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Line mixing effects in Q-branches of CO2 in helium near 4.7 μm: a further test of the ECS formalism
J. Quanr. Spectrosc.
Radiat.
Pergamon PII: SOO22-4073(%)00152-5
Vol. 57. No. 4. pp. 519-524. 1997 k? 1997Elsevier Science Ltd Printed in GreayBritain. All rights reserved 0022-4073/97 $17.00+ 0.00 Transfer
LINE MIXING EFFECTS IN Q-BRANCHES OF COz IN HELIUM NEAR 4.7 pm: A FURTHER TEST OF THE ECS FORMALISM J. BOISSOLES,”
F. THIBAULT,“_F F. RACHET,” and C. BOULETh
A. VALENTIN,’
“Unit6 Mixte de Recherche PALMS (Physique des Atomes, Lasers, Mokcules et Surfaces), UniversitC de Rennes I, Campus de Beaulieu, 35042 Rennes Cedex and “Laboratoire de Physique Moliculaire et Applications, UPR 136 du CNRS (Laboratoire associt aux Universittk Paris-Sud et P. et M. Curie), Tour 13, Bte 76, 4 Place Jussieu, 75252 Paris Cedex 05, France (Received 3 June 1996)
Abstract-We present experimental and theoretical results for the Q-branches of the (12201+-01101) and (20001~01101) bands of ‘Y 1602 lying near 4.7 pm perturbed by He. Measurements were carried out with the LPMA Fourier transform interferometer at room temperature and for atmospheric helium pressures. Computations, within the framework of the impact approximation, take into account line mixing effects. The relaxation matrix is modelled with the Energy Corrected Sudden (ECS) approximation derived from the Infinite Order Sudden (10s) formalism proposed by Green [J. Chem. Phys. 90, 3603 (1989)] which is valid for all type of vibrational band. Strong deviations from the sum of the Lorentz shape are observed in the experimental spectra. The ECS calculations account for these experiments quite satisfactorily. 0 1997 Elsevier Science Ltd
1. INTRODUCTION It is well known that a rigorous treatment of vibration-rotation spectral line shapes must include interference or line mixing effects caused by the overlapping of lines.’ Among the different spectral components, the Q-branches are particularly sensitive to mixing effects. Starting from the formalism proposed by Green’ and based on the infinite order sudden approximation, we have proposed recently3 an improved model, based on the energy corrected sudden approximation, which allows the calculation of all types of coupling cross-sections, i.e., for stretching as well as bending bands of CO2 starting from a single set of basic rates. Predictions of that model with various experiments made on stretching bands had been shown to be rather successful.“’ The same ECS formalism was also tested for various Q-branch shapes of bending modes near 15 pm: the O1’O-OO”Oband at 667.380 cm-’ (H-Z transition), the 10°W1’O bands at 618.028 cm-’ and 720.804 cm-’ (X-II transitions) and the 1 1’&0220 at 597.538 cm-’ and 741.724 cm-’ (l&A transitions). Results were shown to be also rather good.-‘ It was therefore interesting, as a further test, to investigate the shape of different Q-branches. In the present study we compare the ECS predictions with the shape measured under namely those of the bands located at atmospheric He pressures of two Q-branches, 12201 t01101) and at 2129.756 cm-’ &-II, transitions: 2093.345 cm-’ (A&I” transitions: 20001 t01101). It should be noted from now on that these bands are strongly affected by a Coriolis interaction which transfers intensities from the R branch to the P branch, but does not affect the Q-branch intensities.
