FICTION OR REALITY? Jeanna Buldyreva. Institute UTINAM UMR CNRS 6213 University of Franche-Comte, Besancon, France. Jean Vander Auwera

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1 A THEORETICAL MODEL FOR WIDE-BAND IR-ABSORPTION MOLECULAR SPECTRA AT ANY PRESSURE: FICTION OR REALITY? eanna Buldyreva Insttute UTINAM UMR CNRS 613 Unversty o Franche-Comte, Besancon, France ean Vander Auwera Quantum Chemstry and Photophyscs Unversté Lbre de Bruxelles, Brussels, Belgum 1

2 Plan Outlne o the needs Non-Markovan Energy-Corrected Sudden approach Applcatons to hgh-densty IR spectra Applcatons to CO IR spectra at low denstes Conclusons & perspectves

3 Mars Outlne o the needs Earth Venus T, P, chemcal compostons Planets: 3

4 Outlne o the needs Absorpton coecent as a uncton o requency or each spectroscopcally actve molecule Atmospherc radatve transer codes Retreval o geophyscal parameters (temperature, humdty, ) Weather/clmate models Optmzaton o solar photovoltac systems 4

5 Outlne o the needs Regon o molecular resonances low pressures hgh pressures + +/- Courtesy : N.N. Flppov Spectral wngs near ar +/- - Absorpton coecents as unctons o requency Contrbutons rom Collson-Induced Absorpton -/+ Contrbutons rom dmers and hgher-order clusters -/+ 5

6 Outlne o the needs STANDARD APPROACH or allowed absorpton Nro et al., QSRT 88, 483 (004) hc kt ( ) n 1(1 e ) Re k d k d k[ ( 3hc k, k k )] n W ] 1 kk absorpton coecent at wavenumber σ ReWkk ImWkk ReW ImW kk kk Actve-gas densty Rotatonal populaton Dpole matrx element Isolatedlne postons Modelled by the Energy-Corrected Sudden approach or «downward» transtons + detaled-balance relaton ReW ReW or «upward» ones kk One-parameter emprcal modellng usng the detaled balance Calculated by sum rules W kk k k d d k k k k W k kk Bath-gas densty Rotatonal relaxaton matrx In the 1storder mpact approx 6

7 Outlne o the needs ECS parameters tted to expermental LW Sum rules or calculaton o dag. elements Recalculated LW expermental LW Emprcal modelng o Im W STANDARD APPROACH: PROBLEMS «Renormalzaton procedure» 1) Lnes sorted n decreasng ntensty order ) Expt LW mposed on the dagonal 3) O-dagonal elements scaled to satsy the detaled balance Far spectral wngs: break down o the mpact approxmaton Emprcal correctons to the Lorentzan shape: «χ-actors» Far spectral wngs: volaton o the detaled balance Flppov & Tonkov, CP 108, 3608 (1998) One-sded sum rules asymptotc behavor σ -3 n the ar wng negatve ntenstes n low-requency wng General sum rules hold ONLY n the non-markovan case Bulann et al., QSRT 31, 51 (1984) 7

8 Non-Markovan Energy-Corrected Sudden approach r σ k n Symmetrzed spectral densty: S ( r) ( ) 1 ( r) Re Ak k k, k - rank o the couplng tensor - proper requences o the ree actve molecule - gas densty 1 ( r) ( ) n (r) ( ) A A (r) ( r) k - ntenstes o separate lnes r Ak General orm o the o-dagonal relaxaton matrx elements: 1 exp( hc / kt ) n n k, k ' ( r), ( ) Lr ( L 1) F, L ( ) L ( L C k ' n ( r) ) Kouzov, PRA 60, 931 (1999) 8

9 Non-Markovan Energy-Corrected Sudden approach Propertes o the non-markovan relaxaton matrx ( r) ( r ) Symmetry (detaled balance): Γ, ' '( ) Γ' ', ( ) ( r) ( )* Tme-reversal symmetry: Γ, ' '( ) Γ r, ' ' ( ) Double-sded sum rules: ' ' Γ ( r ) ( r ) ( r ) ( r ) ( r ), ' '( ) A ' ' A ' ' Γ' ', ( ) Γ, ( ) ' ' A ( r ) Postve denton:, ' ' B ( r) Γ ( r), ' ' ( ) B ( r) ' ' 0, B ( r) 9

10 Non-Markovan Energy-Corrected Sudden approach ECS modelng o the correlaton uncton Buldyreva & Bonamy, PRA 60, 370 (1999) Re Φ L 1 exp hc kt Φ class L (cb ) 1 nv Φ class L Q ' L Ω c 1, n 1 or Ω Spectroscopyndependent Q L n T 1 Standard ECS parameters ECS-EP: ECS-P : ECS-E : A ( T ),,, A ( T ),, b c A ( T ),, A B exp L L 1 L L kt 10 b c b c

11 ) ( l r k l l l l r A (I) Isolated-lne ntenstes (II) Relaxaton matrx L r l l L l l L F l l r Lr 0 0 1) (, 1 r Modcatons or IR absorpton bands Buldyreva & Daneshvar, CP 139, (013) Lnear molecule wth a bendng mode can be consdered as a symmetrc top wth K l ( 3) 1 v v v l IOSA: Green, CP 70, 816 (1979); CP 90, 3603 (1989) Non Non-Markovan Markovan Energy Energy-Corrected Sudden Corrected Sudden approach approach

