Spectra of isotopically mixed benzene trimers
K. O. Börnsen, S. H. Lin, H. L. Selzle, and E. W. Schlag
Citation: J. Chem. Phys. 90, 1299 (1989); doi: 10.1063/1.456124
View online: http://dx.doi.org/10.1063/1.456124
View Table of Contents: http://jcp.aip.org/resource/1/JCPSA6/v90/i3
Published by the American Institute of Physics.
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Spectra of isotopically mixed benzene trimers
K. O. Bornsen, S. H. Un,a) H. L. Selzle, and E. W. Schlag
Institute for Physical and Theoretical Chemistry, Technical University ofMunich, 8046 Garching,
West Germany
(Received 29 January 1988; accepted 19 October 1988)
Isotopically mixed jets of benzene produced important new detailed structural results from the
various possible isotopic benzene trimers in a supersonic jet. From different isotopic spectral
shifts, a detailed and consistent model of the interaction between the three benzene molecules
can be inferred. The splitting of the 0--0 transition of isotopically mixed trimers can be
predicted from this model. This model is consistent with a "zig-zag" structure for the trimer,
not a cyclic structure. In contrast to the dimer spectra, van der Waals modes were observed.
We also discovered an important, new exciton splitting in the van der Waals modes. This
splitting demonstrates for the first time that the van der Waals modes are uncoupled from
molecular vibrations. Furthermore, it is a sensitive indicator of the identity of the molecules so
coupled. The spectra of higher benzene clusters (dimer to pentamer) have also been measured.
I. INTRODUCTION
A detailed knowledge of elementary interactions
between nonbonded aromatic molecules in the absence of
any interfering many body effects is offundamental interest.
The benzene dimer is the simplest prototype system in which
this interaction between two aromatic molecules can be
studied under the isolated conditions of the gas phase. Fung
et al., I observed unambigously, for the first time, the "exciton" splitting in the dimer. They also developed a new method for gaining information about clusters from studies of
mixed isotopic complexes. In particular, they showed that in
the isotopic mixed benzene heterodimer, the excitation is
localized in either half of the dimer, the other part being
essentially a silent partner. In the case of the homodimer,
however, one observes a very weak exciton coupling which
leads to a 1.7 cm - I splitting of the 0--0 transition. 2 The intensity distribution in this newly discovered exciton doublet of
the dimer negates aT-shape structure but rather infers an
angle of about 70· between the two planes of the benzene
molecules, i.e., C 2v symmetry, and a roof-type structure.
The spectrum of either homodimer is always red shifted relative to the corresponding isotopically mixed heterodimer. A
delocalization and a stabilization effect is responsible for this
effect. Hopkins et al. 3 have also measured the various benzene complexes by resonant two color photoionization with
moderate spectral resolution. Since they could not resolve
the two exciton split peaks of the 0--0 transition of benzene,
they claimed that the broadening of the unresolved 0--0 peak
was caused by a fast nonradiative process on a picosecond
time scale. This nonradiative process was described as a rearrangement of the initial prepared 8 1 dimer configuration
over a low barrier into a deeper excimer well. Our measurements of the isotopic labeled benzene dimer clearly showed
the absence of such a broadening, especially in the case of the
heterodimer, which negates a fast nonradiative process on
the time scale and hence, does not require the stabilization
cited above. If such a relaxed excimer state were present in
the gas phase, as indeed is known in a solution environment, 4
this should exhibit a very different behavior in the ionization
J. Chern. Phys. 90 (3),1 February 1989
process than the ionization from the initially prepared intermediate state. Our measurements of the ionization potentialS
of the isotopic benzene dimers can, on the contrary, only be
interpreted as ionization form the resonant intermediate
state with no contribution from a relaxed excimer state. The
proof for this statement was because a larger energy difference to ionization and different Franck-Condon factors
should be observable but was not seen, although a 12 ns delay
for the second ionizing laser was employed.
In the case of the benzene trimer, there are interactions
between three identical aromatic molecules. The questions
are: (a) does the dimer portion of the trimer change its structure when a third benzene molecule is attached; and (b)
what happens to the exciton splitting? Calculations for potential energy minimization cannot distinguish between the
stability of a zig-zag6 and a triangular structure. 7 We will
show how such information can be obtained from the spectra
of isotopically mixed complexes formed and cooled in supersonic free jets.