tTo whom all correspondence
should be addressed. 519
520
J. Boissoles et al
Since the present study is restricted to perturber pressures high enough to induce mixing of the Q lines but low enough to let the Q-branch relatively well isolated from the P and R branches, it can be reasonably expected that the rigid rotor approximation still remains valid. Experimental details are briefly given in Section 2. Section 3 summarizes the theoretical frame and Section 4 is devoted to the comparison of experimental and theoretical results. 2. EXPERIMENTAL
DETAILS
The spectra have been recorded with the FT spectrometer built in the LPMA (Paris-Jussieu): a short description of this instrument is given in Ref. 9. The chosen experimental conditions are: an absorbing path of 3607 cm in a White-type cell at room temperature. The cell is first filled with CO* at a pressure of 40 torr (measured with a Baratron gauge) and then the perturbing gas is introduced to obtain final pressures up to 1 atm (measured with a U-shaped mercury manometer) and 2.45 atm (measured with a mechanical manometer). Taking into account the spectral width of the fully overlapped Q-branch a sampling distance equal to 0.00603 cm-’ has been used without interpolation procedure. The zero transmission level for each recording is checked using the transmitted level of the saturated Q-branch of the (1 l’O),+OO”O transition centered near 2076 cm-‘. 3. THEORY A detailed description of the ECS formalism exists in the literature.3m8Here we shall only recall the three steps of the theoretical model. (i) The non-diagonal element W, coupling two lines k = u~isiu~$E/and e - uj~s,~vljjsj are expressed through Eq. (4) of Ref. 3. It must be emphasized that the basic adjustable ECS parameter (A, a and e,) have been used in the present calculation without any modification.
I
I
P[CO+Il.5
Torr
P[He]=.95 Atm L3607
cm
(a)
2127
2130 Fig. 1(a>-Caption
opposite.
-
m.
---_
Lor.
2133
cm-1
Line mixing effects in Q-branches of CO2 in He near 4.7 pm
521
384 P[CO2]=40 Ton P[He]=2.4 Atm L=3607 cm
164
fiP*
-- -. .
2127
2133
2130
Lor. E.C.S.
cm-l
Fig. l(b). Fig. 1. n-X Q-branch at 2129.756 cm-‘. Comparison between experimental and computed absorption coefficients: (--) experimental profile, (---) Lorentzian calculations, (0 0 0) ECS predictions. (a) Pat = 0.95 atm, (b) Pat = 2.4 atm. CO lines are also apparent which were used for the calibration of the spectra.
(ii) The diagonal elements, i.e., the pressure broadened linewidths, have been deduced from the sum rule Wkk= -
gw,k.
(1)
/#k k
where dk (respectively do are the dipole reduced matrix elements of transition k s f+-i (respectively / E f ‘ci’) given in the rigid rotor limit by: dk=(-ly
(iii) Finally, the absorption coefficient is given by: a(a) = no%
(1 - exp( -hca/khT))lR,lz~ImCd,
< l’((o - co - iW)-‘lk > dkpk
(3)
k.C
where n, is the CO, density, IRJ* is the square of the vibrational transition dipole moment, pk the population of the initial level of transition k E fci, and (r. the matrix of line wavenumbers.” The elements of the (a - rro - i W)-’ matrices were calculated from the eigenvalues A( and eigenvectors X of (a, + i W) as outlined in Ref. 11. QSRT 57/h-D
522
J. Boissoles et al.
As already mentioned, since we only consider moderate pertuber desities, the Q-branches remain relatively well isolated from the P and R ones. From a practical point of view, this means that the calculation of the eigenvalues and eigenvectors of (a,, + iw) can be undertaken without significant difference by restricting the matrix to the Q-components (no interbranch coupling3). However, it must be emphasized that interbranch coupling can be neglected in the calculation of the eigenvalues and eigenvectors of go + iW, but not in the calculation of the diagonal elements Wkkaccording to Eq. (1). 4. RESULTS
4.1. Z-ll
AND
DISCUSSION
Q-branch at 2129.7.56cm-
Experimental and theoretical absorption coefficients are plotted in Fig. 1 for two typical values of the density. Of course, since the Q components are very closely spaced, the rotational structure in this Q branch is practically washed out and a sum of Lorentzian isolated components does not reproduce at all the observed lineshape. On the opposite, the ECS calculation is in good agreement with experiment, corroborating the assumption of the negligible influence of Coriolis coupling in this domain of perturber pressure. 4.2. d-Xl Q-branch at 2093.345cm-’ Comparison between experimental and theoretical results is shown in Fig. 2 for this Q branch. Here too agreement between ECS theory and experiment is reasonable despite the fact that the rotational structure of this branch is very different from that of the previous one [let us recall that in the present case (due to ez-doubling) the Q-branch is composed of two subbranches which are coupled by collisions3].
