Conformational stability from variable temperature infrared spectra of krypton and xenon solutions, ab initio calculations, vibrational assignment and r0 structural parameters of vinylcyclopropane

Article abstract of DOI:10.1016/j.molstruc.2004.11.071

The infrared spectra (3200-400 cm^-1) of krypton and xenon solutions of vinylcyclopropane c-C₃H₅CHCH₂, at variable temperatures (-55 to -150°C) have been recorded. Additionally, the infrared spectra (3200-250 cm<

Full text of DOI:10.1016/j.molstruc.2004.11.071

Journal of Molecular Structure 744–747 (2005) 3–17
www.elsevier.com/locate/molstruc
Conformational stability from variable temperature infrared spectra of
krypton and xenon solutions, ab initio calculations, vibrational assignment
and r0 structural parameters of vinylcyclopropane
a,
James R. Durig , Chao Zheng , Hamondeh Deeb , Gamil A. Guirgis
a,1
a
b
*
aDepartment of Chemistry, University of Missouri–Kansas City, Kansas City, MO 64110, USA
bDepartment of Chemistry and Biochemistry, College of Charleston, Charleston, SC 29401, USA
Received 3 November 2004; accepted 22 November 2004
Available online 5 February 2005
Abstract
The infrared spectra (3200–400 cmK1) of krypton and xenon solutions of vinylcyclopropane c-C3H5CHaCH2, at variable temperatures
(K55 to K150 8C) have been recorded. Additionally, the infrared spectra (3200–250 cmK1) of the gas and solid have been recorded. From a
comparison of the spectra of the fluid phases with that of the solid, all of the fundamental vibrations of the trans conformer have been
identified and assigned as well as many of those for the gauche form. By utilizing five pairs of fundamentals for these two conformers in the
xenon solutions, an enthalpy difference of 415G42 cmK1 (4.96G0.50 kJ/mol) has been obtained with the trans conformer the more stable
form. There is 21G3% of the gauche conformer present at ambient temperature. Results from ab initio calculations show the cis rotamer is a
transition state. Equilibrium geometries and total energies of both conformers have been determined from ab initio calculations with full
electron correlation by the perturbation method to second order as well as by hybrid density functional theory calculations with the B3LYP
method using a number of basis sets. The MP2 calculations predict the trans conformer to be more stable than the gauche form ranging from
358 to 440 cmK1 whereas the B3LYP calculations predict significantly larger values between 571 and 616 cmK1. By adjusting ab initio
MP2(full)/6-311CG(d,p) predicted structural parameters to fit previously reported rotational constants for the trans conformer, adjusted r0
parameters have been obtained. Comparisons of these parameters to those previously obtained from the microwave and electron diffraction
studies are made. Many of the spectroscopic and theoretical results are compared to the corresponding properties for some similar molecules.
q 2004 Published by Elsevier B.V.
Keywords: Vinylcyclopropane; Conformational stability; Ab initio calculations; Structural parameters
1. Introduction
ambient temperature. However, it is not clear what is the
major factor or factors that determine which conformer is
the most stable form. For example, both cyano [1,2] and
ethynyl [3,4] methylcyclopropanes have large amounts of
the cis conformer present (substituent X over the three-
member ring) at ambient temperature whereas for the
ethynyl molecule it is the more stable rotamer. The
halomethylcyclopropanes [5–12], however, have the gauche
conformer as the more stable form. Initially, it was
suggested [3] that the electronegativity [13] of the
substituent on the methylene group was the controlling
factor, i.e. substituent with higher electronegativity favors
the cis form, but our [12] recent determination of the
conformational stability of fluoromethylcyclopropane ruled
out the electronegativity as the major factor. The cyclopro-
pyl carbonyl compounds, c-C3H5CXO, where XZH, F, and
The mono-substituted cyclopropanes have been of
interest to structural chemists and physicists for decades,
particularly the mono-substituted methylcyclopropanes,
c-C3H5CH2X, where XZCbN, CbCH, CH3, F, Cl, and
Br, since all of them have multiple conformations present at
* Corresponding author. Address: Department of Chemistry and
Geosciences, University of Missouri–Kansas City, 5100 Rockhill Road,
Kansas City, MO 64110-2499, USA. Tel.: C1 816 235 6038; fax: C1 816
235 2290.
E-mail address: durigj@umkc.edu (J.R. Durig).
1 Taken in part from the thesis of C. Zheng, which will be submitted to
the Department of Chemistry of the University of Missouri-Kansas City in
partial fulfillment of the PhD degree.
0022-2860/$ - see front matter q 2004 Published by Elsevier B.V.
doi:10.1016/j.molstruc.2004.11.071

4
J.R. Durig et al. / Journal of Molecular Structure 744–747 (2005) 3–17
Cl are also structurally interesting since they have cis
(oxygen atom over the three-member ring) and trans
(halogen atom over the three-member ring) conformers
very small enthalpy differences (DHz100 cmK1) with
only the chloride having the cis conformer the more
stable form [14–22]. While the cyclopropylcarboxaldehyde,
c-C3H5—CHO, molecule has trans and cis conformers
[21–23], the isoelectronic vinylcyclopropane molecule,
c-C3H5CHaCH2, does not appear to have a stable cis
form [24–26] although a thorough search for this conformer
may not have been made.
the optimized geometries which were combined with the
previously reported rotational constants from the two
microwave studies [27,28] to obtain the adjusted r0
parameters [35]. Additional ab initio and density functional
theory (DFT) calculations by the B3LYP method have been
carried out with a variety of basis sets up to 6–
311G(2df,2pd), as well as with diffuse functions, to predict
the conformational stabilities. The results of these spectro-
scopic and theoretical studies are reported herein.
There have been several experimental [24–30] and
theoretical [31–34] studies of the conformational stability
of vinylcyclopropane and it is clear that the most stable
conformer is the trans form (double bond trans to the three-
member ring) and there is a second conformer in the fluid
phase which has been identified as the gauche form (Fig. 1).
There have been three experimental determinations of the
enthalpy difference between these two conformers with the
first one from an electron diffraction investigation [24] with
a reported DH of 385G70 cmK1 (4.61G0.84 kJ/mol).
There were then two Raman investigations which appeared
in the same year, and in the first study [25], an enthalpy
difference from the temperature dependence of two Raman
lines in the spectrum of the gas gave a value of 500G
50 cmK1 (5.98G0.60 kJ/mol). In the second study [26], the
pair of Raman bands at 1191 and 1203 cmK1 were analyzed
at five different temperatures from 23 to 85 8C from which
an enthalpy value of 1117G91 cal/mol (4.67G0.38 kJ/mol,
391G32 cmK1) was obtained.
As a continuation of our conformational stability studies
of mono-substituted cyclopropanes, we recorded variable
temperature infrared spectra of krypton and xenon solutions
of vinylcyclopropane. We also recorded the infrared spectra
of the gas and solid since these spectra do not appear to
have been previously published. The Raman spectra of the
liquid were recorded from 1500 to 50 cmK1 for comparison
to that previously published [25,26]. We also carried
out MP2(full)/6-311CG(d,p) calculations to obtain
2. Experimental
The sample of vinylcyclopropane was synthesized in two
steps as previously reported by Kisiel et al. [28]. First,
cyclopropylmethyl ketone was treated with 10 equivalents
of toluene-p-sulfonic hydrazide and a catalytic amount of
toluene-p-sulfonic acid in ethanol and refluxed for 1 h. Then
the product cyclopropyl carbonyl tosyl hydrozone was
reduced with sodium hydride in decaline at 170–180 8C for
3 h. Nitrogen was bubbled through the solution and the
volatile vinylcyclopropane was collected in three successive
traps maintained at K80 8C. The product was first purified
using trap-to-trap technique and then subjected to a low-
pressure, low-temperature fractionation column for final
purification. The purity of the sample was checked by
infrared and NMR spectrometry. The purified sample was
kept in the dark at low temperature until it was used.
The mid-infrared spectra of the gas (Fig. 2A) and the
annealed solid (Fig. 2B) from 3200 to 250 cmK1 were
recorded on a Perkin–Elmer model 2000 Fourier transform
spectrometer equipped with a nichrome wire source, Ge/CsI
beamsplitter and DTGS detector. The spectrum of the gas
was obtained with the sample contained in a 12 cm cell
equipped with CsI windows. Atmospheric water vapor was
removed from the spectrometer chamber by purging with
dry nitrogen. For the annealed solid, the spectrum was
recorded by depositing a solid sample film onto a CsI
substrate cooled by boiling liquid nitrogen and housed in
Fig. 1. The trans and gauche conformers of vinylcyclopropane.