II. EXPERIMENTAL
The supersonic jet used in this experiment has been described previously. 8 It is similar to an apparatus used in studies of the benzene dimer. 2 If isotopically mixed benzene
trimers AAB or ABB are required, one also produces ipso
facto the species AAA, BBB, and all other combinations
clusters in this experiment. Hence, the spectroscopy of such
isotopic mixtures is essentially impossible without mass selection. Even mass selection, however, is insufficient to separate AAB from ABA clusters. Highly resolved multi photon
ionizaton mass spectrometry (MUPI-MS) offers the possibility to study the first excited state 8, of each of the neutral
substances AAA, AAB, and BBB separately by scanning a
laser, and then adding a second photon to produce the corresponding ion. One of the major problems even with twocolor MUPI of clusters is that contamination of peaks occurs
as a result of: (a) degradation of higher clusters after ionization; or (b) ion-molecule reactions from lower clusters. The
complication (b) can be neglected in a skimmed jet system
0021-9606/89/031299-08$02.10
@ 1989 American Institute of Physics
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1299
1300
BOrnsen et a/.: Benzene trimers
but (a) is a persistent problem, though it is often ignored.
Our experiments show that this dissociation of higher benzene clusters to smaller clusters is an ever present problem
that requires careful analysis.
Protonated benezene (Merck) and 99.69% perdeuterated benzene (Merck, Sharp, and Dohme, Canada, Ltd.)
were used in equal amounts for the isotope effect studies.
The natural abundance of 13C in benzene was sufficient for
the 13C studies. The benzene was cooled to 5 ·C in a reservoir. Helium carrier gas was used with 5 atm backing pressure.
In the two color experiment, the extracting ion optics of
the mass spectrometer can be pulsed with a delay up to 3 fts
after the first laser pulse. After the ionization, a Coulomb
explosion of the ion cloud takes place. The ion optics were
built in such a way that only the ions of the inner part of this
sphere could get to the detector. The ions contained in the
outer sphere with higher kinetic energy (dissociation products and "hot" ions) were rejected.
The first laser (Coumarin 307) was used to scan the
resonant state, and the wavelength of the second laser (Nafluorescein) was chosen in such a way that it would not ionize the bare benene molecule but only the complexes which
have a somewhat lower ionization potentia1. 9 The laser
bandwidth was 0.3 cm - 1 in the UV range. The ions were
deteceted with a RETOF mass spectrometer of75 cm length
with a resolution of M / tlM of 2800. Excitation spectra for
two selected different masses were recorded simultaneoulsy
with a dual channel boxcar averager. In this way one could
separate overlapping bands of the different isotopic species
and calibrate their spectra relative to each other.
III. RESULTS
Excilabon 5 eclra of Benzene Com Lexes
A
Dimer
o
z
n
c
AJ
AJ
fTl
Z
...,
B
Trimer
o
z
n
c
AJ
AJ
fTl
Z
--1
-40.0
-80.0
-100.0
-120.0
CM-l
FIG. I. Excitation spectra of the benzene dimer (a) and trimer (b) attheO-
otransition with mass selected ion detection. The dimer spectrum shows the
0-0 transition on the left side and the dissociation products of the trimer on
the right. The trimer spectrum (b) shows the vdW modes on the right side
the 0-0 transition.
higher clusters is low and therefore the intensity of the signals is small. To obtain a higher signal, one must increase the
fluence of the lasers but this also increases multiphoton processes, leading to dissociation. To overcome this problem,
one now can delay the extraction of the ions out of the ionization region by several microseconds. The dissociation prod-
A. Ion current excitation spectra of different benzene
clusters
Fluorescence excitation spectra and mass spectra of
pure benzene clusters were observed previously by Levy and
Smalley3,10 with moderate resolution that could not reveal
the exciton splitting uneqlvocally. MUPI-MS offers the possibility to study the first excited state 8 1 of each cluster size
and for all various isotopomers in the supersonic jet. The
data show distinctly different spectra for each cluster, when
we record at the mass of two clusters of different size simultaneously. From the comparison of these two spectra, we
now propose to see which peak is genuine and which peak is
due to a dissociation product from a higher cluster. We can
recognize the dissociation path for the benzene trimer, tetramer, and pentamer. From the analysis of the spectra we
found that in the case of the trimer and tetramer, one benzene molecule is ejected due to dissociation of the complex
ion, whereas the pentamer ion dissociates into a tetramer
and a trimer. The dissociation of these clusters can be seen in
Figs. 1-3. Every peak found at the same wavelength in both
spectra (a) and (b) can be associated with a dissociation
product from higher clusters. This dissociation is caused by
the large amount of excess energy deposited in the benzene
complex ion. Hopkins et al. 3 have shown that this amount of
dissociation can largely be removed by reducing the energy
of the second photon. Unfortunately, the concentration of
-60.0
Exci labon 5 eclra of Benzene Com Lexes
A
Trimer
o
z
n
c
AJ
AJ
fTl
Z
...,
Telramer
o
z
n
c
AJ
::0
fTl
Z
...,
-105.0
-130.0
-155.0
-180.0
-205.0
CM-l
FIG. 2. Excitation spectra of benzene trimer (a) and tetramer (b) at the 0-
o transition with mass selected ion detection. The trimer spectrum shows
the 0-0 transition on the left side and the dissociation products of the tetramer on the right. The tetramer spectrum (b) shows the weak vdW modes
and the peak in the middle arises from dissociation products of the benzene
pentamer.
