- Email: [email protected]
Pressure broadening in the 0–4 through 0–7 overtone bands of H35Cl and H37Cl
J. Quont. Specfrosc. Radial. Transfer Vol. 24, pp. 371-377 Pergamon Press Ltd., 1980. Printed in Great Britain
PRESSURE BROADENING IN THE O-4 THROUGH o-7 OVERTONE BANDS OF H3%3 AND H3’C1 MOHAMMAD ZuoHuLtS and JACKGELFANDS Department
of Mechanical
and Aerospace Engineering, Princeton University,
Princeton, NJ 08544, U.S.A.
HERSCHEL RABITZS Department
of Chemistry,
Princeton University,
Princeton, NJ 08544, U.S.A.
and ANDREW E. DEPRISTO Department
of Chemistry,
University
of North Carolina, Chapel Hill, NC 27514, U.S.A.
(Received 22 February 1980) Abstract-We have measured the pressure broadening coefficients of a number of rotation-vibration lines in the O-4 through O-7 overtone bands of HCI utilizing a Fourier transform spectrometer and a 40!9m path length White cell. These data, when included with previous measurements on the fundamental and lower overtone bands, show a systematic variation of pressure broadening with increasing overtone band. This result reflects a change in the collision dynamics between molecules in the upper state of the transition with ground state molecules. 1. INTRODUCTION Pressure broadened linewidths have been sought after for a number of diverse reasons.’ Recently, significant advances have been made in inverting pressure broadening data to yield elastic reorientation information, as well as inelastic state to state collisional rate constants.” This procedure has been extensively tested on atom-diatom systems and is being extended to include diatom-diatom systems such as self broadening in HCI. Of particular interest with regard to collision dynamics is the fact that the linewidth is due to an average of the interactions between the background gas and molecules in both the lower and upper states of the transition. In a series of overtone spectra originating from v = 0, the lower state is the same. Because of this, its contribution to the linewidth remains constant. The change in pressure broadening as one goes to increasingly higher overtone transitions then reflects the change in collisional interactions of the molecules in the upper state of the transition with ground state molecules. One can acquire simple absorption spectra for transitions to much higher states than would be feasible for double resonance or fluorescence experiments. Therefore, dynamical information can be extracted from properly inverted pressure-broadening data for more highly vibrationally excited molecules than would otherwise be obtainable. For self-broadening in HCI, detailed measurements have been made on the pure rotational, the fundamental and the first overtone bands.‘-” We have obtained pressure-broadening data for a number of lines in both the P and R branches of the O-4 through O-7 bands. In this paper, we report the results of these measurements and preliminary findings with regard to changes in rotationally inelastic collisions with increasing vibrational excitation. A more detailed analysis of these data is in progress. 2. EXPERIMENTAL
Spectra of hydrogen chloride were measured using a Fourier transform spectrometer and White cell at the McMath Solar Telescope complex at Kitt Peak National Observatory. This is a high resolution I.R. through near U.V. instrument with a maximum optical path difference of 1 m. Scan times of the order of 2 hr were required for an S/N ratio of 20,000: 1 in the continuum. A digital mini-computer with the associated electronics allowed for data storage and averaging. Fourier transforms were done on a CDC f%OOcomputer. tPment address: Department of Chemistry, University of Jordan, Amman, Jordan. SVisiting Astronomers, Kitt Peak National Observatory (operated by AURA under the auspices of the National Science Foundation). 371
312
M. ZUGHULet
al.
