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


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


Objectives of this studyObjectives of this study

Adsorption in Adsorption in zeoliteszeolites


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))


The isolated ethylene moleculeThe isolated ethylene molecule

ModelModel


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


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

€

H = t iR ,iV{ } R iR{ } ⊗V iV{ }( )

iR ,iV{ }

∑

Calculated spectra with Calculated spectra with DD2h2hTDSTDS


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


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


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


The ethylene molecule submitted toThe ethylene molecule submitted toan electric field: the Stark effectan electric field: the Stark effect

The Stark HamiltonianThe Stark Hamiltonian


• 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


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


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


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

The Stark spectrum of the The Stark spectrum of the νν1212 band band

Jmax = 15T = 50 K


Conclusion and perspectivesConclusion and perspectives


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

Columbus, June 20--24, 2005 Stark Effect in X 2 Y 4 Molecules: Application to Ethylene M. ROTGER, W....

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