On the formation of a van der Waals complex between ethene and carbon dioxide in liquid argon. An FTIR and ab initio study

Article abstract of DOI:10.1016/j.molstruc.2004.03.031

The mid-infrared spectra of mixtures of ethene and carbon dioxide dissolved in liquid argon have been investigated between 88 and 123 K. At higher concentrations of ethene, evidence was found for the formation of a 1:1 complex in which the carbon atom of the CO₂ moiety binds to the C=C double bond. By recording spectra at different temperatures, the complexation enthalpy for the 1:1 complex was determined to be -4.9(1)kJmol^-1. Using Free Energy Perturbation Monte Carlo simulations to correct for solvent influences and statistical thermodynamics to account for zero-point vibrational and thermal influences, the complexation enthalpy was transformed into a vapor phase complexation energy. The resulting value, -6.8(8)kJmol^-1, is compared with theoretical data obtained from ab initio calculations in which the equilibrium geometry of the complex is calculated using BSSE-corrected gradient techniques.

Full text of DOI:10.1016/j.molstruc.2004.03.031

Journal of Molecular Structure 706 (2004) 107–113
www.elsevier.com/locate/molstruc
On the formation of a van der Waals complex between ethene
and carbon dioxide in liquid argon. An FTIR and ab initio study
*
Wouter A. Herrebout, Sofie N. Delanoye, Benjamin J. van der Veken
Department of Chemistry, Universiteit Antwerpen, Groenenborgerlaan 171, B-2020 Antwerpen, Belgium
Received 26 January 2004; revised 26 January 2004; accepted 24 March 2004
Available online 23 April 2004
Abstract
The mid-infrared spectra of mixtures of ethene and carbon dioxide dissolved in liquid argon have been investigated between 88 and 123 K.
At higher concentrations of ethene, evidence was found for the formation of a 1:1 complex in which the carbon atom of the CO2 moiety binds
to the CyC double bond. By recording spectra at different temperatures, the complexation enthalpy for the 1:1 complex was determined to be
24.9(1) kJ mol21. Using Free Energy Perturbation Monte Carlo simulations to correct for solvent influences and statistical thermodynamics
to account for zero-point vibrational and thermal influences, the complexation enthalpy was transformed into a vapor phase complexation
energy. The resulting value, 26.8(8) kJ mol21, is compared with theoretical data obtained from ab initio calculations in which the
equilibrium geometry of the complex is calculated using BSSE-corrected gradient techniques.
q 2004 Published by Elsevier B.V.
Keywords: Cryospectroscopy; Van der Waals complexes; Ethene; Carbon dioxide
1. Introduction
allowed the barrier towards internal rotation around the axis
connecting the centers of mass of the two monomers to be
determined at the very low value of 6.6 cm21. In the same
study ab initio results at the MP2/6-31G þ (2p,2d) level are
reported. The full structure optimization of the complex
resulted in a stacked structure, however with an angle of
approximately 40 degrees between the axis of the CO2
molecule and the CyC bond. The internal rotation barrier
was calculated at 15 cm21. Fragmentary ab initio results
have also been reported by Jamroz et al. [11], at the
relatively low HF/3-21G* level, and, more recently by
Fedotov et al. [39], who discuss the nature of the interaction
between the monomers, but who do not report on the
optimized structure of the complex.
Although carbon dioxide has no permanent dipole
moment, there is considerable charge separation in the
CyO bonds. This leads to a significant quadrupole moment,
and results in a positive partial charge on the carbon atom
and in negative ones on the oxygen atoms. This character-
istic allows CO2 to act both as a Lewis acid [1–16] and as a
Lewis base [17–28], a property which is recognized
[29–37] as being important in the solvation of molecules
in liquid and supercritical CO2.
