Infrared and raman spectra, conformational stability, normal coordinate analysis, ab initio calculations, and vibrational assignment of 1- methylsilacyclobutane

Article abstract of DOI:10.1016/S0022-2860(98)00602-4

The infrared (3500-40 cm^-1) spectra of gaseous and solid 1- methylsilacyclobutane, c-C₃H₆SiH(CH₃), have been recorded. In addition, the Raman spectrum (3500-30 cm^-1) of the liquid has also been recorded and quantitative depolarization values obtained. Both the axial and equatorial conformers, with respect to methyl group, have been identified in the fluid phases. Variable temperature studies (-55 to - 100°C) of the infrared spectra of the sample dissolved in liquid xenon have been carried out. From these data, the enthalpy difference has been determined to be 122 ± 26 cm^{- 1} (1.46 ± 0.32 kJ/mol), with the equatorial conformer being the more stable structure. However, with repeated annealing of the amorphous solid, it was not possible to obtain a polycrystalline solid with a single conformer. A complete vibrational assignment is proposed for the equatorial conformer based on infrared band contours, relative intensities, depolarization values and group frequencies. Most of the fundamentals for the axial conformer have also been identified. Utilizing the frequency of the silicon-hydrogen (Si-H) stretching mode, the Si-H distance has been determined to be 1.490 A for both conformers. The vibrational assignments are supported by normal coordinate calculations utilizing ab initio force constants. Complete equilibrium geometries have been determined for both rotamers by ab initio calculations, employing the 3-21G* and 6-31G* basis sets at the levels of restricted Hartree-Fock (RHF) and/or Moller-Plesset (MP) to second order. The results are discussed and compared with those obtained for some similar molecules.

Full text of DOI:10.1016/S0022-2860(98)00602-4

Journal of Molecular Structure 477 (1999) 31–47
Infrared and Raman spectra, conformational stability, normal
coordinate analysis, ab initio calculations, and vibrational
assignment of 1–methylsilacyclobutane
1
2
*
James R. Durig , Pengqian Zhen , Yanping Jin, Todor K. Gounev, Gamil A. Guirgis
Department of Chemistry, University of Missouri-Kansas City, Kansas City MO 64110-2499, USA
Received 27 January 1998; received in revised form 21 July 1998; accepted 21 July 1998
Abstract
The infrared (3500–40 cmϪ1) spectra of gaseous and solid 1-methylsilacyclobutane, c-C3H6SiH(CH3), have been recorded.
In addition, the Raman spectrum (3500–30 cmϪ1) of the liquid has also been recorded and quantitative depolarization values
obtained. Both the axial and equatorial conformers, with respect to methyl group, have been identified in the fluid phases.
Variable temperature studies (Ϫ55 to Ϫ100ЊC) of the infrared spectra of the sample dissolved in liquid xenon have been carried
out. From these data, the enthalpy difference has been determined to be 122 ^ 26 cmϪ1 (1.46 ^ 0.32 kJ/mol), with the
equatorial conformer being the more stable structure. However, with repeated annealing of the amorphous solid, it was not
possible to obtain a polycrystalline solid with a single conformer. A complete vibrational assignment is proposed for the
equatorial conformer based on infrared band contours, relative intensities, depolarization values and group frequencies. Most of
the fundamentals for the axial conformer have also been identified. Utilizing the frequency of the silicon–hydrogen (Si–H)
˚
stretching mode, the Si–H distance has been determined to be 1.490 A for both conformers. The vibrational assignments are
supported by normal coordinate calculations utilizing ab initio force constants. Complete equilibrium geometries have been
determined for both rotamers by ab initio calculations, employing the 3-21G* and 6-31G* basis sets at the levels of restricted
Hartree–Fock (RHF) and/or Moller–Plesset (MP) to second order. The results are discussed and compared with those obtained
for some similar molecules. ᭧ 1999 Elsevier Science B.V. All rights reserved.
Keywords: Infrared; Raman; Conformational stability; Ab initio calculations; 1-Methylsilacyclobutane
1. Introduction
ering modes with little attention given to the
remaining portion of the vibrational spectrum. These
earlier results were consistent with the equatorial
conformer energetically favored over the axial form.
It was inferred that a large value of the enthalpy differ-
ence, DH, between the two conformers should result
in little or none of the high-energy axial form, being
present at ambient temperature similar to what was
found initially for the halocyclobutanes [3–6].
However, more recent studies [7,8] of methylcyclo-
butane provided clear evidence that the value of DH
for both the liquid and vapor phases was sufficiently
In the initial far-infrared and low-frequency Raman
investigations [1,2] of methylcyclobutane, the studies
only referred to the methyl torsional and ring puck-
1 Taken in part from the dissertation of P. Zhen which will be
submitted to the Department of Chemistry in partial fulfillment of
his Ph.D. degree.
* Corresponding author. Tel.: ϩ 1-816-235-1136; Fax: ϩ 1-
816-235-5191; e-mail: durigj@smtpgate.umkc.edu
2 Premanent address: Analytical R/D Department, Organic
Products Division, Bayer, Bushy Park Plant, Charleston, SC 29411.
0022-2860/99/$ - see front matter ᭧ 1999 Elsevier Science B.V. All rights reserved.
PII: S0022-2860(98)00602-4

