Fourier transform microwave spectra of the very weakly bound He-CO2 dimer

Article abstract of DOI:10.1016/S0022-2860(01)00853-5

Spectra of pure rotational transitions of the very weakly bound He-CO₂ van der Waals complex were investigated using a pulsed molecular beam Fourier Transform microwave spectrometer. The complex exhibits very large amplitude internal vibrational motions and the rotational transitions were, as a consequence, difficult to locate and to assign. Eight isotopomers, namely He-CO₂, He-¹³CO₂, He-OC¹⁸O, He-O¹³C¹⁸O, He-¹⁸OC¹⁸O, He-¹⁸O¹³C¹⁸O, He-OC¹⁷O, and He-O¹³C¹⁷O, were studied in order to establish the assignments. The hyperfine structures due to the quadrupolar ¹⁷O nucleus were resolved and analyzed in the two ¹⁷O containing isotopomers. The observed nuclear quadrupole hyperfine structures not only provide further confirmation for the assignment but also give new information about the angular anisotropy of the He-CO₂ interaction potential.

Full text of DOI:10.1016/S0022-2860(01)00853-5

Journal of Molecular Structure 599 ;2001) 211±217
www.elsevier.com/locate/molstruc
Fourier transform microwave spectra of the very weakly bound
He±CO2 dimerq
*
È
Yunjie Xu, Wolfgang Jager
Department of Chemistry, University of Alberta, Edmonton, Alberta, Canada T6G 2G2
Received 24 July 2000; accepted 4 October 2000
Abstract
Spectra of pure rotational transitions of the very weakly bound He±CO2 van der Waals complex were investigated using a
pulsed molecular beam Fourier Transform microwave spectrometer. The complex exhibits very large amplitude internal
vibrational motions and the rotational transitions were, as a consequence, dif®cult to locate and to assign. Eight isotopomers,
namely He±CO2, He±13CO2, He±OC18O, He±O13C18O, He±18OC18O, He±18O13C18O, He±OC17O, and He±O13C17O, were
studied in order to establish the assignments. The hyper®ne structures due to the quadrupolar 17O nucleus were resolved and
analyzed in the two 17O containing isotopomers. The observed nuclear quadrupole hyper®ne structures not only provide further
con®rmation for the assignment but also give new information about the angular anisotropy of the He±CO2 interaction
potential. q 2001 Elsevier Science B.V. All rights reserved.
Keywords: He±CO2; Rotational spectrum; van der Waals complex; Molecular beam
1. Introduction
systems for high level ab initio calculations. A quan-
titative knowledge about the interaction between
helium atoms and small molecules is also of signi®-
cant current interest in the context of the exciting high
resolution spectroscopic work on dopants embedded
in liquid He-clusters [1±4]. In particular, a quantita-
tive understanding of the observed increase of
moment of inertia of the dopant molecule inside the
He-cluster will require the availability of accurate He-
molecule interaction potentials. Spectroscopic inves-
tigations of Hen-molecule van der Waals complexes
;n ˆ 1 to a few) can therefore contribute greatly to
this area.
He-molecule van der Waals dimers are, in general,
characterized by very shallow potential wells
;,30 cm21) and by zero point energy levels that can
be located at more than half of the height of the well.
These systems exhibit therefore very complex internal
dynamics and, as a result, complicated spectroscopic
features, making them of interest to both theorists and
experimentalists. The small number of electrons in
He-molecule systems, relative to the heavier rare
gases containing counter parts, makes them attractive
Experimentally, the number of high resolution
spectroscopic studies of He-molecule systems is
quite limited. This is partially because of the consid-
erable dif®culties associated with the synthesis and
stabilization of the complexes even in a molecular
beam environment, and partially because of the
q
This paper is dedicated to Professor Alfred Bauder in apprecia-
tion of his signi®cant contributions to the ®eld of microwave
spectroscopy.
* Corresponding author. Tel.: 11-780-492-5020; fax: 11-780-
492-8231.
È
E-mail address: wolfgang.jaeger@ualberta.ca ;W. Jager).
