Journal of Molecular Structure 524 (2000) 69–85
www.elsevier.nl/locate/molstruc
Microwave spectrum, conformational equilibrium, 14N quadrupole
coupling constants, dipole moment, vibrational frequencies and
quantum chemical calculations for acrylamide
K.-M. Marstokk, H. Møllendal, S. Samdal*
Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway
Dedicated to Professor Peter Klaeboe on the occasion of his 70th birthday.
Received 5 May 1999; received in revised form 3 September 1999; accepted 3 September 1999
Abstract
The microwave spectrum of acrylamide (CH2yCHCONH2) has been investigated in the 20.0–60.5 GHz spectral region at
room temperature. Two conformers were assigned. The most stable rotamer is planar with the carbonyl and vinyl groups in the
syn conformation. Five vibrationally excited states of the C–C torsional motion and six other vibrationally excited states have
been assigned for this conformer, as have three deuterated species (amide group). The frequencies of most of these excited
states have been determined by relative intensity measurements. The dipole moment of this rotamer is (in units of Debye) ma ˆ
0:269…3†; mb ˆ 3:42…2†; mc ˆ 0:12…24† and mtot ˆ 3:44…5†: The 14N quadrupole coupling constants were found to be xaa ˆ
1:87…26† and xbb ˆ 2:73…16† MHz; respectively.
The second, less stable skew form is non-planar with the CyC–CyO chain of atoms approximately 155⬚ from syn. The
ground vibrational state and two excited states were assigned. The syn form was found to be 6.5(6) kJ mol ⫺1 more stable than
the skew conformer by relative intensity measurements.
Quantum chemical calculations at HF, MP2 and DFT levels of theory using the rather large basis sets 6-311⫹G ⴱⴱ, 6311⫹⫹G ⴱⴱ and cc-pVTZ have been made to assist the experimental work. 䉷 2000 Elsevier Science B.V. All rights reserved.
Keywords: Acrylamide; Microwave spectrum; Conformational equilibrium; Dipole moment; Quantum chemical calculations
1. Introduction
This paper is a continuation of our general interest
in the molecular structure and conformation of amides
in the gaseous state where we have used gas electron
diffraction [1–8] and microwave (MW) spectroscopy
[9,10] as well as quantum chemical computations [8–
12] in our studies. The molecules we have investigated
* Corresponding author. Tel.: ⫹47-22-855-458; fax: ⫹47-22-855441.
E-mail address: svein.samdal@kjemi.uio.no (S. Samdal).
so far are primary amides where we have focused
mostly on the molecular structure and the conformation about the Csp3 –Csp2 bond.
In this work we extend our studies to the simplest
conjugated primary amide, acrylamide. This
compound has several important commercial applications, in particular the production of commonly used
plastic [13]. It is an interesting difunctional monomer
containing a reactive electron-deficient double bond
and an amide group, and it undergoes reactions typical
of those two functionalities. The electron withdrawing
carboxamide group activates the double bond, which
0022-2860/00/$ - see front matter 䉷 2000 Elsevier Science B.V. All rights reserved.
PII: S0022-286 0(99)00362-2
70
K.-M. Marstokk et al. / Journal of Molecular Structure 524 (2000) 69–85
Fig. 1. The numbering of the atoms and the two conformations for acrylamide.
consequently reacts readily with nucleophilic reagents
by addition. It exhibits both weak acidic and basic
properties, and the site of protonation has been studied
by ab initio calculations [14]. Acrylamide is highly
toxic to humans and animals [15,16].
The question about the planarity of the amide group
has been asked, and from the IR spectra in the gaseous
state [17] it has been concluded that acrylamide has a
planar amide group. In this work no indication of a
second conformation was seen. It was concluded that
the less stable form must be at least 600 cm ⫺1
(7.2 kJ mol ⫺1) less stable [17].
Some MM2 [18] and ab initio calculations [14,18]
have been carried out. They found the syn conformation as shown in Fig. 1 to be the most stable form, in
agreement with the evidence from the IR spectra [17].
The ab initio calculations [14] were not conclusive
concerning the planarity of the amide group.
It is our purpose to get more experimental and theoretical information on the molecular structure and
conformational properties of the important acrylamide molecule in the free state. Finally, it should be
mentioned that the number of known molecular structures and conformations of the gaseous amides is relatively small owing to their low volatility and tendency
to decompose upon heating. There is a considerable
interest in the properties of free amides because they
are the simplest models for the biologically important
peptides.
2. Experimental
The sample (m.p. 82–85⬚C specified to be at least
99% pure) utilized in this work was purchased from
Fluka AG and used as received. No impurities were
seen in the MW spectrum, which was studied using
the Oslo spectrometer [19]. The 20–39 and the 53–
60.5 GHz spectral range was investigated thoroughly.
Further, selected regions of the 39–60.5 GHz spectral
range were also studied. The MW absorption X-band
brass cell was held at room temperature in the experiments. The pressure was about 2 Pa when the spectra
were recorded, and stored electronically using the
computer programs written by Waal [20]. The accuracy of the frequency measurements is presumed to be
better than ^0.10 MHz. Radio frequency-microwavefrequency double resonance (RFMWDR) experiments were carried out as described in Ref. [21]
using the equipment mentioned in Ref. [22]. The deuterated species (amide group) were produced by
seasoning the wave-guide with heavy water and then
introducing the parent species.