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J.R. Durig et al. / Journal of Molecular Structure 477 (1999) 31–47
Fig. 1. Mid-infrared spectra of 1-methylsilacyclobutane in the: (A) gas; and (B) solid.
small (Ͻ 400 cmϪ1) to allow direct observation of
several of the vibrational modes of the high-energy
axial conformation. Similarly, for the halocyclobu-
tane molecules, the enthalpy differences between the
conformers have been found in the same general range
(300–400 cmϪ1) so that several fundamentals from
the axial conformers have been identified [9–11].
The silacyclobutane molecule has been shown [12]
to be a bent molecule with an inversion barrier of
440 cmϪ1 (5.26 kJ/mol) with the dihedral angle of
the puckered ring of 35.9 ^ 2Њ. This barrier is lower
than the 510 cmϪ1 (6.10 kJ/mol) barrier for cyclobu-
tane [13] so that the equatorial and axial conformers
for the monosubstituted silacyclobutane should more
easily interconvert than the corresponding monosub-
stituted cyclobutane molecules. For methylcyclobu-
tane, DH was found to be 295 ^ 75 cmϪ1 (3.53 ^
0.90 kJ/mol) for the vapor with a barrier to conformer
interconversion of 641 cmϪ1 (7.67 kJ/mol). There-
fore, it was expected that 1-methylsilacyclobutane
should have a comparable or even smaller DH value
for the two expected conformers. Also, the isolation of
the low-energy form in the solid should be easily
accomplished, as the barrier to interconversion of
the conformers should be lower than that of the
corresponding carbon compound. Therefore, we
initiated an infrared and Raman spectroscopic study
of 1-methylsilacyclobutane to determine the presence
or absence of conformers at ambient temperatures,
and to determine their relative stabilities if they are
present. As an aid in interpreting the vibrational
spectra we have carried out ab initio calculations at
the RHF/3-21G*, RHF/6-31G* and MP2/6-31G*
levels. The optimized geometries, conformational
stabilities, harmonic force fields, infrared intensities,
Raman activities, depolarization ratios, and vibra-
tional frequencies have been obtained to compare
with the experimental results where applicable. The
results of these spectroscopic and theoretical studies
are reported herein.
2. Experimental
A sample of 1-chloro-1-methylsilacyclobutane was
prepared by the reaction of dichloro (3-choropropyl)
methylsilane with magnesium in dry diethyl ether
according to the method of Damrauer [14]. This
sample was then used to prepare 1-methylsilacyclo-
butane by reduction with LiAlH4. This sample was

J.R. Durig et al. / Journal of Molecular Structure 477 (1999) 31–47
33
purified with a low-temperature, low-pressure fractio-
nation column.
The mid-infrared spectra of the gas and solid (Fig.
1) were obtained from 3500 to 400 cmϪ1 on a Perkin-
Elmer model 2000 Fourier transform spectrometer
equipped with a Ge/CsI beamsplitter and a DTGS
detector. The gas was contained in a 10-cm cell fitted
with CsI windows. This spectrum was obtained at
0.5 cmϪ1 resolution and transformed with boxcar
truncation function. The spectrum of the solid was
obtained by condensing the sample onto a liquid
nitrogen cooled CsI plate contained in an evacuated
cell equipped with CsI windows, and 256 scans were
collected for both the reference and sample interfero-
grams at 1.0 cmϪ1 resolution and then transformed
with a boxcar truncation function.
The mid-infrared spectra of the sample dissolved in
liquified xenon as a function of temperature were
recorded on a Bruker model IFS 66 Fourier transform
spectrometer equipped with a globar source, a Ge/KBr
beamsplitter and a DTGS detector. In all cases, 100
interferograms were collected at 1.0 cmϪ1 resolution,
averaged and transformed with a boxcar truncation
function. For these studies, a specially designed cryo-
stat cell was used which consists of a copper cell with
a path length of 4 cm with wedged silicon windows
sealed to the cell with indium gaskets as described
previously [15].
Fig. 2. Far-infrared spectra of 1-methylsilacyclobutane in the: (A)
solid; and (B) gas. Features labelled with an asterisk are due to HCl
rotational lines.
The far-infrared spectrum of the gas (Fig. 2) was
recorded with a Bomen model DA3.002 Fourier trans-
form spectrometer equipped with a vacuum bench, a
6.25 mm Mylar beamsplitter, and a liquid helium
cooled Si bolometer with a wedged sapphire filter
and polyethylene window. The spectra were obtained
from the sample contained in a 1 m folded path cell
equipped with mirrors coated with gold, and fitted
with polyethylene windows with an effective
resolution of 0.10 cmϪ1
.
Interferograms were
recorded 512 times at a resolution of 0.10 cmϪ1 and
transformed with a boxcar truncation function. The
spectrum of the crystalline solid was obtained
with the Perkin-Elmer model 2000 spectrometer
equipped with a metal grid beamsplitter and a
DTGS detector.
The Raman spectra were recorded on a SPEX
model 1403 spectrophotometer equipped with a Spec-
traPhysics model 164 argon ion laser operating on the
514.5 nm line. The laser power used was 0.5 W with a
Fig. 3. Raman spectra of 1-methylsilacyclobutane in the: (A) liquid
at 25ЊC; and (B) liquid at Ϫ120ЊC.

