PCCP
Rotational spectrum, hyperfine structure and structure of
2-azetidinoney
K. Demyk,a D. Petitprez,a J. Demaison,a H. Møllendalb and G. Wlodarczak*a
a
b
Laboratoire PhLAM, UMR CNRS 8523, Université de Lille I, F-59655, Villeneuve d’Ascq,
France. E-mail: karine.demyk@univ-lille1.fr
Department of Chemistry, The University of Oslo, P.O. Box 1003, Blindern N-0315 Oslo 3,
Norway
Received 14th July 2003, Accepted 24th September 2003
First published as an Advance Article on the web 7th October 2003
The quadrupole hyperfine structure due to 14N in 2-azetidinone has been measured using microwave
Fourier transform spectroscopy. Furthermore, the rotational constants of the 13C, 15N and 18O isotopomers
have been determined permitting the calculation of the substitution structure of the heavy atom skeleton.
The millimetre-wave spectrum of the main isotopomer has been measured up to 462 GHz for the ground
vibrational state (Jmax ¼ 82) as well as for the first three excited puckering states permitting the determination
of accurate spectroscopic constants. High-level quantum chemical calculations of the structure have been made.
The ab initio equilibrium structure is compared with the experimental structures.
I. Introduction
2-azetidinone, c-C3H5NO, is the simplest four-membered
lactam. It has been extensively studied both in the crystalline
phase and in solution because it is the active agent of a series
of important antibiotics.1–4 The first gas-phase study of 2-azetidinone was made by Marstokk et al.5 using microwave spectroscopy and electron diffraction supplemented by ab initio
calculations. The heavy skeleton of the molecule was found
to be planar in the gas-phase and the rotational and quadrupole coupling constants were determined together with its
dipole moment (ma ¼ 4.12 D, mb ¼ 0.39 D). However only 4
quartic centrifugal distortion constants could be marginally
determined. An rg structure has been determined by making
use of rotational constants of five isotopic species and electron
diffraction data. The ring-puckering potential was also determined from an analysis of the variation of the rotational
constants with the ring-puckering quantum number.
This article presents new spectroscopic results in the microwave and millimetre spectral ranges. These measurements
provide accurate spectroscopic constants of the ground vibrational state. As transitions in the first three excited states of the
ring-puckering mode were observed, the spectroscopic constants for these states were also determined. Furthermore, high
level ab initio calculations were used to determine the structure
of the molecule.
species in natural abundance. To polarize the azetidinone
molecule, 2 ms microwave pulses, perpendicular to the gas
pulses, were used with a power field of 50 mW and 1 mW for
the ma and mb-type transitions, respectively. The pulsed valve
was opened for 900 ms at a repetition rate of 2 Hz. Although
lines were observed with a sufficient S/N at room temperature,
the S/N ratio increased by one order of magnitude by heating
the nozzle at a temperature of 50 C. The sample was introduced into the controlled heated pulsed nozzle whose design
is similar to the one used by Suenram et al.7 Neon, at a backing
pressure of 1 bar, was used as the carrier gas. 4096 data points
per free emission decay are collected at a 10 MHz sample rate
which gives, after Fourier transformation, a spectral resolution
of 2.4 kHz per point. The accuracy of the frequency measurements is estimated to be better than 3 kHz. Transitions in the
8–60 GHz range were measured in Oslo with the Stark spectrometer described in ref. 8. The accuracy of the measurements is
100 kHz.
The millimetre spectra were recorded in the spectral ranges
220–240 GHz, 290–320 GHz and 440–475 GHz, at room
temperature in Lille. Different phase-stabilized backward
wave oscillators (BWO) were used as sources. The signal was
detected on a liquid He-cooled bolometer. The accuracy of
the measurements is about 100 kHz.
III. Microwave spectrum: Analysis of the
hyperfine structure
II. Experimental
A.