3. Results and discussion
3.1. Quantum chemical calculations
The quantum chemical computations have been
made with the Gaussian94 program package [23]
using the IBM RS6000 cluster in Oslo. Calculations
were performed at three different levels of theory;
Hartree–Fock (HF), Møller–Plesset pertubation
(MP2) [24] with all electrons included, as well as
density functional theory (DFT) employing the
B3LYP method [25]. The basis sets utilized were 6311⫹G ⴱⴱ, 6-311⫹⫹G ⴱⴱ and cc-pVTZ [26]. The
Table 1
Molecular structures of the most stable syn conformation of acrylamide from quantum chemical calculations a
HF/6-311⫹G ⴱⴱ
MP2 ˆ full/6-311⫹⫹G ⴱⴱ
HF/cc-pVTZ
DFT/B3LYP/cc-pVTZ
MP2 ˆ full/cc-pVTZ
121.97
136.94
149.65
100.58
100.78
133.07
108.68
108.45
108.34
122.12
137.63
149.57
100.73
100.95
133.95
108.74
108.53
108.42
119.41
135.16
149.48
98.78
99.05
131.42
107.48
107.27
107.32
121.78
136.50
149.43
100.30
100.50
132.62
108.44
108.21
108.10
121.79
135.79
148.44
99.91
100.19
132.82
107.70
107.69
107.54
122.15
123.35
114.51
122.63
118.41
118.96
121.00
118.16
120.83
120.00
121.69
118.31
122.50
123.39
114.06
119.41
115.98
116.74
120.51
118.61
120.89
119.72
121.43
118.85
122.34
123.03
114.63
122.34
118.49
119.17
120.86
118.15
120.99
120.39
121.46
118.15
122.23
123.33
114.43
122.48
118.43
119.09
120.99
118.19
120.82
119.86
121.81
118.33
122.68
123.25
114.07
122.05
118.48
119.46
120.18
118.95
120.88
119.04
121.72
119.25
0.03
180.03
180.03
⫺0.03
0.04
179.98
0.00
180.00
180.00
0.00
⫺2.98
176.90
161.03
13.51
⫺21.01
190.87
0.23
179.98
180.01
0.10
0.01
180.01
180.07
⫺0.03
0.08
179.98
⫺0.01
179.99
179.99
⫺0.01
0.01
180.02
180.19
⫺0.15
0.20
179.87
⫺0.01
180.02
179.98
0.01
0.09
180.09
180.54
⫺0.42
0.60
179.64
⫺0.01
180.00
179.99
⫺0.01
0.26
3.71
0.00
3.72
0.25
3.78
0.75
3.86
0.11
3.74
0.00
3.74
0.42
3.58
0.01
3.61
0.09
3.89
0.02
3.89
K.-M. Marstokk et al. / Journal of Molecular Structure 524 (2000) 69–85
Bond length (pm)
O1yC2
119.54
C2–N3
135.51
C2–C6
149.60
N3–H4
99.06
N3–H5
99.32
C6yC7
131.85
C6–H10
107.72
C7–H8
107.51
C7–H9
107.55
Bond angles (⬚)
O1C2N3
122.31
O1C2C6
122.98
N3C2C6
114.70
C2N3H4
122.47
C2N3H5
118.46
H4N3H5
119.07
C2C6C7
120.85
C2C6H10
118.14
C7C6H10
121.01
C6C7H8
120.47
C6C7H9
121.40
H8C7H9
118.13
Dihedral angles (⬚)
O1C2C6C7
0.00
O1C2C6H10
180.00
O1C2N3H4
179.99
O1C2N3H5
0.02
C6C2N3H4
⫺0.02
C6C2N3H5
180.01
C2C6C7H8
⫺0.01
C2C6C7H9
179.99
H10C6C7H8
180.00
H10C6C7H9
0.00
Dipole moments (Debye)
ma
0.02
mb
3.83
mc
0.00
mtot
3.83
DFT/B3LYP/6-311⫹G ⴱⴱ
71
72
HF/6-311⫹G ⴱⴱ
Rotational constants
DA
DB
DC
DFT/B3LYP/6-311⫹G ⴱⴱ
MP2 ˆ full/6-311⫹⫹G ⴱⴱ
HF/cc-pVTZ
⫺10.31
⫺14.36
⫺10.61
⫺81.72
⫺11.71
⫺10.76
339.78
55.24
52.92
DFT/B3LYP/cc-pVTZ
MP2 ˆ full/cc-pVTZ
b
(MHz)
313.98
37.24
41.55
24.89
9.16
4.31
39.39
75.40
39.49
a
Energies (hartree) for columns 2–7 are: ⫺245.8946737, ⫺247.3774088, ⫺246.7789693, ⫺245.9178246, ⫺247.3958559, ⫺246.9071573, respectively. No symmetry
constraints were used in the calculations.
b
The observed rotational constants are given in Table 7, Ds represent differences between calculated and observed rotational constants, i.e D ˆ calc: ⫺ obs:
K.-M. Marstokk et al. / Journal of Molecular Structure 524 (2000) 69–85
Table 1 (continued)
Table 2
Molecular structures of the least stable skew conformation of acrylamide from quantum chemical calculations
HF/6-311⫹G ⴱⴱ
MP2 ˆ full/6-311⫹⫹G ⴱⴱ
HF/cc-pVTZ
DFT/B3LYP/cc-pVTZ
MP2 ˆ full/cc-pVTZ
122.29
137.78
149.17
100.76
100.98
134.20
108.58
108.55
108.47
119.28
135.87
149.44
98.92
99.21
131.55
107.29
107.38
107.32
121.82
136.85
149.23
100.39
100.61
132.81
108.22
108.27
108.16
121.89
136.45
148.04
100.10
100.35
133.09
107.54
107.69
107.60
122.29
120.74
116.95
121.09
116.74
117.70
125.94
112.97
120.95
122.51
121.11
116.35
122.87
121.32
115.75
118.16
115.01
116.29
124.30
114.41
121.10
121.76
120.86
117.35
122.40
120.44
117.14
120.01
115.96
117.09
125.54
113.21
121.14
122.51
120.94
116.53
122.37
120.72
116.88
120.67
116.45
117.57
126.06
112.87
120.94
122.36
121.22
116.39
122.71
121.15
116.10
119.45
115.76
117.35
125.04
114.04
120.82
121.59
121.01
117.37
154.24
⫺21.53
162.34
6.63
⫺19.34
184.95
1.06
182.98
176.53
⫺1.55
4.98
148.75
⫺26.27
155.05
11.53
⫺27.76
188.71
1.41
183.08
176.11
⫺2.22
3.17
155.54
⫺20.76
158.55
8.54
⫺22.92
187.08
0.96
182.68
176.98
⫺1.30
5.71
155.69
⫺20.19
161.15
7.53
⫺20.60
185.88
0.98
182.85
176.56
⫺1.57
5.79
155.54
⫺20.77
158.36
9.22
⫺23.83
172.96?
