Benzene (Co)

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4ENTATION PAGE la. REPORT SECURITY

A D A 198 364

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Colorado State University

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Department of Chemistry Fort Collins, Colorado 30523 8b. OFFICE SYMBOL (If applicable)

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11. TITLE (Include Security Classification)

"Benzene Clustered with N 2 , CO 2 Nucleation"

and CO:

Energy Levels, Vibrational Structure and

12. PERSONAL AUTHOR(S)

R. Nowak, J.A. Menapace, E.R. Bernstein 13b. TIME COVERED TO_ I FROM Technical Report

13a. TYPE OF REPORT

IS.PAGE COUNT

14. DATE OF REPORT (Year, Month, Day) July 12, 1988

1

16. SUPPLEMENTARY NOTATION The view, opinions, and/or findings contained in this report are those of the author(s) and should not be construed as an official Department of the Army position, policy, or decision, unless so designated by other documentation. 18. SUBJECT TERMS (Continue on reverse ifnecessary and identify by block number)

COSATI CODES

17.

FIELD

GROUP

clusters, van der Waals modes, supersonic jet

SUB-GROUP

-- )

spectroscopy, nucleation, benzene, (,


~10 2)

enierget irs

V

do nof

~rW'i

,

IW

,, _QrV.

suich as

Ire typirIl ly lused eivp sf)Pi:ifi(. infi

1r1d geomtriOs.

PROCEDURES.

Spectroscopic: Techniques.

A.

The S1

-

S~I

rhsi?-pt ini ijje(_tr'd

pulsed superson ic molIet2K . -r Jet, .xpins ion

or the~ (:Ii is ters are obtained cis irng a and two col1or TOFMS.

The details of

the exper iment-tr 1 lppar;rirus ;rid t echn iques employed have been descrcibed earTwo syrrchron ized Nd- 3 'NAG pumped dye lasers are used to probe both

lier. 1,2

thre ouigin and the 6~ regions of the bfeuerre Exci ton LDS 698 dye is

cluster,.

'B2u

used for the pump laser with the output

fregrienc:y doirbied and inixe-d with the 1.0641r

funda mfntal of the, Nd ~3 YAG

Either- Exciton LDS 698 (doubled and mixed)

laser.

used for the iurrization laser.

A1gtransit ion in the

e*r F 548 (doubled) dyes are laser is typical-

The e-nergy of the i 'izatiun

ly lowered to the ionization threshold to limit cluster fragmentation upon ionization.

The spectra are recorded using a boxcar averager,

transient

digitizer and computer. Typial ly, 3- 510 mixtures of the solvent gases wit~h helium as a carrier gas are passed through a liquid benzene trap at room temperature and subseuuently expanded into the apparatus vacuum chamber by using atpulsed nozzle. A nozzle backing pressure of 100 psi pressurre B.

is

maintained below

typically used and the chamber

is

Ux10_6 torr.

Calculations of Cluster Geometries. The cluster ground state geometries and binding fenergies ;Irt

calculated for small clusters

(n=1,2) via an intermolecular

potential

m inimization procedure employing the methods previously described. 1,2

3

energy A

-

Lennard-Jofles

(L-J; 6- 12

pot ntiil1

-~

is Ius ed( withI the 'I"m -at "m

parameters previouslIy reported for s m iIa r (,IIC IlIIat i ons and

;:alculationdl algorithmi yiildl consistent

Of cl uster couf' igUr tios energies,

ITT.

and qolitat ivl gomtries

THEORF.TTCAI. NOTION. A.

(%CA)

clu s ter vi

s truicture,

oai c

respect ive hind in!'

AND

INTERNAL ROTATIONAL

of the c-luster vdW vibrat ions

is performed by using the some methods as described on vdW

the ir

11ii-.1ho

of vdW Vibrations and Vibronic

The normal coord inate analys is

t iOrr

~~fthe.

t

(symmetries).

ANALYSIS OF CLUSTER VIBRATIONAL

Normal Coordinate Analysis TransitLions.

The potpnt ijal form

refsfl ts With

berved experi mental I y,

ir[itir i ,on

in our previous pubi ira-

The GF method of Wilson1

is

employed in which the cluster constituient force fields are generated by uising the central force approximation intramolecular

including out-of-planre mot ion terms.

force constants chosen correspond to -eneral

stretches and be-nds. 14

The intermol(i~iclar

second derivittives of thle intermolecular

nonzero eigenvector normal

mined in the usual fashion.

functional group

force co :-;tants are generated as

L-J potentia;l discussed above.

GF matrix is numerically diagonalized and the 3N-6 (3%--5 instance)

The

The

in the presfent

modes and eigenvalue energies are deter-

The reader is referred to our previous publica-

tio n' for details of the theoretical

procedures

employed.

The eigenvector normal nodes found based on the calcuilated geometries of the rigid clusters

(point groups C2., and Cs) are

t he

which entailis the mot ion of the solvent moleculv in the ular to the beozene molecular plane, translational

motions

parallel

the vdW tors ions ( t yand t z constituents

vtIw stretch

("Y)

V ':-cftion perpendic

2. the vdW bends (bx aIrid h1)) with

to the benzene ring (x or y directions).

ind

wh ichi trans form as the rot at ions of the c ust er

about the y and z axes,

-

respectively.

The-se niormatl

modes are

4 Ajr )f k

'A

X).

p

.

shown

if

Fig.

I for

::tsi, of th, • rigid benzene(N2)

the

I~ preu{sent i f the solvent

tors i ona I mot ion wiIl no: nearly

free rot.at ion add

i1steId

jti r.i

ihol:!

th(- rI uster z axis,

,,

u .1

' ,,)rsr~j r,. ) r L~il.

Chlek'

description of the rot.'' group most

be used

states other thn'

n 'gr.oup F oi5l; is :>)i;." )s

:Il

-v .IS

W- ,ssini, 1z 'i!'

by

elements tising the :id iih;i

rules

for

the

torsions.

Av = 0, In the () I

:2,

benzene(CO)

if

i,

symmetry all 0,

,

.

..

modes even in

,iPronic

approximittion.

li

)

transitions

v _4

ie,

symmetry, ,ig-n-

in the rigid

transit;:':

in the absence of the Herzberg-Teller .

±2-9,

..

for

t.

for the nontotal ly

...

region

the vdW vibronic

the fundamental

(HT)

totally symmetric vdW mmetric vdW bends and

of the nontotally symmetric

This torsion is vibronically induced in For the Cs symmetry of the

the vibronic selection rules for the 00 region are 0

Av = 0, -1, ±2. ... for the vdW stretch S . bend b .' and for the bend b

and torsion

t

the vdW modes are capable of vibronic coupling and, if

Of

i',t es

Ile f,

molecular

IN is

In the C2 v symmetry uf the

rigid clusters,

and Av = 0, ±2, _4, ...

torsion t y,

its hond

the ei gpn

ng:)Io o longe'r .ip

an appropriate

for

HT coupling is active.

slightly different:

in

to

inalyzing qualitatively transition moment matrix

O' region

rigid cluster,

1

perpend i iiular

c.

torsion (t.) is ,dditionally allowed. the 00 region

Th,.