The sample of 2-azetidinone used in this work was purchased
from Aldrich and used without further purification (purity
98%). The Lille pulsed-nozzle MicroWave Fourier Transform
(MWFT) spectrometer described in ref. 6 was used to measure
lines in the 5–20 GHz range for the normal and the isotopic
y Electronic supplementary information (ESI) available: Experimental
frequencies (MHz) of the rotational spectra of the ground state and the
first three excited states of the ring-puckering mode of 2-azetidinone.
See http://www.rsc.org/suppdata/cp/b3/b307958a/
5038
Analysis of the hyperfine structure
The hyperfine structure was analyzed from the transitions
measured with the MWFT spectrometer using Pickett’s
program.9 The fit of the 32 measured transitions, listed in
Table 1, gives a standard deviation of 2.4 kHz. The resulting
14
N quadrupole coupling constants are waa ¼ 2.2172(16)
MHz, wbb ¼ 1.9136(18) MHz and wcc ¼ 4.1308(18) MHz
(Table 2). The off-diagonal constant wab could not be determined. Thanks to the high spectral resolution of the MWFT
measurements and to the relatively large number of observed
Phys. Chem. Chem. Phys., 2003, 5, 5038–5043
This journal is # The Owner Societies 2003
DOI: 10.1039/b307958a
Table 1 Microwave Fourier transform measurements of 2-azetidinone
Table 3 Microwave Fourier transform measurements of
2-azetidinone
J 0 K 0 a ,K 0 b
11,1
00,0
10,1
00,0
20,2
10,1
21,2
11,1
21,1
11,0
21,1
20,2
20,2
11,1
30,3
21,2
J 00 K 00 a ,K 00 b
F0
0
2
1
0
2
1
1
1
3
2
1
2
1
1
3
1
2
2
1
2
3
2
1
2
3
1
3
2
1
3
4
2
F 00
1
1
1
1
1
1
1
2
2
1
0
2
1
2
2
0
1
2
0
2
2
1
1
2
3
1
2
1
0
2
3
1
Obs./MHz
Obs. calc./kHz
J 0 K 0 a ,K 0 b
15 876.147
15 877.009
15 877.581
8718.016
8719.009
8719.675
17 278.450
17 279.118
17 279.598
17 279.796
17 280.116
17 280.461
16 149.177
16 149.744
16 150.484
16 150.602
16 151.242
16 151.810
18 724.167
18 725.068
18 725.680
18 726.306
18 727.265
9890.439
9891.917
9892.745
10 121.890
10 121.602
10 121.988
19 509.252
19 509.463
19 509.811
0.4
1.3
0.7
0.6
4.1
3.2
1.4
1.4
1.3
0.3
1.7
0.1
4.5
2.5
0.1
5.6
4.1
1.9
2.0
1.1
2.0
0.1
1.9
1.7
2.9
3.1
2.2
0.1
4.9
2.0
1.3
0.2
10,1
20,2
21,2
21,1
11,1
transitions, these constants are more accurately determined
than the previous ones (waa ¼ 1.9(5) MHz and wbb ¼ 1.7(2)
MHz) determined from low resolution measurements.5
B. Isotopic species
Table 2 Spectroscopic constants of the ground vibrational state of
2-azetidinone
a
00,0
10,1
11,1
11,0
00,0
N
Obs./MHz
Obs. calc./kHz
8683.560
17 197.346
16 056.481
18 677.707
15 574.411
1.95
0.46
0.20
0.32
0.01
rotational constants are given in Table 8. The small value of
the error on these constants does not mean that they are very
accurately determined but rather comes from the small number
of observed transitions for each isotopomer and from the fact
that in the fitting procedure the quartic centrifugal distortion
constants and the 14N quadrupole coupling constants were
kept fixed to the values obtained from the main species analysis. Using Kraitchman equations, the coordinates of the heavy
atoms were calculated in the principal inertia axis system and
are given in Table 9. The errors on the coordinates were calculated using the empirical rule proposed by Costain:11
s(z) ¼ K/|z| with K ¼ 0.0015 Å2.12 Their large values may in
most cases be explained by the fact that the coordinates are
small. The uncertainty on the coordinate b(C2), which is found
to be imaginary, was calculated using Costain’s formula and
the absolute value of b. The result, 0.036 Å seems large, however it has the same order of magnitude as the ab initio value
for this coordinate. The derived c coordinates are close to zero
showing that the heavy skeleton of the molecule is planar
(Fig. 1) as previously found.5 The derived distances and angles
and their uncertainties are listed in Table 10. They were calculated assuming that the heavy atom skeleton is planar. It has to
be noted that the resulting accuracy is poor, except for the
r(C2=O5) value. This is due to the fact that many Cartesian
coordinates are small.
