ARTICLE
pubs.acs.org/JPCA
Microwave Spectrum and Conformational Composition of
1-Vinylimidazole
Svein Samdal and Harald Møllendal*
Centre for Theoretical and Computational Chemistry (CTCC), Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern,
NO-0315 Oslo, Norway
bS Supporting Information
ABSTRACT: The microwave spectrum of 1-vinylimidazole has been investigated in
the 2180 GHz spectral region. The spectra of two conformers have been assigned.
One of these forms is planar, while the other is nonplanar with the imidazole ring and
the vinyl group forming an angle of 15(4)° from coplanarity. The planar form is found
to be 5.7(7) kJ/mol more stable than the nonplanar rotamer by relative intensity
measurements. The spectra of 10 vibrationally excited states of the planar form and one
excited-state spectrum of the nonplanar form were assigned. The vibrational frequencies of several of these states were determined by relative intensity measurements. The
microwave work has been augmented by quantum chemical calculations at the CCSD/
cc-pVTZ, MP2/cc-pVTZ, and B3LYP/cc-pVTZ levels of theory. The B3LYP calculations predict erroneously that both forms of 1-vinylimidazole are planar, whereas the MP2 and CCSD calculations correctly predict
the existence of a planar and a nonplanar conformer of this compound.
’ INTRODUCTION
Imidazole is a prototype aromatic compound. The imidazole
group is found in the essential amino acid histidine and is
consequently present in a large variety of biologically important
substances. An accurate structure of gaseous imidazole has been
determined,1 but there are relatively few investigations of
the structures and conformations of gaseous imidazole derivatives in spite of the biological importance of this group. However,
one example is histamine, which exists as a mixture of four
rotameric forms in the gas phase, as shown in a microwave (MW)
study.2
1-Vinylimidazole was chosen for study because it is an
important chemical with a wide variety of uses, such as formation of polymers,3,4 complexation with cations,512 and formation of corrosion inhibitors.13 In this work, the focus is on the
structural and conformational properties of free 1-vinylimidazole. A model of this compound with atom numbering is shown
in Figure 1. Rotation about the N4C9 bond can lead to
rotational isomerism. It is, for example, expected that conjugation of the π electrons of the imidazole ring with the π electrons
of the vinyl group would favor two completely planar conformers denoted I and II, which are depicted in Figure 1. Other
effects could result in nonplanar forms. The scant information
available for the gaseous composition of imidazole derivatives
combined with the interesting conformational structural and
conformational properties posed by 1-vinylimidazole motivated
the present research.
MW spectroscopy is an ideal tool to investigate delicate
conformational equilibria such as the one presented by 1-vinylimidazole due to its superior accuracy and resolution. This method
would, for example, reveal even the slightest deviation from
r 2011 American Chemical Society
Figure 1. Two conformers whose MW spectra were assigned in this
work. Atom numbering is given on conformer I. Conformer I was found
experimentally to be nonplanar with the vinyl and imidazole forming an
angle of 15(4)° from planarity, whereas II is planar. II is the preferred
form being 5.7(7) kJ/mol more stable than I.
planarity in a conformer of 1-vinylimidazole. The spectroscopic
work has been augmented by high-level quantum chemical
calculations, which were conducted with the purpose of obtaining
information for use in assigning the MW spectrum and investigating properties of the potential-energy hypersurface.
Received: March 11, 2011
Revised:
April 29, 2011
Published: June 07, 2011
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The Journal of Physical Chemistry A
ARTICLE
Table 1. CCSD/cc-pVTZ Structures of Conformers I and II
of 1-Vinylimidazole and the Experimental Structure of
Imidazole
I
II
imidazolea
136.4
bond length (pm)
C1N4
136.8
136.8
C1H5
107.5
107.7
C1N8
130.6
130.5
131.4
C2C3
C2H6
136.2
107.5
136.3
107.5
137.7
C2N8
138.2
138.3
138.2
C3N4
138.3
138.2
137.7
C3H7
107.5
107.3
N4C9
140.5
140.3
C9H10
108.0
108.1
Figure 2. B3LYP/cc-pVTZ (b) and MP2/cc-pVTZ (9) potential
function for rotation about the N4C9 bond. The C1N4C9C11
dihedral angle is the abscissa, and the internal energy difference is the
ordinate. The B3LYP calculations predict that I is completely planar
(dihedral angle = 0°), whereas MP2 calculations find that this conformer
is nonplanar with a dihedral angle of 17.2° from planarity. Both methods
of calculations predict that II is completely planar and more stable than I
by about 3.5 kJ/mol.
