The effect of ring size on reactivity: The diagnostic value of 'rate profiles'

Article abstract of DOI:10.1002/hlca.200590110

The rates of cycloalkyl phenyl sulfide formation of a series of homologous bromocycloalkanes upon treatment with sodium benzenethiolate have been determined to ascertain the effect of ring size on reactivity. The 'rate profile', i.e., reaction rate vs. ring size, for these nucleophilic substitutions (S_N2) was determined. A linear free-energy relationship could be derived from computed hydride affinities of cycloalkanes and rates of typical S_N1 reactions, whereas rates of S_N2 reactions exhibited a strong discrepancy from the seven- up to the twelve-membered rings. This discrepancy was rationalized by a careful examination of the geometry of the intermediates and transition states involved in these reactions.

Full text of DOI:10.1002/hlca.200590110

Helvetica Chimica Acta ± Vol. 88 (2005)
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The Effect of Ring Size on Reactivity:
The Diagnostic Value of ꢀRate Profilesꢁ
by Eric Massona) and FreÂdeÂric Leroux*b)
a
Â
 Â
) Institut des Sciences et Ingenierie Chimiques, Ecole Polytechnique Federale, BCH, CH-1015 Lausanne
b
 Â
Â
Â
) Laboratoire de Stereochimie associe au CNRS (UMR CNRS 7509), Universite Louis Pasteur (ECPM),
25 rue Becquerel, F-67087 Strasbourg Cedex 2 (e-mail: lerouxf@ecpm.u-strasbg.fr)
Dedicated to Professor Rolf Huisgen on the occasion of his 85th birthday
The rates of cycloalkyl phenyl sulfide formation of a series of homologous bromocycloalkanes upon
treatment with sodium benzenethiolate have been determined to ascertain the effect of ring size on reactivity.
The ꢀrate profileꢁ, i.e., reaction rate vs. ring size, for these nucleophilic substitutions (SN2) was determined. A
linear free-energy relationship could be derived from computed hydride affinities of cycloalkanes and rates of
typical SN1 reactions, whereas rates of SN2 reactions exhibited a strong discrepancy from the seven- up to the
twelve-membered rings. This discrepancy was rationalized by a careful examination of the geometry of the
intermediates and transition states involved in these reactions.
1. Introduction. ± In the early fifties, Brown et al. [1 ± 3] recognized characteristic
effects of ring size on the reactivity of a series of model substrates. They suggested to
use plots of rates vs. ring size, so called ꢀrate profilesꢁ, as tools to diagnose mechanistic
details, in particular the geometry of key intermediates or transition states. According
to this concept, first- and second-order substitution reactions (SN1 and SN2, resp.)
should exhibit like ring dependences. As both processes involve a planarized C-atom as
a high-energy species, the principal reactivity-controlling factor should be the extra
strain (ꢀinternal strainꢁ or ꢀI-strainꢁ) caused by the change of a tetragonal to a trigonal
C-center.
This simplified view raised objections by Sicher [4]. When comparing the rate
profiles of two archetypical SN1 reactions (Fig. 1a, b) [3][5] with intramolecular
(Fig. 1,c) [6] and intermolecular (Fig. 1,d) [5] SN2 displacements, he spotted significant
discrepancies in the C8 ± C15 range.
This comparison was flawed by two experimental shortcomings, however. On one
hand, the kinetic work monitored only the consumption of the substrate, but did not
rigorously quantify the products formed. Thus, important side reactions may have
remained undetected. On the other hand, the juxtaposition was not continued into the
area of the smallest rings, cyclobutyl and cyclopropyl derivatives. Such an extension
should be especially meaningful if one considers the coincidence of five-, six-, and
seven-membered-ring reactivities (Fig. 1). We, thus, set out to bridge these gaps and to
propose a detailed and comprehensive justification of the measured rate constants.
2. Results. ± The benzenethiolate (PhSÀ) anion ranks among the most-powerful
nucleophiles in protic solvents [7]. Moreover, the reactivity of PhSÀ towards bromo- or
ꢂ 2005 Verlag Helvetica Chimica Acta AG, Zürich

