of recent analyses from 3000 to 7930 cm -1 Alain BARBE

Transcription

1 Infrared high resolution spectra of 6 O 3 and 8 O 3 :review of recent analyses from 3 to 793 cm - Alain BARBE

2 Basic elements of theory (reminder) Oone isotopomers different symmetries C v 8 O 6 O 8 O 8 O 8 O 8 O 8 O 6 O 6 O C s 6 O 8 O 6 O 8 O 8 O 6 O

3 Interacting Polyads. ω # ω 3 Coriolis resonances : exemple () () () C C DD < v, v, v 3 H Cor v ±, v, v 3 µ > Darling Dennison resonances : < v, v, v 3 H Anh v ±, v, v 3 µ >. ω ω 3 # 3ω3 3 rd order Coriolis resonance exemple () () () DD C C C < v, v, v 3 H Cor v -, v 3, v 3 -> (3) Polyads interacting states v v 3 = C te and v = C te

4 Predicted Observed

5 prédicted 5 8 3/33 observed 3/ / / et /3 4/3 3/33 3/

6 /43 35/ / /43 35/63 33/ A

7 B et

8 et A A

9 HAMILTONIAN Diagonal block ( ) ( ) ( ) ( ) { } ( ) ( ) { } { } ( ) 8 K xy xy K xy 4 K 3 K 4 K 6 K xy xy K K 4 K xy VV VV L h, h, h H H H H, C B C B C B A E H = δ δ where { } BA AB,B A and y x xy = Extradiagonal blocks ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )... / / C / / C C C / / C / / C C H VV' Coriolis = where y x i ± = ± ( ) ( ) [ ( ) ] ( )... F F F F F F H VV' Anharm = Assignments : vibration : predictions from Vl. G. Tyuterev keep the usual label v v v 3. rotation : use of ASSIGN program (Chichery A.) based on Ground State Combination Differencies (GSCD) - Ka Kc calculation of energy levels, transitions, and intensities : GIP program. (S. A. Taskhun)

10 LINE INTENSITIES The linestrenghths are calculated using the following effective transition moment operators : For A-Type band : { } { } { } { } [ ] { } { } { } { } [ ] { } { } [ x y y x 6 y y x x 5 x y y x 4 3 ()(), i,i d,,i i,, d, i,i d, d, d d ~ ϕ ϕ ϕ ϕ ϕ ϕ ϕ ϕ ϕ = µ { } { } { } { } [ ] { } xy 8 y y x x 7, d,,i i,, d ϕ ϕ ϕ For B-Type band : { } { } { } { } { } { } { } { } { } [ ] y x y xy x 7 x 6 y 5 y 4 x 3 x x ()(),,i i, d,, d,i d, i d, d, d d ~ ϕ ϕ ϕ ϕ ϕ ϕ ϕ ϕ = µ { } { } { } [ ] x y xy x 8,,i i, d ϕ ϕ with { } BA AB B, A = and i vv' i d d =

11 Fourier Transform Spectrometer Working in stepping mode 3 meters path difference. Recent experimental improvement : Use of two detectors

12 Oone generation at 77 K : complete conversion O O 3

13 Reduction of experimental data Use of «MultiFiT» software (.-. Plateaux et L. Régalia-arlot) (GSMA) For simultaneous fit of various spectra recorded at different pressures Experimental parameters are obtained for each of the observed transition: position, intensity, broadening and shift coefficients

14 Spectrum in the 4 cm - region ( 6 O 3 ) ν ν ν 3 ν 4ν 3 ν 3 ν 3ν, 4ν 3 3, 3ν ν ν ν 3ν 3 ν.8 ν ν 3, ν 3ν ν 3 3ν ν 3 Transmission Wavenumber (cm-)

15 6 O 3 : First example of analysis in E/hc (cm - ) the CW-CRDS spectral region 64 (3) B 6 7, 635 (43) A (5) B (4) A ,,3,3,4 8,3,,,,3 (5) A 3,4 63 (5) B 8 6 4,5 7

16 Spectroscopic parameters of the 6 vibrational states (5 observed) in cm - Parameters (5) (5) (4) (5) (43) (3) E VV () (9) (79) () (63) (9) A-(BC)/ (74) 3.4 (6) (56) (98) (48) (36) (BC)/ (33) (49) (35).49 3 (53) (3) (4) (B-C)/.75 7 (6) (6).4 9 (35).4738 () ().67 () D K () (g) ().39 (9) (g) (3) D K () (g) (g).3 8 (9) (g) (6) D (3) (g).95 9 (39) (8).48 8 (8).3434 (6) δ (5) (g) -.94 (9 ) (6) ().4 7 (67) δ K (4) (g).83 (6).97 7 (4) (g).3 6 (96) H K (47) (g) (g) (89) (g) (g) H K (97) (g) (g).9 () (g) (g) 43,3 C =.34958() 4,3 C =.6775(8) 3,5 A =.937(36) 43,4 A =.6() 43,5 C =.654(3) 5,5 C =.5(9) 3,5 A =.768 (95) 4,5 C.467() = 4,5 C.9743() = 5,5 A.669(63) = 935 transitions, 99 energy levels, 49 parameters, rms = cm -.