J. Chern. Phys., Vol. 90, No.3, 1 February 1989
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BOrnsen et a/.: Benzene trimers
Excilation 5 eclra of Benzene Com Lexes
lfl
A
~
:T
'"
c-
~
o
...,
Telramer
1301
•
0
•
•
0
o
z
FIG. 4. Spectroscopic shifts
of benzene clusters relative to
the monomer.
(J
3
n
c
::u
I
:u
I
'"
0
•
fTl
z
--1
2
i
1
i
3
4
5
CLusler Size
B
Pen lamer
o
z
n
c
::u
::u
fTl
z
-l
-110.0
-135.0
-160.0
-185.0
-210.0
CM-l
FIG. 3. Excitation spectra of benzene tetramer (a) and pentamer (b) at the
()...{) transition with mass selected ion detection. The dimer spectrum shows
the ()...{) transition on the right side and the dissociation products of the pentamer in the middle. The pentamer spectrum is shown in (b). It exhibits
only a single peak.
ucts with higher kinetic energy leave the region of the source
from which ions can get to the detector of the reflectron mass
spectrometer and are therefore rejected. An interesting aspect of these measurements and a useful diagnostic is that
the dissociation process is not influenced by the excitation of
a v~n der Waals mode in the intermediate state. The small
amount of energy in a van der Waals mode compared to the
excess energy in the ion does not enhance the reactivity in the
dimer. In the case of the benzene trimer, the 0-0 transition is
shifted 122.5 cm - I to the red relative to the monomer with a
splitting of 1.9 cm -I. This shift is much larger than predicted by simple additivity from the shift in the benzene dimer
( 45 cm -I). The aggregation of the third benzene ring shifts
the 0-0 transition more than twice as much as for the dimer.
This points to an interesting "special" interaction between
these three ~omatic molecules.
The bell;zene tetramer is shifted 161.6 cm- I to the red
relative to the monomer. But this shift amounts to only a 38
cm- I additional shift relative to that of the trimer. Also an
exciton splitting of 2.4 cm - I is still observed. A very interesting point is the case of the benzene pentameter. Here we
could not observe any exciton splitting and the 0-0 transition is now shifted backwards by 15 cm - I to the blue relative
to the tetramer. The total shift amounts to 146.4 cm - 1 to the
red relative to the monomer, i.e., less than that of the tetramer. Figures 1-3 show the excitation spectra of benzene
clusters. 2- 5 For the measurement of the relative shift of each
cluster, two masses were recorded simultaneously. In the
case of the trimer and tetramer, vdW modes were observed.
It is very interesting that the dimer and pentamer spectra do
not show any vdW modes. We find these modes only in the
case of trimer and tetramer clusters. The transition frequencies and shifts are given in Table I and plotted in Fig. 4.
B. 0-0 transition of benzene trimer with isotopiC
labeling
The 0-0 transition is one- and two-photon forbidden in
the benene monomer. In the dimer and higher benzene clusters it can be observed weakly. 2 In the case of the benzene
trimer, the 0-0 band is found 122.5 cm - I to the red of the
forbidden monomer transition and shows two peaks at very
low temperatures. These peaks are separated by 1. 9 cm - I
and show different heights, with a ratio of 7:4 for the red
relative to the blue peak [Fig. 5 (b)]. Towards higher energy
we find many groups of vdW modes of the benzene trimer.
The first group of four peaks is 20 cm - 1 shifted to higher
energy relative to the 0-0 transition of the benzene trimer
complex. The wavelength positions for these peaks are found
- 98.9, 101.1, - 102.6, and - 104.2 cm- I relative to the
0-0 transition of the benzene monomer.
c. Benzene trimer with one perdeuterated molecule
Our benzene dimer spectroscopy has shown that considerable new information could be gained from studying the
difference between spectra of the various dimers as a result of
using an isotopic mixture. Similarly, an isotopic study
proved useful for characterizing the trimer. New information relating to the benzene trimer system emerges when we
TABLE II. Exciton splitting of benzene trimer at the ()...{) transition.
