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Calculation of Pressure Broadened Spectral Line Shapes Including Collisional Transfer of Intensity

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Status and Future Developments in the Study of Transport Properties

Part of the book series: NATO ASI Series ((ASIC,volume 361))

Abstract

Spectral line shapes, including widths and shifts of isolated lines and collisional transfer of intensity among overlapping lines, can be described within the impact approximation by generalized (kinetic theory) collision cross sections. Theoretical determination of line shapes thus requires accurate molecular scattering calculations to obtain collisional S-matrices and this, in turn, requires detailed knowledge of the intermolecular forces. Advances in computational abilities now permit rather accurate calculations, at least for some simple systems. This is illustrated by a review of recent studies of broadening and shifting of isolated lines of CO and D2 in He and of HCl in Ar. Line-coupling cross sections, which describe collisional transfer of intensity, have received much less attention although they are quite important for several practical applications and are no more difficult to compute. Recent work for CO in He demonstrates the ability to obtain an accurate theoretical description for both “micro-windows” in the infrared fundamental band and for the Raman Q-branch.

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References

  1. Anderson, P. W. (1949) Pressure broadening in the microwave and infra-red regions, Phys. Rev. 76, 647–661.

    Article  ADS  MATH  Google Scholar 

  2. Baranger, M. (1958) Simplified quantum-mechanical theory of pressure broadening, Phys. Rev. 111, 481–493; Problem of overlapping lines in the theory of pressure broadening, Phys. Rev. 111, 494–504; General impact theory of pressure broadening, Phys. Rev. 112, 855–865.

    Google Scholar 

  3. Green, S. (1985) Calculation of pressure broadening parameters for the CO-He system at low temperatures, J. Chem. Phys. 82, 4548–4550.

    Article  ADS  Google Scholar 

  4. Green, S., Boissoles J., and Boulet, C. (1988) Accurate collision-induced line-coupling parameters for the fundamental band of CO in He: close coupling and coupled states calculations, J. Quant. Spectrosc. Rad. Transf. 39, 33–42.

    Article  ADS  Google Scholar 

  5. Boissoles, J., Boulet, C., Robert, D. and Green, S. (1989) State-to-state rotational phase coherent effect on the vibration-rotation band shape: an accurate quantum calculation for CO-He, J. Chem. Phys. 90, 5392–5398.

    Article  ADS  Google Scholar 

  6. Hurst, W. S., Rosasco, G. J., and Green, S. to be published.

    Google Scholar 

  7. Blackmore, R., Green, S. and Monchick, L. (1988) Polarized D2 Stokes-Raman Q-branch broadened by He: a numerical calculation, J. Chem. Phys. 88, 4113–4119; Green, S., Blackmore, R., and Monchick, L. (1989) Comment on line widths and shifts in the Stokes-Raman Q-branch of D2 in He, J. Chem. Phys. 91, 52–55.

    Google Scholar 

  8. Blackmore, R., Green, S. and Monchick, L. (1989) Dicke narrowing of the polarized Stokes-Raman Q-branch of the v = 0−1 transition of D2 in He, J. Chem. Phys. 91, 3846–3853.

    Article  ADS  Google Scholar 

  9. Green, S. (1990) Theoretical line shapes for rotational spectra of HC1 in Ar, J. Chem. Phys. 92, 4679–4685.

    Article  ADS  Google Scholar 

  10. Fano, U. (1963) Pressure broadening as a prototype of relaxation, Phys. Rev. 131, 259–268.

    Article  ADS  MATH  Google Scholar 

  11. Snider, R. F. (1960) Quantum-mechanical modified Boltzmann equation for degenerate internal states, J. Chem. Phys. 32, 1051–1060.

    Article  MathSciNet  ADS  Google Scholar 

  12. Monchick, L. and Hunter, L. (1986) Diatomic-diatomic molecule collision integrals for pressure broadening and Dicke narrowing: A generalization of Hess’s theory, J. Chem. Phys. 85, 713–718; (1987) Erratum, J. Chem. Phys. 86, 7251; Blackmore, R. (1987) A modified Boltzmann kinetic equation for line shape functions, J. Chem. Phys. 87, 791–800.

