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Nitrogen-induced broadening and shifts of rotation-vibrational lines in the fundamental, first, second and third overtone bands of HI
Journal of Molecular Spectroscopy 265 (2011) 69–73
Contents lists available at ScienceDirect
Journal of Molecular Spectroscopy journal homepage: www.elsevier.com/locate/jms
Nitrogen-induced broadening and shifts of rotation-vibrational lines in the fundamental, first, second and third overtone bands of HI A.V. Domanskaya a,⇑, R.E. Asfin b, C. Maul c, K. Kerl c, M.O. Bulanin b a
Institut für Physikalische Chemie, Universität Göttingen, D-37077 Göttingen, Germany Department of Physics, St. Petersburg University, Peterhof, 198504 St. Petersburg, Russia c Institut für Physikalische und Theoretische Chemie der Technischen Unversität Braunschweig, D-38106 Braunschweig, Germany b
a r t i c l e
i n f o
Article history: Received 13 August 2010 In revised form 13 November 2010 Available online 20 November 2010 Keywords: Diatomic molecules Hydrogen halides Nitrogen Pressure broadening Pressure shift
a b s t r a c t We report experimental results on the previously unknown broadening and shifting coefficients in the fundamental and three overtone vibration–rotation bands of the HI molecule in mixtures with nitrogen gas. Our data are compared with the previously published results for the fundamental bands of the HF and HCl molecules. It is shown that the line shifts are dominated by the vibrational dependence of the isotropic part of the intermolecular interaction potential. Ó 2010 Elsevier Inc. All rights reserved.
1. Introduction Hydrogen iodide is a special member of the hydrogen halides family because of its unusual electro-optical properties [1]. Apart from the fundamental interest, a possible industrial use of HI is envisaged as a part of the iodine sulphur cycle thermochemical cycle for hydrogen production [2]. An estimate predicts the energy efficiency for the chemical reactions in the iodine sulphur cycle to reach about 50% [3]. HI is also considered as one of the temporary iodine reservoir species that may be formed in reactions of iodine cycling in the marine boundary layer [4]. An accurate sensing of HI and other hydrogen halides requires not only the spectral line positions and absolute intensities, but also line shape parameters such as broadening and shift coefficients. In the recent years, comprehensive data were reported on the pressure broadening and shifting coefficients for spectral lines in the fundamental and overtone vibration–rotation absorption bands of HI and HBr molecules in pure gases [5–7] and in mixtures with rare gas perturbers [8,9]. However, the data on the nitrogeninduced shifts and broadenings for the hydrogen halides remain incomplete. The HCl molecule is the best studied one. The broadening and shifting of lines in the fundamental band of HCl were measured using high-resolution laser techniques [10,11]. The temperature dependence of the broadening coefficients was determined in a wide range of temperatures [10,12], and Dicke narrowing parameters were also obtained [12]. The spectra of the ⇑ Corresponding author. Fax: +49 551 39 3117. E-mail address: [email protected] (A.V. Domanskaya). 0022-2852/$ - see front matter Ó 2010 Elsevier Inc. All rights reserved. doi:10.1016/j.jms.2010.11.005
fundamental band of HF in mixture with N2 were also extensively studied [10]. The broadening and shift coefficients for the P2(3) and P2(6) lines in the first overtone of HF [13] seem to be the only line shape parameters determined for higher vibrational transitions among the hydrogen halides. To the best of our knowledge, broadenings and shifts of the vibration-rotational lines for HI and HBr induced by collisions with nitrogen have not been evaluated even in the fundamental regions. We report here the vibration–rotation line shifts and broadenings of HI diluted with nitrogen for four vibrational bands. Our results for the fundamental transition are compared with the data available from the literature on other hydrogen halides – nitrogen systems. 2. Experimental details Samples of HI were prepared by dehydration of the hydroiodic acid (Fluka, p.a.) with phosphoric anhydride and purified by a trap-to-trap distillation. Compressed nitrogen (Linde Gas 5.0) was used as supplied. Typically, 200–300 mbar of HI were admitted to a cell and then consequently diluted by nitrogen. The total pressure of gas mixtures did not exceed 4 bar. Pressures of HI were measured with a MKS Baratron capacitance manometer; higher pressures of the perturber gas were measured with a Bourdon gauge. Our measurements were carried out at 298 ± 1 K. The spectra were recorded with a Bruker 120HR FTIR instrument equipped with a CaF2/Si beam splitter and a liquid nitrogen cooled InSb detector, with resolution of 0.012–0.020 cm1 for the