0022-2860/01/$ - see front matter q 2001 Elsevier Science B.V. All rights reserved.
PII: S0022-2860;01)00853-5

È
Y. Xu, W. Jager / Journal of Molecular Structure 599 /2001) 211±217
212
complicated spectroscopic patterns which are a
consequence of the shallow potential wells [5,6].
For He±CO2, the only previous high resolution spec-
troscopic study was reported by Weida et al. [7] who
observed the infrared spectra of the complex near the
CO2 asymmetric stretching mode. They found that the
complex is a T-shaped asymmetric rotor with very
large amplitude vibrational motions, as evidenced
the microwave excitation pulses because of the very
small transition dipole moment anticipated. The mole-
cular complexes were generated in a pulsed molecular
expansion through a general valve nozzle ;series 9,
ori®ce B ˆ 0:4 mm) that is mounted near the center
of one of the microwave cavity mirrors [12] such that
the molecular expansion travels parallel to the cavity
axis. Some modi®cations were made to the nozzle cap
to improve the sensitivity of the spectrometer for
Helium containing complexes. The details are
described in the isotopic study of the He±OCS
complex [13]. The full line width at half height of
fully resolved components was ,22 kHz. This is
noticeably larger than the line width of 7 kHz
obtained with Ne as carrier gas [11], due to faster
He expansion and the resulting shorter time of obser-
vation. The accuracy of the line positions was esti-
mated to be better than 2 kHz for single unsplit lines.
The gas mixture used for the measurements
consisted of 0.1% CO2 in He carrier gas at a total
pressure of ,10 atm. Enriched 13CO2 ;99% 13C, 5%
18O, Cambridge Isotope Laboratories) was used for
the measurements of the He±13CO2 and
He±18O13CO isotopomers. Enriched 17OCO, 18OCO,
and 18OC18O were synthesized by introducing normal
CO2 into a glass container with enriched H217O ;30%
17O, Cambridge Isotope Laboratories) and H218O
;98% 18O, Cambridge Isotope Laboratories), respec-
tively. Similarly, enriched 17O13CO, 18O13CO, and
18O13C18O were synthesized by introducing the
enriched 13CO2 ;99% 13C, 5% 18O, Cambridge Isotope
Laboratories) into a glass bulb containing enriched
H217O ;30% 17O, Cambridge Isotope Laboratories)
and H218O ;98% 18O, Cambridge Isotope Labora-
tories), respectively. The mixtures were left standing
for at least a day at room temperature. The synthe-
sized CO2 isotopomer was introduced into the spectro-
meter sample system by slowly warming the CO2/H2O
mixture from liquid nitrogen temperature. This was
done to minimize the contamination of the sample
system with H2O.
Ê 2
by the large positive inertial defect of 8.54 amu A
for the ground state. Furthermore, the ®rst intermole-
cular bending level, at about 9 cm21 above the ground
state, shows spectral patterns that deviate sharply from
those expected from an asymmetric rotor model [7].
Theoretically, a number of empirical potentials exist
that are based mostly on experiments probing the
repulsive parts of the interaction potential energy
surfaces1. More recently, there have been several
reports of ab initio investigations of this dimer [8,9].
It is interesting to note that the barrier connecting the T-
shaped and the linear minima on the potential energy
surface was predicted to be larger in He±CO2 than that
in Ne±CO2 in the latest ab initio calculation [9].
In this paper, we report the observation of rotational
spectra of He±CO2 with a pulsed molecular beam
cavity Fourier Transform microwave spectrometer.
The initial frequency prediction was made using the
spectroscopic constants from the earlier infrared paper
[7]. Seven new isotopomers, namely He±13CO2,
He±18OCO,
He±18O13CO,
He±18OC18O,
He±18O13C18O, He±17OCO, and He±17O13CO were
also studied. The nuclear quadrupole hyper®ne struc-
tures associated with the quadrupolar 17O nucleus
;spin I ˆ 5=2) in He±OC17O and He±O13C17O were
resolved and analyzed to provide valuable new infor-
mation about the angular wave functions of the
complex and thus about the anisotropy of the He±
CO2 interaction potential.