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Fig. 1. Effect of ring size on rates of a) solvolysis of 1-chloro-1-methylcycloalkanes in 80% EtOH at 258,
b) solvolysis of bromocycloalkanes in 40.9% aqueous 1,4-dioxane at 458, c) base-catalyzed cyclization of cis-N-
(2-mercaptocycloalkyl)benzamides in 80% EtOH at 308, d) reaction of bromocycloalkanes with KI in acetone at
608. All rate profiles are normalized to the six-membered ring (log krel ˆ 0.0).
iodoalkanes is increased by factors ranging from 102 to 104 when replacing MeOH by
polar aprotic solvents like DMF [8]. To perform substitution reactions on cyclopropyl
and cyclobutyl substrates in a homogeneous medium, PhSNa was allowed to react in
DMFat 08 with the bromocycloalkanes 1b ± h and 3-bromopentane (1i), the open-chain
reference, to the corresponding cycloalkyl phenyl sulfides 2b ± i (Table 1). As the sole
exception, bromocyclopropane (1a) required higher temperatures. Absolute rate
constants of 5.0 Â 10À5, 1.3 Â 10À4, and 7.7 Â 10À4 l molÀ1 sÀ1 were determined at 958,
1108, and 1428, respectively. Subsequent rate extrapolation to 08 according to the
Arrhenius equation gave a rate constant of 1.1 Â 10À8 l molÀ1 sÀ1. The evolution of the
reactions was followed by gas chromatography (GC), which allowed us to determine
both the substrate and product concentrations. In this way, bromocyclohexane and
-dodecane were found to give rise not only to the corresponding substitution products
2d and 2h, but also to cyclohexene due to elimination, and to cyclododecane and

Helvetica Chimica Acta ± Vol. 88 (2005)
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phenyldisulfide formed probably by a single-electron-transfer side reaction. The
correspondingly corrected SN2 rates are numerically compiled in Table 1, and graphi-
cally presented in Fig. 2.
Fig. 2. Rate profile for the substitution of bromocycloal-
kanes with PhSNa in DMF at 08
Table 1. Pseudo-First-Order Rate Constants [l molÀ1 ´ sÀ1] for the Substitution of Bromocycloalkanes with PhSNa
in DMF at 08
na)
Substrate
Product
ks2ubst:
log ks2ubst:
3
4
5
6
7
1a
1b
1c
1d
1e
1f
1g
1h
1i
2a
2b
2c
2d
2e
2f
2g
2h
2i
1.1 (Æ 0.1) ´ 10À8 b
)
À 8.0( Æ 0.1)
2.97 (Æ 0.11) ´ 10À4
4.99 (Æ 0.09) ´ 10À2
1.76 (Æ 0.17) ´ 10À4 c
1.30( Æ 0.04) ´ 10À2
1.17 (Æ 0.04) ´ 10À3
2.90( Æ 0.07) ´ 10À4
À 3.53 (Æ 0.02)
À 1.30( Æ 0.01)
À 3.75 (Æ 0.02)
À 1.89 (Æ 0.01)
À 2.93 (Æ 0.01)
À 3.54 (Æ 0.01)
À 4.55 (Æ 0.01)
À 1.33 (Æ 0.02)
)
8
10
12
1 )
2.82 (Æ 0.08) ´ 10À5 d
4.70( Æ 0.16) ´ 10À2
)
e
a) Ring size. b) Obtained by extrapolation to 08. c) Cyclohexyl phenyl sulfide and cyclohexene were detected in
a 53 : 47 ratio; ks2ubst: was, thus, corrected by a factor of 0.53. d) Cyclododecyl phenyl sulfide and cyclododecane
were detected in a 70: 30ratio. Phenyldisulfide was also present in 16% yield; ks2ubst: was corrected by a factor of
0.70. e) 3-Bromopentane as open-chain reference compound.

