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High-Sensitivity Overtone Spectroscopy of Carbon Disulfide CS2
JOURNAL OF MOLECULAR SPECTROSCOPY ARTICLE NO.
180, 81–84 (1996)
0226
High-Sensitivity Overtone Spectroscopy of Carbon Disulfide CS2 T. Platz, M. Matheis, Ch. Hornberger, and W. Demtro¨der Fachbereich Physik, Universita¨t Kaiserslautern, D-67663 Kaiserslautern, Germany Received February 29, 1996; in revised form June 10, 1996
With opto-acoustic spectroscopy in a multipass cell, using a NaCl color center laser around 6500 cm 01 , weak overtone transitions in the ( 30 03 ) R ( 00 00 ) band of 12C 32S2 could be detected. The analysis of the band, based on the extrapolation of molecular constants from the literature, revealed Fermi resonances between the levels of a Fermi polyad. q 1996 Academic Press, Inc.
acoustic resonator at f Å 210 Hz, which yielded the best signal-to-noise ratio. Since the laser linewidth ( Dn õ 1 MHz ) is very small compared to the width of the absorption lines, the observed linewidth is identical to the convolution of the Doppler profile and pressure-broadened line profile. The CS2 pressure in the cell was about 100 mbar where we observed a linewidth Dnobs ( FWHM ) of the absorption lines of about 700 MHz. Since the Doppler width of CS2 at T Å 300 K is DnD Å 280 MHz in this spectral region, the self-broadened ( or pressure-broadened ) linewidth Dnpr q 2 2 can be estimated from Dnobs Å Dn D / Dn pr to be about 640 MHz. Although the high pressure of 100 mbar in the cell slightly decreased the spectral resolution, the gain in signal-to-noise ratio outweighed by far this loss in spectral resolution. For wavenumber calibration a traveling Michelson interferometer ( 5 ) was used and the absolute wavenumbers could be determined at the beginning and at the end of each 20-GHz spectral scan with an accuracy of 0.002 cm01 . Deviations from a strictly linear scan rate of the laser could be corrected by frequency markers, provided by a Fabry – Perot interferometer with a 375-MHz free spectral range. The calibration was checked with a second opto-acoustic spectrometer which recorded parallel to the first one the well-known overtone lines of C2H2 [ in the ( 1010 00 0 ) R ( 0000 00 0 ) band with an accuracy of better than 3 1 10 04 cm01 ( 6 ) ] . All line profiles are symmetric. With the attainable relatively small signal-tonoise ratio it is possible to determine the line center within better than 0.003 cm01 . Together with the uncertainty of the wavemeter we reach a total accuracy of 0.005 cm01 for the determination of the line positions.
1. INTRODUCTION
Most of the reported investigations on overtone transitions in carbon disulfide CS2 have been performed with Fouriertransform spectroscopy (1) or with a tunable diode laser spectrometer (2). The highest overtone band detected so far was the (00 03) R (00 00) band around 4570 cm01 , which was measured by Blanquet and Walrand (1) with a Fourier spectrometer. For the detection of still higher and accordingly weaker overtones the sensitivity of Fourier-transform spectrometers is generally not sufficient. The high sensitivity of a resonant enhanced opto-acoustic spectrometer with an optical multipass cell, developed in our laboratory (3, 4), enabled us to measure for the first time the rotationally resolved excitation of the 3£1 / 3£3 combination band (30 03) R (00 0 ). 2. EXPERIMENTAL
The homemade single-mode tunable NaCl:OH 0 color center ring laser with a spectral bandwidth Dn õ 1 MHz and an output power of about 500 mW has been already described in ( 3 ) . The laser wavelength can be continuously tuned between 1.5 and 1.66 mm by a three-plate birefringent filter. Single-mode operation is achieved by a tiltable solid e´ talon with a free spectral range of 100 GHz. The laser system is controlled by a computer which ensures the simultaneous tuning of all wavelength determining elements within the laser resonator. The opto-acoustic spectrometer with a Herriot-type optical multipass cell ( L Å 95 cm with 50 reflections ) and a resonance enhanced cylindrical acoustic cell has a very high sensitivity which allows detection of weak absorptions with absorption coefficients down to a Å 2 1 10 09 cm01 ( 3, 4 ) . The incident laser beam is amplitude-modulated by an acousto-optic modulator. The modulation frequency was chosen to coincide with the resonance frequency of the first longitudinal acoustic eigenresonance of the cylindrical
3. RESULTS
A survey spectrum of the (30 03) R (00 00) band is shown in Fig. 1. The P- and R-branches are clearly recognized. The 81 0022-2852/96 $18.00 Copyright q 1996 by Academic Press, Inc. All rights of reproduction in any form reserved.