0.41
182.37
176.49
⫺1.55
4.75
2.45
3.05
0.86
4.01
2.84
3.04
1.24
4.34
2.52
3.00
0.97
4.04
2.26
2.94
0.83
3.80
2.81
3.02
1.00
4.24
73
122.04
137.15
149.49
100.65
100.87
133.24
108.47
108.51
108.40
K.-M. Marstokk et al. / Journal of Molecular Structure 524 (2000) 69–85
Bond length (pm)
O1yC2
119.40
C2–N3
136.16
C2–C6
149.61
N3–H4
99.18
N3–H5
99.46
C6yC7
131.95
C6–H10
107.52
C7–H8
107.62
C7–H9
107.55
Bond angles (⬚)
O1C2N3
122.39
O1C2C6
120.51
N3C2C6
117.09
C2N3H4
120.20
C2N3H5
116.05
H4N3H5
117.04
C2C6C7
125.41
C2C6H10
113.31
C7C6H10
121.16
C6C7H8
122.59
C6C7H9
121.86
H8C7H9
116.52
Dihedral angles (⬚)
O1C2C6C7
153.78
O1C2C6H10
⫺22.24
O1C2N3H4
158.72
O1C2N3H5
8.27
C6C2N3H4
⫺22.80
C6C2N3H5
186.75
C2C6C7H8
1.15
C2C6C7H9
182.89
H10C6C7H8
176.87
H10C6C7H9
⫺1.38
D Ea
6.34
Dipole moments (Debye)
ma
2.66
mb
3.08
mc
1.02
mtot
4.20
DFT/B3LYP/6-311⫹G ⴱⴱ
74
Rotational constants b
DA
DB
DC
a
b
HF/6-311⫹G ⴱⴱ
DFT/B3LYP/6-311⫹G ⴱⴱ
MP2 ˆ full/6-311⫹⫹G ⴱⴱ
(MHz)
102.7
56.5
66.8
⫺81.4
⫺15.3
9.9
⫺184.2
12.6
43.8
HF/cc-pVTZ
160.4
71.8
72.7
DFT/B3LYP/cc-pVTZ
⫺18.4
5.0
20.5
MP2 ˆ full/cc-pVTZ
56.6
65.4
61.1
Energy difference in kJ/mol relative to the most stable conformation, i.e DE ˆ Ecalc: ⫺ Esyn: .
The observed rotational constants are given in Table 12, Ds represents differences between calculated and observed rotational constants, i.e. D ˆ calc: ⫺ obs:
K.-M. Marstokk et al. / Journal of Molecular Structure 524 (2000) 69–85
Table 2 (continued)
Table 3
Molecular structures of the transition state between the syn and skew forms for acrylamide from quantum chemical calculations
HF/6-311⫹G ⴱⴱ
a
MP2 ˆ full/6-311⫹⫹G ⴱⴱ
HF/cc-pVTZ
DFT/B3LYP/cc-pVTZ
MP2 ˆ full/cc-pVTZ
121.76
136.65
150.69
100.64
100.91
132.89
108.73
108.51
108.41
122.11
137.19
150.14
100.70
100.98
133.92
108.75
108.59
108.46
119.14
135.25
150.28
98.86
99.17
131.22
107.55
107.45
107.33
121.54
136.30
150.47
100.35
100.64
132.45
108.49
108.27
108.17
121.69
135.84
149.08
100.00
100.31
132.83
107.78
107.69
107.59
122.78
122.53
114.65
121.63
118.64
119.18
123.47
115.47
121.00
121.69
121.36
116.95
122.10
122.81
114.02
119.45
115.15
118.01
122.09
116.62
121.45
121.14
121.25
117.60
122.84
122.57
114.55
121.15
118.24
119.06
123.40
115.40
121.18
121.77
121.27
116.95
122.87
122.53
114.57
121.48
118.46
119.19
123.55
115.55
120.86
121.67
121.42
116.90
123.17
122.91
113.89
120.76
118.26
119.36
122.28
116.90
120.80
120.98
121.23
117.78
83.02
⫺94.37
186.17
⫺2.27
8.27
179.73
1.79
182.73
179.04
⫺0.02
18.9
86.00
⫺91.61
195.78
⫺10.61
18.91
172.52
1.45
182.17
178.96
⫺0.22
13.9
85.67
⫺93.10
189.58
⫺4.78
11.78
177.42
0.56
181.47
179.27
0.16
20.1
83.06
⫺94.58
187.49
⫺3.26
9.59
178.83
1.69
182.63
179.22
0.15
20.1
83.12
⫺95.10
189.85
⫺4.73
11.67
177.10
1.10
181.95
179.25
0.10
19.7
K.-M. Marstokk et al. / Journal of Molecular Structure 524 (2000) 69–85
Bond length (pm)
O1yC2
119.27
C2–N3
135.51
C2–C6
150.44
N3–H4
99.13
N3–H5
99.42
C6yC7
131.62
C6–H10
107.78
C7–H8
107.69
C7–H9
107.55
Bond angles (⬚)
O1C2N3
122.81
O1C2C6
122.56
N3C2C6
114.59
C2N3H4
121.37
C2N3H5
118.42
H4N3H5
119.13
C2C6C7
123.41
C2C6H10
115.30
C7C6H10
121.27
C6C7H8
121.82
C6C7H9
121.22
H8C7H9
116.96
Dihedral angles (⬚)
O1C2C6C7
86.38
O1C2C6H10
⫺91.96
O1C2N3H4
188.05
O1C2N3H5
⫺3.94
C6C2N3H4
10.20
C6C2N3H5
178.21
C2C6C7H8
0.80
C2C6C7H9
181.69
H10C6C7H8
179.04
H10C6C7H9
⫺0.07
DE a
19.9
DFT/B3LYP/6-311⫹G ⴱⴱ
Energy difference in kJ/mol relative to the most stable conformation, i.e DE ˆ Ecalc: ⫺ Esyn: :
75
76
Table 4
Molecular structures of the anti transition state for acrylamide from quantum chemical calculations
Bond length (pm)
O1yC2
119.56
C2–N3
135.41
C2–C6
149.72
N3–H4
98.89
N3–H5
99.30
C6yC7
131.90
C6–H10
107.50
C7–H8
107.62
C7–H9
107.54
Bond angles (⬚)
O1C2N3
122.00
O1C2C6
119.75
N3C2C6
118.26
C2N3H4
123.38
C2N3H5
117.73
H4N3H5
118.90
C2C6C7
127.19
C2C6H10
112.16
C7C6H10
120.65
C6C7H8
123.58
C6C7H9
120.64
H8C7H9
115.78
DE a
8.35
a
DFT/B3LYP/6-311⫹G ⴱⴱ
MP2 ˆ full/6-311⫹⫹G ⴱⴱ
HF/cc-pVTZ
DFT/B3LYP/cc-pVTZ
MP2 ˆ full/cc-pVTZ
122.18
136.64
149.52
100.48
100.48
133.20
108.46
108.54
108.39
122.53
136.63
149.31
100.37
100.37
134.12
108.58
108.57
108.45
119.46
135.05
149.55
98.61
99.02
131.51
107.27
107.38
107.31
121.98
136.22
149.27
100.18
100.46
132.75
108.22
108.30
108.16
122.07
135.58
148.12
99.79
100.14
133.02
107.54
107.70
107.60
121.89
120.15
117.96
123.38
117.83
118.80
127.52
111.94
120.55
123.40
120.95
115.65
7.21
122.23
120.31
117.46
123.21
117.64
119.15
127.04
112.65
121.30
123.22
120.51
116.28
6.89
122.05
119.71
118.24
123.21
117.75
119.03
127.19
112.13
120.68
123.49
120.72
115.80
7.71
122.00
120.15
117.86
123.23
117.78
118.99
127.62
111.84
120.54
123.30
121.04
115.66
7.25
122.34
120.36
117.30
122.92
117.69
119.39
126.98
112.79
120.23
122.80
120.75
116.44
6.83
Energy difference in kJ/mol relative to the most stable conformation, i.e DE ˆ Ecalc: ⫺ Esyn: .
