Preparation and dynamics of vibrational hot spots in polyatomics via raman scttering

VO~IIIIIC93. nuinbrr 6

Resonance

Ram

CHCXIICAL

specrroseopy

n (RR) k

has

PHYSICS

where

been a

for the study of Eround- and tacttedslate porentml surfxe properws and dynarmcs. The posittons of the fupdamentals. overtones, and comblnation lines m a RR spectrum orovide mformatlon on the ground-state vlbrattonal force constants and anflarnlonwties [ 1,1] Properly m:erpreted, the mtenaversatrle tooi

ttcs of a RR spectrum yteld rnfo~atton on the es. cited-state potentral surraces and dynamics m the wtnily of the ground-slalc g~omelry [3-61. The he dependent fornuh for Lhe Ramman scatter.

mg amplitude [7-91 provrdes a useful prcture of how

vartous final vibrattond states, of the ground electronic

state, can act as probes of the excited (electromc)

k#Jp= i”gelX/)

,

NJ,)= P,,lX,) ,

I@,(r))= cxp(-tff,r/tl)l@,)

,

3, = wI + E,/it .

In this fornlul~~~e IS the electronic transrtion mow ment between the ground(g) and exerted (e) potential surfaces, ff, IS the excited-state hamlltonian and &, 1s tie elgenvalue of the imtml vibratIonal state. The phenomenological hfetime r” IS introduced to descnbe the “‘extramolecular” degrees of freedom [9], i e the interaction of the molecuie with its sur-

roundrn~. In eq. (1) the overlap between the evolved rrutld state, lb,(t)>, and the final state, I+ ISclearly a probe of the dynamrcs of I@,(r)).This use of I#+, or aI,, was made more explicit in ref [9], where tt was

state dynamics The time dependent formula for the Raman scattenng amplitude from an uutial state Ix,). 10 a fillill stntc IXJ IS

24/31 Dccenlbcr 1982

LETTERS

[71’

shown that

(I) *Work Supported In part by 1 NT bra% *Currentaddress Theoretical ~VI. . I. LANL. NIX hlc\~co, USA. ** Camlllc and tlcndry

586

Dregf~ls

LOS Alamos.

Tcachcr-Scholar . 0 ~9-2614~82~~OO-O~O~S

02.75 0 1982 ~or~-Ho~~d

The quantity

IG##(r)$

LS the probability

III the slate I@$, thusPJjli)

I@,(r))

trme averaged probabdity. avahble

IS

P,(/lr)

of finding

the exponentdy

IS euperunentally

by integratmg over the Raman enhancement

spectrum,

knowledge

vides useful mformatron

ofPI.

or ~+#r~I~,(r))12pro-

about

I@,(f)) only to the ex-

tent that IQ/’ IS well understood, corresponds

wavefunctlons

If I$/‘, IS poorly

coupled, anharmoruc

strongly

characterized

vrbrational

(e.g a

state) and

.I set of pbys~~lly rnterestmg 7ero-order states (on the then the subsequent decay of the correfunctron,

(RI/Z(I)),

of the zero-order We propose

state

[ lo,1 I] ‘, rlrcr~ rlrc Rarrrorr dynamics irr rlrc grortrld

elcctrorlic state. Eqs (I) and (7) refer to a pamcular

dynamtcs. IR) may bc produced by rcso-

Simple wavcfunctions

nancc WIIII cerlam bound&ah? vlbrshonal lcvcls of

the upper potc1111a1, see cq (3c), or from dlrccrly excncd

level of the first cxcrtcd allowed

derrved formula

transform

by exammmg

for the fir/f Raman spec-

ct al.

waiting

ground-srarc

dynrmrcs

the ground vibratronl

smglc? state IS populated

to spontaneously

Alicr

state.

[ 141 dlustrdtes the

of a simple p> m probing

In a scrtes of alkylbenzenes

state

cast

m eq. (3~) to

a s~nglc vrbratronal

The work of tlophms utthty

In the former

wrdth must be small enough

to allow the half-Fourier select predommantly

IS a probe of the ground-state a recently

states

lint

final state, I&, and a partrcular emission frequency, os = w, + (E, - Er>/“. We can euplrculy see that Raman rattermg dynamics

Raman wavcfunc-

trons IfZ). are tdcal to probe ground-state

the phenomcnologrcal

surface vrbrattonal

flow out

of such a &cay

that systems WIIII well-characterrzed

I@,(r)), whtch grve rise to “simple”

todissocratton

scartcnrrg becomes a probe/or

amplitude

will be present m the Raman spectrum

photodrssocratmg

ekcrtcd

indicates

states The signature

lb,(r)) is unknown, then little may be learned about either Id/) or l@,(t)) from the Raman scattermg. However, if I@,(r)) IS well characterized, as in a direct phoor resonance to a low-lymg,

]R) propagated

lower surface),

such as when I$,-)

nearly harmonic oscillator

to low-lymg.

tion mvolving the Raman wdvcfunctton

on the ground potential surface. II’ Ifi) IS cvpdndcd tn

lation

BSseen rn eq (2b).