C9C11
133.1
133.1
C11H12
C11H13
107.8
108.0
107.8
107.9
’ EXPERIMENTAL SECTION
bond angle (deg)
N4C1H5
122.0
121.3
N4C1N8
112.6
112.9
H5C1N8
125.4
125.9
C3C2H6
128.0
127.8
C3C2N8
110.5
110.9
Microwave Experiment. A sample from Aldrich was used as
H6C2N8
121.5
121.4
received. No impurities were detected in the MW spectrum. The
spectrum of 1-vinylimidazole was studied in the 2180 GHz
frequency interval by Stark-modulation spectroscopy using the
microwave spectrometer of the University of Oslo. Details of the
construction and operation of this device have been given
elsewhere.1416 This spectrometer has a resolution of about
0.5 MHz and measures the frequency of isolated transitions with
an estimated accuracy of ∼0.10 MHz. Radio-frequency microwave double-resonance experiments (RFMWDR), similar to
those performed by Wodarczyk and Wilson,17 were also conducted to unambiguously assign particular transitions using the
equipment described elsewhere.14 The spectra were measured at
room temperature with a pressure of roughly 10 Pa, which is
somewhat less than the vapor pressure.
Quantum Chemical Methods. The present ab initio calculations were performed employing the Gaussian 03 suite of
programs,18 running on the Titan cluster in Oslo. Becke’s
three-parameter hybrid functional19 employing the Lee, Yang,
and Parr correlation functional (B3LYP)20 was employed in the
density functional theory (DFT) calculations. MøllerPlesset
second-order perturbation calculations (MP2)21 and coupledcluster calculations with singlet and doublet excitations
(CCSD)22,23 were also performed. The CCSD calculations are
very costly and were speeded up by making use of a B3LYP force
field that was calculated prior to the CCSD calculations.
Peterson and Dunning’s24 correlation-consistent cc-pVTZ
basis set, which is of triple-ζ quality, was used in the calculations.
C2C3N4
C2C3H7
105.9
132.6
105.6
132.0
N4C3H7
121.6
122.4
C1N4C3
106.1
106.1
C1N4C9
128.7
124.8
C3N4C9
C1N8C2
125.2
105.0
129.1
104.6
N4C9H10
113.0
112.8
N4C9C11
H10C9C11
125.7
121.4
125.7
121.5
C9C11H12
119.2
119.3
C9C11H13
122.8
122.7
H12C11H13
117.9
118.0
112.0
110.7
105.5
106.9
104.9
dihedral angle (deg)
’ RESULTS AND DISCUSSION
Quantum Chemical Calculations. The electronic energy
potential function for rotation about the N4C9 bond was first
calculated at both the B3LYP/cc-pVTZ and the MP2/pVTZ
7560
H5C1N4C3
178.9
H5C1N4C9
1.7
0.0
N8C1N4C3
0.1
0.0
N8C1N4C9
179.4
180.0
N4C1N8C2
0.1
0.0
H5C1N8C2
179.0
180.0
180.0
H6C2C3N4
179.9
180.0
H6C2C3H7
N8C2C3N4
0.4
0.3
0.0
0.0
N8C2C3H7
179.8
180.0
C3C2N8C1
0.2
0.0
H6C2N8C1
180.0
180.0
C2C3N4C1
0.2
0.0
C2C3N4C9
179.3
180.0
H7C3N4C1
179.8
180.0
H7C3N4C9
0.3
0.0
dx.doi.org/10.1021/jp202319q |J. Phys. Chem. A 2011, 115, 7559–7565
The Journal of Physical Chemistry A
ARTICLE
Table 1. Continued
Table 2. CCSD/cc-pVTZ and B3LYP/cc-pVTZ Parameters
of Spectroscopic Interest of Conformers I and II of
1-Vinylimidazole
II
C1N4C9H10
C1N4C9C11
169.3
10.5
0.0
180.0
C3N4C9H10
11.3
180.0
C3N4C9C11
168.9
0.0
N4C9C11H12
178.8
180.0
A
8184.1
8325.2
0.0
B
2121.6
2106.2
0.0
C
1689.0
N4C9C11H13
a
imidazolea
I
1.2
H10C9C11H12
1.0
H10C9C11H13
178.9
I
II
rotational constants (MHz)a
1681.0
20
180.0
inertial defect (10
Taken from Christen et al.1
Δ
2 a
um )
0.74
0.00
b
quartic centrifugal distortion constants (kHz)
levels of theory by varying the C1N4C9C11 dihedral angle
and optimizing the geometry at each selected dihedral angle. This
dihedral angle is 0° if I is exactly planar and 180° if II is exactly
planar. The harmonic vibrational frequencies were calculated for
the stationary points to check whether these points were true
extremal points.