8e-4
I .
P[C02]=41 .5 Torr P[He]=.95 Atm L=3807 cm
464
---.
I I
264
.
Lor. E.C.S.
II I I I
2094 Fig. Z(a)-Caption
cm-l opposite.
2097
523
Line mixing effects in Q-branches of CO2 in He near 4.7 pm
I
I P[CO+40
Torr
P[He]=2.4 Atm L=3607 cm
NO
464
-
Exp.
----
Lor.
.
E.C.S.
26-4
Oe+Cl 2092
2094
2096
cm-l
Fig. 2(b). Fig. 2. I&A Q-branch at 2093.345 cm-‘. Comparison between experimental and computed absorption coefficients: (---) experimental profile, (---) Lorentzian calculations, (0 0 0) ECS predictions. (a) PW = 0.95 atm, (b) PH<= 2.4 atm.
5. CONCLUSION
The present work has confirmed the validity of the ECS formalism3 derived from the 10s formalism of Green.’ For the perturber pressures under consideration, the Q-branches are relatively well isolated from the P- and R-branches, and the strong Coriolis interactions which affect these bands leading to a strong decrease of line strengths in the R branch seems to be of minor importance. At higher He densities, as P, Q and R branches overlap, it becomes necessary to include the influence of Coriolis coupling in the calculation of the relaxation matrix as well as in the calculation of the dipole matrix elements. Finally experiments should be carried out at higher perturber densities and it would be highly desirable to develop simultaneously a generalized formalism including the influence of spectroscopic resonances as already mentioned in Ref. 12. REFERENCES I. For a review see for instance: A. Levy, N. Lacome, and C. C. Chackerian Jr, in Collisional Line Mixing in Spectroscopy of the Earth’s Atmosphere and Interstellar Medium, K. N. Rao and A. Weber, eds,
2. 3. 4. 5.
Academic Press, NY (1992); S. Green, Calculation of pressure broadened spectral line shapes including collisional transfer of intensity, in Status and Future Developments in Transport Properties, W. A. Wakeham, ed., Kluwer Academic (1992); C. Boulet and J. Boissoles, in Spectral Line Shapes, A. D. May, J. R. Drummond, and E. Oks, eds, Vol. B, p. 265, 12th ICLS; AIP Press, New York, NY (1995) and references therein. S. Green, J. Chem. Phys. 90, 3603 (1989). J. Boissoles, F. Thibault, and C. Boulet, JQSRT, 56, 835 (1996). F. Thibault, J. Boissoles, R. Le Doucen, V. Menoux, and C. Boulet, J. Chem. Phys. 100, 210 (1994). J. Boissoles, F. Thibault, R. Le Doucen, V. Menoux, and C. Boulet, J. Chem. Phys. 100, 215 (1994).
524
J. Boissoles et al
6. J. Boissoles, F. Thibault, R. Le Doucen, V. Menoux, and C. Boulet, J. Chem. Phys. 101,6552(1994). 7. L. Ozanne, Nguyen-Van-Thanh, C. Brodbeck, J. P. Bouanich, J. M. Hartmann, and C. Boulet, .I. Chem. Phys. 102, 7306 (1995). 8. N. N. Filippov, J. P. Bouanich, J. M. Hartmann, L. Ozanne, C. Boulet, M. V. Tonkov, F. Thibault, and R. Le Doucen, JQSRT 55, 307 (1996). 9. A. Valentin, Spectrochim. Acta SlA, 1127 (1995). 10. L. S. Rothman, R. R. Gamache, R. H. Tipping, C. P. Rinsland, M. A. H. Smith, D. C. Benner, V. Malathy Devi, J. M. Flaud, C. Camy-Peyret, A. Perrin, A. Goldman, S. T. Massie, L. R. Brown, and R. A. Toth, JQSRT 48, 469 (1992). 1I. R. G. Gordon, and R. P. McGinnis, J. Chem. Phys. 49, 2455 (1968); E. W. Smith, J. Chem. Phys. 74, 6658 (1981). 12. A. B. Dokuchaev, A. Yu. Pavlov, E. N. Stroganova, and M. V. Tonkov, Opt. Spectrosc. 60, 585 (1986).
