Synthesis, High-Resolution Infrared Spectroscopy, and Vibrational Structure of Cubane, C8H8

Article abstract of DOI:10.1021/acs.jpca.6b04323

Carbon-cage molecules have generated a considerable interest from both experimental and theoretical points of view. We recently performed a high-resolution study of adamantane (C₁₀H₁₆), the smallest hydrocarbon cage belonging to the diamandoid family (Pirali, O.; et al. J. Chem. Phys. 2012, 136, 024310). There exist another family of hydrocarbon cages with additional interesting chemical properties: the so-called platonic hydrocarbons that comprise dodecahedrane (C₂₀H₂₀) and cubane (C₈H₈). Both possess C-C bond angles that deviate from the tetrahedral angle (109.8°) of the sp³ hybridized form of carbon. This generates a considerable strain in the molecule. We report a new wide-range high-resolution study of the infrared spectrum of cubane. The sample was synthesized in Bari upon decarboxylation of 1,4-cubanedicarboxylic acid thanks to the improved synthesis of literature. Several spectra have been recorded at the AILES beamline of the SOLEIL synchrotron facility. They cover the 600-3200 cm^-1 region. Besides the three infrared-active fundamentals (ν₁₀, ν₁₁, and ν₁₂), we could record many combination bands, all of them displaying a well-resolved octahedral rotational structure. We present here a preliminary analysis of some of the recorded bands, performed thanks the SPVIEW and XTDS software, based on the tensorial formalism developed in the Dijon group. A comparison with ab initio calculations, allowing to identify some combination bands, is also presented.

Full text of DOI:10.1021/acs.jpca.6b04323

Article
pubs.acs.org/JPCA
Synthesis, High-Resolution Infrared Spectroscopy, and Vibrational
Structure of Cubane, C8H8
V. Boudon,*,† M. Lamy,† F. Dugue-Boye,† O. Pirali,*,‡ S. Gruet,‡ L. D’Accolti,*,§,∥ C. Fusco,§,∥
́
C. Annese,§,∥ and M. E. Alikhani*,⊥,#
†Laboratoire Interdisciplinaire Carnot de Bourgogne, UMR 6303 CNRS-Universite
Savary, BP 47870, F-21078 Dijon Cedex, France
́
Bourgogne Franche-Comte,
́
9 avenue Alain
ulaires
‡Ligne AILES − Synchrotron SOLEIL, L’Orme des Merisiers, F-91192 Gif-sur-Yvette, France and Institut des Sciences Molec
́
d’Orsay (ISMO), CNRS, Univ. Paris-Sud, Universite
§Dipartimento di Chimica, Universita
di Bari A. Moro, I-70126 Bari, Italy
∥Istituto di Chimica dei Composti Organometallici ICCOM, Bari Sect, I-70126 Bari, Italy
⊥Sorbonne Universites, UPMC Univ. Paris 06 and #CNRS, MONARIS, UMR 8233, Universite
́
Pierre et Marie Curie, 4 Place Jussieu,
́
Paris-Saclay, F-91405 Orsay, France
̀
́
Case courrier 49, F-75252 Paris Cedex 05, France
ABSTRACT: Carbon-cage molecules have generated a considerable interest
from both experimental and theoretical points of view. We recently per-
formed a high-resolution study of adamantane (C10H16), the smallest hydro-
carbon cage belonging to the diamandoid family (Pirali, O.; et al. J. Chem.
Phys. 2012, 136, 024310). There exist another family of hydrocarbon cages
with additional interesting chemical properties: the so-called platonic hydro-
carbons that comprise dodecahedrane (C20H20) and cubane (C8H8). Both
possess C−C bond angles that deviate from the tetrahedral angle (109.8°) of
the sp3 hybridized form of carbon. This generates a considerable strain in the
molecule. We report a new wide-range high-resolution study of the infrared
spectrum of cubane. The sample was synthesized in Bari upon decarbox-
ylation of 1,4-cubanedicarboxylic acid thanks to the improved synthesis of
literature. Several spectra have been recorded at the AILES beamline of the
SOLEIL synchrotron facility. They cover the 600−3200 cm−1 region. Besides
the three infrared-active fundamentals (ν10, ν11, and ν12), we could record many combination bands, all of them displaying a well-
resolved octahedral rotational structure. We present here a preliminary analysis of some of the recorded bands, performed thanks
the SPVIEW and XTDS software, based on the tensorial formalism developed in the Dijon group. A comparison with ab initio
calculations, allowing to identify some combination bands, is also presented.