TABLE I. Spectral shift of benzene clusters.
Band position
(em - I)
Monomer
Dimer
Trimer
Tetramer
Pentamer
a
38086.1
- 45.4
- 122.5
- 161.6
- 146.4
ReI. shift
(em-I)
Splitting «()...{)
(em-I)
-45.4
-77.1
- 38.1
15.2
1.7u
1.9
2.4
d:J--do--ti6
d:J--d6--tio
d:J--d6--ti6
d6--ti:J--ti6
Band position
Splitting
(em-I)
(em-I)
38086.1
- 122.5
- 121.5
- 116.3
- 120.6
- 116.9
- 118.8
- 115.0
Reference 2.
J. Chern. Phys., Vol. 90, No.3, 1 February 1989
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1.9
1.3
1.9
BOrnsen et al.: Benzene trimers
1302
Excilalion 5 eclra of Benzene Com Lexes
Exei lalion 5 echo of Benzene Com Lexes
A
Trimer H2D
Trimer HD2
o
z
o
n
n
;0
;0
;0
;0
z
c
c
rrJ
Z
rrJ
Z
--,1
--,1
B
Trimer H3
Trimer H3
.....
o
o
z
Z
n
n
C
c
;0
;0
;0
;0
rrJ
Z
rrJ
Z
--,1
--,1
-40.0
-65.0
-90.0
-115.0
-140.0
-40.0
-65.0
CM-l
-90.0
-115.0
-140.0
CM-l
FIG. 5. Excitation spectra of isotopic benzene trimers at the 0-0 transition
of do excitation with mass selected ion detection. A mixture of 60% perprotonated and 40% perdeuterated benzene was used. (a) Excitation spectra of
dt-dO-d6 and dt-d6 -dO with detection of mass 240 u. (b) Simultaneously
recorded excitation spectra of d t -do-do with detection of mass 234 u.
replace one benzene molecule with per4euterated benzene.
In our measurement [Fig. 5 (a) ) a mixture of 40% perdeuterated and 60% of protonated benzene was used. The laser
frequency is tuned to excite only the protonated ring. From
our dimer measurements we know that the excitation is localized in the do part of the trimer and any possible effects
from exciton interaction can only be due to the two do partners in the complex. In this cluster, the 0-0 transition is red
shifted by 120.6 cm- I relative to the monomer [Fig. 5(a»)
and lies 1.9 cm - I, on the blue side of the homotrimer transition [Fig. 5(b»). The splitting of this transition [Fig. 5 (a) )
was found to be 1.9 cm- I with a peak intensity ratio of9:10
referring to the red peak. There is also a third peak shifted
3.7 cm - I to the blue relative to the double peak.
These measurements for the trimer may be compared
with those obtained for the dimers. In the case of the homodimer (d~-do) an exciton splitting of 1.7 cm- I was found
while for the heterodimer (d ~-d6) a single peak is observed
blue shifted relative to the monomer. Towards higher energy, we find the vdW modes of the do-do-d6 complexes [Fig.
5 (a) ). Their positions are changed in the same way, relative
to the pure trimer spectrum in Fig. 5(b), as the 0-0 transition. There are two sharp peaks, 99.5 and 101.2 cm - I, shifted to the red relative to the 0-0 transition of the monomer.
Another large peak is found at - 97.4 cm- I relative to the
monomer. The last peak of this first vdW group is shifted
94.0 cm - I to the red.
FIG. 6. Excitation spectra ofisotopic benzene trimers at the 0-0 transition
of do excitation with mass selected ion detection. A mixture of 40% perprotonated and 60% perdeuterated benzene was used. (a) Excitation spectra of
dt-d6 -d6 and d6 -dt-d6 with detection of mass 246 u. (b) Simultaneously
recorded excitation spectra of d t -do-do with detection of mass 234 u.
ed exclusively in this wavelength region. The 0-0 band displays two peaks with a spacing of 3.8 cm - I . The red shift
relative to the benzene monomer is 118.8 and 115.0 cm- I ,
respectively, for the two peaks, which is less than the shifts
observed for the homodimer. The peak intensity ratio is
nearly equal. In comparison with this result, the excitation
spectra of the heterodimer (d ?;-d6 ) show only one peak and
also a blue shift relative to the homodimer. The first group of
vdW modes (three peaks) is found at -100.1, - 96.3, and
92.7 cm - I. The - 96.3 cm - I band is the strongest while the
- 100.1 cm - I band is the weakest. Further to the blue, progressions in the vdW modes are seen.
