Dr. William Tolles. I. San Diego, CA 91232. Superintendent. Chemistry Division ... Dr. A. Paul Schaap. Department of Chemistry. Dr. G. A. Crosby. Wayne State ...
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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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