Eaton and Cole first synthesized cubane in 1964.2,3 Later on,
I. INTRODUCTION
Barborak and colleagues found an improved synthesis pro-
Carbon-cage molecules like fullerenes have generated consid-
erable interest from both experimental and theoretical points of
cedure.4 This molecule is a spherical-top with Oh octahedral
symmetry. It possesses 18 (nondegenerate and degenerate)
view. Adamantane is the smallest hydrocarbon cage that we could
normal modes of vibration, among which only three (with F1u
study recently at high resolution using the AILES Beamline of
the SOLEIL synchrotron facility.1
symmetry) are infrared active and 8 are Raman-active. It should
be noticed that for such centrosymmetric molecules, the infrared
Platonic hydrocarbons, comprising dodecahedrane (C20H20)
and Raman spectra are mutually exclusive: infrared bands have u
and cubane (C8H8), are another family of hydrocarbon cages
parity, whereas Raman bands have g parity. Thus, both tech-
with additional interesting chemical properties. These species
niques are necessary for a complete spectroscopic character-
possess C−C bond angles that significantly deviate from the
ization. Della and co-workers5 have recorded low-resolution
spectra of C8H8. The only existing high-resolution study is that of
Pine et al.,6 who could record some parts of the three infrared-
active fundamentals using diode lasers. These spectra were
analyzed as isolated bands using a very simple phenomenological
tetrahedral angle (109.8°) of the sp3 hybridized form of carbon,
generating a considerable strain in the molecule. Cubane itself
has the highest density of all hydrocarbons (1.29 g/cm3). This
makes it able to store large amounts of energy, although the
molecule is fully stable. As a matter of fact, cubane and its
derivatives are studied to produce new compact materials for
rocket engines, for instance. From the theoretical chemistry
point of view, this is a very intriguing molecule, because of its
high symmetry combined to these unique bonding properties.
Received: April 29, 2016
Revised: June 7, 2016
© XXXX American Chemical Society
A
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Article
model. More recently, Vlahacos and co-workers7 or also Jursic8
and Karpushenkava et al.9 made theoretical studies of this mole-
cule, using ab initio calculations.
II.B. Infrared Spectroscopy. All spectra were recorded
using the high-resolution Bruker IFS 125 Fourier transform
interferometer located on the AILES beamline of the SOLEIL
synchrotron facility together with the room temperature White
type cell for which the optics were adjusted to obtain 150 m
absorption path length. This setup has been already used
several times in the past to obtain the IR and far-IR spectra of
many relatively large C-bearing molecules, which are low vapor
pressure solids at room temperature (such as, e.g., adamantane1
and naphthalene10). The vibrational bands of cubane studied in
this work span over a large frequency range (600−3200 cm−1)
and exhibit large intensity differences (e.g., the intensity of the
ν11 fundamental band is calculated to be about 4 km.mol−1 and
that of the ν10 fundamental band to be about 135 km.mol−1).
To provide a relatively complete description of the IR spectrum
of cubane, we recorded six spectra with different experimental
conditions listed in Table 1. Our spectra were calibrated using
residual water absorption lines. We used the frequencies available
from HITRAN database11 concerning the H2O ν2 band.
Over this large range of experimental conditions, the rota-
tional analysis of the ν11 and ν12 bands were obtained by using
the conditions of spectrum 2. The very intense ν10 band
(spectrum 3) was obtained at lower resolution (due to a larger
Doppler broadening than for the ν11 and ν12 bands) and by
reducing the pressure. Increasing the gas pressure allowed the
detection of many combination bands (spectrum 4); their
rotational analysis (using spectra 5 and 6) is still in progress
and will be the subject of a next study.
We have chosen here to reinvestigate in detail the infrared
spectrum of this molecule, thanks to the AILES beamline of the
SOLEIL synchrotron facility. After a careful synthesis and char-
acterization of our sample, we could record many high-resolution
spectra over a wide spectral range. We performed a reanalysis of
the ν11 and ν12 fundamentals, leading to new accurate effective
Hamiltonian parameters. Thanks to new ab initio calculations it
was also possible to assign many combination bands, that were
never observed before.
Section II.A details the synthesis and characterization of our
cubane sample. Section II.B presents the experimental infrared
data. Our new quantum chemistry calculations are detailed in
section II.C, and their results relative to the assignment of com-
bination bands are presented in section III. Section III.A dis-
cusses the ground vibrational state rotational constant value.