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3. Discussion. ± 3.1. General Considerations. Before we can undertake an in-depth
analysis of rate profiles, we have to return to the starting point. According to Brown et
al. [1 ± 3], the change in ring strain, when going from a tetragonal substrate to a trigonal
intermediate or transition state, should be the dominant factor dictating the
substitution rate of a cyclic compound in comparison with an acyclic analog. If this is
true, SN1 and SN2 rate profiles should merely reflect the hydride affinities of
‡
cycloalkylcarbenium ions (i.e., the C ´´´ HÀ heterolytic dissociation energies of
cycloalkanes). Such thermodynamic quantities, though readily available for bicyclic
structures [9][10], have never been established systematically for cycloalkanes
[11][12]. This obligated us to calculate these hydride affinities using ab initio methods
(see Exper. Part). The fundamental assumption that these data correlate linearly with
the free activation energies (or simply log krel) of SN1 solvolysis rates seemed plausible,
but had never been validated. Our results confirm, except for the six-membered ring,
the expectations. Contrarily, when one tries to correlate the SN2 rate constants with the
hydride affinities, from the five-membered ring on, no correlation can be observed
(Fig. 3).
Fig. 3. Relationship between SN1 and SN2 relative rate constants (krel) and hydride affinities (DDGr) of the
corresponding alkanes relative to the open-chain compound (see text and Table 3).
In Fig. 4, a series of rate profiles are reproduced in which the ones previously shown
(Figs. 1,a ± d and 2, now Figs. 4a ± e, resp.) appear again. This time, however, they are all
strictly normalized by choosing the open-chain analog as the reference (krel ˆ 1.0). The
newly supplemented ꢀrate profilesꢁ feature the SN1/SN2 borderline solvolysis of
cycloalkyl 4-methylbenzenesulfonates (Fig. 4,f) [2], the base-promoted dehydrobro-
mination of bromocycloalkanes restricted to the formation of (Z)-cycloalkenes

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Fig. 4. Effect of ring size on rates of a) solvolysis of 1-chloro-1-methylcycloalkanes in 80% EtOH at 258,
b) solvolysis of bromocycloalkanes in 40.9% aqueous 1,4-dioxane at 458, c) base-catalyzed cyclization of cis-N-
(2-mercaptocycloalkyl)benzamides in 80% EtOH at 308, d) substitution of bromocycloalkanes with KI in acetone
at 608, e) substitution of bromocycloalkanes with PhSNa in DMF at 08 (this work), f) acetolysis of cycloalkyl 4-
t
methylbenzenesulfonates at 708, g) formation of (Z)-cycloalkenes with BuOLi in DMF at 408, h) reduction of
cycloalkanones with NaBH4 in i-PrOH at 08, and i) quaternarization of N-methylazacycloalkanes with MeI in
MeOH. All rate profiles are normalized to the open-chain analog (log krel ˆ 0.0).

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(Fig. 4,g) [13], the reduction of cycloalkanones with NaBH4 (Fig. 4,h) [14], and the
quaternarization of N-methylazacycloalkanes with MeI in MeOH (Fig. 4,i) [15].
The comparison of these transformations shows that each reaction type has its
typical rate profile, which can be taken as a ꢀfingerprintꢁ to determine the reaction
mechanism. As noticed before, when one compares the rate profile of an SN1 reaction
(Fig. 4,b) with that of an SN2 reaction (Fig. 4,e), the two profiles differ clearly,
indicating that different effects have to be considered. For SN1 as well as SN2 reactions,
the reaction center planarizes at the transition state, which widens the bond angles to
roughly 1208. Sicher called this the ꢀcoplanarity effectꢁ [4]. In addition, a second steric
effect must be considered for SN2 reactions, i.e., that the entering and leaving groups
tend to be collinear (the so-called ꢀcollinearity effectꢁ), as depicted in Fig. 5 [4]. An SN2
reaction can, thus, be treated as an SN1 reaction plus the collinearity effect.
Fig. 5. Coplanarity and collinearity ± at the root of SN1 and SN2 mechanisms
3.2. Small Rings. Avery good correlation of the calculated hydride affinities and the
SN2 rates can be observed for the open-chain reference compound down to the four-
and three-membered rings (see Fig. 3). As the hydride affinity concern only the
stability of the alkane and its corresponding carbocation, the collinearity effect is
assumed to have no influence on the reactivity of small rings. Although X-ray and gas-
phase electron diffractions are useful tools to determine the geometry of cycloalkanes
from cyclopropane to higher ring sizes [16][17], data concerning their respective
carbocations remain unavailable. Therefore, the bond angles of cycloalkanes and of
their corresponding carbocations were determined using ab initio methods (Table 2).
The important Baeyer strains of three- and four-membered rings imply a drastic
increase in energy for the formation of the carbocationic intermediate compared to the
open-chain reference, which rationalizes their low reactivity. These mechanisms can be
related to the amine inversion of Me3N as a reference, compared to those of
methylaziridine and methylazetidine. The inversion of methylaziridine (17 kcal/mol)
[18] and methylazetidine (10kcal/mol) [18] is far slower than that of Me 3N (4.3 kcal/
mol) [19], due to the higher activation energy for the planar transition state.
3.3. MediumRings . For clarity, both SN1 and SN2 rate profiles, as well as the
differences between them, are depicted in Fig. 6. The coplanarity effect (common to
both mechanisms) can, thus, be separated from the collinearity effect (specific to SN2
reactions). Fig. 6 shows that the alignment of the nucleophile, the reaction center, and
the leaving group, from the five- to the ten-membered rings, becomes more and more

