ARTICLE
pubs.acs.org/JPCA
Microwave Spectra and Structures of 1,2-(ortho)- and 1,7-(meta)Carborane, C2B10H12
Svein Samdal,† Harald Møllendal,†,* Drahomir Hnyk,‡ and Josef Holub‡
†
Centre for Theoretical and Computational Chemistry (CTCC), Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern,
NO-0315 Oslo, Norway
‡
ez, Czech Republic
Institute of Inorganic Chemistry of the ASCR, v.v.i., CZ-250 68 Husinec-R
bS Supporting Information
ABSTRACT: The microwave spectra of 1,2- and 1,7-dicarba-closo-dodecaborane(12), C2B10H12 (ortho- and meta-carborane), have been recorded for the first time
at room temperature in the 3288 and 2480 GHz spectral ranges, respectively.
The spectra of the parent species (1,2-C211B10H12 and 1,7-C211B10H12) have been
assigned, together with those of four monosubstituted (10B) 1,2-C210B11B9H12
and 1,7-C210B11B9H12 isotopologues. The microwave spectra confirm that the
structures of each of these two molecules are slightly distorted icosahedrons of C2v
symmetry. A previous determination of the gaseous structures of these two carboranes by the gas electron-diffraction method was
based on several assumptions about the BB bond length differences. All BB bond lengths have now been redetermined using the
substitution (rs) method, which is independent of such restraints. Although several of the rs and electron-diffraction bond lengths are
in good agreement, there are also differences of up to 0.026 Å. Quantum chemical calculations at the B3LYP/6-311þþG(3df,3pd)
level of theory have also been performed.
’ INTRODUCTION
Icosahedral carboranes have been known for about 50 years.13
Many smaller carborane clusters are known, but the most intensively investigated carboranes are based on the 12-vertex
icosahedrons with two carbon and 10 boron atoms. Three such
isomers, 1,2- (ortho), 1,7- (meta), and 1,12- (para), which have
different arrangements of the carbon atoms are known. Each
carbon or boron atom of these cages carries an exo terminal
hydrogen atom. 1,2- and 1,7-C2B10H12 have C2v symmetry,
whereas 1,12-C2B10H12 has D5d symmetry. Figure 1 depicts
the skeletons of 1,2- and 1,7-C2B10H12 with atom numbering,
which differs slightly from that used in previous studies.4,5 These
two compounds were subject to the present study because they
have dipole moments that are different from zero and can therefore
be studied by microwave (MW) spectroscopy.
Substitution of exo hydrogen atoms has resulted in an extensive
chemistry611 with potential applications in a variety of fields,
such as medicine,1214 metal ligands,15 supramolecular chemistry,16,17
extraction of metals,18 and polymers.19 A large number of derivatives
of these three icosahedral carboranes have had their structures
determined by X-ray crystal diffraction,5 and it is therefore highly
desirable to have the structures of the parent carboranes in order
to investigate the effect of substitution. However, no X-ray
determination of the structures of the isolated parent carborane
isomers has so far succeeded because of extensive rotational
cage disorder.5 Fortunately, it has been possible to prepare 1:1
hydrogen-bonded complexes between the three carboranes and a
number of hydrogen-bond acceptors. These complexes are
stabilized by weak CH 3 3 3 X intermolecular hydrogen bonds,
r 2011 American Chemical Society
where X is a suitable acceptor. This stabilization leads to cage
order in some of these crystals, which has facilitated the determination of their crystal structures.5 X-ray structures determined
in this manner haves been reported for 1,2-20,21 and 1,7-C2B10H12.5
However, the extent to which the hydrogen bonds are responsible for the complex formation influence these structures remains
unclear.