Sections III.B, III.C, and III.D present the assignment and analysis
of the ν12 and ν11 fundamentals and discusses the highly perturbed
structures of the ν10 C−H stretching region. Finally, section III.F
compares our preliminary experimental results on combination
bands with the literature data.
II. LABORATORY METHODS
II.A. Synthesis and Characterization. All details con-
cerning the synthesis and characterization of our cubane sample
realized by the Bari group are provided in Appendix A.
Table 1. Experimental Conditions Used To Record Six Infrared Spectra of Cubane
spectrum
pressure/μbar
resolution/cm−1
no. of scans
iris/mm
beam splitter
windows
ZnSe
detector
high-freq filter
source
1
2
3
4
5
6
2
3
0.5
1000
300
80
4
KBr
KBr
KBr
KBr
KBr
KBr
MCT
MCT
InSb
no
synchrotron
synchrotron
globar
0.001
0.003
0.5
1
ZnSe
no
0.7
16
16
49
1.15
4
ZnSe
3200
no
1000
320
800
ZnSe
MCT
MCT
MCT
globar
0.0025
0.003
1.15
1.5
ZnSe
2400
2400
globar
polypropylene
globar
a
Table 2. Vibrational Wavenumbers (cm−1) and IR Intensities (km/mol) with Several Theoretical Approaches
b
c
c
c
experimental
CC/Pople
harmonic
B3LYP/Dunning
harmonic
B3LYP/Pople
IR Intensity
d
e
f
g
mode
sym
deg
type
activity
position
intensity
harmonic
anharmonic
ν1
A1g
A1g
A2u
A2u
Eg
1
1
1
1
2
2
2
2
3
3
3
3
3
3
3
3
3
3
C−H
C−C
C−H
CCH
CCH
C−C
CCH
CCC
CCH
C−H
CCH
C−C
C−H
CCH
C−C
CCC
CCH
C−C
R
3140
1017
3102
1005
1117
912
3125
1016
3090
1053
1112
912
3131
1056
3094
1013
1113
910
0
0
3001
1040
2967
995
ν2
R
ν3
−
−
R
0
ν4
0
ν5
0
1086
897
ν6
Eg
R
0
ν7
Eu
−
−
−
IR
IR
IR
R
1142
600
1180
624
1174
624
0
1179
609
ν8
Eu
0
ν9
F1g
F1u
F1u
F1u
F2g
F2g
F2g
F2g
F2u
F2u
1133
3119
1260
863
1165
3106
1269
867
1163
3113
1267
862
0
1147
2981
1242
850
ν10
ν11
ν12
ν13
ν14
ν15
ν16
ν17
ν18
2991
1235
852
111
4
135
4.2
10
0
10
3113
1204
828
3099
1221
839
3105
1218
833
2976
1196
820
R
0
R
0
R
649
681
680
0
677
−
−
1066
829
1066
836
1066
836
0
1042
820
819
0
a
b
c
Experimental intensity values are estimated from the high-resolution spectra. This work. Pople’s basis set is 6-311++G(2d,2p); the Dunning
d
e
f
one is aug-cc-pVTZ. Irreducible representation in the Oh point group. Degeneracy. C−H, C−C: stretching mode. CCH, CCC: bending mode.
g
IR: infrared. R: Raman. Other modes (−) are inactive, in first approximation.
B
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II.C. Quantum Chemistry Calculations. Geometrical
optimization and vibrational frequency calculations have been
performed at two theoretical levels of theory: (1) the coupled-
cluster singles and doubles excitations with perturbative triples
method CCSD(T) and (2) the most popular hybrid density
functional B3LYP. We have also used two basis sets of triple-ζ
quality for each method, namely, the extended 6-311++G(2d,2p)
basis set of Pople et al.,12,13 and the correlation consistent aug-cc-
pVTZ basis set of Dunning et al.14,15 DFT calculations have been
done using the Gaussian 09-RevA.02 package,16 whereas the
CCSD(T) ones have been carried out with the Molpro code.17
To obtain a set of reference data, geometrical optimization has
been performed at the CCSD(T)/aug-cc-pVTZ level. Vibra-
tional frequencies have been calculated within the harmonic
approximation using both CCSD(T) and B3LYP approaches and
the 6-311++G(2d,2p) basis set. Vibrational frequency corrected
for the anharmonic effect has been performed using second-order
perturbative theory (as implemented in Gaussian 09 package)
only with the B3LYP/6-311++G(2d,2p) method. To do this job,
we slightly lowered the molecular symmetry. However, we
carefully checked that the changes in energetic and harmonic
vibrational frequencies are actually negligible. Some more details
about the calculation output are given as Supporting Information
to this paper.