K.-M. Marstokk et al. / Journal of Molecular Structure 524 (2000) 69–85
HF/6-311⫹G ⴱⴱ
K.-M. Marstokk et al. / Journal of Molecular Structure 524 (2000) 69–85
77
Table 5
Calculated frequencies (Cs symmetry only for B3LYP/cc-pVTZ, the other calculations have no symmetry. Parenthesized values are IR
intensities in KM/mol) for the syn and skew conformation of acrylamide
No.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
SymCs
A 00
A 00
A0
A0
A 00
A0
A 00
A0
A 00
A 00
A 00
A0
A0
A0
A0
A0
A0
A0
A0
A0
A0
A0
A0
A0
Assignment
Tors
v NH
d CyC–C
d skel
t NH2
d OCN
g CH
rCH2
g skel
g CH
g CH
rCH2
rNH2
d CCH
d CCH
scisCH2
scisNH2
strCyC
strCyO
strCH
strCH
strCH
strNH
strNH
Syn
Skew
B3LYP/cc-pVTZ
MP2/6-311⫹⫹G
89.6(107)
137.0(77)
276.9(7)
466.2(5)
469.2(9)
616.8(10)
616.9(3)
811.5(6)
821.2(19)
1008.6((2)
1018.8(44)
1037.9(5)
1113.2(3)
1290.0(108)
1356.3(42)
1443.8(80)
1617.3(113)
1689.6(42)
1764.3(243)
3140.0(9)
3151.1(11)
3236.1(2)
3593.3(45)
3727.6(38)
79.5(3)
424.8(86)
278.6(6)
469.9(75)
478.5(74)
591.0(27)
621.8(28)
783.0(21)
831.5(8)
909.4(27)
1001.5(34)
1049.3(5)
1123.8(9)
1292.7(78)
1360.8(71)
1452.6(86)
1635.7(97)
1688.7(22)
1784.5(280)
3189.8(3)
3209.8(10)
3298.1(1)
3619.3(50)
3755.5(43)
structural parameters from the different calculations
are given in Tables 1–4, and the numbering of the
atoms is shown in Fig. 1.
All computations predict the syn rotamer to be the
most stable form and most of the calculations predict a
planar molecular structure. Only the MP2/6311⫹⫹G ⴱⴱ and the MP2/6-31⫹G ⴱ [14] calculations
predict a pyramidal amide conformation for the syn
form.
The non-planarity of the amide moiety found in
these computations is in agreement with our previous
calculations [12] for other amides. Use of double or
triple zeta basis sets with polarization and in particular
diffuse functions, gives a non-planar conformation for
the amide group when MP2 is used. This is probably
due to an artefact of the basis set and the MP2 method
when applied to amides.
Some bonds lengths (Tables 1–4) are underestimated at the HF level of theory as compared with
the bond lengths predicted from MP2 and DFT.
ⴱⴱ
B3LYP/cc-pVTZ
MP2/6-311⫹⫹G ⴱⴱ
99.9
353.8
277.6
432.0
525.1
561.3
592.9
819.0
824.1
986.4
1040.3
1043.9
1116.6
1311.6
1359.9
1455.7
1617.6
1684.8
1758.6
3137.9
3178.8
3219.3
3584.2
3749.7
108.6
410.0
279.3
490.9
529.1
558.9
611.2
798.1
938.8
937.4
1022.6
1048.6
1129.9
1304.8
1370.1
1464.8
1628.5
1668.7
1774.6
3189.0
3232.3
3287.3
3616.3
3711.1
DFT and MP2 give similar bond length. All bond
angles are remarkably similar at the three levels of
theory even with different basis sets. This is also the
case for the dihedral angles except for the nonplanarity of the amide group which is predicted only
in the MP2 calculation, as mentioned above.
Comparison of the calculated rotational constants
of the syn form with the experimental ones as shown
in Tables 1 and 7, indicates that the DFT/B3LYP
structure is better than both the HF and MP2 structures, because the experimental and theoretical rotational constants are in better agreement. This is a
useful result because the rotational constants and the
dipole moment obtained from theory often are used to
predict the frequencies of the strongest transitions in
the MW spectrum. Good estimates will of course
make the assignments easier.
All calculations predict the existence of a second
skew conformation whose theoretical structures are
given in Table 2. The dihedral angle O1C2C6C7 is
78
K.-M. Marstokk et al. / Journal of Molecular Structure 524 (2000) 69–85
Table 6
Experimental and theoretical findings for the lowest vibrational frequencies of acrylamide
IR
MW
Ab initio (syn)
Proposed assignment
Obs. (cm ⫺1)
Assign.
Obs. (cm ⫺1)
Assign.
Calc. (cm ⫺1)
Assign.
262.8
n 2(1 ← 0)wag NH
torsion
wag NH
d C ˆ C–C
89.6
137.0
276.9
torsion
wag NH
d CyC–C
344.7
352.7
378.5
n 2(2 ← 1)wag NH
fund. out-of-pl
n 2(3 ← 2)wag NH
⬇ 90
⬇ 235 ^ 40
⬇ 307 ^ 40
⬇ 398 ^ 60
n1 ⫹ n2
⬇ 420 ^ 60
n1 ⫹ n3
366.4
466.2
469.2
616.8
616.9
n1 ⫹ n3
456.4
t (CN)
614.9
Comp. band
about 155⬚ from syn (0⬚) in all computations except
for one (148.75⬚; MP2/6-311⫹⫹G ⴱⴱ). All calculations predict a pyramidal amide group for this
rotamer, which is computed to be from 3 to
6 kJ mol ⫺1 less stable than the syn conformation.