17 Example of mixing coefficients () 6 5 Ka = 8 (4) into Ka = 7 (3) Ka = (43) into Ka = (3), even Ka = 3 (43) into Ka = (3), even % into (3) quantum number

18 Example of mixing coefficients () 35 3 Ka =, odd Ka = 3, even 5 % (43) into (5) quantum number

19 Example of mixing coefficients (3) % (4) into (5) Ka =, even Ka =, even Ka =, odd Ka = 3, even Ka = 3, odd quantum number

20 Example of mixing coefficients (4) 6 5 Ka = 6 (4) into Ka = 7 (5) Ka = 3 (5) into Ka = 4, odd (5) Ka = 4 (5) into Ka = 5, odd (5) Ka = 4 (5) into Ka = 5, even (5) 4 % into (5) quantum number

21 Integrated band intensities, S V, in (cm/molecule at 96 K) and Parameters of the effective transition moment operator (in Debye). Operator ϕ { ϕ Z, } { ϕ, } ϕ x { ϕ, } i y ϕ { iϕ y, } { ϕ, } i y ϕ { ϕ Z, } Parameters d ( 4 ) d ( 8 ) d 3 ( 4 ) d ( 5 ) d 5 ( 6 ) d ( 4 ) d 4 ( 5 ) d 5 ( 6 ) ν ν 3ν 3 A-type (S V = ) d ( 4 ) d ( 7 ) Value ν 5ν 3 A-type (S V = ).6396 (7) (48) (5) ν ν 4ν 3 B-type (S V = ).8 6 (76).9 4 (8) 5ν ν 3 A-type (S V = ) (5) 4ν 3ν B-type (S V =.98-5 ).9 6 (4) (5).66 9 (7) -.83 (9) Global rms.9 (%) Number of transitions ( max, K a max) 54 (38, 3) 4 (4, ) 3 (35, ) 9 (35, ) 4 (35, ) rms a deviation (%)

22 Example of energy levels Ka Kc E (cm - ) Nb E O - C E (cm - ) Nb E O - C E (cm - ) Nb E O - C Nb is the number of observed transitions used to determine the upper energy level. E is the rms dispersion of combination differences (in -3 cm - unit). (O-C) is the difference (in -3 cm - unit) between the experimentally determined value and the value calculated from the effective Hamiltonian model.

23 .6.4 Example of agreement between CW- CRDS and calculated spectra. P branches of 5ν ν 3 and ν ν ν 3 Absorption Coefficient ( -6 cm - ) # * O O O O # O O O O (a) CO (b) Calculated O 3 O (a) (b) Observed Wavenumber (cm - ).6. Calculated.5. R branch of ν ν ν 3 Absorption Coefficient ( -6 cm - ) Calculated (with correction) CW-CRDS Wavenumber (cm - )

24 6 O 3 : Second example of analysis (B-C)/ (4).93 6 (39) K () (g) K δ δ K (53) (36) E VV () (98) A-(BC)/ (BC)/ (99) (93) (g).3 8 ().7 7 (7) (38) (3) (7) (g) (g) (g) (g) (36)(53) C =.46 (7) (36)(53) C =.78 5 (6) % of (36) into (53) (a) simulated 6 O 3 Ka=, even Ka=, even quantum number.5. Operator ϕ Z {, } ϕ Z Parameter d ( 4 ) d ( 8 ) Value. 3 (5) (45) Absorption coefficient ( -6 cm - ) (b) simulated 6 O 3 H O (c) CRDS S v =.5-5 cm/molecule at 96 K Wavenumber (cm-)

25 Summarie for 6 O 3 9 vibrational states analyed : 5 A-type bands and 39 B-type bands A-type bands Obs label Pred() O-C Pred() O-C

26 / B-type bands / / Pred() : Global variational predictions (Vl.G. Tyuterev) Pred() th order Contact Transformation (Vl.G. Tyuterev)

27 Obs label A obs A pred (Obs-Pred)/Pred % B obs B pred (Obs-Pred)/Pred % Comparison of the rotational constants A, B and C for the highest energy levels Pred = th order Contact Transformation (Vl.G. Tyuterev) C obs C pred (Obs-Pred)/Pred %

