Transcript Stark_MR.ppt

Columbus, June 20--24, 2005
Laboratoire de Physique de l’Université de Bourgogne
~
Equipe Spectroscopie et Dynamique Moléculaire
Stark Effect in X2Y4 Molecules:
Application to Ethylene
M. ROTGER, W. RABALLAND, V. BOUDON,
and M. LOËTE
Columbus, June 20--24, 2005
Objectives of this study
The isolated ethylene molecule
The ethylene molecule placed in an electric field:
the Stark effect
Conclusion and perspectives
Columbus, June 20--24, 2005
Objectives of this study
Columbus, June 20--24, 2005
Adsorption in zeolites
Zeolites = micro-structurated porous solids
 Capture of industrial pollutants
present in gazeous rejections
 Reversible adsorption process
 Synthesis of zeolites adapted
to the captured molecule
 Choice of a test-molecule:
THE ETHYLENE (C2H4)
Columbus, June 20--24, 2005
The isolated ethylene molecule
Columbus, June 20--24, 2005
Model
Pure quantum model (developed in L.P.U.B.) based on:
Groups theory & tensorial Algebra.
Theory and data processing already tested on molecules
pertaining to the C2v , C3v , C4v , Td and Oh groups.
Same technique has been used for the D2h group.
 Tensorial formalism & operators adapted to the D2h
symmetry.
 Software for the simulation of high-resolution spectra.
Columbus, June 20--24, 2005
The Molecular Hamiltonian
Vibrational
Rotational
H

i R ,iV 
t
i R ,iV 
R
iR 
V
iV 

Rovibrational Hamiltonian
- V vibrational operators are function of a+ and a operators.
- R rotational operators are function of Jx , Jy and Jz operators.
- t are the parameters of the model.
Columbus, June 20--24, 2005
Line Intensity
Calculated spectra with D2hTDS
Transition Frequency
Columbus, June 20--24, 2005
Spectrum of the v2 band of C2H4
Fit of 23 { t }
parameters
- 141 data
- Standard
deviation (rms):
2,3x10-3 cm-1
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
Raman spectrum recorded by D. Bermejo,
Instituto de Estructura de la Materia, Madrid, Spain
Columbus, June 20--24, 2005
Spectrum of the v12 band of C2H4
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
IR spectrum recorded by J. Vander Auwera,
Université Libre de Bruxelles, Belgium
Columbus, June 20--24, 2005
The ethylene molecule submitted to
an electric field: the Stark effect
Columbus, June 20--24, 2005
The Stark Hamiltonian
Electric field along the Z axis
of the laboratory frame
Stark Hamiltonian
1
H S  H 0   ZZ EZ2
2
H0 : zero-field Hamiltonian
ZZ : polarisability tensor
 ZZ 
 tS
iC ,iR ,iV 
iC ,iR ,iV 
C   R V   
iC
iR
iV
• C represents the direction
cosines of the OZ axis
in the (O, x y z) frame
• tS : parameters of the
Stark Hamiltonian
Columbus, June 20--24, 2005
The Stark matrix
Representation of couplings between some states of the Stark Hamiltonian
Shifts and splittings
of the energy levels:
Upper
state
Lower
state
 D2hTDS software
 Stark transitions calculations
E=0
E>0
 Determination of the tS parameters of the polarisability thanks to ab initio
Columbus, June 20--24, 2005
Application to the Stark lines of the v7 band
Yit-Tsong-Chen and T. Oka, J. Chem. Phys. 88, 5282-90 (1988)
(v7 = 1)
state
E / kV.cm-1
J=0
770
26
1260
42
0
f / kHz
v / 10-6 cm-1
0
0
 Shift and splitting of the rovibrational
lines are very small !!!
  (E  0)
 942,905316 cm1

3
0,000050 cm1
 (E  43.10 ) 
J=1
J=1
M=0
J=1
|M| = 1
P(1)
|M| = 1
42,9
J=0
M=0
Ground
State
M = 0
E=0
E>0

 We need a very good accuracy on the
zero-field parameters for the v7 band
Columbus, June 20--24, 2005
Stark matrix and calculation software
Number of non-zero matrix elements of the Stark Hamiltonian
1,0E+07
1,0E+06
Isolated
molecule:
Molecule in an
electric field:
J’ = J
| J’ – J | = 0, 1, 2
| M | = 0, … , J
1,0E+05
1,0E+04
Example for truncation at J = 50:
N0 = 44 200
1,0E+03
NS = 8 200 000
1,0E+02
10
20
30
J
40
50
x 185
Amplitude of the electric field / 107V.cm-1
The Stark spectrum of the 12 band
3.0
2.5
2.0
1.5
1.0
0.5
Jmax = 15
T = 50 K
Zero-field
1420
1430
1440
1450
Wavenumber / cm-1
1460
1470
Columbus, June 20--24, 2005
Conclusion and perspectives
Columbus, June 20--24, 2005
 Tensorial model of the molecular Hamiltonian and transition
moments for the ethylene and all other molecules of D2h
symmetry
 Software (D2hTDS) for the simulation of high resolution spectra
 Analysis of experimental data in IR absorption and Raman
spectroscopy
 Extension of the model and the programs to the Stark effect
 Extension to multipolar electric fields
 Extension of the tensorial model to confinement phenomena
 Comparison with spectra of the adsorbed molecule: 12 ?