In this study we focus on the Lewis acid properties of
CO2. Although there is extensive literature on interactions
of CO2 with Lewis bases, very little is known about its
interaction with p-type electron donors, for which ethene,
C2H4, is the obvious model compound. The structure of the
van der Waals complex between CO2 and ethene has been
determined from a molecular beam rotationally resolved
infrared study to be of the stacked parallel type, in which the
CO2 molecule sits above the ethene plane, with the CO2 axis
parallel to the CyC bond [38]. Detailed analysis of the fine
structure using a two dimensional internal rotation model
It is clear from the above that no experimental data
regarding the stability of the ethene/CO2 complex are
known, and we aim at filling this gap by studying the
formation of the complex in liquid argon, using infrared
spectroscopy. We will show in the following paragraphs that
from the spectra the standard complexation enthalpy for the
reaction in solution has been obtained, which was
subsequently converted into a vapor phase complexation
energy by correcting for solvation and for thermal effects. In
addition, ab initio calculations, to support the vibrational
*
Corresponding author. Tel.: þ32-3-2653372; fax: þ32-3-2653220.
E-mail address: benjamin.vanderveken@ua.ac.be (B.J. van der Veken).
0022-2860/$ - see front matter q 2004 Published by Elsevier B.V.
doi:10.1016/j.molstruc.2004.03.031

108
W.A. Herrebout et al. / Journal of Molecular Structure 706 (2004) 107–113
analysis and to evaluate the experimental complexation
energy, are discussed.
the Gibbs energies of solvation were calculated at
10 different temperatures between 93 and 138 K, at a
pressure of 28.2 bar, i.e. the vapor pressure of LAr at 138 K.
2. Experimental
3. Results and discussion
C2H4 was obtained from Aldrich with a stated purity of
99.9 þ % and was used without further purification. 12CO2
and 13CO2 were prepared by mixing a small amount of the
corresponding sodium carbonate with sulfuric acid. The
gases were purified using a low-temperature, low-pressure
fractionation column. The argon used was supplied by L’
Air Liquide and had a stated purity of 99.9999%.
3.1. Ab initio calculations
Our calculations using the BSSE-corrected PES result in
a packed parallel structure for the complex [38], in
agreement with the experimental one, and in agreement
with the prediction based on the quadrupole moments of
CO2 and ethene, which are of opposite signs [38]. This
result contrasts with the ab initio structure derived by
Bemish et al. [38], where an angle of some 408 between the
CO2 axis and the CyC bond resulted. As in both
calculations rather similar basis sets were used, this
difference must be due to the use of the BSSE-corrected
PES in our calculations. In view of the very low barrier
towards internal rotation, 31 cm21 in the present calcu-
lations, the difference most likely is not as dramatic as the
strongly different relative orientations of the monomers
suggest. Fig. 1 shows the structure, together with the more
relevant calculated structural parameters. The intermolecu-
lar distance, defined as the distance between the centers of
The infrared spectra were recorded using a Bruker IFS
66 v Fourier transform spectrometer, equipped with a Globar
source, a Ge/KBr beamsplitter and a LN2-cooled broad band
MCT detector. All interferograms were averaged over 250
scans, Blackman–Harris 3-Term apodized and Fourier
transformed with a zero filling factor of 4, to yield spectra
at a resolution of 0.5 cm21. The experimental setup consists
of a pressure manifold needed for filling and evacuating the
cell and for monitoring the amount of gas used in a
particular experiment, and the actual cell. The cell has a path
length of 10 mm and is equipped with wedged Si windows.
The geometry of the 1:1 complex and its harmonic
vibrational frequencies were calculated using the CP-
corrected gradient techniques originally developed by
Simon et al. [40], and included in GAUSSIAN 98-Rev. A11
[41]. Unless stated otherwise, all calculations were
performed at the MP2 ¼ FULL/6-311þþG(2d,2p) level.
Solvation Gibbs energies of monomers and complexes
were obtained from Monte Carlo perturbation calculations,
using a modified version of BOSS 4.1 [42]. All simulations
were run in the NPT ensemble, using periodic boundary
conditions. The system consisted of one solute molecule
surrounded by 256 solvent atoms. Preferential Metropolis
sampling was used as described before [43,44]. An attempt
to move the solute molecule was made on every 50th
configuration and a change in volume was tried on every
600th configuration. The ranges for the attempted moves
were the same in each calculation, and provided a ,40%
acceptance probability for new configurations. The quantity
calculated is the Gibbs energy DsolG for the process of
introducing one solute into the box with solvent atoms via a
coupling parameter l: The path for l ¼ 0 (pure argon) to
l ¼ 1 (a solution with one solute molecule) was completed
in 40 equidistant steps. Each step consisted of an
equilibrium phase for 20.0 £ 106 configurations, followed
by a production phase of 50.0 £ 106 configurations. The
Gibbs energy changes between the perturbed and reference
systems were always small enough ð< kTÞ to guarantee
reliable results by the statistical pertubation theory.