Carboranes, which are solids at room temperature, have relatively high sublimation pressures, and this has made it possible
to investigate their gas-phase structures using the gas electrondiffraction (GED) method. In 19651969, Vilkov and coworkers2224 reported the gas-phase structures of these two
compounds. A few years later, another GED study was reported
by Bohn and Bohn,25 who succeeded in obtaining a full structure
for gaseous 1,12-C2B10H12, which has only two different BB
bond lengths because of its D5d symmetry. In contrast, the
1,2- and 1,7-C2B10H12 isomers have lower symmetry (C2v) and
several similar BB bond lengths, which cannot be resolved
using the GED method alone. Recently, Turner et al.4 performed
a new GED investigation. In this determination, several flexible
restraints obtained from MP2/6-311þþG(df,p) calculations
were introduced in the GED analysis. These assumptions made
it possible to obtain different values for all BB bond lengths.4
These three carboranes have not been explored exclusively by
experimental methods. Several semiempirical and quantum chemical
Received: January 26, 2011
Revised:
March 7, 2011
Published: March 29, 2011
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’ EXPERIMENTAL SECTION
Figure 1. Structures and numbering schemes of 1,2-C2B10H12 (left)
and 1,7-C2B10H12 (right).
calculations at various degree of sophistication4,2633 have also
been reported.
1,2- and 1,7-carborane have not previously been studied by
MW spectroscopy. The dipole moments of these molecules were
determined to be 4.53 and 2.85 D, respectively, in benzene.34 Not
surprisingly, the 1,12- isomer was found experimentally to have
zero dipole moment.34 It has also been shown experimentally
that the dipole moment of the 1,2- isomer has its positive end
pointing toward the midpoint of the CC bond.35
Both 1,2- and 1,7-carborane consist of 24 atoms, which is large
by MW standards. However, two similar and “large” compounds,
1-thia-closo-decaborane(9), 1-SB9H9, which has a C4v bicapped
pyramidal molecular shape,36 and 1-thia-closo-dodecaborane(11),
1-SB11H11,37 which is a C5v-symmetric icosahedron, were recently investigated successfully by MW spectroscopy in the Oslo
laboratory, demonstrating that this method can provide important spectroscopic and structural information for these cage
compounds.
The facts that only the X-ray crystal structures of hydrogenbonded complexes of 1,2- and 1,7-C2B10H12 are available5,20 and
that the GED structures of these two prototype compounds are
based on several assumptions4 suggest that a method that is
subject to none of these restrains should ideally be used to obtain
the “true” structures of the two carboranes. Fortunately, the
microwave substitution (rs) method38 has such properties. In this
method, the Cartesian coordinates of an atom are determined by
substituting this atom by an isotope and using the changes of the
moments of inertia caused by this substitution in Kraitchman’s
equations.39
1,2- and 1,7-C2B10H12 are fortunate cases for a determination
of the BB bond lengths by the substitution method. Both
compounds are sufficiently volatile and have high dipole moments. The natural abundances of the boron isotopes are 80.1%
for 11B and 19.9% for 10B, which facilitates the investigation of
the spectra of several isotopologues containing 10B. Moreover,
the extremely high resolution of MW spectroscopy should make
it possible to assign the spectra of 10B-containing isotopologues
regardless of their position in the carborane. The rotational
constants of the parent C211B10H12 and the C210B11B9H12
isotopologues should form the basis for an independent structural determination of the BB bond lengths using the substitution (rs) method.38 The superior quality of the substitution method
over the GED method subjected to several flexible restraints4
motivated the present investigation of the two carboranes.
The present spectroscopic work has been augmented by highlevel quantum chemical calculations, which were conducted with
the purpose of obtaining information for use in assigning the
MW spectra and for comparison with available structural results.
Compounds. The sample of 1,2-C2B10H12 was obtained from
Katchem, Ltd., and was used as received. The same sample was
employed for the preparation of 1,7-C2B10H12 by means of
thermal rearrangement at 470 °C,40 with a calculated activation
energy barrier of 62 kcal/mol.41 The purities of both samples
were greater than 98% as assessed by thin-layer chromatography
and also 11B nuclear magnetic resonance spectroscopy.
Microwave Experiments. The spectra of 1,2-C2B10H12 and
1,7-C2B10H12 were studied in the 3288 and 2480 GHz
frequency intervals, respectively, by Stark-modulation spectroscopy using the microwave spectrometer of the University of Oslo.