The two potential functions are drawn in Figure 2. The B3LYP
curve (circles) has minima at exactly 0° and 180°, which means
that both conformers I and II are predicted to be planar. The
electronic energy difference between I and II was predicted to be
3.73 kJ/mol, with II as the low-energy conformer. The transition
state (maximum of the curve) is found for a dihedral angle of
96.7°, with an energy that is 19.99 kJ/mol higher than that of II.
The MP2 curve (squares in Figure 2) is somewhat different from
its B3LYP counterpart. In this case, the electronic energy difference
is 3.65 kJ/mol, with II as the more stable rotamer. This conformer is
again predicted to be planar. However, I is now found to be
nonplanar with a C1N4C9C11 dihedral angle of 17.2° from
planarity. The barrier to planarity (the C1N4C9C11 dihedral
angle equal to 0°) is as low as 164 J/mol. The transition state at
96.1° is 16.49 kJ/mol higher in energy than II. This value is about
3 kJ/mol less than that found in the B3LYP calculations above.
The optimized B3LYP and MP2 geometries of I and II are
listed in the Supporting Information, Table 1S. The rotational
constants, Watson’s quartic centrifugal distortion constants,
dipole moments, and energy differences are listed in Table 2S,
Supporting Information. The dipole moments have been transferred from the standard orientation system to the principal
inertial axis system using Bailey’s program.25 The energy differences reported in the latter table are electronic energies corrected
for zero-point vibrational effects. These differences differ slightly
from the electronic energy differences quoted above.
Both the B3LYP and the MP2 calculations predict that two
rotamers exist for 1-vinylimidazole: conformers I, which may
(B3LYP) or may not (MP2) be planar, and II, which is predicted
to be planar in both computational procedures. This ambiguity
prompted us to repeat calculations of I and II at the very high
CCSD/cc-pVTZ level of theory. Nonplanar starting geometries
were employed in these two cases. These CCSD calculations
predict that II is planar, while I is found to be nonplanar. The
C1N4C9C11 dihedral angle of I is calculated to be 10.5°,
and the electronic energy difference is 3.46 kJ/mol. The barrier to
planarity (The C1N4C9C11 dihedral angle equal to 0°) was
also calculated and found to be only 20 J/mol. The CCSD
geometries are listed in Table 1; the rotational constants, dipole
moments, and electronic energies are listed in Table 2, which also
includes the B3LYP Watson’s A-reduction quartic centrifugal
distortion constants.26
ΔJ
0.083
0.083
ΔJK
2.11
1.92
ΔK
8.17
8.37
δJ
0.0085
0.0094
δK
0.805
0.752
30
dipole moment (10
a
C m)
μa
9.09
10.46
μb
μc
6.64
0.02
0.79
0.00
μtot
11.26
10.49
electronic energy differencesa,c (kJ/mol)
ΔE
3.46
0.0
CCSD result. b B3LYP result. c Electronic energy of II: 795567.83 kJ/
mol.
a
The accurate substitution27,28 (rs) structure of imidazole1 is
listed in Table 1 for comparison with the CCSD predictions
for the imidazole group. It is seen from this table that the
CCSD bond lengths of this group are in good agreement with
the rs bond lengths. The largest difference is found for the C2C3
bond length, which is about 1.5 pm longer in imidazole. The bond
angles of the imidazole moiety of the title compound agree to
within better than 1° with their counterparts in imidazole.
