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Columbus, June 20--24, 2005

Stark Effect in XStark Effect in X22YY44Molecules:Molecules:Application to EthyleneApplication to Ethylene

M. ROTGER,W. RABALLAND, V. BODON,

!n" M. LO#TE

Laboratoire de Physique de l!ni"ersit# de $our%o%neLaboratoire de Physique de l!ni"ersit# de $our%o%ne

&

Equipe Spectroscopie et 'yna(ique Mol#culaireEquipe Spectroscopie et 'yna(ique Mol#culaire

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)b*ecti"es of this study)b*ecti"es of this study

+onclusion and perspecti"es+onclusion and perspecti"es

,he isolated ethylene (olecule,he isolated ethylene (olecule

,he ethylene (olecule placed in an electric field:,he ethylene (olecule placed in an electric field:the Stark effectthe Stark effect

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)b*ecti"es of this study)b*ecti"es of this study

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A"so$%&'on 'nA"so$%&'on 'n zeoliteszeolites


C!%&u$e o( 'n"us&$'!l %ollu&!n&s%$esen& 'n )!*eous $e+e&'ons

Ree$s'ble !"so$%&'on %$oessRee$s'ble !"so$%&'on %$oess

/n&es's o( *eol'&es !"!%&e"/n&es's o( *eol'&es !"!%&e"&o &e !%&u$e" moleule&o &e !%&u$e" moleule

Zeolites = micro-structurated porous solidsZeolites = micro-structurated porous solids

Co'e o( ! &es&-moleule1Co'e o( ! &es&-moleule1

TE ET3LENE CTE ET3LENE C2244

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Mo"elMo"el


Teo$/ !n" "!&! %$oess'n) !l$e!"/ &es&e" on moleules%e$&!'n'n) &o &e CC2v2v,CC3v3v,CC4v4v,TTdd!n" OOhh)$ou%s)$ou%s.

Tenso$'!l (o$m!l'sm 6 o%e$!&o$s !"!%&e" &o &eTenso$'!l (o$m!l'sm 6 o%e$!&o$s !"!%&e" &o &e DD2h2h

s/mme&$/.s/mme&$/. o(&7!$e (o$ &e s'mul!&'on o( ')-$esolu&'on s%e&$!.o(&7!$e (o$ &e s'mul!&'on o( ')-$esolu&'on s%e&$!.

!me &en'8ue !s been use" (o$ &e!me &en'8ue !s been use" (o$ &e DD2h2h )$ou%.)$ou%.

9u$e 8u!n&um mo"el "eelo%e" 'n L.9..B. b!se" on1 G$ou%s &eo$/ 6 &enso$'!l Al)eb$!.G$ou%s &eo$/ 6 &enso$'!l Al)eb$!.

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Te Moleul!$ !m'l&on'!nTe Moleul!$ !m'l&on'!n


RoRo'b$!&'on!l'b$!&'on!l !m'l&on'!n-V 'b$!&'on!l o%e$!&o$s !$e (un&'on o( aa++!n" aa o%e$!&o$s.o%e$!&o$s.-R$o&!&'on!l o%e$!&o$s !$e (un&'on o(JJxxJJ!!!n"JJ"" o%e$!&o$so%e$!&o$s##

-t!$e &e %!$!me&e$s o( &e mo"el.

RRotationalotationalRRotationalotational

VVibrationalibrationalVVibrationalibrational

H= t i

R,iV{ }

R iR{ }V

iV{ }

( )iR

,iV{ }

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C!lul!&e" s%e&$! 7'&C!lul!&e" s%e&$! 7'&DD2h2hTDTD


T$!ns'&'on :$e8uen/T$!ns'&'on :$e8uen/

L'ne;n&ens'

&/

L'ne;n&ens'

&/

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%e&$um o( &e%e&$um o( &e vv22 b!n" o( Cb!n" o( C2244


R!m!n s%e&$um $eo$"e" b/ D. Be$me+o,$%stituto de &structura de la 'ateria, M!"$'", %!'n

We "e"ue1-v0< =>2>,=?> 24>=-(< 4,@0 =2=0-)< 0,4 @0=0-C< 0,@2 45??0'n m-=

:'& o( 2 t%!$!me&e$s - =4= "!&! - &!n"!$""e'!&'on $ms1 2,=0-m-=

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%e&$um o( &e%e&$um o( &e vv=2=2b!n" o( Cb!n" o( C2244


