Article
pubs.acs.org/JPCA
Conformational Properties of cis- and trans-N‑Cyclopropylformamide
Studied by Microwave Spectroscopy and Quantum Chemical
Calculations
Svein Samdal,† Harald Møllendal,*,† and Jean-Claude Guillemin‡
†
Centre for Theoretical and Computational Chemistry (CTCC), Department of Chemistry, University of Oslo, P.O. Box 1033
Blindern, NO-0315 Oslo, Norway
‡
Institut des Sciences Chimiques de Rennes, École Nationale Supérieure de Chimie de Rennes, CNRS, UMR 6226, 11 Allée de
Beaulieu, CS 50837, 35708 Rennes Cedex 7, France
S Supporting Information
*
ABSTRACT: The microwave spectra of cis- and trans-Ncyclopropylformamide, C3H5NHC(O)H, have been investigated in the 31−123 GHz spectral region at room
temperature. Rotational isomerism about the Cring−N bond
is possible for both cis and trans. MP2/cc-pVTZ and CCSD/
cc-pVTZ calculations indicate that there are two conformers in
the case of cis, called Cis I and Cis II, while only one rotamer,
denoted Trans, exists for trans-N-cyclopropylformamide. The
quantum chemical methods predict that Cis I has an electronic
energy that is 8−9 kJ/mol higher than the energy of Cis II.
The CCSD H−Cring−N−H dihedral angle is 0.0° in Cis I, 93.0° in Cis II and 79.9° in Trans. The CCSD and MP2 calculations
predict a slightly nonplanar structure for the amide moiety in both Trans and Cis II, whereas Cis I is computed to have a planar
amide group bisecting the cyclopropyl ring. Surprisingly, the MP2 and CCSD methods predict practically the same energy for
Trans and Cis II. The spectra of Cis II in the ground state and in two vibrationally excited states were assigned, while the
spectrum of Cis I was not found presumably because of a low Boltzmann population due to a relatively large energy diﬀerence
(8−9 kJ/mol). The spectra of the ground vibrational state and seven vibrationally excited states of Trans, were assigned.
Vibrational frequencies of several of the excited state of both Cis II and Trans were determined by relative intensity
measurements. The experimental and CCSD rotational constants are in satisfactory agreement. The MP2 values of the quartic
centrifugal distortion constants of both species are in relatively poor agreement with their experimental counterparts. The MP2
vibration−rotation constants and sextic centrifugal distortion constants have little resemblance with the corresponding
experimental values.
■
INTRODUCTION
The amide group is a crucial structural element in proteins and
many other biomolecules. The chemical and physical properties
of amides are consequently of great interest both for chemistry
and for biology. Not surprisingly, a large review literature exists
for this functional group.1−12
Amides are often crystals or liquids with low sublimation or
vapor pressures at room temperature, which is at least partly
due to extensive ubiquitous intermolecular hydrogen bonding
in condensed phases of amides. Hydrogen bonding is relatively
strong in most members with this functional group and has a
signiﬁcant inﬂuence on structural and conformational properties of crystalline and liquid amides. X-ray crystallography has
provided a large number of accurate structures of solid amides.
However, structural and conformational properties of gaseous
monomeric amides are much less well-known. This is mainly due
to their low volatility and the fact that they often decompose
upon heating, which make them less prone to experimental gasphase studies. It is desirable to investigate monomeric amides in
© 2015 American Chemical Society
the gas phase to obtain the best possible insight in the true,
unperturbed structural and conformational properties of this
important class of compounds. Such investigations can best be
performed using microwave (MW) spectroscopy or gas
electron diﬀraction (GED) in combination with advanced
quantum chemical calculations. We have for these reasons for a
long time taken an interest in gas-phase studies of them. Our
previous MW and GED studies include cis- and trans-Nvinylformamide (H 2 CCHNHC(O)H), 13 acetamide
(CH3CONH2),14 2-ﬂuoroacetamide (CH2FCONH2),15,16 2chloroacetamide (CH 2 ClCONH 2 ), 16,17 2-iodoacetamide
(CH2ICONH2),18 2,2-diﬂuoroacetamide (CF2HCONH2)19
2,2-dichloroacetamide (CHCl2CONH2),20 2-chloro-2,2-diﬂuoroacetamide (CF 2 ClCONH 2 ), 21 2,2,2-triﬂuoroacetamide
(CF3CONH2),22 2,2,2-trichloroacetamide (CCl3CONH2),23
Received: January 19, 2015
Revised: March 12, 2015
Published: March 16, 2015
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propionamide (CH 3 CH 2 CONH 2 ), 24 formic hydrazide
(H2NNHCHO),25 acrylamide (H2CCHCONH2),26 methyl
carbamate (CH 3 OCONH 2 ), 2 7 , 2 8 methoxyacetamide
(CH3OCH2CONH2),29 and 2-azetidinone.30,31 Experimental
contributions from other laboratories include, for example, the
prototype formamide (HCONH2),32−34 urea (H2NCONH2),35