IV. Millimetre spectrum: Centrifugal distortion
analysis
A. Ground vibrational state
The rotational constants of the isotopic species were predicted
using the ab initio calculated structure and lines were easily
found for substituted heavy atoms of the skeleton. The measured and calculated frequencies are listed in Tables 3 to 7.
The rotational spectra were fitted to a Watson Hamiltonian
using A-reduction in an Ir representation.10 The derived
A/MHz
B/MHz
C/MHz
DJ/kHz
DJK/kHz
DK/kHz
dJ/kHz
dK/kHz
FJK/Hz
FK/Hz
waa/MHz
wbb/MHz
wcc/MHz
J 00 K 00 a ,K 00 b
15
This study
Previous study5
12 161.3333(19)
5003.33826(51)
3715.79097(46)
0.602924(88)
3.92504(52)
3.4872(56)
0.150444(27)
2.09758(92)
0.00359(26)
0.1226(59)
2.2174(16)a
1.9128(19)a
4.1302(19)a
12 161.348(12)
5003.341(11)
3715.787(11)
0.79(37)
3.39(21)
7.2(11)
0.1314(66)
2.70(14)
—
—
1.9(5)
1.7(2)
—
Determined from the analysis of the MWFT measurements, see text.
We identified 383 transitions of the ground vibrational state in
the 4–470 GHz range, covering J value from 1 to 82. These frequencies, corrected from the nuclear quadrupole hyperfine
structure, are given in the supplementary material.y The 64
transitions measured previously5 are included in this list.
All these transitions were used to determine the rotational
Table 4 Microwave Fourier transform measurements of
2-azetidinone
J 0 K 0 a ,K 0 b
11,1
00,0
10,1
00,0
20,2
10,1
21,1
11,0
21,2
11,1
J 00 K 00 a ,K 00 b
F0
0
2
1
0
2
1
3
2
1
3
2
1
3
2
F 00
1
1
1
1
1
1
2
1
0
2
1
0
2
1
13
C2
Obs./MHz
Obs. calc./kHz
15 867.862
15 868.726
15 869.302
8693.406
8694.402
8695.066
17 232.383
17 232.581
17 232.902
18 669.285
18 669.909
18 667.772
16 108.441
16 109.194
2.93
0.35
2.59
0.71
1.08
2.28
0.35
0.33
0.40
0.96
1.20
2.93
0.80
0.03
Phys. Chem. Chem. Phys., 2003, 5, 5038–5043
5039
Table 5 Microwave Fourier transform measurements of
2-azetidinone
J 0 K 0 a ,K 0 b
11,1
00,0
10,1
00,0
20,2
10,1
21,1
11,0
21,2
J 00 K 00 a ,K 0 b
F0
0
2
1
0
2
1
3
2
1
3
2
1
3
2
11,1
F 00
1
1
1
1
1
1
2
1
0
2
1
0
2
1
13
C3
Table 7 Microwave Fourier transform measurements of
2-azetidinone
Obs./MHz
Obs. calc./kHz
J 0 K 0 a ,K 0 b
15 499.801
15 500.662
15 501.237
8664.323
8665.322
8665.991
17 159.114
17 159.32
17 159.627
18 643.994
18 644.62
18 642.479
16 017.413
16 018.169
0.56
0.28
0.96
2.80
1.58
2.22
0.03
1.78
0.13
0.79
0.97
1.10
0.39
1.83
10,1
00,0
20,2
10,1
21,1
11,0
21,2
11,1
parameters. As expected from the small rotational constants
and the large dipole moment (ma ¼ 4.12 D, mb ¼ 0.39 D5),
the microwave and millimetre spectrum of 2-azetidinone is
very rich. Furthermore, transitions from excited states of the
low-frequency ring-puckering vibration mode (n 111 cm1)
are also present (see Section IV B). Because ma is much larger
than mb , the a-type transitions are much stronger. Consequently many fewer b-type transitions were identified although
they are accurately predicted. The 8–62 GHz spectrum is dominated by a rich aQ-branch spectrum whereas in the 220–472
GHz range aR-branch transitions represent the large majority
of the identified transitions. This is also the case for b-types
transitions which represent 13% of the identified lines, with
J values between 3 and 62.