A set of interference filters was used to isolate narrow portions of the spectrum to be recorded. These have a typical full width at half maximum bandwidth of 300-5OOcm-’ with -80% peat transmission. Spectra were recorded in the range 10,700-11,000cm-’ for the O-4 band, 13,150-13,500cm-’ for the O-5 band, 15,500-15,800cm-’ for the O-6 band, and 17,800-18,150cm-’ for the O-7 band. Custom filters which were specially designed to have a flat bandpass in the spectral range of interest were fabricated for the O-4 through O-6 band regions. An off the shelf Gaussian shaped filter was used for the O-7 band spectrum. The absorption cell was a 6 m long White cell with an optical path length of 410 m. The cell was a 40 cm o.d. stainless steel cylinder kept under vacuum (-1 II) through a vacuum system isolated from the roughing pump by a dry-ice trap. The cell was filled through a dry-ice trap and pressure was continuously measured using an MKS Baratron &10,000 torr pressure gauge with an accuracy of 20.1%. Pressure drifts during the course of a spectral scan were found to be of the same order of magnitude. The cell temperature was continuously monitored by a mercury thermometer and was maintained at room temperature in the range of 297-298°K to within +-0.5”C.Hydrogen chloride gas was Matheson Electronic grade with 99.99% purity. Spectral measurements were typically made by examining the interference filter profile first and adjusting the filter angle so that channel spectra due to etaloning effects in the bandpass filters were minimized. This was followed by recording la9 scans of the HCI spectrum at a given pressure, with the same procedure repeated for each wavelength range and gas pressure. In a series of data runs, each spectral run was immediately preceded or followed by the appropriate filter profile. The interferograms were finally Fourier transformed and divided by the corresponding filter profile. The resulting spectra were plotted and examined for effects of thermal drifts in the filter profile as well as for atmospheric absorption in the path between the White cell and interferometer. A total of 44 spectra was obtained. Some of the spectra of the O-4 band showed interference from water lines that could not be properly divided out and were discarded. Absorption due to the atmospheric oxygen b’C+-,X3Z- bands was observed at the edge of the O-5 band but introduced no interference. As each spectrum was taken, the interferogram was studied prior to the final data run. The maximum optical path difference was adjusted such that it was lO-20% greater than the point where the amplitude of the interferogram diminished into the noise. This process insured that all of the spectral information was contained in the unapodized interferogram. Only a small portion of the interferogram, typically the last 6% of the scan, was apodized with a cosine function. This process insures a transformation that gives maximum fidelity in the resultant spectra.” The total optical path differences used were 25 cm for the O-4 band, 21 cm for the O-5 and O-6 bands, and 12.5 cm for the O-7 band. Synthesized spectra were studied to be sure that these optical path differences provided sufficient resolution for the narrowest line in each band. In no case did the distortion exceed a small fraction of a per cent. 3.RESULTS ANDDISCUSSIONS
The lines were fitted to a Voight profile function which was conveniently approximated by the relation”
where O,(i)= (O - ai)’ + CI~+ Bj~j/ln 2, S,(i) = 4&i(w - oi)‘/ln 2, Si, ai, yi, and wi are the individual line intensity, collision-brodened half-width, Doppler half-width, and center frequency, respectively; Aj and Rj are constants and n is the number of overlapping lines within the frequency range over which the absorption coefficient k,(w) is to be evaluated. This function is accurate to within 2 x 10” for rotational lines for which a/r > 3.6. All of the lines studies were within this range. The function was found to be particularly convenient for use with overlapping lines as was the case within the R-branches of the bands which were studied. A nonlinear, least-squares line-fitting routine, which is part of the IMSL program library, was used to fit the spectra to the Voigt profile.r3 In some cases, a sloping baseline or some residual channel spectra remained after division of the spectra by the appropriate filter profile. This result was probably due to slight
313
Pressure broadening in the H”CI and H3’CIovertone bands
temperature drifts, which occurred during the long averaging times of the interferogram recordings. Regions of the spectra, which contained channel spectra but were free of absorption features, were carefully studied and it was found that channel spectra of only one modulation frequency were present in all cases. The baseline was therefore fitted to a function of the form B = $ a,(o - 0,)’ + b sin I=0 where al is a constant, o, is the beginning of the frequency region over which the absorption coefficient is evaluated, b is the amplitude of the sinusoid where period is A, and 4 is a phase factor. The linear term of the power series was retained, as well as the sinusoid term, for portions of the O-4 and O-5 bands. There appeared to be no modulation in the O-6 spectrum except for a sloping base line which was linear. The base line was found to be quadratic for parts of the CL7 band and was steeply sloped compared to the line depth for the higher P-branch lines. In the cases where residual channel spectra were present, at least IOcm-’ on each side of the line or groups of lines was fitted. The channel spectra exceeded a few per cent of the total line depth in only a few cases. Some portions of the fitted spectra in the O-5 band are shown in Figs. 1 and 2. The large difference in the B values of upper and lower states of the transition cause the P-branch lines to be widely separated and portions of the R-branch to be badly overlapped because the band folds back on itself. The pressure-broadening coefficients were obtained by averaging over the measured values of the width per atmosphere at different pressures in the range 500-1000 torr for the three bands O-4through O-6. This procedure is equivalent to determining the slope while constraining the line to pass through the origin. Plots of half-widths for some representative rotational lines against pressure are shown in Figs. 3-5. The O-7 band was measured at 990 torr only. The pressure broadening coefficients for both H”C1 and H”C1 are listed in Table 1 and plotted in Fig. 6. In the o-4 through O-6 bands, the standard deivation of the individual measured points from the fitted line of half-width vs pressure was less than 2%. The standard deviation for overlapped R-branch lines was of the order of 5%. The agreement of the pressure-broadening coefficients of the H”Cl and H3’Cl isotopic species was always found to be within the errors caused by lack of precision of the fitted points. This result is to be expected as the order of magnitude of the differences in thermal velocities or moments of inertia of the two molecules are too small to
0.06
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Fig. 1. Spectra of the two rotational lines “P(3) and “P(3) of the HCI O-5 band. The x points are the measured data and the solid line is a least-squares fit.