Helvetica Chimica Acta ± Vol. 88 (2005)
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‡
Table 2. Bond Angles [8] of Cycloalkanes and Their Corresponding Carbocationic Intermediates (HÀC ÀC
angle)
na)
Alkane
Carbocation
Db)
3
4
5
6
117.9
147.5
132.3
123.7
118.4
116.5
22
110.8/118.1c)
109.3 ± 112.9d)
109.0/110.2c)
109.0
6.7 ± 14
3.3 ± 6.9
0.7 ± 1.9
0.0
e
1 )
a) Ring size. b) Deformation [8] relative to the open-chain compound. c) The left value corresponds to an axial
H-atom, the right one to an equatorial one. d) Depends on which H- and C-atoms are considered. e) Pentane as
open-chain reference; the most-stable conformation of the pent-3-ylium cation mentioned here corresponds to a
double W-shape.
Fig. 6. Solvolysis of bromocycloalkanes in 40.9%
&
aqueous 1,4-dioxane following an SN1 pathway ( ),
and substitution of bromocycloalkanes by PhSNa in
*
DMF (this work) following an SN2 pathway ( ).
The collinearity effect is represented by filled
*
circles ( ).
difficult. Furthermore, from the seven-membered to the ten-membered ring derivatives
on, the rate-enhancing influence of the coplanarity effect no longer dominates the
situation, whereas the opposite collinearity effect operates strongly.
For a SN1 reaction, the rate profile can be explained by Brownꢁs I-strain effect.
Ejection of bromide from medium-sized bromocycloalkanes leads to a decrease in
overlapping of substituents or transannular interactions. Compared to the open-chain
reference, this results in a higher reaction rate for solvolysis, and fits with the decrease

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in hydride affinities (see Fig. 3). For macrocycles (n > 12), their structures tend to look
like those of linear secondary bromoalkanes, having almost no ring strain, and the
reaction rates are slow (see Fig. 4,f).
An important anomaly appears for the six-membered ring. The calculated hydride
affinities predict that bromocyclohexane should react faster than the open-chain
reference 3-bromopentane (see Fig. 3). Contrary, the experimentally obtained rate
profiles reveal a clear rate minimum for the six-membered ring derivative for SN1
solvolysis, as well as SN2 substitution reactions (see Figs. 4,a ± f). Sicher [4] rationalized
this rate minimum with the energetically unfavorable formation of the carbocationic
intermediate. Since cyclohexyl halides or cyclohexane are almost perfectly staggered
and strain-free, ejection of halide or hydride would destabilize the carbocationic
intermediate due to the ecliptic positions of the H-atoms around the reaction center
(Fig. 7). This explanation and the experimental results for the six-membered ring are in
contradiction with the calculated hydride affinities.
Fig. 7. The cyclohexyl carbocation. a) SN1 Intermediate, b) SN2 transition state.
cis-4-tert-Butyl-1-bromocyclohexane (Br-atom in an axial position) reacts with
PhSNa 58-times faster than its thermodynamically more-stable trans isomer (Br-atom
in equatorial position) [20]. However, as bromocyclohexane reacts only four times
slower than cis-1-bromo-4-(tert-butyl)cyclohexane, the axial/equatorial equilibration in
the former cannot justify the poor reactivity towards nucleophilic substitution
compared to the open-chain analog. Until now, we have no rationale for the
discrepancy between the calculated hydride affinities (if one does not consider a
wrong computational prediction) and the rate constants of SN1 and SN2 reactions for
cyclohexyl derivatives.
Due to the high number of possible reactive conformations of bromocyclooctane, it
would be meaningless to compare experimental SN1 rates with computed hydride
affinities.
If one considers now SN2 reactivities and the difference between SN1 and SN2 rate
profiles, as illustrated in Fig. 6, the collinearity effect varies along the sequence
C5 < C6  C7 < C12 < C8 < C10. The cyclopentyl carbocation has a reaction center that is
not at all masked by the ring substituents. The incoming nucleophile, the reaction
center, and the leaving BrÀ can be easily aligned. On the other hand, the
bromocyclohexaneÀPhSÀ transition state does not allow such correct alignment, due
to the axial H-atoms in positions 2, 3, 5, and 6 (see Fig. 7).