Vibrational parameters are gathered in Table 2. Here again,
we compare the harmonic theoretical results to those obtained
at the CCSD(T)/aug-cc-pVTZ level. One can easily note that
the B3LYP functional with both basis sets nicely reproduces the
vibrational reference data (relative error <5%). Consequently,
we can confidently use our theoretical anharmonic frequencies
to compare with the experimental data.
II.D. Effective Hamiltonian. Cubane is a quite large
octahedral spherical top molecule. Its point group symmetry at
equilibrium is Oh. It possesses 18 distinct normal modes of
vibration: 4 nondegenerate mode with A1g or A2u symmetry,
4 doubly degenerate mode with Eg or Eu symmetry and
10 triply degenerate modes with F1g, F1u, F2g, or F2u symmetry.5−9
In the first approximation, only F1u fundamentals are infrared
active, that is, only ν10, ν11, and ν12. Eight modes are Raman-only
active (infrared absorption and Raman scattering spectra, being,
in this sense, mutually exclusive). Again, in the first approxi-
mation, the seven remaining modes are inactive. We show below,
however, that some of these can be slightly active through rovi-
brational interactions with the active modes. Table 2 summarizes
the normal modes of cubane, together with their observed and
calculated frequencies from the present work (section II.C).
To analyze the spectra, we use the formalism developed in
Dijon for spherical top molecules. This one is based on group
theory and tensorial formalism methods as already described in
refs 18−20. This formalism allows a systematic expansion of the
Hamiltonian and transition moment operators up to a given
order and for any vibrational level or polyad (group of inter-
acting vibrational levels).
In the present case, we simply consider isolated fundamental
bands (ν11 and ν12) in detail. Thus, we only need simple
effective Hamiltonian operators:
• The ground state (GS) effective Hamiltonian:
<GS>
<GS>
̃
̃
H
= H{GS}
(1)
(2)
• The νi (i = 11 or 12) effective Hamiltonian:
<ν>
<ν>
<ν>
i
i
i
̃
̃
̃
H
= H{GS} + H{ν}
i
C
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a
Table 4. Effective Hamiltonian Parameters for the ν12 and ν11 Fundamental Bands
vibrational level
order
Ω(K,nC)
ν12/cm−1
ν11/cm−1
1.11195 × 10−1
“usual” notation18,41
b
v = 0
v = 0
v = 1
v = 1
0
0
0
1
2(0g,0A1g)
4(0g,0A1g)
0(0g,0A1g)
1(1g,0F1g)
1.11195 × 10−1
B0
b
−6.14274054 × 10−9
851.779972(45)
−6.14274054 × 10−9
1234.915819(50)
−D0
ν (band center)
Bζ (Coriolis)
−1.004323(29) × 10−1
1.038828(21) × 10−1
3
2
v = 1
v = 1
v = 1
v = 1
2
2
2
3
2(0g,0A1g)
2(2g,0Eg)
2(2g,0F2g)
3(1g,0F1g)
1.46088(91) × 10−4
8.645(12) × 10−5
4.9694(41) × 10−5
−1.00148(42) × 10−4
1.06978(25) × 10−4
−1.311(27) × 10−8
Bv − B0
−(1/2)α220 − 6α224
−(3/4)α220 + 6α224
−1.4024(19) × 10−4
−3.2116(68) × 10−7
−(3
(3/
3
/4
2
)F110
v = 1
3
3(3g,0F1g)
−3.9823(48) × 10−7
−6.14(20) × 10−9
5/2)F134
−(Dv − D0)
v = 1
v = 1
4
4
4(0g,0A1g)
4(2g,0Eg)
−3.89(51) × 10−10
−2.351(73) × 10−10
−7.14(27) × 10−10
−6.51(53) × 10−11
(
3
/8)G220 + (3
3
/2)G224
/2)G224
)(Dvt − D0t)
/2)G244 + ( 21/2 22)G246
b
v = 1
v = 1
v = 1
v = 1
4
4
4
4
4(2g,0F2g)
4(4g,0A1g)
4(4g,0Eg)
4(4g,0F2g)
1.55(55) × 10−10
−3.001(77) × 10−10
1.263(12) × 10−9
3.087(14) × 10−9
0.0
(3
3
/16)G220 − (3 3
/4
2
−3.092(85) × 10−11
−1.222(68) × 10−10
−(3
−(3
−(9
5
7
7
b
0.0
/8)G244 − ( 21
/
22)G246
v = 1
5
5
5
5(1g,0F1g)
5(3g,0F1g)
5(5g,0F1g)
2.736(46) × 10−12
−4.2(1.2) × 10−13
−1.34(13) × 10−12
4909
v = 1
v = 1
assignments
Jmax
3767
84
90
d
rms/10−3 cm−1
0.322
0.378
a
b
One standard deviation is indicated in parentheses, in the unit of the last two digits, for fitted parameters. Fixed value (see text).