cis- and trans- N-methyl formamide (HCONHCH3),36 N,Ndimethylformamide (HCON(CH3)2),37 C−N−C−O-cis-Nethylformamide (HCONHCH2CH3),38 O−N−C−O-trans-methoxyformamide (HCONHOCH3),39 C−N−C−O-cis-formanilide (C6H5NHCHO),40,41 acetamide,42−45 C−N−C−O-cis-Nmethylacetamide (CH3CONHCH3),46 C−N−C−O-cis-Nmethylpropionamide (CH3CONHCH2CH3)47 C−N−C−Otrans-acetanilide (CH 3 CONHC 6 H 5 ), 48 and alaninamide
(CH3CH(NH2)CONH2).49 Rotation isomerism is possible in
several of the compounds listed above, but acrylamide is the
only example of an amide where the MW spectra of more than
one rotamer have been assigned.26
Amide studies are hereby extended to include the ﬁrst MW
investigation of the spectra of cis- and trans-N-cyclopropylformamide, (C3H5NHC(O)H), where cis and trans refer to the
orientation of the Cring−N−C−O dihedral angle, which is about
0° in cis and approximately 180° in trans. A nitrogen-15 NMR
study of the composition of cis- and trans-N-cyclopropylformamide produced by heating ethyl formate and aminocyclopropane showed that 18% cis and 82% trans are formed in this
manner.50 The fact that trans predominates was ascribed to
steric repulsion between the cyclopropyl and carbonyl groups,
which was assumed to be much more important in cis than in
trans due to the close proximity of the two groups.50
Rotation about the carbon−nitrogen single bond joining the
cyclopropyl and formamide moieties may in principle produce
rotational isomerism, but this question was not dealt with in the
NMR work.50 Quantum chemical calculations reported below
found that two conformers may exist for cis-, whereas only one
conformer was predicted for trans-N-cyclopropylformamide.
The three forms have been denoted Cis I, Cis II and Trans.
Models of them, with atom numbering indicated on Cis I, are
shown in Figure 1. The dihedral angle associated with the H6−
C2−N9−H10 chain of atoms may conveniently be used to
describe rotational isomerism in the two isomers of Ncyclopropylformamide. In Cis I, this dihedral angle is exactly
0°, while this angle is 93.0° in Cis II and 79.9° in Trans
according to CCSD/cc-pVTZ computations discussed below.
MW spectroscopy is an ideal method to investigate rotational
isomerism due to its superior accuracy and resolution and this
method was therefore chosen for this study. The MW work has
been augmented by advanced quantum chemical calculations,
which provide both spectroscopic parameters that are useful for
the assignment of the MW spectrum and also make available
valuable information not obtainable from experiment.
Figure 1. Models of three forms of N-cyclopropylformamide found to
be minima on the potential energy hypersurface in the MP2/cc-pVTZ
calculations. Atom numbering is given on the conformer denoted Cis
I. Note that the C2−N9−C11−O12 chain of atoms is cis in both Cis I
and Cis II, and trans in the form called Trans. The H6−C2−N9−H10
dihedral angle, which can conveniently be used to characterize the
conformational properties, is 0.0° in Cis I, 93.0° in Cis II, and 79.9° in
Trans, according to CCSD/cc-pVTZ calculations.
the gas phase according to the MW spectrum. The compound
was kept in a refrigerator at roughly 4 °C when not in use. No
decomposition or polymerization of the sample was observed.
The MW spectrum was recorded at room temperature at a
pressure of 5−10 Pa using the Stark-modulation spectrometer
of the University of Oslo described in details elsewhere.52 It is
only mentioned here that this device has a resolution of about
0.5 MHz and measures the frequency of isolated transitions
with an estimated accuracy of ≈0.10 MHz. The spectrum was
investigated in the whole 31−123 GHz frequency interval.
Radio-frequency microwave double-resonance experiments
(RFMWDR), similar to those of Wodarczyk and Wilson53
were also undertaken. This technique makes it possible to
assign unambiguously particular transitions. The RFMWDR
equipment is described elsewhere.52
■
■
EXPERIMENTAL SECTION
Synthesis and Spectroscopic Experiments. N-cyclopropylformamide, which was synthesized and puriﬁed as
described by Gate et al.,51 was found to have a cis/trans ratio
that was very dependent on the solvent. The percentage cis
determined by 1H NMR was as follows: D2O, 15%; CD3OD,
16%; DMSO-d6, 16%; (CD3)2CO, 21%; CD3CN, 22%; C6D6,
31%; CDCl3, 36%. N-Cyclopropylformamide is a colorless
liquid with a vapor pressure of roughly 30 Pa at room
temperature. Fumes of this liquid were admitted to the MW
cell. The amount of cis and trans seemed to be roughly equal in
RESULTS AND DISCUSSION
Quantum Chemical Calculations. The present frozencore MP254 and CCSD55−58 calculations were performed
employing the Gaussian 0959 and Molpro60 programs running
on the Abel cluster in Oslo. Dunning’s61 correlation-consistent
cc-pVTZ triple-ζ basis set was used in the calculations. The
CCSD computations were undertaken using Molpro, while
Gaussian 09 was used for the MP2 calculations. The default
convergence criteria of the two computer programs were
observed.
