Microwave Spectra, Planarity, and Conformational
Preferences of cis- and trans-N-Vinylformamide
Harald Møllendal* and Svein Samdal
Centre for Theoretical and Computational Chemistry (CTCC), Department of Chemistry,
University of Oslo, P. O. Box 1033 Blindern, NO-0315 Oslo Norway.
Received: September 26, 2012
1
ABSTRACT
The microwave spectra of a mixture of cis- and trans-H‒N‒C‒O forms of Nvinylformamide, (H2C=CHNHC(=O)H) have been measured at room temperature in the 18 – 75
GHz spectral range. The spectra of two forms were assigned. The first of these forms has a cis
arrangement for the H‒N‒C‒O chain of atoms, whereas the second form has a trans arrangement.
The C‒C‒N‒C chain of atoms is antiperiplanar (180º) in both forms. The inertial defect of the
ground vibrational state of cis is ‒0.142(5) × 10‒20 u m2, whereas this parameter is ‒0.087098(26)
× 10‒20 u m2 for trans. It is concluded that the equilibrium structures of both cis and trans are
completely planar. The dipole moment determined from Stark effect measurements is a =
9.96(8), b = 2.22(3), c = 0 (by symmetry), and tot = 10.20(8) × 10‒30 C m [3.06(2) D], for cis,
while a = 7.64(16), b = 9.24(10), c = 0 (by symmetry), and tot = 12.0(2) × 10‒30 C m [3.59(5)
D] for trans. The spectrum of one vibrationally excited state, presumably the first excited state of
the torsion about the C‒N bond of cis, was assigned and the frequency of this state was
determined to be 76(15) cm‒1 by relative intensity measurements. The spectra of two
vibrationally excited states of trans were assigned. These states are assumed to be the first
excited state of the torsion about the C‒N bond, and a low bending vibration. Relative intensity
measurements yielded 101(20) and ca 300 cm‒1, respectively, for the frequencies of these normal
vibrations. Accurate values of the quartic centrifugal distortion constants, the dipole moments,
and the vibration-rotation constants have been obtained for both cis and trans. The experimental
work has been augmented by high-level quantum chemical calculations at the B3LYP/cc-pVTZ
and CCSD(T)/cc-pVTZ levels of theory. The theoretical calculation performed without symmetry
restrictions correctly predict that cis and trans are both planar. The CCSD(T) rotational constants
2
are in excellent agreement with their experimental counterparts, whereas the B3LYP quartic
centrifugal distortion constants and the vibration-rotation constants are in fairly good agreement
with experiments. The CCSD(T) dipole moments deviate more than expected from the
experimental dipole moments. It is estimated that further conformers of cis and trans must be at
least 4 kJ/mol higher in energy.
3
INTRODUCTION
The peptide linkage, ‒C(=O)NH‒, found in amides is an essential feature of proteins. The
properties of amides are therefore of great biological as well as chemical interest.1-3 Amides are
crystalline substances with comparatively low sublimation pressures, or liquids of low volatility
at room temperature. Intermolecular hydrogen bonding is prevalent in condensed phases of Nunsubstituted and N-monosubstituted amides due to the proton accepting oxygen atom and the
hydrogen atom(s) attached to the nitrogen atom. Many of these substances therefore form
hydrogen-bonded networks in the crystalline state.2 Extensive hydrogen bonding and crystal
effects may therefore obscure the genuine structural and conformational properties of this class of
compounds.
X-ray crystallography may provide excellent knowledge of crystal structures and
conformations of solid amides, but the gas phase properties may, for reasons already stated, be
significantly different from the condensed-phase properties. Experimental studies of amides in
the gas phase at low pressures augmented with modern, high-level quantum chemical calculations
are therefore preferred in order to obtain the best possible insight in the true, unperturbed
structural and conformational preferences of this class of compound.
Gas electron diffraction (GED) and microwave (MW) spectroscopy are the experimental
methods of choice for gas-phase investigations due to their high resolution. Unfortunately, the
low vapor pressures of amides and their tendency to decompose when heated have made gasphase studies of amides less accessible than for compounds containing other functional groups
resulting in a relatively limited literature about this class of compounds. The relative scarcity of
studies of gaseous amides and their great biological and chemical interest motivated our
4
laboratory to undertake investigations of them using the GED method and MW spectroscopy in
combination with quantum chemical calculations. Our previous studies include acetamide
(CH3CONH2),4 2-fluoroacetamide (CH2FCONH2),5,
6
2-chloroacetamide (CH2ClCONH2),6,
7
2-
iodoacetamide (CH2ICONH2),8 2,2-difluoroacetamide (CF2HCONH2)9 2,2-dichloroacetamide
(CHCl2CONH2),10 2-chloro-2,2-difluoroacetamide (CF2ClCONH2),11 2,2,2-trifluoroacetamide
(CF3CONH2),12 2,2,2-trichloroacetamide (CCl3CONH2),13 propionamide (CH3CH2CONH2),14
formic hydrazide (H2NNHCHO),15 acrylamide (H2C=CHCONH2),16 methyl carbamate
(CH3OCONH2),17,
18
methoxyacetamide
(CH3OCH2CONH2),19
and
2-azetidinone.20,
21
Experimental contributions from other laboratories include, for example, the prototype
formamide (HCONH2),22-24 urea (H2NCONH2),25 H‒N‒C‒O-cis- and trans- N-methyl formamide
(HCONHCH3),26
N,N-dimethylformamide
(HCON(CH3)2),27
H‒N‒C‒O-trans-N-
ethylformamide (HCONHCH2CH3),28 H‒N‒C‒O-cis-methoxyformamide (HCONHOCH3),29 H‒
N‒C‒O-trans-formanilide
methylacetamide
(C6H5NHCHO),30,
(CH3CONHCH3),36
31
acetamide,32-35
H‒N‒C‒O-trans-N-
H‒N‒C‒O-trans-N-methylpropionamide
(CH3CONHCH2CH3)37 H‒N‒C‒O-trans-acetanilide (CH3CONHC6H5),38 and alaninamide
(H2NCH2CONH2).39
These studies have revealed a number of interesting, and in some cases, unexpected
findings. It has, for example, often been assumed that the amide group as a rule is completely
planar, which is consistent with a significant weight of the ‒O‒C=N+ resonance structure.