"he low-lying intprmo l,u(.i!,r

ion rils

coupling are as follows: stretch ;id

i

h mo

benzene(N 9 ) 1 and benzene(CO2)' selection

th,,Oiu

Ie'

The appropriate sfel't cluster are determined

,nd

rliistetr

mo I ecu] e ran undergo

he present

"vI,s will

,)':,'

!

MT -oupling is

present.

Av = 0, _±1, _-2,

the absence of HT coupling for this latter

...

In

CS

hence.

Av

for all

cluster

in

the vd W the C1

reg ion. B.

Internal Rotational We assume

rotate

Analysis

of the t

z

Torsional Mode.

in the present analysis that the so ivent molecile r',an

in one-dimeniion about

its axis of

largest moment of

inerLid.

i.e.,

the

axis perpendiculIar

to the N-N (C n) mo leri lar, bond ;ind pass inig throuigh

solvent and Solute molecutir center of mass.

(benizene s ix -fuI ca. 5

The rotational axes for N,

sym m,-I I y tx

:tngl E, w itrh t hp

15-

Mmetry. P' Oup) ;ird

struictlrp

ht-nznp

c-'

musLt

sepIerticn

s ix -fIld ix is.

rot at ions

The apprupi- i i t

in mu I i)~lt

-ulos.

jnal transit ions

uiti

in iu a-

ic( molecules.-

ruat

;,illiv

CP .1 (ne

wave funlctions for the mot

ii,

these cl1usters

is

;irac s described in our previous puhi icat ion 8

performed by ulSing the saime in t eriiaI

"xiJ.\ i Sof

11e (1eterm m at ion of the vit t l i na I

!I

Analysis of the irt-! nal

for

ut ;It i o'l

thte (' 0

i

js

IrnI

bond (c luster Z) i..

in the cluster correspund to the solute-solvenit

CO,

t he

The eriergy levels and

di mens ional hindered ro tor are obtained

by sovng the Schrouiluger equl t iori [-P~

in which thl-e potent ial

]

\(O)

Emi()()

il~t,)

form fr- the henizene cluster

cons i (1 red is approxi

-

mated by

6 (I

v(65) = 2

In eq.

-

(1) B is the rntational constant ( 11'87:2 l),

and 0, is the torsional angle for the N9 , CO,

2

and the free

I is the mnoment of inert-ia,

and CO rotors.

the Schrbdinger equation for a free rotor (V(q5)=O)

m

(2)

Cos 60).

e0imz

is of 'he

The solution of form

(3)

rotor energy levels are

Em

~mB.

(4)

The eigenvalues and eigenvectors (if the hindered rigid rotor Hamiltonian eq. (1) are solved for within -4 basis set of 21 free rotor eigenfunctions.

6

The

parameter

V.6 is

adjusted

t;)

hot f~l e-rgy 1evols ,of thIt#h i ndorf.d ro, f)[ .r) tie

experimental data. The energy solute

lc

lab)eled

arp

t:,n of , rt -),,it

leve.',

_-~i

rd: , i

Thp symmet ry ,

rotor.

sym et y

i m im

pian~lt

:

"

er,-

ind

,-iile taking

inltegr,il

in 1

m

~iin.

,tmolt.

1 slb 1'

notation

s y mme tr y a l lo we d ro ta t i ,n,il tr ,,n s i t :o n s w 'ith in the 0 0 mined via the non%-:tn sh;:;g

Onp-d i men."

,ffi

1 n7.,ne((.0 b

,li:stc z' ( .i:'orfting to the

(;2 or the benzenetiC'r),

t

:! rin s g;,ven by, thl- iippropria

)

, !.i

15

rolp

t),.), r1

wi th r~spf ( t tl thf.

the solvenrt

r,

"

illI,

1-

t

Thi,

16 .

b I d s 4 e d t r-

into ac:count the ,7orreldt ion

betweven tile molecular symmetry group of benzene and the appropriate molecular symmetry gro~ups of clusters b,)

are g iven in Tabl e! I

b,),

The alg -- 'Olg (a ,

(e,

b.,

--

P eg

,

)

(P

tr;insitions ar(e

-- al) and b2u

__ b2: ; 'b2

;-t the origin but -are allowed at 601

transltions are nlot. allowed ...... e-"?g (2

eqg

analysis for diff,rent

T'hP r-suts of this

i;s ti, rs

the

12)1

llowed

t-,

a

n ~ 9 .g u - )1a1n' el'

e g (a1

in both spe(

The

:0l regions.

This finding /

is

important

for the interpretation

larly in the O~o region.

and assignments

,,f the spectra,

partirua-

internal rnta-

The dependence of the Pnergy of each

tional level onl the paraimeter V 6 is illustrated for tihe case of the benzene(N2)

1

hbenzene(COl

1

cluster and

between individual moment of

in

Fig.

benzene(C.O2) rotatinnal

inertia of the CO,

2.

Similar

dependences are obtained

1

clusters.

In

tihe

lattor caise

irt- relatively

levels

the spacings

smaller due to a larger

.

Some of the allowed transitions may not be observed due selection

rules.

various rotational spectra s.

(.1str

tOPS

by normal

Moreover. levels cooling

Fo,r the

the different result in

nuclear spin states associalted

hot bands which cannot

techniqlues.

to nLcIlar sjpit

For

th

ezn(2

With

b - removed fr,,rl 1

tht,

and benzene(C(2)

1

' ')

t24 motlprulir symmetry gr-)uD)

th

only thebS "g" internal

rotational

I

levels are populated w ;tli the ro: low ing relit ive stat isticill weighits: pe11.

e2g

: h2u

tingutished in the G13 Inall

syrnmf-try I

BENZENE

,*f ) h'4_

(SOLVENT),

may be poupi t ed.

htetVf)

dis

-

k -Ise . al

CLUSTERS

SPECTRA,

CALCULATTONS AND ASSIGNMENTS-

transitions

benzene (soivent i clusters studied.

Therefore, in detail;

s

t

h9 : P

- P

rotatjonal and i'ibrait jonal

he-izone(N 2~spectra are discussed

rofta

lit The re--i

A simi lar approaich t(, spectrail analysis consisting of internal

noit

molprular symmetry group and all the different

':" i weig h ts i re. il ri

TV.

"g" and~ u" type levels are

0 :0 !2.

1

.1g

is

aluaigthe

employed for aill three

only the assignments

for the

other cluster spectra' are

analyzed based onl thle same arguments. A.

Berizene(N 2 )1. The results of ca Iculat ions of the grourc

itate geometry and vdW

vibrations of the benzene(N 2 ) 1 cluster are shown in Fig. 1.

The calculations

yield a single cluster geometry with the solvent moltecule located in the plane parallel

to benzenie at at distance 3.3 A above the center of the benzene ring.

The c-alculated ground state binding energy is -501 cm-1 potential minima are found in the calculations.

No other local

The eigenvectors of the

vibrational vdW modes and their corresponding energies calculated ire shown in Fig.

1.

Rotating the N2 molecule by an angle 30- around thle z

As (N2 rotational axis) results in an increase of energy by only ca.

1 cm- 1 .

the calculated]

bairrier

182u

the cluister wit'h

to rotation.