Radiat.
Pergamon PII: SOO22-4073(%)00152-5
Vol. 57. No. 4. pp. 519-524. 1997 k? 1997Elsevier Science Ltd Printed in GreayBritain. All rights reserved 0022-4073/97 $17.00+ 0.00 Transfer
LINE MIXING EFFECTS IN Q-BRANCHES OF COz IN HELIUM NEAR 4.7 pm: A FURTHER TEST OF THE ECS FORMALISM J. BOISSOLES,”
F. THIBAULT,“_F F. RACHET,” and C. BOULETh
A. VALENTIN,’
“Unit6 Mixte de Recherche PALMS (Physique des Atomes, Lasers, Mokcules et Surfaces), UniversitC de Rennes I, Campus de Beaulieu, 35042 Rennes Cedex and “Laboratoire de Physique Moliculaire et Applications, UPR 136 du CNRS (Laboratoire associt aux Universittk Paris-Sud et P. et M. Curie), Tour 13, Bte 76, 4 Place Jussieu, 75252 Paris Cedex 05, France (Received 3 June 1996)
Abstract-We present experimental and theoretical results for the Q-branches of the (12201+-01101) and (20001~01101) bands of ‘Y 1602 lying near 4.7 pm perturbed by He. Measurements were carried out with the LPMA Fourier transform interferometer at room temperature and for atmospheric helium pressures. Computations, within the framework of the impact approximation, take into account line mixing effects. The relaxation matrix is modelled with the Energy Corrected Sudden (ECS) approximation derived from the Infinite Order Sudden (10s) formalism proposed by Green [J. Chem. Phys. 90, 3603 (1989)] which is valid for all type of vibrational band. Strong deviations from the sum of the Lorentz shape are observed in the experimental spectra. The ECS calculations account for these experiments quite satisfactorily. 0 1997 Elsevier Science Ltd
1. INTRODUCTION It is well known that a rigorous treatment of vibration-rotation spectral line shapes must include interference or line mixing effects caused by the overlapping of lines.’ Among the different spectral components, the Q-branches are particularly sensitive to mixing effects. Starting from the formalism proposed by Green’ and based on the infinite order sudden approximation, we have proposed recently3 an improved model, based on the energy corrected sudden approximation, which allows the calculation of all types of coupling cross-sections, i.e., for stretching as well as bending bands of CO2 starting from a single set of basic rates. Predictions of that model with various experiments made on stretching bands had been shown to be rather successful.“’ The same ECS formalism was also tested for various Q-branch shapes of bending modes near 15 pm: the O1’O-OO”Oband at 667.380 cm-’ (H-Z transition), the 10°W1’O bands at 618.028 cm-’ and 720.804 cm-’ (X-II transitions) and the 1 1’&0220 at 597.538 cm-’ and 741.724 cm-’ (l&A transitions). Results were shown to be also rather good.-‘ It was therefore interesting, as a further test, to investigate the shape of different Q-branches. In the present study we compare the ECS predictions with the shape measured under namely those of the bands located at atmospheric He pressures of two Q-branches, 12201 t01101) and at 2129.756 cm-’ &-II, transitions: 2093.345 cm-’ (A&I” transitions: 20001 t01101). It should be noted from now on that these bands are strongly affected by a Coriolis interaction which transfers intensities from the R branch to the P branch, but does not affect the Q-branch intensities.