However, a study based on accurate MW data and very high-level quantum chemical
calculations40 of several small amides concluded that only one of the investigated compounds,
namely formamide, is planar, whereas all the other amides in this study were found to have non-
5
planar amide groups in the free state. It therefore appears that a planar amide group in gaseous
amides is the exception rather than the rule.
The planarity problem is not the only interesting feature of amides. Recent studies have
revealed a number of unexpected properties. Acetamide is one example of an amide displaying an
unusual behavior. First, the conformation of the methyl group is exceptional in that one of the C‒
H bonds is almost perpendicular to the heavy atom framework according to very high-level ab
initio calculations,4 which also found that its amide group is non-planar. Interestingly, the barrier
to internal rotation of this group is only 0.30466413(14) kJ/mol,35 much lower than, for example,
the methyl barrier in the isoelectronic compound acetic acid (2.01258(20) kJ/mol).41 There are
also significant changes in the barrier heights of the methyl group when the amide group
hydrogen atoms are substituted with deuterium atoms due to coupling of the methyl torsion with
the amide group inversion.35 Remarkably, the small perturbation caused by deuterium
substitution has a substantial influence on the electronic structure of the peptide linkage.35
Moreover, while conformational mixtures in crystalline amides are very rare, this
phenomenon is expected to be much more prevalent in the gas phase. However, so far acrylamide
appears to be the only amide for which more than one rotameric form has been safely assigned by
MW spectroscopy.16
In this work, our amide investigations are extended to include the first MW study,
augmented with high-level quantum chemical calculations, of cis- and trans-N-vinylformamide
(H2C=CHNHC(=O)H), where cis and trans refer to the configuration of the H‒N‒C=O chain of
atoms. In both the two title compounds, the two -electron systems of the amide and vinyl
groups, respectively, are conjugated. Moreover, the CN bond connecting the amide and vinyl
6
groups has presumably a substantial -character. This opens up for rotational isomerism about
the said CN bond. There appears to be no experimental gas-phase structural work reported for
this kind of vinyl-amide rotational isomerism, but the MW spectra of the trans-forms of
formanilide30,
31
and acetanilide,38 which have some conformational resemblance to the title
compounds, are known.
The -electron conjugation implies that planar, or near-planar forms can be expected for
both cis and trans. Four representative forms, denoted I ‒ IV, are depicted in Figure 1, with atom
numbering indicated on I. The H7N6C8O9 chain of atoms is locked in a cis (forms I and II) or in
a trans (III and IV) configuration due to restricted rotation about the amide N6C8 bond. Rotation
about the C2N6 bond allows for rotational isomerism in both cis and trans. Four representative
conformers, namely, I and II of cis, and III and IV of trans, are indicated in Figure 1. The
C1C2N6C8 chain of atoms is exactly antiperiplanar in I and III, nearly synperiplanar in II, and
exactly synperiplanar in IV.
While no GED or MW studies have been reported for two N-vinylformamides, a recent
quantum chemical investigation exists.42 Using HF and B3LYP calculations with the 6311++G** basis set, it was predicted that I and III are both planar and have approximately the
same energy, while II and IV were found to be several kJ/mol less stable.42 II was predicted to be
slightly non-planar, whereas IV was found to be completely planar in these calculations.
The interesting structural and conformational problems presented by the two Nvinylamides motivated the present MW research, which has been augmented with quantum
chemical calculations performed at a much higher level of theory than previously employed42 in
7
order to obtain information which could be useful for the assignment of the MW spectra and for
investigating properties of the potential energy hypersurface.
RESULTS AND DISCUSSION
Experimental
Compound and MW Experiment. A commercial sample of N-vinylformamide was used
as received. The sample contained roughly 50% of both cis and trans as judged by the intensities
of the MW transitions. No impurities were noted. The MW spectra were recorded at room
temperature. N-Vinylformamide is a liquid at room temperature and has a vapor pressure of about
30 Pa at this temperature. The MW spectrum was studied in the 18 – 75 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.43-45 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 doubleresonance experiments (RFMWDR), similar to those performed by Wodarczyk and Wilson,46
were also conducted to unambiguously assign particular transitions, using the equipment
described elsewhere.
43
The spectra were measured at room temperature at a pressure of roughly
7 Pa.
Quantum Chemical Methods. The present ab initio calculations were performed
employing the Gaussian 0947 and Molpro48 programs, running on the Titan cluster in Oslo.
8
Becke’s three-parameter hybrid functional employing the Lee, Yang, and Parr correlation
functional (B3LYP)49 was employed in the density functional theory (DFT) calculations.
Coupled-cluster calculations with singlet and doublet excitations including non-iterative triplet
excitations, CCSD(T),50 were also performed. Peterson and Dunning’s51 correlation-consistent
cc-pVTZ basis set, which is of triple- quality was used in all the calculations.