    Google Scholar 

  13. Gordon, R. G. (1968) Correlation function for molecular motion, Adv. Mag. Res. 3, 1–42.

    Google Scholar 

  14. Albers, J. and Deutch, J. M. (1973) On the rate equation description of spectral lines, Chem. Phys. 1, 89–98.

    Article  ADS  Google Scholar 

  15. Ben-Reuven, A. (1966) Impact Broadening of Microwave Spectra, Phys. Rev. 145, 7–22.

    Article  ADS  Google Scholar 

  16. Shafer, R. and Gordon, R. G. (1973) Quantum scattering theory of rotational relaxation and spectral line shapes in H2-He gas mixtures, J. Chem. Phys. 58, 5422–5443.

    Article  ADS  Google Scholar 

  17. Ben-Reuven, A. (1975) Spectral line shapes in gases in the binary-collision approximation, Adv. Chem. Phys. 33, 235–293.

    Article  ADS  Google Scholar 

  18. Monchick, L. private communication.

    Google Scholar 

  19. Arthurs, A. M. and Dalgarno, A. (1960) The theory of scattering by a rigid rotor, Proc. Roy. Soc. London A256, 540–551.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  20. Green, S. and Thaddeus, P. (1976) Rotational excitation of carbon monoxide by collisions with He, H and 112 under conditions in interstellar clouds, Astrophys. J. 205, 766–785.

    Article  ADS  Google Scholar 

  21. Nerf, R. B. and Sonnenberg, M. A. (1975) Pressure broadening of the J = 1–0 transition of carbon monoxide, J. Mol. Spectrosc. 58, 474–478.

    Article  ADS  Google Scholar 

  22. Thomas, L. D., Kraemer, W. P. and Diercksen, G. H. F. (1980) Rotational excitation of CO by He impact, Chem. Phys. 51, 131–139.

    Article  Google Scholar 

  23. Green, S. and Thomas, L. D. (1980) On the use of pressure broadening data to assess the accuracy of CO-He interaction potentials, J. Chem. Phys. 73, 5391–5393.

    Article  ADS  Google Scholar 

  24. Willey, D. R., Crownover, R. L., Bittner, D. N. and DeLucia, F. C. (1988) Very low temperature spectroscopy: the pressure broadening coefficients for CO—He between 4.3 and 1.7 K, J. Chem. Phys. 89, 1923–1928; Willey, D. R., Goyette, T. M., Ebenstein, W. L., Bittner, D. N. and DeLucia, F.C. (1989) Collisionally cooled spectroscopy: pressure broadening below 5 K, J. Chem. Phys. 91, 122–125.

    Google Scholar 

  25. Palma, A. and Green, S. (1986) Effect of the potential well on low temperature pressure broadening in CO-He, J. Chem. Phys. 85, 1333–1335.

    Article  ADS  Google Scholar 

  26. Green, S. (1979) Vibrational dependence of pressure induced spectral linewidths and lineshifts: application of the infinite-order sudden approximation, J. Chem. Phys. 70, 4686–4693.

    Article  ADS  Google Scholar 

  27. Bel-Bruno, J. J., Gelfand, J., Radigan, W. and Verges, K. (1982) Helium and self-broadening in the first and second overtone bands of 12C 160, J. Mol. Spectrosc. 94 336–342.

    Article  ADS  Google Scholar 

  28. Green, S., Monchick, L., Goldflam, R. and Kouri, D. J. (1977) Computational tests of angular momentum decoupling approximations for pressure broadening cross sections, J. Chem. Phys. 66, 1409–1412.

    Article  ADS  Google Scholar 

  29. Green, S. unpublished results; cf. Ref. [4]

    Google Scholar 

  30. Meyer, W., Hariharan, P. C. and Kutzelnigg, W. (1980) Refined ab initio calculation of the potential energy surface of the He-H2 interaction with special emphasis to the region of the Van der Waals minimum, J. Chem. Phys. 73, 1880–1897.