E. Benzene trimer with one13C isotope in the system
When there was one 13C atom in one ring of the benzene
trimer complex, we observed the spectrum in Fig. 7 (a). This
excitation spectrum is more complicated. The first feature
from the right shows two peaks with a splitting of 1.3 cm - I .
The left peak shows a small peak in the shoulder to the left
side. The peak intensity ratio of the main two peaks is 3:7.
This double peak is red shifted 121.5 cm- I relative to the
monomer and 0.5 cm - I blue shifted relative to the pure
trimer [Fig. 7(b»). In addition, we find one single peak 5.2
cm - I to the blue. There are also peaks on the blue side of the
spectra arising from the vdW modes.
The peak positions of the 0-0 transitions and the exciton
splitting of all trimers are given in Table II.
D. Benzene trimer with two perdeuterated molecules
Figure 6(a) shows the excitation spectra of the trimer
with one protonated benzene molecule and two perdeutered
benzene rings. A mixture of 60% C6D6 and 40% C6H6 was
employed. The 0-0 transition of the protonated ring is excit-
IV. DISCUSSION
A. van der Waals modes
We now show for the first time how structural features
of the vdW modes of the benzene trimer provide new infor-
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1303
BOrnsen et al.: Benzene trimers
"C-Spectra af Benzene Trimer
Trimer 13C
A
a
z
n
c
:;0
:;0
rn
Z
--l
B
a
z
n
c
FIG. 7. Excitation spectra of isotopic benzene trimers at the (}...()
transition of do excitation with
mass selected ion detection. Perprotonated benzene with the natural abundance of Uc was used. (a)
Excitation spectra of 13C d ~ --do--d"
with detection of mass 235 u. (b)
Simultaneously recoreded excitation spectra of d ~--do--do with detection of mass 234 u.
:;0
:;0
rn
z
--l
-80.0
-105.0
-130.0
CM-l
mation about the trimer structure. The spectra of the isotopically mixed trimer do-d6-d6 (HDD) with excitation of the
do ring can be understood easily with a structure in which the
contributing rings are not equivalent and are here assumed
to form a zig-zag structure. In this case, there are two possible locations to arrange the protonated ring in this complex:
At one end (HDD); orin the middle (DHD). TheO-Otransition has in each case a single peak. Here we expect no exciton splitting and find none by excitation of the do ring. For
each conformer of the zig-zag structure there are two vdW
vibrations with oscillator strength observed. They are blue
shifted relative to the 0-0 transition fo the trimer (HDD) by
20.2 and 23.3 cm- I (Table 111), respectively. These shifts
are the same for both conformers. The transition frequency
of the lower vdW mode of the conformer coincides with the
transition frequency of the upper mode of the other conformer and therefore we observe three peaks, whereas the
middle peak is nearly twice as high.
In the case ofthe pure trimer (HHH), we have only one
conformer. Therefore, we should observe only two vdW
modes in the 20 cm -12 region to the blue of the 0-0 transition. For this complex, we discovered a weak exciton coupling. The exciton coupling leads to a splitting of the 0-0
transition. Interestingly, this exciton splitting also manifests
itself in the vdW modes and we consequently observed four
lines. The frequency shifts of these vdW modes are nearly the
same as in the HDH case with 20.3 and 23.3 cm - I, respectively. The exciton splitting of the two vdW vibrations are
also present but larger (2.0 and 2.3cm -1) than the exciton
splitting of the 0-0 transition (1.9 cm - 1 ).
The vdW spectra of the (HHD) complex is even more
instructive. Here there are two possible conformers: (HHD)
and (HDH). In the first case the complex (HHD) has two
vdW vibrations, now with an excition splitting in each peak.
In this way, we obtain four peaks. The other compelx also
has two vdW vibrations but display no exciton splitting as is
expected from the structure, since the neighbors are all different. The observed spectra show two narrow and two
broad peaks under which two peaks are hidden. This spectrum can also be explained with two vdW modes of20.2 and
23.3 cm- I and a value of2 cm- I for the exciton splitting.
The interesting observation is that the shifts in all vdW
modes are nearly constant. More importantly, exciton splittings in the trimer are now revealed to be a direct signature
for the nature of the neighboring species. i.e., whether they
are identical or not. This splitting is a new signature of the
structure of van der Waal molecules.
