1. Pressure-broadening of water lines in the THz frequency region: improvements and confirmations for spectroscopic databases G. Cazzoli, C. Puzzarini Dipartimento di Chimica “G. Ciamician”, Università di Bologna G. Buffa G. Buffa IPCF-CNR and Dipartimento di Fisica "E. Fermi", Pisa 10th International HITRAN Conference — 22-24 June, 2008

2. OUTLINES 1) Experimental set-up: The THz spectrometer The THz spectrometer 2) Theoretical calculations: The semiclassical approach The semiclassical approach 1) Experimental details: The THz spectrometer The THz spectrometer 2) Theoretical calculations: The semiclassical approach The semiclassical approach 3) Experiment & Theory: Results Results 3) Experiment & Theory: Results Results

3. 1) Experimental details: The THz spectrometer The THz spectrometer - set up - set up - techniques - techniques - procedure - procedure 1) Experimental details: The THz spectrometer The THz spectrometer - set up - set up - techniques - techniques - procedure - procedure

4. FREQUENCY RANGE covered @ LMSB (2) 50-600 GHz (from fundamental to the 6th harmonic) + 600-800 GHz (8th harmonic) + 600-800 GHz (8th harmonic) (3) 1.0-1.2 THz (9th harmonic) + 1.33-1.6 THz (12th harmonic) + 1.33-1.6 THz (12th harmonic) (1) 8-120 GHz (wave-guide Stark cell – P band) (3) 1.0-1.2 THz (9th harmonic) + 1.33-1.6 THz (12th harmonic) + 1.33-1.6 THz (12th harmonic)

5. BLOCK DIAGRAM of the 1.0-1-6 THz SPECTROMETER MULTIPLIER SYNTH 10 kHz-1 GHz MULT fSfS nfSnfS MIX MULT SYNCR ref: 20 MHz RF OSCILL 3.7- 7.6 GHz f RF 20 MHz 73 MHz |f G - mf RF | GUNN P. SUPPLY and SYNCR ref: 73 MHz |f RF - nf S | HP8642A SYNTH MIX corr fGfG Ge DETECTOR PREAMPL 10 MHz freq. standard ref GUNN DIODES CELL FUNCTION GENERATOR 300 Hz CHOPPER LOCK-IN AMPLIFIER  FREQUENCY MODULATION TECHNIQUE 2x frequency modualtion

6. BLOCK DIAGRAM of the 1.0-1-6 THz SPECTROMETER MULTIPLIER SYNTH 10 kHz-1 GHz MULT fSfS nfSnfS MIX MULT SYNCR ref: 20 MHz RF OSCILL 3.7- 7.6 GHz f RF 20 MHz 73 MHz |f G - mf RF | GUNN P. SUPPLY and SYNCR ref: 73 MHz |f RF - nf S | HP8642A SYNTH MIX corr fGfG Ge DETECTOR PREAMPL 10 MHz freq. standard ref GUNN DIODES CELL FUNCTION GENERATOR 300 Hz CHOPPER LOCK-IN AMPLIFIER  AMPLITUDE MODULATION TECHNIQUE chopper frequency revolution

7. (3) EXPERIMENTAL SET-UP in the THz REGION Quartz cell (1cm long)THz scource (gunn + multiplier) Chopper Bolometer The 1.0-1.6 THz SPECTROMETER

8. (3) EXPERIMENTAL SET-UP in the THz REGION The 1.0-1.2 THz SPECTROMETER THz scource Cell

9. 1) Experimental details: The THz spectrometer The THz spectrometer - set up - set up - techniques - techniques - procedure - procedure 1) Experimental details: The THz spectrometer The THz spectrometer - set up - set up - techniques - techniques - procedure - procedure

10. AMPLITUDE MODULATION TECHNIQUE Natural line profile Lambert-Beer law I = I 0 exp[  ( - 0 )L]

11. LINE SHAPE ANALYSIS To retrieve COLLISIONAL HALF-WIDTH  L : by fitting the observed line profiles – natural line profiles - directly to the chosen line profile model (Voigt profile, Galatry profile, Speed Dependent Voigt profile, … …) Residuals: Residuals: Obs. – Calc.