2. Experimental
The spectra were measured with a pulsed molecular
beam Fourier Transform microwave spectrometer of
the Balle±Flygare type [10], which has been
described in detail previously [11]. A microwave
power ampli®er was used to increase the power of
3. Spectral search, assignment, and discussion
The JK K ˆ 101 2 000 rotational transition for the
a
c
normal isotopomer was predicted from the spectro-
scopic constants of the infrared work [7] to be at
1
For a list of references, see Ref. [7].

È
Y. Xu, W. Jager / Journal of Molecular Structure 599 /2001) 211±217
213
17671 MHz. An extensive search was carried out in
the region and two transitions were located. Both of
these have fairly small transition dipole moments,
about a quarter of that of the Ne±CO2 complex
;0.0244;13) Debye) [14], estimated by comparing
the p=2 microwave excitation pulse lengths. The rela-
tive intensities of these two transitions and their rela-
tive frequencies suggested that one might be a
candidate for the normal isotopomer and the other
one for the 13C isotopomer in its natural abundance.
However, the frequency of the candidate for the
normal isotopomer was about 70 MHz higher than
predicted from the infrared constants. Unfortunately,
the next higher J transitions are located in the 35 GHz
frequency region, outside the operating range of our
Fourier Transform microwave spectrometer. It was
therefore critical to con®rm the assignment with addi-
tional information, such as isotopic data and nuclear
quadrupole hyper®ne structures.
lower than expected, by comparing the intensity of
He±O13CO in natural abundance ;,1.1%) and that
of He±O13C18O ;,5% in the enriched sample).
At this point, the samples of OC18O, OC17O,
O13C18O, and O13C17O were prepared using enriched
H218O ;99%) and H217O ;35%) with normal CO2 and
13CO2 ;99%), respectively, to ensure high observable
intensity for all the isotopomers under consideration.
The intensity of the candidate transition for He±
O13C18O increased dramatically upon using the
enriched sample prepared with H218O and 13CO2. An
intensity increase was also observed when using the
sample prepared with H217O and 13CO2. This ®nding
was a surprise initially and caused some concern
about the assignment to He±O13C18O. The assignment
could only be correct if the H217O sample contained
substantial amounts of H218O. This was veri®ed by
carrying out parallel experiments on the known tran-
sitions of the various isotopomers of Ne±CO2 [15].
The tests veri®ed a signi®cant percentage of H218O in
the H217O sample and support therefore the original
assignment. A similar search and con®rmation proce-
dure was carried out for the rotational transition of
He±OC18O. It was located 18.5 MHz above the He±
O13C18O line, consistent with the measured frequency
difference of 22.6 MHz in the He±OCO/He±O13CO
pair.
The searches for transitions of the He±OC17O and
the He±O13C17O isotopomers were carried with the
hopes to resolve their 17O nuclear quadrupole hyper-
®ne structures. This would not only further secure the
assignment but would also provide valuable new
information about the angular isotropy of the He±
CO2 interaction potential energy surface. In the
studies of various isotopomers of Ar±CO2
[16,17,18] and Ne±CO2, [14,19] it was found that
the transition frequencies of the 17O containing isoto-
pomers could be interpolated from the 16O and 18O
data with an accuracy of better than 100 kHz. This
interpolation procedure, however, appeared not to
work well for the He±CO2 system. An initial scan
of the region where the J ˆ 1±0 transitions of the
He±OC17O and He±O13C17O isotopomers were
expected, was unsuccessful. A wider frequency scan
of about 400 MHz with the He±OC17O sample,
produced one set of lines, resembling nuclear hyper-
®ne pattern of a J ˆ 1±0 transition for a nucleus with
spin 5/2. The corresponding hyper®ne pattern was
We anticipated large uncertainties in the frequency
predictions for other minor isotopomers of He±CO2
when using the usual rigid structure model. The
Ê 2
unusually large inertial defect of 8.54 amu A , deter-
mined in the infrared study [7], emphasizes this
concern. However, since there was no other informa-
tion available for the further isotopic studies, we used
the ground state geometric parameters obtained in the
infrared investigation as the initial starting point. The
rotational constants for the various isotopomers were
then empirically adjusted to reproduce the same iner-
tial defect as in the normal isotopomer. This proce-
dure worked reasonably well with He±O13CO
isotopomer mainly because the 13C substitution
produces very little change in the rotational frequen-
cies since the carbon atom is quite close to the center
of mass of the complex. The assignment of the weaker
observed transition to He±O13CO was thus con®rmed
by the frequency position and, additionally, by a
drastic increase in intensity when enriched 13CO2
was used.