which contains both the ground state and νi = 1
i.e., we use a three-dimensional oscillator with vibrational angular
momentum quantum number li and Oh symmetry F1u. The Ham-
iltonian and dipole moment matrix elements are calculated in the
coupled rovibrational basis set:
operators and parameters.
As discussed later in section III, the case of the ν10 C−H
stretching region appears more complex, the ν10 fundamental
band being obviously in strong interaction with some other
vibrational levels. This problem will be the subject of a future
work. The different terms in the above effective Hamiltonians
are written in the form:
(J ,nCr)
(li=1,F1u
(C=F1u⊗Cr)
g
|Ψ ⟩ = |(Ψ
) ⊗ Ψr
)
⟩
rv
ν=1
(5)
i
Ψ(rJ,nC ) being a rotational wave function with angular momentum
quantum number J (considered to have g parity), rotational sym-
metry species Cr and multiplicity index n (see ref 18), whereas C
is the overall rovibrational symmetry species.
r
<ν >
Ω(K,nΓ)Γ Γ
Ωv(Γ Γ )Γ
v v′
⊗ RΩ(K,nΓ) (A
)
ε
)
i
v
v′
1g
̃
H{GSorν}
=
t
β( V{s}{s′}
∑
{s}{s′}
i
allindexes
(3)
Ω(K,nΓ) ΓvΓv′
{s}{s′}
In this equation, the t
are the parameters to be deter-
III. RESULTS AND DISCUSSION
Ωv(ΓvΓv′)Γ
ε
mined, whereas V{s}{s′}
and RΩ(K,nΓ) are vibrational and
III.A. Ground State Rotational Constants. In the case of
an isolated infrared-active triply degenerate fundamental band
of a spherical-top molecule, it is not possible to simultaneously
fit the ground and excited vibrational state rotational constant,
due to strict selection rules that forbid combination differences.
Such a molecule has no permanent dipole moment and, more-
over, strictly no pure rotational lines because of the parity
selection rule for such a molecule with a center of symmetry.
rotational operators of respective degree Ωv and Ω. Their
construction, based on symmetrized polynomials of the
elementary rotational angular momentum and creation and
annihilation operators for each normal mode, is described in
ref 18. β is a factor that allows the scalar terms (Γ = A1g) to
match the usual terms like B0J2, etc. The symbol ⊗ represents
the tensorial (coupling) product. The order of each individual
term is defined as Ω + Ωv − 2. Let us also notice that we have
here s = s′ = GS or νi only.
It is thus necessary to fix the ground state rotational constants
to some value. We choose here to expand H
<GS>
̃
up to order
To compute line intensities and to obtain simulated spectra,
the dipole moment operator is expanded in the same way.
The reader is referred for instance to refs 18 and 21 for general
details about its construction. This time, the order of the
development in our model is defined as Ω + Ωv − 1. In the
present case, because we do not consider absolute line inten-
sities, the effective dipole moment is expanded up to order zero
only, resulting into a single parameter for each fundamental
band, whose value is arbitrarily set to 1.
2 only, retaining only scalar parameters, namely, the rotational
constant B0 and the centrifugal distortion constant D0.
Concerning B0, different values derived from calculations or
previous experimental results are summarized in Table 3. Cole
et al.,22 Pine et al.,6 and Hirota et al.23 published rotational
constants obtained from gas phase spectroscopy, and
Almenningen et al.24 and Hedberg et al.25 derived the GS
rotational constants from electron diffraction measurements.