Microwave radio frequency double resonance experiments were
also performed as described by Wodarczyk and Wilson42 in order
to assign particular transitions. Details of the construction and
operation of the Oslo spectrometer have been given elsewhere.43,44
This spectrometer, which was recently upgraded with a new
Millitech active multiplier chain (AMC-10-RFH00110) and a
general-purpose detector (DET-10-RPFW0) now operates in
the 7110 GHz range. The resolution of this instrument is about
0.5 MHz, and frequencies of isolated transitions are measured
with an estimated accuracy of ∼0.10 MHz. The experiments
were performed at room temperature using a 2-m HewlettPackard absorption cell. The sublimation pressure at this temperature is a few pascals in the case of 1,2-C2B10H10, whereas 1,7C2B10H10 has a sublimation pressure of roughly 50 Pa. These
comparatively low sublimation pressures excluded an investigation at much lower temperatures, where the MW spectra would
have been more intense than at room temperature.
’ RESULTS AND DISCUSSION
Quantum Chemical Calculations. The present density functional theory (DFT) calculations were performed employing the
Gaussian 03 suite of programs,45 running on the Titan cluster in
Oslo. Electron correlation was taken into consideration using Becke’s
three-parameter hybrid functional46 employing the Lee, Yang, and
Parr correlation functional (B3LYP).47 The 6-311þþG(3df,3pd)
basis set was used in the calculations. This basis set is of triple-ζ
quality and is augmented with diffuse functions. It is expected
that the present B3LYP/6-311þþG(3df,3pd) calculations should
predict accurate structures for the two compounds because they
contain only first- and second-period elements (H, B, and C).
The geometrical structures, dipole moments, vibrational, frequencies and Watson’s quartic centrifugal distortion constants48
of the two carboranes were calculated. The B3LYP rotational
constants, the A-reduction48 quartic centrifugal distortion constants, and principal-axis dipole moment components of 1,2- and
1,7-carborane are listed in Table 1. The two molecules each
contain 24 atoms; a full listing of their structures is rather lengthy
and is therefore given in the Supporting Information, where the
B3LYP structure of 1,2-C2B10H12 is found in Table 1S (Supporting
Information) and the structure of 1,7-C2B10H12 is provided in
Table 2S (Supporting Information). However, the B3LYP BB
bond lengths are listed in Tables 6 (1,2-) and 7 (1,7-), where they
are compared with experimental results. The signs of the Cartesian
coordinates in the principal-inertial-axis system are useful for the
structure determination (see below), and these coordinates are
therefore listed in Tables 3S and 4S in the Supporting Information. Both compounds were found to be comparatively rigid, as
the lowest uncorrected harmonic vibrational frequencies were
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calculated to be 455 cm1 for the 1,2-carborane and 480 cm1
for 1,7-carborane.
All three rotational constants for each of the two compounds
(Table 1) are rather similar, which reflects the fact that these
molecules are slightly distorted icosahedrons. The quartic centrifugal distortion constants (same tables) are unusually small,
which is a result of the rigid structures and relatively small rotational
constants of these species. The fact that these two compounds
have C2v symmetry means that two of the principal-axis dipole
moment components are zero by symmetry. The third component, which is different from zero, turned out to be the c-axis
component both for 1,2- and 1,7-carborane. The theoretical
values of 4.25 D (1,2-) and 2.68 D (1,7-) agree well with the
solution values34 of 4.53 and 2.85 D, respectively.
Microwave Spectra and Assignments. The fact that both
species are relatively polar did not result in a strong microwave
spectrum because the rotational partition function, which increases
rapidly with increasing temperature, is comparatively large because
of rotational constants that are roughly 1.62 GHz on average
(Table 1). The spectrum of the 1,2-carborane appeared to be
weaker than that of the 1,7- variant despite the fact that the 1,2form has the larger dipole moment. It is suggested that the lower
volatility of 1,2-C2B10H12 compared with 1,7-C2B10H12 might
explain this difference. The appearances of the two spectra were
similar and consisted of regions of strong lines with practically no
lines between these regions. The cR-branch lines, which are the
strongest ones in each case, were readily assigned. The weighted
transition frequencies were fitted to Watson’s Hamiltonian in the
A-reduction form48 using Sørensen’s program Rotfit.49
The full spectrum (310 transitions with weights) of the parent
1,2-C211B10H12 species is listed in Table 5S in the Supporting
Information. Values of the J quantum number between 10 and 23
were assigned for this species. The spectroscopic constants are
listed in Table 2. The centrifugal distortion effect was seen to be
small, as expected. It was therefore possible to determine a significant
Table 1. B3LYP Parameters of Spectroscopic Interest for 1,2and 1,7-C2B10H12
1,2-carborane
1,7-carborane
Rotational Constants (MHz)
A
1640.9
1642.6
B
1621.8
1627.0
C
1599.9
1609.1
a
Centrifugal Distortion Constants (kHz)
ΔJ
0.0369
0.0366
ΔJK
0.00117
0.000704
ΔK
0.000346
0.000364
δJ
0.000460
0.000335
δK
0.000789
0.000117
Dipole Moment Components (D)
a
μa
0.0b
0.0b
μb
0.0
b
0.0b
μc
4.25
2.68
A-reduction.48 b For symmetry reasons.