34
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J.R. Durig et al. / Journal of Molecular Structure 477 (1999) 31–47
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J.R. Durig et al. / Journal of Molecular Structure 477 (1999) 31–47
37
Table 2
Structural parametersa , rotational constants, dipole moments, and energy for 1-methylsilacyclobutane
Internal
coordinates
RHF/3-21G*
Equatorial
RHF/6-31G*
Equatorial
MP2/6-31G*
Equatorial
Parameter
Axial
Axial
Axial
Si–C2(C3)
Si–C11
Si–H
C4–C2(C3)
C–H7
C–H8
C–H9
C–H10
C–H5
C–H6
R1,R2
R5
r7
R3,R4
r1
r2
r3
r4
r5
r6
1.893
1.882
1.481
1.586
1.086
1.082
1.086
1.082
1.081
1.083
1.087
1.088
79.95
100.1
87.43
109.2
108.6
108.8
108.8
111.1
111.1
107.9
107.6
110.0
113.9
110.4
114.6
112.8
121.2
120.0
112.6
24.5
1.893
1.882
1.482
1.586
1.083
1.086
1.083
1.086
1.083
1.081
1.087
1.088
79.94
100.1
87.49
109.2
108.5
108.7
108.7
110.9
111.2
107.8
107.7
113.9
110.1
114.6
110.4
120.9
113.1
114.7
118.0
24.2
1.898
1.887
1.482
1.561
1.087
1.083
1.087
1.083
1.086
1.086
1.086
1.087
78.56
100.7
87.16
109.0
107.3
108.1
108.1
111.4
111.1
107.8
107.5
109.9
114.5
110.8
115.4
112.0
121.9
120.6
112.7
27.5
1.899
1.888
1.482
1.562
1.084
1.086
1.084
1.086
1.086
1.085
1.086
1.087
78.69
100.9
87.42
108.8
107.2
108.0
108.0
111.4
111.1
107.7
107.5
114.4
109.9
115.2
111.1
121.5
112.3
115.7
117.8
25.6
1.897
1.882
1.494
1.557
1.096
1.092
1.096
1.092
1.096
1.096
1.094
1.094
78.03
100.2
86.22
109.6
107.4
108.5
108.5
110.9
111.0
108.0
107.7
109.6
114.9
110.4
116.1
111.4
122.5
121.6
111.3
33.2
1.899
1.883
1.494
1.557
1.093
1.096
1.093
1.096
1.096
1.096
1.094
1.094
78.10
100.4
86.56
109.3
107.2
108.4
108.4
110.8
111.2
107.9
107.8
114.9
109.7
115.9
110.7
122.0
111.7
114.3
119.0
31.3
C–H13
r8
r9,r10
u1
C–H14(H15)
ЄC2Si3C
ЄC2C4C3
ЄCCSi
n1
a1,b1
u2
ЄH12SiC11
ЄH5C4H6
ЄH7C2H8
ЄH9C3H10
ЄSiCH13
ЄSiCH14(H15)
ЄH13CH14(H15)
ЄH14CH15
ЄCCH6
ЄCCH5
ЄCCH7(H9)
ЄCCH8(H10)
ЄSiCH7(H9)
ЄSiCH8(H10)
ЄCSiC11
ЄH12SiC2(C3)
Puckering angle
t(H12SiC11H13)
A
n6
a4
b4
l1
l2,l3
s3,s2
s1
n3,n5
n2,n4
a5,b5
a6,b6
a2,b2
a3,b3
w1,w2
d1,d2
t
180.0
7346
180.0
6270
180.0
7480
180.0
6359
180.0
7595
180.0
6208
B
2859
3054
2843
3027
2836
3084
C
2419
2719
2415
2704
2412
2796
͉ma͉
͉mb͉
͉mc͉
͉mt͉
0.461
0.000
0.431
0.631
0.91793
0.250
0.000
0.329
0.413
0.91778
32
0.409
0.000
0.416
0.583
3.19763
0.226
0.000
0.339
0.407
3.19714
107
0.476
0.000
0.444
0.651
3.80122
0.222
0.000
0.330
0.397
3.80059
137
Ϫ(E ϩ 443)
DE(cmϪ1
)
a
˚
Bond distances in A, bond angles in degrees, rotational constants in MHz, dipole moments in Debye, and energies in Hartrees.
spectral bandpass of 3 cmϪ1. The spectra of the liquid
were recorded with the sample sealed in a Pyrex
glass capillary held in a Miller-Harney apparatus
[16]. Depolarization measurements were obtained
for the liquid sample using a standard Ednalite
35 mm camera polarizer with 38 mm of free aper-
ture affixed to the SPEX instrument. The measure-
ments of Raman frequencies are expected to be
accurate to ^ 2 cmϪ1 and typical spectra are
shown in Fig. 3. All the observed bands in both

