1. Columbus 2005, 20/6/05 -- 24/6/05 ANALYSIS OF THE 3 / 7 / 9 BENDING TRIAD OF THE QUASI-SPHERICAL TOP MOLECULE SO 2 F 2 M. Rotger, V. Boudon, M. Lo ë te, L. Margul è s, J. Demaison, F. Hegelund, I. Merke and H. B ü rger SO 4 2  SO 2 F 2 SF 5 Cl SF 6

2. Columbus 2005, 20/6/05 -- 24/6/05 Theoretical aspects  Theoretical aspects Spectra analysis: the ground-state  Spectra analysis: the ground-state and the bending triad (510-580 cm -1 ) and the bending triad (510-580 cm -1 ) of SO 2 F 2 of SO 2 F 2 Perspectives  Perspectives

3. Columbus 2005, 20/6/05 -- 24/6/05 MAIN IDEAS Consider a symmetric or asymmetric top as deriving from a spherical top Examples: SF 5 Cl can be seen as deriving from the SF 6 molecule. SO 2 F 2 can be seen as deriving from the SO 4 2  molecular ion. Associate a group chain to these molecules For example, the following group chains O(3)  T d  C 2v orO(3)  O h  C 4v O(3)  T d  C 2v or O(3)  O h  C 4v.

4. Columbus 2005, 20/6/05 -- 24/6/05 GROUP CHAIN Group of rotations in space : O(3) Spherical intermediate group Group of the molecule Direct orientation (Watson)

5. Columbus 2005, 20/6/05 -- 24/6/05 TENSORIAL FORMALISM AND EFFECTIVE HAMILTONIAN : parameters, t i : parameters, andare the rotational and vibrational operators. R and V are the rotational and vibrational operators. Systematic development of all the operators at any order and for any polyad, Vibrational extrapolation of the parameters, Suitable for programing.

6. Columbus 2005, 20/6/05 -- 24/6/05 A SIMPLE CASE, THE GROUND STATE OF SO 2 F 2 : v = 0

7. Columbus 2005, 20/6/05 -- 24/6/05 Watson’s Hamiltonian: THEORY Tensorial Hamiltonian: ~~

8. Columbus 2005, 20/6/05 -- 24/6/05 ROTATIONAL TENSORS Groups Chain: andare some orientation coefficients. G and G’ are some orientation coefficients. ~ ~

9. Columbus 2005, 20/6/05 -- 24/6/05 MATRIX ELEMENTS OF THE TENSORIAL HAMILTONIAN Matrix elements of the pure rotational operator: Pure rotational basis: ~ Rotational labels: ~ ~ ~ ~ ~ ~~~

10. Columbus 2005, 20/6/05 -- 24/6/05 COMPARISON AT ORDER ZERO

11. Columbus 2005, 20/6/05 -- 24/6/05 or PRINCIPAL AXES Watson(OXYZ) Moret-Bailly(Oxyz)

12. Columbus 2005, 20/6/05 -- 24/6/05 LINKS BETWEEN TENSORIAL AND WATSON’S MODELS Kets : Parameters : For all reduction types (A, S or 6) and till the 6 degree. … ~ ~

13. Columbus 2005, 20/6/05 -- 24/6/05 DETAILS OF THE ANALYSIS (v = 0 ) S-Reduction 6-Reduction † t 9 = 0 opt. t 9 RMS (kHz) 102.8579.2772.8569.87 (kHz)262123.4723.29 assigned lines (J max = 99). 1071 assigned lines (J max = 99).  :standard deviation calculated from the median of absolute residuals. residuals. † K. Sarka et al., Journal of Molecular Spectroscopy, 200, 55 – 64, (2000).

14. Columbus 2005, 20/6/05 -- 24/6/05 A MORE COMPLEX CASE, THE ( 3, 7, 9 ) BENDING TRIAD

15. Columbus 2005, 20/6/05 -- 24/6/05 DETAILS OF THE ANALYSIS « Classical » Model † Tensorial Model Nber of parameters 79 (3 interactions) 42 (10 interactions) Degree of development 86 J MAX 8686 Number of IR assignments 4806 4732 + 148 Number of MW assignments 499384 RMS IR (mk) 0,5530,608 RMS MW (.10 -6 cm -1 ) 5,22,1 † H. Bürger et al., Journal of Molecular Structure, 612, 133 – 141, (2002).

16. Columbus 2005, 20/6/05 -- 24/6/05 OVERVIEW IR spectrum: H. B ü rger (Wuppertal)

17. Columbus 2005, 20/6/05 -- 24/6/05 THE 7 BAND

18. Columbus 2005, 20/6/05 -- 24/6/05 THE Q BRANCH OF THE 7 BAND

19. Columbus 2005, 20/6/05 -- 24/6/05 PERSPECTIVES Analysis of the 5 (a 2 )/ 4 (a 1 ) dyad of SO 2 F 2 deriving from the 2 (E) band of SO 4 2  Global analysis of the first vibrational levels: the ground-state, the dyad and the triad Ref. :- M. Rotger, V. Boudon et M. Loëte, J. Mol. Spectrosc., 216, 297–307, (2002). - M. Rotger, V. Boudon, M. Loëte, L. Margulès, J. Demaison, H. Mäder, - M. Rotger, V. Boudon, M. Loëte, L. Margulès, J. Demaison, H. Mäder, G. Winnewisser et H.S.P. Müller, J. Mol. Spectrosc., 222, 172–179, (2003). G. Winnewisser et H.S.P. Müller, J. Mol. Spectrosc., 222, 172–179, (2003). - Ch. Wenger, M. Rotger et V. Boudon, JQSRT, 93, 429-446, (2004). - Ch. Wenger, M. Rotger et V. Boudon, JQSRT, 93, 429-446, (2004). Other quasi-spherical top molecules: IOF 5 (C 4v ), H 2 SO 4 (atmosphere of Venus, C 2 ), …

20. Columbus 2005, 20/6/05 -- 24/6/05 C 2v TDS DATABASE http://www.u-bourgogne.fr/LPUB/c2vTDS.html  C 2v TDS for XY 2 Z 2 molecules.

21. Columbus 2005, 20/6/05 -- 24/6/05 C 4v TDS DATABASE http://www.u-bourgogne.fr/LPUB/c4vTDS.html  C 4v TDS for XY 5 Z molecules.

22. Columbus 2005, 20/6/05 -- 24/6/05 MANY THANKS TO THESE PERSONS: « Classical » analysis: I. Merke and F. Hegelund, « Classical » analysis: I. Merke and F. Hegelund, IR spectra: H. Bürger, IR spectra: H. Bürger, Millimeter and microwave spectra: L. Margulès and J. Demaison, Millimeter and microwave spectra: L. Margulès and J. Demaison, H. Mäder, H.S.P. Müller and G. Winnewisser, H. Mäder, H.S.P. Müller and G. Winnewisser, V. Boudon, J.-P. Champion, M. Loëte, N. Zvereva-Loëte and V. Boudon, J.-P. Champion, M. Loëte, N. Zvereva-Loëte and Ch. Wenger. Ch. Wenger.