Assignment of the Spectrum of II. Searches for the a-type
R-branch spectrum of II were first made because this rotamer was
predicted to be 34 kJ/mol more stable than I. Moreover, II has
a substantial dipole moment of 10.46 1030 C m along the
a-inertial axis (Table 2). The rotational and centrifugal constants
of Table 2 were used to predict the approximate spectral positions
of the aR spectrum. The asymmetry parameter k29 is approximately 0.87 in this case, and pile ups of high-K-1 a-type R-branch
transitions would occur at frequencies separated by roughly the
sum of the rotational constants B þ C. These transitions are
modulated at low Stark voltages because pairs of K-1 lines are
practically degenerate. The pile-up regions were expected to
contain not only the spectrum of the ground vibrational state
but also the spectra of several vibrationally excited states as well,
because the MP2 calculations found that there are four harmonic
fundamental vibrational frequencies below 500 cm1, namely, at
69, 222, 242, and 488 cm1 (not given in Table 2), indicating that
several excited states will be well populated. The first two of these
fundamentals are out-of-plane vibrations of A00 symmetry, while
the last two are in-plane vibrations of A0 symmetry.
A survey spectrum taken at a Stark field strength of about
110 V/cm revealed a series of such pile ups, which are relatively
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The Journal of Physical Chemistry A
ARTICLE
Table 3. Spectroscopic Constantsa of Conformer II of 1-Vinylimidazole
first torsionb
ground
second torsionb
third torsionb
fourth torsionb
A (MHz)
8244.13(15)
8201.95(12)
8161.26(17)
8122.76(20)
8085.74(33)
B (MHz)
2100.6250(34)
2102.3985(40)
2103.9410(49)
2105.2849(52)
2106.4105(94)
C (MHz)
1675.5178(33)
1680.3515(40)
1684.9555(49)
1689.3671(52)
1693.647(10)
Δc (1020 u m2)
0.261(2)
1.241(2)
2.194(2)
3.117(3)
4.030(5)
ΔJ (kHz)
0.0973(44)
0.1041(18)
0.1094(22)
0.1141(26)
0.1313(43)
ΔJK (kHz)
0.568(24)
0.4948(43)
0.4612(48)
0.4382(65)
0.513(16)
ΔK (kHz)
8.37d
8.37d
8.37d
8.37d
8.37d
δJ (kHz)
δK (kHz)
0.0216(26)
1.05(24)
0.0192(28)
0.99d
0.0261(44)
0.99d
0.0295(38)
0.99d
0.0281(63)
0.99d
rmse
1.62
1.87
1.95
2.21
2.69
no. of transitionsf
370
324
292
246
135
a
A Reduction Ir representation.26 Uncertainties represent one standard deviation. Spectra are listed in Tables 3S7S in the Supporting Information.
Torsion about the N4C9 bond. c Δ = Ic Ia Ib, where Ia, Ib, and Ic are the principal moments of inertia. d Fixed. e Root-mean-square deviation for a
weighted fit. f Number of transitions used in the fit.
b
Table 4. Spectroscopic Constantsa of Exited States of Bending Vibrations of 1-Vinylimidazole
Table 5. Spectroscopic Constantsa of Exited Combination
States of 1-Vinylimidazole
first ex.
second ex.
first ex. second
first ex. N4C9 first ex. N4C9
first ex. N4C9
lowest bend.
lowest bend.
lowest bend.
torsion þ lowest torsion þ lowest
torsion þ second
bending vib.
bending vib.
lowest bending vib.
A (MHz)
B (MHz)
8155.34(28)
2102.0485(66)
8120.02(27)
2103.5345(80)
8269.95(27)
2102.5767(64)
0.545(3)
C (MHz)
1682.0145(73)
1686.4814(96)
1679.1901(62)
0.1023(78)
Δb (1020 u m2)
1.931(4)
2.862(4)
0.506(3)
0.0846(71)
A (MHz)
8192.43(22)
8144.63(44)
8315.94(29)
B (MHz)
C (MHz)
2100.3316(50)
1677.3196(52)
2100.200(9)
1679.138(9)
2100.7707(59)
1674.0725(62)
Δb (1020 u m2)
1.006(3)
1.709(5)
ΔJ (kHz)
0.0989(68)
0.1075(45)
ΔJK (kHz)
0.650(39)
0.740(12)
0.415(44)
ΔJ (kHz)
0.0788(77)
0.1023(75)
ΔK (kHz)
8.37c
8.37c
8.37c
ΔJK (kHz)
0.779(45)
0.628(43)
0.143(39)
δJ (kHz)
0.0114(42)
0.0260(65)
0.0317(52)
ΔK (kHz)
8.37c
8.37c
8.37c
δK (kHz)
1.29(39)
0.994c
0.44(44)
δJ (kHz)
0.0424(44)
0.0291(57)
0.0304(44)
1.87
247
1.93
95
1.97
236
δK (kHz)
rmsd
2.10(49)
2.07
1.55(45)
2.06
0.88(40)
2.00
155
139
d
rms
no. of transitionse
a
Reduction Ir representation.26 Uncertainties represent one standard
deviation. Spectra are listed in Tables 8S10S in the Supporting Information. b Inertial defect defined by Δ = Ic Ia Ib, where Ia, Ib, and Ic are the
principal moments of inertia. c Fixed. d Root-mean-square deviation for a
weighted fit. e Number of transitions used in the least-sqares fit.