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compared to about 20 and 12 kJ/mol in trans. The diﬀerent
potential functions are not surprising given that the highly
electronegative oxygen atom (O12) will be in rather close
contact with the cyclopropyl ring during most of the rotation
about the C2−N9 bond in cis, whereas the electropositive
hydrogen atom (H13) takes this role in trans. This should
indeed result in diﬀerent nonbonded interactions in the two
cases resulting in dissimilar potential functions.
Optimized MP2 structures, dipole moments, harmonic and
anharmonic vibrational frequencies, quartic and sextic Watson
centrifugal distortion constants,62 vibration−rotation constants
(the α’s),63 and the diﬀerences between the equilibrium and the
eﬀective ground-state rotational constants were computed for
the two conformers corresponding to the two minima of the cis
form and the one minimum of the trans conﬁguration. The
centrifugal distortion constants and the α’s were calculated
observing the precautions of McKean et al.64 The results are
given in Tables S1 (Cis I), S3 (Cis II), and S7 (Trans) of the
Supporting Information.
The MP2 H6−C2−N9−H10 dihedral angle is 0.0° in Cis I
(Table S1) and 92.9° in Cis II (Table S3). The amide moiety is
planar in Cis I (Table S1) and bisects the cyclopropyl ring.
This group is slightly nonplanar in Cis II (Table S3) and in
Trans (Table S7). The electronic energy diﬀerence between
Cis I and Cis II is 8.61 kJ/mol, with Cis II as the lower-energy
conformer. Correction for zero-point vibrational eﬀects (Table
S1 and S3) yields 8.87 kJ/mol for this energy diﬀerence. The
H6−C2−N9−H10 dihedral angles of the two maxima
(transition states) of the cis potential function (Figure 2)
were calculated to be 42.5° (Table S5) and exactly 180.0°
(Table S6), respectively. The corresponding electronic energies
are 12.03 and 6.99 kJ/mol above the energy of the Cis II
rotamer.
In trans, the MP2 minimum of the potential function occurs
at 80.4° for the H6−C2−N9−H10 dihedral angle, 12.5°
smaller than in Cis II (92.9°; see above). The maxima are
located at 0°, 19.54 kJ/mol higher than the electronic energy of
the Trans conformer (Table S9), and at 180°, 11.44 kJ/mol
higher (Table S10). The energy of Cis II corrected for
harmonic vibrational zero-point energy (Table 3) is 0.69 kJ/
mol lower than the corresponding energy of Trans (Table S7),
a remarkably small energy diﬀerence.
CCSD/cc-pVTZ computations of optimized structures,
dipole moments and electronic energies of the cis and trans
conformers were carried out. Unfortunately, it is not possible to
calculate vibrational frequencies and centrifugal constants at the
CCSD level given our present computational resources. The
full CCSD structures of Cis I, Cis II, and Trans are listed in
Tables S2, S4, and S8 of the Supporting Information,
respectively. A selection of important structural parameters of
the three forms is repeated in Table 1, which also contains the
rotational constants calculated from these structures. The MP2
quartic centrifugal distortion constants in the S-reduction
form62 taken from Tables S1, S3, and S7, and the CCSD
principal inertial axis dipole moment components are also given
in Table 1.
The CCSD results warrant comments: Cis II is predicted to
be 9.54 kJ/mol lower in electronic energy than Cis I (from
entries in Tables S2 and S4). This energy diﬀerence is more
than 1 kJ/mol larger than the MP2 electronic energy diﬀerence
(see above). The CCSD H6−C2−N9−H10 dihedral angles
(Table 1) are 0° in Cis I, just as in the MP2 case, 93.0° in Cis
II, and 79.9° in Trans. The two last values are close to the MP2
MP2/cc-pVTZ potential functions for rotation about the
C2−N9 bond were calculated for the cis and trans forms in
order to localize possible conformer(s). The H6−C2−N9−
H10 dihedral angle was stepped in 10° intervals in these
calculations while all other structural parameters were allowed
to vary freely. The resulting potential functions are drawn in
Figure 2 (cis) and Figure 3 (trans). The two functions are
Figure 2. MP2 electronic potential energy function for rotation about
the C2−N9 bond of cis-N-cyclopropylformamide. The function was
calculated by stepping the H6−C2−N9−H10 dihedral angle in 10°
intervals. The global minimum occurs at a value of 92.9° for this angle
corresponding to Cis II. The second minimum is found at 0° (Cis I).
The electronic energy diﬀerence is 8.61 kJ/mol. The function has
maxima at 42.5 and 180.0° with energies that are 12.03 and 6.99 kJ/
mol higher than the energy of the global minimum.
Figure 3. MP2 electronic potential energy function for rotation about
the C2−N9 bond of trans-N-cyclopropylformamide. The function was
calculated by stepping the H6−C2−N9−H10 dihedral angle in 10°
intervals. The minimum energy occurs at 80.4° for the H6−C2−N9−
H10 dihedral angle. The corresponding conformer is called Trans.