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fundamental (the corresponding instrumental widths were 0.011 and 0.018 cm1 if one uses the Rayleigh criterion of resolution), 0.03 cm1 for the first and second overtones (instrumental width was 0.027 cm1), and 0.02 cm1 for the third overtone region. A globar source was used for measurements in the fundamental transition; overtones were recorded with a tungsten lamp as a source. Conventional optical filters were used for the fundamental and third overtone regions. Two stainless steel sample cells of 9.6 and 107 cm optical path lengths were used in our experiments. Protection of the cell interiors by a fluorinated polymer coating [14] prevented gradual decomposition of hydrogen iodide. The intensity distribution in the fundamental band is strongly perturbed due to the vibration– rotation coupling effect on the dipole moment function of HI [1], which results in ca. 5 times stronger absorption in the R-branch compared to that in the P-branch. The R-branch of the fundamental band was measured using the shorter cell, the spectra of overtones and weak lines of the P-branch of the fundamental band were measured using a specially designed long path cell [7]. Spectral line shapes were fitted with Lorentzians. The Doppler half-widths increase with frequency and reach a value of ca. 4.6 103 cm1 in the spectral range of the third overtone. The observed line widths for narrow lines (high J) for the third overtone are at least 10 times broader than the Doppler widths, even at the lowest pressure used in the experiments (1.13 bar). The resulting width of the corresponding Voigt profile would differ by less than 0.5% from the pure Lorentzian line width for our experimental conditions. The accuracy of the experimental widths in the region of the third overtone are not better than 1% which validates the use of Lorentzians instead of Voigts as fitting profiles. The quality of the fitting is demonstrated in Fig. 1. The maximum relative deviation of the fitted profile from the experimental shape in the region of the band head of the second overtone shown in Fig. 1 does not exceed 1.5%. The spectral data obtained for the third overtone are less accurate compared to those obtained in other spectral regions and we consider them only semi-quantitatively valid. Line widths and frequencies change in a linear manner with the nitrogen gas pressures. No statistically meaningful line asymmetries or Dicke collisional narrowing were detected at the conditions of our experiments. The least squares values of the pressure broadening (d) and shift (c) coefficients for each spectral line were determined from the slopes of such linear dependencies (see Fig. 2). 3. Results and discussion 3.1. Broadening coefficients The measured broadening coefficients cm ðmÞ for the lines in the four vibrational bands of HI are collected in Table 1 and plotted in Fig. 3 as a function of the line number m (m = J + 1 in the R-branch
Fig. 1. An example of the Lorentzian fits to the band head in the second overtone band of HI. The partial pressure of HI is 250 mbar, pressure of nitrogen is 1.27 bar.
Fig. 2. Dependence of the full line widths at half height (FWHH) on nitrogen pressure. Three rotational lines in the first overtone of HI show significantly different broadening.
Table 1 Measured nitrogen-broadening coefficients cv ðmÞ of hydrogen iodide lines of four vibrational bands (in 103 cm1 atm1). m
Vibrational transition (1
12 11 10 9 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
0)
– – – 37(2) 39(1) 47.2(3) 53.7(5) 62.0(6) 65.5(8) 71.1(8) 75.0(6) 85(1) 84(1) 75.5(7) 66.2(7) 61.4(9) 53.9(7) 50.0(7) 47.0(7) 43.2(8) 37(1) 34(2) 30(1) 26.7(2) 24.1(7) 23(2) 19(1)
(2
0)
29(1) 34(1) 36(2) 36.3(6) 40.7(8) 46.4(8) 50.0(8) 57(1) 63(1) 68(1) 75(2) 82(2) 89.0(5) 81.8(7) 75(1) 69.8(9) 63.3(8) 56.3(6) 49.8(6) 44.6(6) 39.8(7) 36.4(2) 34.3(4) 30.9(4) 27.6(4) 26.9(9) 27(1)
(3
0)
41(3) 42(2) 39(1) 41.0(9) 44.1(7) 48(1) 56.0(4) 65.7(5) 72.6(8) 80.8(9) 89(2) 97(2) 91(2) 79(1) 71.1(9) 65(1) 59(1) 53.1(9) 46.9(7) 43.2(5) 40.3(6) 37(1) 33(3) 30(3) 29(3) 35(8) –
(4
0)
– – 33(3) 46(3) 53(3) 58.2(4) 61(3) 70(2) 78(2) 72(2) 83(2) 100(4) 84.2(4) 77(2) 78(4) 69(1) 62(2) 61(1) 57.1(4) 53(4) 34(2) 61(5) 63.1(8) 16(1) – – –
Standard deviations are shown in parentheses.