The rotational spectrum was fitted to a Watson Hamiltonian
using A-reduction in an Ir representation.10 The initial prediction of the millimetre spectrum was calculated from the rotational parameters determined from previous spectroscopic
measurements performed in Oslo in the 18–38 GHz range.5
It was then improved step by step as new identified lines were
added. The derived parameters are given in Table 2. Owing to
the much larger number of transitions, the rotational parameters are much more accurately determined than in ref. 5.
This is particularly true for the centrifugal constants.
The equilibrium values of the centrifugal distortion constants were calculated using density functional theory (DFT).
We used the hybrid functional B3LYP (Becke’s three parameter functional employing the Lee, Yang and Parr correlation functional13) with the 6-311+G(3df,2pd) basis set as
J 0 K 0 a ,K 0 b
20,2
11,0
11,1
00,0
10,1
00,0
21,2
11,1
21,1
11,0
5040
J 00 K 00 a ,K 00 b
F0
1
3
2
1
2
0
1
2
0
2
1
3
2
3
2
F 00
1
2
1
0
2
1
1
1
1
1
1
2
1
2
1
13
C4
Obs./MHz
Obs. calc./kHz
16 944.809
16 945.951
16 946.143
16 946.472
16 946.807
15 811.854
15 812.716
15 813.287
8544.466
8545.461
8546.125
15 852.862
15 853.618
18 329.102
18 329.727
0.35
0.20
0.11
0.34
1.09
0.07
1.35
1.40
1.25
1.54
2.74
0.23
1.99
0.24
1.00
Phys. Chem. Chem. Phys., 2003, 5, 5038–5043
F0
0
2
1
1
3
2
1
2
3
2
3
2
F 00
1
1
1
1
2
1
0
2
2
1
2
1
O
Obs./MHz
Obs. calc./kHz
8269.009
8270.005
8270.669
16 413.557
16 414.694
16 414.875
16 415.220
16 415.537
17 701.047
17 701.670
15 379.095
15 379.847
0.36
1.43
2.63
0.11
1.38
1.01
0.10
2.19
1.08
0.16
1.35
0.43
implemented in Gaussian 98.14 Comparison with the experimental ground state constants shows significant deviations
for the constants DJK and DK (Table 11). These differences
may be explained by the vibrational dependence of the constants. It is possible to correct the ground state constants for
the contribution of the ring puckering vibration either by using
the experimental constants of the ground state and of the first
excited puckering state (see Section IV B) or by calculating this
contribution using the potential of ref. 5. Both methods give
almost identical results and this correction significantly
improves the agreement between experimental and calculated
constants.
B.