J.R. Durig et al. / Journal of Molecular Structure 744–747 (2005) 3–17
5
Fig. 2. Infrared spectrum of: (A) gaseous; and (B) polycrystalline solid vinylcyclopropane.
a vacuum cell fitted with CsI windows. The sample was
annealed until no further change was observed in the
spectrum. Interferograms obtained after 256 scans for the
gas sample and reference as well as 128 scans for the
amorphous and annealed solid sample and reference were
transformed by using a boxcar truncation function with
theoretical resolutions of 0.5 and 1.0 cmK1, respectively, for
the gaseous and solid samples.
length and wedged silicon windows sealed to the cell with
indium gaskets. The temperature was monitored by two Pt
thermoresistors and the cell was cooled by boiling liquid
nitrogen. The complete cell was connected to a pressure
manifold to allow for the filling and evacuation of the cell.
After the cell was cooled to the desired temperature, a small
amount of sample was condensed into the cell. Next, the
pressure manifold and the cell were pressurized with noble
gas, which immediately started condensing in the cell,
allowing the compound to dissolve.
The far infrared spectra of the gas and solid were
recorded on the previously described Perkin–Elmer model
2000 spectrometer equipped with a metal grid beamsplitter
and a DTGS detector. The gas was contained in a cell with
a 12 cm path length and equipped with polyethylene
windows. For obtaining the spectra of the solid, the sample
was deposited on a Si substrate held at 77 K with boiling
liquid nitrogen which was contained in a cryostat cell
equipped with polyethylene windows. Normally 256 scans
at resolutions of 0.5 and 1.0 cmK1 were used for the far
infrared spectrum of the gas and the solid, respectively, to
give a satisfactory signal-to-noise ratio.
The observed wavenumbers for the fundamentals of the
trans and gauche conformers are listed in Tables 1 and 2,
respectively, along with their predicted values.
3. Theoretical calculations
The LCAO-MO-SCF restricted Hartree–Fock (RHF)
calculations were performed with the GAUSSIAN-03 program
[36] using Gaussian-type basis functions. The energy
minima with respect to nuclear coordinates were obtained
by simultaneous relaxation of all geometric parameters
consistent with symmetry restrictions using the gradient
method of Pulay [37]. A number of basis sets starting from
6-31G(d), increasing to 6-311CG(2df,2pd) were employed
at the level of Hartree–Fock, Møller–Plesset perturbation
theory to the second order (MP2), and hybrid density
functional theory by the B3LYP method to obtain energy
differences between the two stable conformers (Table 3).
From all levels of calculation conducted in the present
The mid-infrared spectra of the sample dissolved in
liquefied krypton (Fig. 3A) and xenon were recorded on a
Bruker model IFS-66 Fourier interferometer equipped with
a Globar source, Ge/KBr beamsplitter, and DTGS detector.
The spectra were recorded at variable temperatures ranging
from K55 to K100 8C in krypton solutions as well as K105
to K150 8C in krypton solutions with 100 scans at a
resolution of 1.0 cmK1. The temperature studies in these
rare gases were carried out in a specially designed cryostat
cell, which is composed of a copper cell with a 4 cm path

6
J.R. Durig et al. / Journal of Molecular Structure 744–747 (2005) 3–17
Fig. 3. Infrared spectra of vinylcyclopropane: (A) krypton solution at K130 8C; (B) simulated spectrum, at K130 8C, of a mixture of the two conformers with
DH of 415 cmK1 with the trans form more stable; (C) simulated spectrum for pure gauche form; (D) simulation spectrum for pure trans form.
investigation, the trans conformer is always predicted to be
the more stable form. The MP2 calculations predict
conformational energy differences between 358 and
440 cmK1, whereas B3LYP calculations predict about
50% larger conformational energy differences ranging
between 571 and 616 cmK1. Energies of two distinctive
transition states, i.e. the cis and the gauche0 conformers
were also calculated with the above described methods/
basis sets (Table 3).
in Fig. 4. By using the B matrix, the force field in Cartesian
coordinates was converted to a force field in internal
coordinates [38] in which the pure ab initio vibrational
frequencies were reproduced. Subsequently, scaling factors
of 0.88 for the CH stretches, 1.0 for heavy atom bends and
torsions and 0.90 for all other modes were used, along with
the geometric average of scaling factors for interaction force
constants, to obtain the fixed scaled force field and the
resultant wavenumbers. A set of symmetry coordinates
(Table 5) was used to determine the corresponding potential
energy distributions (PEDs). The observed and calculated
wavenumbers of the trans and gauche conformers of
vinylcyclopropane, along with the calculated infrared
intensities, Raman activities, depolarization ratios and
PEDs are given in Tables 1 and 2.
In order to obtain a more complete description of the
nuclear motions involved in the fundamental vibrations of
vinylcyclopropane, we have carried out normal a coordinate
analysis. The force field in Cartesian coordinates was
calculated by the GAUSSIAN-03 program [36] at the
MP2(full)/6-31G(d) level. The internal coordinates used to
calculate the G and B matrices are listed along with the
structural parameters in Table 4 and the numbering is shown
In order to identify the fundamental vibrations for
the trans and gauche conformers of vinylcyclopropane,