Quantum Chemical Calculations. The conformational properties of the O9C8N6H7 cis
and trans forms were first explored. The variation of the energy with the C1C2N6C8 dihedral
angle can conveniently be used for this purpose. The energies were calculated while stepping the
dihedral angle in intervals of 10° allowing all remaining structural parameters to vary freely. The
B3LYP method was employed for these potential function calculations because CCSD(T)
calculations would have been far too expensive. The first calculations indicate that cis has
minima at 180 (I) and at about 20° (II), whereas trans has minima at 180 (III) and 0° (IV) of the
C1C2N6C8 dihedral angle. Calculations of the structures, dipole moments, vibrational
frequencies, quartic and sextic Watson A-reduction centrifugal distortion constants, and
vibration-rotation constants (the ´s), were then undertaken for the corresponding four
conformers. Due precautions were observed in the calculations of the vibration-rotation
interactions.52 All structural parameters were varied freely in these calculations with no symmetry
restrictions. No imaginary vibrational frequencies were found for any of these four forms, which
indicate that they are minima on the potential energy hypersurface. Selected results of these
calculations are listed in Tables 1S – 4S in the Supporting Information.
It is seen from these tables that I, III, and IV are predicted to be exactly planar, whereas
II is non-planar with a C1C2N6C8 dihedral angle of ‒20.6°. All four forms were predicted to
9
have completely planar amide groups. The electronic energy difference between I and II is
calculated to be rather large (12.2 kJ/mol) with I as the more stable conformer. Likewise, III is
predicted to be 8.9 kJ/mol more stable than IV. The energy differences corrected for harmonic
zero-point-vibrational interaction are 12.2 for the I – II pair, 9.7 for the III ‒ IV pair, and 0.3
kJ/mol for the difference between cis represented by I and trans III, with cis as the more stable
form.
The transition states of cis and trans were also explored. Two transition states, at 0º and
were 99.5º of the C1C2N6C8 dihedral angle were located for cis. The first of these transition
states at 0º has an energy of 12.4 kJ/mol above the energy of I, or only 0.2 kJ/mol above the
energy of II. The energy of the second transition state at 99.5º is 31.5 kJ/mol higher in energy
than the energy of I. The trans form has only one transition state at 90.9º of the said dihedral
angle. The energy of this state is 34.6 kJ/mol above the energy of III. The comparatively small
energies of the cis and trans transition states indicates that there is little double bond character in
the C2N6 bond. The data above allow potential functions for rotation about the C2N6 bond to be
drawn for cis and trans, as shown in Figures 2 and 3.
Much more comprehensive CCSD(T)/cc-pVTZ calculations of optimized structures,
dipole moments, nuclear quadupole coupling constants, and electronic energies of the four forms
I ‒ IV were finally undertaken. It was important to investigate whether these extensive
calculations predict a planar amide group. All starting conformations were therefore chosen to be
non-planar. The optimizations were done without symmetry restrictions employing the default
convergence criteria of Molpro. All four forms were predicted to have completely planar amide
groups. Moreover, conformers I, III, and VI were calculated to be exactly planar in this case,
10
while II was found to be non-planar with a C1C2N6C8 dihedral angle of ‒26.7°. The resulting
structures are listed in Table 1. The rotational constants calculated from these structures are
shown in Table 2. The dipole moment components of the Molpro calculations were transferred to
the principal-axes dipole moment components using Bailey’s program Axis53 with the results
listed in Table 2. The CCSD(T) electric field gradients were calculated with Gaussian 09 using
the structures in Table 2. Results of these calculations were employed to calculate the principal
axis nuclear quadrupole coupling constants of the
14
N nucleus shown in Table 2 using the
program Nqc53. Calculation of the centrifugal distortion constants by the CCSD(T) method is
beyond our computational resources. The B3LYP quartic centrifugal distortion constants in the
A-reduction form are therefore included in Table 2.
The results in Tables 1 and 2 warrant further comments. The non-planarity of II may
result from non-bonded repulsion between the H4 and H10 atoms. This CCSD(T) distance (not
given in Table 1) is 228 pm, compared to 240 pm, which is twice the Pauling van der Waals
radius of hydrogen.3 A planar conformation of II would have brought these two hydrogen atoms
into considerable closer proximity with increased repulsion as a result. The effect of a maximal
conjugation stabilization of a completely planar II therefore appears to be insufficient to offset
the ensuing non-bonded repulsion in this case.
The situation in the planar IV rotamer is different. There is a short contact between H4
and O9 atoms in this case. The CCSD(T) non-bonded distance is as short as 231 pm compared to
the Pauling van der Waals3 sum (260 pm) of hydrogen (120 pm) and oxygen (140 pm). It is
possible that the overall effect of this close contact results in stabilization of the planar form due
to the electronegative character of oxygen and the electropositive property of hydrogen. Whether
11
this contact should be called an intramolecular hydrogen bond is a matter of semantics.
The corresponding bond lengths (Table 1) of all forms are remarkably similar, varying by
less than 0.5 pm. Partial loss of -electron conjugation in II relative to the three other forms (I,
III, and IV) therefore seems to influence its C2N6 bond length, as well as other bond lengths, to
a minor degree.
The N6C8 bond lengths of I ‒ IV vary between 137.0 and 137.3 pm (Table 1), compared
to 135.47 pm found for the equilibrium NC bond length in formamide.40 A lengthening of this
bond in the title compound compared to the corresponding bond in formamide could perhaps be
due to delocalization of -electron density of the amide group into the vinyl part with an
increased bond length as a result. The C8O9 bonds of I – IV should also be affected by
conjugation, but their lengths vary little and are about 0.4 pm longer than the corresponding
equilibrium bond length in formamide.40 Conjugation should also influence the C1C2 bond
length in the title compound. There is a report of the rz value [133.91(13) pm] of the CC bond
length in ethylene,54 which is the same as 133.9 – 134.0 pm calculated for the C1C2 bond lengths
of the four conformers in Table 1.