The search for the He±O13C18O isotopomer was
originally done using the enriched 13CO2 sample
;99% 13C, 5% 18O). A frequency region of about
400 MHz was scanned and a transition with the
right magnitude of transition dipole moment was
located at 17619.0744 MHz. This was much higher
in frequency than anticipated. Furthermore, the
observed intensity was found to be considerably

È
Y. Xu, W. Jager / Journal of Molecular Structure 599 /2001) 211±217
214
Fig. 1. 17O nuclear quadrupole hyper®ne patterns of the JK K ˆ 101 2 000 rotational transitions of ;a) He±OC17O and ;b) He±O13C17O. The
a
c
spectra are composite ones, obtained from a number of experiments at different excitation frequencies. For spectrum ;a) four individual
experiments were recorded, each with 100 averaging cycles. Six individual experiments with 500 averaging cycles each were used for spectrum
;b).
also found for the He±O13C17O isotopomer. The
frequency difference between the He±OC17O and
He±O13C17O transitions is about 19.3 MHz, consis-
tent with the differences in the He±OCO/He±O13CO
and He±OC18O/He±O13C18O pairs. These two sets of
hyper®ne components are shown in Fig. 1, together
with the quantum number assignments. No extra split-
ting due to spin 1/2 13C nucleus was detected in case
of He±O13C17O. The consistent frequency spacing in
the three 12C/13C isotopomer pairs and the observed
hyper®ne patterns in the 17O containing isotopomers
provide a solid foundation for the assignment.
To explain some of the unusual observations
mentioned above, such as the poor scaling of the tran-
sition frequencies with reduced mass and some incon-
sistencies in the line intensities, we take a closer look
at some interesting differences between the He±CO2
complex and the heavier rare gas±CO2 complexes.
For example, substitution of one 16O by 18O in He±
CO2 tilts the angle between the C±He intermolecular
axis and the a-axis from 0 to 23.78, while in the case of
Ne±CO2 a tilt of only 1.38 results. Substitution of both
16O atoms with 18O switches the a- and b-axes in the
case of He±CO2, while the orientation of the principal
inertial axis system remains unchanged in Ne±CO2.
This helps to explain the low intensity observed for
the transition of the He±O13C18O complex. Because
of the rotation of the complex in the principal inertial
axis system, the a-dipole moment component in He±
O13C18O is now only a fraction of the total induced
dipole moment between He and CO2. In addition, b-
type transitions are now also allowed with the b-
component of the dipole moment being of a similar
magnitude as the a-component. The larger amplitude
vibrational motions in He±CO2, as compared to Ne±
CO2, lead also to a smaller average dipole moment.
Lastly, the substitution of one 16O with 18O removes
the equivalence of the two oxygen atoms, and both
K ˆ 0 and K ˆ 1 levels exist. The K ˆ 1 levels can
be populated in the beam and effectively reduce the
populations in the K ˆ 0 levels. In case of substitution
of one 16O atom by 17O, the angle tilt is about 7.98 in

È
Y. Xu, W. Jager / Journal of Molecular Structure 599 /2001) 211±217
215
Table 1
Relative observed intensities for some He±CO2 isotopomers
Synthesized
H218O ꢀ98%† 1 normal CO2
H218O ꢀ98%† 1 13CO2 ꢀ99% 13C; 5% 18O†
Frequency/MHz
Rel. Int.
Assignment
Frequency/MHz
Rel. Int.