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At first glance, increased ring size in the medium-sized rings would lead to a
decreased steric hindrance at the reaction center. A more-careful analysis shows that
the problem is more complex, and leads to the opposite conclusion. The attack of the
nucleophile at bromocyclooctane is hindered by the H-atoms in positions 2, 3, 7, and 8
of the chair/chair and chair/boat structures, similarly to the six-membered ring. In
addition, hindrance due to the H-atoms in positions 4 and 6 of the boat/chair
conformer, and in position 5 of the boat/boat structure strongly affects the collinearity
effect (Fig. 8). Such transannular interactions culminate at the ten-membered ring, and
then start to vanish from the twelve-membered ring to the open-chain compound (see
Fig. 6).
Fig. 8. Conformers of the cyclooctyl carbocation
Of course, changes in reactivity are a sum of various effects. But, in a simplified way,
the SN1 and SN2 rate profiles can be rationalized by three effects: the angular distortion,
which is peculiar to small rings, the decrease in overlapping and transannular effects
between the ground state and the transition state of medium-sized rings, and the
collinearity effect, important only for medium-sized rings.
4. Conclusions. ± The present study was didactically motivated. The influence of a
given ring size on chemical reactivity was observed more than 40years ago, when data
on reactivity of ring compounds began to accumulate. We intended to draw attention to
the so-called ꢀrate profileꢁ approach as one of the rare tools to probe the geometry of
transition states. Therefore, various rate profiles were presented as ꢀfingerprintsꢁ for
different reaction mechanisms. Our experimental data are meant to bridge the present
gaps dealing with the rate profiles for the important class of SN2 displacements and
substitutions to small rings. High-level ab initio calculations provided hydride affinities
for three- to eight-membered cycloalkanes. These correlate well, except for the
cyclohexyl carbocation, with the experimentally determined SN1 solvolysis rates. While
the three- to seven-membered rings exhibit common behavior in both SN1 and SN2
profiles, measuring rate constants of eight- to twelve-membered cycloalkyl derivatives,
and comparing them with an open-chain-analog rate, is a crucial and flexible test to

