Synthesis, conformation and dynamics of 4,4,5,5,6,6,7,7,8,8-decamethyl-1-oxa-spiro[2.5]octane and 1,2,3,3,4,4,5,5,6,6-decamethyl-cyclohexene

Article abstract of DOI:10.1016/j.tet.2010.04.068

The fragmentation of a suitable methylated 1-oxa-spiro[2.5]octane yields permethyl-cyclohexene. The activation parameters for the chair to chair interconversion of the 1-oxa-spiro[2.5]octane and the half-chair to half-chair interconversion of permethyl-cyclohexene were determined via bandshape analyses of exchange-broadened ¹H and ¹³C NMR spectra, respectively.

Full text of DOI:10.1016/j.tet.2010.04.068

Tetrahedron 66 (2010) 4510e4514
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Tetrahedron
journal homepage: www.elsevier.com/locate/tet
Synthesis, conformation and dynamics of 4,4,5,5,6,6,7,7,8,8-decamethyl-
1-oxa-spiro[2.5]octane and 1,2,3,3,4,4,5,5,6,6-decamethyl-cyclohexene
*
Stefan Dressel, Norbert Schormann, Lutz Fitjer
€
€
€
Institut für Organische und Biomolekulare Chemie der, Universitat Gottingen, Tammannstrasse 2, D-37077 Gottingen, Germany
a r t i c l e i n f o
a b s t r a c t
Article history:
Received 3 March 2010
Received in revised form 12 April 2010
Accepted 16 April 2010
Available online 21 April 2010
The fragmentation of a suitable methylated 1-oxa-spiro[2.5]octane yields permethyl-cyclohexene. The
activation parameters for the chair to chair interconversion of the 1-oxa-spiro[2.5]octane and the half-
chair to half-chair interconversion of permethyl-cyclohexene were determined via bandshape analyses of
exchange-broadened 1H and 13C NMR spectra, respectively.
Ó 2010 Elsevier Ltd. All rights reserved.
Keywords:
Cyclohexanes
Cyclohexenes
Conformational analysis
Dynamic NMR
1. Introduction
The stereodynamics of cyclohexanes1 and cyclohexenes2 are of
fundamental interest in organic chemistry. Of the basic systems,
cyclohexane adopts a chair conformation (symmetry D3d) in the
ground state and inverts via a half-chair (symmetry C2) as transi-
tion state. In contrast, cyclohexene adopts a half-chair conforma-
tion (symmetry C2) in the ground state and inverts via a boat
(symmetry Cs) as transition state. According to dynamic NMR, the
chair
half-chair
1
free energy of activation (DG
s) amounts to 43.1 kJ/mol for cyclo-
hexane,3 and to 22.2 kJ/mol for cyclohexene.4
Interestingly, the barriers of inversion of lower substituted
cyclohexanes5 and cyclohexenes4b,6 differ from those of their par-
ent system only slightly. This indicates that in most cases energy
demanding ecliptic arrangements of substituents in the corre-
sponding transition states may be avoided. However, in fully
substituted systems such arrangements must occur. An example is
1,1,2,2,3,3,4,4,5,5,6,6-dodecamethyl-cyclohexane (1).7 This com-
pound passes a doubly eclipsed arrangement of two geminal
dimethyl groups in the half-chair as transition state (Fig. 1) and
half-chair
boat
2
Figure 1. Ground and transition state geometries of permethyl-cyclohexane and per-
methyl-cyclohexene.
transition state of 1, a doubly eclipsed arrangement of two geminal
dimethyl groups is unavoidable. As the two flagpole methyl groups
in the boat of 2 should cause additional strain,8 it was tempting to
speculate that the increase of the barrier of inversion in going from
cyclohexene to 2 could even be larger than in going from cyclo-
hexane to 1. In the following, we report on the synthesis, confor-
mation and dynamics of 2, and its direct precursor, the 1-oxa-spiro
[2.5]octane 7.
exhibits
a
barrier of inversion
(D
Gs ¼72.3 kJ/mol),7 which
298
exceeds that of cyclohexane by far.