It is noted that most corresponding bond angles in Table 1 are quite similar. The largest
differences are seen for the C1C2N6 and C2N6C8 angles of the III – IV pair, where the larger
angles (by 3 ‒ 4°) are found in IV. The short non-bonded contact between H4 and O9 mentioned
above may have resulted in a opening up of this angle due to a repulsive interaction, which is
effectively countered by electron conjugation and hydrogen-bond like stabilization.
The energy differences of the rotamer pairs are interesting. The CCSD(T) electronic
12
energy of I is lower than that of II by 9.6 kJ/mol (Table 2) compared to 12.2 kJ/mol obtained in
the B3LYP calculations above. A difference of this order of magnitude found in the two methods
is to be expected.
A much larger variance is found for the III – IV pair. The CCSD(T) method yields 2.4
kJ/mol, whereas the B3LYP method predicts 9.7 kJ/mol. A smaller energy difference was
expected for the III – IV pair than for the I – II pair because the two conformers of the first pair
are both planar and the full effect of -electron conjugation is preserved for both forms. The nonbonded interaction between the oxygen atom O9 the hydrogen atom H4 could also be of
importance for the reduced energy difference for this pair compared to the I – II pair.
Finally, the energy difference between trans and cis is also of interest. The CCSD(T)
electronic energy difference between cis and trans represented by I and III is 2.8 kJ/mol, with I
as the global minimum, while the corresponding B3LYP difference given above is 0.3 kJ/mol.
MW Spectrum and Assignment of the MW Spectrum of Form I. The MW spectrum
of the two N-vinylformamides was found to be dense with absorption lines occurring every few
MHz throughout the MW region. A high spectral density was expected because both cis and
trans forms contribute to the spectrum.
The spectrum of I was first searched for. This rotamer was predicted to be the preferred
form of cis in the quantum chemical calculations above. This conformer is very prolate with
Ray’s asymmetry parameter55  ≈ ‒0.99. Its major dipole moment component is a, predicted to
be as large as 10 ‒ 11 × 10‒30 C m (Table 2). A relatively intense series a-type R-branch pile-ups
of MW transitions separated by almost exactly the sum of the B and C rotational constants was
13
predicted for its spectrum.
These predictions turned out to be correct and the spectrum of the ground vibrational
state, which is shown in Table 5S in the Supporting Information, was readily assigned. The
assignments of several of its transitions were confirmed by RFMWDR experiments. Only aRtransitions with J values up to 15 with K‒1between 0 and 4 were used to determine the
spectroscopic constants listed in Table 1 because other K‒1-transitions were frequently
overlapped. b-type lines were searched for, but not definitely identified presumably because they
are comparatively weak, which is consistent the fact that a is almost than 5 times larger than b
(see dipole moment section below). The quadrupole hyperfine structure of the assigned lines
caused by the nitrogen nucleus, were predicted using the program MB0956 employing the nuclear
quadrupole coupling constants listed in Table 2. However, the splittings were predicted to be too
small to be resolved and this effect was therefore not taken into consideration. A total of 57
transitions were assigned and least-squares fitted to Watson’s A-reduction Hamiltonian in the Irrepresentation using Sørensen’s program Rotfit.57 It was only possible to determine two quartic
centrifugal distortion constans J and JK. The remaining centrifugal distortion constants were
preset at zero in the least-squares fit with the resulting spectroscopic constants listed in Table 3.
Comparison of the experimental (Table 3) and CCSD(T) (Table 2) rotational constants
show that there is very good agreement between the two sets of constants. The B and C rotational
constants differ by 0.5 %, while the A rotational constant differs by 1.4 %. The effective rotational
constants in Table 3 are defined differently from the approximate equilibrium rotational constants
in Table 2. The differences between the two sets of constants are expected to be relatively small,
similar to what has been found in the present case. This indicates that the structure in Table 1 is
14
very close to the equilibrium structure. Interestingly, the inertial defect is ‒0.142(5) × 10‒20 u m2
(Table 3). The inertial defect of a completely planar molecule is zero. It is also noted that the
experimental values of the J and JK quartic centrifugal distortion constants (Table 3) are quite
similar to their B3LYP counterparts (Table 2).
There could be two main reasons for the observed, relatively small inertial defect, zeropoint vibrations and/or a non-planar amide group. The fact that the CCSD(T) calculations predict
a completely planar structure for I, including the amide group, is strong indication that this is
indeed the case. The observed inertial defect of ‒0.142(5) × 10‒20 u m2 is therefore thought to
arise mainly from low-frequency out-of-plane vibration(s). This inertial defect is similar to that of
acrylamide (‒0.131300(34) × 10‒20 u m2),16 which is isomeric with N-vinylformamide.
Acrylamide is planar, or very nearly planar.16 The inertial defect of the planar formamide
molecule is +0.00862 × 10‒20 u m2,22 whereas ‒0.60 × 10‒20 u m2 has been reported for
formanilide, which is assumed to be planar.30, 31
Vibrationally Excited State of I. The ground-state spectrum was accompanied by several
satellite lines presumably originating from vibrationally excited states. One such state, whose
spectrum is shown in Table 6S of the Supporting Information, was assigned in the same manner
as described for the ground state. Maximum value of J is 15 and maximum value of K‒1 is 4. The
spectroscopic constants are listed in Table 3. Attempts were made to assign further vibrationally
excited states, but complete unambiguous assignments were not achieved.