The most accurate experimental determination of the rotational
constant B0 has been published by Hedberg et al.25 It associates
gas phase electron diffraction measurements with numerous
experimental results and, in particular, with very accurate GS
pure rotation spectroscopy of mono deuterated cubane.23
Finally, we use here a vibrational basis set restricted to the
νi = 1 level:
(li=1,F1u
)
|Ψ ⟩ = |Ψ
⟩
v
ν=1
(4)
i
D
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Figure 1. Overview of the ν12 fundamental band, compared to the simulation. The bottom panel displays the fit residuals for line positions.
Figure 2. Detail in the P branch of the ν12 fundamental band, compared to the simulation. The bottom panel displays the fit residuals for line
positions. Some cluster line symmetries are indicated in the case of the P(51) lines (parity index is omitted).
In the present work, the molecular structure optimized in our
quantum chemistry calculations are in very good agreement
with the experimental values from Hedberg et al.25 Two geo-
metrical parameters, C−C = 157.4 pm and C−H = 108.8 pm
at the equilibrium configuration, calculated at the CCSD(T)/
aug-cc-pVTZ level are well reproduced with CCSD(T)/ 6311+
+G(2d,2p) [157.8 and 109.4 pm], B3LYP/aug-cc-pVTZ [156.8
and 108.6 pm], and B3LYP/6-311++G(2d,2p) [156.9 and
108.6 pm] methods. The corresponding relative error is less
than 1%. These parameters agree well with the r−g structure
(vibrationnally averaged) from Hedberg et al.25 (Table 3). In
the same way, our D0 centrifugal distortion constant agrees well
with that of Hirota et al.23
we have chosen to use the rotational constant B0 and the cen-
trifugal distortion constant D0 obtained from our calculations.
III.B. ν12 Band. The ν12 fundamental band displays a clear P,
Q, and R branch structure with well-resolved line clusters for
each J value. Its assignment and analysis is quite straightfor-
<ν12>
̃
ward. H
was expanded up to order 5. A total of 4909
transitions could be assigned up to J = 90. All 16 effective
Hamiltonian parameters could be fitted with a small standard
deviation. The overall root-mean-square deviation is 0.278 ×
10−3 cm−1. This result is comparable to that of Pine et al.,6
although we could assign considerably (more than six times)
more transitions. We get more effective Hamiltonian parameter
values (adding that these authors fitted more phenomenological
transition parameters). The resulting effective Hamiltonian
parameters are given in Table 4. As shown in Table 3, the ΔB
Therefore, to compare the variation of rotational constants
between the ground and excited states studied here (α matrix),
E
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Figure 3. Overview of the ν11 fundamental band, compared to the simulation. The bottom panel displays the fit residuals for line positions.
Figure 4. Detail in the R branch of the ν11 fundamental band, compared to the simulation. The bottom panel displays the fit residuals for line
positions. Some cluster line symmetries are indicated in the case of the R(42) lines (parity index is omitted) .
and ζ Coriolis parameter values for ν12 obtained from the
anharmonic calculations agree very well with the experimental
ones.
(Oh point group irreducible representations; the parity index,
which is g, is omitted for sake of clarity). As for all heavy
spherical-top molecules, lines appear to cluster as it has been
observed and explained in many other cases.26−32
Figure 1 shows an overview of the ν12 fundamental band,
compared to the simulation, along with the fit residuals for line
positions. These are well distributed between 2 × 10−3 cm−1
with no systematic deviation as J increases (toward the ends of
the branches), showing the consistency and completeness of
the model we use. Some saturation occurs for the strongest
Q branch lines, resulting in artifacts in the absorbance calcu-
lation. This did not prevent us, however, to assign many Q
lines.
III.C. ν11 Band. The ν11 fundamental band also displays a
clear and well-resolved P, Q, and R branch structure. A total of
<ν11
3767 transitions could be assigned up to J = 84. H > needs to
̃
be expanded up to order 4 only. Eleven effective Hamiltonian
parameters could be fitted with a small standard deviation, the
two remaining parameters being nondeterminable and thus
fixed to zero. The overall root-mean-square deviation is 0.350 ×
10−3 cm−1. Again, this result largely extends that of Pine et al.6
The resulting effective Hamiltonian parameters are also given in
Table 4. As for ν12, the comparison of observed and calculated
ΔB and ζ constants for ν11 is very satisfying (Table 3).
Figure 2 shows a detail in the R(50) to R(52) region, com-
pared to the simulation and along with some examples of assign-
ments of line clusters in the form of the ground state symmetry
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Figure 5. Q branch of the ν11 fundamental band, compared to the simulation. The bottom panel displays the fit residuals for line positions.