12. SOURCE MODULATION TECHNIQUE FREQUENCY MODULATION (sine wave): (t) = ( - 0 ) +  cos  m t (t) = ( - 0 ) +  cos  m t  = modulation depth  = modulation depth  m = modulation frequency K(x, y, z) = Voigt, Galatry or SP-Voigt or … function Line profile expanded in a cosine Fourier series. 2nd harmonic detection: 2nd harmonic detection: a 2 (  ) = 2/   K(x,y,z) cos 2  d  a 2 (  ) = 2/   K(x,y,z) cos 2  d  0 Validity: Absorption  6% I = I 0 [1-  ( - 0 )L]

13. LINE SHAPE ANALYSIS COLLISIONAL HALF-WIDTH  L : by fitting the observed line profiles to a model that explicitly accounts for frequency modulation [Cazzoli & Dore JMS 141, 49 (1990); Dore JMS 221, 93 (2003)]. Residuals: Residuals: Obs. – Calc.

14. 1) Experimental details: The THz spectrometer The THz spectrometer - set up - set up - techniques - techniques - procedure - procedure 1) Experimental details: The THz spectrometer The THz spectrometer - set up - set up - techniques - techniques - procedure - procedure

15. LINE SHAPE ANALYSIS: Which line profile model? Voigt profile Galatry profile The 301.8 GHz line of O 3 broadened by N 2 LINE SHAPE ANALYSIS: Which line profile model?

16. Galatry vs Speed-dependent Voigt profile

17. RETRIEVAL PARAMETERS PRESSURE BROADENING COEFFICIENT  : PRESSURE BROADENING COEFFICIENT  : linear fit of  L against P by a weighted linear fit of  L against P  perturb 0000  L =  0 +  perturb  P perturb Lorentzian halfwidth Broadening due to absorber

18. RETRIEVAL PARAMETERS PRESSURE SHIFT COEFFICIENT s : PRESSURE SHIFT COEFFICIENT s : linear fit of against P by a weighted linear fit of against P = 0 + s perturb  P perturb = 0 + s perturb  P perturb Transition frequency Frequency at P pertub = 0 s 0

19. 2) Theoretical calculations: The semiclassical approach The semiclassical approach 2) Theoretical calculations: The semiclassical approach The semiclassical approach

20. THEORETICAL DETAILS COLLISIONAL RELAXATION EFFICIENCY FUNCTION P COLLISIONAL RELAXATION described within the IMPACT APPROXIMATION by the EFFICIENCY FUNCTION P. P For a line i  f P = 1 - S = scattering matrix, H 0 = Hamiltonian of internal degrees, V = collisional interaction, O = time ordering operator. SEMICLASSICAL APPROXIMATIONb SEMICLASSICAL APPROXIMATION (impact parameter b, relative velocity v, internal state of perturber r): P = P(b,v,r) P = P(b,v,r). linewidth  lineshift s P The linewidth  and lineshift s : real and imaginary parts of P:  r = population of level r, f(v) = Maxwellian velocity distribution, n = perturber density.

21. 3) Experiment & Theory: Results Results - H 2 O: which lines - H 2 O: which lines - theo & exp results: - theo & exp results: detailed comparison detailed comparison 3) Experiment & Theory: Results Results - H 2 O: which lines - H 2 O: which lines - theo & exp results: - theo & exp results: detailed comparison detailed comparison

22. J = 3 1,2 - 3 0,3 * (1.097 THz) J = 3 1,2 - 3 0,3 * (1.097 THz) J = 1 1,1 - 0 0,0  (1.113 THz) J = 1 1,1 - 0 0,0  (1.113 THz) J = 7 2,5 - 8 1,8  (1.147 THz) J = 7 2,5 - 8 1,8  (1.147 THz) J = 3 1,2 - 2 2,1 * (1.153 THz) J = 3 1,2 - 2 2,1 * (1.153 THz) J = 6 3,4 - 5 4,1 * (1.158 THz) J = 6 3,4 - 5 4,1 * (1.158 THz) J = 3 2,1 - 3 1,2 * (1.163 THz) J = 3 2,1 - 3 1,2 * (1.163 THz) J = 8 5,4 - 7 6,1  (1.168 THz) J = 8 5,4 - 7 6,1  (1.168 THz) J = 7 4,4 - 6 5,1  (1.173 THz) J = 7 4,4 - 6 5,1  (1.173 THz) J = 8 5,3 - 7 6,2  (1.191 THz) J = 8 5,3 - 7 6,2  (1.191 THz) J = 6 3,3 - 5 4,2  (1.542 THz) J = 6 3,3 - 5 4,2  (1.542 THz) H 2 O: THz pure rotational lines investigated  Self-broad: amplitude modulation  N 2 - & O 2 -broad frequency modulation frequency modulation  Self-broad: amplitude modulation  N 2 - & O 2 -broad frequency modulation frequency modulation  Cazzoli et al. JQSRT 2008  Cazzoli et al. JQSRT submitted * Cazzoli et al. JQSRT in preparation