The same could be true for the hitherto unknown
1,2,3,3,4,4,5,5,6,6-decamethyl-cyclohexene (2). In this case the
transition state is a boat (Fig. 1), but, as in the half-chair as
2. Results
Previous work from this laboratory had shown that on treat-
* Corresponding author. Tel.: þ49 551 393278; e-mail address: lfitjer@gwdg.de
(L. Fitjer).
ment with acid the 1-oxa-spiro[2.4]heptanes 39 and 510 yield
0040-4020/$ e see front matter Ó 2010 Elsevier Ltd. All rights reserved.
doi:10.1016/j.tet.2010.04.068

S. Dressel et al. / Tetrahedron 66 (2010) 4510e4514
4511
1,2,3,3,4,4,5,5-octamethyl-cyclopentene (4) as the main product
(Scheme 1). For the synthesis of 2 we therefore envisaged an acid
catalyzed fragmentation of the 1-oxa-spiro[2.5]octane 7. For the
synthesis of the latter, we treated the methylene-cyclohexane 67
under two-phase conditions11 with m-chloroperbenzoic acid
(MCPBA) and obtained the desired epoxide 7 as a colorless solid
(mp 78 ꢀC; yield 92%). According to 1H NMR (200 MHz, CD2Cl2,
CHDCl2 int), this compound exists at ꢁ51.7 ꢀC as 4:1 mixture of two
chair conformations (symmetry C2v) as indicated by two singlets12
(s), 130.81 (s)]. Molecular mechanics calculations using the force
field MM317 in connection with our conformational search program
HUNTER18 yielded a half-chair (Hf0¼ꢁ43.05 kcal/mol) as the sole
minimum conformation. This means that the bandshape analysis
given below describes a half-chair to half-chair interconversion via
a boat as transition state.
For the determination of the barriers of the chair to chair
interconversion of the major and minor conformer of 1-oxa-
4,4,5,5,6,6,7,7,8,8,-decamethyl-spiro[2.5]octane (7) we performed
a bandshape analysis of exchange-broadened 1H NMR spectra.
Towards this end, six 1H NMR spectra (79.6 MHz, CDCl3, CHCl3
int) within a temperature range from þ42.4 ꢀC to ꢁ47.5 ꢀC were
taken and the resonances of the methylene protons analyzed
using the program DNMR5.19 The static parameters [d(CH2a)¼2.44,
d(CH2e)¼2.92; p(CH2a)¼0.79, p(CH2e)¼0.21] were taken from the
spectrum at ꢁ47.5 ꢀC, assumed to be independent of temperature,
and used in the computational analysis of the high temperature
spectra throughout. Experimental and computed bandshapes and
the corresponding rate constants are shown in Figure 3.
for the protons of the methylene group [
d
¼2.44 (major, CH2-a) and
2.92 (minor, CH2-e)]. In contrast to lower substituted 1-oxa-spiro
[2.5]octanes,13 the chemical shift difference for the protons of the
equatorially and axially positioned methylene groups in 7 is large
(
Dd¼0.48 ppm). Therefore, our assignment is based on the data of
the structurally related tris-epoxide 8. This compound adopts in the
crystal state14 and in solution15 a chair conformation and exhibits
for the protons of the equatorially (
d
¼2.76 ppm, s, 2H) and axially
bound methylene groups (
d
¼2.26 ppm, AB-system, 4H) 15 a chem-
ical shift difference (Dd¼0.50 ppm) nearly identical with that of the
two conformers of 7 (Fig. 2). However, a definite proof for the
correctness of our assignment cannot be given.
O
O
H+
H+
52%
50%
3
4
5
O
MCPB
NaHCO3
H+
92%
57%
6
7
2
Scheme 1.
δ = 2.26
(AB, 4H)
δ = 2.44
(s, 2H)
O
O
O
O
O
δ = 2.76
(s, 2H)
δ = 2.92
(s, 2H)
(CH -a)
(CH -e)
8
7
7
2
2
Figure 2.
For the synthesis of 2, we treated the 1-oxa-spiro[2.5]octane 7
with an equivalent amount (w/w) of Nafion HÒ16 in benzene at 80 ꢀC.
After 0.5 h the reaction was completed. Work up and gas chroma-
tography yielded 2 as colorless solid (mp 101 ꢀC, yield 57%). Within
the fastexchange limit (þ60.1 ꢀC), 2 showedin the 1HNMRspectrum
(200 MHz, C6D5CD3, C6D5CHD2 int) three singlets [
d
¼0.87 (6H), 0.98
(12H),1.56 (12H)] for a rapidly inverting species (effective symmetry
C2v). Within the slowexchange limit (ꢁ75.1 ꢀC), five singlets [
¼0.87
d
(6H), 0.93 (6H), 0.97 (6H), 1.13 (6H), 1.59 (6H)] for a fixed half-chair
(symmetry C2) or boat conformation (symmetry C2v) appeared.