˚
mass of the two monomers, equals 3.38 A, in good
˚
agreement with the experimental value of 3.43 A [38].
The complexation energy calculated at this level equals
25.81 kJ mol21, which puts the compound in the realm of
The enthalpy of solvation DsolH and the entropy of
solvation DsolS in LAr were extracted from the Gibbs
energies of solvation DsolG; using a method similar to that
described by Levy et al. [45]. To this end, for each species,
Fig. 1. MP2/6-311þþG(2d,2p) equilibrium geometry for the complex of
C2H4 with CO2. The structural parameters obtained for the monomers are
given between brackets.

W.A. Herrebout et al. / Journal of Molecular Structure 706 (2004) 107–113
109
weak complexes. In line with this, comparison of the
structural data of the complex with those of the monomers,
given in brackets in Fig. 1, shows that the complexation
hardly influences the internal structures of the monomers.
It is clear from the above that the complex should
preferably be discussed in terms of the symmetry group of
the freely internally rotating structure. This is not a
straightforward exercise, the more so because the energetic
feasibility of other internal rotations, like the one of the
ethene moiety around the CyC axis, is unknown. Therefore,
and in view of the very limited number of complex modes
observed (vide infra), we have chosen to take the low road
and not to touch upon symmetry aspects of the complex.
The very weak coupling between vibrational modes
localized in different moieties of the complex allows, with
the exception of the van der Waals modes, an unambiguous
correlation of monomer and complex modes. Therefore,
vibrational modes of the complex that are localized in one of
the monomers will be identified with the Herzberg number
and symmetry of the corresponding monomer mode.
compared with the shift of 0.843 cm21 derived from the high
resolution infrared study [38]. A more significant influence is
calculated for the bending mode of the CO2 moiety: upon
complexation, the degeneracy of this mode is lifted, one
component giving rise to a small blue shift of 0.5 cm21, the
other red-shifting by 8.6 cm21. At this stage the possibility
must be considered that the predicted splitting of the bending
mode is an artefact of the semi-rigid structure assumed in the
ab initio force field calculations. Simple arguments,
however, show that this is not the case. Thus, in view of the
very low internal rotation barrier, the bending mode localized
in the plane perpendicular to the internal rotation axis will be
hardly influenced by the presence of the ethene molecule,
while the opposite is true for the other bending mode, in
which the atoms of the CO2 molecule move back and forth
the ethene molecule. Hence, also in the freely internally
rotating complex the two CO2 bending modes must have
different frequencies. Refering to the symmetry plane of the
global minimum structure of the complex, the former can be
described as the out-of-plane bending, and the latter as the in-
plane bending. A similar splitting of the bending mode has
been observed for other complexes of CO2 [14–16], and also
for solutions of CO2 in certain strong Lewis bases such as
tertiary amines and dimethyl sulfoxide [4,11]. For the
complex of CO2 with dimethyl ether [14], the corresponding
shifts are 4.9 and 212.1 cm21, and the ab initio complexa-
The harmonic vibrational frequencies and infrared
intensities calculated for the monomers and for the complex
have been collected in Table 1. In agreement with the
weakness of the complex, only minor shifts of the monomer
frequencies upon complexation are predicted. For example,
the predicted shift for nC9 H equals 0.1 cm21, which must be
2
4
tion energy, at the same level, equals 213.06 kJ mol21
,
which makes clear that the complexation shifts of these
modes are related to the strength of the complex.
Table 1
MP2/6-311þþG(2d,2p) vibrational frequencies (cm21) and infrared
intensities (km mol21) for C2H4·CO2, C2H4 and CO2
3.2. Vibrational spectra
Monomer
Complex
Due to the limited solubility of CO2 at lower tempera-
tures, measurable fractions of complexes can be obtained
only by using a large excess of C2H4. Therefore, in all
experiments, the mole fraction of C2H4 was chosen to be
much higher than that of CO2, typical values being in the
order of 1022 for C2H4 and 1024 for CO2.
n
Int.
n
Int.