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locate a given reaction in the SN1ÀSN2 continuum, halogen substitution by PhSÀ being
considered an extreme SN2-type process.
The authors are indebted to the Swiss National Science Foundation (Grant 20-63'584-00) for financial
support and are much grateful to Prof. M. Schlosser, Lausanne, for generous support and precious advices.
Experimental Part
General. For laboratory routine and abbreviations, see recent publications from this laboratory [21 ± 23].
Compounds 1a ± f and 1i are commercially available. Cycloalkyl phenyl sulfides 2a ± f and 2i have been reported
in the literature, but were insufficiently characterized. Compounds 2g and 2h have never been described.
Therefore, complete and optimized working procedures, as well as ample evidence for identity and purity, are
presented below for compounds 2a ± i.
Bromocyclodecane (1g). A slow stream of HBr was passed for 2 h through a soln. of (Z)-cyclodecene (14 g,
0.10 mol) in CH2Cl2 (0.20 l) at 258. A 1.0m aq. soln. (0.20 l) of NaOH was added, and the product was extracted
with pentane (5 Â 0.20 l). The org. layers were dried (Na2SO4) and evaporated, and the residue was distilled to
afford a colorless oil (12 g, 55%). B.p. 84 ± 858/4 Torr (lit. b.p. 1288/14 Torr [24]). n2D0 ˆ 1.5132 (lit. nD20 ˆ 1.5134
1
[5]. d2D0 ˆ 1.212. H-NMR: 4.26 (sym. m, 1 H); 2.0( m, 4 H); 1.4 (br. m, 15 H).
Bromocyclododecane (1h). During 1 h, PBr3 (54 g, 0.20 mol) was added dropwise to molten cyclo-
dodecanol (74 g, 0.40 mol) at 1008, maintaining the temperature below 1308. The reaction mixture was poured
onto crushed ice (0.20 kg) and extracted with Et2O (4 Â 0.30 l). The combined org. layers were washed with a
sat. aq. soln. of NaHCO3 (0.20 l), and dried (Na2SO4). After evaporation of the solvents, distillation afforded a
colorless oil (34 g, 34%). B.p. 108 ± 1098/3 Torr (lit. b.p. 111 ± 1128/3 Torr [25]). n2D0 ˆ 1.5094 (lit. nD20 ˆ 1.5097
1
[25]). d2D0 ˆ 1.164. H-NMR: 4.26 (sym. m, 1 H); 2.1 (m, 2 H); 1.9 (m, 2 H); 1.4 (br. m, 15 H).
Cyclopropyl Phenyl Sulfide (2a). PhSNa (20g, 0.15 mol) and 1a (6.0g, 50mmol) were heated for 20h at
1008 in DMF (50ml). Then, H 2O (0.20 l) was added, and the mixture was extracted with pentane (4 Â 0.20 l).
The combined org. layers were washed with H2O (0.20 l), dried (Na2SO4), and evaporated. Distillation afforded
a colorless oil (4.8 g, 64%). B.p. 70± 72 8/3 Torr (lit. b.p. 62 ± 638/1 Torr [26]. n2D0 ˆ 1.5817 (lit. nD20 ˆ 1.5801 [26]).
d2D0 1.052. 1H-NMR: 7.37 (d, J ˆ 7.3, 2 H); 7.28 (tm, J ˆ 7.6, 2 H); 7.13 (t, J ˆ 7.5, 1 H); 2.19 (sym. m, 1 H); 1.1