Accordingly, the 13C NMR spectrum (50.3 MHz, C6D5CD3, C6D5CHD2
int) showed six resonances at þ60.1 ꢀC [
¼15.68 (q), 23.46 (q), 26.92
d
(q), 41.80 (s), 42.36 (s), 131.02 (s)], but eight resonances at ꢁ49.2 ꢀC
Figure 3. Chair-to-chair interconversion of 7. Experimental (left) and computed
bandshapes (right) at different temperatures and rate constants derived therefrom.
[
d¼16.02 (q), 20.47 (q), 24.60 (q), 26.64 (q), 26.69 (q), 41.27 (s), 42.03

4512
S. Dressel et al. / Tetrahedron 66 (2010) 4510e4514
A weighted least-squares adjustment of the rate data to the
Eyring equation using the program ACTPAR,20 shown graphically
in Figures 4 and 5, then yielded the activation parameters and
activation parameters and their standard deviations for the half-
chairtohalf-chairinterconversion of 2 as
D
Hs¼53.8ꢂ0.7 kJ/mol and
D
Ss¼ꢁ13.7ꢂ2.4 J/mol K. From the equation
D
Gs
¼D
HsꢁT
DS
s the
their standard deviations as
D
Hs¼52.0ꢂ1.1 kJ/mol and
free energy of activation followed as
D
Gs ¼57.8ꢂ0.1 kJ/mol.
298
D
Ss¼ꢁ28.6ꢂ3.6 J/mol K for the conversion of the major to the
As may be seen from to the free energies of activation for the
inversion of the cyclohexanes and cyclohexenes given in Figure 8,
the values for 7 fall in between those of cyclohexane and 1. Obvi-
ously, in the transition state of 7 a doubly eclipsed arrangement of
two geminal dimethyl groups, as in the transition state of 1, can be
avoided. An energetically less demanding singly eclipsed arrange-
ment of the epoxide ring and a neighbouring geminal dimethyl
group is passed through instead.
minor, and as
D
Hs¼52.9ꢂ1.1 kJ/mol and
D
Ss¼ꢁ17.9ꢂ3.6 J/mol K
for the conversion of minor to the major conformer. The free
energies of activation were calculated from the equation
D
Gs
and
¼
D
HsꢁT
D
Ss to give
D
Gs ¼57.8ꢂ0.1 kJ/mol for the major
298
D
Gs ¼57.3ꢂ0.1 kJ/mol for the minor conformer.
298
Interestingly, the difference between the free energies of acti-
vation of the half-chair to half-chair interconversions of 2 and
cyclohexene (DDGs¼35.6 kJ/mol) exceeds that of the chair to chair
-23
interconversions of cyclohexane and
1
(
DDGs¼29.2 kJ/mol)
-24
-25
-26
-27
-28
3.0
3.2
3.4
3.6
3.8
4.0
Figure 4. Eyring plot for the rate data of 7 [CH2(a/e)].
ln(k h/kB T)
-22
-23
-24
-25
-26
-27
103/T
3.0
3.2
3.4
3.6
3.8
4.0
Figure 5. Eyring plot for the rate data of 7 [CH2(e/a)].
For the determination of the barrier of the half-chair to half-chair
interconversion of 1,2,3,3,4,4,5,5,6,6-decamethyl-cyclohexene (2)
we analyzed eight 13C NMR spectra (20 MHz, CDCl3, CDCl3 int) taken
at þ50.3 ꢀC to ꢁ44.7 ꢀC in CDCl3. In this solvent, within the slow
exchange limit (ꢁ44.7 ꢀC), a coincidence of the resonances of the
equatorial methyl groups at C-4/C-5 and the pseudo-equatorial
methyl groups at C-3/C-6 was observed. The static parameters
[
d
¼20.08 (C-4/C-5)a, 24.15 (C-3/C-6)pseudo-a, 26.21 (C-4/C-5)e and
(C-3/C-6)pseudo-e] were taken from the spectrum at ꢁ44.7 ꢀC,
assumed to be independent from temperature, and used in the
analysis of the high temperature spectra throughout. The experi-
mental and computed bandshapes and the corresponding rate
constants are shown in Figure 6. A weighted least-squares adjust-
ment of the rate constants to the Eyring equation with the computer
program ACTPAR,20 shown graphically in Figure 7, then yielded the
Figure 6. Half-chair to half-chair interconversion of 2. Experimental (left) and com-
puted bandshapes (right) at different temperatures and rate constants derived
therefrom.