Dn
C2H4 submolecule
Ag
n1
3198.4
1681.2
1384.5
1070.8
3270.2
1245.7
974.3
0.0
3197.9
1678.1
1383.4
1071.8
3270.3
1244.9
977.2
0.0
20.5
23.1
21.1
1.0
Ag
n2
0.0
0.0
0.0
0.0
Ag
n3
Au
n4
0.0
0.0
In Fig. 2, the nC3 O region recorded for a mixed solution
2
B1g
B1g
B1u
B2g
B2u
B2u
B3u
B3u
n5
0.0
0.0
0.1
with mole fractions xCO ¼ 2:0 £ 1024 and xC H ¼ 1:8 £
n6
0.0
0.0
20.8
2.9
2
2
4
1022; studied at temperatures between 88 and 98 K, and that
of a solution containing only 12CO2 are compared. Apart
from the 664.3 cm21 monomer band, in the spectra of the
mixed solution a new band appears at 659.8 cm21. This
band is not observed in the spectra containing only 12CO2 or
C2H4, and we assign it to the in-plane CO2 bending of 1:1
complex C2H4.12CO2. A similar band is observed for
solutions containing C2H4 and 13CO2: on the low frequency
side of the 645.5 cm21 monomer band, the new band is
n7
99.0
0.0
105.7
0.2
n8
913.0
910.0
23.0
0.1
n9
3296.8
834.8
14.8
0.1
3296.9
833.7
11.4
0.1
n10
n11
n12
21.1
20.1
20.2
3179.6
1493.1
10.4
8.8
3179.5
1492.9
7.0
8.3
12CO2 submolecule
su
sg
pu
pu
n1
2403.0
1320.5
665.6
286.5
0.0
2403.7
1321.6
666.1
483.3
0.0
0.7
1.1
n2
n3a
n3b
21.9
21.9
19.0
33.0
0.5
being observed at 640.9 cm21
.
665.6
657.0
28.6
It must be stressed that even at the lowest temperatures
studied, no evidence was found for the occurence of a
van der Waals modes
74.1
71.4
63.7
55.0
7.2
0.0
0.3
0.0
0.0
0.0
complex band on the high frequency side of the n3CO
2
monomer band. It must, therefore, be concluded that the out-
of-plane bending vibration of the complex occurs acciden-
tally degenerate with the monomer mode.

110
W.A. Herrebout et al. / Journal of Molecular Structure 706 (2004) 107–113
recorded in this study corroborate this, as no induced bands
could be detected.
3.3. Relative stability
The stability of the complex in LAr was established from
temperature studies in which spectra were recorded at
temperatures between 88 and 128 K. From these, the
complexation enthalpy was determined using the Van’t
Hoff isochore. In this method, the complexation enthalpy
D
LArH0 is determined form the slope of the plot obtained
by plotting the logarithm of the equilibrium constant,
expressed in terms of band areas I of infrared bands assigned
to the different species involved, against the inverse
temperature T :
!
Icomplex
D
LArH0
ln
¼ 2
þ cst
ð1Þ
IC H £ ICO
T
2
4
2
Because all observed C2H4 transitions overlap with the
corresponding modes in the complex, the determination of
the monomer band area IC H is not straightforward. More-
2
4
over, the 664.3 cm21 band is assigned to the bending
vibration in monomer CO2 as well as to the out-of-plane
bending mode in the complex, and its band area cannot be
Fig. 2. The CO2 bending region for a solution in liquid argon contaning both
C2H4 and CO2. From top to bottom, the temperature of the solution
decreases, from 97 to 88 K. The bottom trace is the spectrum obtained for a
solution containing only CO2. The tick mark interval on the vertical axis
equals 0.5 absorbance units.
used directly as a measure of the monomer intensity ICO
:
2
In was observed above that due to experimental
circumstances, the large majority of the C2H4 molecules
were not involved in complexe. Thus, the intensity
contributions of the complex to bands due to transitions
Close scrutiny of the regions of the spectra in which
transitions due to ethene occur has yielded no bands due to
the complex. This is explained by the large excess of ethene
used in the experiments. It is clear from Fig. 2 that only a
small fraction of the CO2 used was converted into complex.
Thus, with an excess by two orders of magnitude in ethene,
the fraction of ethene converted into complex is very small.