Assignment
17637.6032
17350.0541
17329.0204
Strong
Weak
a-type, He±OC18O
b-type, He±18OC18O
b-type, He±OC18O
17619.0744
17331.8162
17321.9260
Strong
Medium
Weak
a-type, He±O13C18O
b-type, He±18O13C18O
b-type, He±O13C18O
Medium
He±CO2, as compared to less than 0.68 in the heavier
rare gas±CO2 complexes.
Ne±18O13C18O were predicted, measured, and identi-
®ed straightforwardly, thus establishing that the
enriched sample contains a signi®cant amount of
doubly substituted 18OC18O. It should be noted that
the spectra observed using the He/CO2 sample
mixtures are very sparse. In fact, no other low dipole
moment transitions than those mentioned above were
observed. Careful testing with variation of sample
composition veri®ed that these two lines are due to
He plus the particular CO2 isotopomer. The assign-
ment of the transitions to the singly or doubly 18O
substituted species is based on their relative intensities
;see Table 1). The relative percentage of doubly
substituted 18O isotopomer in the ;H218O 1 13CO2)
sample is expected to be higher than that in the
;H218O 1 CO2) sample. This is because the enriched
13CO2 already contained about 5% 18O. In addition,
the H218O/carbon dioxide ratio was higher in the
H218O/13CO2 sample than in the H218O/CO2 sample.
This explains the opposite intensity pattern observed
for the two b-type transitions in the respective 12C and
13C containing isotopomers ;see Table 1). Based on all
these indicators, there is considerable con®dence in
To support the above argument, we attempted to
locate the b-type transitions for He±OC18O and He±
O13C18O. In a close to 1 GHz scan with 0.15 MHz step
size, only two possible candidates with the right
magnitudes of the dipole moments were detected for
each isotopomer. The sets of two transitions were
tentatively assigned to the JK K ˆ 111±000 b-type
a
c
transition of He±OC18O and the JK K ˆ 111±000 b-
a
c
type transition of He±18OC18O and the corresponding
transitions of the 13C substituted isotopomers, respec-
tively. The assignment was based on the consistent
spacings between the corresponding transitions of
the 12C and 13C isotopomers, sample composition, as
will be explained below, and comparison to the initial
frequency predictions for these two transitions based
on the rigid rotor model.
To con®rm that the additional transitions found
belong to the doubly substituted He±18OC18O and
He±18O13C18O species, the enriched CO2 samples
were again tested with parallel measurements on
Ne±CO2. Transitions of Ne±18OC18O and
Table 2
Measured transition frequencies ;in MHz) of the He±CO2 isotopomers
Isotopomer
Frequency
Isotopomer
Frequency
JKaKc±JKaKc
101±000
101±000
111±000
111±000
101±000
He±16O12C16O
He±16O12C18O
17735.0458
17637.6032
17329.0204
17350.0541
17613.8194a
He±16O13C16O
He±16O13C18O
17712.4646
17619.0744
17321.9260
17331.8162
17594.5391a
He±18O12C18O
He±16O12C17O
He±18O13C18O
He±16O13C17O
F±F
2.5±2.5
3.5±2.5
1.5±2.5
17614.0340
17613.7494
17613.6348
17594.7636
17594.4666
17594.3450
a
The hypothetical unsplit center line frequency.

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Y. Xu, W. Jager / Journal of Molecular Structure 599 /2001) 211±217
216
Table 3
Comparison of the 17O nuclear quadrupole hyper®ne constants ;in MHz) of He±CO2 and other rare gas±CO2 complexes
Complex
He±16O12C17O
He±16O13C17O
Ne±OC17Oa
Ar±OC17Ob
xaa
xbb
1.342;19)
1.406;14)
1.8311;35)
2 4.031;59)
2.200;59)
81.5
1.8587;11)
2 3.7661;11)
1.9074;11)
82.5
±
±
xcc
kualc ;8)
±
±
71.1
72.1
a
Ref. [16].
b
c
Ref. [18].