Figure 6. Experimental spectrum of the ν10 fundamental band. The insets show details in the P and R branches.
P and R branches. Contrary to the two previous bands, no straight-
forward assignment can be performed. Considering Table 2, the
most likely perturber is the nearby ν3 nondegenerate funda-
mental band with A2u summetry (only vibrational levels with
u parity can interact in the infrared absorption spectrum of a
centrosymmetric molecule). Literature values situate this band a
few cm−1 apart from ν10, although no precise determination exists
Figure 3 shows an overview of the ν11 fundamental band,
compared to the simulation, along with the fit residuals for line
positions.
Although the octahedral splitting is in this case quite large, so
that there is an overlap between successive J values, the
structure remains well resolved.
Figure 4 shows a detail in the R(40) to R(43) region,
compared to the simulation and along with some examples of
assignments of line clusters (as for ν12, see Figure 2 above).
Figure 5 displays the very characteristic structure of the Q
branch, which also could be largely assigned, despite a very high
line density.
III.D. ν10 C−H Stretching Region. As already noticed by
Pine et al.,6 the ν10 C−H stretch fundamental band displays a
complex and highly perturbed structure. As we can see in Figure 6,
J clusters cannot be easily recognized and distinguished in the
at present. Thus, quadratic Coriolis interaction of type
2(2,0F2g) F1uA2u
{ν10}{ν3}
t
is very likely to occur between the v10 = 1 and
the ν3 = 1 vibrational levels, forming a closely interacting dyad.
The first attempts to include such an interaction, although leading
to a quite similar overall structure of this region proved to be
unsuccessful to allow detailed assignments. Further investigations
are still needed, from the theoretical side, to estimate initial
rovibrational parameters. This will be the subject of a future
work.
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III.E. Infrared Intensities. Taking into account the optical
path length and gas pressure (see section II.B and Table 1), we
estimated integrated band intensities using both high-resolution
(rotationally resolved) and low-resolution spectra. Both esti-
mations agree well. These intensities for the three active funda-
mental modes are in excellent agreement with the calculated
values as shown in Table 2.
III.F. Combination Bands and “Forbidden” Bands. The
above-described anharmonic quantum chemistry calculations
allow to identifiy some combination bands, although some
ambiguities remain. It should be recalled that, for such a centro-
symmetric molecule, only combination bands with u parity can
be observed in infrared dipolar absorption. Moreover, only those
featuring a vibrational sublevel with F1u symmetry can display a
significant intensity. Our spectra show many of these combination
bands, all of them displaying a nicely resolved rovibrational
structure. Figure 7 shows six regions for which bands of group of
bands (polyads) can be identified when comparing to calcu-
lations.
We can notice a very unusual intensity pattern with
abnormally strong lines in the P branch region of the ν8 +
ν16 combination band. This is likely to be quite similar to what
we previously oberved in the case of the ν25 fundamental band
of adamantane.1 It is thus probably due to a Coriolis interaction
with a nearby rovibrational band, yet to be identified. The ν11
fundamental level is a plausible candidate, although it does not
seem to be perturbed in the present analysis (see above). But,
as a matter of fact, in the case of adamantane, the ν24 perturber
also has itself a regular structure and lies at a similar wave-
number distance of ca. 40 cm−1. For cubane, the detailed analysis
of ν8 + ν16 is, however, not yet possible, because this necessitates
knowledge of the ν8(Eu) and ν16(F2g) fundamental bands
themselves and a good estimate of the position of the two
vibrational sublevels of the combination level (there are two
sublevels, because Eu⊗F2g = F1u⊕F2u).
Figure 7. Experimental spectra of the various combination bands. Insets show details of the resolved rovibrational structure.
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active. This is the case of at least ν18 whose Q branch is slightly
visible in our spectra around 819 cm−1 (estimated value from a
very preliminary tentative simulation of the Q branch). This case
is fully similar to that of the ν6 fundamental band of SF6, with the
same F2u symmetry and that was recently observed at the AILES
beamline of the SOLEIL synchrotron facility.37
Table 5 summarizes the different fundamental and combi-
nation band (or combination band regions in case of complex
polyads) that can be observed in our spectra (Figure 7), compared
with anharmonic calculations.