Compounded by the fact that complexation shifts for these
modes likely are very small, as suggested by the ab initio
calculations, this makes that complex bands due to
transitions localized in the ethene moiety of the complex
are completely overshadowed by the corresponding mono-
mer bands. One way out is to look for complex bands due to
modes that are symmetry-forbidden in the monomers, of
which there are several in the present case. Some of these
modes can acquire small but non-negligible induced
intensities, and have been experimentally observed for
other complexes [14,46]. In most of those cases, the
intensity for a mode localized in the one moiety was
induced by the dipole moment of the other moiety. In the
present complex, however, both moieties lack a permanent
dipole moment, so that infrared intensity must be quadru-
pole-induced. Combined with the weakness of the complex,
and the ensuing larger distance between the monomers in
the complex, this suggests that the induced modes will be
very weak. This anticipation is supported by the ab initio
localized in the ethene moiety can be neglected without
problem. Therefore, the areas of the nC3 H þ n
C2H4
10
2
4
and the
combination bands at 2167.3 and
C2H4
10
nC6 H þ n
2
4
2042.8 cm21, respectively, determined by numerical inte-
gration, were used as IC H
:
4
2
In order to be used as a measure for ICO ; the area of the
2
664.3 cm21 band must be corrected for the presence of the
out-of-plane bending mode of the complex. This was
accomplished by relating the band areas of the in- and
out-of-plane modes via Beer’s law as:
1oop
Ioop
¼
Iip
ð2Þ
1ip
in which 1oop and 1ip are the infrared intensities of the out-
of-plane and the in-plane mode, respectively. Then, ICO can
be expressed as:
2
1oop
ICO ¼ I664:3 2 Ioop ¼ I664:3
2
I658:9
ð3Þ
2
1ip
in which I664:3 and I658:9 are the band areas of the
experimental 664.3 and 658.9 cm21 bands, respectively.
Unfortunately, no experimental value for the ratio 1oop=1ip is
available, because the out-of-plane band was not observed
in a separable manner.
data in Table 1, which show that a very small induced
only. Inspection of the spectra
Insight into the effect of this correction was gained by
calculating DLArH0 as function of the value of 1oop=1ip:
C2H4
10
intensity is predicted for n

W.A. Herrebout et al. / Journal of Molecular Structure 706 (2004) 107–113
111
For this, ICO was determined at each temperature via
Eq. (3), with I664:3 and I658:9 determined from least squares
2
band fitting, and with I658:9 taken as Icomplex: The resulting
complexation enthalpies are shown in Fig. 3. It can be
seen that DLArH0 changes from 24.2(2) kJ mol21 for
1
oop=1ip ¼ 0:0 to 26.0(2)kJ mol21 for 1oop=1ip ¼ 1:5: It is
clear that the influence of the out-of-plane bending
mode is too big to allow the determination of a reliable
enthalpy without information on the intensity ratio
1
oop=1ip: Here, the ab initio calculations come to the
rescue, and we have used the predicted value for 1oop=1ip;
calculated from the data in Table 1. This choice can be
justified as follows.
For the complex of CO2 with dimethyl ether [14], the
components of the bending doublet are observed well
separated from the monomer mode and can be reliably
integrated using least squares band fitting. This was
preformed for a series of 20 spectra recorded at various
temperatures and concentrations, and from the linear
regression of Ioop against Iip; the ratio 1oop=1ip was found
to be 0.48(2). Ab intio calculations on that complex [14]
lead to infrared intensities of 22.6 and 49.7 km mol21 for
the oop and ip bending modes, respectively. Their ratio,
0.46, is in excellent agreement with experiment. For weaker
complexes the ratio must approach its value in the
monomer, equal to 1.0. In line with this, for the present
complex, the data in Table 1 result in 1oop=1ip ¼ 0:57: Thus,
there is no reason why the ab intio ratio for the ethene
complex should be less good than that for the dimethyl ether
complex. Consequently, it may be assumed that a reliable
value for the complexation enthalpy can be derived using
the ab initio ratio.
