65th Ohio State University Symposium on Molecular Spectroscopy June 21–25, 2010 Stark spectrum simulation of X 2 Y 4 asymmetric molecules: application

65th Ohio State University Symposium on Molecular Spectroscopy • June 21–25, 2010

Stark spectrum simulation of XStark spectrum simulation of X22YY44

asymmetric molecules: application to asymmetric molecules: application to ethylene in a MFI-type host zeoliteethylene in a MFI-type host zeolite

M. Sanzharov, M. Rotger, M. Sanzharov, M. Rotger, V. BoudonV. Boudon, M. Loëte, , M. Loëte, N. Zvereva-Loëte, A. Ballandras, G. WeberN. Zvereva-Loëte, A. Ballandras, G. Weber

Laboratoire interdisciplinaire Carnot de Bourgogne, UMR 5209 CNRS - Université de Bourgogne

9 av. A. Savary, BP 47870, F-21078 DIJON Cedex – France


ContentsContents

1. Introduction

2. Theoretical model

3. Experimental details

4. Simulations

5. Conclusion and perspectives


1.Introduction


Porosity of MFI zeolite Adsorption of ethylene on Adsorption of ethylene on highly siliceous ZSM-5 highly siliceous ZSM-5

zeolitezeoliteApproachesApproaches

ab initio calculations of ethylene in zeolithe

ab initio calculations for ethylene-ethylene complex

Stark calculations


2. Theoretical model


H s =H0 +hs =H0 + μZE +12αZZEZ

2

L m value

0 0

2 -2 0

2 -1 0

2 0

2 1 0

2 2 0

−1

3

2

3

αZZ = −1

3A(0) +

2

3A(2)

A(L ) = α L ,n({ i} ,Γ)

{ i}∑

n,Γ∑ C(L ,nΓ)⊗P({ i} ,Γ)⎡⎣ ⎤⎦

(Ag)

αZZ = 0;0 ZZ A(0) + 2;m ZZm∑ A(2)

%μΘ = 1;m Θ

m∑ %μ (1g ,0Γu ),{i} C (1g ,0Γg )⊗M ({i},Γu )⎡⎣ ⎤⎦

{i}∑

Γ∑

(Au )

m X Y Z

1 0

0 0 0 1

-1 0

1

2

−1

2

−i

2

−i

2

P({i},Γ) andand M ({i},Γu ) are rovibrational operatorsare rovibrational operators

Stark HamiltonianStark Hamiltonian


H =H{P0=GS} +H{P1 }+...+H{Pk }

+...+H{Pn}

Initial Initial HamiltonianHamiltonian

Effective HamiltonianEffective Hamiltonian

H <Pn> =P<Pn>HP<Pn> =H{GS}

<Pn> +H{ P1}

<Pn> +...+H{ Pn}

<Pn>

H{Pk }= t{ns}{ms}

Ω(K ,nΓ)Γ1Γ2Γvβ RΩ(K ,nΓ)⊗ε V{ns}{ms}Γ1Γ2Γv( )

indices∑

(Ag)

t – model parameterst – model parametersV – vibrational operatorV – vibrational operatorR - rotational operatorR - rotational operator

Rovibrational coupled basisRovibrational coupled basis

J,nrCr ⊗ {vs} ,Cv{ }

The zero-field Hamiltonian operatorThe zero-field Hamiltonian operator


Selection rulesSelection rules

C '=CΔM =0ΔJ =0,1,2

Stark matrixStark matrixEvolution of the energy Evolution of the energy levels with the rise of an levels with the rise of an

electric fieldelectric field


SifS =K ifgie

hcEi /kT Φ fS μZ

(Au ) ΦiS

2+ Φ f

S μX(Au ) Φi

S2+ Φ f

S μY(Au ) Φi

S2

{ }

Kif =8π 3

hcQ(T )LT0

Tσ if 1−e

−hcσ if

kT⎛

⎝⎜⎞

⎠⎟

-the Loschmidt constant L=2,686754.10the Loschmidt constant L=2,686754.1019 19 cmcm-1-1

-the reference temperature Tthe reference temperature T00=273,15 K=273,15 K-the temperature of gas T in Kthe temperature of gas T in K-the partition function of system Q(T)the partition function of system Q(T)

gi =

7siCi =Aτ 3siCi =B1τ

3siCi =B2τ

3siCi =B3τ

⎧

⎨⎪⎪

⎩⎪⎪

€

Φ fS μΘ

(Au ) Φ iS = V CMσ( )

JCαM

Jα

∑J 'α '

∑ VJ 'Cα 'M 'CM 'σ '( ) Φ f

RV μΘ(Au ) Φ i

RV

Stark electric dipole moment intensitiesStark electric dipole moment intensities


The truncation of Stark matrix problem (I)The truncation of Stark matrix problem (I)


The truncation of Stark matrix problem (II)The truncation of Stark matrix problem (II)


3. Experimental details


In situ experimental set-up

UHV magnetic sampletransporter

Baratron pressuregauges (10 et 1000 hPa)

Infrared cell

Input of drynitrogen gas

Heat chamber

Gas supply & high vacuum

Gas andvacuum valves


4. Simulations


Spectrum Spectrum simulationsimulation of the of the 1212 band with band with

a zero-fielda zero-field


High resolution Stark spectrumHigh resolution Stark spectrum


ComparisonComparison95,5 mbar, Mmax=20, Res=3 cm-1


5. Conclusion and perspectives


Conclusion and perspectivesConclusion and perspectives

- For the value of an electric field E≈10 GV/m we observe a For the value of an electric field E≈10 GV/m we observe a shift of the νshift of the ν1212 band of Δω=8 cm band of Δω=8 cm-1-1

- The obtained results are consistant with the experimental The obtained results are consistant with the experimental results and the results of results and the results of ab initio ab initio calculations (5.14 GV/m calculations (5.14 GV/m with PBE1PBE/6-31++(2d,2p) level of theowith PBE1PBE/6-31++(2d,2p) level of theory)

- Stark spectrum simulation of the Stark spectrum simulation of the 99 and and 11 11 bands bands

- Stark Raman spectraStark Raman spectra

- Multipole electric fieldsMultipole electric fields

Documents

65th Ohio State University Symposium on Molecular Spectroscopy June 21–25, 2010 Stark spectrum simulation of X 2 Y 4 asymmetric molecules: application