The spectra benzene

binding

This indicates no barrier to rotation in the

ground state and suggests that the N2 molecule can rotate in little

from the NCA

of the benzene(N)

cluster in thle 00 and 61

'Ag transition are shown

8

in Fig. 3.

~~

~j

Such spectra are, typi

h

cal ly understood

ail lowed origins for the 01), and 6i1 regions and a

on

5based

lV'u7w

rvrl U-

r~~vrr WONJ

The origin

of assigned vdW normal modes built onl these origins.

For the lhe:

not able to understaind th,-e -:p

anal1yzed i n the vibration energy

i gh t

(peP P !W j] t:

2

f2g -

2

2g , and

4

e2g -4ep~ tz

would coincide in energy

vdW mode)

due either, to vibronif

:r nuclear spin selection

Tf the, harrier to rotation chogeZFs upon S1

tothe energies of the 2eq F different;

t heory and the vdW rota t ion

The first two of these transitio;,s are

it the origin.

not allowed in the 00 rePg;Of rules (see Table 1).

o

(replacing the t.

and give only one peak

1,P

eIast ,moust

00

Leh.

en

Oag-'g

rotational transitions

at

spf,'Ct rum.

The

in the henzene(N 2 ) 1 cluster were freely rotating in

Tf the N2 molecule both S0 and S1

t~siio

di sr:issed aibove,.

se!

level

Weire

I

find approprijat e ass igztmt'nit,

oi, ind

hiwi-%v'r

this now standard approalch.

this shi ft eqJualS -() C-m

uiste

:~n,7- X

of

e t ro

i milar to thit, observed in the G,

from the herwzene 0 0ttr.:his t thO Cluster.

a shift. in Hnergy

would typically exhibit

aillowel)

cluster 00 spectrum (if

in) the

2

e2g and 4 eg

-

-

S0excita-

4e.,trnioswulbIe

if the magnitude of the change were small,

a doublet would be

Thus an intense doublet in the spectrum most prob-

produced in the spectrum.

ably corresponds to the allowed 2e2)

2egand 4g-4e2,transitions.

-

A reasonable fit to the 00 spectrum

is obtained by assuming that

in the

c'luster ground state the N2 molecule can freely rotate iround the henzene-N., bond and in the excited state the rotation is slightly hindered by itca. 20 cm

potential barrier.

The f inal calculated spectrum shown in Fig.

superposition of both one-dimensional

3a is a

rotor and vdW vibrit ionil 1transition';:

due to the rotational degree of freedom, the tztorsion is not. taken into) account in the vibratijonal

analys is.

and e-xperimental spectra are givn

Speci fi c assignments of the calruolitt ed

in Tablp [I.

9

As c-an

be- se-en in Fig. 3a .Ind

prV

I 11 "

Tkh

the agreement bet wt,,n the oxperimenta 1 and ,,alctilated spec I rum

very good. Hither

t--iisit

tr,'m

The fit

state

is

considerably

worsened

if

the rotational

barr'er

T'

6

spectrut'm

ion

is

illowed !(-;i p,ir' T, I

in Fig. 3h.

is

pasie:

shifte ! h:v -6

unanihigiiously ascribed

ved in agreement The spect ral

in

is changed more than 10 cm-1 to .tialyze since

,m

l)

in

this

The strongest

-is-

tile

i

teat ir, i;n tho sp,.,

with respect to the benzene (1 tr,in,



is

s

i

Ir. n

(1

ti

the

with ti- si:ig!

!uster P0 orgili.

,.:>'ulated

A single origin

is ohsor

cluster geometry shown in Fig. 1.

feoaturres observed to the red of the origin are assigned as

hotbarids since their intensity changes considerably with the carrier gas backing pressure but tiot with ionizat ion energy.

Several relatively weak

peaks observed to the blue of the cluster 61) origin are vdW vibrational and rotational hands:

their assignments arte given in Table I.

The 61 spectru00

is

more than an order of magnitude more intense thu.

the 00 spectrum,

relatively intense vdW vibrations built on the all(,Aed 61 origin. 0

with

The rota-

ional transitions which are seen in the 0o spectrum are almost entirely hidden tinder the 6 1 origin spectrum.

-I to Moreover, in the region ca. 15 tm

the blue of the cluster origin (around the benzene 6o transition), where some of the rotational transitions are calculated to appear, the mass detector is still saturated by the ionized benzene molecule signal.

This effect elimin-

ates observation of any weak features and is visualized by a dip in the spectrum.

Further to the blue only weak rotational transitions may be present

along with vtW vibrations as indicated in the 6 1 spectrum in Fig. 3b. Calculations of the rotational barrier, rotational energy levels, -ind vdW vibrations confirm that the benzene(N2 )1 cluster 00 spectrum must. he assigned as a superposition of both one-dimensional rotor and vdW vib, tiona! transitions.

This approach gives the best arid most satisfactory assignment

10 r

of

I

features in iigreement with the select ion rule-, given

the spectral

intense feture-1-ts in thesp-

In order to reproduce niore accurately the most trum a small. is

ca. 20

rotation in the

tiarrijer to

-m-.

in Table I.

CXU itfed

el ectron K( stat e

assumed.

~ f

The (:I s. r ene cM

and

-63 cm

-

for

unexpec ted diif fer Hrice itY upon1

.in

th.iii ,ifts

ie t

t ransitLions,

iriso

from

v Iu-ihr ;i

iP (i

Inca 1 changes of polar izab ii-

iii the cluister.

the

At. present we do not have clustLer shifts.

Benzene(C0 2 )1 . The 00 and 6

F ig.

d uF

This

respectively.

a satisfactory explanation for these apparently different B.

i

-iZefid can only partially be explained by

eXCitiation ot' th-

change of the benzene 6

G

It

tranrs it i on s int hpriz

'd t

))

spectra of the bt-nzene(C0 2 ) 1 cluster are shown in

41. The Cluster energy shifts are

4c an ad 4cm

1

,

in Fig.

1),

is

calculated for

teOad61

fo

or

One cluster configurati *oi, almost

transitions, respectively. nitrogen case (shown

I-m1

'nzene(C0

he

0

n60

identical 9 )1

to the

with the

binding energy -868 cm-1 The arguments given above for the assignment of benzene(N,2 ) 1 cluster are valid in the present case,

The specific assignments of both spectra

rules are identical. given

in Table 111.

since both Cluster symmetries and selection 4 are

The CO2 barrier for rotation in the excited state is

taken to be 16 cm-1 and good fit to the 00eprmna as shown in Fig.

in Fig.

4a.

sotie

petu

The relatively smaller energies of particular rotational

transitions of the benzene(C0 2 ) 1 cluster compared to the betizfne(.'

arise because the moment of inertia for C02 (B =1.547 cm-

I)

is

2) 1

larger

clllstfe:' thani

For Nt.. Tine 61 spectrum transitions

to the blue.

in Fig. 4lb shows a strong origin peak with severail Wfeak These weak transitLions can again be assigned (Table

XI- I

11l)

as intertial

rotations and vdW vibrations.

The origin corresponds to a

single calculated cluster ge'ometry. Benzene(CO)1 .

C.