These numbers are smaller than the estimate of at
least 600 cm ⫺1 (7.2 kJ mol ⫺1) from the IR spectra
[17], and our value of 6.5(6) kJ mol ⫺1 from our relative intensity measurements.
We succeeded in assigning the skew form (see
below). It is shown in the same table that the best
agreement between the calculated and experimental
rotation constants again is found for the DFT/
B3LYP calculations, which are therefore assumed to
produce the most accurate structure.
The structures of the two transitional states are
given in Tables 3 and 4. The transition state between
the syn and the skew conformations occurs for a dihedral angle where the vinyl group is approximately
perpendicular to the amide group. The barrier height
is computed to be about 20 kJ mol ⫺1 relative to syn
from all calculations except for the MP2/6311⫹⫹G ⴱⴱ computations, which yield a barrier height
of 14 kJ mol ⫺1. The anti barrier is predicted to be
between 1.2 and 3.7 kJ mol ⫺1 in the different calculations.
3.2. Vibrational frequencies
The calculated frequencies for the two conformations are given in Table 5. Tentative assignments
based on the displacement of the atoms for each
d OyC–N
g CH
n 1 ⬇ 90
n 2ˆ262.8
n 3 ⬇ 307 ^ 40
n 2(2 ← 1) ˆ 344.7
n 1 ⫹ n 2 ⬇ 353
n 2(3 ← 2) ˆ 378.5
n1 ⫹ n3
n4
n5
n6
n7
CC torsion
wag NH
sk bend
wag NH
wag NH/n 1 ⫹ n 3
sk bend
CN torsion
sk bend
CH out-of-pl
fundamental mode for the syn conformations are
also given in this table.
For the skew conformation the calculated frequencies are quite similar at both levels of theory. It should
be noted (see above) that these two calculations both
predict a non-planar amide group for the skew form.
However, the corresponding computations of the
frequencies for the syn form yield a widely different
result. The N–H wagging frequency changes radically
from 137.0 to 424.8 cm ⫺1 in these two calculations. It
is remarked above that the B3LYP/cc-pVTZ procedure predicts a planar conformation while the MP2/6311⫹⫹G ⴱⴱ method predicts a pyramidal amide group
for the syn rotamer.
There are not many experimentally reported
observed frequencies for acrylamide, but some are
available [14,17,27]. In Table 6 the experimental findings for the lowest frequencies are summarized.
The crucial point about the amide planarity is the IR
assignment [17] of the very weak band NH wag
n2 …3 ! 2† ˆ 378:5 cm⫺1 which can also be the n1 ⫹
n3 combination band which is expected to fall in this
region (Table 6). The assignment of the NH wag
n2 …3 ! 2† ˆ 378:5 cm⫺1 is likely to be correct, and
then the IR investigation shows that the amide unit is
planar.
Vibrational frequencies can be obtained from MW
spectroscopy by means of relative intensity measurements which have been carried out as described in
Ref. [28]. The large uncertainties for this method
are due to the difficulties of estimating the position
of the base line.
K.-M. Marstokk et al. / Journal of Molecular Structure 524 (2000) 69–85
79
Table 7
Spectroscopic constants (A-reduction, I r representation [44]) for the ground vibrational state and five C2–C6 torsion vibrational states
Av (MHz)
Bv (MHz)
Cv (MHz)
DJ (kHz)
DJK (kHz)
DK (kHz)
dJ (kHz)
dK (kHz)
FJ (Hz)
FJK (Hz)
FKJ (Hz)
FK (Hz)
fJ (Hz)
fJK (Hz)
fK (Hz)
IC ⫺ IA ⫺ IB (10 ⫺20u m 2)
No a
RMS b
a
b
vˆ0
vˆ1
vˆ2
vˆ3
vˆ4
vˆ5
10732.8296(34)
4218.7012(13)
3030.7434(13)
0.7043(33)
3.370(22)
5.403(8)
0.2417(7)
3.20(4)
⫺0.066(6)
⫺0.222(34)
⫺1.54(13)
0.57(4)
0.00170(34)
⫺0.60(5)
1.98(16)
⫺0.131300(34)
354
0.081
10660.7092(33)
4216.4693(11)
3038.0502(17)
0.696(14)
3.15(7)
5.100(24)
0.2394(26)
3.37(7)
⫺0.208(33)
⫺2.3(4)
⫺3.5(5)
0.38(4)
⫺0.0022(4)
⫺0.74(12)
1.85(17)
⫺0.91431(7)
322
0.063
10594.1266(38)
4214.2765(14)
3044.8733(16)
0.776(7)
3.658(31)
5.055(15)
0.2418(19)
3.41(5)
⫺0.007(7)
⫺0.65(11)
⫺0.57(17)
0.11(10)
⫺0.0107(26)
0.64(13)
0.40(34)
⫺1.64738(6)
317
0.090
10531.951(6)
4212.1010(22)
3051.3677(26)
0.824(9)
3.94(5)
5.119(24)
0.2403(35)
3.52(9)
0.036(11)
⫺1.27(28)
2.3(7)
⫺1.6(5)
⫺0.20(6)
1.19(25)
⫺5.5(15)
⫺2.34419(10)
206
0.112
10473.259(21)
4209.902(15)
3057.626(15)
0.81(11)
3.69(15)
5.9(8)
0.227(8)
3.26(17)
⫺0.066
⫺0.222
⫺1.54
0.57
0.0017
⫺0.60
1.98
⫺3.01477(35)
42
0.193
10417.592(23)
4207.719(20)
3063.765(19)
0.87(15)
3.87(9)
5.1(5)
0.241(6)
3.44(13)
⫺0.066
⫺0.222
⫺1.54
0.57
0.0017
⫺0.60
1.98
⫺3.6661(4)
48
0.202
Number of transitions.
Root-mean-squares deviation.
For the C2–C6 torsional frequency of the syn
rotamer relative intensity measurements gave 90 ^
10 cm⫺1 :
This frequency can also be estimated for planar
molecules from the inertial defect [29,30]. Oka [30]
has shown that the torsional fundamental can be
calculated from the formula:
1=2
D0 ˆ ⫺33:715=n1 ⫹ 0:0186Icc
where D 0 is the inertial defect for the ground state and
Icc is the principal moment of inertia about the c-axis.