Relative intensity measurements performed largely as described by Esbitt and Wilson58
yielded 76(15) cm‒1 for the torsional vibration. It is seen from Table 3 that the inertial defect is ‒
1.058(5) × 10‒20 u m2 for this state. The increase in the absolute value of this quantity from the
15
ground state (‒0.142(5) × 10‒20 u m2) indicates that this state is an out-of-plane vibration,59
presumably the first excited state of the torsion about the C2N6 bond. The B3LYP calculations
yield 116 cm‒1 (anharmonic value; Table 1S) for this mode, significantly higher than the
experimental value.
It is possible to compare the experimental and theoretical vibration-rotation constants
defined by ex = X0 – Xex, where X0 is the rotational constants of the ground state and Xex are the
rotational constants of the excited state under consideration. The experimental vibration-rotation
constants derived from the entries in Table 3 are A = 1461(18), B = ‒5.25(1), and C = ‒
8.28(1) MHz, compared to 1644, ‒4.74, and ‒7.27 MHz, respectively (Table 1S). The agreement
between the two sets of vibration-rotation constants is satisfactory.
Planarity of I. The three lowest normal vibrations have anharmonic frequencies of 116,
222, and 241 cm‒1 according to the B3LYP calculations shown in Table 1S. Two semi-empirical
equations by Oka60 and by Hanyu et al61 can be employed to derive a fairly accurate value for the
lowest torsional vibration provided it is well isolated from other vibrational modes. The B3LYP
torsional vibration at 116 cm‒1 is well separated from other vibrational modes. According to
Oka,60 the dependency of the inertial defect, 0, of the ground vibrational state of planar
molecules on the torsional frequency, 1, and the largest principal moment of inertia, Icc, of the
molecule, is given by 0 = (‒33.715/1) + 0.0186 Icc in units of u Å2. Insertion of the inertial
defect (‒0.142(5) × 10‒20 u m2; Table 3) of the ground state and Icc derived from the C rotational
constant in the same table, one gets 1 = 80 cm‒1, in good agreement with the experimental
torsional frequency of 76(15) cm‒1.
16
An alternative equation by Hanyu et al,61 1 is given by 1 = ‒67.4/1, where 1 is the
change in the inertial defect (in u Å2 units) upon excitation of an out-of-plane vibration. Using the
inertial defects of the ground and of the first excited state, one gets a torsional frequency of 74
cm‒1 in this manner. This value is smaller than 80 cm‒1 derived from the Oka60 formula. A
smaller value was expected because the equation by Hanyu et al61 neglects interaction terms.60
It is concluded that the low torsional frequency about the C2N6 bond is the major
contributor to the inertial defect of I, whose equilibrium structure is completely planar. This
conclusion is strongly supported by the advanced CCSD(T) calculations.
Dipole Moment of I. The second order Stark coefficients of the ground vibrational state
shown in Table 4 were used to determine the dipole moment of I. The cell was calibrated using
OCS whose dipole moment was taken to be 2.38568(66) × 10‒30 C m.62 The theoretical second
order Stark coefficients were calculated using the Golden and Wilson formalism,63 which is
implemented in the program MB04.56 The out-of-plane component of the dipole moment, c, was
preset at zero in the least-squares fit with the results shown in Table 4. The experimental dipole
moment components of this table, a = 9.96(8), b = 2.22(3), and tot = 10.20(8) × 10‒30 C m,
deviate more than expected from the the CCSD(T) predictions (10.56, 3.15, and 11.02 × 10‒30 C
m, respectively; Table 1). It is somewhat surprising that the very advanced CCSD(T) calculations
are not able to reproduce the dipole moment components more accurately.
Assignment of the MW Spectrum of Form III. This conformer has a sizable a
component of about 6 × 10‒30 C m, according to the CCSD(T) calculations (Table 2) and a value
of Ray’s asymmetry parameter ( = ‒0.95) that is not much different from the corresponding
17
asymmetry parameter of I. A typical, quite strong aR-pile-up series was therefore expected for
this form and searches for this series were first undertaken with immediate success. Several
assignments were confirmed by MWRFDR experiments. The a-type lines assigned in this manner
were used to predict bQ-branch lines which were soon identified because most of them are among
the strongest lines of the spectrum caused by a relatively large b of approximately 11 × 10‒30 C
m (CCSD(T) value; Table 2). The assignments of the strongest bR-branch lines were now
straightforward. Additional P- and R-branch lines were gradually assigned and included in the
least squares fit. In this manner, 349 transitions with maximum value of J = 71 and K‒1 = 14 were
assigned. All quartic and one sextic (KJ) centrifugal distortion constants were fitted using
Rotfit,57 with the remaining sextic constants preset at zero. The spectrum is listed in Table 7S and
the resulting spectroscopic constants are shown in Table 5.
Attempts to get the nuclear quadrupole coupling constants of the nitrogen nucleus failed
for III, just as for I, because no well resolved quadrupole hyperfine structures suitable for
exploitation were observed for the b-type transitions, which were explored in an attempt to derive
these constants. However, the shapes of several of these transitions were unsymmetrical and
definitely perturbed by this effect.
The experimental (Table 5) and CCSD(T) rotational constants (Table 2) all agree to
within about 0.5 %, which is again taken as an indication that the CCSD(T) structure is close to
the equilibrium structure. The inertial defect of III is ‒0.087098(27) × 10‒20 u m2, even smaller,
in absolute terms, than that of I (‒0.142(5) × 10‒20 u m2). The experimental and B3LYP quartic
centrifugal distortion constants are in quite good agreement (Tables 2 and 5). The sextic
centrifugal distortion constant KJ = ‒0.1342(89) Hz (Table 4) should be compared with the
18
B3LYP value (‒0.219 Hz), shown in the Supporting Information, Table 3S.