and m = J in the P-branch). The line widths in nitrogen are weakly dependent on the upper vibrational state quantum number (v = 1, 2, 3, 4), although their m-dependencies are significant. The broadening coefficients are close within the accuracy limits for the fundamental, first and second overtone bands. Results for the third overtone are less accurate due to experimental uncertainties and lie somewhat above the general trend. A similar weak v-dependence was earlier observed for the line widths for HI perturbed by Ne and Ar [7]. A strong m-dependence is characteristic for the broadening coefficients of hydrogen halides (see Fig. 4a). The HF–N2 broadenings for m = ±10 are an order of magnitude smaller than those for m = ±1. The broadening coefficients decrease faster with increasing jmj for absorbing molecules with larger values of the dipole moments (Fig. 4a). Comparison of the nitrogen broadening with the self- and Ar-broadenings shows that collisions with N2 produce an
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Table 2 Measured nitrogen shift coefficients dv ðmÞ of hydrogen iodide lines of four vibrational bands (in 103 cm1 atm1). m
Vibrational transition
12 11 10 9 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
– – – 3.7(5) 4.2(3) 4.3(1) 3.8(1) 4.5(2) 4.71(7) 3.3(2) 2.5(1) 1.0(4) 0.1(1) 2.3(1) 2.6(1) 2.8(2) 3.3(1) 4.5(1) 5.6(1) 5.20(9) 4.5(2) 4.1(1) 2.99(9) 1.90(8) 1.3(1) 1.41(7) –
(1
Fig. 3. Nitrogen-broadening coefficients for the HI molecule.
intermediate effect on the line widths (Fig. 4b). Self-broadening coefficients have the largest values and a weaker m-dependence, showing stronger perturbations of all rotational states due to collisions between dipolar molecules. N2-broadening coefficients are ca. 1.5 times greater probably due to an additional interaction caused by quadrupole moment of the nitrogen molecule [15] (Ar and N2 have similar polarizability – 1.642 and 1.741 Å3 respectively [15,16]). 3.2. Shift coefficients The nitrogen-induced shift coefficients of HI are listed in Table 2. Shift coefficients dv ðmÞ are easier to interpret if they are separated into two parts: symmetric in the line number, defined as dvS ðmÞ ¼ ðdv ðmÞ þ dv ðmÞÞ=2, and asymmetric, defined as dvA ðmÞ ¼ ðdv ðmÞ dv ðmÞÞ=2. The symmetric shifts were shown to depend on the isotropic components of the interaction potential, whereas the asymmetric shifts depend on the anisotropic components [17,18]. The difference between symmetric and asymmetric shift coefficients for different vibrational transitions reflects predominantly the v-dependence of the corresponding parts of the interaction potential. Symmetric and asymmetric shifts are plotted in Fig. 5. The dvA ðmÞ are practically identical and almost negligible for most of the lines in all vibrational bands (Fig. 5a). Values of d4A ðmÞ are omitted in the plot due to their greater inaccuracy. Only the lines with
0)
(2
0)
8(2) 9(1) 8(1) 8.7(7) 9.7(6) 10.2(6) 10.1(6) 10.5(7) 10.7(7) 8.5(7) 6.6(7) 10(1) 2.2(6) 6.8(8) 7.7(9) 8.0(7) 8.8(6) 10.6(6) 10.4(7) 10.0(7) 9.4(6) 8.2(6) 7.2(6) 5.8(9) 4.0(7) 6(1) 2(1)
(3
0)
14(2) 12(1) 12(1) 12.2(9) 13.6(6) 14.5(8) 14.8(7) 14.8(8) 13.5(7) 10.6(5) 10.0(5) 10(1) 6(1) 9(1) 10(1) 11.3(7) 12.4(6) 14(1) 14.5(7) 13.8(8) 13.1(8) 12(1) 13(3) 10(4) 9(2) 3(2) –
(4
0)
– 22(4) 22(3) 18(3) 22(1) 17.9(5) 19(2) 22.3(7) 19(2) 15.4(8) 12(4) 14(4) 11.0(7) 16(5) 18(2) 16.0(9) 18.7(6) 18(2) 20(1) 15(2) 19(4) 17.4(2) 21.7(5) – – – –
Standard deviations are shown in parentheses.
m = ±1 show v-dependent values of dvA ðmÞ. The irregular behavior of the first m = ±1 lines due to transitions that involve zero angular momentum molecular states is common for HI/HBr – rare gas mixtures. For the most systems studied [5,7–9] the Rv(0) line shows a weak blue shift dominated by its asymmetric part and hence it is very sensitive to the behavior of the anisotropic potential. All measured symmetric line shifts are red, and become larger with increasing vibrational quantum number v and, to a certain extent, with the rotational angular momentum J (Fig. 5b). This illustrates the fact that the attractive (causing red shifts) isotropic components for the HI–N2 potential dominate the repulsive parts
Fig. 4. Comparison of HI broadening by nitrogen with other systems; (a) nitrogen-broadening coefficients for the fundamental transition of different hydrogen halides. Solid circles show the data for HI (this work). Data for HCl (open triangles) and HF (open diamonds) are taken from Ref. [10]. (b) m-Dependence of nitrogen- (solid circles, this work), argon- (open triangles, Ref. [8]) and self-broadening (open squares, Ref. [5]) in the fundamental band of HI.