The discovery of new exciton splittings in vdW modes is
really most interesting, not only as an important diagnostic
for testing the neighborhood of excited molecules, but also as
a process itself. It is, after all, well known that exciting a
vibration, such as V6 in the benzene dimer, lifts the exciton
splitting observed in the 0-0 transition. One quantum of a
van der Waals mode is also much larger than the exciton
interaction and should also lift the degeneracy if it is strongly
enough coupled to the ring modes-but it does not. This
result is then direct evidence for the fact that the vdW mode
does not affect the identity of the two benzene rings-these
modes are indeed vdW modes and not coupled to the ring. In
other words, this finding is the first direct proof of the fact
TABLE III. van der Waals modes of the benzene trimer.
Band position of
the (}...() transition
(em-I)
d*o
d~--do--do
38086.1
-122.5
- 121.5
- 116.3
-120.6
- 116.9
- 118.8
- 115.0
vdW shift relative
to the (}...() transition
(em-I)
19.6
23.3
20.2
23.4
20.3
23.3
20.3
23.2
20.2
23.3
20.2
23.3
Splitting
(em-I)
2.0
2.3
2.0
2.3
2.0
2.3
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BOrnsen sf a/.: Benzene trimers
1304
that these vdW modes do not couple to the ring modes. This
result also points to the isolation ofvdW modes from the ring
moiety, a result also with important consequences in chemical dynamics.
calculate the transition moments
Uei=CilUl+C,"2U2+Ci3U3'
The observed splittings and isotopic shifts of the 0--0
transition gives us important additional data reflecting the
weak vdW bonding and interaction. In the dimer we observed the splitting of the homodimer as an exciton coupling.
In the case of the benzene dimer and the isotopically mixed
dimers, one can apply first order perturbation theory to successfully explain the splittings. The energy difference in the
homodimer has been given by
t:.E = 2{J,
where t:.E is the observed splitting and {J is the interaction
matrix element, which is found to be 0.8 cm - I is for the dodo complex. The benzene trimer in many cases is similar to
the dimer. Therefore, a perturbation theory may also explain
the observed spectra of isotopically mixed trimers.
Williams6 calculated the detailed conformation of different benzene clusters (n == 2-15). The nonbonded potential energy of the clusters was minimized by the NewtonRaphson method with exp-6-1 potential functions. For the
benzene trimer, he finds a zig-zag structure like an UN". van
de Waals 7 however, calculated a triangle structure with the
same energy as for the zig-zag structure. 6 With our measurements we can distinguish clearly between these alternatives.
c. Theoretical model of spectral intensities, shifts, and
spllttings in trimers
To interpret the intensities, splittings, and shifts in the
spectra in benzene trimers, we shall use the exciton model.
Suppose we have a trimer system represented by ABC. Then
the excited electronic wave function e can be expressed as
(1)
where tPl' tP2' and tP3 represent the wave functions at A *BC,
AB*C, and ABC*, respectively. Here, for example, A*BC
implies that A is excited.
By using the variational method, the energy W of the
excited trimer can be determined from
+ c2H 12 + C3H13 = 0,
c H + c2 (H22 - W) + C3H23 = 0,
c IH 31 + c2H 32 + c3 (H33 - W) = O.
I
21
W)
(6)
IUei 12 = C71 uf + C~ ui + C;"3 ui
B. Exciton splitting of the 0-0 transition
C I (HI I -
i=I,2,3.
The observed spectral intensity is determined by
+
2(cil ca U I U2 +
+ C,2C,"3 U2U3 ),
Cil C,"3 U IU 3
(7)
i = 1,2,3,
with
(8)
f.lil"j = If.li IIf.lj Icos ()u·
From Eqs. (2)- ( 4) we can determine the spectral shifts and
splittings of the trimer and from Eq. (7) we can determine
the spectral intensities and plausible structures of trimer,
when one fits the angle ()ij between the benzene rings, which
influences the cross terms in the transition moment.
In the following, the structure is discussed on the basis
of a structure of the benzene trimer that is not symmetry
equivalent for the three benzene moleules but has only two
different "sites" within the trimer, as there are only two different peaks found in the do-d6-d6 trimer. From possible
structures, like parallel displaced, parallel stacked, double
T-shape, etc., we choose the zig-zag structure that, from
theoretical calcualtions,6 correlates to the structure of solid
benzene and can be constructed by simple adding one more
benzene molecule to an existing dimer.