The average angle between the a-axis and the axis of the CO2 monomer, as described in the text.
the assignment of these two sets of b-type transitions.
The probability that these two sets of transitions, with
the expected 12C/13C isotopic frequency spacing,
belong to some other complex is very low.
He±C bond and the a-axis: ꢀ908 2 kual†: From the
values of kual given in Table 3, angles of 18.9 and
17.98 are obtained for the average angle between the
a-axis and the He±C bond. In case of a complex with
C2v symmetry, this angle represents an average excur-
sion of the rare gas atom from the equilibrium posi-
tion. In the heavier rare gas±CO2 complexes, the
substitution of one 16O atom by 17O tilts the angle
between the He±C van der Waals bond and the a-
inertial axis only by about 0.68. The interpretation of
ꢀ908 2 kual† as an average excursion from the equili-
brium position remains therefore still valid. For He±
CO2, however, the same substitution tilts the angle
between He±C bond and a-axis by about 7.98. There-
fore, there are contributions to kual from two parts,
both the rotation of the complex in the principal axis
system as a result of the substitution, and from aver-
aging over the large amplitude vibrational motions
about the new equilibrium position.
An attempt was made to approximately separate the
contributions to ꢀ908 2 kual† from equilibrium struc-
ture and large amplitude motions. A numerical one
dimensional simulation was done in which values
for P2;cos ua) were calculated and averaged over a
range of angles f around the equilibrium angle
between b-axis and CO2 axis of 7.98. f corresponds
to the instantaneous excursion from equilibrium. The
average was weighted with a cos2 f type function to
approximate the shape of the ground state vibrational
wavefunction and normalized. The extreme values of
f, i.e. the turning points, were then adjusted until the
experimental value for P2;cos ua) was reproduced at
fmax;min ˆ ^458: The average value for P2;cos ua)
was then recalculated with the same fmax,min, but
with an equilibrium angle between b-axis and CO2
axis of 08. The resulting value for kual came to 748,
No attempt was made to locate the b-type transi-
tions of the He±OC17O and He±O13C17O complexes.
These transitions were expected to be too weak to be
observable because of the lower 17O content in the
enriched water sample and the additional hyper®ne
pattern. Furthermore, the rotation of the principal
inertial axis system upon substitution is only about
88 as opposed to 248 for the case of 18O substitution.
This results in a much smaller contribution of the total
induced dipole moment to the b-component.
Table 2 summarizes all the observed microwave
transition frequencies and their assignments,
including the components of the 17O nuclear quadru-
pole hyper®ne structures. The nuclear quadrupole
hyper®ne coupling constants were obtained by
analyzing the observed hyper®ne structure using a
®rst order program. The resulting 17O nuclear quadru-
pole coupling constants are listed in Table 3, together
with the corresponding constants for the heavier rare
gas±CO2 complexes. The values of xaa obtained from
the ®ts are very similar for the He±OC17O and He±
O13C17O isotopomers, further con®rming the assign-
ment.
From the coupling constant xaa and the known
monomer coupling constant x0 ˆ 23:92ꢀ9† MHz;
[20] one can derive an average angle kual using the
expression: xaa ˆ x0kP2ꢀcos ua†l: Here, ua is the angle
between the CO2 axis and the instantaneous a-inertial
axis of the complex, P2 is the second order Legendre
polynomial, and the brackets indicate averaging over
the ground state vibrational motions. From the value
of kual; one can derive the average angle between the

È
Y. Xu, W. Jager / Journal of Molecular Structure 599 /2001) 211±217
217
corresponding to an average excursion from the equi-
librium position of about 168.
and Engineering Research Council of Canada. Y.X.
thanks the Izaak Walton Killam Trust for a postdoc-
toral fellowship.
The average excursion of 168 from the equilibrium
position in He±OC17O is almost twice that determined
for Ne±O13C17O ;8.58), consistent with the expected
lower anisotropy of the He-atom containing system.
This value is also in line with an angle of 158, that can
be determined from the A-rotational constant from the
infrared work and the b0 rotational constant of the CO2
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Acknowledgements
This work was supported by the Natural Sciences