Table 1
Observed and calculated frequencies (cmK1) for trans vinylcyclopropane
Vib.
No.
Fundamental
Ab
initioa
Fixed
scaledb
IR
int.c
Raman
act.d
dp
IR
Raman
gase
IR
Krf
Raman
liquid
IR solid
Raman
solide
P.E.D.g
Ah
Bh
Ch
Ratio
gas
A0
n1
n2
aCH2 antisymmetric
stretch
98S1
99S2
3307
3305
3103
3100
14.5
11.8
61.2
47.1
0.67
0.65
3093
–
–
3089
3080
–
3087
–
–
21
15
–
–
79
rCH2 antisymmetric
stretch
3087
–
3078
85
n3
aCH2 symmetric stretch
rCH stretch
94S3
3216
3215
3208
3185
1733
1569
1515
1400
1350
1275
3017
3016
3010
2988
1645
1488
1437
1328
1281
1218
3.2
6.2
9.8
8.9
15.4
1.2
0.2
0.5
3.2
2.3
127.8
87.5
91.8
43.6
28.9
10.8
24.8
7.5
0.11
0.12
0.06
0.39
0.22
0.59
0.36
0.69
0.41
0.75
3020
3020
3010
2987
1646
1459
1437
1328
1294
1220
–
–
3017
3016
3005
2988
1644
1457
1441
1327
1292
1220
–
–
3016
3016
–
–
78
8
–
–
–
–
–
–
–
–
–
–
22
92
49
99
1
n4
83S4, 14S5
85S5, 14S4
93S6
n5
rCH2 symmetric stretch
aCH stretch
–
–
2998
–
51
1
n6
–
–
2988
–
n7
CaC stretch
64S7, 14S9
80S8, 13S13
63S9
1647
1461
1437
1330
1296
1219
1641
1453
1430
1323
1293
1214
1635/1638
1459
1636
1452
1433
1325
1295
1214
99
15
0
n8
rCH2 deformation
aCH2 deformation
rCH in-plane bend
aCH in-plane bend
aC–C stretch
85
100
54
64
1
n9
1427/1431
1319/1322
1293/1295
1212/1229
n10
n11
n12
34S10, 18S9, 16S7, 12S13
64S11, 13S15, 10S7
46
36
99
8.4
23S12,15S18,13S15
,
9.4
12S10,11S19
n13
n14
n15
n16
n17
n18
n19
n20
Ring breathing
rCH2 wag
58S13, 24S10
85S14, 13S16
1264
1105
1038
1005
856
1200
1052
985
969
818
758
441
268
2.0
2.0
29.8
5.2
0.15
0.43
0.55
0.75
0.50
0.59
0.29
0.75
1190
1024
990
941
819
761
446
273
1191
1188
1023
993
940
817
762
445
–
1187
1022
993
938
816
763
452
276
1185/1189
1018/1021
998/1001
934/938
820/828
771/773
444
1186
1023
989
987
821
767
443
284
85
9
–
–
–
–
–
–
–
–
15
91
5
–
–
aCH2 wag
42S15, 17S17, 16S18, 12S11
57S16, 14S12, 13S14
38S17, 19S12, 17S15, 16S16
48S18, 31S17
5.9
1.0
95
91
14
64
88
89
Ring deformation
rCH2 rock
34.3
0.6
14.7
3.2
–
9
–
86
36
12
11
rCH2 twist
798
0.1
5.7
764
–
CaC–C bend
Ring-C in-plane bend
42S19, 27S20
452
0.9
6.4
58S20, 37S19
273
1.1
1.1
–
279/280
A00
n21
rCH2 antisymmetric
stretch
100S21
3293
3089
0.1
78.0
0.75
3086
3080
–
3078
–
–
100
–
n22
n23
n24
n25
n26
n27
n28
n29
n30
n31
n32
n33
rCH2 symmetric stretch
rCH2 deformation
rCH2 twist
100S22
3205
1526
1238
1168
1108
1029
959
3006
1448
1175
1108
1051
977
13.2
1.5
28.0
10.4
7.7
0.75
0.75
0.75
0.75
0.75
0.75
0.75
0.75
0.75
0.75
0.75
0.75
3012
w1456
1176
1101
1049
985
3015
1454
1174
1099
1046
985
896
890
814
663
–
–
1453
w1175
–
2998
1448/1448
1171/1182
1108/1111
1050/1054
986/992
899/902
894/899
811/815
674/676
323/324
–
–
1445
1175
–
–
–
–
–
–
–
–
–
–
–
–
–
100
100
100
100
100
100
100
100
100
100
100
100
–
–
–
–
–
–
–
–
–
–
–
–
100S23
44S24, 46S30
65S25, 29S24
98S26
0.7
rCH out-of-plane bend
rCH2 wag
2.4
0.9
5.5
0.05
0.3
–
–
aCH2 twist
61S27, 34S31
58S28, 12S32
98S29
11.0
9.4
984
896
w886
816
–
984
903
888
816
–
Ring deformation
aCH2 rock
931
15.4
0.3
900
909
862
42.5
4.6
892
rCH2 rock
27S30, 35S28, 18S25, 15S24
41S31, 30S27
73S32
864
830
5.7
816
aCH out-of-plane bend
Ring-C out-of-plane bend
Asymmetric torsion
686
656
4.7
3.7
663
319
316
1.3
6.7
308
315
120
325
153
90S33
120
120
0.1
6.5
–
–
a
b
c
d
e
MP2(full)/6-31G(d) predicted values.
MP2(full)/6-31G(d) fixed scaled frequencies with factors of 0.88 for CH stretches, 0.90 for heavy atom stretches and CH bends and 1.0 for all other modes.
Scaled infrared intensities in km/mol from MP2(full)/6-31G(d).
4
Scaled Raman activities in A /u from MP2(full)/6-31G(d).
˚
Ref. [26]. For the gas the spectral region from 0 to 700, 800–1150, 1350–1400 and above 1700 were not reported; for the solid, spectral data for the regions 530–750, 1030–1160, and above 1650 were not reported; a dash indicates the
regions which were omitted.
f
Frequencies from Kr solution at K130 8C.
g
Calculated with MP2(full)/6-31G(d) and contributions of less than 10% are omitted.
h
A, B and C values in the last three columns are percentage infrared band contours.