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Fig. 5. Symmetric dmS ðmÞ and asymmetric dmA ðmÞ shifts of HI lines in nitrogen.
(causing blue shifts) with increasing of the vibrational and rotational kinetic energy of the diatomic. The symmetric line shifts do not reach any evident constant asymptotic value in the HI bands studied here. For each band, they reach a minimum at m = ±6, ±7 and then tend to increase with increasing |m|, except for d4S ðmÞ which behavior is rather unclear for jmj > 8 due to higher inaccuracy. Larger shifts of the higher overtones could be further commented. Perturbation theory [19] that did not take into account the rotational degrees of freedom of molecules, predicted the interaction-induced red shifts of the vibrational transition frequencies to be proportional to the quantum number of the upper vibrational state. We have evaluated the vibrational transition shifts by fitting the vibration-rotational frequencies for every band by a polynomial function at different pressures of nitrogen (see Fig. 6). One can see that the vibrational frequencies decrease linearly with the perturber pressure and the absolute values are larger for the overtones, in agreement with predictions of Ref. [19]. We found that the vibrational shifts are indeed proportional to the v-quantum number with the coefficient of 1.83(6), i.e. dv ib ðv ¼ 2Þ= dv ib ðv ¼ 1Þ ¼ 1:83ð6Þ. Nitrogen-induced shifts of HI spectral lines are the smallest compared to other hydrogen halides (see Fig. 7). One can see that
Fig. 7. Symmetric d1S ðmÞ and asymmetric d1A ðmÞ shifts of the fundamental band of hydrogen halides in mixtures with nitrogen. Data for HCl and HF are taken from Ref. [10].
the HF–N2 interaction potential is significantly more anisotropic compared to the HI–N2 pair, which leads to an order of magnitude larger values for the asymmetric shifts (Fig. 7a). The orientationally averaged dipole-induction interactions play a dominant role for the hydrogen halide – rare gas systems, making the symmetric shifts proportional to the squares of the vibrational ground state dipole moments [8]. One could expect that it remains the same for a molecular non-polar perturber. Indeed, the absolute values of the symmetric shift coefficients induced by nitrogen are greater for the molecules with higher dipole moment with an exception for the lines at the center of the band (Fig. 7b). 4. Concluding remarks We have reported here for the first time experimental data on the line broadening and shifting coefficients for the lines in the first four vibrational transitions of hydrogen iodide diluted in nitrogen. Collision-induced line shifts in the vibration–rotation bands provide information on the differences between the interaction potentials in different vibrational states. Our data suggest that the anisotropic part of the interaction potential plays a minor role during collisions and remains similar for the studied transitions. Similarly to the case of the atomic perturbers [9], the observed line shifts are dominated by the vibrational dependence of the isotropic component of the potential. Broadening coefficients of all studied bands are found to be sensitive to the rotational relaxation processes. Acknowledgments The authors are grateful to Dr. H. Franz for preparing pure samples of hydrogen iodide. This work was supported by Deutsche Forschungsgemeinschaft (DFG). References
Fig. 6. Nitrogen-induced shifts of the vibrational frequencies for four studied bands of HI.
[1] M.O. Bulanin, A.V. Domanskaya, K. Kerl, J. Mol. Spectrosc. 218 (2003) 75–79. [2] J.E. Funk, Int. J. Hydrogen Energy 26 (2001) 185–190.
A.V. Domanskaya et al. / Journal of Molecular Spectroscopy 265 (2011) 69–73 [3] S. Goldstein, J.-M. Borgard, X. Vitart, Int. J. Hydrogen Energy 30 (2005) 619– 626. [4] R. Vogt, R. Sander, R. von Glasow, P.J. Crutzen, J. Atm. Chem. 32 (1999) 375– 395. [5] J.-M. Hartmann, J.-P. Bouanich, C. Boulet, M.O. Bulanin, A.V. Domanskaya, K. Kerl, J. Quant. Spectrosc. Radiat. Transfer 95 (2005) 151–163. [6] M.O. Bulanin, A.V. Domanskaya, C. Maul, K. Kerl, J. Mol. Spectrosc. 230 (2005) 87–92. [7] A.V. Domanskaya, M.O. Bulanin, K. Kerl, C. Maul, J. Mol. Spectrosc. 256 (2009) 75–79. [8] A.V. Domanskaya, M.O. Bulanin, K. Kerl, C. Maul, J. Mol. Spectrosc. 243 (2007) 155–161. [9] A.V. Domanskaya, M.O. Bulanin, K. Kerl, C. Maul, J. Mol. Spectrosc. 253 (2009) 20–24. [10] A.S. Pine, J.P. Looney, J. Mol. Spectrosc. 122 (1987) 41–55.