12 Non-Markovan Energy-Corrected Sudden approach (III) Vbraton-rotaton nteractons: (A) Isolated-lne ntenstes: Correcton va Herman-Walls actors F( m) (1 a m F( m) (1 b m m 3 1 m am a3 ) ) P- & R- Q- ( P); m ( Q); m 1 ( R) A (1) k A (1) HW k A (1) k F( m) Corols nteractons between vbratonal levels: Hartmann et al., CP 110, 7733 (1999) I sum rules are restrcted to one band, unperturbed dpole elements should be used Modcatons o rel. matr. or Corols eects have no nluence on the absorpton shape (B) Relaxaton matrx modelng: (1) A k CO : Eectve correcton allowed or dagonal elements 1

13 Applcatons to hgh-densty IR spectra OCS-He ν atm 98 K Intensty (a.u.) expt sum o Lorentzans ECS-P ECS-E 5 atm 98 K Intensty (a.u.) expt sum o Lorentzans ECS-P ECS-E W avenumber (cm -1 ) W avenumber (cm -1 ) Buldyreva et al., CP 138, (013) 13

14 Applcatons to hgh-densty IR spectra OCS-He ν 0 70 atm 98 K atm 98 K Intensty (a.u.) 10 5 expt sum o Lorentzans ECS-P ECS-E Intensty (a.u.) expt sum o Lorentzans ECS-P ECS-E W avenumber (cm -1 ) W avenumber (cm -1 ) Buldyreva et al., CP 138, (013) 14

15 Applcatons to hgh-densty IR spectra CO -CO ν 1 + ν 3 30 Absorpton, 10-3 cm -1 amagat expt ECS Sére5 Sére a 1 = , a = amagat 0 amagat 300 K a 1 = , a = No emprcal correcton Wavenumber, cm -1 HW actors: Rothman et al., QSRT 48, 537 (199) Flppov et al., PCCP 15, 1386 (013) 15

16 Applcatons to hgh-densty IR spectra CO -CO 3ν 3 Absorpton, 10-3 cm -1 amagat a expt ECS ECS-ec 0 amagat K 0 amagat Wavenumber, cm -1 Absorpton, 10-3 cm -1 amagat b expt ECS ECS-ec 9 amagat amagat K Wavenumber, cm -1 Emprcal correcton ' v = cm -1 amagat -1 a 1 = HW actors: Rothman et al., QSRT 48, 537 (199) Flppov et al., PCCP 15, 1386 (013) 16

17 Applcatons to hgh-densty IR spectra Absorpton, 10-3 cm -1 amagat a 1 = , a = , b = HW actors: Rothman et al., QSRT 48, 537 (199) a expt ECS ECS-ec 0 amagat ( 1 + ) I 0 amagat 300 K Absorpton, 10-3 cm -1 amagat -1 CO -CO b expt ECS ECS-ec (ν 1 + ν ) I 46 amagat ( 1 + ) I 46 amagat 300 K Wavenumber, cm -1 Absorpton, 10-3 cm -1 amagat -1 ' v = cm -1 amagat c expt ECS ECS-ec 9 amagat ( 1 + ) I 9 amagat 300 K Wavenumber, cm -1 ' v = 0.00 cm -1 amagat -1 ' v = cm -1 amagat Wavenumber, cm -1 Flppov et al., PCCP 15, 1386 (013) 17

18 Applcatons to hgh-densty IR spectra 1.E-01 CO -CO ν 3 wng 96 K Absorpton, cm -1 amagat - 1.E-0 1.E-03 1.E-04 1.E-05 1.E-06 expt calc calc (mpact approx) 1.E W avenumber, cm -1 expt: Le Doucen et al., Appl. Opt. 4, 897 (1985) Buldyreva & Daneshvar, CP 139, (013) 18

19 Applcatons to CO IR spectra at low denstes SOIR spectra o the atmosphere o Venus (Venus Express) alttude Courtesy : A.C. Vandaele (IASB) Wavenumber (cm 1 ) 19

20 Applcatons to CO IR spectra at low denstes Transmttance 10 FTS spectra recorded (55 m, 93 K) Resoluton = cm hpa 0 Daneshvar et al., QSRT 014 (under revson) 16 une 014 ISMS

21 Applcatons to CO IR spectra at low denstes 0.89 atm 93 K Daneshvar et al., QSRT 014 (under revson) 1

22 Applcatons to CO IR spectra at low denstes 0.09 atm 93 K Daneshvar et al., QSRT 014 (under revson)

23 Applcatons to CO IR spectra at low denstes 0.09 atm Q-branch zoom Daneshvar et al., QSRT 014 (under revson) 3

24 Conclusons & perspectves Man results Immedate good agreement wth expt OCS-He spectra up to 300 atm wthout any addtonal ttng parameter Satsactory agreement or CO up to nearly lqud phase (+ 1 ttng parameter) Excellent agreement wth low-densty expt CO spectra down to 0.03 atm The model has a unversal character (IR, Raman so, anso) Further mprovements/tests/applcatons Studes o extremely low pressures (narrowng eects) Modelng o Im Γ Studes o ar wngs (non-markovan eects) Modelng o temperature dependences Calculatons o correlaton unctons rom ab nto PES Studes o other bands and other molecular systems 4