Electric-field-induced two-photon processes

135

Journal of Molecular Structure, 175 (1988) 135-140 Elsevier Science Publishers B.V., Amsterdam -Printed

ELECTRIC-FIELD-INDUCED

TlU-PHOTON

David

P. Blake

L. Andrews,

Nick

School of Chemical Sciences,

in The Netherlands

PROCESSES

and Kevin

P.

Hopkins

University of East Ilnglia, Norwich NR47TJ, England,

ABSTRACT

In this paper we outline the novel features associated with two-photon processes in the presence of intense static electric fields. Both electrical polarisation effects and non-linear electro-optical effects are discussed, and It is illustrated how the their likely orders of magnitude estimated. interaction of the electric field with a molecular centre can lead to a relaxation of conventional two-photon selection rules, allowing spectroscopic access to otherwise forbidden excited states. Selection rules for the electro-optical channel are tabulated for some of the more common point groups. IRTRODUCTION

The

application

optical

of

spectroscopy

electrical

polarisation

polar

anisotropy

of

leading

to

spectrum.

the

usually

second

which

normal

suitable

absent.

molecular

wavefunctions,

otherwise

application

Here

be

of

the

which

the

of

thereby

field

more

This

the

the

the

is

an

containing macroscopic results

allowed

in a

transitions,

various

lines

enables

universal

of

other

an

application,

the lines

and

certain

rise lines

to

to

be

mixes

take

a novel

to

one

in

fnteractfon

partially

some transitions give

is

electro-optical

perturbs

allowing

enables

alignment.

on

first

fluids

produce

in

through

can

The

to appear.

field

This

influence

to

beam configuration

of

static

an

can

on

intensity

spectrum is

forbidden.

field

restrictions

proceed

the

a

molecular

of

choice

from

transitions

normally

would

symmetry

exert

mechanisms.

specifically

of of

can

distinct

and relates

changes

absent

field

two

application

mechanism,

molecular

by

a degree

distinctive Moreover,

are

The

Here,

by introducing

relaxation

electric

fluids effect,

molecules.

which

a static of

place

effect

switched

the which

wherein into

the

spectrum. The

distinct

absorption However, such scant

as

roles

spectroscopy the

influence

two-photon attention

0022-2860/88/$03.50

of

these

have of

discussed

a static

electric

absorption from

mechanisms

been

in in

conventional two earlier

field

and Raman scattering

spectroscopists

(refs.

on

two-photon

has, 3-4).

0 1988 Elsevier Science Publishers B.V.

(single-photon), papers

l-2).

interactions,

as yet, Studies

trefs.

received of

both

only these

136

processes

in

structure.

It

a

field-free

additional

information

is

the

field-dependence effects

in

double

layer

environment

purpose

of

which these

systems

provide

this

can

paper

be

large

hey

to

information

demonstrate

obtained

interactions,

where

(ref.

of

by

studying

and to consider

local

fields

exist,

on

the the

amount

novel

electric

e.g.

molecular

large

electric

field

within

the

of

induced

electrical

5).

SELECTION RULES The

(ElxEl)-allowed

optically

transitions

occur

in

tElxElxEl)-allowed associated

with

involving

the

selection

rules

operators

(one

a

D'""

R^,Y,z*

and

Although

electric

For

the is

‘1-l

Since seven This

,

each

absorption

type in

one and

rules

is

the

operators

ungerade

implies rules, rules

that

the

induced

by

absorption

selection

characteristic

the

of

the

rotations

two

line

intensities

set

of

selection

field

with

the

in

the

be governed

by

interaction

rules

will

transform:(2)

denoted

must

all

be of

electro-optical the

(g w g)

and

two-

channel

field

scattering

sign,

ungerade

optically

and field-induced

hyper-Raman

by the minus

between

whereas

electric

tensor.

apply.