38
J.R. Durig et al. / Journal of Molecular Structure 477 (1999) 31–47
Table 3
Symmetry coordinates for 1-methysilacyclobutane
Species
A0
Description
Symmetry Coordinatea
CH3 antisymmetric stretch
(CH2)2 antisymmetric stretch
CH2 antisymmetric stretch
(CH2)2 symmetric stretch
CH2 symmetric stretch
CH3 symmetric stretch
Si–H stretch
CH2 deformation
(CH2)2 deformation
CH3 antisymmetric deformation
CH3 symmetric deformation
(CH2)2 twist
(CH2)2 wag
Si–H bend
CH3 rock
C–C ring stretch
(CH2)2 rock
S1 ˆ 2r8Ϫr9Ϫr10
S2 ˆ r2Ϫr1 ϩ r4Ϫr3
S3 ˆ r5Ϫr6
S4 ˆ r1 ϩ r2 ϩ r3 ϩ r4
S5 ˆ r5 ϩ r6
S6 ˆ r8 ϩ r9 ϩ r10
S7 ˆ r7
S8 ˆ 4n6Ϫn2Ϫn3Ϫn4Ϫn5
S9 ˆ 4a4 ϩ 4b4Ϫ a2Ϫ a3Ϫ a5Ϫ a6Ϫ b2Ϫ b3Ϫ b5Ϫb6
S10 ˆ 2s1Ϫs2Ϫ s3
S11 ˆ s1 ϩ s2 ϩ s3Ϫl1Ϫl2Ϫ l3
S12 ˆ a2Ϫa3Ϫa5 ϩ a6 ϩ b2Ϫ b3Ϫ b5 ϩ b6
S13 ˆ a2 ϩ a3Ϫa5Ϫa6 ϩ b2 ϩ b3Ϫ b5Ϫ b6
S14 ˆ 4u2Ϫd1Ϫd2Ϫw1Ϫw2
S15 ˆ 2l1Ϫl2Ϫl3
S16 ˆ R3 ϩ R4
S17 ˆ a2Ϫa3 ϩ a5Ϫa6 ϩ b2Ϫb3 ϩ b5Ϫb6
S18 ˆ R5
Si–C stretch
CH2 rock
C–Si ring stretch
ring deformation
ring puckering
S19 ˆ n3Ϫn2 ϩ n5Ϫn4
S20 ˆ R1 ϩ R2
S21 ˆ a1 ϩ b1Ϫn1Ϫu1
S22 ˆ a1 ϩ b1 ϩ n1 ϩ u1
S23 ˆ w1 ϩ w2Ϫd1Ϫd2
S24 ˆ r2Ϫr1 ϩ r3Ϫr4
Si–C bend
A00
(CH2)2 antisymmetric stretch
CH3 antisymmetric stretch
(CH2)2 symmetric stretch
CH3 antisymmetric deformation
(CH2)2 deformation
CH2 wag
CH2 twist
(CH2)2 wag
(CH2)2 twist
C–C ring stretch
Si–H bend
CH3 rock
C–Si ring stretch
(CH2)2 rock
Si–C bend
CH3 torsion
S25 ˆ r9Ϫr10
S26 ˆ r1 ϩ r2Ϫr3Ϫr4
S27 ˆ s 3Ϫs 2
S28 ˆ 4a4Ϫa2Ϫa3Ϫa5Ϫa6Ϫ4b4 ϩ b2 ϩ b3 ϩ b5 ϩ b6
S29 ˆ n4 ϩ n5Ϫn2Ϫn3
S30 ˆ n2Ϫn3Ϫn4 ϩ n5
S31 ˆ a5 ϩ a6Ϫa2Ϫa3 ϩ b2 ϩ b3Ϫb5Ϫb6
S32 ˆ a3Ϫa2 ϩ a5Ϫa6 ϩ b2Ϫb3Ϫb5 ϩ b6
S33 ˆ R3ϪR4
S34 ˆ w1Ϫw2 ϩ d1Ϫd2
S35 ˆ l2Ϫl3
S36 ˆ R1ϪR2
S37 ˆ a3Ϫa2Ϫa5 ϩ a6 ϩ b2Ϫb3 ϩ b5Ϫb6
S38 ˆ w2Ϫw1 ϩ d1Ϫd2
S39 ˆ t
a Not normalized; for definitions of internal coordinates see Table 2.
the infrared and Raman spectra, along with the
proposed assignments, are listed in Table 1.
SIAN-94 program [17] using Gaussian-type basis
functions. The energy minima with respect to nuclear
coordinates were obtained by the simultaneous relaxa-
tion of all the geometric parameters consistent with
the symmetry restrictions using the gradient method
of Pulay [18]. The structural optimization for both the
equatorial and the axial conformers were carried
out with initial parameters taken from those of
3. Ab initio calculations
The LCAO-MO-SCF restricted Hartree–Fock
(RHF) calculations were performed with the GAUS-

J.R. Durig et al. / Journal of Molecular Structure 477 (1999) 31–47
39
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J.R. Durig et al. / Journal of Molecular Structure 477 (1999) 31–47
41
normal co-ordinate analysis. The force fields in Carte-
sian co-ordinates were calculated by the GAUSSIAN-
94 program [16] with the MP2/6-31G* basis set.
Internal co-ordinates (Table 2) were used to calculate
the G and B matrices using the structural parameters
given in Table 2. Using the B matrix [20], the force
field in Cartesian coordinates was then converted to a
force field in internal co-ordinates, and the pure ab
initio vibrational frequencies were reproduced. The
force constants for both the equatorial and axial
conformers can be obtained from the authors. Subse-
quently, scaling factors of 0.9 for stretching and
bending and 1.0 for the torsional co-ordinates, and
the geometric average of scaling factors for interac-
tion force constants were used to obtain the fixed
scaled force field and resultant wavenumbers. A set
of symmetry co-ordinates was used (Table 3) to
determine the corresponding potential energy distri-
butions (PED). A comparison between the observed
and calculated frequencies of 1-methylsilacyclobu-
tane along with the calculated infrared intensities,
Raman activities, depolarization ratios, and PED are
given in Table 4.
Fig. 4. Temperature-dependent Raman spectrum (380–520 cmϪ1
of liquid 1-methylsilacyclobutane.
)
1,1-diethylsilacyclobutane [19]. The 3-21G* and
6-31G* basis sets were employed at the level of
RHF and Moller–Plesset (MP2) to second order.
The determined structural parameters are listed in
Table 2.
In order to obtain a complete description of the
molecular motions involved in the normal modes of
1-methylsilacyclobutane, we have carried out a
4. Conformational stability
The determination of the conformational stability is
not straightforward as most of the fundamentals of the
two conformers are predicted to be near coincident.
Nevertheless, it is clear from the spectral data that
conformers are present in the fluid phases. For
Table 5
Table 6
Temperature and intensity ratio for the conformational stability
determination of 1-methylsilacyclobutane dissolved in liquid
xenona
Temperature and intensity ratio for the conformational stability
determination of 1-methylsilacyclobutane in the liquid statea
T(ЊC)
1000/T
I439(eq)/I483(ax)
ϪlnK
T(Њ C)
1000/T(KϪ 1
)
I481(ax)/I437(eq)
Ϫlnk
ϩ 6
Ϫ11
Ϫ30
Ϫ44
Ϫ56
Ϫ68
Ϫ78
Ϫ91
Ϫ101
Ϫ121
3.58
3.81
4.11
4.36
4.60
4.87
5.12
5.49
5.81
6.58
4.8262
4.9364
4.8076
4.7386
5.6686
5.3136
5.9895
6.5464
6.8157
8.0251
Ϫ1.5741
Ϫ1.5699
Ϫ1.5702
Ϫ1.5557
Ϫ1.7349
Ϫ1.6703
Ϫ1.7900
Ϫ1.8789
Ϫ1.9192
Ϫ2.0826
Ϫ55
Ϫ60
Ϫ65
Ϫ70
Ϫ80
Ϫ85
Ϫ90
Ϫ95
Ϫ100
4.58
4.65
4.80
4.92
5.18
5.31
5.46
5.61
5.78
2.06
2.06
1.88
1.74
1.88
1.77
1.76
1.62
1.67
Ϫ0.724
Ϫ0.724
Ϫ0.633
Ϫ0.552
Ϫ0.629
Ϫ0.573
Ϫ0.566
Ϫ0.480
Ϫ0.515
a DH ˆ 122 ^ 26 cmϪ1 (1.46 ^ 0.32 kJ/mol) with the equatorial
a DH ˆ 127 ^ 14 cmϪ1 (1.52 ^ 0.17 kJ/mol) with the equatorial
form the more stable conformer.
form the more stable conformer.