AID
JMS 7101
/
6t10$$$181
09-13-96 15:15:08
mspas
AP: Mol Spec
82
PLATZ ET AL.
FIG. 1. Survey spectrum of the (30 03) R (00 00) transition in CS2 recorded with a NaCl color center laser and a multipass opto-acoustic cell.
bandhead of the R-branch at about 6466 cm01 is formed by rotational lines with rotational quantum numbers around J Å 40. The assignment of the lines is based on the method of combination differences, where the molecular constants B0 and D0 of the ground state level were taken from heterodyne measurements of Wells et al. (7). The upper state rotational constants B *£ and D *£ and the band origin n0 are obtained from a least-squares fit of all assigned line positions to the formula n(m) Å n0 / (B * / B0 )m / (B * 0 B0 )m2 0 D * [m(m / 1)] 2 / D0[m(m 0 1)] 2
[1]
with m Å J / 1 for R 0 lines and m Å 0J for P 0 lines. Table 1 lists the observed line positions and their differences qto the fit values. The rms standard deviation s Å (1/n) ( ( nobs 0 ncal ) 2 of the differences nobs 0 ncal for all lines included in the fit is 4.5 1 10 03 cm01 . The molecular constants of this band are given in Table 2. From the expression for the vibrational term values
S
T v Å ∑ v i £i / i
1
S
1 di 2
1 £j / dj 2
D
JMS 7101
/
6t10$$$181
09-13-96 15:15:08
/
S
1 2
∑ xij £i / di i£j
D [2]
3
/ y222 ( £2 / 1) / g22l
2
with the molecular constants taken from (2, 8), the band origin of the (30 03) R (00 00) band is obtained at n0 Å 6484.442 cm01 , which is about 22.6 cm01 higher than the experimental value n0 Å 6461.854 cm01 . This discrepancy indicates vibrational pertubations of the upper (30 03) level, which can interact through a Fermi resonance with the nearby (2203) level. The energy difference between these two levels is about 109 cm01 as calculated from Eq. [2]. The (22 03) level itself can furthermore interact with the energetically close (1403) level which in turn is perturbed by the (06 03) level. This shows that for the correct calculation of the perturbed term values the entire Fermi polyad has to be taken into account, which includes the four levels (30 03), (22 03), (14 03), and (06 03). Their unperturbed term values, which form the diagonal elements of the perturbation matrix, are calculated from Eq. [2]. The nondiagonal matrix
Copyright q 1996 by Academic Press, Inc.
AID
D
mspas
AP: Mol Spec
83
OVERTONE SPECTROSCOPY OF CS2
TABLE 1 Observed Wavenumbers (cm01 ) of the (30 03) R (00 00) Transition in CS2
TABLE 2 Constants (cm01 ) for the (30 03) R (00 00) Transition in CS2
* Fixed to the values of Wells et al. (7).
1 W122 Å [ £1 [( £2 / 2) 2 0 l 2 ]] 1 / 2 2
F
1 0
S D G
kq122 1 / l1£1 / l2 ( £2 / 2) / l3 £3 / 2 2
[3]
/ d[J(J / 1) 0 l 2 ] .
With the constants k122 , l1 , l2 , and l3 , given in (2) the following 4 1 4 matrix can be set up, where the values are given in cm01 : 6484, 442
048, 991
0
0
048, 991
6593, 930
079, 377
0
0
079, 377
6719, 624
083, 529
0
0
083, 529
6861, 398
.
The diagonalization of this matrix yields the perturbed vibrational term values of the Fermi polyad with the Fermi interaction taken into account. They are listed in Table 3 and show a remarkable agreement with the measured band origin of the (30 03) band. The difference of 0.07 cm01 is only slightly larger than the experimental uncertainty, which proves the good quality of the parameters taken from (2, 8). Within the tuning range of our color center laser we expected to find also the (22 03) R (00 00) band at n0 Å 6571 cm01 . However, we could not detect this band, probably due to its lower intensity, which might be too low even for the high sensitivity of our opto-acoustic spectrometer.