S. Dressel et al. / Tetrahedron 66 (2010) 4510e4514
4513
conformational isomerism at room temperature (
D
Gs298>100 kJ/
ln(k h/kB T)
-22
mol), we believe that a similar phenomenon will be observed in
going from 2 to 11, regardless of whether the double bond is
substituted or not.
-23
In summary, we have synthesized the oxaspirooctane 7 and
permethyl-cyclohexene 2 and have determined the activation
parameters for the chair to chair interconversion of 7 and the half-
chair to half-chair interconversion of 2 via analyses of exchange-
broadened 1H (7) and 13C NMR spectra (2). Most interesting is the
fact that the increase in the free energy of activation in going from
cyclohexene to 2 exceeds that in going from cyclohexane to 1. This
means that in a boat as transition state of 2, in addition to a doubly
eclipsed arrangement of two geminal dimethyl groups, also present
in a half-chair as transition state of 1, an energy demanding inter-
action of two flagpole methyl groups is operative.
-24
-25
-26
-27
103/T
3.0
3.2
3.4
3.6
3.8
4.0
3. Experimental
3.1. General
Figure 7. Eyring plot of the rate data of 2.
1H and 13C NMR spectra were recorded on a Varian FT 80A or XL
200 spectrometer. For standards other than TMS the following
chemical shifts were used: dH (CHDCl2)¼5.32, dH (CHCl3)¼7.24, dH
(C6H5CD2H)¼2.09, dC (CD2Cl2)¼53.80, dC (CDCl3)¼77.00, dC
(C6H5CD3)¼127.60. Mass spectra were obtained with a Varian MAT
311A spectrometer operated at 70 eV. Analytical and preparative
GC was carried out on a Carlo Erba FTV 2450 instrument using
a thermal conductivity detector and hydrogen as carrier gas. Rf
values are quoted for Machery and Nagel Polygram SIL G/UV 254
plates. Colorless substances were detected by oxidation with 3.5%
alcoholic 12-molybdophosphoric acid and subsequent warming.
Melting points were obtained on a Reichert microhotstage and are
not corrected. Microanalytical determinations were done at the
Microanalytical Laboratory of the Institute of Organic Chemistry,
O
7
1
9
ΔG≠487 = 156.8
ΔG≠213 = 43.1
ΔG≠298 = 57.3 (e-a)
ΔG≠298 = 57.8 (a-e)
ΔG≠298 = 72.3
R
R
€
Gottingen.
10
2
11
R = H, CH3
ΔG≠109 = 22.2
ΔG≠156 = 35.1
ΔG≠298 = 57.8
3.1.1. 4,4,5,5,6,6,7,7,8,8-Decamethyl-1-oxa-spiro[2.5]octane (7). To
a solution of 67 (236 mg, 1.00 mmol) in dichloromethane (10 ml)
was added a 0.5 M aqueous solution of sodium bicarbonate (4 ml).
Under vigorous stirring, a solution of 3-chloroperbenzoic acid
(263 mg, 80% w/w, 1.60 mmol) in dichloromethane (2.0 ml) was
added drop wise. According to GC [1.2 mꢃ1/400 all-glass system,15%
OV 210 on Chromosorb W AW/DMCS 60/80 mesh, 190ꢀ; rel
retention times (min): 1.00, 1.57 (6), 3.36 (7)], after 1.5 h 6 had been
consumed. The mixture was diluted with dichloromethane (5 ml)
and the organic phase was separated and washed with aqueous 2 N
Figure 8. Free energies of activation (in kJ/mol) for the chair to chair interconversion
of selected cyclohexanes, and the half-chair to half-chair interconversion of selected
cylohexenes.