A sinugle cAI stf-r- geomnt ri- shown

berizene (CO), located

cluster w

ht1the hindi ig energy

3.21 A-ahove the hetnzere

to the benzene six-fold axis, Therefore,

.5

is (a Iculiated for- t lif The CO molIecu ile

12 cm

angle with the hvn/elI!

lies closer to heoizene than dojes

the oxygen

The rigid( r:Iluster symmetry is C

Found for N, and CO 2 clusters.

another.

-6

'

form ing a 15

ii

molecular plane in such it wayLhit the carbon atom.

i Fi

inste(ad of the Cq %mt.

The CO rotational axis is no longer parallel the axes Forming a 15~ angle with respect to one

if an internal

rotation is

axis must be undergoing a smai!] processional

present,

the CO rotational

mnotion in order to avoid a high

potential barrier to rotation~ The appropriate selection rules for the rotatransitions are based on the

tional

moeuaG3nerygop(e

al

Assignment of the benzone(CO) I spectra is simi;,lar to the assignment of the berizene(N 2 ) 1 spectra,

except for the above mentioned selection rules.

calculated] and experimental

spectra are compared in Fig. 6,

fic assignments given in Table TV.

Thle benzene(CO),

The

with their speci-

spectra are similar

to

the analogous henzene(N 2 )1 spectra since both these clusters are of identical masses,

have very similar geometries,

rotational constants quently,

(B

1.913 cm- 1 for CO and 1.917 cm I for N2 ).

Conse-

both clusters exhibit similar vdW vibrations and have similar ener-

gies for rotational transitions; in the benizene(CO), in Fig.

and N2 and CO have almost identical

3a,

however,

spectrum in Fig.

fewer and broader bands are obsterved

6a compared to the spectrum

due to an increased number of allowed transitions

clusters (Table 1).

The overlap of transit

12

onls

is

of benzellM)

for benze-ne-(CO)l

also responsiblte

for the

WWN

change of

the re lotive

int ensi t ites i n the 0Oo benzee,(C))

to the 00 spectra of the analogous The 61 spectrum rotational

clusters of

in Fig. Bb

is

N2

loin ated by a strong origin ;tnd vdW vihr;tt ions. can also be

transitions

V.

as compared

and ('0 9 .

well i assigned as

mode transitions

and vdW vi brationa

specrtrum

(Table

i siiperposit ion

IV).

of

The spectrum

is

weak rotat ional

;tlthough

listinguished.

BENZENE(SOLVENT) 2 CLUSTERS. The analysis

of the berizene(solvent)

2

cluster spectra differs from the

detailed approach taken for the benzene(solvent) 1 above since

the benzene(solvent)

spectra are less well resolved and thus do

2

not contain sufficient experimental

and.'or rotations.

cluster spectra presented

information

about possible vibrations

The analysis of the benzene(solvent) 2 cluster spectra is

based primarily on calculitions of cluster geometries and assignment determined in our previous st.udies A.

I-

6 of other vdW

rules

lusters.

Benzene(N 2 ),. Two ground state minimum energy cluster geometries are calculated

for

the benzene(N2)}

cluster

(Fig.

binding energy of -1007 cm -1 the aromatic ring.

7).

The

isotropic configuration

with

features a nitrogen molecule on either side of

In the anisotropic geometry both nitrogen molecules are

attached to one side of the benzene ring with the binding energy -962 cm - I No other local minima are found in the potential energy calculations. The benzene(N2 )2 This symmetry

cluster spectra are not detected in the 00 region. 2)2

induced transition

0

(forbidden

in benzene)

is

certainly very weak

for the isotropic cluster geometry, since the six-fold symmetry of benzene may be preserved

in

the cluster

in

some averaged sense,

especially considering the

rotations of the N 2 molecules.

Why the anisotropic cluster spectrum

ohserved is difficult to say.

The 61 spectra taken at two different

13

is not

ioniza-

.

tion energies

in Fig. 8.

ire shown

One relatively broad peak shifted -16

cm

Another ppak at

9

to the red of benzene transition dominates both spectra cm

-1

visible as a shonI U,'r ,n the main feature

mass

channel.

The twtj

ft,,

m-

is at -16

Benzene vdW ci ,s for the isotropic

(s. tne at. -16

cm

-I

to featur's in othor

and the other at

-) rm

-I

The cluster whose 61

11ppar.nt Iv has a higher ionization energy. with other solvents1.2 show that the energy shift

e.s

,.lustir

anisotropic cluster.

e

!irferent cluster geometries.

are thus assiyned to tw,. transition

in ,reaises in intensity it I wer

Thi, iVeiture does not correspond

ionizatiol; ,ne rI',is

is larger than the energy shift for the analogous

This

is due to a better overlap of the solvent molecules

with the aromatic - cloiid of benzene in the isotropic cluster, resulting larger polarizability changes upon cluster excitation. tropic

-1

in

Typically, the aniso-

benze'ne(solvent)2 cluster exhibits a shift roughly equal to the one

found for the henzene(solvent)1

cluster.

Given thi-

assumption, the more

shifted peak in the spectrum is assigned to the symmetrical (isotropic) cluster and

the less shifted peak to the anisotropi., cluster.

Comparing the

relative intensities of both features in the spectrum one concludes that the concentration of the benzene(N2 )2 isotropic cluster in the beam than of

the anisotropic cluster by roughly a factor of 2 or 3. B.

Benzene(C0 2 )2 " The benzene(CO)

01 regions and are shown

2

cluster spectra are detected in both the 00 and

in Fig. 9.

The origin, shifted in both spectra

cm - I to the red of the benzene transition (at 0 cm- ), cluster geometry. -2 cm -1

is greater

is ascribed to one

Clearly, another cluster geometry gives rise to a peak at

in the 0Q spectrum in Fig. 9a.

This feature (geometry) is not seen in

the 6o spectrum due to the saturation of the mass detector by ionized precisely

in

this

-22

spectral

region (see (lip in

14

the spectrum

benzene

in Figure 9b).

The

I

j)osi t i on I)f

thp Sekcure!

-It

11ref

-11 rm

It

in the C61 spectruim corresponds to

the origin of the benzene( C(12)3 clutster' (compare with Figs thus is ascribed to diss;i

in

f' lhis ( !us'.er givi:isg

i

the- 1enzenP(CO,t.) mass

ion~zrilion ene-rgy

mum energy c. uIs t-er gp

-1955 Cm-

-m- 1

tios,

isit ctipit-

i u'-els ir

±sgrnei

twot grotniild slate Min;

1v'i)tthoise founriifr

1-int-M.

~

The binding energ;!-s ;te

-17716

(m1

I

rire ',ri;>ited

for the

12) and

(1e' 1o~~nI

onuf irms this

In igrepment with the '--pehri montal observaltion.

in Fig. 7)

;drI

93-o-1 leiounced uhange (if the rel at ive

of this ha.!with v~trvinr 'he

(shown

I1

mid ;inisotropic clulster-s.

respect ivfly.

lse .inid

The -22

shifted origin in the two spectra is assigned to the isotropic Cluster, shifted origin in the 000 spectrum

whereas the 2 cm-anisotrotpicCcluster.