Table 5. Some Calculated and Observed Vibrational Bands
of Cubane
calculated
observed band
centers/cm−1
spectral region
bands
(anharmonic)/cm−1
Fundamental Bands
820.2
814−821
ν18
819
830−880
1220−1250
2960−3020
ν12
ν11
ν10
849.7
851.8
1234.9
2991
1241.8
2980.9
Combination Bands
1286.0
1265−1290
1620−1645
1680−1780
ν8 + ν16
ν15 + ν18
ν6 + ν18
ν4 + ν16
ν16 + ν17
1275.3
1634.8
IV. CONCLUSION AND PERSPECTIVES
1639.6
1715.7
After a careful synthesis and characterization of a sample of the
cubane molecule, we reinvestigated the high-resolution spectrum
of this molecule over a wide spectroscopic range. We could
significantly improve the detailed rovibrational assignment and
analysis of the ν11 and ν12 fundamental bands. Many other combi-
nation bands were also recorded for the first time, displaying a
nicely resolved rovibrational structure in each case. Anharmonic
quantum chemistry calculations have been performed to help the
identification of several bands. In a near future, an important effort
will be devoted to the spectral analysis of these combination bands
that might provide new information on the structure and force
field of this peculiar molecule in its electronic ground state. As
shown in the previous sections, the ΔB values of ν11 and ν12
obtained from the anharmonic calculations agrees very well with
the experimental one (within few 10−5 cm−1). This further
confirms the quality of the calculations to predict spectroscopic
parameters for the GS and fundamental bands. The anharmonic
calculations provides ΔB estimates for the other fundamental
bands (slightly IR active through rovibrational interactions) and
also for combination bands and overtones. As it was used recently
to study numerous IR and far-IR band of large aromatic
molecules,38 the accuracy of these estimates might be an invalu-
able support to forthcoming spectral analysis of the rotational
structures observed in many combination modes.
1716.7
1718.3
(1715.4, 1716.7,
1749.4)
ν6 + ν12
ν8 + ν9
1745.9
1755.1
1804.7
1843.9
1856.8
1860.6
1863.1
1905.2
1917.9
1934.8
1939.4
1965.9
1995.6
1780−1860
1880−2040
ν8 + ν14
ν2 + ν12
ν7 + ν16
ν4 + ν15
ν15 + ν17
ν5 + ν18
ν16 + ν11
ν5 + ν12
ν6 + ν17
ν9 + ν18
ν9 + ν12
(1824.6, 1857.8)
(1904.9, 1955.8,
1979.3, 2011.0)
ν7 + ν15
ν14 + ν18
ν12 + ν14
ν11 + ν12
ν7 + ν14
1917.9
2015.6
2045.3
2062.4
2347.7
2360−2380
2369
Beyond these general qualitative comments, it is clear,
however, that a detailed assignment and fit of rovibrational effec-
tive Hamiltonian for these bands is still a very difficult task. It will
require first a better knowledge of all fundamental bands implied
in the present combinations. This is complicated by the fact that
most of the fundamentals are not active in infrared absorption
(Table 2). High-resolution Raman spectroscopy could be of great
help in some cases, as already proved by our previous works on
the SF6 molecule.33−36
APPENDIX A: SYNTHESIS AND
CHARACTERIZATION
■
1. Materials and Methods
Melting points were not corrected. GC/MS experiments
were run using a ZB-1 column (30 m × 0.25 μm id); the
MS were performed in EI mode (70 eV). The 1H NMR spectra
were recorded on a 500 MHz NMR spectrometer; resonances
are referenced to residual isotopic impurity CHCl3 (7.26 ppm)
of solvent CDCl3 and/or to TMS. The 13C NMR spectral data
Some other “forbidden” fundamental bands may also be
observed through rovibrational interactions, making them slightly
Figure 8. Cubane synthesis scheme.
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AUTHOR INFORMATION
■
Corresponding Authors
*V. Boudon. Electronic address: Vincent.Boudon@u-bourgogne.fr.
*O. Pirali. Electronic address: Olivier.Pirali@synchrotron-soleil.fr.
*L. D’Accolti. Electronic address: lucia.daccolti@uniba.it.
*M. E. Alikhani. Electronic address: esmail.alikhani@upmc.fr.
Notes
The authors declare no competing financial interest.
ACKNOWLEDGMENTS
■
The authors are grateful to SOLEIL staff for providing
synchrotron radiation under proposal number 20130032. We
also thank Dr. Manuel Goubet (PhLAM laboratory in Lille,
France) for fruitful discussions.
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