Maxima occur at 0° and at 180° for this dihedral angle, where the
energies are 19.54 and 11.44 kJ/mol, respectively, higher than the
energy of Trans.
remarkably diﬀerent. The cis function has two minima, while
the trans function has only one minimum. The barrier heights
are signiﬁcantly lower in cis (approximately 12 and 7 kJ/mol)
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Table 1. Selected CCSD/cc-pVTZ Structure Parametersa,
Rotational Constants, and Dipole Moments and MP2
Centrifugal Distortion Constants,b of Cis I, Cis II, and Trans
Forms of cis- and trans-N-Cyclopropylformamide
than the energy diﬀerence deﬁnitely play a role for the cis/trans
composition of this compound.
The equilibrium structure of the amide group is generally
nonplanar.65 Formamide, the prototypical amide, is planar, but
this is an exception.65 The formamide moiety of the title
compound is planar and bisects the cyclopropyl ring in Cis I
according to CCSD. It is slightly nonplanar in Cis II, and
rotated 93.0° about the C2−N9 bond relative to its position in
Cis I. The rotation about the C2−N9 is 79.9° in Trans (Table
1), in good agreement with the MP2 ﬁndings. The amide group
is nonplanar in Trans too.
Moreover, the equilibrium CO bond length is 120.97 pm
and the C−N bond length is 135.47 pm in formamide,65 about
the same as the CCSD predictions for the corresponding bond
lengths in the three forms of N-cyclopropylformamide (Table
1). In the cyclopropyl moiety, the C1−C3 bond length varies
between 151.5 (Cis I) and 150.5 pm (Trans), while C1−C2
and C2−C3 vary between 149.8 and 150.5 pm. The C−C
equilibrium bond length in cyclopropane is 150.30(10) pm66
for comparison.
Microwave Spectrum and Assignment of the GroundState Spectrum of Trans. Survey spectra revealed a dense
spectrum with absorption lines occurring every few MHz
throughout the entire MW region. A prominent feature of the
spectrum was lumps of strong transitions occurring at intervals
of about 3.71 GHz. This behavior is typical for a-type R-branch
transitions of an asymmetric rotor having Ray’s asymmetry
parameter67 κ close to −1, as well as a relatively large dipole
moment component along the a-inertial axis. It is seen from
Table 1 that this is indeed the case for the Trans conformer,
where B + C = 3.7117 GHz, κ = −0.977, and μa = 3.94 D.
The assignment of the spectrum of the ground vibrationalstate aR-transitions was thus straightforward due to these
precise predictions. The assignments of several selected
transitions were checked by RFMWDR experiments providing
unequivocal proofs of their assignments.53 The RFMWDR
spectrum of a portion of the 204 ← 194 shown in Figure 4 is a
conformer
Cis I
Cis II
Bond Distance (pm)
C1−C2
150.1
150.3
C1−C3
151.5
150.7
C2−C3
150.1
149.8
C2−H6
108.0
108.2
C2−N9
144.0
143.1
N9−H10
100.2
100.3
N9−C11
135.2
136.1
C11−O12
121.3
120.9
C11−H13
110.1
110.1
Angle (deg)
C1−C2−N9
122.9
117.4
C3−C2−N9
122.9
118.1
H6−C2−N9
110.2
115.4
C2−N9−H10
116.9
118.7
C2−N9−C11
126.4
122.3
H10−N9−C11
116.6
117.5
N9−C11−O12
125.9
125.2
N9−C11−H13
111.7
112.0
O12−C11−H13
122.4
122.8
Dihedral Angle (deg)
H6−C2−N9−H10
0.0
93.0
H6−C2−N9−C11
180.0
−72.8
C2−N9−C11−O12
0.0
−5.3
C2−N9−C11−H13
180.0
175.7
H10−N9−C11−O12
180.0
−171.2
H10−N9−C11−H13
0.0
9.8
Rotational Constants (MHz)
A
6832.1
8998.9
B
3009.6
2471.6
C
2506.0
2111.1
Quartic Centrifugal Distortion Constantsb (kHz)
DJ
1.30
1.68
DJK
−0.0513
−9.84
DK
0.651
33.4
d1
−0.261
−0.421
d2
0.0698
−0.006 31
Dipole Momentc (D)
μa
0.95
2.09
μb
3.63
2.96
μc
0.0d
0.31
μtot
3.75
3.64
Trans
150.3
150.5
150.5
108.3
142.9
100.6
136.3
120.9
110.0
117.8
118.2
116.1
118.8
123.2
115.6
124.8
112.2
123.0
79.9
−81.7
169.6
−11.7
7.4
−173.9
12525.5
1917.4
1794.3
0.385
−4.97
65.1
−0.0153
0.001 03
3.94
0.18
0.76
4.01
a
Full CCSD structures are given in Tables S2 (Cis I), Table S4 (Cis
II), and Table S8 (Trans) of the Supporting Information. bSreduction; Ir-representation.62 c1 D = 3.33564 × 10−30 C m. dFor
symmetry reasons.
results above. The electronic energy of Cis II, is only 0.17 kJ/
mol lower than the energy of Trans, similar to 0.69 kJ/mol
found above in the MP2 calculations. This surprisingly small
energy diﬀerence suggests that cis and trans should be formed
in about equal amounts provided the reaction was thermodynamically controlled. However, the previous NMR work
reported that only 18% cis was formed in the synthetic
procedure they chose,50 while 15−36% were found in the
solvents mentioned above. It is concluded that factors other
Figure 4. RFMWDR spectrum of the 204 ← 194 transitions of Trans
using a RF of 12.60 MHz. The two lines marked a are assumed to
belong to the ﬁrst excited state of the torsional vibration; lines b
represent the ground vibrational state, lines c and d are the ﬁrst and
second excited states of the lowest bending vibration, while line e is
tentatively assigned as the ﬁrst excited state of the second lowest
bending vibration.