As call be seen from thle compar~snr. of thle relat ive

intensities in Fig. 9i.

"if!

-oncent ration fif thp isotropir cluster fir thie

su-tpersonic molecular jot is lar-er cluster.

than the concentrition of the anisotropic

The intensity of' the pe-ak ascribpri to thi- :iisotropic cluster c-art he

diminished by increasing the ionization energy, zene(CO 2 ) 2 cluster is benzene() C.

is assigned to the

V,.

behavior of the beni-

thus very similar to the one rpportedl above for the

2 C IUS t er.

Benzene(CO),. Four cluster geometries (one isotropic and three anisotropir) atre

calculited for the benzene (CO) and -1580 cm 1, -1601 cmThe 6 1 spectrum

2

Cluster with the binding energies -1284 cm-

and -1697 cm- 1. respectivel--y.

of the benzene(CQ)q

from the spectra of analogous clusters with

cluster (Fig

N2 aInd CO%.

10)

It

with re~spect to the benze-ne or'igin.

differ'ent

The spectrum is

relatively weak and exhibits fouir distinct features at- -56 rm CnrM and -88 cm-

is,

-6

The strongost

1c

-7

feiture

-16 CM- 1 probably corresponds to thle isotropic calculated cluster geometry

15

wh ich

is5 foutnd to0 occ ur w it h t fie I a rges t p ro ba bi Iit v.1

The broad hackgrwo!ii(n hi'her order

V.

izat ion er

tri

Thmv:

however,

V1.

do

ci us!

tet-

;n

LARGE CLUSTERS

1:-s!

'

hs

'y ri uster symme :-

0

The 6~ spec!

the peaks

9 3

cIinst r spectrum the 000 region.

if'

ndurr'd -ind thiis

in the sppct rim

i:He

with COf r e no.

of

11,

spectra

The benzene no trans i0

One origin shifted by -9

heitzene solvated by tip to 12 and 13,

seven C09 molecules are shown in Figs.

shown in Fig.

is, not expectedi to be intense for

3 : speot (1rcum of the Ihenzpene(CO- 2311 r'r:

of

el irn :fat-,r! by lowe-rinig thtei~

rder rlusters of heuizene

low concentra t iOnis (if specific clusters. ill the

1likely doe to dissojiit ion[

TRANSITION ENERGY SHIFTS.

-

of large clusters are not detected

obse rved

gepmetries.

Cluster

NrnImn

Except for the- hezri!0

t ion is

fea tures

to

instead of bei;ng inherenrt ly rp! itfol to

's

'Highor'

:;

is

thbat some of

J

dbue to di:ssocirtlrorl f t-he benzeie co),

thv- spectrum

i.nnof he vs-iitirly

2itrst::t

;uiisot rrpic.

!-, threie,; lcitPd

may be assigned to the Wthi

Thp

cm-

is

ster. Ight N2 molecuiles and

1ispectively.

Progressive

transition energy shifts toward lower energies with increasing cluster size ;ire observed

for the large clusters.

One rather broad peak dominates the

spectra of Nq clusters, whereas spectra of progressively larger CO2 clusters are also generally broad but do show some structure oni a broad background. The CO 2 cluster spectra are in addition somewhat obscurpd by a pronounced dip due to the saturation of the mass detector by ionized nonclustered benizene molecules.

Plots of an average cluster transition energy shift as a function A linear depenidence of the energy shift

of cluster size are given in Fig. 14. on the cluster size is

observed for n'2.

Addition of each solvent

molecule-

thlus causes a similar pe-rturbationi of the- benizene trainsit ion once the first two solvent molecul~es are attajched.

For clusters with seven and eight

16

tr-

gen molecules, the charge in transition energy shift seems to be slightly smaller, possibly due to

*i

gradually weaker interaction of the solvent molec loud of benzene as the (:luster si z

cules with the aromati

.

iic'reosedS

- ,rgst that the cluster shi fts ite not P-mt ;rel}

The above resti 's

saturated by one solven! mole,'ult found for benzene-alkant,

otn each side of the aromat ic '

ne-alkane 2 cli sters.

ring,

is

is

Larger shifts st ill

arise with addition of mere than tIwo molecules indicat ing th;l sevtri I soIvin t molecules may effectively interact with benzene.

This is

certainly the case

for the solute-solvent systems studied here for which the sizes of linear solvent molecules are relatively small compared to benzene.

The N2 clusters

with benzene exhibit larger energy shifts than the corresponding clusters of C02 , even though the CO, molecule has a relatively larger polarizability.

The

increase of the energy shift with cluster size is also larger for benzene(N 2 )n than for benzene(CO 2 )n .

This is probably due to the smaller size of the N2

molecule and thus a better spatial packing of nitr( ,,n around the benzene and concomitant stronger interaction with the electric

cloud.

Many solvent molecules effectively interact with benzene and contribute to the cluster transition energy shift in large clusters.

Since only one

rather broad feature is observed in the large cluster spectra, the spectral energy differences between various cluster configurations must be relatively small.

Comparison of the spectra of benzene(N 2 )n clusters with the spectra of

benzene(C0 2 )n clusters suggests that the N2 clusters exhibit fewer and more unique orientations than the CO2 clusters;spectra of N2 clusters show one relatively narrow peak, while those of CO2 are broader and have some structure on the main background.

This difference may be due to the larger size of the

CO2 as compared to N 2.

Calculations of the possible large cluster geometries

are presently being carried out in order to confirm this interpretation.

17

p

Preliminary results indicate that clusters with more than two solvent molecules exhibit a large number, of

local potential energy minima differing ir(creasf-s with

The number of local minima

slightly in cluster bindinp Petrgy. the cluster size. If large cl uster', '11, systems,

models of condensed phase

gas to cluster enel'v shifts must be explored and compared

with those

The. l-irgest energy shift observed in

our exper-

of condensed phase soloit i)sr. I li iments for benzene(N9 )l, molecules.

er;

kg m -3 (at T = 295 K and P

is

-42

cm - 1 for a

cluster with eight N2

is measured 1 8 for benzene dissolved in

the gas phase)

ca. 300 bar). c

ing fluid density (pressure) due to that

ca.

50 (-M-

A shift of about

supercritical nitrogen fluid (in

solute so

as potential

I,) srVe

forced

more molecules effpectively

at a

fluid density of ca.

220

This shift increases with increascrowding of the solvent around interact with benzene.

the

In the

liquid phase and high density flluid phase the energy shift increases up to 180 cm - 1 due to the additional

interaction of nitri,,Pn molecules

forced to

crowd about the benzene molecule at its periphery. Based on the comparison of benzene(N 2 )n cluster shifts with the supercritical nitrogen fluid results, one concludes

that in

the low density conden-

sed phase "solvation" of benzene takes place mostly about the 'r system and not at

the more repulsive C-H periphery positions.

This latter type of solvation

must be forced, however, in high density fluids and the liquid state.

VII.

NUCLEATION. The nucleation process

for small vdW clusters can be largely understood

only if various spectral features can be ascribed to specific cluster geometries.