Table 2. Experimental Spectroscopic Constantsa of 1,2-C2B10H12
substituted atom
none
B3
B4
B9
B10
A (MHz)
B (MHz)
1627.0171(10)
1609.1269(11)
1632.4217(14)
1624.0868(21)
1639.7080(9)
1611.4952(11)
1632.3624(10)
1624.0966(16)
1642.1830(15)
1621.2757(24)
C(MHz)
1587.193(4)
1596.795(15)
1601.6660(17)
1596.529(28)
1589.765(7)
ΔJb (kHz)
0.0359(11)
0.0339(14)
0.0373(11)
0.0360(10)
0.0411(18)
κc
0.10154(6)
0.53210(18)
0.48235(5)
0.53865(9)
0.20229(8)
rmsd
1.461
1.424
1.412
1.222
1.715
no. of transitionse
310
140
298
224
177
a
Full spectra are listed in Tables 5S9S in the Supporting Information. Uncertainties represent one standard deviation. b Further quartic constants
preset at the values shown in Table 1; see text. c Ray’s asymmetry parameter.50 d Dimensionless root-mean-square deviation of a least-squares fit.
e
Number of transitions used in the least-squares fit.
Table 3. Experimental Spectroscopic Constantsa of 1,7-C2B10H12
substituted atom
none
B2
B3
B4
B9
A (MHz)
B (MHz)
1629.5179 (10)
1614.167(29)
1642.1699(9)
1616.162(37)
1635.1934(16)
1629.061(12)
1644.5786(13)
1626.438(63)
1642.5285(10)
1616.020(18)
C(MHz)
1595.341(57)
1610.158(20)
1604.485(77)
1597.677(15)
1610.605(20)
ΔJb (kHz)
0.0338(10)
0.03438(90)
0.0341(18)
0.0365(14)
0.0340(10)
κc
0.102(3)
0.625(4)
0.6006(18)
0.226(5)
0.661(2)
rmsd
1.186
1.200
1.4193
1.296
1.232
no. of transitionse
160
210
89
121
210
a
Full spectra are listed in Tables 10S14S in the Supporting Information. Uncertainties represent one standard deviation. b Further quartic constants
preset at the values shown in Table 1; see text. c Ray’s asymmetry parameter.50 d Dimensionless root-mean-square deviation of a least-squares fit.
e
Number of transitions used in the least-squares fit.
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value only for ΔJ. The remaining quartic distortion constants were
preset at their B3LYP values (Table 1) in the final least-squares fit.
Because of the symmetry of the structure of this species, there are
only four different spectra for the isotopologues where one of the 11B
atoms has been replaced by one 10B atom. Spectra of the 1,2C210B11B9H12 isotopologues with 10B in positions 3 (6), 4 (5, 7, 8),
9 (11), and 10 (12) were then assigned. The number(s) in each
of the sets of parentheses indicates which of the corresponding 10B
Table 4. Substitution Coordinatesa (Å) of Boron Atoms in
1,2-C2B10H12
coordinate
|a|
|b|
|c|
B3/B6
1.4634(8)
0.0b
0.8679(9)
B4/B5/B7/B8
0.8890(12)
1.4403(8)
0.001(10)c
B9/B11
B10/B12
1.4606(8)
0.0b
0.0b
0.8899(12)
0.8821(13)
1.4379(8)
a
Uncertainties derived as described by van Eijck.51 b For symmetry
reasons. c This value was taken from the B3LYP calculations and
assigned an uncertainty limit of 0.010 Å; see text.