Vibrationally Excited State of III. The spectra of two vibrationally excited states were
assigned for this rotamer in the same manner as described for the ground state. The spectra
consisting of 141 and 65 transitions, respectively, are listed in Tables 8S and 9S of the
Supporting Information and the spectroscopic constants are displayed in Table 5.
The strongest of these spectra, which has an inertial defect of ‒0.900684(74) × 10‒20 u m2
(Table 5) is presumed to belong to the first excited state of the C2N6 torsion for similar reason as
stated above for I. A total of 141 transitions with Jmax = 30 and K‒1max = 4 were used to derive the
spectroscopic constants. Relative intensity measurements yielded 101(20) cm‒1 for this vibration,
compared to 131 cm‒1 predicted by the B3LYP method (Table 3S).
The experimental vibration-rotation constants calculated from the entries in Table 5 are in
this case: A = 364.38 (2), B = ‒7.08(1), and C = ‒9.77(1) MHz, compared to 403.4, ‒6.26,
and ‒8.59 MHz (Table 3S). The agreement between the two sets of vibration-rotation constants is
again satisfactory.
The second excited state whose spectroscopic constants are found in Table 5 is
presumably an out-of-plane vibration because its inertial defect (‒0.1996(1) × 10‒20 u m2) is in
absolute terms larger than that of the ground state (‒0.087098(27) × 10‒20 u m2). 65 transitions of
this form with with Jmax = 31 and K‒1max = 2 were employed to obtain the spectroscopic constants
of this excited state. Relative intensity measurement yielded ca 300 cm‒1, compared with the
B3LYP frequency of 296 cm‒1 (Table 3S). The experimental vibration-rotation constants are: A
= 21.90(3), B = ‒2.32(1), and C = ‒2.87(1) MHz, compared to 26.89, ‒1.49, and ‒2.58 MHz,
19
respectively, (Table 3S). The agreement between the two sets of vibration-rotation constants is
satisfactory in this case too.
Planarity of III. The inertial defect of the ground vibrational state (Table 5) yields 97
cm‒1 for the torsion about the C2N6 bond using the Oka formalism.60 This value agrees with
101(20) cm‒1 found by relative intensity measurements. The Hanyu et al equation61 yields a lower
value of 83 cm‒1, compared to the result using Oka’s formula,60 as expected.. The torsional
fundamental is well separated from the other vibrational modes according to the B3LYP
calculations (Table 3S), just as in the case of I. All this, combined with the CCSD(T) result, is
taken as evidence that III has a completely planar equilibrium structure.
Dipole Moment of III. The determination of the dipole moment of III was made in the
same manner as reported above for I. The results are presented in Table 6. The experimental
dipole moment components of this table, a = 7.64(16), b = 9.24(10), and tot = 12.0(2) × 10‒30
C m, is again found to deviate significantly from the CCSD(T) predictions (6.11, 10.65, and
12.28 × 10‒30 C m; Table 1).
Searches for the Hypothetical Forms II and IV. The theoretical calculations predict
that there should be an energy difference of 7 – 13 kJ/mol between I and II, and the latter form
was therefore expected to be present in small concentration, if it exists at all as a stable form of
cis-N-vinylformamide. This conformer was calculated to have a as the major dipole moment
component (Table 2). Searches were therefore undertaken for the a-type R-branch transitions of
this compound using the spectroscopic constants of Table 2 to predict their approximate
frequencies. However, no assignments could be made.
20
The B3LYP and CCSD(T) methods predict rather different (9.7 and 2.4 kJ/mol) energy
differences between III and IV, as discussed above. IV is predicted to have a comparatively large
b of about 13 × 10‒30 C m. Extensive searches for the spectrum of IV were undertaken
employing the spectroscopic constants of Table 2, but no assignments could be made. It is very
unlikely that the spectrum of IV would have been overlooked if the energy difference were as
small as 2.4 kJ/mol. It is concluded that IV must have a higher energy relative to III than 2.4
kJ/mol. A conservative estimate is that the hypothetical form IV is at least 4 kJ/mol less stable
than III.
CONCLUSIONS
The MW spectra of a mixture of cis- and trans-H‒N‒C‒O forms of N-vinylformamide,
(H2C=CHNHC(=O)H) have been measured and analyzed. Rotational isomerism is possible for
both cis and trans. However, the MW spectra of only one form of cis and one form of trans were
assigned. Both these forms have the C‒C‒N‒C chain of atoms in an antiperiplanar conformation.
The behavior of the inertial defects, as well as CCSD(T)/cc-pVTZ calculations, of the two forms
strongly indicates that the equilibrium structures of both forms are exactly planar.
The experimental work has been augmented with quantum chemical calculations at the
B3LYP/cc-pVTZ and the very high CCSD(T)/cc-pVTZ level of theory. The two theoretical
methods predict that the identified forms are both planar. The CCSD(T) rotational constants are
in excellent agreement with their experimental counterparts. The B3LYP quartic centrifugal
distortion constants and the vibration-rotation constants are in fair agreement with experiments,
21
while larger discrepancies are seen for the CCSD(T) dipole moments. The theoretical calculations
predict that an additional rotameric form exists for each of cis and trans with an energy that is
several kJ/mol higher than those of the identified forms. However, searches for the spectra of
these two hypothetical conformers were unsuccessful. It is estimated that the additional rotamers
must be at least 4 kJ/mol less stable than the identified forms, if they exist at all.
ASSOCIATED CONTENT
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
* Tel: +47 2285 5674; Fax: +47 2285 5441; E-mail: harald.mollendal@kjemi.uio.no
ACKNOWLEDGEMENTS
We thank Anne Horn for her skillful assistance. The Research Council of Norway (Program for
Supercomputing) is thanked for a grant of computer time.