Two basic types of nucleation can be distinguished:

homogeneous

nucleation in which solvent molecules are added to the solute molecule or cluster one molecular at a time;

and inhomogeneous nucleation in which more

18

thani one solvent molecule

is added

to the sol ute or CIluster at

time.

i g i veI

Reid t i ye in tens ity data for c us t ers of benzene and tolIuenie wi t ihydTW

hr

solvyen ts has led to the ciir: I is ion that solvent mci Iecu 1es ex i ;t

iqwr

ini

I lie s

~itI ~p i

so n ic ex ptnsioni in the form of di iners or larger aggrega tes an d t ha~it benzene(solvent )2chs Iis t ers dre isotrop ic deperds on

n

r

ilC

irlhlomogerueuis Iy

clIus ters) or

ed.1.2

i rihomogeneouis

t

[) i

Whether homogeneous r1iur len-t i (M

inr Iueat ion (;i

the relative size of the solvent dimer

to the solute--solvent (clIust er)

rePs pe (-t

ari

tcetdai

rm~.riosl

-

binding energy (E, i

hi nding energy

(F.)

ri ses

liust e r's)

so t r)p i'

Wi Ih

in the clIuster.

The smd ller the binding energy of a solvent dimer compared to the binding energy of the ci us tpr,

the, hipiher the concentrat ion of isotropic clius ters.

Inhomogeneous nuicleat ion is

Found to predominate for small clusters of ('-lzene

and toluene with two hydrocarbon solvent molecules because Ed'Ec is relatively large

(0.3

-

0.8 depending on

the

solvent).

The hinding energies of N2 and CO2 dimers at. -150 cMfor

and -442 cm -1, respectively.

the b#-nze-ne(N

2 )2

howev-r,

As shown in Table V the Ed Ec val'ue

and benzene((C0 2 ) 2 clusters is only 0.15 and 0.23,

Clusters,

s ince solvent dimers can easi ly be dissociated w ith very l iLtle

excess energy.

Our spectra confirm this implication because in all cases

studied the peak ascribed to isotropic benzene(solvent) intense than the peak due to anisotropic clusters. strong in the case of N2 clusters for which Ed/Ec is Clusters larger than benzene (solIven t) irhomogenvous nucloatiun.

ion.

re~spec-

This clearly favors homogeneous nucleation and formation of isotropic

t ively.

eniergy.

quite small:

2

2

clusters is mulch more

This effect

is especially

small.

are most likely formed by

First, larger solvent clusters have larger binding

High solvent aggregate binding energy favors inhomogeneous riciIoaComparison of the calculated solvent dimer and trimer binding enierv'ies

given in Table V shows ;in almiost- threefold increase binding energy (Ea)

)f' the solvent aggregdte

for the to imer with re-spect. to the dimer.

At

the same

time only a twofold increase of the cluster binding energy takes place for the (sol1vent )2 cluster

benzene

results in

compared

in increase of the E;jI;

This st rongly favors

inhomnoeeeoi:

clusters.

the ciistqf~

Second,

to distribute

as

the binding

.- nery

to) the benzene

(solvent),

clus ter whic

ratio with the increase of cluster siz~e ic [eation t ws

41

in size

for

large-

benzenelso Ivenit-

the nuimber of bonds, over wh ii-

the, collIision partner increases great ly,

and thus the ability of lthe cluster to dissipate the added binding energy increases.

VIII.

CONCLUSIONS.

Two color time of flight- mass spect-roscopy has been employed to small and lartge clusters of benzene with nitrogen, dioxide created in a supersonic molvrolir- jet.

carbon monoxide,

and carbon

Pol !itial energy calculations,

normal coordinate and internal rotational analyses lve been employed assgnen

o

te

0 an

metries of small clusters to experimental spectra.

0 spectra (n=1,2)

of the benzene(so Ivent) I clusters.

have been

study

for thle (leo-

computer calculated anid assigned

Transition energy shifts for both small and large

clusters with up to eight solvent molecules are investigated for the first time as a funct ion of cluster size.

The fol lowing major concluisions emerge

from this study: 1.

The calculated cluster binding energies scale well with the solvent

polarizabilities;

the larger the polarizability

the higher the binding energy.

2. The cluster spectral shifts depend on the solute-solvent geometry -id interaction but are less dependent on solvent polarizability. ence of the energy shift on the cluister geometry is

found to he less pr'ominent

than inl our previo us studies of benzene-alkane clusters.

20

The depend-

Both red and blute

Cluster energy shi fts art obse rved and the addi tive energy shirt rule for the isotropic benzene-solvent c lust ers does riot apply in general1

'3.

.Arialvs is (of !he

herizene(so Ivpnt -,-(W vi brat

c~lustp'rni odes

jona

oil

rt)taLionud

,pt-

inrterral

;10

',t

;vf-

ccounted for. around

illi

All

to

he

ind vdIW viir',j-

thre1'e So)let moleClIES studoied rotate nearly freiely

to rotation

CM1 barrier

I

It''

cluster spectrP and must. he

ll#,heieies~ert~

the berizerke-solverit

no hairrier'

the

rotat ion modes of

solvent molecule rotat iug tt otind the solute-solvent bond axis ion jut

is? t'Ls

iissignmerut of the rojtat iorrl

the

Both

I*-.

motIiuts within

diidl vibrai onal

possible

rn;tkt-tte

1

I

for the

in

rotation

bond axis. the ground in the

Cx(

The spectra state

(free

ted state

are

well assigned assuming

rotor) and a small

ca.

20

(slightly hindered rotor).

The

solvent rotational axis for, these linear diatomic and t, atomic molecular sOlvenits is oriented along the herizene-solvent bond and thus little or no barrier for, the 4.

internal

The benzene(solveut),

bending motions parallel

exists.

rotation

vdW vibrations obs. rved are those involving

to the benzene molecular plane (b.

stretching motion along the solute-solvent. bond (S.), (t

I. The tz mot ion is

5.

and b Y),

anid a torsional

a motion

niot present because of the free rotation around

Differences pertaining to energy shifts,

the z

intensity distribution anid

aippearance of the rotational and vdW modes are found between the 0 0 and 6 cluster spectra. rules:

the origin

These differences

arise- mostly from different select ion

is allowed at the 61 transition but forbidden at the 00 0 0

Conseque-nt-ly,

relatively weak internal rotational mode structure is ident ifi6-d 1 e () spectra but is difficult to distinguish in the 60 in th inte0( etrawic r

dominated by a strong origiii andl associated vdW vibrations.

-~~~~3

6.

Large viiW iltisttrs

oif up to eight N2

111l ecul1es sol1vat inrg benzenie Cluster feature- dominate. - i/i

increasinty r luter'p solvent

niol t' u 1 t-cn

spet-i

Ldf

ie'

s malIl b e i z et p-1 ,t n e r 1 11 t-t of

flt t i' alo

al

ic

t i me.

i i~

seven C. One

stIi i ft

shifts. are

ra ther b roadi

w ji

the irtd

Ii

(lot saiturated b%.

15 was isg

i it- t o t he

maiy h e

Ii

fi rs t

A I in-.i-r e-ntrjy

The cluister

is found

t-,ti hi

a.

~iand

mcil-'

fo r the

jrep observed

t ho

WO~~,

--

foundi

(rI.