Ring-puckering vibration
We also observed transitions from the first three excited states
of the ring-puckering mode (n 111 cm1). The 156 transitions observed for v ¼ 1, 118 for v ¼ 2 and 91 for v ¼ 3 are
given in the supplementary material.y As in the case of the
ground vibrational state, aQ-branch transitions dominate the
spectra in the 8–62 GHz range whereas in the 222–472 GHz
range, aR-branch transitions dominate. No b-type transitions
were identified in the third excited state but 15 and 8 Q-branch
transitions were identified for v ¼ 1 and v ¼ 2, respectively.
Table 8 Rotational constants for the isotopic species of the azetidinone molecule
Rms/ No.
Species kHz a lines
13
Table 6 Microwave Fourier transform measurements of
2-azetidinone
J 00 K 00 a ,K 00 b
18
C2
C3
13
C4
15
N
18
O
13
1.5
1.4
1.2
0.9
1.3
5
5
5
5
4
b
A/MHz
B/MHz
C/MHz
12 161.7577(12)
11 824.6680(9)
12 159.0654(12)
11 887.9508(28)
12 160.906(84)
4987.4438(5)
4989.3380(3)
4891.8220(2)
4997.0952(10)
4715.5221(5)
3707.0725(5)
3676.0988(3)
3653.7538(2)
3686.4691(9)
3554.5975(5)
a
Rms ¼ standard deviation of the fit.
tions in the MWFT measurements.
b
Number of observed transi-
Table 9 Kraitchman coordinates (Å) of azetidinone
Atom
aa
ba
ca
C2
C3
C4
N
O
0.5702(26)
0.5308(28)
1.5253(10)
0.3553(42)
1.7785(8)
i(0.036)b
1.0966(14)
0.0870(172)
0.9869(15)
0.0337(445)
0.0172(873)
ib
0.0238(630)
0.0049(3078)
ib
a
The error given in parentheses is the Costain error: s(z) ¼ K/|z| with
K ¼ 0.0015 Å2, see Section IIIB. b Imaginary value.
V. Ab initio structure
Fig. 1
Structure of 2-azetidinone.
All these transitions were used to determine the centrifugal
parameters of each of the excited states presented in Table 12.
These parameters are significantly different from those determined previously,5 especially for the v ¼ 1 and v ¼ 3 states.
The variation of the centrifugal distortion constants with the
ring-puckering quantum number shows a zigzag behavior
which is typical of the ring-puckering vibration mode but
which may also be explained by interactions between the puckering states and other vibrational states. However, an attempt
to reproduce this variation using the potential of ref. 5 failed.
This is probably due to the fact that the third excited puckering
state at 327(50) cm1 might be in interaction with the N–H
out-of-plane bending vibration which lies at 367(60) cm1.5
The substitution structure of the ring determined from
Kraitchman equations (see Section III B) is not expected to
be reliable because all the atoms have at least one rather small
coordinate,15 see Table 9. The ab initio structure has already
been calculated5 but the level of theory used (HF/6-31G**)
does not warrant an accurate structure either. Higher level
ab initio calculations were thus performed for this study, the
results are presented in Table 10.