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J.R. Durig et al. / Journal of Molecular Structure 477 (1999) 31–47
Fig. 5. Temperature-dependent infrared spectrum (420–500 Ϫ1) of 1-methylsilacyclobutane dissolved in liquid xenon.
example, a comparison of the Raman spectrum of the
liquid as a function of temperature indicates that the
band at 481 cmϪ1 decreases in intensity relative to the
band at 437 cmϪ1 with decreasing temperature (Fig.
4). The ab initio calculations indicate that the band at
481 cmϪ1 is due to the axial conformer where the ring
deformation, n21, is predicted at 478 cmϪ1. Similarly,
the 437 cmϪ1 band is assigned as the corresponding
ring deformation for the equatorial conformer with a
predicted frequency of 429 cmϪ1. No other fundamen-
tals for either conformer are predicted between 550
and 260 cmϪ1, so the assignment for these two bands
to the individual conformers can be made with confi-
dence. Finally, it should be noted that this conformer
pair has the largest predicted frequency separation,
which further supports the assignment as given.
There is other evidence for conformers in the fluid
phases but it is not as definitive. For example, the
(CH2)2 rock and C–Si ring stretch are predicted as
the next higher frequency fundamentals after the n21
conformer doublets and both of these fundamentals
have identifiable doublets at 569/583 and 617/
612 cmϪ1 with the first listed frequencies due to the
equatorial conformer. Also, the ring puckering/Si–C
bend, n22, is well-defined for both conformers with
bands at 253 and 238 cmϪ1 for the equatorial and
axial conformers, respectively. Other conformer
doublets are listed in Table 4 but none are as clear
as the conformer doublet in the 400 cmϪ1 region.
The conformer pair at 481/437 cmϪ1 was used to
determine the enthalpy difference between the confor-
mers by the temperature-dependent infrared spectra of
xenon solutions. The spectral changes are shown in
Fig. 5 and from these data, the increase in the intensity
of the infrared band assigned to the equatorial
conformer as the temperature decreases, confirms
the stability of the equatorial form over the axial
conformer in the xenon solution. In order to obtain
the enthalpy difference, ten sets of spectral data
were obtained for these bands over the temperature
range Ϫ55ЊC to Ϫ100ЊC (Table 5). The intensity data
for the conformer pair were fit to the van’t Hoff equa-
tion, ln K ˆ (DH/RT) Ϫ(DS/R), where K is the inten-
sity ratio (Iax/Ieq), and it was assumed that DH is not a
function of temperature. Using the least-squares fit
and the slope of the van’t Hoff plot, a DH value of
122 ^ 26 cmϪ1 (1.46 ^ 0.32 kJ/mol) was obtained.
This value should be near the value for the gas [21,22]
as both conformers have similar sizes. We also deter-
mined the enthalpy difference in the liquid state by the
temperature-dependent Raman spectra (Fig. 4).
Utilizing the same conformer doublet as used in the

J.R. Durig et al. / Journal of Molecular Structure 477 (1999) 31–47
43
Fig. 6. Raman spectra of 1-methylsilacyclobutane: (A) experi-
mental spectrum of the liquid; (B) calculated spectrum of the
mixture of both conformers; (C) calculated spectrum of the axial
conformer; and (D) calculated spectrum of the equatorial
conformer.
infrared study, a DH value of 127 ^ 14 cmϪ1 (1.52 ^
0.17 kJ/mol) was obtained from the data listed in
Table 6.
Fig. 7. Mid-infrared spectra of 1-methylsilacyclobutane: (A) xenon
solution at Ϫ65ЊC; (B) calculated spectrum of the mixture of both
conformers; (C) calculated spectrum of the axial conformer; and (D)
calculated spectrum of the equatorial conformer.
on the predicted frequency order, infrared intensities,
and Raman activities from the ab initio calculations.
In the CH stretching region (3000–2900 cmϪ1),
there are nine expected fundamentals. The three
sharp Q-branches in the infrared spectrum of the gas
at 2985, 2979, and 2948 cmϪ1, respectively, must be
attributed to the CH3 (A0), (CH2)2 (A0), and CH2 anti-
symmetric stretches of both conformers. The three
corresponding symmetric stretches are associated
with the two strong polarized Raman bands at
2923 cmϪ1 for the A0 (CH2)2 vibration and at
2908 cmϪ1 for the CH2 and CH3 modes. The A00
(CH2)2 and CH3 antisymmetric stretches are over-
lapped in the shoulder at 2964 cmϪ1 in the infrared
spectrum of the xenon solution, whereas the A00
(CH2)2 symmetric stretch is coincident with the
5. Vibrational assignment
Both the axial and equatorial conformers of 1-
methylsilacyclobutane have a plane of symmetry
and their 39 normal modes are classified by the
symmetry species of the Cs symmetry group, A0 and
A00. There are 23 A0 vibrations which are expected to
produce polarized Raman bands and A/C-type hybrid
infrared band contours. The remaining 16 A00 modes
should give rise to depolarized lines in the Raman
spectrum and yield B-type infrared band envelopes.
Thus, to identify the A0 and A00 vibrations, we utilized
the measured depolarization ratios and observed
infrared band contours, whereas to distinguish the
equivalent modes of the two conformers we relied