M.
314
ZUGHUL etal.
FRECUENCY(Cm? Fii.2.
A portion of the R-branch spectra for the O-SHCI band. The x points are the measured data and the solid line is a least-squares fit.
influence the line width at the level of precision of these measurements. The O-7 band data were obtained primarily for line positions and strengths measurements. l4 The line widths are reported here, but at considerably reduced accuracy compared to those for the other bands. Several trends are discernable on examining the pressure broadening coefficient data shown in Fig. 6 along with data in the literature on the pure rotational, fundamental, and first overtone bands. In all of these bands, pressure broadening shows an expected peak at low values of M 0.4
I
I *ccl
I
I
I
600
600
1000
O-4
0 P(3) A P(6) 0 R(9)
0p-
0
200
400
P (TORR)
Fig. 3. A plot of collision-broadened half-widths against pressure for three rotational lines of the H”CI O-4 band. The solid line is a least-squares fit of the corresponding data points, constrained to go through the
375
Pressure broadening in the H”C1 and H”CI overtone bands Table 1. Pressure-broadened half-widths (cm-‘atm-‘1 for CHI in the 0-4 through O-7 overtone bands.
I
O-4
had
Iwtopl3
H35Cl
B35Cl
H37Cl
I
o-5 B37Cl
H37Cl
H35Cl
o-7
I
o-6
H35Cl
837Cl
l
..*
0.182
..*
..*
. . .
0.163
-6
0.181
0.182
0.197
0.193
0.214
0.200
0.210
9.9
-5
0.202
0.202
0.207
0.206
0.220
0.218
0.228
0.191
-II
0.219
0.213
0.217
0.218
0.219
0.218
0.226
0.200
-3
0.229
0.228
0.225
0.222
0.222
0.223
0.222
0.209
-2
0.226
0.224
0.223
0.223
0.220
0.217
0.212
0.202
-1
0.214
0.209
0.216
0.210
0.209
0.209
0.214
0.217
1
0.202
0.1%
0.198
0.197
0.192
0.195
0.193
0.203
0.193
0.190
0.195
0.194
0.199
0.198
0.217
0.208 ..*
2
0.206
0.202
0.195
0.1%
3
0.210
0.212
0.205
0.201
0.190
H.
-7
4
0.206
0.206
0.205
0.206
0.211
0.203
.*.
5
0.192
0.189
0.1%
0.193
0.1%
0.202
l
6
0.173
0.177
0.169
0.180
0.189
0.179
0.180
0.177
7
0.149
0.155
0.156
0.147
0.153
0.143
0.162
0.136
0
0.126
0.124
0.134
0.127
0.132
0.138
0.151
0.158
9
0.107
0.101
0.111
0.106
O.ll8
o.ll3
0.132
0.127
10
0.096
0.089
0.102
l
*.
0.112
l
.*
0.092
l
**
l
.*
0.107
l
*.
.H
l
..
...
.*a
l
..
11
0.087
0.071
12
0.064
...
I
I
0
IPCI
l
.*
.**
I
...
I
l
I
..
I
I
*.
l
.*
I
o-5 0
P(3)
0 T
E
2 I)
C
Fig. 4. A plot of collision-broadened half-widths against pressure for three rotational lines of the H3%JIO-5 band. The solid line is a least-squares tit of the corresponding data points, constrained to go through the origin.
316 7
13 -
.2 -
).I -
Ok 0
400
600
600
1000
P t TORR )
Fii. 5. A plot of collision-broadened half-widths against pressure for three rotational lines of the H’5CIO-6 band. The solid line is a least-squares fit of the corresponding data points, constrained to go through the origin.
.24 A
20
AA l
.QtP
.I6 .I2 i AOOdb* .201 A* .I6 .I2
.20
pbA4 A’
.I6 .I2 f
4 .I6
A
.20 F
06 -6
-6
-4
-2
0
2
4
6
6
IO
12
m Fig. 6. A plot of the pressure-broadening coefficients for the vibrational bands o-4,0-5,0-6, and O-7.
Pressure broadening in the H”CI and H”CI overtone bands
317
because of the predominant contribution of near-resonant collisions of the form HCI(J) + HCl(J ? 1) = HCl(J + 1) + HCU).