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[11] D. Hurtmans, A. Henry, A. Valentin, C. Boulet, J. Mol. Spectrosc. 254 (2009) 126–136. [12] C. Chackerian Jr., D. Goorvitch, L.P. Giver, J. Quant. Spectrosc. Radiat. Transfer 43 (1990) 127–132. [13] S.-I. Chou, D.S. Baer, R.K. Hanson, J. Mol. Spectrosc. 196 (1999) 70–76. [14] M.O. Bulanin, A.V. Domanskaya, K. Kerl, C. Maul, Mol. Phys. 104 (2006) 2685– 2690. [15] G. Maroulis, J. Chem. Phys 118 (2003) 2673–2687. [16] P.J. Leonard, At. Data Nucl. Data Tables 14 (1974) 21–37. [17] R.M. Herman, Phys. Rev. 132 (1963) 262–275. [18] C. Luo, R. Wehr, J.R. Drummond, A.D. May, F. Thibault, J. Boissoles, J.M. Launay, C. Boulet, J.-P. Bouanich, J.-M. Hartmann, J. Chem. Phys. 115 (2001) 2198– 2206. [19] A.D. Buckingham, Proc. R. Soc. London 255A (1960) 32–38.
Contents lists available at ScienceDirect
Journal of Molecular Spectroscopy journal homepage: www.elsevier.com/locate/jms
Nitrogen-induced broadening and shifts of rotation-vibrational lines in the fundamental, first, second and third overtone bands of HI A.V. Domanskaya a,⇑, R.E. Asfin b, C. Maul c, K. Kerl c, M.O. Bulanin b a
Institut für Physikalische Chemie, Universität Göttingen, D-37077 Göttingen, Germany Department of Physics, St. Petersburg University, Peterhof, 198504 St. Petersburg, Russia c Institut für Physikalische und Theoretische Chemie der Technischen Unversität Braunschweig, D-38106 Braunschweig, Germany b
a r t i c l e
i n f o
Article history: Received 13 August 2010 In revised form 13 November 2010 Available online 20 November 2010 Keywords: Diatomic molecules Hydrogen halides Nitrogen Pressure broadening Pressure shift
a b s t r a c t We report experimental results on the previously unknown broadening and shifting coefficients in the fundamental and three overtone vibration–rotation bands of the HI molecule in mixtures with nitrogen gas. Our data are compared with the previously published results for the fundamental bands of the HF and HCl molecules. It is shown that the line shifts are dominated by the vibrational dependence of the isotropic part of the intermolecular interaction potential. Ó 2010 Elsevier Inc. All rights reserved.
1. Introduction Hydrogen iodide is a special member of the hydrogen halides family because of its unusual electro-optical properties [1]. Apart from the fundamental interest, a possible industrial use of HI is envisaged as a part of the iodine sulphur cycle thermochemical cycle for hydrogen production [2]. An estimate predicts the energy efficiency for the chemical reactions in the iodine sulphur cycle to reach about 50% [3]. HI is also considered as one of the temporary iodine reservoir species that may be formed in reactions of iodine cycling in the marine boundary layer [4]. An accurate sensing of HI and other hydrogen halides requires not only the spectral line positions and absolute intensities, but also line shape parameters such as broadening and shift coefficients. In the recent years, comprehensive data were reported on the pressure broadening and shifting coefficients for spectral lines in the fundamental and overtone vibration–rotation absorption bands of HI and HBr molecules in pure gases [5–7] and in mixtures with rare gas perturbers [8,9]. However, the data on the nitrogeninduced shifts and broadenings for the hydrogen halides remain incomplete. The HCl molecule is the best studied one. The broadening and shifting of lines in the fundamental band of HCl were measured using high-resolution laser techniques [10,11]. The temperature dependence of the broadening coefficients was determined in a wide range of temperatures [10,12], and Dicke narrowing parameters were also obtained [12]. The spectra of the ⇑ Corresponding author. Fax: +49 551 39 3117. E-mail address: [email protected] (A.V. Domanskaya). 0022-2852/$ - see front matter Ó 2010 Elsevier Inc. All rights reserved. doi:10.1016/j.jms.2010.11.005