A new ab initio structure was first calculated using the
second-order Møller–Plesset perturbation theory (MP2)16
and Dunning’s correlation consistent polarized valence basis
sets, cc-pVTZ and cc-pVQZ.17 These calculations were performed with the Gaussian 98 suite of programs14 using the frozen core approximation and without making any assumption
on the symmetry of the molecule. They confirm that the heavy
atom skeleton of the molecule is indeed planar. Furthermore,
the comparison between the cc-pVTZ and cc-pVQZ results
indicates that convergence is practically achieved for the bond
angles (the largest variation is only 0.06 for the cN1C4H8
angle) but not for the bond lengths although the variations
are small, the largest variation being only 0.003 Å for the
C2–C3 bond. At the MP2/cc-pVQZ level of theory, the bond
angles are expected to be rather accurate18 and reliable C–H
and C=O bond lengths may also be obtained provided a small
offset correction is taken into account.19
On the other hand, it is rather unlikely that reliable bond
lengths may be obtained in this way for the ring because there
is no reason to assume that the offsets (re rab initio) for the C–
C and C–N bond lengths are constant. For this reason, we
have performed one calculation using the coupled cluster
method with single and double excitations20 augmented by a
perturbational estimate of the effects of the connected triple
excitations, CCSD(T),21 with the cc-pVTZ basis set. These
calculations were performed with the MOLPRO2000 program22,23 using the frozen core approximation and assuming
that the heavy atom skeleton of the molecule is planar. The
CCSD(T) method is known to give reliable results24 provided
the non-dynamical correlation is not important. This is the
case for azetidinone because the coupled cluster T1 diagnostic25 is only 0.0148. Furthermore it is established that the
Table 10 Geometrical structure of 2-azetidinone (distances in Å and angles in degrees)
MP2
MP2/MT
MT(fcb )
MT(aec )
fc-ae
cc-pVTZ
cc-pVQZ
Q-T
CCSD(T) cc-pVTZ
rea
re(ED)d
N1–C2
C2C3
C3C4
N1C4
C2=O5
N1–H6
C3–H7
C4–H8
cN1C2C3
cC2C3C4
cC3C4N1
cC4N1C2
cC4N1H6
cC3C2O5
cC2C3H7
cN1C4H8
cH7C3C2O5
cH8C4N1H6
1.3703
1.5382
1.5441
1.4603
1.2023
1.0060
1.0843
1.0864
90.98
85.87
87.44
95.71
132.89
136.07
113.87
113.99
63.88
63.86
1.3675
1.5345
1.5405
1.4574
1.2002
1.0049
1.0826
1.0848
90.99
85.87
87.46
95.67
132.91
136.06
113.86
113.99
63.87
63.87
0.0028
0.0037
0.0036
0.0029
0.0021
0.0011
0.0017
0.0016
0.01
0.00
0.02
0.04
0.02
0.01
0.01
0.00
0.01
0.01
1.3735
1.5409
1.5473
1.4631
1.2063
1.0076
1.0858
1.088
90.95
85.91
87.42
95.73
132.85
136.09
113.84
113.97
63.89
63.88
1.3709
1.5379
1.5448
1.4613
1.2044
1.0067
1.0849
1.0869
91.00
85.90
87.41
95.69
132.90
136.09
113.81
113.91
63.88
63.89
0.0026
0.0030
0.0025
0.0018
0.0019
0.0009
0.0009
0.0011
0.05
0.01
0.01
0.04
0.05
0.00
0.03
0.06
0.01
0.01
1.3751
1.5468
1.5553
1.4685
1.2054
1.0071
1.0883
1.0906
91.044
85.800
87.308
95.849
132.785
136.060
113.885
114.002
63.930
63.840
1.370
1.540
1.549
1.464
1.201
1.005
1.086
1.088
91.12
85.810
87.32
95.77
132.85
136.05
113.84
113.94
63.92
63.86
1.371(2)
1.526(3)
1.541(5)
1.470(3)
1.195(1)
0.968(3)
1.075(5)
1.075(5)
91.1(2)
86.0(2)
87.6(1)
95.3(2)
131.0(6)
136.6(3)
115.1(8)
114.4(9)
rs
1.353(26)
1.554(25)
1.546(13)
1.476(11)
1.209(3)
0.986(3)
91.7(2)
85.2(10)
87.5(2)
95.6(12)
132.2(7)
136.7(22)
a
re ¼ CCSD(T)/cc-p VTZ + [MP2/cc-pVQZ-MP2/cc-pVTZ] + [MP2(ae)/MT-MP2(fc)/MT]. b fc ¼ frozen core approximation. c ae ¼ all
electrons correlated. d re(ED) the bond distances are derived from rg values, the bond angles are derived from ra , see ref. 5. The given errors
are those for the rg values, the errors for the re values are expected to be larger. e rs ¼ substitution structure of azetidinone, see Section IIIB.