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Table 2. Spectroscopic Constantsa of the Ground and Excited States of Trans
vibr state
ground
Av (MHz)
Bv (MHz)
Cv (MHz)
DJ (kHz)
DJK (kHz)
DK (kHz)
d1 (kHz)
d2 (kHz)
HJK (Hz)
HKJ (Hz)
rmse
Nf
12298.34(84)
1917.2153(26)
1796.1162(25)
0.39681(46)
−5.1418(50)
65.1c
−0.01561(75)
0.00948(58)
−0.0126(31)
0.2572(76)d
1.221
413
ﬁrst ex. lowest
bend.
second ex. lowest
bend
ﬁrst ex. torsion
second ex.
torsionb
third ex. torsionb
fourth ex.
torsionb
ﬁrst ex. second lowest
bendb
12243.0(15)
1916.3974(40)
1798.1345(38)
0.43068(71)
−5.373(20)
65.1c
−0.0202(11)
0.00731(90)
12235.2(39)
1915.8932(90)
1799.9266(87)
0.4370(19)
−5.307(36)
65.1c
−0.01561c
0.00948c
12335.2(18)
1911.4479(36)
1793.3894(34)
0.36741(63)
−4.554(15)
65.1c
−0.0140(13)
0.0056(13)
12308.1(17)
1908.0223(47)
1792.9749(48)
0.38678(79)
−4.768(22)
65.1c
−0.0118(14)
0.01035(99)
12330.1(16)
1907.6578(40)
1792.4640(35)
0.37449(92)
−3.842(25)
65.1c
−0.0080(11)
0.00539(98)
12471(10)
1906.508(27)
1792.900(28)
0.3766(15)
−5.168(48)
65.1c
−0.01561c
0.00948c
12182.2(31)
1919.7755(79)
1802.1603(87)
0.4578(16)
−4.511(80)
65.1c
−0.01561c
0.00948c
1.566
158
1.380
88
1.554
183
1.480
111
1.464
89
1.493
47
1.659
51
a
S-reduction; Ir-representation.62 Uncertainties represent one standard deviation. bTentative assignment; see text. cFixed. dFurther sextic constants
preset at zero. eRoot-mean-square deviation deﬁned as rms2 = Σ[(νobs − νcalc)/u]2/(N − P), where νobs and νcalc 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 of
spectroscopic constants used in the ﬁt. fNumber of transitions used in the ﬁt.
Table 3. Rotation−Vibration Constants of Transa
a
vibr state
ﬁrst ex. lowest
bend
second ex. lowest
bend
ﬁrst ex. torsion
second ex.
torsion
third ex. torsion
fourth ex. torsion
ﬁrst ex. second lowest
bend
αA (MHz)
αB (MHz)
αC (MHz)
55.3(17)
0.8179(48)
−2.0183(45)
63.1(40)
1.3221(94)
−3.8104(91)
−36.9(20)
5.7674(44)
2.7268(42)
−9.8(19)
9.1930(54)
3.1413(54)
−31.8(18)
9.5575(48)
3.6522(43)
−173(10)
11.207(29)
3.216(29)
116.1(32)
−2.5602(83)
−6.0468(91)
Obtained by subtracting the exited-state rotational constants from the corresponding ground-state rotational constants; see text.
MHz larger than the ground-state equivalent, while B and C are
smaller by 3.3 and 1.8 MHz. This is an indication that although
the CCSD structure of Trans is very likely close to the
equilibrium structure, there is still room for improvement.
Unfortunately, more comprehensive quantum chemical calculations than those reported here could not be undertaken due
to the limited resources available.
The experimental quartic centrifugal distortion constants
(Table 2) deviate from the MP2 constants (Table 1) by about
13% for DJ, 3% for DJK, and 2% for d1, while d2 deviates by
much more, but this constant has a relatively much larger
uncertainty than DJ, DJK, and d1. The MP2 sextic HJK and HKJ
constants listed in Table S7 deviate very much from their
experimental counterparts (Table 2). The reason for this is
assumed to be the poor quality of the MP2 anharmonic part of
the force ﬁeld, which is discussed further below in connection
with the vibration−rotation constants of the vibrationally
excited states.
Vibrationally Excited States of Trans. The MP2
calculations (Table S7) predict that the ﬁve lowest anharmonic
fundamental vibrational frequencies are 90, 147, 201, 382, and
452 cm−1. Further fundamentals are above 550 cm−1. The
Boltzmann factors relative to the ground vibrational state are
thus 0.64, 0.49, 0.37, 0.15, and 0.11 for these vibrations. Spectra
of several vibrationally excited states were therefore expected to
be present with notable intensities. This was indeed observed.
