1. Columbus, June 20--24, 2005 Stark Effect in X 2 Y 4 Molecules: Application to Ethylene M. ROTGER, W. RABALLAND, V. BOUDON, and M. LOËTE Laboratoire de Physique de l’Université de Bourgogne ~ Equipe Spectroscopie et Dynamique Moléculaire

2. Columbus, June 20--24, 2005 Objectives of this study Conclusion and perspectives The isolated ethylene molecule The ethylene molecule placed in an electric field: the Stark effect

3. Columbus, June 20--24, 2005 Objectives of this study

4. Adsorption in zeolites Columbus, June 20--24, 2005 Capture of industrial pollutants present in gazeous rejections Reversible adsorption process Reversible adsorption process Synthesis of zeolites adapted Synthesis of zeolites adapted to the captured molecule to the captured molecule Zeolites = micro-structurated porous solids  Choice of a test-molecule: THE ETHYLENE (C 2 H 4 ) THE ETHYLENE (C 2 H 4 )

5. Columbus, June 20--24, 2005 The isolated ethylene molecule

6. Model Columbus, June 20--24, 2005  Theory and data processing already tested on molecules C 2v C 3v C 4v T d O h groups pertaining to the C 2v, C 3v, C 4v, T d and O h groups. Tensorial formalism & operators adapted to the D 2h symmetry. Tensorial formalism & operators adapted to the D 2h symmetry. Software for the simulation of high-resolution spectra. Software for the simulation of high-resolution spectra.  Same technique has been used for the D 2h group.  Pure quantum model (developed in L.P.U.B.) based on: Groups theory & tensorial Algebra. Groups theory & tensorial Algebra.

7. The Molecular Hamiltonian Columbus, June 20--24, 2005 Rovibrational Rovibrational Hamiltonian a + a operators. - V vibrational operators are function of a + and a operators. J x J y J z operators. - R rotational operators are function of J x, J y and J z operators. - t are the parameters of the model. R otational V ibrational

8. Calculated spectra with D 2h TDS Columbus, June 20--24, 2005 Transition Frequency Line Intensity

9. Spectrum of the v 2 band of C 2 H 4 Columbus, June 20--24, 2005 Raman spectrum recorded by D. Bermejo, Instituto de Estructura de la Materia, Madrid, Spain We deduce: - v 0 = 1626,176 24(61) - A = 4,830 12(10) - B = 0,994 80(10) - C = 0,823 457(70) in cm -1 Fit of 23 { t } parameters - 141 data - Standard deviation (rms): 2,3x10 -3 cm -1

10. Spectrum of the v 12 band of C 2 H 4 Columbus, June 20--24, 2005 IR spectrum recorded by J. Vander Auwera, Université Libre de Bruxelles, Belgium Fit of 20 { t } parameters - 822 data - standard deviation (rms): 1,9x10 -3 cm -1 We deduce: - v 0 = 1442,440 13(22) - A = 4,924 85(27) - B = 1,007 52(27) - C = 0,826 54(18) in cm -1

11. Columbus, June 20--24, 2005 The ethylene molecule submitted to an electric field: the Stark effect

12. The Stark Hamiltonian Columbus, June 20--24, 2005 C represents the direction cosines of the OZ axis in the (O, x y z) frame t S : parameters of the Stark Hamiltonian Stark Hamiltonian H 0 : zero-field Hamiltonian H 0 : zero-field Hamiltonian  ZZ : polarisability tensor Electric field along the Z axis of the laboratory frame

13. The Stark matrix Columbus, June 20--24, 2005 Representation of couplings between some states of the Stark Hamiltonian  D 2h TDS software  Stark transitions calculations Shifts and splittings of the energy levels: Upper state Lower state E=0 E>0  Determination of the t S parameters of the polarisability thanks to ab initio

14. Application to the Stark lines of the v 7 band Columbus, June 20--24, 2005 E > 0 J = 1 M = 0 J = 0 M = 0 J = 1 |M| = 1 Ground State (v 7 = 1) state E = 0 J = 0 J = 1 P(1)  Shift and splitting of the rovibrational lines are very small !!!  We need a very good accuracy on the zero-field parameters for the v 7 band Yit-Tsong-Chen and T. Oka, J. Chem. Phys. 88, 5282-90 (1988)  M = 0|  M| = 1 E / kV.cm -1 42,9 0 f / kHz 0 770 1260 v / 10 -6 cm -1 0 26 42

15. Stark matrix and calculation software Columbus, June 20--24, 2005 Number of non-zero matrix elements of the Stark Hamiltonian Isolatedmolecule: J’ = J Molecule in an electric field: | J’ – J | = 0, 1, 2 | M | = 0, …, J Example for truncation at J = 50: N 0 = 44 200 N S = 8 200 000 x 185

16. The Stark spectrum of the 12 band J max = 15 T = 50 K

17. Columbus, June 20--24, 2005 Conclusion and perspectives

18. Columbus, June 20--24, 2005  Extension of the model and the programs to the Stark effect  Extension to multipolar electric fields D 2h TDS  Software (D 2h TDS) for the simulation of high resolution spectra D 2h symmetry  Tensorial model of the molecular Hamiltonian and transition moments for the ethylene and all other molecules of D 2h symmetry  Analysis of experimental data in IR absorption and Raman spectroscopy  Comparison with spectra of the adsorbed molecule: 12 ?  Extension of the tensorial model to confinement phenomena