TABLE 3 Calculated n0 Values of the Polyad with Regard to Fermi Resonance
* Not used in the analysis.
elements »£1 , £ l2 , £3ÉHÉ£1 0 1, ( £2 / 2) l , £3 … for the Fermi interaction between levels ( £1 , £ l2 , £3 ) and ( £1 0 1, ( £2 / 2) l , £3 ) are given in (2, 8). Their explicit form is
Copyright q 1996 by Academic Press, Inc.
AID
JMS 7101
/
6t10$$$181
09-13-96 15:15:08
mspas
AP: Mol Spec
84
PLATZ ET AL.
ACKNOWLEDGMENT We thank the Deutsche Forschungsgemeinschaft for financial support.
REFERENCES 1. G. Blanquet and J. Walrand, J. Mol. Spectrosc. 152, 137–151 (1992). 2. G. Blanquet, E. Baeten, I. Cauuet, J. Walrand, and C. P. Courtoy, J. Mol. Spectrosc. 112, 55–70 (1985).
3. Ch. Hornberger, M. Ko¨nig, S. B. Rai, and W. Demtro¨der, Chem. Phys. 190, 171–177 (1995). 4. Ch. Hornberger, Ph.D. thesis, University of Kaiserslautern, Germany, 1995. 5. R. Castell, W. Demtro¨der, A. Fischer, R. Kullmer, and K. Wickert, Appl. Phys. B 38, 1–10 (1985). 6. Q. Kou, G. Guelachvili, M. A. Temsamani, and M. Herman, Can. J. Phys. 72, 1241–1250 (1994). 7. J. S. Wells, M. Schneider, and A. G. Maki, J. Mol. Spectrosc. 132, 422–428 (1988). 8. P. F. Bernath, M. Dulick, and R. W. Field, J. Mol. Spectrosc. 86, 275– 285 (1981).
Copyright q 1996 by Academic Press, Inc.
AID
JMS 7101
/
6t10$$$181
09-13-96 15:15:08
mspas
AP: Mol Spec
180, 81–84 (1996)
0226
High-Sensitivity Overtone Spectroscopy of Carbon Disulfide CS2 T. Platz, M. Matheis, Ch. Hornberger, and W. Demtro¨der Fachbereich Physik, Universita¨t Kaiserslautern, D-67663 Kaiserslautern, Germany Received February 29, 1996; in revised form June 10, 1996
With opto-acoustic spectroscopy in a multipass cell, using a NaCl color center laser around 6500 cm 01 , weak overtone transitions in the ( 30 03 ) R ( 00 00 ) band of 12C 32S2 could be detected. The analysis of the band, based on the extrapolation of molecular constants from the literature, revealed Fermi resonances between the levels of a Fermi polyad. q 1996 Academic Press, Inc.
acoustic resonator at f Å 210 Hz, which yielded the best signal-to-noise ratio. Since the laser linewidth ( Dn õ 1 MHz ) is very small compared to the width of the absorption lines, the observed linewidth is identical to the convolution of the Doppler profile and pressure-broadened line profile. The CS2 pressure in the cell was about 100 mbar where we observed a linewidth Dnobs ( FWHM ) of the absorption lines of about 700 MHz. Since the Doppler width of CS2 at T Å 300 K is DnD Å 280 MHz in this spectral region, the self-broadened ( or pressure-broadened ) linewidth Dnpr q 2 2 can be estimated from Dnobs Å Dn D / Dn pr to be about 640 MHz. Although the high pressure of 100 mbar in the cell slightly decreased the spectral resolution, the gain in signal-to-noise ratio outweighed by far this loss in spectral resolution. For wavenumber calibration a traveling Michelson interferometer ( 5 ) was used and the absolute wavenumbers could be determined at the beginning and at the end of each 20-GHz spectral scan with an accuracy of 0.002 cm01 . Deviations from a strictly linear scan rate of the laser could be corrected by frequency markers, provided by a Fabry – Perot interferometer with a 375-MHz free spectral range. The calibration was checked with a second opto-acoustic spectrometer which recorded parallel to the first one the well-known overtone lines of C2H2 [ in the ( 1010 00 0 ) R ( 0000 00 0 ) band with an accuracy of better than 3 1 10 04 cm01 ( 6 ) ] . All line profiles are symmetric. With the attainable relatively small signal-tonoise ratio it is possible to determine the line center within better than 0.003 cm01 . Together with the uncertainty of the wavemeter we reach a total accuracy of 0.005 cm01 for the determination of the line positions.