44
J.R. Durig et al. / Journal of Molecular Structure 477 (1999) 31–47
conformer which overlaps with the CH2 rock of the
axial form of the strong infrared band at 911 cmϪ1 in
the spectrum of the xenon solution. Thus, the sharp C-
type Q-branch at 677 cmϪ1 is assigned to the CH2 rock
of the equatorial conformer. The ‘‘out-of-plane’’ Si–
H band of the equatorial form is associated with the B-
type band with a minimum at 825 cmϪ1 in the infrared
spectrum of the gas, where it is overlapped with the
CH3 rock of the axial conformer.
The A0 CH3 and (CH2)2 rocks are assigned to the
four Q-branches located at 881/827 cmϪ1 for the
equatorial conformer and 856/819 cmϪ1 for the axial
form, respectively. The corresponding A00 modes are
depolarized in the Raman spectrum of the liquid and
appear at 754/569 cmϪ1 for the equatorial rotamer.
The Si–C stretch of the methyl group is observed at
723 cmϪ1 in the infrared spectrum of the xenon solu-
tion, whereas the C–Si ring stretch is found as a very
strong, polarized band at 617 cmϪ1 in the Raman
spectrum of the liquid. For both C–Si stretching
modes, double Q-branches are observed in the
infrared spectrum of the gas due to the two different
conformers. The weak B-type band at 649 cmϪ1 is
then assigned to the A00 C–Si ring stretch.
The ring deformation conformer doublet at 480/
436 cmϪ1 is well separated and has been discussed
earlier. A C-type band at 253 cmϪ1 and a maximum
at 238 cmϪ1 in the far-infrared spectrum of the gas are
observed for the ring puckering/Si–C bend motions of
the two conformers. The Si–C bend/ring puckering
mode is observed at 118 cmϪ1 for both conformers.
These vibrational modes are strongly coupled with
nearly equal contribution from the Si–C bend and
ring puckering vibrations for the lower wavenumber
band. Surprisingly, these two fundamentals in the
200 cmϪ1 region are not separated in the Raman spec-
trum of the liquid. Finally, the ‘‘out-of-plane’’ Si–C
bend is assigned to the B-type band located at
190 cmϪ1 in the far-infrared spectrum of the gas,
whereas the CH3 torsion is associated with the weak
absorption at 150 cmϪ1 in the far-infrared spectrum of
the solid.
Fig. 8. Equatorial conformation of 1-methylsilacyclobutane.
respective A0 vibration. The Si–H stretches of the
equatorial and axial conformers give rise to the very
strong Q-branches located at 2131 and 2128 cmϪ1
respectively.
,
The intensities of the bands in the C–H deformation
region are quite low, in both the infrared and Raman
spectra. Nevertheless, the CH2 deformations from the
A0 symmetry block are observed in the Raman spec-
trum of the liquid at 1455 and 1418 cmϪ1, respec-
tively. Three of the remaining four C–H
deformational modes, n10, n27, and n28, are masked
on the low-frequency side of the latter band, but in
the infrared spectrum of the solid they appear to be
separated. The remaining CH3 symmetric deformation
produces the Q-branch at 1256 cmϪ1
.
The CH2 wagging and twisting fundamentals are
both in the A00 block and, therefore, give rise to the
B-type bands at 1216 and 1193 cmϪ1, respectively, in
the infrared spectrum of the gas. In the same spec-
trum, A/C-type bands are observed for the A0 (CH2)2
wag and twist at 1133 and 1191 cmϪ1, respectively.
The corresponding A00 wag and twist, n31 and n32,
yield the depolarized Raman bands at 1050 and
928 cmϪ1
.
The strongest band in the infrared spectrum of the
sample dissolved in liquid xenon is due to the A00 C–C
ring stretch at 920 cmϪ1. The A0 C–C ring stretches of
the axial and equatorial conformers are separated in
the Raman spectrum of the liquid and appear at 903
and 874 cmϪ1, respectively. Due to apparent differ-
ences in the PEDs (Table 4) of the two conformers,
the Si–H ‘‘in-plane’’ band of the axial form is
assigned at a much lower frequency of 652 cmϪ1
than the corresponding vibration of the equatorial
6. Results and discussion
To aid in the vibrational assignment, we
predicted the Raman and infrared spectra (Figs.