Naturally.

24/3 I Drccmbcr I981

CHI-LtICAL PHYSICS LCTTCRS

Volume 93. number 6

and

emtt to the ground electronic

40-50

ps the sample IS photo-

totized and the photon ion signal IS monttorcd as a runctron of laser frequency Tlus techmquc measures

trum [9]

tile

relative popular~ons of groundmre vlbrrnonal AT after thctr mttlal preparation. A

levels at 3 time comparrson

J

X

exp[r(wf

- wS + E,/tl)l]

U?IR(r))

dl

, (3a)

erg

--m

m the ground

state during

Pgc163 .

WJ

eup[l( w, + E,/tr)f - rt] I&(r)) ,

(3c)

0

=

exp(-IH,t/A)lR)

.

(3‘0

whtch IS closely related IO others dewed [ 12,13], shows that the Raman spectrum IS gtven by an autocorrelatlon func-

Tha fomlula,

for Raman processes in solids

* J.L RI,ISC~.nd one of US (EJH) havehad rvcrnl d~usSIO~Sabout the use of Raman scatterm as a probe for wound (cl~c~romic) state dynnmrcs.

cn-

states

by resonance

IO a smgJe IowJying vrbrattonal level tn the excited. s~atc manifold. This resonance condrtron IS most easily satisfied

by molecules

Condon drsplaccments,

It drfficult

and

spec-

tune AT

ansmg from bound

arc most useful when they are obtamed

163 = J

B(r))

transfer

Raman wavefunctrons

where IR) =

of these spectra to the lluoresccncc

tra [ 151 provides a measure of the mtramolccular

w~lh

small Frdnck-

but small dtsplacements

to obtam detectable

mtcnsrty

vrbrational

levels of the ground state

amplrtude

to these h&lymg

be Increased by strmulated gested by Depristo

make

m the l11gb

The scattering

levels may. however. resonance Rainan as sug-

et al. [ I1 1. Such experiments

have been performed by Koffend et al. [IO] on I2 w~tb an optically pumped 1, laser. In this cast states as hrgh as u” = 96 were populated by stimulated emrssion from the Bo; excited state. Scattermg

amplitude

can also be obtamed

m high-

lying vibrational

levels when the excited electronic state is dissochttve Consider, for example, tl~e recent 587

Volu~w 93 number 6

CIIEMICAL

c~pcnmcnts of Imre ct al. [ 16j on ozone

Raman scattenng

(1111that products

high-lymg

of thssoclation.

vrbrauonal

Thus scattcrmg

but before comple tral dlstnbutmn

dissociation,

of the emltted

brahon III

IS due to the few molethus retummg hot

l&t

LSa tell-tale

a symmetric

clue

Ozone does not

dynamics.

is not

“predlssoclatton”

occurs durmg the dlssocratlon.

the absorption

to the

The spec-

I+,(r)) since the dluoc;ntlon

direct.

band

500 cm-l

artcr the UV absorption,

lo excited. and ground-state completely

states wlthm

surface vtbratlonally

have the simplest

point

out of the UV Hartley

cults which emit a photon ground potential

They

VI-

The structure

truss sectlon [ 17) Indicates that at

least some of the rrduck-Condon

wave packet

I@,(t)> remdms m the Franck-Condon few vlbrptronal periods [ IS].

regton for a

Perhaps the sunplcst possible Raman WavefunctIon involvmg large displacements would be produced m I dtrect bond dissociation Although

of a locahzed chromophore.

cq. (3~) contnms long-tinie

uill typvally

dynamics

be quite small), the transttlon

frag.

oi the Raman wavcfunction KR spectrum

ckclted state may be Illustrated

II?)

=yo = -2.0.

= l/2 (-r -.Yo)3_ + I/? Q -y#

surFace has

(1’ -yo)

t_v) + 3,.0(x -JI)’

WIII constder the three tralcctortes

plotted along wnh lh(! evcitedstalecilnlours in fig. 1, These three trqectories dose out of three dlstmct choices forxO and _I’,, m I’,&._v) All Raman wavcfunctlons were calcu(FCA)

gausstans. The

is reflected

is

m the RR

spot”

preparation

expected

m

a rhrect dissociation. B has the imtlal conditlons.ro

Trajectory We

The Raman wavefunction

bond stretch rn~t~al condmon,Thiscor-

)po = -7.0,

and the excited potenttal

[ 191, with 8 to I6 two-dunenslonal

- u&

spectrum, see fig 2b Tha spectrum may be analyzed m terms of fundamentals and overtones of a local

mode s&e

lated usmg the frozen gausslan approxtmatlon

- 0 Il(r

quite sunplr and tlus sunplicity

responds to the “hot

the rorm Y,(.r,_v)

= -~.O(X

dltionsx

by a model two-dtmen-

The ground potential

surface 19 V&J?)