1. INTRODUCTION
Most of the reported investigations on overtone transitions in carbon disulfide CS2 have been performed with Fouriertransform spectroscopy (1) or with a tunable diode laser spectrometer (2). The highest overtone band detected so far was the (00 03) R (00 00) band around 4570 cm01 , which was measured by Blanquet and Walrand (1) with a Fourier spectrometer. For the detection of still higher and accordingly weaker overtones the sensitivity of Fourier-transform spectrometers is generally not sufficient. The high sensitivity of a resonant enhanced opto-acoustic spectrometer with an optical multipass cell, developed in our laboratory (3, 4), enabled us to measure for the first time the rotationally resolved excitation of the 3£1 / 3£3 combination band (30 03) R (00 0 ). 2. EXPERIMENTAL
The homemade single-mode tunable NaCl:OH 0 color center ring laser with a spectral bandwidth Dn õ 1 MHz and an output power of about 500 mW has been already described in ( 3 ) . The laser wavelength can be continuously tuned between 1.5 and 1.66 mm by a three-plate birefringent filter. Single-mode operation is achieved by a tiltable solid e´ talon with a free spectral range of 100 GHz. The laser system is controlled by a computer which ensures the simultaneous tuning of all wavelength determining elements within the laser resonator. The opto-acoustic spectrometer with a Herriot-type optical multipass cell ( L Å 95 cm with 50 reflections ) and a resonance enhanced cylindrical acoustic cell has a very high sensitivity which allows detection of weak absorptions with absorption coefficients down to a Å 2 1 10 09 cm01 ( 3, 4 ) . The incident laser beam is amplitude-modulated by an acousto-optic modulator. The modulation frequency was chosen to coincide with the resonance frequency of the first longitudinal acoustic eigenresonance of the cylindrical
3. RESULTS
A survey spectrum of the (30 03) R (00 00) band is shown in Fig. 1. The P- and R-branches are clearly recognized. The 81 0022-2852/96 $18.00 Copyright q 1996 by Academic Press, Inc. All rights of reproduction in any form reserved.
AID
JMS 7101
/
6t10$$$181
09-13-96 15:15:08
mspas
AP: Mol Spec
82
PLATZ ET AL.
FIG. 1. Survey spectrum of the (30 03) R (00 00) transition in CS2 recorded with a NaCl color center laser and a multipass opto-acoustic cell.
bandhead of the R-branch at about 6466 cm01 is formed by rotational lines with rotational quantum numbers around J Å 40. The assignment of the lines is based on the method of combination differences, where the molecular constants B0 and D0 of the ground state level were taken from heterodyne measurements of Wells et al. (7). The upper state rotational constants B *£ and D *£ and the band origin n0 are obtained from a least-squares fit of all assigned line positions to the formula n(m) Å n0 / (B * / B0 )m / (B * 0 B0 )m2 0 D * [m(m / 1)] 2 / D0[m(m 0 1)] 2
[1]
with m Å J / 1 for R 0 lines and m Å 0J for P 0 lines. Table 1 lists the observed line positions and their differences qto the fit values. The rms standard deviation s Å (1/n) ( ( nobs 0 ncal ) 2 of the differences nobs 0 ncal for all lines included in the fit is 4.5 1 10 03 cm01 . The molecular constants of this band are given in Table 2. From the expression for the vibrational term values
S
T v Å ∑ v i £i / i
1
S
1 di 2
1 £j / dj 2
D
JMS 7101
/
6t10$$$181
09-13-96 15:15:08
/
S
1 2
∑ xij £i / di i£j
D [2]
3
/ y222 ( £2 / 1) / g22l
2
with the molecular constants taken from (2, 8), the band origin of the (30 03) R (00 00) band is obtained at n0 Å 6484.442 cm01 , which is about 22.6 cm01 higher than the experimental value n0 Å 6461.854 cm01 . This discrepancy indicates vibrational pertubations of the upper (30 03) level, which can interact through a Fermi resonance with the nearby (2203) level. The energy difference between these two levels is about 109 cm01 as calculated from Eq. [2]. The (22 03) level itself can furthermore interact with the energetically close (1403) level which in turn is perturbed by the (06 03) level. This shows that for the correct calculation of the perturbed term values the entire Fermi polyad has to be taken into account, which includes the four levels (30 03), (22 03), (14 03), and (06 03). Their unperturbed term values, which form the diagonal elements of the perturbation matrix, are calculated from Eq. [2]. The nondiagonal matrix
Copyright q 1996 by Academic Press, Inc.