J.R. Durig et al. / Journal of Molecular Structure 477 (1999) 31–47
45
6 and 7) for 1-methylsilacyclobutane using the calcu-
lated frequencies, scattering activities and intensities
determined from the ab initio calculations. The GAUS-
SIAN-94program[17]withtheoptionofcalculatingthe
polarizability derivatives (RHF/6-31G*) was used. The
Raman scattering cross sections, 2sj/2V, which are
proportional to the Raman intensities, can be calculated
from the scattering activities and the predicted frequen-
cies for each normal mode using the following relation
[23]:
transformation matrix between the Cartesian displace-
ment coordinates and normal coordinates. The
infrared intensities were then calculated by
"
#
ꢂ
ꢃ
ꢂ
ꢃ
ꢂ
ꢃ
2
2
2
2my
Np
3c2
2mx
2mz
Ii ˆ
ϩ
ϩ
2Qi
2Qi
2Qi
In Fig. 7D and E, the predicted infrared spectra of
the axial and equatorial conformers Fig. 8, respec-
tively, are shown. The combination of the spectra of
the two conformers with a DH of 122 cmϪ1 is shown
in Fig. 7C and the experimental spectrum of the
sample dissolved in liquid xenon is shown in Fig.
7B along with that for the gas (Fig. 7A). Again,
these spectra were very valuable for making the vibra-
tional assignment particularly in the region from 400
0
1
ꢀ
ꢁ
4
!
!
24p4
h
n0 Ϫ nj
h
2sj
2V
B
@
C
A
i
ˆ
Sj
8p2cnj
45
1 Ϫ exp Ϫhcnj=kT
where n0 is the exciting frequency, nj the vibrational
frequency of the jth normal mode, h, c and k are
universal constants, and Sj the corresponding Raman
scattering activity. To obtain the polarized Raman scat-
tering cross section, the polarizabilities are incorporated
into Sj by Sj [(1Ϫrj)/(1 ϩ rj)] where rj is the depolar-
ization ratio of the jth normal mode. The Raman scat-
teringcross sections and calculated frequencies are used
together with a Lorentzian line shape function to obtain
the calculated spectrum. Since the calculated frequen-
cies are Ϸ 10% higher than those observed, the
frequency axis of the theoretical spectrum was
compressed by a factor of 0.9. The predicted Raman
spectra of the pure equatorial and axial conformers are
shown in Fig. 6C and D, respectively. The predicted
Raman spectrum of the mixture of the two conformers
with an assumed DH of 127 cmϪ1 is shown in Fig. 6B
whichshouldbecomparedtotheexperimentalspectrum
of the liquid (Fig. 6A). The calculated Raman spectrum
is quite similar to the experimental spectrum particu-
larly in the 500–1500 cmϪ1 region which makes it
very useful for making the vibrational assignment.
Infrared intensities were also calculated based on
the dipole moment derivatives with respect to the
Cartesian coordinates. The derivatives were taken
from the ab initio calculations at the MP2/6-31G*
level and transformed to normal coordinates by
to 1500 cmϪ1
.
The assignment of the C–H stretching modes
depends almost entirely on the ab initio predictions
and it is necessary to assign several degeneracies.
Also, we have rather arbitrarily assigned the same
frequencies for the corresponding bands for the two
conformers. We similarly relied on the ab initio calcu-
lations for the assignment of the CH2 and CH3 defor-
mations. It should be noted that for both the CH3
symmetric deformation and the (CH2)2 deformation
the predicted values are about 40 cmϪ1 too high.
Beginning with the Si–H bend, n14 in the A0
symmetry block, there is so much mixing that the
descriptions are rather arbitrary except for the ring
modes. The mixing is considerably less for the corre-
sponding modes in the A00 symmetry block.
In the low-frequency region, there is extensive
mixing of the ring puckering mode with the silicon-
methyl bending mode where the band at 118 cmϪ1 has
about equal amounts of each motion. The band at
253 cmϪ1 has 46% ring puckering and 25% Si–
C(H3) bend with 11% contributions from the Si–H
bend and the (CH2)2 rock. Thus, it would not be
possible to use excited state transitions from either
of these bands to obtain information on the potential
function governing interconversion of the conformers.
The vibrational assignments for both conformers
are summarized in Table 4. There were only a limited
number of bands which could be identified with a
single conformer. Nevertheless, the ab initio predicted
spectra made it possible to assign a few of the bands to
one or the other conformer so the presence of both
!
ꢂ
ꢃ
X
2mm
2mm
ˆ
Lji
2Qi
2Xj
j
where Qi is the ith normal coordinate, Xj the jth Carte-
sian displacement coordinate, and Lji the