tTo whom all correspondence
should be addressed. 519
520
J. Boissoles et al
Since the present study is restricted to perturber pressures high enough to induce mixing of the Q lines but low enough to let the Q-branch relatively well isolated from the P and R branches, it can be reasonably expected that the rigid rotor approximation still remains valid. Experimental details are briefly given in Section 2. Section 3 summarizes the theoretical frame and Section 4 is devoted to the comparison of experimental and theoretical results. 2. EXPERIMENTAL
DETAILS
The spectra have been recorded with the FT spectrometer built in the LPMA (Paris-Jussieu): a short description of this instrument is given in Ref. 9. The chosen experimental conditions are: an absorbing path of 3607 cm in a White-type cell at room temperature. The cell is first filled with CO* at a pressure of 40 torr (measured with a Baratron gauge) and then the perturbing gas is introduced to obtain final pressures up to 1 atm (measured with a U-shaped mercury manometer) and 2.45 atm (measured with a mechanical manometer). Taking into account the spectral width of the fully overlapped Q-branch a sampling distance equal to 0.00603 cm-’ has been used without interpolation procedure. The zero transmission level for each recording is checked using the transmitted level of the saturated Q-branch of the (1 l’O),+OO”O transition centered near 2076 cm-‘. 3. THEORY A detailed description of the ECS formalism exists in the literature.3m8Here we shall only recall the three steps of the theoretical model. (i) The non-diagonal element W, coupling two lines k = u~isiu~$E/and e - uj~s,~vljjsj are expressed through Eq. (4) of Ref. 3. It must be emphasized that the basic adjustable ECS parameter (A, a and e,) have been used in the present calculation without any modification.
I
I
P[CO+Il.5
Torr
P[He]=.95 Atm L3607
cm
(a)
2127
2130 Fig. 1(a>-Caption
opposite.
-
m.
---_
Lor.
2133
cm-1
Line mixing effects in Q-branches of CO2 in He near 4.7 pm
521
384 P[CO2]=40 Ton P[He]=2.4 Atm L=3607 cm
164
fiP*
-- -. .
2127
2133
2130
Lor. E.C.S.
cm-l
Fig. l(b). Fig. 1. n-X Q-branch at 2129.756 cm-‘. Comparison between experimental and computed absorption coefficients: (--) experimental profile, (---) Lorentzian calculations, (0 0 0) ECS predictions. (a) Pat = 0.95 atm, (b) Pat = 2.4 atm. CO lines are also apparent which were used for the calibration of the spectra.
(ii) The diagonal elements, i.e., the pressure broadened linewidths, have been deduced from the sum rule Wkk= -
gw,k.
(1)
/#k k
where dk (respectively do are the dipole reduced matrix elements of transition k s f+-i (respectively / E f ‘ci’) given in the rigid rotor limit by: dk=(-ly
(iii) Finally, the absorption coefficient is given by: a(a) = no%
(1 - exp( -hca/khT))lR,lz~ImCd,
< l’((o - co - iW)-‘lk > dkpk
(3)
k.C
where n, is the CO, density, IRJ* is the square of the vibrational transition dipole moment, pk the population of the initial level of transition k E fci, and (r. the matrix of line wavenumbers.” The elements of the (a - rro - i W)-’ matrices were calculated from the eigenvalues A( and eigenvectors X of (a, + i W) as outlined in Ref. 11. QSRT 57/h-D
522
J. Boissoles et al.
As already mentioned, since we only consider moderate pertuber desities, the Q-branches remain relatively well isolated from the P and R ones. From a practical point of view, this means that the calculation of the eigenvalues and eigenvectors of (a,, + iw) can be undertaken without significant difference by restricting the matrix to the Q-components (no interbranch coupling3). However, it must be emphasized that interbranch coupling can be neglected in the calculation of the eigenvalues and eigenvectors of go + iW, but not in the calculation of the diagonal elements Wkkaccording to Eq. (1). 4. RESULTS
4.1. Z-ll
AND
DISCUSSION
Q-branch at 2129.7.56cm-
Experimental and theoretical absorption coefficients are plotted in Fig. 1 for two typical values of the density. Of course, since the Q components are very closely spaced, the rotational structure in this Q branch is practically washed out and a sum of Lorentzian isolated components does not reproduce at all the observed lineshape. On the opposite, the ECS calculation is in good agreement with experiment, corroborating the assumption of the negligible influence of Coriolis coupling in this domain of perturber pressure. 4.2. d-Xl Q-branch at 2093.345cm-’ Comparison between experimental and theoretical results is shown in Fig. 2 for this Q branch. Here too agreement between ECS theory and experiment is reasonable despite the fact that the rotational structure of this branch is very different from that of the previous one [let us recall that in the present case (due to ez-doubling) the Q-branch is composed of two subbranches which are coupled by collisions3].
8e-4
I .