Phys. Chem. Chem. Phys., 2003, 5, 5038–5043
5041
Table 11 Experimental and ab initio [B3LYP/6-311+G(3df,2pd)]
centrifugal distortion constants of 2-azetidinone (in kHz)
Dj
Djk
Dk
dj
dk
v¼0
(exp.)
v¼e
(calc.)a
v¼0
(exp.) calc.
v ¼ eb
(exp.)
v ¼ e (exp.) calc.
0.603
3.925
3.487
0.150
2.098
0.584
4.432
2.688
0.146
1.957
3.2%
12.9%
22.9%
2.9%
6.7%
0.589
4.086
2.944
0.150
1.989
0.8%
8.5%
8.7%
3.0%
1.6%
a
Equilibrium ab initio value. b Approximate experimental equilibrium value of the centrifugal distortion constant calculated with the
formula Pe ¼ P0 + (P0 P1)/2 where P is the considered centrifugal
distortion constant.
Table 12 Spectroscopic constants of the first three excited states of
ring-puckering vibration of 2-azetidinone
Parameter/
unit
v¼1
v¼2
v¼3
A/MHz
B/MHz
C/MHz
DJ/kHz
DJK/kHz
DK/kHz
dJ/kHz
dK/kHz
12 091.0267(49)
5013.1540(14)
3725.9087(13)
0.6316(11)
3.6025(69)
4.573(87)
0.150311(53)
2.315(24)
12 030.7153(67)
5020.8015(23)
3734.8554(22)
0.71781(62)
4.2096(47)
1.164(86)
0.17248(18)
1.893(13)
11 982.006(13)
5026.3652(16)
3742.2239(14)
0.37665(48)
6.5323(24)
13.184(68)
0.24888(17)
0.444(12)
variation from CCSD(T)/cc-pVTZ to CCSD(T)/cc-pVQZ
may be rather accurately predicted at the MP2 level26 which
allows us to improve the accuracy of the ab initio structure.
However, this structure is still different from the equilibrium
structure because the core and core-valence correlations effects
on the computed molecular geometry have been neglected.27
To estimate them, the Martin–Taylor (MT) basis set27 was
used with the MP2 method which is known to be accurate
enough for first row atoms.28 This core-correlation correction
is negligible for the angles and has the expected order of
magnitude for the bond lengths,27 see Table 10. The final
equilibrium structure is also given in Table 10.
lesser extent N–H bond lengths, using high level ab initio
methods.29 Comparing bond angles between heavy atoms
(the position of the H atoms is not accurately determined from
the experiments), there is a good agreement within two standard deviations. Finally, taking into account the experimental
uncertainty (a few thousandths of an Å), the agreement is also
good for the bond lengths, except for the C2–C3 bond where
the equilibrium ab initio value is larger by 0.014 Å than the
experimental value (Table 10). The rg value itself is smaller
than the ab initio value which is surprising. However, it is possible to estimate the equilibrium bond length in another way,
starting from the ab initio results and applying an offset correction.30 This gives consistent results indicating that the ab initio
equilibrium structure (re in Table 10) is probably reliable.
Furthermore, the substitution structure gives rs(C2–C3) ¼
1.554(5) Å which is much larger than re(ED) ¼ 1.526 Å.
Although the substitution structure is not expected to be accurate (see Section V), an error as large as 0.028 Å is unlikely. In
conclusion, it seems that the rg value for r(C2–C3) might be
inaccurate.
Appendix: Internuclear distance parameters
re
rs
rg
ra
Acknowledgements
We thank Dr. J.C. López (Valladolid) for helpful comments
and for having performed the calculations of the ring puckering dependence of the molecular constants.
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VI. Discussion
The main uncertainty in the ab initio structure comes from the
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It is interesting to compare the equilibrium structures determined either ab initio or experimentally, (re(ED) in Table 10,
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5042
Phys. Chem. Chem. Phys., 2003, 5, 5038–5043
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