Columbus, June 20--24, 2005 Stark Effect in X 2 Y 4 Molecules: Application to Ethylene M. ROTGER, W....
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Transcript of Columbus, June 20--24, 2005 Stark Effect in X 2 Y 4 Molecules: Application to Ethylene M. ROTGER, W....
Columbus, June 20--24, 2005
Stark Effect in XStark Effect in X22YY44 Molecules: Molecules: Application to EthyleneApplication to Ethylene
M. ROTGER, W. RABALLAND, V. BOUDON,
and M. LOËTE
Laboratoire de Physique de l’Université de BourgogneLaboratoire de Physique de l’Université de Bourgogne~
Equipe Spectroscopie et Dynamique MoléculaireEquipe Spectroscopie et Dynamique Moléculaire
Columbus, June 20--24, 2005
Objectives of this studyObjectives of this study
Conclusion and perspectivesConclusion and perspectives
The isolated ethylene moleculeThe isolated ethylene molecule
The ethylene molecule placed in an electric field: The ethylene molecule placed in an electric field: the Stark effectthe Stark effect
Adsorption in Adsorption in zeoliteszeolites
Columbus, June 20--24, 2005
Capture of industrial pollutants present in gazeous rejections Reversible adsorption processReversible adsorption process Synthesis of zeolites adapted Synthesis of zeolites adapted to the captured moleculeto the captured molecule
Zeolites = micro-structurated porous solidsZeolites = micro-structurated porous solids
Choice of a test-molecule:Choice of a test-molecule:
THE ETHYLENE (CTHE ETHYLENE (C22HH44))
ModelModel
Columbus, June 20--24, 2005
Theory and data processing already tested on molecules pertaining to the CC2v2v , CC3v3v , CC4v4v , TTdd and OOhh groupsgroups.
Tensorial formalism & operators adapted to the Tensorial formalism & operators adapted to the DD2h 2h
symmetry.symmetry.
Software for the simulation of high-resolution spectra.Software for the simulation of high-resolution spectra.
Same technique has been used for the Same technique has been used for the DD2h 2h group.group.
Pure quantum model (developed in L.P.U.B.) based on: Groups theory & tensorial Algebra.Groups theory & tensorial Algebra.
The Molecular HamiltonianThe Molecular Hamiltonian
Columbus, June 20--24, 2005
RoRovibrational vibrational Hamiltonian- V vibrational operators are function of aa++ and a a operators.operators.- R rotational operators are function of JJxx , JJyy and JJz z operatorsoperators..- t are the parameters of the model.
RRotationalotational RRotationalotational VVibrationalibrational VVibrationalibrational
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H = t iR ,iV{ } R iR{ } ⊗V iV{ }( )
iR ,iV{ }
∑
Calculated spectra with Calculated spectra with DD2h2hTDSTDS
Columbus, June 20--24, 2005
Transition FrequencyTransition Frequency
Lin
e In
ten
sity
Lin
e In
ten
sity
Spectrum of the Spectrum of the vv2 2 band of Cband of C22HH44
Columbus, June 20--24, 2005
Raman spectrum recorded by D. Bermejo,Instituto de Estructura de la Materia, Madrid, Spain
We deduce:- v0 = 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
Spectrum of the Spectrum of the vv1212 band of C band of C22HH44
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:- v0 = 1442,440 13(22)- A = 4,924 85(27)- B = 1,007 52(27)- C = 0,826 54(18)in cm-1
Columbus, June 20--24, 2005
The ethylene molecule submitted toThe ethylene molecule submitted toan electric field: the Stark effectan electric field: the Stark effect
The Stark HamiltonianThe Stark Hamiltonian
Columbus, June 20--24, 2005
• C represents the direction cosines of the OZ axisin the (O, x y z) frame• tS : parameters of the Stark Hamiltonian
{ } { } { } { }( )[ ]{ }∑ ⊗⊗=
VRC
VRCVRC
iii
iiiiiiSZZ VRCt
,,
,,α
Stark HamiltonianStark Hamiltonian
HH00 : zero-field Hamiltonian : zero-field Hamiltonian
ZZ ZZ : polarisability tensor: polarisability tensor
20S 2
1H ZZZ EH −=
Electric field along the Electric field along the Z Z axisaxis of the laboratory frame of the laboratory frame
The Stark matrixThe Stark matrix
Columbus, June 20--24, 2005
Representation of couplings between some states of the Stark HamiltonianRepresentation of couplings between some states of the Stark Hamiltonian
DD2h2hTDS softwareTDS software
Stark transitions calculationsStark transitions calculations
Shifts and splittings Shifts and splittings of the energy levels:of the energy levels:
Upperstate
Lowerstate
E=0 E>0
Determination of the Determination of the ttSS parameters of the polarisability thanks to parameters of the polarisability thanks to ab initioab initio
Application to the Stark lines of the Application to the Stark lines of the vv7 7 bandband
Columbus, June 20--24, 2005
E > 0
J = 1M = 0
J = 0M = 0
J = 1|M| = 1
GroundState
(v7 = 1)state
E = 0
J = 0
J = 1
P(1)
Shift and splitting of the rovibrational Shift and splitting of the rovibrational lines are very small !!!lines are very small !!!
€
ν (E = 0) = 942,905316 cm−1
Δν (E = 43.103) < 0,000050 cm−1
⎧ ⎨ ⎩
We need a very good accuracy on the We need a very good accuracy on the zero-field parameters for the zero-field parameters for the vv7 7 bandband
Yit-Tsong-Chen and T. Oka, J. Chem. Phys. 88, 5282-90 (1988)M = 0 |M| = 1E / kV.cm-1
42,9
0
f / kHz 0 770 1260v / 10-6 cm-1 0 26 42
Stark matrix and calculation softwareStark matrix and calculation software
Columbus, June 20--24, 2005
Number of non-zero matrix elements of the Stark Hamiltonian
1,0E+02
1,0E+03
1,0E+04
1,0E+05
1,0E+06
1,0E+07
10 20 30 40 50
J
IsolatedIsolatedmolecule:molecule:
JJ’ = ’ = J J
Molecule in an Molecule in an electric field:electric field:
| | JJ’ – ’ – JJ | = 0, 1, 2 | = 0, 1, 2
| | MM | = 0, … , | = 0, … , JJ
Example for truncation at J = 50:
N0 = 44 200 NS = 8 200 000
x 185x 185
Columbus, June 20--24, 2005
Extension of the model and the programs to the Stark effect
Extension to multipolar electric fieldsExtension to multipolar electric fields
Software (DD2h2hTDSTDS) for the simulation of high resolution spectra
Tensorial model of the molecular Hamiltonian and transition moments for the ethylene and all other molecules of DD2h2h
symmetrysymmetry
Analysis of experimental data in IR absorption and Raman spectroscopy
Comparison with spectra of the adsorbed molecule: Comparison with spectra of the adsorbed molecule: νν1212 ? ?
Extension of the tensorial model to confinement phenomenaExtension of the tensorial model to confinement phenomena