28 Band intensities Band center S v (cm/molecule at 96 K) 4 ν ν ν 3 ν ν ν ν ν 3 ν 3ν ν 3ν 3ν 3 ν 3ν 3 3ν 3 5ν ν ν 3 ν ν 5ν Remark : ratio of almost -9 between v=9 and v=

29 Number of vibrational energy levels derived from observed bands, for 6 O 3 Pred Obs % Range cm - Range 4 cm Range 4 6 cm Range 6 8 cm TOTAL

30 8 O 3 : First example of analysis CRDS spectra in the range cm - % (43) into (5) K a = 7 K a = 7 K a = 8 K a = 9 K a = quantum number K a = 6 K a = 5 % (4) into (5) % (3) into (5) quantum number K a = 8 Scheme of rovibrational resonances quantum number

31 Effective Hamiltonian parametres Paramètre (5) (43) (5) (4) (5) (3) E VV (3) (3) (3) (76) 67.3 (3) 6. 4 (34) A-(BC)/ ().888 (46) (84) (55).7883 (95).85 (9) (BC)/ (8) (7) (45).35 (35) (55) (3) (B-C)/.459 () (85) (6) () ().38 4 (4) K (9).54 7 (7).75 8 () g.89 7 (7) 3.35 (8) K () 4.76 (4) (5) (8) () g (5).983 (57).3 (74) (48) g g δ (5).4 3 (35) (93) (49).699 (6) g δ K 5 g g.4 (6).798 (8).66 7 (9) g H K (93) g.43 (4) g.473 (84) g H K 7 -. () g (4) g g g 4,43 A = 5 5,5 A = (48).7 (94) 43,5 C y/ =.757(6) 4,5 C y/ =.35() 4,5 5,43 C =.587(45) C y/ =.7675(88) 5,43 C = (95) 5,3 C y/ = 7.98 (35) 5,3 C =.675 (46) Statistics for positions État vibrationnel (5) (43) (5) (4) (5) Total Centre de bande (cm - ) max K a max Nombre de transitions Nombre de niveaux rms ( 3 cm - ) Total rms( 3 cm - ) 9.5

32 8 O 3 : Second example of analysis CRDS Spectrum in the range сm - Paramètre (55) (54) E VV 5 ka=4 for odd (97) (8) max =7 A-(BC)/.766 (4) (p) 4 ka=4 for odd K (BC)/ (67) () a max = 6 Nb. transitions = 9 3 (B-C)/ (3).7 4 () K (5) g Nb. levels = 4 K (3) g rms ( -3 cm - ) = (6) g I (%) = 9.8 δ 6.63 () g δ K () g % (54) into (55) k a = for odd,3 Absorption coeffitients (* -6 cm - ),,, ,3,, calculated spectrum, Wavenumbers (cm - ) Absorption coeffitients (* -6 cm - ),,,, 768,4 768,8 769, 769,6 763,, * H O R Branch of the 5ν 5ν 3 band Observed spectrum * H O, 768, 768,4 768,8 769, 769,6 763, Wavenumbers (cm - )

33 Analyses of CRDS 8 О 3 spectra in the range 59-7 сm - : Comparaison between observed bands and calculated from P.E.S Attribution spectroscopique centre de bande (cm - ) experimental Obs- Pred. Transitions max Statistique de l ajustement Nombre K a rms des. max ( 3 cm - ) niveaux ν 5ν ν 3ν * ν ν ν ν 4ν ν ν 5ν ν 6ν 3 * ν 5ν ν 3ν 3ν 3 () ν 5ν ν 3ν 4ν 3 * ν ν ν ν 3ν 3ν 3 () ν ν 5ν ν 3ν ν RMS (obs.-pred.) = cm - rms I (%)

34 Example of Comparison between the observed rotational constants and the theoretical predictions ( 8 O 3 ) state Obs A-(BC)/ Pred (O-P)/O % Obs (BC)/ Pred (O-P)/O % Obs (B-C)/ Pred (O-P)/O % (35) (7) (45) (63) (44) (7) (55) (53)

35 Summary for 8 O 3 49 vibrational states analyed : 3 A-type bands and 7 B-type bands A-type bands Obs Label Pred () O-C Pred () O-C B-type bands

36 Overview of the 8 O 3 CRDS spectra in the range cm -.4 Absorption coefficient ( -6 cm - ) ν 5ν 3 4ν 3ν 5ν ν 3 ν ν 4ν 3 ν ν 5ν 3 ν 6ν 3 ν 5ν 3 ν 3ν 3ν 3 ν 3 ν 4ν 3 3ν 5ν 3 5ν ν ν 3 ν 3ν 3ν 3 ν ν 5ν 3 4ν 3 ν ν W a v e n u m b e r (c m - )