weak and have the expected complicated fine structure. Only very
weak lines were observed between the pile ups. The transitions of
the pile ups were used to get the first assignment of the spectrum.
The assignments of several of these lines were confirmed by
RFMWDR experiments. The low K-1 aR lines were assigned next.
No b-type lines were found, presumably because μb is predicted
to be as small as 0.79 1030 C m (Table 2). 1-Vinylimidazole
has two nitrogen nuclei, which may produce a quadrupole
hyperfine structure. However, no splittings due to this effect
were seen. Ultimately, a total of 370 aR transitions shown in
Table 3S in the Supporting Information were included in the
least-squares fit. The resulting Watson A reduction26 spectroscopic constants are listed in Table 3. The centrifugal distortion
effect is not large in this spectrum, and only four of the five
quartic centrifugal distortion constants could be determined. The
fifth, ΔK, was preset in the fit at the B3LYP/cc-pVTZ value
(Table 2). It is noted that the inertial defect, Δ, is 0.261(2) 1020 u m2, which is typical for a planar molecule (CS symmetry)
with a low-frequency out-of-plane vibration.30
no. of transitionse 145
a
Reduction Ir representation.26 Uncertainties represent one standard
deviation. Spectra are listed in Tables 11S13S in the Supporting
Information. b Inertial defect defined by Δ = Ic Ia Ib, where Ia, Ib, and
Ic are the principal moments of inertia. c Fixed. d Root-mean-square
deviation for a weighted fit. e Number of transitions used in the leastsqares fit.
Vibrationally Excited States of II. The ground-state transitions were accompanied by several less intense lines, which
presumably belong to vibrationally excited states of this conformer.
A total of 10 vibrationally excited states were assigned. Their
spectroscopic constants are listed in Tables 3 5. The assignments
of these excited-state spectra were made in the same manner as
described for the ground state.
The strongest excited-state spectrum was assumed to belong
to the first excited state of the torsion about the N4C9 bond,
whose MP2 harmonic vibrational frequency is 69 cm1. A total of
324 transitions (Table 4S, Supporting Information) were assigned for this state, whose spectroscopic constants are listed in
Table 3.
Relative intensity measurements observing the precautions of
Esbitt and Wilson31 yielded 72(25) cm1 for this vibration, in fair
agreement with the calculations (69 cm1). It is also possible to
derive the torsional frequency by using the changes in the inertial
7562
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The Journal of Physical Chemistry A
defect, Δ, upon excitation provided the torsional frequency is
well separated from the other fundamentals, which is the case for
rotamer II, since the second lowest B3LYP frequency is
244 cm1. Using the expression of Hanyu et al.,32 a frequency
of 69 cm1 is obtained in excellent agreement with the experimental value of 72(25) cm1 and identical with the MP2 value.
Three further vibrationally excited states of the torsion were
assigned, as indicated in Table 3 (spectra in Tables 5S7S,
Supporting Information). The changes in the rotational constants upon excitation as well as the inertial defect vary regularly,
as can be seen from the entries in Table 3. This regular variation is
typical for a harmonic vibration.3335
Three excited states of two bending vibrations were assigned.
The spectroscopic constants of these excited states are listed in
Table 4, whereas the spectra are found in Tables 8S10S,
Supporting Information. The inertial defect of what is assumed
to be the lowest bending vibration is seen to take a negative value
of the inertial defect of 1.006(3) 1020 u m2 (Table 4),
which is typical for an out-of-plane vibration. Relative intensity
measurements yielded 170(30) cm1 for this mode, compared to
the MP2 value of 222 cm1. The second excited state of this
vibration was also assigned (Table 4). The variation of the
rotational constants upon excitation is again seen to be smooth
for these two excited states, which is a criterion for an essentially
harmonic vibration.