RFMWDR spectra revealed the existence of at least seven
vibrationally excited state spectra in addition to the ground
vibrational state spectrum.
The ﬁrst assignments of transitions of vibrationally excited
states were obtained from the RFMWDR spectra such as the
one shown in Figure 4 and subsequently extended to include
additional transitions from the Stark spectrum. A total of seven
vibrationally excited states were ultimately assigned. The aR-
typical example, displaying the spectra of the ground state and
of four vibrationally excited states. The 14N nucleus has a small
quadrupole moment, but none of the transitions displayed
clearly resolved quadrupole splittings caused by this nucleus.
The spectrum was least-squares ﬁtted to Watson’s S-reduced
Hamiltonian in the Ir-representation using Sørensen’s program
Rotﬁt.68 A total of 413 aR-transitions with Jmax = 32 and K−1max
= 25 listed in Table S11 of the Supporting Information were
employed to obtain the spectroscopic constants listed in Table
2. It was possible to determine all quartic centrifugal distortion
constants but DK, which was preset at the MP2 value, 65.1 kHz,
(Table 7S) in the least-squares ﬁt. Two of the sextic distortion
constants, HJK and HKJ were also ﬁtted. Further sextic constants
with standard deviations less than their absolute values could
not be obtained and they were therefore preset at zero in the
least-squares ﬁt.
The hypothetical frequencies of b- and c-type transitions can
be quite accurately predicted using the spectroscopic constants
shown in Table 2. However, no unambiguous assignments
could be made, presumably because these transitions are much
weaker than the a-type transitions due to the fact that μa is
much larger than the two other dipole moment components
(Table 1). The high spectral density with the occurrence of
frequent overlapping transitions and Stark lobes was another
severe obstacle for obtaining deﬁnite assignments of b- and ctype lines.
Equilibrium (re) rotational constants are normally larger than
eﬀective (r0) rotational constants. The MP2 method (Table S7)
predicts that the equilibrium values of the A, B, and C rotational
constants of Trans are larger than the observed values by
111.66, 15.72, and 13.54 MHz, respectively, which is typical for
the performance of this method. Comparison of the CCSD
rotational constants (Table 1) with the ground-state constants
(Table 2) shows that the CCSD A rotational constant 227.2
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However, the rather sizable μb = 3.6 D should produce a
relatively strong spectrum. A search for the b-type spectrum of
this form was performed but no assignments could be made. It
is concluded that Cis I in all likelihood is a high-energy form of
cis-N-cyclopropylformamide.
Assignment of the Spectrum of Cis II. The spectroscopic
constants in Table 1 were used to predict the spectrum of aRtransitions. Several of these were easily assigned in the
RFMWDR spectrum in the same manner as described above
for Trans. The frequencies of further transitions of this
category could now be predicted fairly accurately and they were
assigned in a straightforward manner and included in the leastsquares ﬁt. a-type lines with a maximum value of Jmax = 27
(Table S19) were ultimately assigned and used to predict the
frequencies of b-type lines with J < 20. These transitions were
found close to their predicted frequencies. Additional b-type
lines including higher and higher values of J were gradually
assigned and included in the ﬁt. Ultimately, 835 transitions of
the a- and b-type varieties with Jmax = 85 and K−1max = 20 listed
in Table 19S of the Supporting Information were used to
determine the spectroscopic constants displayed in Table 4.
spectra are listed in Tables S12−S18 of the Supporting
Information, and the spectroscopic constants are collected in
Table 2. The quartic centrifugal distortion constants, with the
exception of DK, were determined for most of the excited-state
spectra. d1 and d2 were not obtained for three excited states and
were preset at the ground-state values in the least-squares ﬁt.
It is not always obvious to which vibrationally excited state
each of these excited-state spectra belongs. Comparison of
experimental and theoretical α-vibration−rotation63 constants
as well as vibrational frequencies can be useful for making
assignments. In Table 3, we have listed the α-constants of the
seven excited-state spectra. These values have been found by
subtraction of the excited-state rotational constants from their
ground-state counterparts.
Relative intensity measurements yielded 82(20) cm−1 for the
strongest excited state listed in Table S12. This value is close to
the MP2 result (90 cm−1, Table S8) for the lowest bending
vibration. The α-values of Table 3 for this vibration are αA =
55.3(17), αB = 0.8179(48), and αC = −2.0183(45) MHz, in
quite poor agreement with the MP2 (Table S7) results, 85.02,
−0.86, and −3.47 MHz, respectively.
The spectrum of what is assumed to be the second excited
state of this mode (Table S13) was also assigned. αB and αC are
almost twice as large as those of the ﬁrst excited state (Table 3).
However, αA (63.1(40) MHz) is not much diﬀerent from that
of the ﬁrst excited state (55.3(17) MHz). It is therefore
concluded that the lowest bending vibration is very
anharmonic.