22
23
Figure 1. Models of four forms (I – IV) of N-vinylformamide found to be minima on the
potential energy hypersurface in the B3LYP/cc-pVTZ calculations. Atom numbering is indicated
on I. Note that the H7N6C8O9 chain of atoms is cis in I and II, and trans in III and IV. The
C1C2N6C8 link of atoms is antiperiplanar (dihedral angle = 180º) in I and in III, and
synperiplanar in II (~20º) and in IV (0º). The MW spectra of I and III are reported herein.
24
Energy / kJ mol
-1
30
20
10
0
0
50
100
150
200
Cis-C1-C2-N6-C8 dihedral angle / degree
Figure 2. B3LYP/cc-pVTZ potential function for rotation about the C2N6 bond for the
H7N6C8O9 cis configuration. This function has minima at 20.6º of the C1C2N6C8 dihedral
angle (form II) and at 180º (I) and transitions states at 0º and 99.5º. The B3LYP electronic
energy difference between II and I is 12.2 kJ/mol, with I as the more stable conformer. The
energy of the transition state at 0º is 12.4 kJ/mol, and the energy of the transition state at 99.5º is
31.0 kJ/mol higher than the energy of I.
25
40
Energy / kJ mol
-1
30
20
10
0
0
50
100
150
200
Trans-C1-C2-N6-C8 dihedral angle / degree
Figure 3. B3LYP/cc-pVTZ potential function for rotation about the C2N6 bond for the
H7N6C8O9 trans configuration. This function has minima at 0º (form III) and at 180º (IV) and a
transition state at 90.9º. The B3LYP energy difference between IV and III is 8.9 kJ/mol, with III
as the more stable conformer. The energy of the transition state is 34.6 kJ/mol above the energy
of III.
26
Table 1. CCSD(T)/cc-pVTZ Structures of Four Forms of N-Vinylformamide
forma:
I
II
III
IV
Bond length (pm)
C1–C2
133.9
134.0
133.9
134.0
C1–H3
108. 0
108.0
108.0
108.1
C1–H4
108.3
108.2
108.4
107.8
C2–H5
108.4
108.3
108.1
108.3
C2–N6
139.6
140.4
140.0
140.7
N6–H7
100.9
100.8
100.7
100.5
N6–C8
137.1
137.3
137.2
137.0
C8–O9
121.3
121.4
121.4
121.4
C8–H10
110.2
109.9
110.1
110.2
(Table 1 continues next page)
27
(Table 1 continued)
Angle (deg)
C2–C1–H3
119.8
119.3
119.9
118.0
C2–C1–H4
121.9
122.7
122.0
122.3
H3–C1–H4
118.3
118.1
118.1
119.7
C1–C2–H5
121.5
120.5
123.2
120.7
C1–C2–N6
124.9
125.8
124.0
127.0
H5–C2–N6
113.6
113.7
112.8
112.3
C2–N6–H7
119.6
118.9
119.1
117.0
C2–N6–C8
124.0
125.6
123.0
127.1
H7–N6–C8
116.3
115.3
118.0
115.9
N6–C8–O9
124.4
123.9
124.9
125.9
N6–C8–H10
112.2
112.6
111.9
111.3
O9–C8–H10
123.4
123.5
123.2
122.8
(Table 1 continues next page)
28
(Table 1 continued)
Dihedral angle (deg)
H3–C1–C2–H5
0.0
–2.8
0.0
0.0
H3–C1–C2–N6
180.0
176.3
180.0
180.0
H4–C1–C2–H5
180.0
177.2
180.0
180.0
H4–C1–C2–N6
0.0
–3.8
0.0
0.0
C1–C2–N6–H7
0.0
156.7
0.0
180.0
C1–C2–N6–C8
180.0
–26.7
180.0
0.0
H5–C2–N6–H7
180.0
–24.3
180.0
0.0
H5–C2–N6–C8
0.0
152.4
0.0
180.0
C2–N6–C8–O9
180.0
177.7
0.0
0.0
0.0
–3.5
180.0
180.0
C2–N6–C8–H10
(Table 1 continues next page)
29
(Table 1 continued)
H7–N6–C8–O9
H7–N6–C8–H10
a
0.0
–5.5
180.0
180.0
180.0
173.2
0.0
0.0
The four forms are depicted in Fig. 1. The parameters of the forms whose MW spectra were
assigned, are in boldface.
30
Table 2. Theoretical Spectroscopic Contants of Four Forms of N-Vinylformamide
Forma:
I
II
III
IV
Rotational constantsb (MHz)
A
37516.9
19598.4
19817.0
10220.2
B
2407.3
2887.8
2960.8
4491.5
C
2262.2
2542.8
2575.9
3120.3
Inertial defectc (10‒20 u m2)
0.0
‒2.00
0.0
0.0
Quartic centrifugal distortion constantsd (kHz)
J
JK
K
0.190
–3.81
280
0.686
–11.5
165
0.664
–9.10
108
2.62
–6.93
12.6
(Table 1 continued next page)
31
(Table 2 continued)
J
0.0162
0.0983
0.133
0.918
K
1.11
4.05
2.60
3.89
Dipole momente (10-30 C m)
a
10.56
11.67
6.11
3.21
b
3.15
2.86
10.65
13.50
c
0.00
1.16
0.00
0.00
tot
11.02
12.07
12.28
13.87
Principal axis quadrupole coupling constantsb (MHz)
aa
2.05
2.27
1.96
2.04
(Table 1 continues next page)
32
(Table 1 continued)
bb
1.98
1.63
2.14
2.03
cc
‒4.03
‒3.90
‒4.10
‒4.07
Energy difference (kJ/mol)
E
a
0.0f
9.6g
0.0h
2.4i
The four forms are depicted in Fig. 1. The parameters of the forms whose MW spectra were
assigned, are in boldface.
b
Calculated from the CCSD(T) structures given in Table 1.
c
Conversion factor: 505379.0 × 10‒20 MHz u m2. d B3LYP/cc-pVTZ values. e CCSD(T) principalaxes dipole moment components and total dipole moment. f Total CCSD(T) electronic energy: ‒
648187.60 kJ/mol.
g
Relative to I.
h
Total CCSD(T) electronic energy: ‒648206.31 kJ/mol.
i
Relative to III.