electric

differences

the

type,

(refs.6~8)

of

different static

symmetry,

(g 0 u),

of

of

still

the dipole

as

'30

important

the

two

rank

change

each case,

centre,

the

(1-I +

((1-t D - t

of

of

are

former

molecular

a radiation-molecule

three dipole

the

that

rules

completely

representations

of

selection

transitions

selection

i

one

D“"

an associated

the

field

In

traceless

causes

as

the

two-photon

electro-optic

can be expressed

two-photon

of

which the

product

This

Consequently

iI-,

at

direct

a scalar,

a

of

rules.

photons

of

of and

application

the

interaction

irreducible

selection

three-photon

selectton

D

means field,

index-symmetric

viewed

of

term

processes,

results

of

product

resultant

photon

may be

dipole

two how

channel The

by

transforms.

an

polarisation

trequency.

highlights

Laporte-

of

by

static

selection

representation

that

DC'-'.

of

photon)

electro-optical

zero

up

by

conventional

how the direct

D

each

the

of

action

governed

is the

species

oi

set

applicable.

absorbing 1 imit

opened

distinct

D’“‘,

in the spectra,

of

channel

are for

channel,

absence

concerted

Here the

rules

the

symmetry. and

will

threelead

allowed Thus

have

two-photon

characteristics

Raman transitions (refs.9-11).

to

channel

(u e, u). the

the

obey

137 In point minuses that

can

the

since

where

be dropped

the

allowed

of

eqns.

transitions

the

can

rank

two-photon

processes

accessibility

of

to

Single-photon

still also

three

does

have

tensor.

the

the

1 given also

pluses

conditions

It

is

to new excited

transformation

are

how the

exist,

access

Table

The results

highlight

not

Under these

provide

representations,

groups.

further

element

1 and 2.

can

irreducible

more common point

Group

inversion

route

traceless,

properties

the

from

electro-optical

symmetric

the

groups

shows in

electro-optical

clear

states,

properties the

eqn.

given

and

a

transformation 2,

for

of

for

some

normal

channel

one-

leads

to

of and the

states.

Two-photon

process

process

Electra-optfcally allowed

two-photon

process

C

C 2v C 3v C

* u’

Bu

A

Al,

Dl’

Ai,

A

E

A 1, *2,

E

E

A 1, *2’

g,,

A

QV

1’ 1’

B

8’

B2

e;

*2,

Dl,

B2 g2,

B

Ag,B lg’B2g’ B3g Ai ,A; ,E’,E” A

D6h

A 2u’ Eu A 2u’ Eu

Td

T2

1~‘~2u’~3u A; , E’

D2h D3h D 4h

Ig’ *2g*

F

*U’

B”

Al,

A29 Dl,

Al> A2,

E

Al,

Ul,

*2,

82

B2,

E

*A*” lt1’~2u’~3u ,A” , Ah , A; ,E’ ,E” *i 1 A _&‘*2LCBl” B2u’ Eu A B _l&*2u -- lu’B2u1Elu’EgU A1,*2,E,TI,T2

B

lg’ B2g’ Eg E lg’ *zg’ lg’ E2g Al,E,T1,T2

A

A’ -“,I lu cu *G

Tlu’ T2u JI,l~~

Table 1: Representations of the transition operators for single-photon, twoand electro-optically allowed two-photon processes. The under1 ining photon, in the fourth column denotes representations which are uniquely allowed through the electro-optical two-photon interaction, and the asterisk denotes a representation which is only allowed in double-beam EFITPA and electric field induced resonance-Raman scattering.

ELECTRIC-FIELD-INDUCED

In

EFITPA,

intensity allow

IWO-PHOTON

electrical

enhancement,

observation

of

ABSORPTION

polarisation but

with

transitions

careful forbidden

@FITPA)

effects choice

do of

not

only

give

beam configuration

in the absence

of

the field.

rise

to

they

can

Fig.1

138

I

2. 2

2. 1

2. 0

1.9

2

1.8

8 z

1.7

ae 2 w A ::

1.6 1.5

w 43 g

1.4

5 1.3 1.2

1. 1 1.0

2

0

4

6

6

10

12

14

p.E,,.z

Fig-l:

Intensity p.E,,,/kT

shows the

the

enhancement

field-dependence

intensity

fluid.

nitrobenzene

fields

would

field

molecules times show

of

transition

amplifying

that

10e

rates

of with

large than

an

20

22

24

26

transition

as a function

transition.