(m, 2 H); 0.7 (m, 2 H). Anal. calc. for C9H10S (150.24): C 71.95, H 6.71; found: C 72.19, H 6.87.
Cyclobutyl Phenyl Sulfide (2b). Analogously from bromocyclobutane (1b; 6.8 g, 50mmol) for 2 h at 25 8:
5.2 g (63%). Colorless oil. B.p. 82 ± 848/3 Torr (lit. b.p. 67.5 ± 688/1 Torr [27]. n2D0 ˆ 1.5787. d420 ˆ 1.039. 1H-NMR:
7.3 ( m, 4 H); 7.2 (m, 1 H); 3.89 (qt, J ˆ 7.8, 1 H); 2.5 (m, 2 H); 2.0( m, 4 H). Anal. calc. for C10H12S (164.27): C
73.11, H 7.36; found: C 72.93, H 7.25.
Cyclopentyl Phenyl Sulfide (2c). Analogously from bromocyclopentane (1c; 7.5 g, 50mmol) for 2 h at 25 8:
4.5 g (51%). Colorless oil. B.p. 89 ± 918/2 Torr (lit. b.p. 97 ± 998/2 Torr [26]). n2D0 ˆ 1.5740(lit. nD20 ˆ 1.5734 [28]).
d240 ˆ 1.040. 1H-NMR: 7.36 (dm, J ˆ 7.3, 2 H); 7.28 (tm, J ˆ 7.5, 2 H); 7.18 (tm, J ˆ 7.5, 1 H); 3.60( m, 1 H); 2.1
(m, 2 H); 1.8 (m, 2 H); 1.6 (m, 4 H). Anal. calc. for C11H14S (178.30): C 74.10, H 7.91; found: C 73.96, H 7.85.
Cyclohexyl Phenyl Sulfide (2d). Analogously from bromocyclohexane (1d; 8.2 g, 50mmol) for 2 h at 100 8:
5.5 g (57%). Colorless oil. B.p. 97 ± 998/2 Torr (lit. b.p. 160± 165 8/17 Torr [29]). M.p. À 7 to À 48. n2D0 ˆ 1.5718
(lit. n2D0 ˆ 1.5683 [28]). d240 ˆ 1.037. 1H-NMR: 7.40( dm, J ˆ 7.3, 2 H); 7.28 (tm, J ˆ 7.3, 2 H); 7.21 (tm, J ˆ 7.3, 1 H);
3.1 (m, 1 H); 2.0( m, 2 H); 1.8 (m, 2 H); 1.6 (m, 1 H); 1.3 (m, 5 H). Anal. calc. for C12H16S (192.32): C 74.94, H
8.38; found: C 74.73, H 7.97.
Cycloheptyl Phenyl Sulfide (2e). Analogously from bromocycloheptane (1e; 8.9 g, 50mmol) for 2 h at 25 8:
5.8 g (56%). Colorless oil. B.p. 125 ± 1288/4 Torr (lit. b.p. 179 ± 1818/17 Torr [29]). n2D0 ˆ 1.5705. d420 ˆ 1.037.
1H-NMR: 7.37 (dm, J ˆ 7.5, 2 H); 7.28 (tm, J ˆ 7.3, 2 H); 7.19 (tm, J ˆ 7.3, 1 H); 3.3 (m, 1 H); 2.0( m, 2 H); 1.7
(m, 2 H); 1.6 (m, 6 H); 1.5 (m, 2 H). Anal. calc. for C13H18S (206.35): C 75.67, H 8.79; found: C 75.50, H 8.71.
Cyclooctyl Phenyl Sulfide (2f). Analogously from bromocyclooctane (1f; 9.6 g, 50mmol) for 2 h at 100 8:
6.9 g (63%). Colorless oil. B.p. 132 ± 1358/4 Torr (lit. b.p. 1858/13 Torr [30]). n2D0 ˆ 1.5736 (lit. n2D0 ˆ 1.5846). d240
ˆ
1.038. 1H-NMR: 7.38 (dm, J ˆ 7.3, 2 H); 7.28 (tm, J ˆ 7.3, 2 H); 7.20( tm, J ˆ 7.3, 1 H); 3.4 (m, 1 H); 2.0( m, 2 H);
1.6 (br. m, 12 H). Anal. calc. for C14H20S (220.38): C 76.30, H 9.15; found: C 76.22, H 8.84.
Cyclodecyl Phenyl Sulfide (2g). Analogously from bromocyclodecane (1g; 5.5 g, 25 mmol) for 2 h at 1008:
1
5.0g (81%). Colorless oil. B.p. 148 ± 151 8/4 Torr. n2D0 ˆ 1.5652. d420 ˆ 1.020. H-NMR: 7.39 (d, J ˆ 8.1, 2 H); 7.28
(tm, J ˆ 7.5, 2 H); 7.20( tm, J ˆ 7.5, 1 H); 3.47 (qt, J ˆ 6.2, 1 H); 1.6 (br. m, 18 H). 13C-NMR: 136.1; 131.4 (2 C);