33
Table 3. Spectroscopic Constantsa of Form I of cis-N-Vinylformamide
Vibrational state:
A (MHz)
First Ex. Tors. Stateb
Ground
37001(14)
35540(11)
B (MHz)
2419.1292(38)
2424.3806(45)
C (MHz)
2272.1181(40)
2280.3965(48)
‒0.142(5)
‒1.058(5)
c (10‒20 u m2)
J (kHz)
JKd (kHz)
rmse
Nf
a
0.2042(75)
‒3.39(23)
0.2057(81)
‒2.79(18)
1.078
1.226
57
53
A-reduction Ir-representation.64
b
First excited state of the torsion about the C2N6 bond.
Inertial defect. Conversion factor: 505379.01 × 10‒20 MHz u m2.
d
c
Further quartic constants
preset at zero in the least-squares fit. e Root-mean-square deviation of a weighted fit defined by
rms2 = [(obs – calc)/u]2/(N – P), where obs and calc are the observed and calculated
frequencies, u is the uncertainty of the observed frequency, N is the number of transitions used in
the least-squares fit, and P is the number spectroscopic constants used in the fit. f Number of
transitions used in the least-squares fit.
34
Table 4: Second Order Stark Coefficientsa and Dipole Moment of Form I of Cis-NVinylformamide
 E-2/10-6 MHz V-2 cm2
Transition
obs.
calc.
−15.8(4)
−16.3
41,3 ← 31,2
M = 1
50,5 ← 40,4
M = 1
−2.10(4)
−1.97
51,4 ← 41,3
M=0
−1.57(3)
−1.59
51,4 ← 41,3
M = 1
−3.90(3)
3.81
51,4 ← 41,3
M = 2
51,5 ← 41,4
M=0
‒0.548(10)
‒0.554
51,5 ← 41,4
M = 1
2.48(4)
2.63
51,5 ← 41,4
M = 2
−10.9(5)
12.4(4)
−10.6
12.1
(Table 4 continues next page)
35
(Table 4 continued)
Dipole moment (10-30 C m)
a = 9.96(8)
a
b = 2.22(3)
c = 0.0b
Uncertainties represent one standard deviation.
b
tot = 10.20(8)c
By symmetry; see text.
c
In debye units:
3.06(2) D. Conversion factor 1 D = 3.33564 × 10-30 C m.
36
Table 5. Spectroscopic Constantsa of Form III of Trans-N-Vinylformamide
Vibrational state:
A (MHz)
Ground
19723.2338(55)
First Ex. Tors. Stateb
19358.851(19)
In-plane Bend.c
19701.332(33)
B (MHz)
2976.65651(78)
2983.7425(17)
2978.9758(58)
C (MHz)
2587.47826(79)
2597.2452(18)
2590.3460(58)
d (10‒20 u m2)
J (kHz)
‒0.087098(26)
‒0.900684(74)
‒0.1996(1)
0.6874(10)
0.7269(28)
0.633(26)
JK (kHz)
‒8.866(15)
K (kHz)
103.162(69)
‒9.193(65)
‒9.17(20)
91.6(11)
92.5(73)
J (kHz)
0.13766(23)
0.14229(80)
0.1420(15)
K (kHz)
2.754(36)
2.292(99)
2.96(25)
KJe (Hz)
‒0.1342(89)
‒4.5(32)
‒f
(Table 5 continues next page)
37
(Table 5 continued)
rmsg
Nh
a
1.336
349
A-reduction Ir-representation.64
plane bending vibration?
d
b
1.702
1.773
141
65
First excited state of the torsion about the C2N6 bond.
c
In-
Inertial defect. Conversion factor: 505379.01 × 10‒20 MHz u m2.
e
Further sextic centrifugal distortion constants preset at zero in the least-squares fit. f Preset at zero
in the least-squares fit. g Root-mean-square deviation of a weighted fit, as defined in the footnote
of Table 3. h Number of transitions used in the least-squares fit.
38
Table 6: Second Order Stark Coefficientsa and Dipole Moment of Form III of Trans-NVinylformamide
 E-2/10-4 MHz V-2 cm2
Transition
obs.
calc.
11,1 ← 00,0
M=0
1.24(2)
1.31
11,0 ← 10,1
M = 1
9.36(13)
9.22
21,1 ← 20,2
M = 2
1.95(8)
2.00
31,2 ← 30,3
M = 3
1.18(3)
1.10
41,3 ← 40,4
M = 4
0.918(15)
0.855
41,3 ← 40,4
M = 3
0.349(5)
0.353
51,4 ← 50,5
M = 5
0.758(10)
0.732
51,4 ← 50,5
M = 4
0.406(5)
0.408
51,4 ← 50,5
M = 3
0.149(2)
0.156
(Table 6 continues next page)
39
(Table 6 continued)
Dipole moment (10-30 C m)
a = 7.64(16)
a
b = 9.24(10)
c = 0.0b
Uncertainties represent one standard deviation.
b
tot = 12.0(2)c
By symmetry; see text.
c
In debye units:
3.59(5) D. Conversion factor 1 D = 3.33564 × 10-30 C m.
40
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