The increase

molecular

greater

Vm-‘.

by

DLu-’

weight-0

degree

lo-100

16

26

kT

a component

the

typically

strengths

/

a component

to

show

local

applied

of

corresponds

Calculations

experience

for

16

intensity This

alignment

in

within

the

electric-susceptibilities the

external

enhancement

property

choosing

of

solvents

fleld. of

Thus

about

could

be

with

large

2

at

exploited

in

electric-

susceptibilities. The electro-optical inaccessible previous nature

component. size

to

channel,

the

dipole

local

of

new states moment

three-photon

fields

permits

two-photon

can

be

can

operator

electro-optical

In fact,

those

normal

these

section, of

mechanism

through

access

to

vibronically As

absorption. be and

accessed the

because

incorporation

EFITPA intensities absorption.

exploited,

As with especially

excited

should the since

states

discussed of

the of

be of

electrically the

in

rate

a

the

ungerade weight-3

comparable polarised has

an E”-

139 A local

dependence. a one

transitions under

could

be

the

multiphoton

recorded

an of

with

effects

apparent

the

formed.

field

when

the

of

between the

Al ternat

are

the

and

complete

of

give

media

with

intensities electric distinguish

is

only

intensity

the

is

likely

a

high

to

therefore

the

be

a

large

method

techniques

is

so

a high shift use

fluorescence.

the

(ref.

state(s) with

particular

of

of

In

frequency of

yield

one

the

consistent

excited

be conducted

quantum

to

EFITPA spectra.

can

consider

infra-

proportional

are

to This

on the

an electro-optical

is

from

photons

show,

many available

15).

may be over coupled electric-

for

intensity

forbidden

applied.

the

less

in

Because vibrational

(ref.20),

specific

confirms

to

in characterising

is

Raman

analysis

straightforward

scattering

angles

for

a

13). a high

It

can

intensities

magnitude be

to

shown

100 times

more

should that

hyper-Raman

constants,

with

is

example,

at

lead

transitions

fluids

for

allowed

evidence

can

field

used

isotropic

surfaces,

dielectric

Vm-’

Furthermore,

analysis

of

experimental

107-10e

1).

intensities

when an electric

valid

such

the

and

of

Fig.

(ref.

of

field

mSSsUrementS

analysis

comparable

the

fluorescence

electric

electrode

fields

field

and

for

process

photons.

ratio

five

high

yield

rate

of

ionisation

(see

phenomena.

should

reaction

the

collection

to

observed

to

electro-optical

12)

the

fields

2-3

may be

symmetry

(ref.

for

useful

a static

close

In addition,

Bergh

above.

Calculations

symmetry

requires

field

discussed

have

prove

depolarisation

molecules

EFITPA

transitions

den

van

kind

there

electric

ratios media

transition of

to

RAMN SPECTROSCOPY @FIRS)

of

that

standard

that

two-photon

the

emitted

multiphoton

change.

isotropic

feasible

lead

electric

between

fluorescent

as

may

presence

16-19),

lead

the

and

ELECTRIC-FIELD-INLWCED

enhancement

thus

and

The observations

of

involved

it

resonance-enhanced

(refs.

would

is

pure

Gozel

absorption

available will

incident

transitions

it

to

external

CF,HCl,

13-14).

of

molecules

In the

field

Thus,

strength

relationship

effect

process

ively,

of

(refs.

sensitivity

the

in

multiphoton

The detection

degree

external

The quantum electrodynamical

methods

some cases

the

an applied

linear

field.

an electro-optical

Several

of

dissociation

the

of

times

comparable

electric-field-induced square

ten

enhancement.

conditions.