Fig. 4. Van ’t Hoff plots for the complex of C2H4 with CO2 observed in
liquid argon. The monomer intensity ICO required for the analysis was
2
obtained by assuming an intensity ratio 1oop=1ip equal to 0.574. The plots
were obtained using temperature studies of two different solutions, and
C2H4
10
C2H4
10
using the band areas of the nC3 H þn
(top) and the nC6 H þn
2
4
2
4
(bottom) combination bands as a measure of the C2H4 monomer intensity.
The vapor phase complexation enthalpy, DvapH0; can be
obtained by correcting the solution value for solvation
effects. This has been accomplished by Monte Carlo Free
Energy Perturbation calculations, at different temperatures,
using a procedure similar to that used before [14]. In short,
the Monte Carlo calculations yield the solvation Gibbs
energies DsolG; as function of the temperature. From these,
the solvation entropies are calculated as DsolS ¼ 2›ðDsolGÞ=
›T; while the solvation enthalpies are obtained as DsolH ¼
DsolG þ TDsolS: The resulting enthalpies DsolH for a
solution in LAr are 213.1(2) kJ mol21 for C2H4,
216.8(3) kJ mol21 for CO2 and 229.8(2) kJ mol21 for
C2H4·CO2. Combining these values with the experimental
In Fig. 4, Van ‘t Hoff plots obtained by using the ab initio
ratio 1oop=1ip ¼ 0:57 are shown for two different tempera-
ture studies. The value for the complexation enthalpy,
derived from linear regressions, averaged over the two
experiments, and corrected for density variations of the
D
LArH0 yields a vapor phase complexation enthalpy DvapH0
equal to 25.1(4) kJ mol21. Comparison with the value in
LAr shows that there is hardly a solvation influence on the
complexation enthalpy. This is surprising, because for
sterical reasons the monomers must give up an important
fraction of their solvation in order to form a complex. It
follows that the interaction of the complex with solvent
atoms from the solvation sphere must be stronger than in the
monomers. A possible explanation for this is offered by
induced dipole moment in the complex. For the global
minimum, the ab initio calculations predict a dipole moment
of 0.17 D, while for the structure in which the CO2 axis is at
right angle to the CyC bond the calculated value is
0.16 D. In both cases the dipole moment is oriented along
the axis connecting the monomer centers of mass, and the
similarity of the two values suggest that also for free internal
solvent [47,48], is 24.9(1) kJ mol21
.
Table 2
BSSE-corrected complexation energies for C2H4·CO2
MP2 ¼ FULL/6-311þþG(2d,2p)
MP2 ¼ FULL/aug-cc-PVDZ
MP2 ¼ FULL/aug-cc-PVTZ
MP2 ¼ FULL/aug-cc-PVQZ
175 bf
151 bf
322 bf
584 bf
2 5.81 kJ mol21
26.54 kJ mol21
27.38 kJ mol21
27.72 kJ mol21
Fig. 3. Complexation enthalpies for the complex of C2H4 with CO2 as
function of the intensity ratio 1oop=1ip:

112
W.A. Herrebout et al. / Journal of Molecular Structure 706 (2004) 107–113
The influence of a further increase of the basis set was
obtained by extrapolation of the plot of the complexation
energies for the aug-cc-PVXZ (X ¼ D, T and Q) levels as a
function of 1=n; in which n is the number of basis functions.
The plot and the linear regression line are shown in Fig. 5.
The abscissa of the linear regression line,
28.1(2) kJ mol21, gives the energy for an infinite basis
set and can be considered as the basis set limit. This value is
in acceptable agreement with the experimental value of of
26.8(8) kJ mol21
.
Acknowledgements
Fig. 5. Extrapolation of the calculated complexation energies obtained for
the complex of C2H4 with CO2. The complexation energies obtained by
using the different basis sets, and the number of basis functions in each
calculations were taken from Table 2.
S.N.D. thanks the FWO-Vlaanderen for an appointment
as a research assistant. Gratitude is expressed to the FWO-
Vlaanderen for their assistance toward the purchase of
spectroscopic equipment used in this study. The authors
thank the Flemish Community for financial support through
the Special Research Fund (BOF).
rotation states of the complex a similar dipole moment will
be present. This relatively small but not insignificant dipole
moment, and the absence of a permanent dipole moment in
the monomers, will certainly contribute to the increased
solute/solvent interaction for the complex. Then, the Monte
carlo calculations show that this very nearly compensates
the sterical loss of solvation.
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