Table 5. Substitution Coordinatesa (Å) of Boron Atoms in
1,7-C2B10H12
coordinate
|a|
|b|
|c|
b
B2/B6
0.9082(12)
1.4259(8)
0.0
B3/B5/B8/B11
1.4437(9)
0.002(10)c
0.8797(12)
B4/B12
0.0b
0.8786(13)
1.4365(8)
B9/B10
0.9104(12)
1.4483(8)
0.0b
a
Uncertainties derived as described by van Eijck.51 b For symmetry
reasons. c This value was taken from the B3LYP calculations and
assigned an uncertainty limit of 0.010 Å; see text.
species has the same spectrum. The spectra of these species are
listed in Tables 6S9S in the Supporting Information, and the
spectroscopic constants are collected in Table 2.
Inspection of this table reveals that the spectroscopic constants of the B3 and B9 species are very similar. The assignment
of a spectrum to the B3 or the B9 isotopologue was made by
comparing the changes that 10B substitution in these two places
caused in the rotational constants calculated from the B3LYP
structure. These changes were compared with those found experimentally.
Ray’s asymmetry parameter κ,50 which is also listed in Table 2,
was seen to vary unusually much for the relatively small changes
in the rotational constants that substitution caused.
The spectrum of the 1,7-C211B10H12 isomer was assigned in a
similar manner as the 1,2-isomer and is listed Table 10S in the
Supporting Information. In this case, 160 transitions with J
quantum numbers between 7 and 24 were assigned for the 1,7isomer. Spectra of the 1,7-C210B11B9H12 isotopologues with 10B
in positions 2 (6), 3 (5, 8, 11), 4 (12), and 9 (10) are listed in
Tables 11S14S, respectively, in the Supporting Information.
The spectroscopic constants of the isotopologues of 1,7-C2B10H12
are collected in Table 3.
The rotational constants of the B2 and B9 species are very similar,
and the assignments were made in the same manner as described
for 1,2- species. There is a large variation in the asymmetry
pararamer κ in this case as well (Table 3).
Unfortunately, low-J transitions, which are used to determine
the dipole moment from their Stark effects, were too weak to
allow a dipole-moment determination for both isomers.
Interestingly, a comparison of the experimental (Tables 2 and 3)
and B3LYP rotational constants of the 1,2- and 1,7- compounds
(Table 1) of the two parent C211B10H12 species reveals that the
experimental rotational constants are smaller than their B3LYP
counterparts by less than 1% in each case. A difference between
the experimental and B3LYP constants has to be expected because
the experimental constants are effective parameters, whereas the
B3LYP rotational constants were calculated from an approximate
Table 6. BoronBoron Bond Lengths (Å) in 1,2-C2B10H12
substitutiona
B3LYPa
GEDb
X-rayc
B3B4, B5B6, B3B8, B6B7
1.777(5)
1.774
1.788(6)
1.769(4)
B4B5, B7B8
B4B9, B5B11, B7B11, B8B9
1.778(2)
1.779(5)
1.780
1.776
1.794(8)
1.787(6)
1.775(3)
1.774(4)
1.773(4)
bond type
a
B4B10, B5B10, B7B12, B8B12
1.777(8)
1.773
1.787(6)
B3B9, B6B11
1.750(2)
1.759
1.774(9)
1.758(3)
B9B10, B9B12, B10B11, B11B12
1.790(1)
1.787
1.808(8)
1.786(4)
B10B12
1.780(2)
1.780
1.787(9)
1.776(3)
This work. b From Turner et al.4 c From Hardie and Raston.20
Table 7. BoronBoron Bond Lengths (Å) in 1,7-C2B10H12
substitutiona
B3LYPa
GEDb
X-rayc
B2B3, B2B8, B5B6, B6B11
1.761(8)
1.764
1.771(6)
1.763(3)
B2B6
1.816(2)
1.782
1.786(9)
1.778(2)
B3B4, B4B5, B8B12, B11B12
1.778(5)
1.778
1.801(5)
1.777(3)
B3B8, B5B11
1.759(2)
1.766
1.778(9)
1.767(2)
bond type
a
B3B9, B5B10, B8B9, B10B11
1.775(8)
1.775
1.780(6)
1.778(3)
B4B9, B4B10, B9B12, B10B12
1.794(1)
1.773
1.783(6)
1.772(3)
B9B10
1.821(2)
1.788
1.795(9)
1.782(2)
This work. b From Turner et al.4 c From Fox and Hughes.5
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The Journal of Physical Chemistry A
equilibrium structure. The small differences (less than 1%) between
the two sets of constants are, however, one indication that the
B3LYP structures (Tables 1S and 2S, Supporting Information)
are close to the equilibrium structures.