    Article  ADS  Google Scholar 

  31. Smyth, K. C., Rosasco, G. J. and Hurst, W.S. (1987) Measurement and rate law analysis of D2 Q-branch line broadening coefficients for collisions with D2, He, Ar, H2 and CH4, J. Chem. Phys. 87, 1001–1011; Rosasco, G. J. and Hurst, W. S. private communication.

    Google Scholar 

  32. Hutson, J. M. (1988) The intermolecular potential of Ar-HC1: determination from high-resolution spectroscopy, J. Chem. Phys. 89, 4550–4557.

    Article  ADS  Google Scholar 

  33. Hutson, J. M. and Howard, B.J. (1981) The intermolecular potential energy surface for Ar—HC1, Molec. Phys. 43, 493–516; Hutson, J. M. and Howard, B. J. (1982) Anisotropic intermolecular forces I. Rare gas-hydrogen chloride systems, Molec. Phys. 45, 769–790.

    Google Scholar 

  34. Green, S. (1990) Raman Q-branch line shapes as a test of the H2-Ar intermolecular potential, J. Chem. Phys. 93, 1496–1501.

    Article  ADS  Google Scholar 

  35. Green, S., DeFrees, D. J. and McLean, A. D. (1991) Calculations of H2O microwave line broadening in collisions with He atoms: sensitivity to potential energy surfaces, J. Chem. Phys. 94, 1346–1359.

    Article  ADS  Google Scholar 

  36. Green, S. (1991) Pressure broadening data as a test of a recently proposed Ar—H2O interaction potential, J. Chem. Phys. 95, 3888–3890.

    Article  ADS  Google Scholar 

  37. DeLucia, F. C. and Green, S. (1988) Recent advances in pressure broadening experiment and theory, J. Mol. Struct. 190, 435.

    Article  ADS  Google Scholar 

  38. Millot, G. (1990) Rotationally inelastic rates over a wide temperature range based on an energy corrected sudden-exponential-power theoretical analysis of Raman line broadening coefficients and Q branch collapse, J. Chem. Phys. 93 8001–8010.

    Article  ADS  Google Scholar 

  39. Green, S. (1989) Pressure broadening and line coupling in bending bands of CO2, J. Chem. Phys. 90, 3603–3614.

    Article  ADS  Google Scholar 

  40. Gordon, R. G. and McGinnis, R. P. (1971) Intermolecular potentials and infrared spectra, J. Chem. Phys. 55, 4898–4906.

    Article  ADS  Google Scholar 

  41. Lam, K. S. (1977) Application of pressure broadening theory to the calculation of atmospheric oxygen and water vapor microwave absorption, J. Quant. Spectrosc. Rad. Transf. 17, 351–383.

    Article  ADS  Google Scholar 

  42. Smith, E. W. (1981) Absorption and dispersion in the 02 microwave spectrum at atmospheric pressures, J. Chem. Phys. 74, 6658–6673.

    Article  ADS  Google Scholar 

  43. Braun, C. (1982) Calculation of the absorption coefficient of the 15 micron v2 band of CO2 using the theory of overlapping lines, J. Mol. Spectrosc. 93, 1–15.

    Article  ADS  Google Scholar 

  44. Gordon, R. G. and McGinnis, R. P. (1968) Line shapes in molecular spectra, J. Chem. Phys. 49, 2455–2456.

    Article  ADS  Google Scholar 

  45. Rosenkranz, P. W. (1975) Shape of the 5mm oxygen band in the atmosphere, IEEE Trans. Antennas Propag. 23, 498–506.

    Article  ADS  Google Scholar 

  46. Brunner, T. A. and Pritchard, D. (1982) Fitting laws for rotationally inelastic collisions, in `Dynamics of the Excited State’, K. P. Lawley (ed.), Wiley, New York, 589–641.

    Google Scholar 

  47. Goldflam, R. Green, S. and Kouri, D. J. (1977) Infinite-order sudden approximation for rotational energy transfer in gaseous mixtures,J. Chem. Phys. 67 4149–4161.