distinctly. This indicates that in the transition state of 2 (a boat), in
addition to a doubly eclipsed arrangement of two geminal dimethyl
groups also present in the transition state of 1 (a half-chair), an
energy demanding 1,4-interaction of two flagpole methyl groups
exists. Support comes from the fact that the free energy of activa-
tion for the half-chair to half-chair interconversion of 3,3,6,6-
tetramethyl-cyclohexene (10)8 exceeds that of cyclohexene by far
ꢀ
NaOH (5 ml), water (2 ml) and dried (molecular sieves 4 A). The
solvent was distilled off (bath temperature 50 ꢀC/10 Torr), and the
residue (250 mg) was chromatographed on silica gel (0.2e0.5 mm)
coated with 5% (w/w) of sodium bicarbonate [pentane/ether 93:7,
column 55ꢃ2 cm, control by TLC, Rf¼0.39 (7), 0.63 (6)] to yield
231 mg (92%) of pure 7 as colourless solid, mp 78 ꢀC. 1H NMR
(200 MHz, CDCl2, TMS int) (þ21.6 ꢀC): largely unresolved with
(
DDGs¼12.9 kJ/mol), (Fig. 8).
An unsolved problem concerns the energy profile of the half-
chair to half-chair interconversion of 2. Recent ab initio calcula-
tions21 have shown that the half-chair to half-chair interconversion
of cyclohexene proceeds via a flat energy plateau representing
a nearly free twist-boat to twist-boat interconversion via a boat.
With 2 the situation may be different. In this case, a strongly neg-
broad resonances at
d
¼0.7e1.4 (30H) and 2.52 ppm (2H);
(ꢁ51.7 ꢀC): 4:1 mixture of two conformers; major conformer:
d
¼0.77 (s, 6H), 0.95 (s, 6H), 1.00 (s, 3H),1.05 (s, 6H),1.26 (s, 9H), 2.43
ative entropy of activation (
D
Ss¼ꢁ13.7ꢂ2.4 J/mol K) points to
(s, 2H, CH2-a); minor conformer:
d
¼0.75 (s, 6H), 0.97 (s, 6H), 1.03
a well defined transition state, and hence to an energy profile
without a plateau. However, as entropy data are notoriously diffi-
cult to obtain and values outside a range of ꢂ10 J/mol K have been
questioned,3 this assumption remains to be proved.
A concluding remark concerns the hitherto unknown tetra-
spirane 11. In view of the fact that in going from 1 to the hex-
aspirane 922 the free energy of activation passes the border to
(s, 6H), 1.23 (s, 6H), 2.92 (s, 2H, CH2-e); the resonances of two
methyl groups of the minor conformer were hidden; 13C NMR
(20.1 MHz, CDCl3, CDCl3 int) [þ20 ꢀC]: partially unresolved with
broad resonances at
onances at
d
¼22.8e26.7 (q) and 65.9 (t), and sharp res-
d
¼42.10 (s), 43.19 (s) and 44.16 (s) and 81.75 (s). In view
of the successful analysis of exchange-broadened 1H NMR spectra
(see Section 2), no temperature dependent 13C NMR spectra were

4514
S. Dressel et al. / Tetrahedron 66 (2010) 4510e4514
recorded. MS (EI): m/z¼222 (1, MþꢁCH2O), 57 (100). Anal. Calcd for
Supplementary data
C17H32O: C, 80.36; H, 12.78. Found: C, 80.87; H, 12.63.
Supplementary data associated with this article can be found in
the online version at doi:10.1016/j.tet.2010.04.068.
3.1.2. 1,2,3,3,4,4,5,5,6,6-Decamethyl-cyclohexene (2). To a solution
of 7 (202 mg, 0.80 mmol) in dry benzene (10 ml) was added under
nitrogen with stirring Nafion HÒ (200 mg).16 Afterwards the mix-
ture was heated to 80 ꢀC. According to GC [1.2 mꢃ1/400 all-glass
system,15% OV 210 on Chromosorb WAW/DMCS 60/80 mesh, 130ꢀ;
rel retention times (min): 1.00 (2), 3.00 (7)], after 30 min the
fragmentation was complete. The mixture was filtered, and the
filtrate was concentrated and purified by preparative GC to yield
101 mg (57%) of 2 as colourless solid, mp 101 ꢀC. 1H NMR (200 MHz,
References and notes
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chemistry of alkanes and cycloalkanes; Patai, S., Rappoport, Z., Eds.; John Wiley:
New York, NY, 1992; pp 118e123; (c) Eliel, E. L.; Wilen, S. H. Stereochemistry of
Organic Compounds; John Wiley: New York, NY, 1994, pp 686e709.
2. (a) Anet, F. A. L. In The Conformational Analysis of Cyclohexenes, Cyclo-
hexadienesand Related Hydroaromatic Compounds; Rabideau, P. W., Ed.; VCH:
New York, NY, 1989; pp 3e45.