(1)
Because the probability of finding suitable partners for this type of collision is controlled by the Boltzmann distribution and the degeneracy of the rotational states, pressure broadening peaks in the same way. As we go to higher overtone bands, our data show that this maximum value of pressure broadening diminishes and the shape of the curve becomes flatter. Also, the P and R-branches become noticeably asymmetric, with the peak of the P-branch being higher. A full analysis of these data, utilizing the inversion procedure of Refs. 2-4, is in progress. However, in view of the cited variations in pressure broadening, we can discuss what qualitative mechanistic changes in rotational interactions may be taking place as HCI becomes more excited vibrationally. These effects are most likely attributable to a change in the contributions of near resonant collisions to the pressure-broadened half width relative to other processes, such as off-resonant rotation-rotation, rotation-translation or elastic reorientation collisions. This result is to be expected since, as we go to higher overtone transitions, the energy defect of near-resonant collisions increases because of a change in the rotational spacing with vibrational level. In the pure rotational tL0 band spectrum, both the upper and lower states of the transition are in the ground vibrational state and all collisions of the kind described by Eq. (1) have exactly zero energy defect. In any other band, collisions of that type between upper state and ground state molecules are no longer exactly resonant. This effect can be appreciable in view of the fact that the B value of HCI changes from 10.44 in the ground state to 8.33 in the V = 7 state. A diminished contribution of near-resonant collisions results in a smaller peak value for the pressure-broadening coefficient. This fact could result in a flattening of the curve because the other types of collisions produce an m dependence for pressure broadening that is not sharply peaked in the same way as the near-resonant contribution. The asymmetries in the P- and R-branches are similar to that reported for the first and second overtones in HF.” This result is produced by the differences between the upper and lower states of the P- and R-branch transitions with corresponding m and their effect on the contributions of near-resonant collisions. The lower .I state of a P-branch transition is one higher than the lower state of the corresponding R-branch transition. The upper J-state of a P-branch transition is one lower than that of the corresponding R-branch transition. Thus, a molecule in these particular states will see collision partners from a different portion of the Boltzmann distribution. Since the J-state differences are opposite in the upper and lower states of the transitions, the asymmetries will cancel exactly if the cross sections contributing to the linewidths are equal for the same J-states of the upper and lower vibrational state. The asymmetry is indicative of a change in processes for which there must be a dependence of the cross section on the J-state of the collision partner. In this way, molecules interacting with different portions of the Boltzmann distribution will contribute differently to the linewidth. A full inversion procedure of the kind described in Refs. 24 is required in order to ascertain which particular processes are responsible for the trends observed here. This analysis is in progress and will be reported in a future publication.i6 Acknowledgements-We wish to thank Dr. James Brault and Mr. Roger Jakoubek for helpful discussions and assistance in recording and transforming the spectra at the Kitt Peak National Observatory. This work was supported by ONR, NSF, and an unrestricted research grant from the Exxon Research and Engineering Corporation. REFERENCES H. Rabitz, Ann. Rev. Phys. Chem. 25, I55 (1974). A. DePristo and H. Rabitz, J. Chem. Phys. 68, 1981(1978). A. DePristo and H. Rabitz, JQSRT 22,65 (1979). A. DePristo, J. Chem. Phys. in press (1980). A. Rosenberg, A. Lightman, and A. Ben-Reuven, JQSRT 12,219 (1972). W. Benedict, R. Herman, G. Moore, and S. Silverman, Can. .I. Phys. 34, 850 (1956). H. Babrov, G. Ameer and W. Benesch, J. Chem. Phys. 33, 145 (1960). 8. H. Goldring and W. Benesch, Can. 1. Phys. 40, 1801(l%2). 9. J. Jaffee, S. Kimel, and M. Hirschfeld, Can. J. Phys. 48, 113(1%2). IO. R. Toth, R. Hunt and E. Plyer, 1. Molec. Spectrosc. 35, II0 (1970). 11. J. Brault and 0. White, Astron. Asfrophys. 13, 169(1971). 12. J. BelBruno, M. Zughul, J. Gelfand, and H. Rabitz, J. Molec. Spectrosc., submitted (1980). 13. International Mathematical and Statistical Library, Houston, Texas, Program ZXSSQ. 14. J. Gelfand, M. Zughul, H. Rabitz, and C. J. Han, JQSRT submitted, (1980). 15. R. Spellicy, R. Meredith, and F. Smith, J. Chem. Phys. 57,5119 (1972). 16. A. E. DePristo, J. BelBmno, J. Gelfand, and H. Rabitz, .I. Chem. Phys. in press (1980). I. 2. 3. 4. 5. 6. 7.