Table 2
Observed and calculated frequencies (cmK1) for gauche vinylcyclopropane
Vib. No. Fundamental
Ab
initioa
Fixed
scaledb
IR int.c
Raman
act.d
dp Ratio IR gas
Raman
gase
IR Krf
Raman
liquide
P.E.D.g
Ah
Bh
Ch
n1
aCH2 antisymmetric
stretch
rCH2 antisymmetric stretch 3307
3310
3105
7.5
73.4
0.65
3098
76S1, 22S2
22
72
6
n2
n3
n4
n5
n6
n7
n8
n9
n10
3102
3022
3002
3015
2995
1642
1489
1425
1371
20.4
3.2
9.8
179.5
54.7
8.3
0.74
0.09
0.40
0.10
0.69
0.21
0.61
0.34
0.44
75S2, 23S1
66
76
3
1
24
46
35
58
5
33
0
aCH2 symmetric stretch
rCH stretch
3221
3200
3214
3193
1730
1570
1501
1444
85S3
16.4
5.6
72S4, 17S6
51
2
rCH2 symmetric stretch
aCH stretch
CaC stretch
74S5, 17S22
75S6, 20S4
63
32
95
7
13.5
8.7
58.9
13.4
8.5
10
0
1636
1423
1638
1426
1633
1639
66S7, 16S9
rCH2 deformation
aCH2 deformation
rCH in-plane bend
0.9
79S8, 16S13
66S9, 12S12
42S10, 12S8, 11S9,
10S13
38
84
5
55
16
0
4.5
17.7
6.5
1419
1375
1419
1375
0
0.5
95
n11
n12
aCH in-plane bend
aC–C stretch
1357
790
1288
754
0.7
1.4
11.7
6.3
0.41
0.57
1307
754
1310h
750h
62S11, 16S7, 12S15
21S12, 34S18, 19S16
14S17
81
1
13
83
6
751
752
,
16
n13
n14
n15
n16
n17
n18
n19
n20
n21
n22
n23
n24
n25
n26
n27
n28
n29
n30
Ring breathing
rCH2 wag
1271
1098
1130
995
1207
1043
1080
959
2.7
9.2
6.1
8.8
1.5
1.8
0.1
0.7
0.6
13.2
2.9
1.5
0.4
4.9
21.2
5.2
37.5
6.5
14.4
0.6
4.3
9.8
1.8
2.1
2.1
6.5
73.8
67.5
8.0
9.3
5.8
0.4
0.8
14.9
0.1
4.4
0.21
0.20
0.50
0.72
0.47
0.69
0.65
0.71
0.74
0.14
0.75
0.74
0.27
0.47
0.21
0.70
0.67
0.73
1206
1034
1075
1203
1207
1199
49S13, 23S10
73S14, 14S26
32S15, 10S13
49S16, 12S12, 11S15
58S17, 14S12
24S18, 20S10, 16S17
43S19, 13S20, 10S15
40S20, 34S32
97S21
100
27
88
69
16
1
0
50
6
0
23
6
aCH2 wag
Ring deformation
rCH2 rock
w1075
31
83
54
86
12
66
71
93
60
78
7
0
843
802
1
rCH2 twist
1158
538
1102
525
1091
w1089
45
13
73
5
CaC–C bend
Ring-C in-plane bend
527h
524
1
315
310
15
29
20
1
rCH2 antisymmetric stretch 3296
3092
3008
1445
1175
1118
1056
983
rCH2 symmetric stretch
rCH2 deformation
rCH2 twist
3206
1524
1238
1177
1113
1036
954
79S22, 15S5
99S23
9
6
1177
1173
1180
42S24, 46S30, 10S25
53S25, 20S24
83S26, 13S14
60S27, 30S31
64S28, 18S15
98S29
28
3
12
19
48
85
70
87
5
rCH out-of-plane bend
rCH2 wag
45
10
2
aCH2 twist
991
913
993
5
Ring deformation
aCH2 rock
rCH2 rock
925
28
0
934
886
w913
13
18
871
834
30S30, 18S25, 18S28
,
77
16S24
n31
n32
n33
aCH out-of-plane bend
Ring-C out-of-plane bend
Asymmetric torsion
671
276
100
641
272
100
11.2
0.2
5.5
1.1
4.6
0.58
0.34
0.75
650
w650
38S31, 28S27
31S32, 38S19, 25S20
90S33
11
78
77
3
21
19
86
1
0.5
4
a
b
c
d
e
f
MP2(full)/6-31G(d) predicted values.
MP2(full)/6-31G(d) fixed scaled frequencies with factors of 0.88 for CH stretches, 0.90 for heavy atom stretches and CH bends and 1.0 for all other modes.
Scaled infrared intensities in km/mol from MP2(full)/6-31G(d).
4
Scaled Raman activities in A /u from MP2(full)/6-31G(d).
˚
Ref. [26]. For the gas the spectral region from 0 to 700, 800–1150, 1350–1400 and above 1700 were not reported.
Frequencies from Kr solution at –130 8C. Frequencies with an asterisk from Xe solution at K75 8C.
Calculated with MP2(full)/6-31G(d) and contributions of less than 10% are omitted.
g
h
A, B and C values in the last three columns are percentage infrared band contours.

J.R. Durig et al. / Journal of Molecular Structure 744–747 (2005) 3–17
9
Table 3
Calculated energies (hartree) and energy differences (cmK1) for the stable trans and gauche conformers as well as the cis and gauche0 transition states of
vinylcyclopropane
Gauche0 (TS) DE
Method/basis set
Trans
Gauche DE
Cis (TS) DE
RHF/6-31G(d)
K193.940214
K193.945565
K194.604834
K194.617749
K194.804386
K194.809074
K194.858889
K194.862511
K194.938953
K194.941895
K195.291782
K195.300798
K195.347045
K195.349090
K195.355388
K195.357524
K195.361783
K195.363731
469
506
358
440
401
437
405
418
420
440
573
603
571
581
590
600
606
616
912
942
621
656
529
546
581
591
574
586
806
823
820
824
834
845
833
844
1055
1085
1042
1055
1116
1129
1213
1237
1244
1268
1242
1228
1227
1233
1249
1261
1272
1285
RHF/6-31CG(d)
MP2/6-31G(d)
MP2/6-31CG(d)
MP2/6-311G(d,p)
MP2/6-311CG(d,p)
MP2/6-311G(2d,2p)
MP2/6-311CG(2d,2p)
MP2/6-311G(2df,2pd)
MP2/6-311CG(2df,2pd)
B3LYP/6-31G(d)
B3LYP/6-31CG(d)
B3LYP/6-311G(d,p)
B3LYP/6-311CG(d,p)
B3LYP/6-311G(2d,2p)
B3LYP/6-311CG(2d,2p)
B3LYP/6-311G(2df,2pd)
B3LYP/6-311CG(2df,2pd)
0
@
1
A
ꢀ
vsj
ꢁ
ꢀ
ꢁ
the infrared spectra were predicted by using the fixed scaled
frequencies. Infrared intensities determined from
MP2(full)/6-31G(d) calculations were calculated based on
the dipole moment derivatives with respect to Cartesian
4
24p4
h
ðn0 KnjÞ
1 Kexp
h
i
Z
Sj
8p2cnj
Khcnj
kT
vU
45
where n0 is the excitation wavenumber, nj is the
vibrational wavenumber of the jth normal mode, and Sj is
the corresponding Raman scattering activity. To obtain the
polarized Raman scattering cross sections, the polarizabil-
ities are incorporated into Sj by multiplying Sj with (1Krj)/
(1Crj), where rj is the depolarization ratio of the jth normal
mode. The Raman scattering cross sections and calculated
wavenumbers obtained from the GAUSSIAN-03 program [36]
were used together with a Lorentzian function to obtain the
simulated Raman spectra.
coordinates. The derivatives were transformed with respect
P
to normal coordinates by ðvmu=vQiÞZ ðvmu=vXjÞ Lij,
j
where Qi is the ith normal coordinate, Xj is the jth Cartesian
displacement coordinate, and Lij is the transformation
matrix between the Cartesian displacement coordinates
and the normal coordinates. The infrared intensities were
then calculated with (Np)/(3c2) [(vmx/vQi)2C(vmy/vQi)2C
(vmz/vQi)2]. In Fig. 3C and D, the simulated infrared spectra
of the pure trans and gauche conformers, are shown. The
simulated spectra which was calculated at K130 8C, of the
mixture of two conformers with a DH of 415 cmK1 is shown
in Fig. 3B. It should be compared to the experimental
spectrum of the krypton solution at K130 8C (Fig. 3A). The
predicted spectrum is in remarkable resemblance to the
experimental spectrum, indicating the utility of the scaled
predicted data in distinguishing the fundamentals for the
two conformers.
The simulated Raman spectra of the pure trans and
gauche conformers are shown in Fig. 5C and D, respect-
ively. In Fig. 5B the mixture of the two conformers at 25 8C
is shown utilizing the experimentally determined DH value
of 415 cmK1 with the trans conformer the more stable form.
The previously reported experimental Raman spectra of the
liquid [26] at 23 and K120 8C are shown in Fig. 5A for
comparison and the agreement between the simulated and
the experimental spectra is considered satisfactory, but not
nearly as good as that of the infrared spectra, probably due
to the significant extent of intermolecular association in the
liquid phase.
To further support the vibrational assignments, we have
simulated the Raman spectra from ab initio MP2(full)/6-
31G(d) results. The evaluation of Raman activity by using
the analytical gradient methods has been developed [39,40].
The activity Sj can be expressed as: SjZgjð45a2j C7bj2Þ,
where gj is the degeneracy of the vibrational mode j, aj is the
derivative of the isotropic polarizability, and bj is that of the
anisotropic polarizability. The Raman scattering cross
sections, vsj/vU, which are proportional to Raman activi-
ties, can be calculated from the scattering activities as well
as the predicted wavenumbers for each normal mode, using
the relationship [41,42]
4. Vibrational assignment
In order to obtain the conformational stability it is
necessary to assign the fundamentals correctly for the two
different conformers. In the two previous Raman studies
[25,26] only limited portions of the spectra were

