) 11.4(2) 10.44(3) 9.2(2) 8.0(1) 6.1(1) 4.8(5) 2.9(8)
31(1) 33.6(6) 33.5(5) 33.2(3) 32.2(3) 29.3(4) 23.6(5) 20.5(4) 20.3(3) 12.6(3) 18.7(5) 7.7(3) 8.3(4) 17.4(4) 17.1(4) 19.2(4) 25.4(4) 29.1(6) 30.8(5) 32.2(6) 32.9(6) 31.9(9) 31.4(8) 31.6(7)
15.9(9) 16.3(5) 18.8(3) 21.1(2) 23.5(6) 26(1) 27.3(5) 28.7(6) 30.2(8) 31.8(7) 33.5(5) 32.9(3) 30.9(4) 29.3(5) 27(1) 26(1) 21.3(9) 19.4(8) 18.4(7) 18.0(7) 17.1(7) 16.2(5) 15.3(6) 14.3(4)
18(1) 21(2) 22.2(8) 25(1) 28.5(5) 31.8(5) 35.8(3) 39.9(7) 41.1(9) 44(1) 61(2) 62(2) 46(2) 42(2) 36(1) 32(1) 30(2) 29(3) 25(2) 23(2) 21(2) 20(2) 17(2) 15(1)
24(1) 28.3(9) 30.0(5) 32(2) 36(2) 42(3) 48(2) 45(3) 49(2) 55(2) 62(2) 57.1(4) 48.9(5) 48.4(9) 47(2) 45(2) 42(1) 37.8(7) 33(1) 31(1) 27.0(9) 23(1) 22.1(8) 20.6(5)
Standard deviations are shown in parentheses.
first vibrational overtone bands of HBr and HI diluted in several rare gases. These data may serve for parameterization of the model intermolecular interaction potentials. Collision-induced line shifts in the vibration–rotation bands provide information on the differences between the interaction potentials of molecules in different combining vibrational states. Separation of the shifts measured in the fundamentals and overtones into symmetric and asymmetric parts allows probing the vibrational dependence of the isotropic and anisotropic components of the potential. We confirmed that the vibrational dependence of the asymmetric shifts is significantly weaker than that for the sym-
Fig. 3. Symmetric dS(m) (a) and asymmetric dA(m) (b) shift coefficients of HBr lines in rare gases.
metric ones. It follows that the observed line shifts are indeed dominated by the vibrational dependence of the isotropic component of the potential. Variations of the line broadening param-
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eters for hydrogen halides in the baths of the monoatomic buffer gases appear to be comparably sensitive to both vibrational and rotational relaxation processes. The previously reported P/R line broadening asymmetry in the fundamental band of HF mixed with monoatomic buffers and later suggested to be caused by the vibration–rotation coupling effect upon the interaction potentials [9] might be explained by a particularly slow vibrational relaxation in the HF-containing systems [25]. No such band line-broadening asymmetries were observed in our studies of the spectra of HBr–Rg and HI–Rg systems.
Acknowledgments The authors are grateful to Dr. H. Franz for preparing pure sample of hydrogen iodide. This work was supported by Deutsche Forschungsgemeinschaft (DFG).
References
Fig. 4. Symmetric dS(m) (a) and asymmetric dA(m) (b) shift coefficients of HI lines in rare gases.
Fig. 5. Correlation between asymptotic symmetric line shifts dlim in the overtone S bands of HI, HBr, HCl, and HF as functions of the mixed C6(HX–Rg) potential energy constants. The values of C6 in atomic units taken from Murdachaew et al. [24].
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