23. H 2 O: THz pure rotational lines investigated J = 3 1,2 - 3 0,3 * (1.097 THz) J = 3 1,2 - 3 0,3 * (1.097 THz) J = 1 1,1 - 0 0,0  (1.113 THz) J = 1 1,1 - 0 0,0  (1.113 THz) J = 7 2,5 - 8 1,8  (1.147 THz) J = 7 2,5 - 8 1,8  (1.147 THz) J = 3 1,2 - 2 2,1 * (1.153 THz) J = 3 1,2 - 2 2,1 * (1.153 THz) J = 6 3,4 - 5 4,1 * (1.158 THz) J = 6 3,4 - 5 4,1 * (1.158 THz) J = 3 2,1 - 3 1,2 * (1.163 THz) J = 3 2,1 - 3 1,2 * (1.163 THz) J = 8 5,4 - 7 6,1  (1.168 THz) J = 8 5,4 - 7 6,1  (1.168 THz) J = 7 4,4 - 6 5,1  (1.173 THz) J = 7 4,4 - 6 5,1  (1.173 THz) J = 8 5,3 - 7 6,2  (1.191 THz) J = 8 5,3 - 7 6,2  (1.191 THz) J = 6 3,3 - 5 4,2  (1.542 THz) J = 6 3,3 - 5 4,2  (1.542 THz) What was available for these lines? What was available for these lines? - experimental values for 1 1,1 - 0 0,0 (N 2 & O 2 ) - calculated and/or extrapolated data for others - experimental values for 1 1,1 - 0 0,0 (N 2 & O 2 ) - calculated and/or extrapolated data for others

24. 3) Experiment & Theory: Results Results - H 2 O: which lines - H 2 O: which lines - theo & exp results: - theo & exp results: previous exp data previous exp data 3) Experiment & Theory: Results Results - H 2 O: which lines - H 2 O: which lines - theo & exp results: - theo & exp results: previous exp data previous exp data

25. J = 1 1,1 – 0 0,0 transition of H 2 O T = 297 K Cazzoli et al. JQSRT 2008

26. J = 1 1,1 – 0 0,0 transition of H 2 O T = 297 K Cazzoli et al. JQSRT 2008

27. J = 1 1,1 – 0 0,0 transition of H 2 O T = 297 K Cazzoli et al. JQSRT 2008

28. Self N2N2N2N2 O2O2O2O2Air 297 K ExpTheoExpTheoExpTheoExpTheo This work 19.72(46)19.84.38(15)4.22.40(12)2.53.96(13)3.8 Gasster Gasster et al. 3.67(10) 2.99(37) 3.53(8) HITRAN 4.74 3.53(8) J = 1 1,1 – 0 0,0 transition of H 2 O Improvements wrt old measurements Improvements wrt old measurements

29. 3) Experiment & Theory: Results Results - H 2 O: which lines - H 2 O: which lines - theo & exp results: - theo & exp results: HITRAN self broad HITRAN self broad 3) Experiment & Theory: Results Results - H 2 O: which lines - H 2 O: which lines - theo & exp results: - theo & exp results: HITRAN self broad HITRAN self broad