Table 4
Structural parameters (A and degree), rotational constants (MHz) and dipole moments (debye) for trans and gauche rotamers of vinylcyclopropane
˚
e
Parameter
Internal
coordinates
MP2(full)/6-311CG(d,p)
Trans Gauche
ED(trans/gauche)a
ED(trans/gauche)b
EDCMWc
MWd
Adjusted r0
I
II
I
II
III
Trans
Trans
Trans
r(C1–C2)
r(C1–C3)
r(C2–C3)
r(C1–C4)
r(C4aC5)
r(C1–H6)
r(C4–H7)
r(C5–H8)
r(C5–H9)
R1
R2
R3
R4
R5
r4
1.516
1.506
1.517
1.510
1.484
1.342
1.087
1.090
1.085
1.085
1.083
1.083
1.084
1.084
1.510
1.510
1.510
1.510
1.334
1.099
1.099
1.099
1.099
1.099
1.099
1.099
1.099
1.522
1.522
1.522
1.475
1.334
1.099
1.099
1.099
1.099
1.099
1.099
1.099
1.099
1.525(1)
1.525(1)
1.500
1.521(1)
1.521(1)
1.511
1.517(1)
1.517(1)
1.517
1.521(4)
1.521(4)
1.510(8)
1.481(7)
1.340(3)
1.098(3)
1.098(3)
1.098(3)
1.098(3)
1.098(3)
1.098(3)
1.098(3)
1.098(3)
60.2(3)
1.516(3)
1.521(5)
1.521(5)
1.510(5)
1.474(5)
1.343(5)
1.086(3)
1.091(3)
1.086(3)
1.084(3)
1.084(3)
1.084(3)
1.084(3)
1.084(3)
60.3(5)
1.516
1.503
1.474
1.343
1.086
1.091
1.086
1.084
1.084
1.084
1.084
1.084
1.516(3)
1.509(3)
1.467(3)
1.344(3)
1.087f
1.087f
1.087f
1.087f
1.087f
1.087f
1.087f
1.470(2)
1.336(1)
1.097(1)
1.097(1)
1.097(1)
1.097(1)
1.097(1)
1.097(1)
1.097(1)
1.097(1)
1.466(2)
1.336(1)
1.099(1)
1.099(1)
1.099(1)
1.099(1)
1.099(1)
1.099(1)
1.099(1)
1.099(1)
1.467(2)
1.336(1)
1.101(2)
1.101(2)
1.101(2)
1.101(2)
1.101(2)
1.101(2)
1.101(2)
1.101(2)
r3
r1
r2
r(C2–H10
r(C2–H11
r(C3–H12
r(C3–H13
)
)
)
)
r5
r6
r7
1.087f
r8
:C1C2C3
:C1C3C2
:C2C1C3
:C2C1C4
:C3C1C4
:C1C4C5
:H6C1C2
:H6C1C3
:H6C1C4
:H7C4C5
:H8C5C4
:H9C5C4
:H10C2C3
:H10C2C1
:H11C2C3
:H11C2C1
:H12C3C2
:H12C3C1
:H13C3C2
:H13C3C1
tH6C1C4C5
A
60.3
60.4
60.3
59.4
59.7
59.9
60.2(3)
60.3(5)
59.5(5)
59.4(5)
q1
q2
f1
32
119.1
119.1
124.5
116.1
116.1
115.6
119.4
121.1
121.3
117.8
116.9
118.2
117.5
117.8
116.9
118.2
117.5
0.0
121.6
119.3
125.4
115.7
114.5
114.8
118.8
121.6
120.9
118.0
117.7
117.1
118.0
118.4
118.2
117.0
116.5
126.9
118.7(7)
120.1(9)
118.2(5)
118.2(5)
125.8(6)
116.5f
119.3(2)
120.2(5)
120.2(5)
123.6(5)
116.1(5)
116.1(5)
115.6(5)
119.4(5)
121.1(5)
121.3(5)
117.8(5)
116.9(5)
118.2(5)
117.5(5)
117.8(5)
116.9(5)
118.2(5)
117.5(5)
119.3(2)
124.2(2)
118f
118f
118f
119.1f
121.6f
121.6f
114.1f
114.1f
114.1f
114.1f
114.1f
114.1f
114.1f
114.1f
123.8(12)
126.2(14)
127.3(3)
127.6(3)
127.7(3)
33
116.8(15)
116.8(15)
119.7(15)
119.7(15)
119.7(15)
116.8(15)
116.8(15)
116.8(15)
116.8(15)
116.8(15)
116.8(15)
116.8(15)
116.8(15)
116.8(15)
116.8(15)
119.7(15)
119.7(15)
119.7(15)
116.8(15)
116.8(15)
116.8(15)
116.8(15)
116.8(15)
116.8(15)
116.8(15)
116.8(15)
116.5f
115.8f
115.8f
115.8f
31
f3
g1
g2
a4
a2
a3
a1
b4
b2
b3
b1
116.8(25)
117.8f
117.8f
124.1(11)
124.8(11)
125.2(11)
118.0(6)
118.0(6)
118.0(6)
118.0(6)
15124
11597
15076.2239(14)
3061.4049(4)
2941.3364(5)
15080
B
3058
2942
3694
3308
3061
2941
C
jmaj
0.586
0.374
jmbj
0.000
0.045
0.587
0.137
0.082
0.407
jmcj
jmtj
a
Ref. [29].
b
c
d
e
f
Ref. [24].
Ref. [30].
Ref. [28].
This study.
Assumed parameters.