PRESSURE BROADENING IN THE O-4 THROUGH o-7 OVERTONE BANDS OF H3%3 AND H3’C1 MOHAMMAD ZuoHuLtS and JACKGELFANDS Department
of Mechanical
and Aerospace Engineering, Princeton University,
Princeton, NJ 08544, U.S.A.
HERSCHEL RABITZS Department
of Chemistry,
Princeton University,
Princeton, NJ 08544, U.S.A.
and ANDREW E. DEPRISTO Department
of Chemistry,
University
of North Carolina, Chapel Hill, NC 27514, U.S.A.
(Received 22 February 1980) Abstract-We have measured the pressure broadening coefficients of a number of rotation-vibration lines in the O-4 through O-7 overtone bands of HCI utilizing a Fourier transform spectrometer and a 40!9m path length White cell. These data, when included with previous measurements on the fundamental and lower overtone bands, show a systematic variation of pressure broadening with increasing overtone band. This result reflects a change in the collision dynamics between molecules in the upper state of the transition with ground state molecules. 1. INTRODUCTION Pressure broadened linewidths have been sought after for a number of diverse reasons.’ Recently, significant advances have been made in inverting pressure broadening data to yield elastic reorientation information, as well as inelastic state to state collisional rate constants.” This procedure has been extensively tested on atom-diatom systems and is being extended to include diatom-diatom systems such as self broadening in HCI. Of particular interest with regard to collision dynamics is the fact that the linewidth is due to an average of the interactions between the background gas and molecules in both the lower and upper states of the transition. In a series of overtone spectra originating from v = 0, the lower state is the same. Because of this, its contribution to the linewidth remains constant. The change in pressure broadening as one goes to increasingly higher overtone transitions then reflects the change in collisional interactions of the molecules in the upper state of the transition with ground state molecules. One can acquire simple absorption spectra for transitions to much higher states than would be feasible for double resonance or fluorescence experiments. Therefore, dynamical information can be extracted from properly inverted pressure-broadening data for more highly vibrationally excited molecules than would otherwise be obtainable. For self-broadening in HCI, detailed measurements have been made on the pure rotational, the fundamental and the first overtone bands.‘-” We have obtained pressure-broadening data for a number of lines in both the P and R branches of the O-4 through O-7 bands. In this paper, we report the results of these measurements and preliminary findings with regard to changes in rotationally inelastic collisions with increasing vibrational excitation. A more detailed analysis of these data is in progress. 2. EXPERIMENTAL
Spectra of hydrogen chloride were measured using a Fourier transform spectrometer and White cell at the McMath Solar Telescope complex at Kitt Peak National Observatory. This is a high resolution I.R. through near U.V. instrument with a maximum optical path difference of 1 m. Scan times of the order of 2 hr were required for an S/N ratio of 20,000: 1 in the continuum. A digital mini-computer with the associated electronics allowed for data storage and averaging. Fourier transforms were done on a CDC f%OOcomputer. tPment address: Department of Chemistry, University of Jordan, Amman, Jordan. SVisiting Astronomers, Kitt Peak National Observatory (operated by AURA under the auspices of the National Science Foundation). 371
312
M. ZUGHULet
al.