D. IsotopiC effect
In the benzene homotrimer, there is a weak exciton coupling between three molecules leading to a splitting of the 0a transition of 1.9 cm - I. This value is similar to the splitting
in the case of the homodimer with 1.7 cm - I. In the calculation for the zig-zag structure with first order perturbation
theory, which was also successful in the case of the dimer, we
find here from the observed splitting of 1.9 cm - I a value of
0.7 cm - I for the interaction matrix element between the
three benzene molecules. From the intensity ratio of the exciton split peaks (1: 1.4), we deduce an angle () of 80° ± 10°
for the symmetrical «()\2 = ()23) zig-zag conformation. Figure 8 shows this structure. The relative orientation of the
benzene rings with respect to rotation around the molecular
axis is chosen arbitrarily and cannot be deduced from the
(2)
(3)
(4)
In a cyclic system with symmetry equivalent molecules,
like a triangle, the interaction matrix element HI2 and H13
can be assumed to be equal, whereas in a noncyclic system,
like a zig-zag structure, we can set H13 to zero. This factor is
important for the determination of the structure of the
trimer.
Ifwe let WI' W2 , and W3 denote the three eigenvalues of
Eqs. (2)-(4), then the corresponding wave functions are
given by
FIG. 8. Zig-zag structure of
the benzene trimer. The angles between the planes of the
molecules were determined
from the analysis of the peak
height distribution.
tPei=CiltPl+C,"2tP2+Ci3tP3' i=I,2,3.
(5)
Using the wave functions tPei given by Eq. (5) we can
J. Chem. Phys., Vol. 90, No.3, 1 February 1989
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BOrnsen et a/.: Benzene trimers
model and the spectra. Clearly these are indirect results,
which must be checked by sub-Doppler absorption spectros.
.
.
copy with rotational resolution.
In the benzene trimer, the isotopic shift of the 1sotop1cally mixed trimeres could be due to the in~emal .zero point
energies of the individual partners and an 1SOtOP1C effect affecting the vdW bond. The zero-point energy difference. for
the do and d 6 benzene monomer in the ground and exc1ted
states leads to a difference ofthe excitation energy of 202.9
cm -1 for the 0--0 transition. When there are two perdeuterated benzene molecules in the trimer system, we get in the
case of the zig-zag structure two possible arrangements of
the three molecules (do-d6-d6 and d6-do-d6 ). Both possibilities should have different spectral shifts. The excitation is
compeletely localized in the do benzene molecule and a s~ift
caused by a weak exciton interaction with the far off IY10g
level of the d benzene molecule can be neglected. In the case
of the triang~lar structure, there must be only one poss~ble
arrangement of the trimer and therefore th~ model pred1c~s
only one single peak. The measurement (F1g. 8) shows d~­
rectly that only the symmetry inequivalent zig-zag model1s
the right one.
In the case of one perdeuterated benzene molecule in the
trimer system, we also have also two possibilities to arrange
the d 6 molecule. In the arrangement with the protonated
benzenes in the middle of the zig-zag structure (dO-d6-dO )'
we have something like a "double heterodimer." The spectra
should show only one blue shifted peak. This single peak is
shifted 3.7 cm - 1 relative to the other possible arrangement
with the perdeuterated molecule at the end. The shift is larger as in the dimer case where one finds 1.9 em - I. In the other
arrangement, the perdeuterated molecule is at the end of the
trimer system (dO-dO-d6 ). Here we have a weak exciton coupling between the two protonated benzene rings. The spectra
show a splitting of the 0--0 transition of 1.9 cm - I. The calculation with first order perturbation theory gives the same
splitting using the value of the homotrimer for the interaction matrix element, where we use 0.7 cm - 1for the benzene
d o-d0 interaction and 209 cm - 1 for the zero point energy
shift of d 6 benzene.
Further isotopic study can be carried out for the trimer
with one 13C isotope in the system, which represents a much
weaker perturbation. The mass difference when one substitutes a 13C isotope is of the order of 0.6%. The effect on the
vdW bond will be very small for this system. We have determined the zero-point energy difference between 13C-benzene and 12C-benzene as 3.9 cm -1. 2 Perturbation theory exPlains the behavior observed for this trimer that can be
. the
described as a heterotrimer A *BB when t h e 13C'1S 10
excited molecule as AB*B when the 13C is in the nonexcited
part of the trimer. If we assume a benzene-benzene interaction of 0.7 cm - 1and an energy difference of 3.9 cm -1 for the
12C-benzene-13C-benzene, we predict three peaks when the
13C isotope is in the end ring do-do_13Cdo. For this case, we
calculate an exciton splitting of 1.36 em - 1 and a further
single peak blue shifted by 4.7 em - I. In the case where ~he
13C is in the middle of the trimer dO-13Cdo-do the calculatIon
predicts only two peaks with a spacing between them of ~.4
em - I. Experimentally, one always prepares both speCIes,
1305
hence the spectrum must display five peaks. Our measurement at present shows only four peaks, although it is possible
that there are two transitions contributing to the apparent
single peak on the blue side. If this interpretation is permitted one can simulate the spectrum shown in Fig. 7.