+ l/2 @’ -yo+

for a photodlsscaatmg

s~onal calculatton.

- 0 I I(x --_~,,)~c~* -.I’~)

= l/2 dr - rI#

moment

ments separate. Consequently, if?) = P,, I&) wtll contam only the slmplc, early tmle dynamics. The sunphcny

I n: I. Contour plot of IIIC c\cltcd potential surface, V&.y) = -2 0~ --)‘I + z 0t.x +J )?. nlc II~~EC traJ~c~orlrsshoan ,IIISC front 1r.mL.k-Condon tmnwlons lor three distmct cholcca OTXI, and) ,, I” the paand-state potcnhd V&c y)

(r

fipl: m eq. (3b) will vamsh as the chromophorc

and the resultmg

24/31 December 1982

PHYSICS LCl-fCKS

and undergoes a small amphtude

in the (x -JJ) coordtnate

on

= - 1.0, osclllatlon

way out the exit chan-

IIS

nel. The effect of tlus oscLla?lon can be seen in the square plotted

of IR) shown

IS

in fig. 3a. The RR spectrum

3b, and It mny

m fig.

still

be analyzed

terms of a local mode mitral condition.

The broaden-

ing of the local mode peaks in the spectrum the decay of amphtude

out of the zero-order

mode states into the remaining

in

is due to local

modes. All of the RR

results are quite .Iccurate for this potential smce the wavy: packet quickly evolves away from the FrwckCondon region. The RR spectra were then calculated

spectra wdl have sharp hnes for the first four vibrational spacings since there are only a few states that

by ekpandmg

low

IR) m terms of the numerical

ground-

which were obtamed by diaganalizallon m a complex gaussian basis set [20] aThe state elgcnfunctions

spectra as well as WR)are calculated tional umts below the absorption r= 0.17-5, see eq. (3~).

with w, two vlbramaxunum

588

A, ia direct

bssocistion

with

the init&

the (-r -u)

C has a large amphtude coordinate

to encounter

whch

several “sharp”

oscillation

m

allows the wave packet (x -u)

turning

pomts

and to have one shght recurrence. The square of W wffl show the turmng points as regtons of increased

and

Fig. ?a shows the square of II?) which results from traJectory

in the ground-statemanifold, Trajectoty

con-

amplitude

and the recurrence

to IR), see fig.

will also add structure

4a. Asexpectedthe RR spectrum

Volume

93, number

CHEMICAL

6

PHYSICS

24/31

LI-I-TIIRS

Dcrcntbrr

1982

300

(b) 0

3 RELATI \‘E

IO

I5

SCATTERED

20

25

30

i~Cl,Sll \‘I: SCSI”I’URCDFRCQUCNC\

FRCQLIEKY

the photon and we have spectral evldcnce of the dccay of these local modes, i.c band widths of ~hc

overtones Thcrc are llmitatlons on quantrfylng the dynamrcs and the mechanrsm for the decay smce the exact form of lrans~tlon moment and vlbratronl w~er~nctlons

shownin fig.4b hasbecomemorecomplicatedsmce w) ISno longer a stmple local mode tnltial state. Using

Raman scattenng

chromophore,

from a photodIssocIating

or “dlssoclaphore”,

to produce

a local

OF hot spot is in many ways analogous to one photon overtone spectroscopy on a C-H local mode 111 J_ In the C-H local mode case, we have a good intuitive guess of the excitation produced by

excitation

are unknown.

Consequently,

the

preciseformof Ihe spectroscoputllyproducedRIP

teal state I$,) is unknown, There arc several arguments

in

the

Ltcralurc about the meaning of

bandwIdths,

srde bands, etc. whrch can be traced to the questIon:

arethe spectral

features a result of the assumed form of I#,) or the sub~quent dynamics of I##))? (The spectrum IS the Founer transform of @#(I)).) The matn psinl of thispaper IS that LheRanran589