A set of interference filters was used to isolate narrow portions of the spectrum to be recorded. These have a typical full width at half maximum bandwidth of 300-5OOcm-’ with -80% peat transmission. Spectra were recorded in the range 10,700-11,000cm-’ for the O-4 band, 13,150-13,500cm-’ for the O-5 band, 15,500-15,800cm-’ for the O-6 band, and 17,800-18,150cm-’ for the O-7 band. Custom filters which were specially designed to have a flat bandpass in the spectral range of interest were fabricated for the O-4 through O-6 band regions. An off the shelf Gaussian shaped filter was used for the O-7 band spectrum. The absorption cell was a 6 m long White cell with an optical path length of 410 m. The cell was a 40 cm o.d. stainless steel cylinder kept under vacuum (-1 II) through a vacuum system isolated from the roughing pump by a dry-ice trap. The cell was filled through a dry-ice trap and pressure was continuously measured using an MKS Baratron &10,000 torr pressure gauge with an accuracy of 20.1%. Pressure drifts during the course of a spectral scan were found to be of the same order of magnitude. The cell temperature was continuously monitored by a mercury thermometer and was maintained at room temperature in the range of 297-298°K to within +-0.5”C.Hydrogen chloride gas was Matheson Electronic grade with 99.99% purity. Spectral measurements were typically made by examining the interference filter profile first and adjusting the filter angle so that channel spectra due to etaloning effects in the bandpass filters were minimized. This was followed by recording la9 scans of the HCI spectrum at a given pressure, with the same procedure repeated for each wavelength range and gas pressure. In a series of data runs, each spectral run was immediately preceded or followed by the appropriate filter profile. The interferograms were finally Fourier transformed and divided by the corresponding filter profile. The resulting spectra were plotted and examined for effects of thermal drifts in the filter profile as well as for atmospheric absorption in the path between the White cell and interferometer. A total of 44 spectra was obtained. Some of the spectra of the O-4 band showed interference from water lines that could not be properly divided out and were discarded. Absorption due to the atmospheric oxygen b’C+-,X3Z- bands was observed at the edge of the O-5 band but introduced no interference. As each spectrum was taken, the interferogram was studied prior to the final data run. The maximum optical path difference was adjusted such that it was lO-20% greater than the point where the amplitude of the interferogram diminished into the noise. This process insured that all of the spectral information was contained in the unapodized interferogram. Only a small portion of the interferogram, typically the last 6% of the scan, was apodized with a cosine function. This process insures a transformation that gives maximum fidelity in the resultant spectra.” The total optical path differences used were 25 cm for the O-4 band, 21 cm for the O-5 and O-6 bands, and 12.5 cm for the O-7 band. Synthesized spectra were studied to be sure that these optical path differences provided sufficient resolution for the narrowest line in each band. In no case did the distortion exceed a small fraction of a per cent. 3.RESULTS ANDDISCUSSIONS
The lines were fitted to a Voight profile function which was conveniently approximated by the relation”
where O,(i)= (O - ai)’ + CI~+ Bj~j/ln 2, S,(i) = 4&i(w - oi)‘/ln 2, Si, ai, yi, and wi are the individual line intensity, collision-brodened half-width, Doppler half-width, and center frequency, respectively; Aj and Rj are constants and n is the number of overlapping lines within the frequency range over which the absorption coefficient k,(w) is to be evaluated. This function is accurate to within 2 x 10” for rotational lines for which a/r > 3.6. All of the lines studies were within this range. The function was found to be particularly convenient for use with overlapping lines as was the case within the R-branches of the bands which were studied. A nonlinear, least-squares line-fitting routine, which is part of the IMSL program library, was used to fit the spectra to the Voigt profile.r3 In some cases, a sloping baseline or some residual channel spectra remained after division of the spectra by the appropriate filter profile. This result was probably due to slight
313
Pressure broadening in the H”CI and H3’CIovertone bands
temperature drifts, which occurred during the long averaging times of the interferogram recordings. Regions of the spectra, which contained channel spectra but were free of absorption features, were carefully studied and it was found that channel spectra of only one modulation frequency were present in all cases. The baseline was therefore fitted to a function of the form B = $ a,(o - 0,)’ + b sin I=0 where al is a constant, o, is the beginning of the frequency region over which the absorption coefficient is evaluated, b is the amplitude of the sinusoid where period is A, and 4 is a phase factor. The linear term of the power series was retained, as well as the sinusoid term, for portions of the O-4 and O-5 bands. There appeared to be no modulation in the O-6 spectrum except for a sloping base line which was linear. The base line was found to be quadratic for parts of the CL7 band and was steeply sloped compared to the line depth for the higher P-branch lines. In the cases where residual channel spectra were present, at least IOcm-’ on each side of the line or groups of lines was fitted. The channel spectra exceeded a few per cent of the total line depth in only a few cases. Some portions of the fitted spectra in the O-5 band are shown in Figs. 1 and 2. The large difference in the B values of upper and lower states of the transition cause the P-branch lines to be widely separated and portions of the R-branch to be badly overlapped because the band folds back on itself. The pressure-broadening coefficients were obtained by averaging over the measured values of the width per atmosphere at different pressures in the range 500-1000 torr for the three bands O-4through O-6. This procedure is equivalent to determining the slope while constraining the line to pass through the origin. Plots of half-widths for some representative rotational lines against pressure are shown in Figs. 3-5. The O-7 band was measured at 990 torr only. The pressure broadening coefficients for both H”C1 and H”C1 are listed in Table 1 and plotted in Fig. 6. In the o-4 through O-6 bands, the standard deivation of the individual measured points from the fitted line of half-width vs pressure was less than 2%. The standard deviation for overlapped R-branch lines was of the order of 5%. The agreement of the pressure-broadening coefficients of the H”Cl and H3’Cl isotopic species was always found to be within the errors caused by lack of precision of the fitted points. This result is to be expected as the order of magnitude of the differences in thermal velocities or moments of inertia of the two molecules are too small to
0.06
r
IL3
I
I 13315
,
I I33 I7
I
I
13322 FREauENcY km-‘)
I
, 13324
I
1 13326
1
Fig. 1. Spectra of the two rotational lines “P(3) and “P(3) of the HCI O-5 band. The x points are the measured data and the solid line is a least-squares fit.