J.R. Durig et al. / Journal of Molecular Structure 744–747 (2005) 3–17
11
Fig. 4. The trans conformer of vinylcyclopropane with atom numbering and internal coordinates.
investigated and no attempt was made to provide a
vibrational assignment. Since the most abundant conformer
is the trans form with the plane of symmetry coinciding
with the plane of a and c figure axes, the gas phase infrared
band contours help immensely in making the assignment.
All A00 modes will have pure B-type bands which makes
them easily distinguishable. The predicted pure A-, B- and
C-type contours in the IR are shown in Fig. 6 and those for
the Raman Q-branches in Fig. 7. The n31 fundamental
provides an excellent example for this point since the trans
conformer fundamental (A00) is predicted at 656 cmK1 with
a pure B-type contour whereas the corresponding mode for
the gauche conformer is predicted at 641 cmK1 with
mainly a 11%A/84%C hybrid contour. There is no doubt on
the correct assignment based on the observed contours
(Fig. 7). Additionally, in one of the earlier Raman studies
[26] a portion of the spectra of both the gas and solid were
reported, for the trans form only the A0 modes should
appear in the spectrum of the gas, all bands observed in the
gas phase had corresponding lines in the solid, thus the
trans conformer is the only form in the solid. Similarly, the
infrared spectra of rare gas solutions and the solid along
with the predicted frequencies and intensities for the
fundamentals for both conformers from the ab initio MP2
(full)/6-31G(d) calculations make the assignment reason-
ably certain. Also, the infrared spectrum of the rare gas
solution makes it possible to identify the band centers and
separate closely spaced bands. By utilizing all of this
information, practically all of the fundamentals of the trans
conformer can be assigned confidently (Table 1). As an
example, the rCH2 (818 cmK1) of A symmetry is predicted
to have a lower frequency than the corresponding A mode
(830 cmK1). However, the band contours clearly show
the A rCH2 rock at 816 cmK1 whereas the corresponding
A mode is observed. Assignment of several of the
fundamentals for the gauche rotamer was made even
though there is a relatively small amount of this conformer
present at ambient temperature.
Initially, the fundamentals which were predicted to have
significantly different values for the two conformers were
identified when possible. As examples, the fundamentals
between 400 and 1000 cmK1 are expected to be the most
sensitive to conformational interchange and the predicted
frequencies (with the observed values in parentheses) for the
trans conformer are: 441 (446, n19), 656 (663, n31), 758
(761, n18), 818 (819, n17), 830 (816, n30), 862 (892, n29), 931
(900, n28), 969 (441, n16), and 985 (990, n15) cmK1. Only
three modes for the gauche conformer are expected to have
higher frequencies than the corresponding trans modes and
they are n19, n29, and n30, with predicted conformational
frequency differences of 84, 24, and 4 cmK1, respectively.
The experimental differences of 86, 21, and 4 cmK1
,
respectively, are in excellent agreement. The other six
modes are predicted to have lower frequencies for the
gauche form compared to the values for the corresponding
vibrations for the trans form with predicted differences
ranging from 2 to 16 cmK1. The average predicted
difference is 8 cmK1 and a 9 cmK1 average difference was
observed. The largest difference between predicted and
observed value is for n18 with a predicted difference of 4 and
an experimental value of 11 cmK1 (761 vs. 750 cmK1).
Thus, many of the fundamentals of the gauche conformer
could be assigned even though there is a relatively small
amount present. The assignment of the fundamentals for the
trans conformer are listed in Table 1 and those for the
gauche form in Table 2.

12
J.R. Durig et al. / Journal of Molecular Structure 744–747 (2005) 3–17
Table 5
Symmetry coordinates for trans vinylcyclopropane
Species
A0
Description
Symmetry coordinatea
aCH2 antisymmetric stretch
rCH2 antisymmetric stretch
aCH2 symmetric stretch
rCH stretch
S1Zr1Kr2
S2 Zr5 Kr6 Cr7 Kr8
S3Zr1Cr2
S4Zr4
rCH2 symmetric stretch
aCH stretch
CaC stretch
S5 Zr5 Cr6 Cr7 Cr8
S6Zr3
S7ZR5
rCH2 deformation
S8 Z4d1 Ka1 Ka2 Ka3
Ka4 C4d2 Kb1 Kb2 Kb3
Kb4
aCH2 deformation
rCH in-plane bend
aCH in-plane bend
aC–C stretch
S9 Z2g3 Kg1 Kg2
S10 Z231 K32 K33
S11Zf2Kf?
S12ZR4
ring breathing
S13 ZR1 CR2 CR3
S14 Za1 Ca2 Ka3 Ka4
Cb1 Cb2 Kb3 Kb4
S15Zg1Kg2
S16 Z2R3 KR1 KR2
S17 Za1 Ka2 Ca3 Ka4
Cb1 Kb2 Cb3 Kb4
S18 Za1 Ka2 Ka3
Ca4 Cb1 Kb2 Kb3 Cb4
S19Zf1
rCH2 wag
aCH2 wag
Ring deformation
rCH2 rock
rCH2 twist
CaC–C bend
Ring-C in-plane bend
S20Zq1Cq2
A00
rCH2 antisymmetric stretch
rCH2 symmetric stretch
rCH2 deformation
S21 Zr5 ꢀ r6 Kr7 Cr8
S22 Zr5 Cr6 Kr7 Kr8
S23 Z4d1 Ka1 Ka2 Ka3
Ka4 K4d2 Cb1 Cb2 Cb3
Cb4
rCH2 twist
S24 Za1 Ka2 Ka3 Ca4
Kb1 Cb2 Cb3 Kb4
S25Z32K33
S26 Za1 Ca2 Ka3 Ka4
Kb1 Kb2 Cb3 Cb4
S27Zh
rCH out-of-plane bend
rCH2 wag
Fig. 5. Raman spectra of vinylcyclopropane: (A) liquid at 24 and K120 8C
Ref. [25]; (B) simulatedspectrumat 25 8C of amixtureofthe two conformers
with DH of 415 cmK1 with the trans form more stable; (C) simulated
spectrum for pure gauche form; (D) simulated spectrum for pure trans form.
aCH2 twist
Ring deformation
aCH2 rock
S28ZR1KR2
S29Zk
conformer which can be used for the conformational
stability studies, except for the questionable 1325 cmK1
band which is presumably a combination band of the gauche
conformer since it is not observed in the infrared spectrum
of the solid. In the earlier Raman studies [25,26] the
1203 cmK1 line of the gauche form was used for the
enthalpy studies since it is quite pronounced in the Raman
spectrum. However, it is not useful for similar infrared
studies since it is between two relatively strong infrared
bands of the trans conformer as well as shoulders on both
sides of the band. Therefore, only limited information can
be obtained from the 1203 cmK1 band from the infrared
spectrum. However, utilizing the weak band at 749 cmK1
for the gauche conformer along with three bands of the trans
conformer with comparable intensities gave DH values
ranging from a high value of 531 cmK1 to a low value of
365 cmK1 with an average of 460 cmK1. Two additional
conformer pairs were used (Table 6), which gave signifi-
cantly lower values so the average DH value of the five pairs
is 415G16 cmK1. Assuming 10% uncertainty rather than
the statistical uncertainty from these determinations gives
rCH2 rock
S30 Za1 Ka2 Ca3 Ka4
Kb1 Cb2 Kb3 Cb4
S31Zl
S32Zq1–q2
S33Zt
aCH out-of-plane bend
Ring-C out-of-plane bend
Asymmetric torsion
a
Not normalized.
5. Conformational stability
There are only nine bands in the infrared spectrum of the
gas which can be confidently assigned to the gauche
conformer. These bands are also observed in the infrared
spectrum of the krypton solution, but, practically all of them
are shoulders on much more intense bands arising from
fundamentals of the more stable trans conformer. In fact the
only reasonably isolated bands in the infrared spectrum of
the gauche conformer are the 650 cmK1 (Kr) band which is
relatively pronounced, and the 751 cmK1 (Kr) (749 cmK1 in
Xe) band which is relatively ‘isolated’ but very weak. These
became the only two infrared bands of the gauche