The spectrum of one more excited state was assigned
(Table 4) as the first excited state of the second lowest bending
vibration. The inertial defect is 0.545(3) 1020 u m2. The
positive value of this parameter is typical for an excited state of
an in-plane vibration (A0 species vibration). Relative intensity
measurements yielded 248(30) cm1 for this fundamental,
compared to 242 cm1 (MP2) for this mode.
The spectroscopic constants of three combination modes are
collected in Table 5, while the spectra are found in Tables 11S13S
of the Supporting Information. It is seen that their spectroscopic
constants are almost, but not exactly, the sum of the changes of the
rotational constants upon excitation of the two modes in question.
This criterion was used to assign the spectra of these excited states.
Assignment of the Spectrum of I. This rotamer was predicted
(Table 2) to be 34 kJ/mol less stable than II. The lowest MP2
harmonic vibrational frequencies (not given in Table 2) are 57,
203, 238, and 490 cm1. The a-axis CCSD dipole moment is 9.09 1030 C m (Table 2), somewhat less than that of II (10.46 1030 C m). The rotational constants (Table 2) were calculated
to be rather similar to those of II, which means that the spectrum
of I would occur at frequencies close to those of II. The energy
difference and the lower dipole moment indicated that the
spectrum of I would be substantially weaker than that of II and
could also be overlapped by spectra of vibrationally excited states
of II. The RFMWDR method was used in an attempt to assign
the spectrum of I, because this method is so specific. These
experiments met with success, and we got the first assignments of
the comparatively weak spectrum of this conformer. The aRbranch transitions of this form were assigned in the same manner
as described above for conformer II. No b-type transitions were
identified, presumably because they are too weak, which is
consistent with the fact that μb is significantly smaller than μa
(Table 2). The spectrum of conformer I consisting of 199
transitions is listed in Table 14S of the Supporting Information,
and the spectroscopic constants are shown in Table 6. Interestingly, the inertial defect is 2.135(4) 1020 u m2, strikingly
different from 0.261 1020 u m2 found for the ground
ARTICLE
Table 6. Spectroscopic Constantsa of Conformer I of
1-Vinylimidazole
ground
first torsion
A (MHz)
8079.86(29)
8050.88(26)
B (MHz)
C (MHz)
2116.6368(79)
1689.2253(84)
2117.2088(77)
1693.8907(76)
Δb (1020 u m2)
2.135(4)
3.120(4)
ΔJ (kHz)
0.1035(41)
0.1181(43)
ΔJK (kHz)
0.454(10)
0.4515(88)
ΔK (kHz)
8.37c
8.37c
δJ (kHz)
0.0268(54)
0.0201(61)
δK (kHz)
0.99
0.990c
rmsd
no. of transitionse
2.67
199
2.58
170
a
Reduction Ir representation.26 Uncertainties represent one standard
deviation. Spectra are listed in Tables 14S and 15S in the Supporting
Information. b Inertial defect defined by Δ = Ic Ia Ib, where Ia, Ib, and Ic
are the principal moments of inertia. c Fixed. d Root-mean-square deviation
for a weighted fit. e Number of transitions used in the least-sqares fit.
vibrational state of II (Table 3). This large increase in the
absolute value of the inertial defect is evidence that I is nonplanar.
The spectrum of one vibrationally excited state of I was
assigned. The rotational constants of this state are displayed in
Table 6 (spectrum in Table 15S, Supporting Information). The
fact that the absolute value of the inertial defect increases
compared with its ground-state counterpart indicates that this
is an out-of-plane vibration, presumably the first excited state of
the torsion about the N4C9 bond.
Energy Difference. The energy difference between I and II was
obtained by comparing the intensities of selected ground-state lines
of the two conformers observing most of the precautions of Esbitt
and Wilson.31 The RFMWDR technique was used to modulate the
transitions and at the same time minimize the influence of overlapping lines. The internal energy difference of the ground states was
obtained as described by Townes and Schawlow,36 assuming a
Boltzmann population of the two forms. The energy difference was
found to be 5.7(7) kJ/mol, with II as the more stable form. The
statistical weight of I was assumed to be 2 compared to 1 for rotamer
II because there are two mirror-image forms of I but only one planar
form of II. This value is about 2.2 kJ/mol larger than predicted in
the CCSD (3.46 kJ/mol; Table 2) and the MP2 (3.45 kJ/mol;
Table 2S, Supporting Information) calculations.