C6D5CD3, C6D5CHD2 int) (þ60.1 ꢀC):
¼0.87 (s, 12H), 0.98 (s, 12H),
d
1.58 (s, 6H); (ꢁ75.1 ꢀC):
d
¼0.87 (s, 6H), 0.93 (s, 6H), 0.97 (s, 6H), 1.13
3. (a) Anet, F. A. L.; Bourn, A. J. R. J. Am. Chem. Soc. 1967, 89, 760e768; (b) Anet, F.
A. L.; Anet, R. In Dynamic Nuclear Magnetic Resonance Spectroscopy; Jackman, L.
(s, 6H), 1.59 (s, 6H); 13C NMR (50.3 MHz, C6D5CD3, C6D5CD3 int)
€
M., Cotton, F. A., Eds.; Academic: New York, NY, 1975; pp 543e619; (c) Hofner,
(þ60.1 ꢀC):
¼15.68 (q), 23.46 (br, q), 26.92 (q), 41.80 (s), 42.36 (s),
d
D.; Lesko, S. A.; Binsch, G. Org. Magn. Reson. 1978, 11, 179e196.
4. (a) Anet, F. A. L.; Haq, M. Z. J. Am. Chem. Soc. 1965, 87, 3147e3150; (b) Jensen, F.
R.; Bushweller, C. H. J. Am. Chem. Soc. 1969, 91, 5774e5782.
131.02 (s); (ꢁ49.2 ꢀC):
¼16.02 (q), 20.47 (q), 24.60 (q), 26.64 (q),
d
26.69 (q), 41.28 (s), 42.04 (s), 130.81 (s); MS (EI): m/z¼222 (14, Mþ),
207 (11), 151 (100). Anal. Calcd for C16H30: C, 86.40; H, 13.60. Found:
C, 86.49; H, 13.45.
5. (a) Friebolin, H.; Faißt, W.; Schmid, H. G.; Kabuß, S. Tetrahedron Lett. 1966,
1317e1321; (b) Murray, R. W.; Kaplan, M. L. Tetrahedron 1967, 23, 1575e1581;
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147e162; (d) St. Jaques, M.; Bernard, M.; Vaziri, C. Can. J. Chem. 1970, 48,
2386e2392; (e) Dalling, D. K.; Grant, D. M.; Johnson, L. F. J. Am. Chem. Soc. 1971,
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3127e3140.
3.2. Variable temperature measurements
The 1H NMR spectra of 7 and the 13C NMR spectra of 2 used
for the bandshape analyses were recorded on a Varian FT 80
spectrometer equipped with a variable temperature probe. Pre-
cision 5 mm o.d. NMR tubes (No. 507 PP, Wilmad Glass Co.) were
filled with solutions of 12 mg of 7 and 40 mg of 2, respectively, in
8. Bernard, M.; St. Jaques, M. Tetrahedron 1973, 29, 2539e2544.
9. Fitjer, L.; Wehle, D.; Scheuermann, H.-J. Chem. Ber. 1986, 119, 1162e1173.
400 ml of CDCl3. A temperature sensor consisting of a 1.8 mm-
€
€
diameter high precision PT 100 resistor (1/5 DIN; accuracy
ꢂ0.05 ꢀC from 0 ꢀC to 200 ꢀC) at the end of a glass rod was in-
troduced such that the active zone (15 mm length) was posi-
tioned 10 mm above the height of the receiver coil but was still
immersed in the solution. Immediately before and after taking
a spectrum, the sensor was moved precisely to the height of the
receiver coil, connected to a dual channel digital temperature-
measuring instrument (Model S 1220, Systemteknik, Sweden;
resolution 0.01 ꢀC) and the temperature measured against mol-
ten ice. Spectra for which the temperatures from these two
measurements differed by more than 1.0 ꢀC were discarded and
rerun. The calculations of the static and dynamic spectra and the
weighted least-squares adjustments of the rate data to the Eyring
equation were performed on the Sperry Univac 1100 computer
of the Gesellschaft für Wissenschaftliche Datenverarbeitung
10. Scheuermann, H.-J. Dissertation, Universitat Gottingen, 1982.
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12. In each of three possible twist-boat conformations of 7 (all of symmetry C1), the
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€
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(GWDG) at Gottingen, employing the computer programs
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DNMR519 and ACTPAR,20 respectively.