30. Cazzoli et al. JQSRT submitted

33. Cazzoli et al. JQSRT in preparation

35. ExpTheo This work J = 3 1,2 - 3 0,3 21.98(22)21.54 HITRAN 18.40 This work J = 1 1,1 - 0 0,0 19.72(46)19.8 HITRAN 4.74 This work J = 7 2,5 - 8 1,8 17.96(34)17.93 HITRAN 12.93 This work J = 3 1,2 - 2 2,1 19.57(18)21.22 HITRAN 18.33 This work J = 6 3,4 - 5 4,1 14.97(8)16.27 HITRAN 16.94 This work J = 3 2,1 - 3 1,2 19.23(11)19.80 HITRAN 18.40 This work J = 8 5,4 - 7 6,1 11.12(26)11.33 HITRAN 15.16 This work J = 7 4,4 - 6 5,1 11.98(27)13.03 HITRAN 16.69 This work J = 8 5,3 - 7 6,2 11.66(8)11.88 HITRAN 15.16 This work J = 6 3,3 - 5 4,2 17.56 HITRAN 16.94 What’s the problem? What’s the problem?SELF-broadening

36. COMPARISON : semiclassical calc. (SC) vs HITRAN (assumption*) values * dependence of the broadening parameter on J”

37. COMPARISON : semiclassical calculations (SC) vs HITRAN (exp*) values * IR lines: 600-1000 cm -1 (R. A. Toth)

38. COMPARISON : semiclassical calculations (SC) vs EXP* values * Markov 1994, Cazzoli et al. 2007, Cazzoli et al. 2008

39. Suggestion: Make use of calculated values when no reliable experimental data are available HITRAN ref.# linesMean %error#lines with %err > 25% 3988.310 13643.34 15 37.38 2313.70 3036.80 31239.62 36124.70 504314.77 51133337.5595 52176.61 53324.11 Ref. 51: Averaged values as a function of J”

40. 3) Experiment & Theory: Results Results - H 2 O: which lines - H 2 O: which lines - theo & exp results: - theo & exp results: N 2, O 2 & air broad N 2, O 2 & air broad 3) Experiment & Theory: Results Results - H 2 O: which lines - H 2 O: which lines - theo & exp results: - theo & exp results: N 2, O 2 & air broad N 2, O 2 & air broad

41. Cazzoli et al. JQSRT submitted

43. ExpTheo This work J = 3 1,2 - 3 0,3 3.970(82)4.00 HITRAN 4.13 This work J = 1 1,1 - 0 0,0 3.96(13)3.8 HITRAN3.53(8) This work J = 7 2,5 - 8 1,8 3.508(20)3.13 HITRAN 3.24 This work J = 3 1,2 - 2 2,1 3.935(75)3.77 HITRAN 3.65 This work J = 6 3,4 - 5 4,1 2.911(60)2.80 HITRAN 2.99 This work J = 3 2,1 - 3 1,2 3.857(57)3.77 HITRAN 3.93 This work J = 8 5,4 - 7 6,1 2.287(66)2.07 HITRAN 2.18 This work J = 7 4,4 - 6 5,1 2.765(34)2.42 HITRAN 2.59 This work J = 8 5,3 - 7 6,2 2.462(24)2.18 HITRAN 2.27 This work J = 6 3,3 - 5 4,2 3.805(72)3.28 HITRAN 3.32 Good agreement! Good agreement!AIR-broadening

44. 3) Experiment & Theory: Results Results - H 2 O: which lines - H 2 O: which lines - theo & exp results: - theo & exp results: shift & SD param shift & SD param 3) Experiment & Theory: Results Results - H 2 O: which lines - H 2 O: which lines - theo & exp results: - theo & exp results: shift & SD param shift & SD param

45. Cazzoli et al. JQSRT 2008

46. Cazzoli et al. JQSRT submitted

48. Cazzoli et al. JQSRT in preparation

49. Conclusions  10 pure rotational THz water lines have been experimentally and theoretically been experimentally and theoretically investigated investigated  Good agreement between experiment and SC calculations and SC calculations  Update for HITRAN self broadening parameters is suggested parameters is suggested  Rather accurate experimental results have been obtained have been obtained

50. Thank you for your attention!

52. temperature exponent n Least-square fit: ln(X/X 0 ) = n ln(T 0 /T) TEMPERATURE DEPENDENCE TEMPERATURE DEPENDENCE

53. Laboratory of Millimetre-wave Spectroscopy of Bologna PRAHA 2006 temperature exponent n Least-square fit: ln(X/X 0 ) = n ln(T 0 /T)