Structures. Comparison of the theoretical rotational constants
of II (Table 2) with their ground-state experimental counterparts
(Table 3) reveals that there are small differences of ca. 6 MHz for
B and C, whereas a larger difference of 81 MHz (∼1%) exists for
A. The CCSD and experimental rotational constants are defined
differently. The CCSD constants are derived from an approximate
equilibrium structure, while the experimental rotational constants
reflect an effective (r0) structure. Differences of less than 1% are in
fact a good indication that the CCSD structure of II is indeed close
to the equilibrium structure. The fact that the experimental
structure of imidazole1 and the structure of the CCSD imidazole
moiety of 1-vinylimidazole are so similar, as discussed above, is
evidence pointing in the same direction.
The situation for I is more complicated than for II because I is
nonplanar. It is seen from Table 2 that the CCSD inertial defect is I
is 0.74 1020 u m2 for a C1N4C9C11 dihedral angle of
10.5°, whereas the MP2 inertial defect is 2.01 1020 u m2 for a
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The Journal of Physical Chemistry A
dihedral angle of 17.2° (Table 2S, Supporting Information). The
C1N4C9C11 dihedral angle must therefore be somewhat
larger than the CCSD value (10.5°) in order to reproduce the
observed inertial defect of 2.135(4) 1020 u m2. An estimate of
it was made in the following manner: The MP2 calculations (not
given in Table 2) predict that the torsional frequency of rotamer I of
the N4C9 bond is 57 cm1. Using the expression by Oka30 for the
inertial defect’s dependence of the lowest torsional mode, the
contribution from this mode should be roughly 0.50 1020 u m2. Subtracting this value from the observed inertia
defect, one finds 1.61 1020 u m2, which should be due to the
out-of-plane atoms. The C1N4C9C11 dihedral angle was
varied in order to reproduce this value keeping the bond
distances and angles fixed at the CCSD values (Table 1). A
C1N4C9C11 dihedral angle of 15° was found to reproduce the inertial defect of 1.61 1020 u m2. A liberal
uncertainty limit is estimated to be (4°.
’ DISCUSSION
There are presumably several reasons why conformer II is
preferred by 5.7(7) kJ/mol relative to I. Nonbonded repulsion is
one of the factors that should be considered. It is seen from
Figure 1 that there are short nonbonded contacts between H5
and H13 and between H7 and H10 in conformer I. A similar
situation is found in II for the H5 and H10 pair and between the
H7 and H13 pair. These distances are 236 and 250 pm,
respectively, in I where the C1N4C9C11 dihedral angle
has been fixed at 15° and the other structural parameters kept at
the CCSD values shown in Table 1. These values should be
compared to the CCSD distances of 243 and 231 pm for the
nonbonded H5 3 3 3 H10 and H7 3 3 3 H13 in II. The sum of the
Pauling van der Waals distances of two hydrogen atoms is 240 pm.37
There should be no or very little repulsion in both forms because the
nonbonded contacts are roughly equal to twice the van der Waals
distance of hydrogen.
Another effect that needs consideration is the conjugation
of the π electrons of the imidazole ring with the π electrons of the
vinyl moiety. This effect should have a maximum for completely
planar forms of 1-vinylimidazole, and this is consistent with the
conformational choice of II. However, some of the π-electron
conjugation must be lost for unknown reasons in the nonplanar rotamer I, and this increases the energy of this form by
5.7(7) kJ/mol at the same time.
’ ASSOCIATED CONTENT
bS
Supporting Information. Results of the theoretical calculations and the microwave spectra. This material is available
free of charge via the Internet at http://pubs.acs.org.
’ AUTHOR INFORMATION
Corresponding Author
*Phone: þ47 2285 5674. Fax: þ47 2285 5441. E-mail:
harald.mollendal@kjemi.uio.no.
’ ACKNOWLEDGMENT
We thank Anne Horn for her skillful assistance. We are grateful
to an anonymous reviewer for pointing out errors in the manuscript. The Research Council of Norway (Program for Supercomputing) is thanked for a grant of computer time.
ARTICLE
’ ADDITIONAL NOTE
An anonymous reviewer suggested using the M05-2X functional38
in the DFT calculations instead of the B3LYP functional in order to
see whether a nonplanar form would be predicted for conformer I.
M05-2X/cc-pVTZ calculations have therefore been undertaken.
These calculations indeed predict I to be nonplanar with a
C1N4C9C11 dihedral angle of 11°.
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