[)ri-vi iii'.,

r uI'-i t i v-H'Iy

~z

, mal I I

the so IvenitmeIuues H.Iomogerneous

benzene(solvent )2

niill;

Vat ion

is

This is

(clusters.

fmuind to)

due

t

ii

him inate, the format ilm[

a very small

energy with respect to the WAnster binding energy.

solvent di mer

If

sma 1 bindi:,l

In large clusters the

ratio of the solvent aggregate binding energy to the cluster binding energy and the number of' ways to share the binding energy between the cluster bonds increase cons iderably; hence,

inhomogeneous nucleation may be favored in the

format ion of large clusters.

ACKNOWLEDGMENTS

One

C us (Romuald Nowak)

appreciates many hi"lpful discussions conrrern-

ing Molecular symmetry groups with Hoong-Sun We wish to thank C. Lilly, B. LaRoy, Research Centier U.S.A.)

i7,

Im (Colorado State Universi .. Y).

K. Cox and J.I. Seeman (Philip Morris

their support

22

and assistance

in this research.

REFERENCES 1 985)L

82, 726

.J. ('hem. Phys.

Bernsteir,

1.

M. Schauer and E.R.

2.

M. Schauer.

3.

J. Wanii

4.

J. Wa ria, .A. (1986)

5.

J.A.

6.

J.A. Menapace

7.

K. Okuyama, N. Mikami rind 1. Ito.

8.

P..J. Breen,

9.

J. Forges, M.F. Feraudy, 5067 (1983).

B. Raoult and G. Torchet,

10.

G. Torchet, H. Bouchier, Phys. 81 2137 (1984).

J. Farges,

11.

J.A. Barnes and T.E. Gough,

12.

E.R. Bernstein.

13.

E.B Wilson Jr., J.C. Decius and P.C. Cross, "Mf,, Tcular Vibrations, Theory New York. 1955). of Infrared and Raman Vibrational Spectra" (McGraw-Hill,

14.

1I. Infrared and G. Herzberg, "Molecular Spectra and Molecular Structure: New York, Nostrand-Reinhold, (Van Molecules" Polyatomic of Raman Spectra 1945).

15.

P. Bunker. "Molecular Symmetry and Spectroscopy" (Academic Press, London, 1979). C..J. Bradley and AP. Cracknell, "The Mathematical Theory of Symmetry in

16.

K.S.

Law and E.R.

aind E.R. Berristein. Mvt!' i vj't -

Menapace rnd E.R. ind E.R

m

_.

Phys.

Chem.

d F R. Bernstein.

J. Chem. Phys. 85. 1795

.1. Phys. Chem.

B~t-nstein,

J.

Phys.

J. Phys. Bernstein,

.J. Chem.

M.S.

Chem.

Oxford,

91, 2533 (1987). 91. 2843

(1987).

Chem. 89, 5617 (1985). .1. Chem.

Phys.

87,

1917 (1987).

J. Chem. Phys. 78.

de Feraudy arid B. Raoult,

Phys. 86.

K. Law and M. Schauer, J. Chem

Solids" (Clarendon Press,

736 (1985).

82.

84. 927 (1986).

Rernsre in,

J.A. Warren and E.R.

Phys.

.1. (hem.

Bernstein,

-012

.1 Chem.

(1987).

Phys. 80,

207 (1981).

1972).

R. Nowak and E.R. Bernstein, unpublished results.

17.

S. Li,

18.

R. Nowak and E.R. Bernstein, J. Chem. Phys. 86, 4783 (1987).

23 ...

,-.

.

.

.,

A,

,

.

,

-.

TABLE I

Rovibronic and nuclear spin selection rules. and

-stand

for an allowfed and forbidden transition,

re~spe-ctiv(ely.

Transitions not indicated are completely forbidden.

Molecular Symmetry Group

Cluster

Possible Transitions

a

-

Ig benzene(N 2 )1 &24 benzene(C0 2 )2

a-

Ig

('2g

(2g

aig

P2g

Ei,

Selection Rules Nuclear Spin Rovibronic 0 1 00 610

-

elu

b2 u

b2 u

e2

e2

b relO)

+

el

e 1 -b

2

+

+

TABLE IH Assignments of the 00 '11d 61 benzene(N )1

Transition Region

Calculated Rotaitional Transitions

Experimental Peak Positions (Relative to cIu stE ori:) cm!

Value em-1

-8

2

e2 g

-

-1

2

e2 g -

2

e2 g

-

4

~

4

e2g

-

2

e2g

-

4

e2 g

23

-6

7

37

-

Oa 1 g

e2g

-

Oa lg

-

25

2

32

Oalg -4e2g

e2g

-

Assignmont

h

31bY2

50

-

-46

b

65

-

-62:60

h, Y 4s 7

32

25

2

32

Oag

6137

(Fig. 3b) [38,602 cm-1

2

ValIup cm-1

-

-8

[812m-123

Assignment

e2 g

-24

1

Cillculated .-(W Vih ra t iun s

4

-23

00 (Fig. 3a)

c-,ust,>!r spwctr;i.

e 2g -4e 2 g -

4

e-gg

23

hx

31b2

41

46

b

67 1)10

61;60

b

:S7

TABLE f[r Assignments of the 0O0 and 61 benzene(C0 2 ) rInster spectra shown in Fig. 4.

-V

cm!

dflltl

Calculated Rotational Transitions

Experimental Peak Positions (Relative to ciluster' origin)

Transition Region

vdW Vlibrations

Ass ignment

VIlue cm 1 I

-6

-7

2e,

Oa Ig

-1

-1

2e 2 g

2

o

1

1

(Fig. 41)

7

6

17

19

2

25

26

Oa I

[805c1

61 (Fig. 4b) 1 [38,612 cm- ]

ValIute cm'1

Ass ignment

e2g

4e~g-4~ Oa 1 g

-

e2g -

2

e2g

4

e2g e2

33

-35;38

bX

65

-72;70

s7 ;b

9

6

16

19

28

26

2

-

2

-4~ -

4

e2g

Oa Ig

Oalg

b

4

e2g

1-35b y2

.54

-38

63

-71:70

s7 ;bx 4

70

-70;76

bN4 :b y

KOMMMMMxXy

_

TABLE IV

Assignments of the 00 and 61 benzene(CO), cluster spectra shown in Fig. 6.

cm-1

00 (Fig. 6a)

[38,110 cm

1

Calculated vdW Vibrations

Calculated Rotational Transitions

Experimentdl Peak Positions (Relative to cluster origin)

Transition Region

Value cm-I

Assignment

-23

-24

4e 2

-15

-16

3b 2 - Oa 1

-

Value cm- 1

Assignment

2e2 -

-8

-8

2e 2 - Oa1

0

-1

2e2

0

0.5

0

1

4e 2 -le,

10

7

Oa1

10

11

Oa 1 - 3b2

14

b

23

21

Oa I

-

3b 2

18

by

23

24.5

2e2

-

4e 2

35

33

Oa 1

-

4e 2

42

-

42

bx

2e2

-

3b2 - 3b 2

-

-

-

-

2e 2

55

54

66

68

tyby3 s

TABLE IV

-

Continued ...2 of 2.