37 =.989 A (Fermi)= Transmittance.95 3ν ν ν 3 5ν 3 Sv (5ν 3 ) = Sv (3ν ν ν 3 ) = Comparisons 6 O 3 8 O Wavenumber (cm - ) (not observed) = Sv (5ν 3 ) =.6 - Transmittance Note : for the 4 isotopologues 668, 686, 886 and 868, the 5ν 3 band has been observed and analyed and the 3ν ν ν 3 band has NOT been observed Wavenumber (cm - )

38 Very interesting observation : isotopic shifts Absorption coefficient ( -6 cm - ) Absorption coefficient (a.u.) O 3 ν 5ν 3 5ν ν 3 ν ν 5ν wavenumber (cm - ). 6 O ν 5ν 3 5ν ν 3 ν ν wavenumber (cm - )

39 Isotopic shifts 6 O 3 8 O 3 : observations E(666)-E(888) / cm partners states <=> global assignment Boo Boc Aoo Aoc 666: max vib. mixing coefficient (%) % (A) % (B) E(666)-E(888) / cm E(888)/cm - partners states <=> normal mode assignment Boo Boc Aoo Aoc 888: max vib. mixing coefficient (%) E(666)/cm - % (A) % (B) E(888)/cm - Isotopic shifts for observed band centres E(888)/cm - Mixing coefficients for the various vabrational states

40 Some of the encountered difficulties at the end of the analyses : Vibrational labeling : Effective Hamiltonian model to represent energies up to 6 cm - 3: Effective Transition moment model to represent intensities, mostly B-type bands Theoretical predictions and experimental values of band centres ( 8 O 3 ) Centre de bande (cm - ) Coefficients de mélange * calc obs Obs-calc P(%) W P(%) W P3(%) W (6) 4 (43) 4 (5) (35) (53) 5 (5) p 4 (7) 3 (43) 8 (5) p 5 (45) (333) (35) (63) (44) (53) (44) (63) 8 (35) (6) 3 (36) (34) (7) 6 (5) (333) (55) 36 (36) 7 (343) (54) (6) 6 (5) (53) 9 (7) 9 (5)

41 rms versus vibrational energy rms ( x -3 cm - ) vibrational energy (cm - )

42 Number of observed transitions versus vibrational energy 4 35 number of fitted energy levels observed energy level (cm - )

43 Calculated spectra of ν ν 4ν 3 in 3 cases (normalisation on observed lines in the 655 cm - region).99 All µ of A and B bands All µ of B band; µa = Only µ for B band ( µ 5 =):

44 EXAMPLE OF SERVEY OF THE ν ν 3 BANDS OF 8 O ENRICHED SAMPLE..8 Transmittance Near future: CRDS Spectra of mixed 8 O- 6 O isotopes.8 Transmittance Wavenumber (cm-)

45 Example of results in the 6 cm - spectral range calculé tous les isotopes expérimental expérimental

46 Results for mixed 8 O- 6 O oone 6 O 8 O 6 O 6 O 6 O 8 O 8 O 6 O 8 O 8 O 8 O 6 O

47 Summary : Numbers are given for states through analyses of cold bands (v v v 3 ) ( ) Many hot bands confirm the spectroscopic parameters. Only two states derived from hot bands (3) and (3) for 6 6 O 3 C v 6 O 3 : 9 8 O 3 : 5 6 O 8 O 6 O : 6 8 O 6 O 8 O : 9 C s 6 O 6 O 8 O : 8 O 8 O 6 O : 7 6 vibrational states known for 6 O- 8 O isopotomers of oone (more than 3 bands)

48 Conclusion 6 derived vibrational states for enriched 8 O isopotomers of oone Band centres and rotational constants obtained Transition moment and S v derived for 6 O 3 and 8 O 3 Comparison of band centres with theoretical predictions Comparison of rotational constants with theoretical predictions Necessity of «shuttles» between analyses and predictions Some problems of model in high energy ranges New works on other mixed isopotomers needed and expected

49 Co-authors : M.-R. De Backer E. Starikova X. Thomas Vl. Tyuterev S. Kassi D. Mondelain A. Campargue Acknowledgments G.S.M.A. Reims, France.. Plateaux L. Régalia arlot Technical team G.S.M.A., Reims Institut of Atmospheric Optics Tomsk, Russie S. Mikhailenko S. Tashkun D. Décatoire P. Von der Heyden