J.R. Durig et al. / Journal of Molecular Structure 744–747 (2005) 3–17
13
ab initio calculations will be retained in the final results in
the following way: bond lengths in the same set will keep
their relative ratio and bond angles (including torsional
angles) in the same set will keep their difference in degrees.
This assumption is based on the fact that the errors from ab
initio calculations are systematic which is commonly
acknowledged. To avoid the possibility of falling into a
local minimum instead of the global minimum, a simplex
algorithm instead of a gradient method was used. The A&M
program adds ab initio structural parameters, although with
much smaller weights, to the rotational constants, so that the
number of observable is always larger than the number of
unknown parameters. As a consequence, unique results can
be obtained without any arbitrary assumptions on the values
of structural parameters.
The adjusted r0 parameters for vinylcyclopropane are
listed in Table 4 along with ab initio MP2(full)/6-311C
G(d,p) predicted values. The fit of the previously reported
[28] microwave rotational constants is given in Table 7 and
the differences between the observed B and C values for five
isotopomers and the fitted values is 0.3 MHz or less. The
differences for the A moments is considerably higher but
these constants have very large uncertainties.
7. Discussion
The enthalpy value of 415G42 cmK1 from the rare gas
solutions should be near the value in the gas phase [45–49]
since the size and polarity of the two conformers are very
similar. In the earlier Raman studies, two different enthalpy
values were reported for the vapor from variable temperature
studies of the 1191(t)/1203(g) cmK1 conformer pair with a
low value [26] of 385G35 cmK1 (4.61G0.42 kJ/mol) and a
high value [25] of 500G50 cmK1. A smaller value had
previously been reported [24] from the electron diffraction
study. It was suggested [25] that the two different values
probably arose from taking slightly different baselines as
well as the spectral resolution used. Since it is possible to
obtain the enthalpy difference from the previously reported
spectra [25,26] at a single temperature by using the ab initio
predicted Raman activities for this pair of lines, we
calculated the enthalpy values for this conformer pair from
both Raman studies (Fig. 7). For the Raman lines reported at
the two different temperatures [26], enthalpy values of
377 cmK1 (85 8C) and 392 cmK1 (23 8C) were obtained,
whereas the value obtained from the spectral data recorded
[25] with a spectral slit width of 1 cmK1 gave a value of
399 cmK1. Both of these values support the lower value of
415 cmK1 which we obtained from the variable temperature
infrared spectra of the rare gas solutions. Also this lower
value is in good agreement with the predicted values from
the ab initio MP2 calculations with the largest value of
440 cmK1 obtained with the 6–311CG(2df,2pd) basis set.
The vibrational assignment for the trans conformer could
be made with confidence because of the band contours and
Fig. 6. Predicted pure A-, B- and C-type gas-phase infrared band contours
for the trans and gauche conformers of vinylcyclopropane.
a value of 415G42 cmK1 (4.96G0.50 kJ/mol) for the
experimental DH value from the infrared studies.
6. Structural parameters
We [43] have recently shown that ab initio MP2(full)/6-
311CG(d,p) calculations predict the r0 structural par-
ameters for more than 50 carbon-hydrogen distances better
˚
than 0.002 A compared to the experimentally determined
[44] values from ‘isolated’ CH stretching frequencies. We
have also found [35] that we can obtain good structural
parameters by systematically adjusting the structural
parameters obtained from the ab initio calculations to fit
the rotational constants (computer program A&M, Ab initio
and Microwave, developed in our laboratory) obtained from
the microwave experimental data. In order to reduce the
number of independent variables, the structural parameters
are separated into several sets according to their type. Each
set uses only one independent parameter in the optimization
and all structural parameters in one set will be changed by
the same adjustment factor. The information about the
difference between similar structural parameters from

14
J.R. Durig et al. / Journal of Molecular Structure 744–747 (2005) 3–17
Fig. 7. Raman spectra of the vapor: (A) Ref. [25], and (B) Ref. [26].
the spectral data in the rare gas solutions and many of the
fundamental for the gauche conformer could be identified.
For those that not assigned it is assumed that they are in near
coincidence with bands from the trans conformer. This is
particularly true in the fingerprint region.
values for the carbon-hydrogen distances as well as values
for the angles.
The values for the structural parameters for the gauche
conformer can be readily predicted by simply taking the
predicted values from the MP2(full)/6-311CG(d,p) ab
initio calculations and adjust them with the difference of
the adjusted values of corresponding parameters from the
trans conformer and the ab initio predicted values. For
The adjusted r0 parameters (Table 4) are very similar to
the values obtained from the more recent electron diffrac-
tion study [24] where the microwave rotational constants
were used as additional constraints. They are also within the
values obtained from the more recent microwave study [28]
if the listed uncertainties are taken into account. However,
the results which we obtained in this study have confident
˚
example the C2–C3 distance is predicted to be 0.007 A
longer in the gauche conformer than the corresponding bond
distance for the trans form so this difference should be
added to the adjusted value for this bond of the trans
Table 6
Temperature dependent intensity ratios for the trans and gauche conformers of vinyl cyclopropane dissolved in liquid xenon
T (8C)
1000/T (KK1
)
I440t/I749g
I761t/I749g
I1321t/I749g
I440t/I1325g
I761t/I1325g
I1321t/I1325g
K55.0
K60.0
K65.0
K70.0
K75.0
K80.0
K85.0
K90.0
K95.0
K100.0
DH (cmK1
4.5840
4.6915
4.8042
4.9225
5.0467
5.1773
5.3149
5.4600
5.6132
5.7753
1.22001
1.36471
1.50883
1.63089
1.80467
2.20746
2.04365
2.21247
2.55778
2.96193
482G33
0.9629
3.12606
3.48896
3.85698
4.42706
4.55784
5.38140
5.50212
6.31863
7.13498
7.93111
531G19
0.9901
2.21145
2.25743
2.38500
2.64297
2.72697
3.04928
3.08542
3.40779
3.74458
4.08111
365G12
0.9910
0.54734
0.62118
0.67344
0.68610
0.75623
0.87158
0.82223
0.84530
0.92843
1.02399
325G32
0.9300
1.40247
1.58808
1.72148
1.86242
1.90992
2.12475
2.21370
2.41411
2.58987
2.74192
373G19
0.9803
0.99214
1.02752
1.06449
1.11187
1.14271
1.20395
1.24138
1.30198
1.35921
1.41091
208G4
0.9975
)
Individual pair
Linearity coefficient (R2)
DH (cmK1
Statistical average
)
381G17 (trans conformer more stable)