fundamental band of HF in mixture with N2 were also extensively studied [10]. The broadening and shift coefficients for the P2(3) and P2(6) lines in the first overtone of HF [13] seem to be the only line shape parameters determined for higher vibrational transitions among the hydrogen halides. To the best of our knowledge, broadenings and shifts of the vibration-rotational lines for HI and HBr induced by collisions with nitrogen have not been evaluated even in the fundamental regions. We report here the vibration–rotation line shifts and broadenings of HI diluted with nitrogen for four vibrational bands. Our results for the fundamental transition are compared with the data available from the literature on other hydrogen halides – nitrogen systems. 2. Experimental details Samples of HI were prepared by dehydration of the hydroiodic acid (Fluka, p.a.) with phosphoric anhydride and purified by a trap-to-trap distillation. Compressed nitrogen (Linde Gas 5.0) was used as supplied. Typically, 200–300 mbar of HI were admitted to a cell and then consequently diluted by nitrogen. The total pressure of gas mixtures did not exceed 4 bar. Pressures of HI were measured with a MKS Baratron capacitance manometer; higher pressures of the perturber gas were measured with a Bourdon gauge. Our measurements were carried out at 298 ± 1 K. The spectra were recorded with a Bruker 120HR FTIR instrument equipped with a CaF2/Si beam splitter and a liquid nitrogen cooled InSb detector, with resolution of 0.012–0.020 cm1 for the
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fundamental (the corresponding instrumental widths were 0.011 and 0.018 cm1 if one uses the Rayleigh criterion of resolution), 0.03 cm1 for the first and second overtones (instrumental width was 0.027 cm1), and 0.02 cm1 for the third overtone region. A globar source was used for measurements in the fundamental transition; overtones were recorded with a tungsten lamp as a source. Conventional optical filters were used for the fundamental and third overtone regions. Two stainless steel sample cells of 9.6 and 107 cm optical path lengths were used in our experiments. Protection of the cell interiors by a fluorinated polymer coating [14] prevented gradual decomposition of hydrogen iodide. The intensity distribution in the fundamental band is strongly perturbed due to the vibration– rotation coupling effect on the dipole moment function of HI [1], which results in ca. 5 times stronger absorption in the R-branch compared to that in the P-branch. The R-branch of the fundamental band was measured using the shorter cell, the spectra of overtones and weak lines of the P-branch of the fundamental band were measured using a specially designed long path cell [7]. Spectral line shapes were fitted with Lorentzians. The Doppler half-widths increase with frequency and reach a value of ca. 4.6 103 cm1 in the spectral range of the third overtone. The observed line widths for narrow lines (high J) for the third overtone are at least 10 times broader than the Doppler widths, even at the lowest pressure used in the experiments (1.13 bar). The resulting width of the corresponding Voigt profile would differ by less than 0.5% from the pure Lorentzian line width for our experimental conditions. The accuracy of the experimental widths in the region of the third overtone are not better than 1% which validates the use of Lorentzians instead of Voigts as fitting profiles. The quality of the fitting is demonstrated in Fig. 1. The maximum relative deviation of the fitted profile from the experimental shape in the region of the band head of the second overtone shown in Fig. 1 does not exceed 1.5%. The spectral data obtained for the third overtone are less accurate compared to those obtained in other spectral regions and we consider them only semi-quantitatively valid. Line widths and frequencies change in a linear manner with the nitrogen gas pressures. No statistically meaningful line asymmetries or Dicke collisional narrowing were detected at the conditions of our experiments. The least squares values of the pressure broadening (d) and shift (c) coefficients for each spectral line were determined from the slopes of such linear dependencies (see Fig. 2). 3. Results and discussion 3.1. Broadening coefficients The measured broadening coefficients cm ðmÞ for the lines in the four vibrational bands of HI are collected in Table 1 and plotted in Fig. 3 as a function of the line number m (m = J + 1 in the R-branch
Fig. 1. An example of the Lorentzian fits to the band head in the second overtone band of HI. The partial pressure of HI is 250 mbar, pressure of nitrogen is 1.27 bar.
Fig. 2. Dependence of the full line widths at half height (FWHH) on nitrogen pressure. Three rotational lines in the first overtone of HI show significantly different broadening.