Helvetica Chimica Acta ± Vol. 88 (2005)
1385
128.8 (2 C); 126.4 (2 C); 46.3; 30.8; 25.3; 25.1; 24.6 (2 C); 23.6 (2 C). Anal. calc. for C16H24S (248.43): C 77.35, H
9.74; found: C 77.27, H 9.69.
Cyclododecyl Phenyl Sulfide (2h). Under an inert gas atmosphere and in the dark, PhSNa (9.9 g, 75 mmol)
was dissolved in DMF (50ml) at 100 8. 18-Crown-6 (20g, 75 mmol) and 1h (6.2 g, 25 mmol) were added. After
1 h, the mixture was allowed to cool down, and H2O (0.20 l) was added. The product was extracted with pentane
(4 Â 0.20 l), the combined org. layers were washed with H2O (0.20 l), dried (Na2SO4), and evaporated. To
destroy traces of phenyldisulfide, the residue was dissolved in EtOH (50ml) and treated with NaBH 4 (0.95 g,
25 mmol). After 1 h, the mixture was poured into H2O (0.20 l), and extracted with pentane (4 Â 0.20 l). The
combined org. layers were dried (Na2SO4) and evaporated. The product was obtained upon crystallization from
hexane/AcOEt 1 :1. Colorless needles. M.p. 38 ± 398. 1H-NMR: 7.35 (d, J ˆ 7.0, 2 H); 7.29 (tm, J ˆ 7.5, 2 H); 7.22
(t, J ˆ 7.5, 1 H); 3.3 (m, 1 H); 1.6 (br. m, 22 H). 13C-NMR: 136.0; 131.2; 128.7 (2 C); 126.3 (2 C); 44.7; 29.9; 24.1
(2 C); 23.7 (2 C); 23.4 (2 C); 23.3 (2 C); 22.1 (2 C). Anal. calc. for C18H28S (276.19): C 78.20, H 10.21; found: C
78.28, H 10.08.
1-Ethylpropyl Phenyl Sulfide (2i). Analogously, as described for 2c, from 3-bromopentane (1i; 7.6 g,
50mmol). Colorless oil. B.p. 80± 81 8/3 Torr (lit. b.p. 125 ± 1288/15 Torr [31]). n2D0 ˆ 1.5386 (lit. nD20 ˆ 1.5385 [32]).
1H-NMR: 7.39 (dm, J ˆ 7.0, 2 H); 7.27 (tm, J ˆ 7.3, 2 H); 7.20( tm, J ˆ 7.3, 1 H); 2.99 (qt, J ˆ 6.2, 1 H); 1.6
(m, 4 H); 1.0( t, J ˆ 7.3, 6 H). Anal. calc. for C11H16S (180.31): C 73.27, H 8.94; found: C 73.49, H 8.92.
General Kinetics Procedure. PhSNa (2.61 g, 19.7 mmol) was dissolved in DMF (100 ml). The soln. was
cooled to 08 in an ice/H2O (dist.) bath. Under vigorous stirring, a mixture of 1b ± i (1.00 ± 1.12 mmol) and
tridecane (approx. 0.10 g, serving as ꢀinternal standardꢁ, i.e., inert reference compound for quantification) were
added. Samples (1.0ml) were withdrawn in intervals, poured into a mixture of H 2O (15 ml) and pentane
(3.0ml). The org. layer was separated, dried (Na 2SO4), and repeatedly injected into two GC columns of
different polarity. The concentrations of substrate and product were determined by comparison of their peak
areas with that of the internal standard, unequal detector sensitivities for the various compounds being
corrected by calibration factors.
Evaluation of Rate Constants. The rate constants k of the reaction of bromocycloalkanes in the presence of a
large excess of PhSNa were calculated according to pseudo-first-order reaction kinetics from the relationship
k ˆ À1/(t ´ [Nu]) ´ ln([S]/[S]0), where [Nu] is the concentration of the nucleophile (PhSÀ), which can be
considered as constant, and where [S] and [S]0 are the concentrations of the substrates at times t and t0, resp. The
initial concentration [S]0 was known by weighing in. The amounts of unconsumed substrate [S] were directly
determined by GC using an internal standard for calibration. The absolute rate constants k were obtained by
plotting 1/[Nu] ´ ln([S]/[S]0) vs. t, and by determining the slope of the best straight line through the measured
points, as calculated by the method of least squares. As a control, it was also indirectly determined by subtraction
Table 3. Total Energies (MP2/6-311G), Zero-Point Vibrational Energies (ZPE), Total Entropy Values (S) for
Cycloalkanes and Cycloalkyl Carbocations (most-stable conformers), and Absolute (DGr) and Relative (DDGr)
Hydride Affinities
n
Alkane
6-311Gb)
Carbocation
6-311Gb)
DGrc)e)
DDGrc)f)
ZPEc)
Sd)
ZPEc)
Se)
3
4
5
À 117.32
À 156.45
À 195.6079.1
À 234.74
À 273.85
À 312.86
À 312.97
À 196.78
46.4
62.6
59.4
64.6
À 116.36
À 155.52
À 194.70
À 233.84
À 272.96
À 311.98
À 312.09
À 195.88
36.7
53.2
70.6
59.1
63.8
70.7
76.3
79.9
84.7
79.4
291.1
265.9
252.7
249.1
248.3
238.5
236.1
.0
36.4
11.2
67.8
À 2.0
À 5.6
À 6.4
À 16.2
À 18.6
6g)
7
95.5
111.9
129.2
127.5
90.3
74.6
81.0
86.1
80.9
81.5
88.1
104.5
121.7
120.8
83.079.5
8h)
8i)
j
1 )
254.7
0
c
a) Ring size. b) In hartrees. ) In kcal molÀ1
.
d) In cal molÀ1 KÀ1
.
e) The MP2/6-311G energy of the hydride anion
is À 0.47616 hartree, and its entropy is 25.6 cal molÀ1 KÀ1
.
f) Relative to pentane and 3-pentyl carbocation.
g) Chair conformation. h) Chair/chair conformation; values obtained with MP2/6-31G. ) Values obtained with
MP2/6-311G; the most-stable structure for the carbocation is a m-hydrido form according to this basis set.
j) Pentane; the pent-3-ylium cation has a double W-shape.
i

1386
Helvetica Chimica Acta ± Vol. 88 (2005)
of the amount of product, applying the relationship [S]/[S]0 ˆ 1 À ([P]/[S]0), where [P] is the concentration of
cycloalkyl phenyl sulfide at time t. Two sets of measurements were performed for each substrate.
Computational Methods. Geometries of cycloalkanes and their corresponding carbocations were fully
optimized at the MùllerÀPlesset level of theory [33 ± 36] using the 6-311G basis set (Table 3). Computations
were carried out with the program GAMESS [37]. The temperature was corrected to 273.15 K, and zero-point
energies were multiplied by the empirical factor of 0.89 [38].
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Received February 4, 2005