J.R. Durig et al. / Journal of Molecular Structure 744–747 (2005) 3–17
15
Table 7
Comparison of rotational constants obtained from modified ab initio,
MP2/6-311CG(d,p) structural parameters and those from microwave
spectra for trans-vinylcyclopropane
Isotopomer
Rotational Observeda
constants
Calculated
D
(MHZ)
c-(12CH122CH122
A
B
C
A
B
C
A
B
C
A
B
C
A
B
C
15076.2
3061.4
15080.0
3061.5
2941.4
14832.3
3022.6
2896.2
15006.5
3057.5
2940.5
15010.8
3040.9
2924.9
15073.0
2973.1
2860.0
3.8
0.1
0.0
CH)12CHa12CH2
2941.4
c-(13CH122CH122
CH)12CHa12CH2
14821(7)
3022.7
11.3
K0.1
K0.3
K7.5
0.3
2896.5
c-(12CH122CH123
CH)12CHa12CH2
15014(15)
3057.2
2940.6
K0.1
K5.5
K0.2
K0.2
K2.0
K0.2
0.2
c-(12CH122CH122
CH)13CHa12CH2
15016.3(9)
3041.1
2925.1
c-(12CH122CH122
CH)12CHa13CH2
15075(6)
2972.9
2859.8
a
Values for the rotational constants taken from Ref. [28].
conformer. From these parameters it should be relatively
easy to assign the rotational spectrum arising from the
gauche conformer.
In one of the earlier Raman studies [26] the spectra of the
solid were reported where two significantly different
reproducible spectra were observed. The spectra were
assigned to two crystal forms, which were attributed to the
rate of cooling. Also, these authors suggested that the
differences in the spectra were probably due to differences
in the crystal packing. We initially expected that the
spectrum of the solid which had a good correspondence [26]
with the spectrum of the liquid could have been mainly due
to annealing with the sample being more like an amorphous
solid. Therefore, we reinvestigated the vibrational spectra of
vinylcyclopropane utilizing the infrared spectrum of the
sample on a flat plate, which makes the annealing
considerably easier since the temperature can be more
easily controlled and the sample can be continuously
observed. The results of these studies are shown in Fig. 9
and it is clear that the initially obtained spectrum is in fact
Fig. 9. Mid-infrared spectra (850–1120 cmK1) of vinylcyclopropane: (A)
gas; (B) krypton solution; (C) amorphous solid; (D) first annealed solid; (E)
second annealed solid.
quite crystalline and has at least four molecules per
primitive cell since several of the fundamentals split into
four peaks with many of them observed in both the infrared
and Raman spectra. However, by repeated additional
annealing many of the peaks disappear leaving two well-
defined bands for most of the fundamentals.
A single-crystal X-ray study [50,51] has been reported
for vinylcyclopropane with the measurements made at 94 K.
In addition to the conventional full-angle refinements
(sin q=l!1:22 AK1) higher-order refinements (sin q=l!
˚
0:70 AK1) were performed to obtain accurate parameters
˚
for the C atoms [51]. For the full angle refinement on 3480
observed independent reflections it was found that the
molecules in the crystal deviated slightly from the trans-
bisected conformation in a monoclinic P21 (D22) cell [aZ
4.879(1), bZ7.161(1), cZ6.923(1)] and ZZ2. The two
molecules must occupy the two C1 sites and one, therefore,
expects each fundamental to be a doublet from the factor
group with the Raman and infrared bands having the same
frequencies. Since the molecular symmetry is Cs with both
the A0 and A00 modes being active in both the infrared and
Raman spectra, the lower C1 symmetry of the site will not
affect the vibrational spectrum. However, the skeletal
movement from the symmetry plane for the molecule in
the fluid phases to the crystal should affect the vibrations,
which are the most sensitive to the molecular conformation.
An inspection of the data in Tables 1 and 2 shows significant
Fig. 8. Infrared spectra of vinylcyclopropane showing the band contours.

16
J.R. Durig et al. / Journal of Molecular Structure 744–747 (2005) 3–17
calculations. The doubly degenerate gauche conformers
appear as minima on the plot, with skeletal dihedral
angles of wG608. The local maximum at dihedral 08
assumes the cis orientation while the two doubly
degenerate gauche0 transition states (global maxima)
assume wG1158 dihedral angle. The trans-to-gauche
barrier (via gauche0 maxima) was predicted to be
1042 cmK1 from MP2(full)/6-31G(d) level and slightly
higher at 1055 cmK1 from MP2(full)/6-31CG(d) level,
whereas the gauche-to-gauche barrier (via cis maximum)
was predicted to be only 263 and 216 cmK1, respectively
(Table 6). The calculated potential functions are shown in
Fig. 10. By fitting a Fourier cosine series to represent
the asymmetric potential function with the form
Fig. 10. Calculated potential functions governing asymmetric torsion in
vinylcyclopropane. Solid curve from MP2(full)/6-31G(d) and dotted curve
from MP2(full)/6-31CG(d) calculations. Dihedral angle 1808 defined for
the trans conformer.
P
6
VðfÞZ iZ1ðVi=2Þð1Kcos ifÞ, the potential constants for
the first six cosine terms were obtained. All predicted
potential constants with the exception of the V1 terms
agree reasonably well between the two levels of
calculation. These potential constants, fitted from
MP2(full)6-31G(d) and MP2(full)6-31CG(d) results, are
listed in Table 8.
frequency differences for n12 which is predicted to be
10 cmK1 higher for the gauche form as well as the out-of-
phase rCH2 wag (n26). Therefore, the observed shifts of the
bands between the two observed infrared spectra of the two
solids as well as the Raman spectra of the two different
crystals appears to be consistent with the initially obtained
spectrum being due to four molecules with Cs symmetry per
primitive cell. The second crystal phase gives spectral data
consistent with the published crystal structure with the
partially rotated heavy atom frame, which destroys the
molecular plane of symmetry. (Fig. 9)
The potential constants determined by fitting the
observed two quantum jumps in the Raman spectrum of
the gas [25] are also listed in Table 8. The major
differences are the much larger values for the V2 and V4
terms compared to the predicted values. Also it should be
noted that the gauche-to-gauche barrier is more than twice
the predicted ones. These investigators [25] also obtained
the potential constants by using the smaller DH value from
the other Raman study [26] where the most significant
difference is the V1 term. These experimental results
clearly indicate a much different frequency separations
should be found for the gauche excited torsional states
from those predicted from the ab initio calculations.
Unfortunately, no experimental information is available
on the torsional excited state frequencies for the gauche
conformer which could be used to obtain more definitive
information on the gauche well.
The asymmetric torsional potential governing confor-
mational interchange has been predicted from ab initio
calculations. Beginning at the global minimum for the most
stable trans conformer (dihedral 1808), the potential function
was determined by rotating the vinyl moiety at increments of
158 throughout a 3608 cycle. The energies were calculated
with full optimization of all structural parameters, except
for the varying dihedral angle, at each point from
both MP2(full)/6-31G(d) and MP2(full)/6-31CG(d)
Table 8
Calculated potential barriers and Fourier potential coefficients of vinylcyclopropane
Coefficients (cmK1
)
MP2(full)/6-31G(d)
MP2(full)/6-31CG(d)
Ref. [25]
Ref. [26]
V1
V2
V3
V4
V5
V6
DE
DH
K60
396
K131
439
K279G60
699G60
K782G32
K199G35
–
K111
752
K652
111
K613
103
K784
K203
–
81
81
K14
358
K15
440
–
–
500
385
Potential barriers (cmK1
)
Trans/gauche
Gauche/trans
Gauche/gauche
Gauche dihedral angle
Gauche (min)
1042
684
1055
615
1373
877
1361
980
263
216
564
514
60.58
116.08
60.18
114.88
Gauche0 (max)

J.R. Durig et al. / Journal of Molecular Structure 744–747 (2005) 3–17
17
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support of this research.
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