AID
D
mspas
AP: Mol Spec
83
OVERTONE SPECTROSCOPY OF CS2
TABLE 1 Observed Wavenumbers (cm01 ) of the (30 03) R (00 00) Transition in CS2
TABLE 2 Constants (cm01 ) for the (30 03) R (00 00) Transition in CS2
* Fixed to the values of Wells et al. (7).
1 W122 Å [ £1 [( £2 / 2) 2 0 l 2 ]] 1 / 2 2
F
1 0
S D G
kq122 1 / l1£1 / l2 ( £2 / 2) / l3 £3 / 2 2
[3]
/ d[J(J / 1) 0 l 2 ] .
With the constants k122 , l1 , l2 , and l3 , given in (2) the following 4 1 4 matrix can be set up, where the values are given in cm01 : 6484, 442
048, 991
0
0
048, 991
6593, 930
079, 377
0
0
079, 377
6719, 624
083, 529
0
0
083, 529
6861, 398
.
The diagonalization of this matrix yields the perturbed vibrational term values of the Fermi polyad with the Fermi interaction taken into account. They are listed in Table 3 and show a remarkable agreement with the measured band origin of the (30 03) band. The difference of 0.07 cm01 is only slightly larger than the experimental uncertainty, which proves the good quality of the parameters taken from (2, 8). Within the tuning range of our color center laser we expected to find also the (22 03) R (00 00) band at n0 Å 6571 cm01 . However, we could not detect this band, probably due to its lower intensity, which might be too low even for the high sensitivity of our opto-acoustic spectrometer.
TABLE 3 Calculated n0 Values of the Polyad with Regard to Fermi Resonance
* Not used in the analysis.
elements »£1 , £ l2 , £3ÉHÉ£1 0 1, ( £2 / 2) l , £3 … for the Fermi interaction between levels ( £1 , £ l2 , £3 ) and ( £1 0 1, ( £2 / 2) l , £3 ) are given in (2, 8). Their explicit form is
Copyright q 1996 by Academic Press, Inc.
AID
JMS 7101
/
6t10$$$181
09-13-96 15:15:08
mspas
AP: Mol Spec
84
PLATZ ET AL.
ACKNOWLEDGMENT We thank the Deutsche Forschungsgemeinschaft for financial support.
REFERENCES 1. G. Blanquet and J. Walrand, J. Mol. Spectrosc. 152, 137–151 (1992). 2. G. Blanquet, E. Baeten, I. Cauuet, J. Walrand, and C. P. Courtoy, J. Mol. Spectrosc. 112, 55–70 (1985).
3. Ch. Hornberger, M. Ko¨nig, S. B. Rai, and W. Demtro¨der, Chem. Phys. 190, 171–177 (1995). 4. Ch. Hornberger, Ph.D. thesis, University of Kaiserslautern, Germany, 1995. 5. R. Castell, W. Demtro¨der, A. Fischer, R. Kullmer, and K. Wickert, Appl. Phys. B 38, 1–10 (1985). 6. Q. Kou, G. Guelachvili, M. A. Temsamani, and M. Herman, Can. J. Phys. 72, 1241–1250 (1994). 7. J. S. Wells, M. Schneider, and A. G. Maki, J. Mol. Spectrosc. 132, 422–428 (1988). 8. P. F. Bernath, M. Dulick, and R. W. Field, J. Mol. Spectrosc. 86, 275– 285 (1981).
Copyright q 1996 by Academic Press, Inc.
AID
JMS 7101
/
6t10$$$181
09-13-96 15:15:08
mspas
AP: Mol Spec