    Article  ADS  Google Scholar 

  48. Sitz, G. O. and Farrow, R. L. (1990) Pump-probe measurements of state-to-state rotational energy transfer rates in N2 (y = 1), J. Chem. Phys. 93, 7883–7893.

    Article  ADS  Google Scholar 

  49. Strow, L. L. and Gentry, B. M. (1986) Rotational collisional narrowing in an infrared CO2 Q branch studied with a tunable-diode laser,J. Chem. Phys. 84 1149–1156; Gentry, B. and Strow, L. L. (1987) Line mixing in a N2-broadened CO2 Q branch observed with a tunable diode laser,J. Chem. Phys. 86 57225730.

    Google Scholar 

  50. Bulanin, M. O., Dokuchaev, A. B., Tonkov, M. V. and Filippov, N. N. (1984) Influence of line interference on the vibration-rotation band shape, J. Quant. Spectrosc. Rad. Transf. 31, 521–543.

    Article  ADS  Google Scholar 

  51. Cousin, C., LeDoucen, R., Boulet, C., Henry, A. and Robert, D. (1986) Line coupling in the temperature and frequency dependences of absorption in the microwindows of the 4.3 micron CO2 band, J. Quant. Spectrosc. Rad. Transf. 36, 521–538.

    Article  ADS  Google Scholar 

  52. Boissoles, J., Boulet, C., Robert, D. and Green, S. (1987) IOS and ECS line coupling calculation for the CO-He system: influence on the vibration-rotation band shapes, J. Chem. Phys. 87, 3436–3446.

    Article  ADS  Google Scholar 

  53. Banks, A. J. and Clary, D. C. (1987) Coupled states calculations on vibrational relaxation in He + CO2 (0110) and He + CO, J. Chem. Phys. 86, 802–812.

    Article  ADS  Google Scholar 

  54. Clary, D.C. (1982) Ab initio computation of vibrational relaxation rate coefficients for the collisions of CO2 with helium and neon atoms, Chem. Phys. 65, 247–257.

    Article  ADS  Google Scholar 

  55. Strow, L. L. and Green, S. unpublished results.

    Google Scholar 

  56. Ma, Q. and Tipping, R. H. (1990) Water vapor continuum in the millimeter spectral region, J. Chem. Phys. 93, 6127–6139; Ma, Q. and Tipping, R. H. (1990) The atmospheric water continuum in the infrared: extension of the statistical theory of Rosenkranz, J. Chem. Phys. 93, 7066–7075.

    Google Scholar 

  57. Boulet, C., Boissoles, J. and Robert, D. (1988) Collisionally-induced population transfer effect in infrared absorption spectra. I. A line-by-line coupling theory from resonances to the far wings, J. Chem. Phys. 89, 625–634; Boissoles, J., Menoux, V., LeDoucen, R., Boulet, C. and Robert, D. (1989) Collisionallyinduced population transfer effect in infrared absorption spectra. II. The wing of the Ar broadened v 3 band of CO2, J. Chem. Phys. 91, 2163–2171; Bois-soles, J., Boulet, C., Hartmann, J. M., Perrin, M. Y. and Robert, D. (1990) Collision-induced population transfer in infrared absorption spectra. III. Temperature dependence of absorption in the Ar—broadened wing of the CO2 v3 band, J. Chem. Phys. 93, 2217–2221.

    Google Scholar 

  58. Farrow, R. L., Rahn, L. A., Sitz, G. O. and Rosasco, G. J. (1989) Observation of a speed-dependent collisional inhomogeneity in H2 vibrational line profiles, Phys. Rev. Lett. 63, 746–749.

    Article  ADS  Google Scholar 

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Green, S. (1992). Calculation of Pressure Broadened Spectral Line Shapes Including Collisional Transfer of Intensity. In: Wakeham, W.A., Dickinson, A.S., McCourt, F.R.W., Vesovic, V. (eds) Status and Future Developments in the Study of Transport Properties. NATO ASI Series, vol 361. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-3076-1_12

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  • DOI: https://doi.org/10.1007/978-94-017-3076-1_12

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