An excited-state spectrum assumed to be the ﬁrst excited
state of the torsion about the C2−N9 bond is shown in Table
S14. Its frequency is 138(25) cm−1 according to relative
intensity measurements, compared to 147 cm−1 (MP2 result)
for the lowest torsional vibration. The α-values of Table 3
(−36.9(20), 5.7674(44), and 2.7268(42) MHz) are again in
poor agreement with theory (−93.05, 7.05, and 4.43 MHz;
Table S7). Very tentative assignments are suggested for the
second, third, and fourth excited states of this vibration, whose
spectra are listed in Tables S15−S17. The vibration−rotation
constants of these modes (Table 3) indicate that the torsional
mode has a very anharmonic nature.
We have also assigned the spectrum (Table S18) of what we
believe is the ﬁrst excited state of the lowest bending vibration
calculated to have a frequency of 201 cm−1, compared to ca.
210 cm−1 from relative intensity measurements. There is poor
agreement between the MP2 (last column of Table 2) and the
corresponding experimental α-values in Table S7 in this case as
well.
The overall poor performance of MP2/cc-pVTZ calculations
of vibration−rotation α-values seen in the case of Trans
indicates that this computational method, which is very
demanding since computations of third derivatives are involved,
is still too primitive. Unfortunately, calculations at higher levels
of theory of these constants are beyond our present
computational possibilities.
Searches for the Spectrum of Cis I. The energy of this
rotamer is 8−9 kJ/mol higher than the energy of Cis II
according to the quantum chemical calculations above. This
indicates that this form should be present in a very low
concentration (Boltzmann factor less than 0.04 relative to the
ground vibrational state of Cis II, which means that the gas
consists of more than about 96% of Cis II and less than
approximately 4% Cis I).
Table 4. Spectroscopic Constantsa of Cis II
vibrational
state
ground
ﬁrst ex. torsion
Av (MHz)
Bv (MHz)
Cv (MHz)
DJ (kHz)
DJK (kHz)
DK (kHz)
d1 (kHz)
d2 (kHz)
HJ (Hz)
HJK (Hz)
HKJ (Hz)
hJ (Hz)
hJKb (Hz)
rmsa
Na
8999.0439(27)
2450.13114(99)
2101.4817(10)
1.8145(24)
−10.9264(24)
37.783(29)
−0.483479(62)
−0.011664(24)
−0.0061(18)
−0.03296(49)
−0.2633(90)
−0.001978(16)
−0.0003707(79)
1.436
835
9032.6547(38)
2434.8459(15)
2096.4883(16)
1.7253(42)
−10.4418(33)
37.777(50)
−0.46680(11)
−0.014028(40)
−0.0109(34)
−0.0329(12)
−0.187(30)
−0.002142(31)
−0.000378(16)
1.489
580
ﬁrst ex. lowest
bend.
9026.6880(79)
2447.79828(95)
2098.85060(88)
1.6932(8)
−10.4764(47)
35.40(17)
−0.44663(33)
−0.00959(15)
1.494
366
a
Deﬁned in the footnote of Table 2. The spectra are listed in Tables
S19 − S21 of the Supporting Information. bFurther sextic constants
preset at zero in the least-squares ﬁt.
Transitions with J > 85 were too weak due to an unfavorable
Boltzmann factor and could not be assigned. c-type lines, whose
hypothetical frequencies can be very accurately predicted from
the spectroscopic constants in Table 4, were searched for but
not assigned. This is consistent with a small μc predicted to be
only 0.31 D (Table 1) producing insuﬃcient intensities.
It is seen from Table 4 that very accurate values have been
obtained for the rotational and quartic centrifugal distortion
constants. Five of the seven sextic centrifugal distortion
constants, HJ, HJK, HKJ, hJ, and hJK, were determined. Values
of HK and hK signiﬁcantly diﬀerent from zero could not be
obtained and these constants were preset at zero in the leastsquares ﬁt.
A comparison of the rotational constants reveals that the
CCSD constants (Table 1) are larger than the experimental
equivalents (Table 4) by 0.1, 21.5, and 9.6 MHz in the cases A,
B, and C, respectively. The MP2 method (Table 3S) predicts
66.10, 18.88, and 14.01 MHz for these diﬀerences and it is
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between these two atoms is relatively short (227.0 pm; Table
S2), while twice the van der Waals radii of hydrogen is 240 pm.
Another force that may destabilize Cis I is the interaction
between the lone pair electrons of O12 and the pseudo-π
electrons70 of the cyclopropyl ring. Interaction between the πelectrons of the amide group and the ring pseudo-π electrons
could have a similar eﬀect.
The situation in Cis II is quite diﬀerent from that of Cis I. In
Cis II, there is no repulsion between H6 and H10 and possibly
attraction between O12 and H6, which are separated by 310
pm (Table S4), as well as a weak intramolecular hydrogen bond
between H10 and the pseudo-π electrons along the C1−C2
bond, because the nonbonded distances between H10 and C2
is 210.5 pm and the nonbonded distance between H10 and C1
is 281.1 pm (Table 4S). The O12 atom is further away from the
ring in this case than in Cis I, which may result in less
repulsion. It appears that there are more important repulsive
forces in Cis I than in Cis II, which may be the reason why Cis
II is 8−9 kJ/mol lower in energy than Cis I.