This gives a value of 91 cm ⫺1 in our case.
Hanyu, Britt and Boggs [29] have obtained yet
another formula for the calculation of the torsional
frequency from the difference between the inertial
defect of two consecutive torsionally excited states:
Dnt⫹1 ⫺ Dnt ˆ ⫺67=nt
where D n t⫹1 and D n t are the inertia defects of the two
states and n t is the torsional frequency. This yielded a
frequency of 85 cm ⫺1. The other frequencies of the
syn form given in Table 6 were obtained from relative
intensity measurements.
3.3. MW spectrum and assignment of the syn form
The MW spectrum consists of a relatively strong
and dense b-type spectrum. The most stable conformation is predicted from the quantum chemical
computations to be the syn form. The largest component of the dipole moment of this rotamer is mb ⬇
3:7 D (Table 1). Searches were first made for the
strong bQ-branch transitions using rotational
constants obtained from the B3LYP/6-311⫹G ⴱⴱ
calculations as the starting point. These ground state
transitions were readily identified close to their
predicted frequencies. The b-type R-branch transitions were assigned next.
The strongest bQ-branch transitions for the first
vibrationally excited states of the torsional motion
about the C2–C6 bond were then assigned. Following
the progression of these transitions we were able to
assign altogether five vibrational excited states of this
molecule. The results (A reduction, I r representation)
for the ground state and the five vibrationally excited
states of the torsion are given in Table 7.
The n 2 wag NH was expected to have rotational
constants close to the ground state rotational constants
mainly because the light H-atoms attached to the
80
K.-M. Marstokk et al. / Journal of Molecular Structure 524 (2000) 69–85
Table 8
Spectroscopic constants a for six vibrational excited states (same units as in Table 7. The seven sextic centrifugal distortions constants are fixed
at zero)
Av
Bv
Cv
DJ
DJK
DK
dJ
dK
IC ⫺ IA ⫺ IB
No.
RMS
n 2 ˆ d CyC–C
n 3 ˆ wag NH
n1 ⫹ n2
n1 ⫹ n3
2n 1 ⫹ n 2
2n 1 ⫹ n 3
10765.263(13)
4217.684(4)
3025.270(4)
0.725(12)
4.06(9)
5.30(5)
0.243(5)
3.40(12)
0.28333(14)
57
0.144
10724.935(10)
4209.4293(31)
3029.3310(33)
0.784(10)
3.77(16)
5.31(13)
0.225(4)
3.21(8)
⫺0.35208(12)
65
0.139
10684.740(19)
4214.551(15)
3032.921(14)
1.18(12)
3.85(12)
5.1(7)
0.239(6)
3.32(13)
⫺0.5809(4)
38
0.159
10652.745(20)
4206.784(16)
3035.993(16)
0.86(12)
4.05(11)
5.0(7)
0.236(6)
2.92(12)
⫺1.1130(4)
44
0.185
10614.352(14)
4212.680(5)
3040.947(6)
0.814(20)
4.15(11)
4.2(6)
0r.251(7)
3.03(13)
⫺1.38762(23)
36
0.153
10587.472(16)
4205.643(11)
3043.632(10)
0.67(8)
3.41(11)
7.5(6)
0.220(7)
4.75(14)
⫺1.85584(27)
28
0.131
N-atom are involved in this out-of-plane motion.
By comparing the Stark effect of the strongest
unassigned bQ-branch transitions in the vicinity
of the ground state transitions, this vibrationally
excited state was identified. The negative inertial
defect confirms that this excited state belongs to
an out-of-plane motion [32,33].
The n 3 in-plane skeleton bending transition was
searched for further away from the ground state transitions, and the positive inertial defect confirms
[32,33] that the assigned excited state belongs to an
in-plane motion. The two n1 ⫹ n2 and n1 ⫹ n3 vibrational excited states were readily assigned from their
estimation of their rotational constants as:
Xn1⫹n2 ˆ Xn1 ⫹ Xn2 ⫺ X0
where X is the rotational constants A, B or C. The
estimated values for the n1 ⫹ n2 rotational constants
are 10693.2, 4215.5 and 3032.7 MHz which can be
compared with observed values (Table 8) 10684.7,
4214.5 and 3032.9 MHz. The estimated values for
the n1 ⫹ n3 rotational constants are 10652.8, 4207.2
and 3036.4 MHz which can be compared with
observed values (Table 9) 10652.7, 4206.8 and
3036.0 MHz. The same procedure was used to assign
Table 10
Stark coefficients and dipole moment of acrylamide (uncertainties
represent one standard deviation)
Table 9
Spectroscopic constants (same units as in Table 7. D4 means that
the H-atom numbering 4 (see Fig. 1) has been replaced with
deuterium. The seven sextic centrifugal distortions constants are
fixed to zero) for three isotopic species
D4
A
B
C
DJ
DJK
DK
dJ
dK
IC ⫺ IA ⫺ IB
No
RMS
D5
D4D5
10122.825(25) 10716.108(22) 10116.491(18)
4139.638(9)
4017.565(9)
3947.488(6)
2940.775(6)
2924.594(9)
2842.336(4)
0.72
0.72
0.72
3.10(19)
3.59(15)
3.13(13)
5.43
5.43
5.43
0.243(17)
0.202(15)
0.184(8)
3.1
3.1
3.1
⫺0.1553(4)
⫺0.1499(5)
⫺0.17731(24)
14
16
17
0.104
0.143
0.082
Transition
93,6 ← 92,7
兩M兩
9
8
7
6
5
83,5 ← 82,6
8
7
6
5
4
53,2 ← 52,3
5
Dipole moment a (Debye)
ma ˆ 0:269…3† mb ˆ 3:42…2†
a
Dn E ⫺2/10 ⫺5 (MHz V ⫺2 cm 2)
Obs.
Calc.
3.360
2.680
2.000
1.460
0.987
1.870
1.380
1.020
0.637
0.402
⫺1.390
3.390
2.661
2.014
1.461
0.986
1.865
1.412
1.009
0.673
0.397
⫺1.390
mc ˆ 0:12…24†
1 Debye ˆ 3:33564 × 10⫺30 C m:
K.-M. Marstokk et al. / Journal of Molecular Structure 524 (2000) 69–85
Table 11
14
N nuclear quadrupole splitting (Eq) of acrylamide and diagonal
elements of the 14N quadrupole coupling tensor
Transition
F0 ← F
Eq (MHz)
Obs.