;R s%e&$um $eo$"e" b/ J. V!n"e$ Au7e$!,*%iversit ,ire de )ruxelles, Bel)'um

:'& o( 20 t

%!$!me&e$s- @22 "!&!- s&!n"!$" "e'!&'on$ms1 =,=0-m-=

We "e"ue1

-v0< =442,440 =22-(< 4,24 @52?-)< =,00? 522?-C< 0,@2> 54=@'n m-=

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,he ethylene (olecule sub(itted to,he ethylene (olecule sub(itted toan electric field: the Stark effectan electric field: the Stark effect

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Te &!$F !m'l&on'!nTe &!$F !m'l&on'!n


C$e%$esen&s &e "'$e&'onos'neso( &e O

!'s'n &e O,x ! " ($!me

t.1 %!$!me&e$s o( &e &!$F!m'l&on'!n

{ } { } { } { }( )[ ]{ } =

VRC

VRCVRC

iii

iiiiii

SZZVRCt

..

..

Stark HamiltonianStark Hamiltonian

HH00 : zero-field Hamiltonian: zero-field Hamiltonian

ZZZZ : polarisability tensor: polarisability tensor

2

/S2

0

1 ZZZ EH =

Electric field along theElectric field along the ZZ axisaxisof the laboratory frameof the laboratory frame

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Te &!$F m!&$'Te &!$F m!&$'


Representation of couplings between some states of the Stark HamiltonianRepresentation of couplings between some states of the Stark Hamiltonian

DD2h2hTD so(&7!$eTD so(&7!$e

&!$F &$!ns'&'ons !lul!&'ons&!$F &$!ns'&'ons !lul!&'ons

Shifts and splittingsShifts and splittings

of the energy levels:of the energy levels:

Upper

state

Lower

state

E=0 E>0

De&e$m'n!&'on o( &eDe&e$m'n!&'on o( &e tt..%!$!me&e$s o( &e %ol!$'s!b'l'&/ &!nFs &o%!$!me&e$s o( &e %ol!$'s!b'l'&/ &!nFs &o a i%itioa i%itio

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A%%l'!&'on &o &e &!$F l'nes o( &eA%%l'!&'on &o &e &!$F l'nes o( &e vv?? b!n"b!n"


E > 0

J = 1

M= 0

J = 0

M= 0

J = 1

|M|= 1

Ground

State

(v7= 1)

state

E = 0

J = 0

J = 1

P(1)

'(& !n" s%l'&&'n) o( &e $o'b$!&'on!l'(& !n" s%l'&&'n) o( &e $o'b$!&'on!ll'nes !$e e$/ sm!ll HHHl'nes !$e e$/ sm!ll HHH

(E= 0) = 942,905316 cm1

(E= 43.103) < 0,000050 cm

1

We nee" ! e$/ )oo" !u$!/ on &eWe nee" ! e$/ )oo" !u$!/ on &e

*e$o-('el" %!$!me&e$s (o$ &e*e$o-('el" %!$!me&e$s (o$ &e vv?? b!n"b!n"

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

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&!$F m!&$' !n" !lul!&'on so(&7!$e&!$F m!&$' !n" !lul!&'on so(&7!$e


Numbe$ o( non-*e$o m!&$' elemen&s o( &e &!$F !m'l&on'!n

1,0E+02

1,0E+03

1,0E+04

1,0E+05

1,0E+06

1,0E+07

10 20 30 40 50

J

;sol!&e";sol!&e"moleule1moleule1

JJI

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Te &!$F s%e&$um o( &eTe &!$F s%e&$um o( &e =2=2b!n"b!n"

147014601450144014301420

Wavenumber / cm-1

3.0

2.5

2.0

1.5

1.0

0.5

Zero-field Jmax= 15

T= 50 K

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E&ens'on o( &e mo"el !n" &e %$o)$!ms &o &e &!$F e((e&

E&ens'on &o mul&'%ol!$ ele&$' ('el"sE&ens'on &o mul&'%ol!$ ele&$' ('el"s

o(&7!$e DD2h2hTDTD (o$ &e s'mul!&'on o( ') $esolu&'on s%e&$!

Tenso$'!l mo"el o( &e moleul!$ !m'l&on'!n !n" &$!ns'&'onmomen&s (o$ &e e&/lene !n" !ll o&e$ moleules o(DD2h2h

s/mme&$/s/mme&$/

An!l/s's o( e%e$'men&!l "!&! 'n ;R !bso$%&'on !n" R!m!n

s%e&$oso%/

Com%!$'son 7'& s%e&$! o( &e !"so$be" moleule1Com%!$'son 7'& s%e&$! o( &e !"so$be" moleule1 =2=2

E&ens'on o( &e &enso$'!l mo"el &o on('nemen& %enomen!E&ens'on o( &e &enso$'!l mo"el &o on('nemen& %enomen!

stark_mr

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