M.
314
ZUGHUL etal.
FRECUENCY(Cm? Fii.2.
A portion of the R-branch spectra for the O-SHCI band. The x points are the measured data and the solid line is a least-squares fit.
influence the line width at the level of precision of these measurements. The O-7 band data were obtained primarily for line positions and strengths measurements. l4 The line widths are reported here, but at considerably reduced accuracy compared to those for the other bands. Several trends are discernable on examining the pressure broadening coefficient data shown in Fig. 6 along with data in the literature on the pure rotational, fundamental, and first overtone bands. In all of these bands, pressure broadening shows an expected peak at low values of M 0.4
I
I *ccl
I
I
I
600
600
1000
O-4
0 P(3) A P(6) 0 R(9)
0p-
0
200
400
P (TORR)
Fig. 3. A plot of collision-broadened half-widths against pressure for three rotational lines of the H”CI O-4 band. The solid line is a least-squares fit of the corresponding data points, constrained to go through the
375
Pressure broadening in the H”C1 and H”CI overtone bands Table 1. Pressure-broadened half-widths (cm-‘atm-‘1 for CHI in the 0-4 through O-7 overtone bands.
I
O-4
had
Iwtopl3
H35Cl
B35Cl
H37Cl
I
o-5 B37Cl
H37Cl
H35Cl
o-7
I
o-6
H35Cl
837Cl
l
..*
0.182
..*
..*
. . .
0.163
-6
0.181
0.182
0.197
0.193
0.214
0.200
0.210
9.9
-5
0.202
0.202
0.207
0.206
0.220
0.218
0.228
0.191
-II
0.219
0.213
0.217
0.218
0.219
0.218
0.226
0.200
-3
0.229
0.228
0.225
0.222
0.222
0.223
0.222
0.209
-2
0.226
0.224
0.223
0.223
0.220
0.217
0.212
0.202
-1
0.214
0.209
0.216
0.210
0.209
0.209
0.214
0.217
1
0.202
0.1%
0.198
0.197
0.192
0.195
0.193
0.203
0.193
0.190
0.195
0.194
0.199
0.198
0.217
0.208 ..*
2
0.206
0.202
0.195
0.1%
3
0.210
0.212
0.205
0.201
0.190
H.
-7
4
0.206
0.206
0.205
0.206
0.211
0.203
.*.
5
0.192
0.189
0.1%
0.193
0.1%
0.202
l
6
0.173
0.177
0.169
0.180
0.189
0.179
0.180
0.177
7
0.149
0.155
0.156
0.147
0.153
0.143
0.162
0.136
0
0.126
0.124
0.134
0.127
0.132
0.138
0.151
0.158
9
0.107
0.101
0.111
0.106
O.ll8
o.ll3
0.132
0.127
10
0.096
0.089
0.102
l
*.
0.112
l
.*
0.092
l
**
l
.*
0.107
l
*.
.H
l
..
...
.*a
l
..
11
0.087
0.071
12
0.064
...
I
I
0
IPCI
l
.*
.**
I
...
I
l
I
..
I
I
*.
l
.*
I
o-5 0
P(3)
0 T
E
2 I)
C
Fig. 4. A plot of collision-broadened half-widths against pressure for three rotational lines of the H3%JIO-5 band. The solid line is a least-squares tit of the corresponding data points, constrained to go through the origin.
316 7
13 -
.2 -
).I -
Ok 0
400
600
600
1000
P t TORR )
Fii. 5. A plot of collision-broadened half-widths against pressure for three rotational lines of the H’5CIO-6 band. The solid line is a least-squares fit of the corresponding data points, constrained to go through the origin.
.24 A
20
AA l
.QtP
.I6 .I2 i AOOdb* .201 A* .I6 .I2
.20
pbA4 A’
.I6 .I2 f
4 .I6
A
.20 F
06 -6
-6
-4
-2
0
2
4
6
6
IO
12
m Fig. 6. A plot of the pressure-broadening coefficients for the vibrational bands o-4,0-5,0-6, and O-7.
Pressure broadening in the H”CI and H”CI overtone bands
317
because of the predominant contribution of near-resonant collisions of the form HCI(J) + HCl(J ? 1) = HCl(J + 1) + HCU).