In the Trans conformer, there are also nonbonded contacts
that seem to be of importance. The nonbonded distance
between H13 and C2 is 257.7 pm. The distance between H13
and C3 is 287.9 pm, whereas H10 and C1 is separated by 289.8
pm (Table S8). The van der Waals half-thickness of aromatic
carbon is 170 pm.69 The sum (290 pm) of this parameter (170
pm) and hydrogen (120 pm) is longer than the aforementioned
nonbonded distances and this is indicative of stabilization by
internal hydrogen bonding between H10 and H13 on the one
side and the pseudo-π electrons of the ring on the other. It is
again diﬃcult to assess the importance of a possible interaction
between the π-electrons of the amide group and the pseudo-π
electrons of the cyclopropyl ring. However, rotation about the
C2−N9 bond away from the minimum position will
presumably decrease the attraction between the pseudo-π
electrons and the H10 and H13 atoms resulting in the
potential-energy function displayed in Figure 3.
concluded that the CCSD structure of Cis II (Table 1) is
subject to the same rather minor deﬁciencies discussed above
for Trans.
The experimental quartic centrifugal distortion constants
(Table 4) are all larger than the MP2 constants (Table 1). The
smallest diﬀerence is seen for DJ (7.7%) and the largest for d2
(46.1%), a disappointing result. It comes as no surprise that the
experimental sextic centrifugal distortion constants (Table 4)
deviate so much from their MP2 equiv to render a comparison
meaningless.
Vibrationally Excited States of Cis II. The MP2
anharmonic frequencies of the lowest vibrational fundamentals
of this species are 55, 176, 225, 368, 407, and 504 cm−1 (Table
S3). RFMWDR spectra revealed the existence of several
vibrationally excited state spectra in addition to the spectrum of
the ground vibrational state. The two strongest of these were
assigned in the same manner as described above for the ground
vibrational state spectrum. 580 transitions with Jmax = 65 were
assigned for what is assumed to be the ﬁrst excited state of the
torsion about the C2−N9 bond, while 366 transitions with Jmax
= 39 were assigned for the ﬁrst excited state of what is supposed
to be the lowest bending vibration. The spectra are listed in
Tables S20 and S21, respectively, of the Supporting
Information and the spectroscopic constants are listed in
Table 4. The same ﬁve sextic centrifugal distortion constants as
determined for the ground state were also obtained for the ﬁrst
excited torsional state. Only quartic centrifugal distortion
constants are given for the ﬁrst excited bending vibration.
Inclusion of sextic constants was attempted in the ﬁtting of this
spectrum, but relatively large standard deviations were obtained
and it was concluded that sextic constants of physical
signiﬁcance cannot be obtained from the spectroscopic material
in Table S21.
Relative intensity measurements yielded 74(20) cm−1 for the
torsion and 176(25) cm−1 for the lowest bending vibration
compared to 55 and 176 cm−1, respectively (Table S3). The
rotation-vibration constants calculated from the entries of Table
4 (not given here) were very diﬀerent from those shown in
Table S3 and it is concluded that the MP2 calculations are too
primitive to reproduce well the α-constants in this case, just as
in the case of Trans above.
The energy of the ﬁrst excited state of the lowest bending
vibration [176(25) cm−1] is the highest energy of the cis
conﬁguration observed experimentally. The Boltzmann factor
of the ground vibrational state of Cis I (discussed above) is
0.08 relative to this excited state. This is another illustration of
how weak the spectrum of the hypothetical conformer Cis I is
expected to be.
■
ASSOCIATED CONTENT
S Supporting Information
*
Results of the theoretical calculations, including MP2 and
CCSD electronic energies, molecular structures, and rotational
constants, dipole moments, MP2 harmonic and anharmonic
vibrational frequencies, rotational and centrifugal distortion
constants, and rotation−vibration constants, and microwave
spectra of the ground and vibrationally excited states. This
material is available free of charge via the Internet at http://
pubs.acs.org.
■
■
DISCUSSION
The reason for the existence of two rotameric forms for cis-Ncyclopropylformamide is probably a complicated compromise
of several forces. In Cis I, which has a symmetry plane, the
distances between the oxygen atom O12 and the two hydrogen
atoms H5 and H8 of the ring are identical. This nonbonded
distance is 252.3 pm (Table S2) compared to 260 pm, which is
the sum of the Pauling and van der Waals radii69 of hydrogen
(120 pm) and oxygen (140 pm). This oxygen−hydrogen
contact, which may be called a weak intramolecular hydrogen
bond, is assumed to stabilize Cis I.
There are also repulsive forces that are likely to destabilize
Cis I. One such force is the interaction between the two
hydrogen atoms H6 and H10. The nonbonded separation
AUTHOR INFORMATION
Corresponding Author
*(H.M.) Telephone: +47 2285 5674; Fax: +47 2285 5441; Email: [email protected].
Notes
The authors declare no competing ﬁnancial interest.
■
ACKNOWLEDGMENTS
We thank Anne Horn for her skillful assistance. This work has
been supported by the Research Council of Norway through a
Centre of Excellence Grant (Grant No. 179568/V30). It has
also received support from the Norwegian Supercomputing
Program (NOTUR) through a grant of computer time (Grant
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DOI: 10.1021/acs.jpca.5b00542
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