Transition Region

Value cm-1

cm-1

77

11

6111 -21

(Fig. 6b)

[38,592 cm1

CillCU1lited vdW Vibrations

Calculated Rotational Transitions

Experimental Peak Positions (Relative to cluster origin)

-21.6

33

3

Assignment

Value cm-1

Oa 1

-

2e 2

0al

-

3b2

OaI

- 3b 2

-

2e2

-

4e2

-

Oa 1 -4e

38

-

-36b

46

-

-42

2

b

28

b

54

--

Assignmpnt

t

b 3 Yy

69

-68

s

76

-72

b y4

C~(C

(C1

-Z

-

NN

E

cc

C\J

t

-

7

-

x -: >

U'.

-L;

C -

-

-

--

-

-

('

-

C

*

cl

-. -r

I

.

4(Lv

u-

i-I

.-

I-

.~

-

>U -

';

-

FIGURE CAPTIONS

Figure 1

eigenvalues zene(N 2 )11.

Figure 2

and eigenvectors

of the vdW modes

Rigid cluster symmetry

is

Energies of the internal rotational the benzene(N2),

rotor rotational are OaIg,

lelu,

(b-f) for bpri- -

taken to be C2v

levels of the N 2 molecule in

levels at 0 cm 2

e2g.

3

b 2 u,

4

-1

The symmetries of the free

, in order of increasing energy,

e2g, 5elu, 6alg and 7eju.

0i

Two color TOFMS of the benzene(N 2 )1 ,iuster 61 (b) regions.

and

cluster calculated with B = 1.917 cm - 1 as a

function of a V 6 potential barrier.

Figure 3

(a)

Calculatd grouind state minimum energy configuration

The

internal rotational

in the 00 (a) and 0

(continuous line) and

vdW vibrational (dashed line) transitions are calculated as described in the text with the potential barrier in the excited state V 6 (SI) = 20 cm - I .

The 0 energy in the 00 spectrum corres-

ponds to the calculated position of the forbidden origin.

The

intensities in the calculated spectra are chosen arbitrarily in agreement with the experimental spectra. are given in Table (38086.1

I.

cm - 1 ) and 61

The arrows (38608.5 cm -

Specific assignments

indicate positions of the 00 0 1

) transitions

in

bare benzene.

Figure 4

Two color TOFMS of

clustfer in the on

h'le beon7,ne(C0),

61

Indd

20

(b)

regions.

rotat im

(_1Clculted spectra (%'( (S)

I (:crit i nuoni

Lra Its i t io005

'fhi'

line)

q oeergy

o f thfe f or b ididenr o r irz ii. [Hl.

0)

16

(r-m-1)

ind( vdW v ihrat ional

rons ist

of

(dislwd li jo)

co rres ponds to the cal culIa ted pos it Spec i f ic ass igint-nris arc! gi ven

ionr

i it TableP

The arrows i nd icate correspond ing benzene trans i t ions (se

captiLon for Fig. 3).

The d ip to thfe Ile ft, o f the o r ig in

in h i s

due to the saturation of the( mass detector by ionized benzene molecules.

Figure 5

Calculated ground statc, minimum energy configuration for the benizene(CO),

cluster.

The rigid cluster symmetry

vibrations are very similair to those benzerre(N 2 )l lIIIA.

Figure 6

rules given

in section

line indicates the C,) rotational axis.

Two color TOFMS of the benzene(CO), (h) regions.

The vdW

O~own in Fig. 1 for the

cluster with the selectio;.

The solid

is Cs.

cluster in the 00 (a) and 61

Specific assignments of both experimental and cal-

culated spectra are shown in Table [V.

The arrow indicates the

benzene origin (compare Fig. 3).

Figure?7

Calculated ground state minimum energy configurations of benzene(N 2 )2 clusters:

isotropic (a) and anisotropic (b).

Figure 8

Two color TOFMS of benzene(N 2 )2 clusters taken at two different 37270 cm-1

ionization enerfirios: (0

covrrespo ndu to

"The most

the

in

and 36550 cm

of henzene

transition

't

intfense peak

(upper)

-

(lower).

at 38608.5

is assigned to the

the spectrum

cm 1. iso-

tropic cluster

Figure 9

The benzene(.,").,).,

The scale is

Lions.

Figure 10

two rolor TOFMS reIative

at

and 61

00 (a)

to the benzene

to benzene 61

transi-

transitions.

Two color TOFMS of the benzene(CO)2 cluster at 60 . relative

(h)

is

The scale

transition.

Figure 11

Two color TOFMS of the benzene(COn)3

Figure 12

The 61

two color TOFMS of the benzene(

;ster in the 0o region.

2_)n

clusters.

The spectra

are numbered according to the number of N 2 molecules in the cluster.

0 corresponds to the benzene 61 transition at

38608.5 cm - 1 .

Figure 13

The 61 two color TOFMS of the benzene(CO 2 )n clusters. numbers reflect the number of CO2 molecules in scale is analogous

Figure 14

The

the cluster.

The

to that of Fig. 12.

Clusters transition energy shifts plotted as a function of the cluster size.

The error bars indicate uncertainty due to the

broadness of the spectral

features.

Benzene( N2 ), a)

b)

d

C) Z B.E=-501 cm "'

c)

x

x Sz(a,) 62cm-I

d)

bx(b1 ) 12cm1 l

e)

Z

by(b 2 ) 16 cm

1

,f)

ty (b1) 53 cm 1

-

tz((P) 14 cm -

Fig. I

125

E 75-

z u

25.

0

20

40 V6

60

80

;'cr

Fig. 2

a)

-50

(D C H6 (9

0 5010 ENERGY / cm1I

Fig.

3a

60 C6 H6 (N291

x15

I.IR

Fig.

3b

QN

I! o C6 6 (CO02)l ii

II II

I

I

II

-50

i

50

100

ENERGY / cml

Fig.

4a

b)61

C6 H6 (C02)1

A5

0

ENERGY

50

10

crri-

Ii

g.

4b

Benzene (Co),

Z

Fig.

5

I

O

~

CCH (CO),

6

I6

I

, i l l

I

I

100

050 ENERGY

cm c 1-

Fig. 6a

6

C6H6 (CO),

x5

-50

0 ENRG

0

o

cryf

Fig

6b

zBenzene (N)

2

.,'

a)

B.E.: -1007 cm'h

z b)

B.E.=- 962 crff Fig.7

S6~

-50

0

ENERGY /cmyf

C6 H6 (N2 )2

50 1

Fig.

a)

-50

~o~

0

C H6 (0)

50

ENERGY /cm'f

b)

-50

610 C6H6 (002)2

0 50 ENERGY /cmli-

Fig,,

9

6'

-100

-50 ENERGY

CrH 6 (CO0) 2

0

50

/cm f1

Fig. 10,

0a C6 H6 CO2)3

-50

0

50

100

ENERGY /cm ft

Fig.

11

44 32I"a

5

-50 0 Enry

ri

IN

UP

12

r~i

w

S/

'4S

3

C6H6(Co2)n 2

-50

0

50

Energy / cnFig.

13

-

n6

n 6( 2 )~

40H

H

C-

00

w

0

8 6 4 Number of Solvent Molecules 2

Fig.I!

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