(1)
Because the probability of finding suitable partners for this type of collision is controlled by the Boltzmann distribution and the degeneracy of the rotational states, pressure broadening peaks in the same way. As we go to higher overtone bands, our data show that this maximum value of pressure broadening diminishes and the shape of the curve becomes flatter. Also, the P and R-branches become noticeably asymmetric, with the peak of the P-branch being higher. A full analysis of these data, utilizing the inversion procedure of Refs. 2-4, is in progress. However, in view of the cited variations in pressure broadening, we can discuss what qualitative mechanistic changes in rotational interactions may be taking place as HCI becomes more excited vibrationally. These effects are most likely attributable to a change in the contributions of near resonant collisions to the pressure-broadened half width relative to other processes, such as off-resonant rotation-rotation, rotation-translation or elastic reorientation collisions. This result is to be expected since, as we go to higher overtone transitions, the energy defect of near-resonant collisions increases because of a change in the rotational spacing with vibrational level. In the pure rotational tL0 band spectrum, both the upper and lower states of the transition are in the ground vibrational state and all collisions of the kind described by Eq. (1) have exactly zero energy defect. In any other band, collisions of that type between upper state and ground state molecules are no longer exactly resonant. This effect can be appreciable in view of the fact that the B value of HCI changes from 10.44 in the ground state to 8.33 in the V = 7 state. A diminished contribution of near-resonant collisions results in a smaller peak value for the pressure-broadening coefficient. This fact could result in a flattening of the curve because the other types of collisions produce an m dependence for pressure broadening that is not sharply peaked in the same way as the near-resonant contribution. The asymmetries in the P- and R-branches are similar to that reported for the first and second overtones in HF.” This result is produced by the differences between the upper and lower states of the P- and R-branch transitions with corresponding m and their effect on the contributions of near-resonant collisions. The lower .I state of a P-branch transition is one higher than the lower state of the corresponding R-branch transition. The upper J-state of a P-branch transition is one lower than that of the corresponding R-branch transition. Thus, a molecule in these particular states will see collision partners from a different portion of the Boltzmann distribution. Since the J-state differences are opposite in the upper and lower states of the transitions, the asymmetries will cancel exactly if the cross sections contributing to the linewidths are equal for the same J-states of the upper and lower vibrational state. The asymmetry is indicative of a change in processes for which there must be a dependence of the cross section on the J-state of the collision partner. In this way, molecules interacting with different portions of the Boltzmann distribution will contribute differently to the linewidth. A full inversion procedure of the kind described in Refs. 24 is required in order to ascertain which particular processes are responsible for the trends observed here. This analysis is in progress and will be reported in a future publication.i6 Acknowledgements-We wish to thank Dr. James Brault and Mr. Roger Jakoubek for helpful discussions and assistance in recording and transforming the spectra at the Kitt Peak National Observatory. This work was supported by ONR, NSF, and an unrestricted research grant from the Exxon Research and Engineering Corporation. REFERENCES H. Rabitz, Ann. Rev. Phys. Chem. 25, I55 (1974). A. DePristo and H. Rabitz, J. Chem. Phys. 68, 1981(1978). A. DePristo and H. Rabitz, JQSRT 22,65 (1979). A. DePristo, J. Chem. Phys. in press (1980). A. Rosenberg, A. Lightman, and A. Ben-Reuven, JQSRT 12,219 (1972). W. Benedict, R. Herman, G. Moore, and S. Silverman, Can. .I. Phys. 34, 850 (1956). H. Babrov, G. Ameer and W. Benesch, J. Chem. Phys. 33, 145 (1960). 8. H. Goldring and W. Benesch, Can. 1. Phys. 40, 1801(l%2). 9. J. Jaffee, S. Kimel, and M. Hirschfeld, Can. J. Phys. 48, 113(1%2). IO. R. Toth, R. Hunt and E. Plyer, 1. Molec. Spectrosc. 35, II0 (1970). 11. J. Brault and 0. White, Astron. Asfrophys. 13, 169(1971). 12. J. BelBruno, M. Zughul, J. Gelfand, and H. Rabitz, J. Molec. Spectrosc., submitted (1980). 13. International Mathematical and Statistical Library, Houston, Texas, Program ZXSSQ. 14. J. Gelfand, M. Zughul, H. Rabitz, and C. J. Han, JQSRT submitted, (1980). 15. R. Spellicy, R. Meredith, and F. Smith, J. Chem. Phys. 57,5119 (1972). 16. A. E. DePristo, J. BelBmno, J. Gelfand, and H. Rabitz, .I. Chem. Phys. in press (1980). I. 2. 3. 4. 5. 6. 7.