46
J.R. Durig et al. / Journal of Molecular Structure 477 (1999) 31–47
conformers in the fluid states was definitively shown
from the data.
tions for the conformation with the methyl group in
the axial position. This conclusion is supported by the
much larger puckering angles of ϳ 32Њ calculated for
1-methylsilacyclobutane (Table 2) compared to the
values of 20.7Њ and 16.4Њ for the equatorial and axial
conformers of methylcyclobutane [7], respectively.
It is clear from the structural parameters listed in
Table 2 that the main differences in the geometry of
the conformers arise from the conversion of the equa-
torial hydrogen atoms in the axial position and vice
versa during the inversion of the molecule. The equa-
torial hydrogens in both rotamers have slightly shorter
Utilizing the Si–H stretching frequencies, it is
possible to calculate the Si–H distances (r0) for both
conformers [24]. Utilizing the frequencies of 2131
and 2128 cmϪ1 for the Si–H vibrations for the equa-
torial and axial conformers, respectively, the Si–H
˚
bond distances are calculated to be 1.490A. This
˚
value compares very well with the 1.494 A predicted
for this bond distance for both conformers from the
MP2/6-31G* calculations. The predicted Si–H bond
distances from the RHF/3-21G* and RHF/6-31G*
calculations are shorter with values of 1.481 and
˚
(by about 0.004A) C–H distances and much larger
˚
˚
1.482A, which makes them smaller by 0.008 A than
the r0 values obtained from the infrared spectrum.
Therefore, the agreement from the MP2/6-31G*
calculation is quite good and indicates that the struc-
tural parameters obtained from the relatively small 6-
31G* basis set with electron correlation at the MP2
level provides good predictions of the structural para-
meters for the Si–H bonds of these types of
molecules.
CCH and SiCH angles. For example, the CCH bond
angles are about 5Њ larger and the SiCH bond angles
are about 10Њ larger for the equatorial hydrogen
atoms. Similarly, the CSiC(H3) bond angle of the
equatorial conformer is about 7Њ larger than that in
the axial form. As it was expected, the puckering
angle in the axial form is approximately 2Њ smaller
than the angle in the equatorial form and this is consis-
tent with the results for the carbon analog of 1-methyl-
silacyclobutane.
The barrier to conformer interconversion of 1-
methylsilacyclobutane was obtained through the ab
initio energies of the axial and equatorial conformers
and the energy of the transition state along the puck-
ering coordinate calculated with the MP2/6-31G*
basis set. A value of 686 cmϪ1 (8.21 kJ/mol) was
obtained for the equatorial-to-axial puckering barrier.
This value compares well with the barrier to inversion
of 641 ^ 20 cmϪ1 (7.67 ^ 0.24 kJ/mol) for methyl-
cyclobutane [7], which was determined from the ring
puckering transitions in the low-frequency Raman
spectrum. However, the axial-to-equatorial barrier of
methylcyclobutane [7] is about 150 cmϪ1 (1.80 kJ/
mol) lower than the one obtained in this study for 1-
methylsilacyclobutane (549 cmϪ1). The reason for
this difference is mainly due to the different DH values
of the two compounds. It should also be noted that the
barrier heights evaluated through the ab initio method
may be different from the actual experimental quan-
tities which are not available at this time for c-
C3H6SiH(CH3).
The apparent resemblance in the geometric para-
meters of the two conformers reflects in very similar
values for the diagonal elements of the two force
constant matrices. The only significant difference is
found in the values of the CCSi and CCC ring bending
force constants, which are about 5% larger for the
axial form. This fact results in a lower frequency of
the ring deformation fundamental (see Table 4) for the
equatorial compared to the axial rotamer. Thus, the
only well separated conformer doublet appears to be
the ring deformation located at 434/481 cmϪ1
.
As no experimental structural parameters have been
reported for 1-methylsilacyclobutane it is not possible
to assess how well the other parameters are predicted
from the MP2/6-31G* calculation. Nevertheless,
based on some of our earlier studies [25,26] of the
four-membered rings, we believe the C–H and C–C
bond distances should be well predicted, i.e. the C–H
˚
distances within 0.005 A and C–C distances within
˚
0.008A. The angles are usually predicted within
The enthalpy difference of 122 ^ 26 cmϪ1 between
the axial and equatorial conformers of 1-methylsila-
cyclobutane is less than one-half the respective value
for the carbon analog, 295 ^ 75 cmϪ1. Evidently, the
larger size of the Si atom reduces the spatial restric-
about one degree from the MP2/6-31G* calculations
so we expect the listed parameters given in Table 2 are
about as accurate as one could obtain from an electron
diffraction or microwave investigation of this
molecule.

J.R. Durig et al. / Journal of Molecular Structure 477 (1999) 31–47
47
[10] J.R. Durig, Min Joo Lee, T.S Little, J. Raman Spectrosc. 21
(1990) 529.
[11] J.R. Durig, Min Joo Lee, Wenyun Zhao, T.S. Little, Struct.
Chem. 3 (1992) 329.
[12] J. Laane, R.C. Lord, J. Chem. Phys. 48 (1968) 1508.
[13] H. Li, C.C. Miller, L.A. Philips, J. Chem. Phys. 100 (1994)
8590.
[14] R. Damrauer, J. Organomet. Chem. 43 (1971) 121.
[15] T.K. Gounev, J.W. Weston, S. Shen, M. Dakkouri, A. Grun-
vogel-Hurst, J.R. Durig, J. Phys. Chem. 101 (1997) 8614.
[16] F.A. Miller, B.M. Harney, Appl. Spectrosc. 24 (1970) 291.
[17] Gaussian 94 (Revision B. 3), Frisch, M.J., Trucks, G.W.,
Schlegel, H.B., Gill, P.M.W., Johnson, B.G., Robb, M.A.,
Cheeseman, J.R., Keith, T.A., Petersson, G.A., Montgomery,
J.A., Raghavachari, K., Al-Laham, M.A., Zakrzewski, V.G.,
Ortiz, J.V., Foresman, J.B., Cioslowski, J., Stefanov, B.B.,
Nanayakkara, A., Challacombe, M., Peng, C.Y., Ayala,
P.Y., Chen, W., Wong, M.W. Andres, J.L., Replogle, E.S.,
Gomperts, R., Martin, R.L., Fox, D.J., Binkley, J.S., Defrees,
D.J., Baker, J., Stewart, J.P., Head-Gordon, M., Gonzalez, C.,
Pople, J.A., Gaussian Inc., Pittsburgh PA, 1995.
It is not clear why it was not possible to obtain one
conformer in the polycrystalline state. However, the
molecule remained as a liquid at very low tempera-
tures where it became very viscous but it did not
appear to be a solid. Since the barrier to inversion is
comparable with that for methylcyclobutane and the
enthalpy difference is smaller than that of the carbon
compound it should be possible to obtain a single
conformer as was found for methylcyclobutane.
Acknowledgements
JRD acknowledges the University of Kansas City
Trustees for a Faculty Fellowship award for partial
financial support of this research.
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