In studying

square

of

intensity

favourable

red

field

hundred-fold

Square-wave

processes

rise

to observable

electro-optical

aqueous

phase-sensitive

field-induced

the

scattering,

e.g.

intense.

give

detection from

and media,

route in

certain

transition

modulation could conventional

of help

the to

Raman

140 scattering. Analysis specific

the

selection

selection normal

of

rules

electro-optical rule

for

this

Av = *l

vibrations

which

are

optical These

In this

allowed

Raman scattering

Raman scattering.

To

determination transition

can

is (ref.

in

perform it be

scattering

dominates, are

quite

case,

infra-red

(two-photon

Raman transitions intensities

still

interaction

Raman spectroscopy.

normal

Ramn

necessary

used

sufficient

to

to

and

symmetry to

specify

cheracterise

to

take

the

those

1 illustrates

absorption

a complete is

shows

and consequently different

Table

process),

tensor

(single-photon

intensity symmetry

for of

process), allowed

of

the

five intensity

the

symmetry

symmetry

electro-optically

two

the

obtained

the

analysis

that

electro-

measurements. ratios class

whose of

each

21).

ACKNOWLEDGMENTS K. P.H and N. P.B and Engineering

gratefully

Research

acknowledge

financial

support

from

the

Science

Council.

REFERENCES

6 7 8 9 10 11 12 13 14 15 16 17 18

19 20 21

D.L. Andrews and B.S. Sherborne, Chem. Phys., 88, (1984), l-5. D.L. Andrews and B.S. Sherborne, Chem. Phys., 108, (19861, 357-363. G.F. Thomas, J. Chem. Phys., 86, (1987), 71-76. G.E. Stedman, Adv. Phys., 34, (1985), 513-587. in L. Neel (Editor), Nonlinear Behaviour of Molecules, Atoms W.J. Plieth, in Electrfc, Magnetic or Electromagnetic Fields, Elsevier, and Ions Amsterdam, 1979, pp. 251-259. W.M. MC Clain, J. Chem. Phys., 57, (1972), 2264-2272. R.N. Dixon, J.M. Bayley and M.N.R. Ashfold, Chem. Phys., 84, (19831, 21-34. D.L. Andrews and P.J. Wilkes, J. Chem. Phys., 83, (1985), 2009-2014. J.H. Christie and D.J. Lockwood, J. Chem. Phys., 54, (1971), 1141-1154. C.D. Churcher, Mol. Phys., 48, (1982), 621-628. D.L. Andrews and M. J. Harlow, Mol. Phys., 49, (1983), 937-944 P. Gozel and H. van den Bergh, J. Chem. Phys., 74, (1981), 1724-1727. D.L. Andrews, N.P. Blake and K.P. Hopkins, in preparatfon. D.L. Andrews and K.P. Hopkins, in preparation. P.M. Johnson, Act. Chem. Res., 13, (1980), 20-26. 50A, F.R. Aussenegg, M.E. Lippitsch, R. Moller and J. Wagner, Phys. Lett., (1974), 233-234. F.R. Aussenegg, ME. Lippitsch, H.M. Noll, and E.J. Schieffer, Phys. Lett., 68A, (1978)) 194-196. ME. Lippitsch, H.M. Noll, and E.J. Schieffer, in E.D. F. R. Aussenegg. Proc. Sixth Int. Conf. Raman Spectroscopy, Vol. 2, Schmid (Editor), Heyden, London, 1978, pp. 176-177. M.E. Lippitsch, R. Moller, H.M. Noll, E.J. Schieffer and F.R. Aussenegg, J. Phys. E 11, (1978), 621-622. Molecular Quantum Electrodynamics, D.P. Craig and T. Thirunamachandran, Academic, London, 1984, pp. 128-141. D.L. Andrews and N.P. Blake, fn preparation.