P[C02]=41 .5 Torr P[He]=.95 Atm L=3807 cm
464
---.
I I
264
.
Lor. E.C.S.
II I I I
2094 Fig. Z(a)-Caption
cm-l opposite.
2097
523
Line mixing effects in Q-branches of CO2 in He near 4.7 pm
I
I P[CO+40
Torr
P[He]=2.4 Atm L=3607 cm
NO
464
-
Exp.
----
Lor.
.
E.C.S.
26-4
Oe+Cl 2092
2094
2096
cm-l
Fig. 2(b). Fig. 2. I&A Q-branch at 2093.345 cm-‘. Comparison between experimental and computed absorption coefficients: (---) experimental profile, (---) Lorentzian calculations, (0 0 0) ECS predictions. (a) PW = 0.95 atm, (b) PH<= 2.4 atm.
5. CONCLUSION
The present work has confirmed the validity of the ECS formalism3 derived from the 10s formalism of Green.’ For the perturber pressures under consideration, the Q-branches are relatively well isolated from the P- and R-branches, and the strong Coriolis interactions which affect these bands leading to a strong decrease of line strengths in the R branch seems to be of minor importance. At higher He densities, as P, Q and R branches overlap, it becomes necessary to include the influence of Coriolis coupling in the calculation of the relaxation matrix as well as in the calculation of the dipole matrix elements. Finally experiments should be carried out at higher perturber densities and it would be highly desirable to develop simultaneously a generalized formalism including the influence of spectroscopic resonances as already mentioned in Ref. 12. REFERENCES I. For a review see for instance: A. Levy, N. Lacome, and C. C. Chackerian Jr, in Collisional Line Mixing in Spectroscopy of the Earth’s Atmosphere and Interstellar Medium, K. N. Rao and A. Weber, eds,
2. 3. 4. 5.
Academic Press, NY (1992); S. Green, Calculation of pressure broadened spectral line shapes including collisional transfer of intensity, in Status and Future Developments in Transport Properties, W. A. Wakeham, ed., Kluwer Academic (1992); C. Boulet and J. Boissoles, in Spectral Line Shapes, A. D. May, J. R. Drummond, and E. Oks, eds, Vol. B, p. 265, 12th ICLS; AIP Press, New York, NY (1995) and references therein. S. Green, J. Chem. Phys. 90, 3603 (1989). J. Boissoles, F. Thibault, and C. Boulet, JQSRT, 56, 835 (1996). F. Thibault, J. Boissoles, R. Le Doucen, V. Menoux, and C. Boulet, J. Chem. Phys. 100, 210 (1994). J. Boissoles, F. Thibault, R. Le Doucen, V. Menoux, and C. Boulet, J. Chem. Phys. 100, 215 (1994).
524
J. Boissoles et al
6. J. Boissoles, F. Thibault, R. Le Doucen, V. Menoux, and C. Boulet, J. Chem. Phys. 101,6552(1994). 7. L. Ozanne, Nguyen-Van-Thanh, C. Brodbeck, J. P. Bouanich, J. M. Hartmann, and C. Boulet, .I. Chem. Phys. 102, 7306 (1995). 8. N. N. Filippov, J. P. Bouanich, J. M. Hartmann, L. Ozanne, C. Boulet, M. V. Tonkov, F. Thibault, and R. Le Doucen, JQSRT 55, 307 (1996). 9. A. Valentin, Spectrochim. Acta SlA, 1127 (1995). 10. L. S. Rothman, R. R. Gamache, R. H. Tipping, C. P. Rinsland, M. A. H. Smith, D. C. Benner, V. Malathy Devi, J. M. Flaud, C. Camy-Peyret, A. Perrin, A. Goldman, S. T. Massie, L. R. Brown, and R. A. Toth, JQSRT 48, 469 (1992). 1I. R. G. Gordon, and R. P. McGinnis, J. Chem. Phys. 49, 2455 (1968); E. W. Smith, J. Chem. Phys. 74, 6658 (1981). 12. A. B. Dokuchaev, A. Yu. Pavlov, E. N. Stroganova, and M. V. Tonkov, Opt. Spectrosc. 60, 585 (1986).