34/3

CIICSIICAL PilYSlCS LLTTCRS

VO~IIIIIC93 nuinbcr 6

dissoctaphorc

where

Dcccnibcr 1982

will greatly extend the num-

techntque

ber of systems

I

local excitation

can be pro-

duced. Such systems wdl provide an intmtrve, bLt not precise. tdea of the form of the spectroscopically produced initial state, in thts case IR). Just as HI C-H local mode spectroscopy, ambiguities may stall exist about features bemg due to tR) or the dynamtcs uqr)). Some light can be shed on tha problem

of

m any par-

trcular case by examining the Raman scattering Just off resonance. When off resonance, the lntensltles of the fundamentals

and overtones

normal modes contam the upper potential totally

symmetrtc

of the ground-state

mformatron

about the slope of

of the modes and changes n force consurface m the dtrectton

tants of non-totally

modes [9]. These

symmetric

upper surf.rce parameters play a large role in shapmg lR) as we have seen in ases A, B and C. Indeed, the abthty

to tune over the absorption

profiie

socuumg state IS o mezms of changing

we effectrvely

trollable

way. By detunmg,

hfetmre

m the exerted state, If?) to be locnhzed

function

Condon

region

forcing

the effect

the

shorten

the Raman

around

and the drrectron

FIN. 4c dlustrates

for the dtsin a con-

Rj

wave-

the Franck-

of steepest

of detuning

descent.

from

reso-

nance on the RR spectrum for case C. The optron of changmg the inrtral state by tunmg the Incident fre,())

0

-I

IO

lii:~. \‘I’1 \‘E

1

quency

A \‘I”I’CI?I:D

I’Rl~Q~‘ESC\

IS not available

eupenmcnts Concrete

examples of dissociaphore

mclude methyl

Ij

overtone

to the one photon

spectroscopy

Iodide, ethyl iodtde, etc., whtch all

absorb near 260 nm m a continuous

broad

band of

As the alkane cham gets longer, the “hot spot” becomes increasmgly isolated from tire rest of the molecule. The first member, CH,I, has already frequenctes

been investigated

tcally [22,23] mant

by phorodisrocidotl,

and experrmentally

force

in the excited

photodissociation

state,

cross sections

ttonal states of the methyle C-l (C)

15 ORCI.,\;‘I \‘C IOSC~\‘I”I’ERED

20

23

F’RCQUENC’r

;

both theoret-

[24,25]. as inferred mto

fragment,

The domfrom

the fiial

the

vtbra-

is along the

bond, with less force along the CH3 umbrella

coordtnate strcching

and even smaller force along the at C-H coordmate.

Eventually,

by exammmg

the off resonance

Raman. the resonance Raman, and the photodssoctatron at many should

tncident

emerge

Meanwhde,

frequencres,

of ground

a coherent

picture

and excited

state dynamss.

for the larger alhylhalides,

the dephasmg

Voluux 93, number 6

CHfXlCAL

and decay of the hot spot produced VIBRaman scattering should remam an interestmg problem.

PHYSlCS LLTTCKS 1121 J.D. Page and D L. Tanks, J Chcm

Plrys 75 (1981)

5694 [ 131 Y H~lfny~ko~ 755.

Sbt

and I Tctmr,

P&s

Soi. 21 f 1967)

[ 141J 6. tloph~ns.P K R. La~gnd&&n~~l~ auf R C Smalley, J. Chcm Phys , subnuttcd ior pubhcstfon.

References

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111 G Hetzbcrg, MoIc~uhr spectra .md molecuk~r structure, Voi. 1 Spectraofdtatomlc molecules, 2nd Cd. (Van Noslnnd, Pnnccton. 1950). hlolccular spccrn and molcculrr struclure, Vol. Z Infrared and Ram.m spec~n of poiyatomic molecutcs (Van Nostr.md, princeton, 1945) [I j Sf.MtngaxiiandW. Siebrand. J Chrm. Phys 62 (1975) 1074

131A C. Albrccbt tid h1.C.IluIlcy.

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1981) 191 t.3. Heller, R L. Sundhrg and D J Tannor, J. Phys Chem 86 (1982) 1812. [lOI J B lioffcnd. R. llacfsand R.W. IMd, m Procccdmg of lhc lnternat~onol Conference on Lasers (1978) pp 240-251. f II

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J-B ifapkmr. D C Powxs S Mubmtcl And R r. Snuaey, I Chrm. PfiY.5 72 (1980) so49 If61 DC fmrc. J L Kmscy. R IV I reld and D.II K.I~J~JXIIJ. preprint [ 171 P J Hay. R T Pah. K.U Walhicr and I. J Ilcllur. J Phys Chcm 16 f 1981) 862 [ISI CJ ffcflet, J.Chan Phys 68 (1978) 3891,ALcounts Chcm Res. 14 (1981) 368. 119) I; J ticllcr, J Chcm. Phys 75 (1981 b 1923. [lol [zlj

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582 1221 hl. Shpro

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3810 1331 S-Y Lce~ndCJ.ficlfcr..l Chcm Phys 76f1982) 3035 1741 S L Uauytcum and S K Leone. J Chcm. Phys. 71. (1980)6531 1251 R K Sparks. K ShobatJhc. L K. C&on and Y T Leu. J Chcm Phps 75 t1981) 383s