Substitution Structures. The assignment of the spectra of the
10
B isotopologues allows the substitution coordinates38 of the
boron atoms to be calculated by Kraitchman’s equations.39 The
Kraitchman coordinates used to calculate the BB bond lengths
are listed in Tables 4 (1,2-) and 5 (1,7-). No uncertainties have
been assigned to the coordinates that are zero for symmetry
reasons. The c coordinate of B4 (B5, B7, B8) of the 1,2- isomer
and the b coordinate of B3 (B5, B8, B11) of 1,7-C2B10H12 were
assumed to be the same, as was found for the B3LYP structures.
These two coordinates were assigned liberal uncertainty limits of
0.010 Å. The remaining uncertainties of the coordinates reported
in these two tables were calculated as recommended by van Eijck.51
The substitution coordinates of Tables 4 and 5 were used
to calculate the BB bond lengths appearing in Tables 6
(1,2-C2B10H12) and 7 (1,7-C2B10H12), where they are listed
together with the B3LYP, GED,4 and X-ray5,20 values. It can be
seen from these two tables that most of the bond lengths determined by the substitution method agree fairly well with the GED
values, but there are some notable differences too. For example,
the rs B3B9 and B6B11 bond lengths of 1,2-, which are
identical, are 0.024 Å shorter than the GED value (Table 6),4
whereas the rs B9B10 bond length of 1,7- is 0.026 Å longer than
its GED counterpart (Table 7).4 Interestingly, the substitution
bond lengths of the 1,2- isomer are shorter than the GED values
in most cases (see Table 6) and more similar to the B3LYP and
X-ray values, whereas there is no such trend for the substitution
bond lengths of 1,7-C2B10H12 (Table 7).
’ CONCLUSIONS
The MW spectra of the parent ortho- and meta-carboranes
(1,2-C211B10H12 and 1,7-C211B10H12) have been recorded and
assigned for the first time, together with those of the four monosubstituted (10B) isotopologues of each of 1,2-C210B11B9H12 and
1,7-C210B11B9H12.
These two compounds contain more atoms (24) than the vast
majority of asymmetrical tops assigned thus far by MW spectroscopy. The MW spectra confirm that the structures of both of
these molecules are slightly distorted icosahedrons with C2v
symmetry. Accurate values for all BB bond lengths have been
determined by the substitution method.38 Comparison with the
bond lengths obtained by GED analysis subject to restrictions
from quantum chemical calculations reveals differences of up to
0.026 Å in a nonsystematic manner.
Most rs BB bond lengths are, in fact, more similar to the
B3LYP/6-311þþG(3df,3pd) and X-ray5,20 values than to the
GED4 results.
’ ASSOCIATED CONTENT
bS
Supporting Information. Results of the B3LYP/6311þþG(3df,3pd) calculations and microwave spectra. This material is available free of charge via the Internet at http://pubs.acs.org.
’ AUTHOR INFORMATION
Corresponding Author
*Tel.: þ47 2285 5674. Fax: þ47 2285 5441. E-mail:
harald.mollendal@kjemi.uio.no.
ARTICLE
’ ACKNOWLEDGMENT
We thank Anne Horn for her skillful assistance and the Czech
Science Foundation (Project P208/10/2269) for financial support.
’ REFERENCES
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(2) Fein, M. M.; Bobinski, J.; Mayes, N.; Schwartz, N. N.; Cohen,
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(3) Grafstein, D.; Dvorak, J. Inorg. Chem. 1963, 2, 1128.
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