Table 1 Measured nitrogen-broadening coefficients cv ðmÞ of hydrogen iodide lines of four vibrational bands (in 103 cm1 atm1). m
Vibrational transition (1
12 11 10 9 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
0)
– – – 37(2) 39(1) 47.2(3) 53.7(5) 62.0(6) 65.5(8) 71.1(8) 75.0(6) 85(1) 84(1) 75.5(7) 66.2(7) 61.4(9) 53.9(7) 50.0(7) 47.0(7) 43.2(8) 37(1) 34(2) 30(1) 26.7(2) 24.1(7) 23(2) 19(1)
(2
0)
29(1) 34(1) 36(2) 36.3(6) 40.7(8) 46.4(8) 50.0(8) 57(1) 63(1) 68(1) 75(2) 82(2) 89.0(5) 81.8(7) 75(1) 69.8(9) 63.3(8) 56.3(6) 49.8(6) 44.6(6) 39.8(7) 36.4(2) 34.3(4) 30.9(4) 27.6(4) 26.9(9) 27(1)
(3
0)
41(3) 42(2) 39(1) 41.0(9) 44.1(7) 48(1) 56.0(4) 65.7(5) 72.6(8) 80.8(9) 89(2) 97(2) 91(2) 79(1) 71.1(9) 65(1) 59(1) 53.1(9) 46.9(7) 43.2(5) 40.3(6) 37(1) 33(3) 30(3) 29(3) 35(8) –
(4
0)
– – 33(3) 46(3) 53(3) 58.2(4) 61(3) 70(2) 78(2) 72(2) 83(2) 100(4) 84.2(4) 77(2) 78(4) 69(1) 62(2) 61(1) 57.1(4) 53(4) 34(2) 61(5) 63.1(8) 16(1) – – –
Standard deviations are shown in parentheses.
and m = J in the P-branch). The line widths in nitrogen are weakly dependent on the upper vibrational state quantum number (v = 1, 2, 3, 4), although their m-dependencies are significant. The broadening coefficients are close within the accuracy limits for the fundamental, first and second overtone bands. Results for the third overtone are less accurate due to experimental uncertainties and lie somewhat above the general trend. A similar weak v-dependence was earlier observed for the line widths for HI perturbed by Ne and Ar [7]. A strong m-dependence is characteristic for the broadening coefficients of hydrogen halides (see Fig. 4a). The HF–N2 broadenings for m = ±10 are an order of magnitude smaller than those for m = ±1. The broadening coefficients decrease faster with increasing jmj for absorbing molecules with larger values of the dipole moments (Fig. 4a). Comparison of the nitrogen broadening with the self- and Ar-broadenings shows that collisions with N2 produce an
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Table 2 Measured nitrogen shift coefficients dv ðmÞ of hydrogen iodide lines of four vibrational bands (in 103 cm1 atm1). m
Vibrational transition
12 11 10 9 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
– – – 3.7(5) 4.2(3) 4.3(1) 3.8(1) 4.5(2) 4.71(7) 3.3(2) 2.5(1) 1.0(4) 0.1(1) 2.3(1) 2.6(1) 2.8(2) 3.3(1) 4.5(1) 5.6(1) 5.20(9) 4.5(2) 4.1(1) 2.99(9) 1.90(8) 1.3(1) 1.41(7) –
(1
Fig. 3. Nitrogen-broadening coefficients for the HI molecule.
intermediate effect on the line widths (Fig. 4b). Self-broadening coefficients have the largest values and a weaker m-dependence, showing stronger perturbations of all rotational states due to collisions between dipolar molecules. N2-broadening coefficients are ca. 1.5 times greater probably due to an additional interaction caused by quadrupole moment of the nitrogen molecule [15] (Ar and N2 have similar polarizability – 1.642 and 1.741 Å3 respectively [15,16]). 3.2. Shift coefficients The nitrogen-induced shift coefficients of HI are listed in Table 2. Shift coefficients dv ðmÞ are easier to interpret if they are separated into two parts: symmetric in the line number, defined as dvS ðmÞ ¼ ðdv ðmÞ þ dv ðmÞÞ=2, and asymmetric, defined as dvA ðmÞ ¼ ðdv ðmÞ dv ðmÞÞ=2. The symmetric shifts were shown to depend on the isotropic components of the interaction potential, whereas the asymmetric shifts depend on the anisotropic components [17,18]. The difference between symmetric and asymmetric shift coefficients for different vibrational transitions reflects predominantly the v-dependence of the corresponding parts of the interaction potential. Symmetric and asymmetric shifts are plotted in Fig. 5. The dvA ðmÞ are practically identical and almost negligible for most of the lines in all vibrational bands (Fig. 5a). Values of d4A ðmÞ are omitted in the plot due to their greater inaccuracy. Only the lines with
0)
(2
0)
8(2) 9(1) 8(1) 8.7(7) 9.7(6) 10.2(6) 10.1(6) 10.5(7) 10.7(7) 8.5(7) 6.6(7) 10(1) 2.2(6) 6.8(8) 7.7(9) 8.0(7) 8.8(6) 10.6(6) 10.4(7) 10.0(7) 9.4(6) 8.2(6) 7.2(6) 5.8(9) 4.0(7) 6(1) 2(1)
(3
0)
14(2) 12(1) 12(1) 12.2(9) 13.6(6) 14.5(8) 14.8(7) 14.8(8) 13.5(7) 10.6(5) 10.0(5) 10(1) 6(1) 9(1) 10(1) 11.3(7) 12.4(6) 14(1) 14.5(7) 13.8(8) 13.1(8) 12(1) 13(3) 10(4) 9(2) 3(2) –
(4
0)
– 22(4) 22(3) 18(3) 22(1) 17.9(5) 19(2) 22.3(7) 19(2) 15.4(8) 12(4) 14(4) 11.0(7) 16(5) 18(2) 16.0(9) 18.7(6) 18(2) 20(1) 15(2) 19(4) 17.4(2) 21.7(5) – – – –
Standard deviations are shown in parentheses.