V. CONCLUSIONS
The supersonic jet experiment is certainly an important
tool for the study ofvdW complexes but it becomes far more
interesting if isotopic mixtures are measured. 1 In this way,
we measure spectral shifts at the 0--0 transition of the benzene clusters from the trimer, tetramer, and pentamer. In
comparison with the benzene dimer work, we discovered, in
the case of the trimer complex, an exciton coupling that
leads to a splitting of the 0--0 transitions of 1.9 cm - 1. This
splitting is in the same order as it was found for the dimer
splitting (1.7 cm -1). The intensity distribution in this exciton doublet of the benzene trimer infers an angle of 80·
between the planes of the benzene molecules. Hence, the
three molecules are arranged as a zig-zag structure. The occurence of two peaks for the dO-d6-d6 trimer reveals only
two different "sites" and negates any trimer models that are
cyclical or triangular in structure. The various splittings and
peaks of the isotopic trimers can be predicted correctly with
a first order perturbation theory, which confirms the zig-zag
structure and reflects the interaction between the rings.
In the case of the benzene trimer, we also discovered
vdW modes in the spectra. From the isotopic studies, we can
show that only two vibrations have oscillator strength. In the
homotrimer (HHH), these van der Waals modes exhibited
interesting exciton splitting, a novel finding that represents
an important structural signature. The discovery of the exciton splitting in the trimer is shown to be a direct diagnostic
for the nature of the neighboring species. Furthermore, the
very existence of these splittings is only possible if the van der
Waals modes are almost completely isolated from the ring
modes. This uncoupling of vdW modes from molecular vibrations is important evidence for the isolation of molecular
species in vdW complexes, an experimental observation with
far reaching consequences in spectroscopy and dynamics.
ACKNOWLEDGMENTS
We thank the Deutsche Forschungsgemeinschaft for financial support of this work. One of us (S. H. Lin) also
wants to thank the NFS for financial support.
'K. H. Fung, H. L. Selzle, and E. W. Schlag, J. Phys. Chern. 87, 5113
(1983).
2K. O. Biimsen, H. L. Selzle, and E. w. Schlag, Z. Naturforsch. Teil A 39,
1225 (1984); J. Chern. Phys. 85,1726 (1985).
'J. B. Hopkins, D. E. Powers, and R. E. Smalley, J. Phys. Chern. 85, 3739
(1985); R. E. Smalley (private communication 1984).
4M. T. Vala, I. H. Hiller, S. A. Rice, and J. Jortner, J. Chern. Phys. 44, 23
(1966).
sK. O. Biimsen, H. L. Selzle, and E. W. Schlag, J. Phys. Chern. 92, 5482
(1988).
6D. E. Williams, Acta Crystallogr. Sect. A 36,715 (1980).
J. Chern. Phys., Vol. 90, No.3, 1 February 1989
Downloaded 23 Oct 2011 to 140.113.224.194. Redistribution subject to AIP license or copyright; see http://jcp.aip.org/about/rights_and_permissions
1306
BOrnsen et al.: Benzene trimers
7B. W. Van de Waal, Chern. Phys. Lett. 123, 69 (1986).
BK. H. Fung, W. E. Henke, T. R. Hays, H. L. Selzle, and E. W. Schlag, J.
Phys. Chern. 85, 3739 (1981).
9J. R. Grover, E. A. Walters, and E. T. Hui, J. Phys. Chern. 91, 3233
(1986); E. Riihl, P. G. F. Bisling, B. Brutschy,and H. Baurngiirtel, Chern.
Phys. Lett. 126, 232 ( 1986); S. H. Lin, K. O. Bomsen, H. L. Selzle, and E.
W. Schlag, J. Phys. Chern. 92,1469 (1988).
lOp. R. R. Langridge-Srnith,D. V. Brumbaugh, C. A. Haynam, and D. H.
Levy, J. Phys. Chern. 85, 3742 (1985).
J. Chern. Phys., Vol. 90, No.3, 1 February 1989
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