2←1
0.65
22,1 ← 11,0
22,1 ← 11,0
3←2
⫺0.07
22,0 ← 11,1
3←2
0.26
31,3 ← 20,2
3←2
0.64
42,3 ← 41,4
4←4
⫺1.10
52,4 ← 51,5
5←5
⫺1.13
6←6
⫺1.15
62,5 ← 61,6
71,6 ← 70,7
7←7
⫺1.49
81,7 ← 80,8
8←8
⫺1.38
82,6 ← 81,7
8←8
⫺0.82
92,7 ← 91,8
9←9
⫺0.91
14
N nuclear quadrupole coupling constants a (MHz)
xaa ˆ 1:86…26†
xbb ˆ 2:73…16†
Calc.
0.68
⫺0.10
0.31
0.70
⫺1.19
⫺1.13
⫺1.09
⫺1.45
⫺1.32
⫺0.81
⫺0.93
a
Uncertainties represent one standard deviation. Some constants
(xaa ,xbb )/MHz for other amides are: formamide [45]
(1.94(3),1.90(3)); acetamide [46] (1.9368(24),2.0090(22)); 2fluoroacetamide [46] (1.6595(26),2.0413(27)); propionamide [8]
(2.2(8),2.3(5)).
the 2n1 ⫹ n2 and the 2n1 ⫹ n3 vibrational excited
state.
We believed that we would be able to calculate very
accurately the shift in the rotational constants of the
ground state to the respective isotopic species using
the B3LYP/6-311⫹G ⴱⴱ molecular structure. This was
done for the all the 13C isotopic species, but we were
not able to assign any of these isotopic species in their
natural abundance owing to insufficient intensities. This
81
was also done for the three isotopomers obtained
when the H-atoms in the amide group were replaced
with deuterium. All the three isotopic species were
assigned in a straightforward manner.
3.4. Dipole moment of the syn form
The 11 Stark coefficients (Table 10) of transitions
with comparatively small quadrupole splittings were
used to determine the dipole moments following the
standard procedure [31]. Field strengths were typically in the 500–1000 V cm ⫺1 range. Quadrupole
interaction is small and is not taken into account in
the least-squares fit. All three principal axis dipole
moment components were fitted in order to get information of the planarity of the amide group.
3.5. 14N quadrupole coupling constants of the syn
form
All transitions were split by a small amount by
quadrupole interaction caused by the 14N nucleus.
Resolved quadrupole components were only observed
in a few cases. The components appearing in Table 11
were used to determine the quadrupole coupling
constants of the 14N nucleus following the procedure
of Ref. [31]. The spectroscopic constants in Table 7
were used to predict the unperturbed center frequencies. The 14N nuclear quadrupole splittings (Eq in
Table 11) were found by subtracting the calculated
center frequencies from the frequencies of the
resolved components. A rigid-rotor Hamiltonian was
used in the least squares fitting procedure in order to
Table 12
Spectroscopic constants (same units as in Table 7. The seven sextic centrifugal distortions constants are fixed to zero.) for the skew conformation
Av
Bv
Cv
DJ
DJK
DK
dJ
dK
IC –IA –IB
No.
RMS
a
Ground state v ˆ 0
10049.549(22)
4287.924(12)
3035.806(12)
1.14(9)
4.20(12)
8.0(6)
0.283(9)
3.23(15)
⫺1.67697(35)
53
0.196
Ex. state v ˆ torsion
10002.8(5)
4292.160(24)
3050.385(33)
1.15(16)
3.35(18)
8.0
0.28
3.2
⫺2.591(4)
14
0.129
a-type R-branch transitions from the MWRFDR experiment.
Ex. state a v ˆ dCyC–C
9999.4(47)
4287.50(27)
3047.86(30)
1.1
4.2
8.0
0.28
3.2
⫺2.60(5)
6
0.122
82
K.-M. Marstokk et al. / Journal of Molecular Structure 524 (2000) 69–85
Table 13
Comparison of calculated (calculated rotational constants using
nT ˆ 0 through nT ˆ 5:† and observed (observed rotational
constants are listed in Table 7) rotational constants (MHz) using
B ˆ 2:8
nT
A (MHz)
Calc.⫺obs.
B (MHz)
Calc.⫺obs.
0
⫺0.76
⫺0.004
1
1.57
⫺0.004
2
0.36
0.000
3
⫺0.89
⫺0.011
4
⫺0.98
⫺0.013
5
1.19
⫺0.006
Calculated rotational constants (MHz)
An ˆ 10774.3(21)⫺159(5)具z 2典n ⫺11.4(14)具z 4典n
Bn ˆ 4219.86(2)⫺4.13(4)具z 2典n ⫺0.832(11)具z 4典n
An ˆ 3026.66(17)⫺15.3(4)具z 2典n ⫹ 1.55(11)具z 4典n
C (MHz)
Calc.⫺obs.
0.059
⫺0.085
⫺0.011
0.095
0.140
⫺0.034
determine the 14N nuclear quadrupole coupling
constants x aa and x bb. The results are shown in
Table 11, and some constants for other amides are
given for comparison.
3.6. Assignment of the skew form
This rotamer is predicted to have a sizeable dipole
moment along the a-inertial axis. MWRFDR-searches
were therefore carried out in order to assign the a-type
R-branch transitions of this conformer. The strongest
transitions were expected to occur in the 50–60 GHz
region, and the searches were carried out here using
the DFT/B3LYP rotational constants to predict the
spectrum.
The rather weak aR-lines were readily found using
this method. Confirmation of their assignments were
obtained from Stark effect studies, rigid-rotor fit and
b-type Q-branch transitions that were subsequently
assigned. The resulting spectroscopic constants are
listed in Table 12. The dipole moment of this rotamer
could not be measured owing to insufficient intensities. The quadrupole coupling constants of the 14N
nucleus with the molecular rotation were not determined because of the weakness of the spectrum.
Two vibrationally excited states were found for this
rotamer; their spectroscopic constants are found in
Table 12. Rough relative intensity measurements
yielded 91(20) cm ⫺1 for what is assumed to be the
C–C torsional vibration, and ca. 208(70) cm ⫺1 for
the lowest heavy-atom bending vibration. These two
values compare well with the corresponding frequencies in Table 5 (99.9 and 277.6 cm ⫺1, B3LYP).