m = ±1 show v-dependent values of dvA ðmÞ. The irregular behavior of the first m = ±1 lines due to transitions that involve zero angular momentum molecular states is common for HI/HBr – rare gas mixtures. For the most systems studied [5,7–9] the Rv(0) line shows a weak blue shift dominated by its asymmetric part and hence it is very sensitive to the behavior of the anisotropic potential. All measured symmetric line shifts are red, and become larger with increasing vibrational quantum number v and, to a certain extent, with the rotational angular momentum J (Fig. 5b). This illustrates the fact that the attractive (causing red shifts) isotropic components for the HI–N2 potential dominate the repulsive parts
Fig. 4. Comparison of HI broadening by nitrogen with other systems; (a) nitrogen-broadening coefficients for the fundamental transition of different hydrogen halides. Solid circles show the data for HI (this work). Data for HCl (open triangles) and HF (open diamonds) are taken from Ref. [10]. (b) m-Dependence of nitrogen- (solid circles, this work), argon- (open triangles, Ref. [8]) and self-broadening (open squares, Ref. [5]) in the fundamental band of HI.
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Fig. 5. Symmetric dmS ðmÞ and asymmetric dmA ðmÞ shifts of HI lines in nitrogen.
(causing blue shifts) with increasing of the vibrational and rotational kinetic energy of the diatomic. The symmetric line shifts do not reach any evident constant asymptotic value in the HI bands studied here. For each band, they reach a minimum at m = ±6, ±7 and then tend to increase with increasing |m|, except for d4S ðmÞ which behavior is rather unclear for jmj > 8 due to higher inaccuracy. Larger shifts of the higher overtones could be further commented. Perturbation theory [19] that did not take into account the rotational degrees of freedom of molecules, predicted the interaction-induced red shifts of the vibrational transition frequencies to be proportional to the quantum number of the upper vibrational state. We have evaluated the vibrational transition shifts by fitting the vibration-rotational frequencies for every band by a polynomial function at different pressures of nitrogen (see Fig. 6). One can see that the vibrational frequencies decrease linearly with the perturber pressure and the absolute values are larger for the overtones, in agreement with predictions of Ref. [19]. We found that the vibrational shifts are indeed proportional to the v-quantum number with the coefficient of 1.83(6), i.e. dv ib ðv ¼ 2Þ= dv ib ðv ¼ 1Þ ¼ 1:83ð6Þ. Nitrogen-induced shifts of HI spectral lines are the smallest compared to other hydrogen halides (see Fig. 7). One can see that
Fig. 7. Symmetric d1S ðmÞ and asymmetric d1A ðmÞ shifts of the fundamental band of hydrogen halides in mixtures with nitrogen. Data for HCl and HF are taken from Ref. [10].
the HF–N2 interaction potential is significantly more anisotropic compared to the HI–N2 pair, which leads to an order of magnitude larger values for the asymmetric shifts (Fig. 7a). The orientationally averaged dipole-induction interactions play a dominant role for the hydrogen halide – rare gas systems, making the symmetric shifts proportional to the squares of the vibrational ground state dipole moments [8]. One could expect that it remains the same for a molecular non-polar perturber. Indeed, the absolute values of the symmetric shift coefficients induced by nitrogen are greater for the molecules with higher dipole moment with an exception for the lines at the center of the band (Fig. 7b). 4. Concluding remarks We have reported here for the first time experimental data on the line broadening and shifting coefficients for the lines in the first four vibrational transitions of hydrogen iodide diluted in nitrogen. Collision-induced line shifts in the vibration–rotation bands provide information on the differences between the interaction potentials in different vibrational states. Our data suggest that the anisotropic part of the interaction potential plays a minor role during collisions and remains similar for the studied transitions. Similarly to the case of the atomic perturbers [9], the observed line shifts are dominated by the vibrational dependence of the isotropic component of the potential. Broadening coefficients of all studied bands are found to be sensitive to the rotational relaxation processes. Acknowledgments The authors are grateful to Dr. H. Franz for preparing pure samples of hydrogen iodide. This work was supported by Deutsche Forschungsgemeinschaft (DFG). References
Fig. 6. Nitrogen-induced shifts of the vibrational frequencies for four studied bands of HI.
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