3.7. Energy difference between syn and skew form
Relative intensity measurements were carried out
as described in Ref. [28] to determine the energy
difference. This difference depends on the ratio of
the dipole moments. The values taken from the
B3LYP calculations (Tables 1 and 2) were used to
derive a value of 6.5(6) kJ mol ⫺1, slightly larger
than the B3LYP/cc-pVTZ value of 5.8 kJ mol ⫺1.
The estimated standard deviation of ^0.6 kJ mol ⫺1
is assumed to take both systematic and random errors
into account.
3.8. Heavy atom planarity and potential function of
the syn form
The smooth variation of the rotational constants for
the vibrationally excited torsional fundamental vibration of the syn rotamer indicates that there is no barrier
to the planar syn form [32], and that this torsional
mode is nearly harmonic. Gwinn et al. [34] and
Legon [35] have given a quantitative treatment of
this problem. They have shown that it is possible to
define a potential function for the torsion as:
V ˆ A…具z4 典 ⫹ B具z4 典†
where z is a dimensionless coordinate. If B is positive,
the heavy atom skeleton has a symmetry plane, if B is
negative, the equilibrium conformation will be nonplanar. According to this theory the rotational
constants can be expanded in a power series of the
expectation values 具z2 典 and 具z4 典; where bn is the An, Bn
or Cn rotational constants in the nth excited state of the
torsion. The empirical parameters b0, b2 and b4 are
adjusted to give the best fit to the data. The values
具z2 典n and 具z4 典n depend only on the constant B in the
equation given above. The rotational constants of
successively excited states of the torsional vibration
were least-squares fitted to the equation:
Bn ˆ b0 ⫹ b2 具z2 典n ⫹ b4 具z4 典n
employing a program described in Ref. [36] for a
series of B-values. It was found that the value B ˆ
2:8 yield the best overall fit (Table 13). This positive
B-value indeed shows that the heavy atom skeleton is
K.-M. Marstokk et al. / Journal of Molecular Structure 524 (2000) 69–85
83
Fig. 2. Potential function 22:2…具z4 典 ⫹ 2:8具z2 典† describing the torsional vibration around the C2–C6 bond. Eigenstates are indicated.
planar. The constant A was then adjusted to reproduce
the torsional fundamental frequency of 90 cm ⫺1. This
was achieved with A ˆ 22:2 cm⫺1 : The potential
function derived in this manner is sketched in Fig. 2.
3.9. Planarity of the amide group of the syn form
A non-planar conformation of the amide group of
the syn form would produce a component of the dipole
moment along the principal inertial c-axis …mc † that
would be non-zero. The theoretical calculations indicate a very small mc except for MP2/6-311⫹G ⴱⴱ
where mc ˆ 0:75 D: The dipole moment is a rather
sensitive test of planarity. However, with the transitions we have used, the dipole moment along the principal inertial c-axis is not very accurately determined
(mc ˆ 0:12(24) D, Table 10) which indicates that the
amide group is less non-planar than the MP2/6311⫹G ⴱⴱ calculations predict. When mc is fixed to
zero the fit is insignificantly larger. A definite conclusion cannot be drawn from the mc dipole moment
component, but it can safely be stated that a large
deviation from planarity is ruled out.
Another evidence that acrylamide is planar, or very
nearly planar, comes from the value of inertial defect
which is zero for a completely rigid planar molecule.
The inertial defect for syn acrylamide is as large as
⫺0:131300…34† × 10⫺20 u m2 (Table 7).
However, an amide group with floppy hydrogen
atoms could produce a deviation from the ideal zero
value. This has in fact been found for the related
compound formamide [37,38] which has an inertial
defect of ⫺0:006510…2† × 10⫺20 u m2 [37] and is
planar.
If the contribution from the out-of-plane hydrogen
atoms of the methyl group is arbitrarily assumed to be
a
pseudo-inertial
defect
3:20 × 10⫺20 u m2 ;
(10 ⫺20 u m 2) of some other amides have been estimated to be: ⫺0.122 for acetamide [39], ⫺0.078 for
2-fluoroacetamide [11], ⫺0.314 for propionamide [8]
and ⫺0.156 for acetidinone [36]. The values for some
other related compounds are: 0.0169 for trans acrolein
[40], ⫺0.0195 for cis acrolein [41], ⫺0.041 and
⫺0.049 for cis and trans acrylic acid [42]. All of
these molecules are assumed to be planar. Acrylamide
is also planar in the solid state [43] where it again
prefers the syn conformation. The inertial defects of
the normal (Table 7) and the deuterated species (Table
9) vary little. This is expected for a planar or nearly
planar molecule.
We are again led to the conclusion that the syn
rotamer has a planar, or very nearly planar amide
group. There is no sufficient experimental evidence
84
K.-M. Marstokk et al. / Journal of Molecular Structure 524 (2000) 69–85
to say anything definite about the planarity of the
amide group of the skew conformer.
at the University of Oslo. Anne Horn is thanked for
the artwork.
3.10. Structures
References
Comparison of the experimental (Table 7 and 12)
and the theoretical rotational constants (Table 1 and 2)
show the best agreement in the case of the B3LYP
computations. This agreement is not believed to be
fortuitous but to reflect the fact that the B3LYP structures of the syn and skew forms are indeed accurate.
The B3LYP structures are taken to be plausible structures of the two forms. It is expected that any experimental structures that are determined in the future for
the syn and skew rotamers will be very close to the
B3LYP structures in Tables 1 and 2.
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[2]
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4. Conclusions
Gaseous acrylamide exists in the heavy-atom syn
and skew conformations. The syn form (Fig. 1) is the
most stable conformation being 6.5(6) kJ mol ⫺1 more
stable than skew. The syn rotamer has a planar heavy
atom skeleton and a planar, or very nearly planar,
amide group. Eleven vibrationally excited states, the
dipole moment and the quadrupole coupling constants
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The torsion around the C–C single bond is close to
harmonic near the syn bottom of the potential well.
The torsional fundamental frequency is 90(10) cm ⫺1.
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approximately 155⬚ around the C–C bond. The
quantum chemical calculations predict a non-planar
amide group for the skew form, but there is insufficient
evidence to confirm or reject this prediction.
Elaborate quantum chemical calculations have
been carried out for the two forms. The best agreement with experimental values is found in the B3LYP/
cc-pVTZ calculations.
Acknowledgements
We are grateful to The Research Council of
Norway (Programme for Supercomputing) for a
grant of computer time at the IBM RS6000 cluster
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