A kinetic investigation, supported by theoretical calculations, of steric and ring strain effects on the oxidation of sulfides and sulfoxides by dimethyldioxirane in acetone

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A kinetic investigation, supported by theoretical calculations, of steric

and ring strain eﬀects on the oxidation of sulﬁdes and sulfoxides by

dimethyldioxirane in acetonew

Peter Hanson,* Ramon A. A. J. Hendrickxz and John R. Lindsay Smith*

Received (in Montpellier, France) 3rd September 2009, Accepted 29th September 2009

First published as an Advance Article on the web 17th November 2009

DOI: 10.1039/b9nj00452a

The oxidations of alkyl 4-nitrophenyl, and dialkyl, sulﬁdes and sulfoxides by dimethyldioxirane in

acetone occur by concerted mechanisms but the sulﬁdes respond diﬀerently from the sulfoxides to

variation in the alkyl group. The reactions of the sulﬁdes are inhibited by the steric eﬀects of

alkyl groups and these predominate over their inductive eﬀects. By contrast, the reactions of these

limited sets of sulfoxides are insensitive to alkyl steric eﬀects but there is an indication of steric

acceleration when a broader set of sulfoxides is considered. This behaviour is rationalised in terms

of the diﬀerences in dipolar charge and its solvation between the ground state and transition state

for the two types of substrate. The oxidations of cyclic sulﬁdes and sulfoxides also exhibit

contrasting behaviour. The reactivity of the sulﬁdes is insensitive to ring strain but is explicable in

frontier orbital terms whereas that of the sulfoxides is partly dependent upon the change in ring

strain between reactant and product on oxidation, a diﬀerence rationalised in terms of the relative

positions of the transition states in the reaction coordinates of the two oxidations. The reactivity

of 4-, 5- and 6-membered cyclic sulfoxides is also dependent on a ring-size related property of the

transition state. Calculations at the B3-LYP/6-31G* level of density functional theory on both

ground states and transition states, including simulation of solvation by acetone, strongly support

the mechanistic conclusions reached in this and earlier work.

transition state 4, to give the sulfone, 5, also with one molecule

Introduction

of ketone (n = 1). This mechanism prevails when the oxidant

For over two decades dioxiranes have been known to be

is 1a in acetone or in mixtures of acetone with aprotic

eﬃcient electrophilic oxidants for a wide range of organic

substrates.^1,2Dimethyldioxirane, 1a, and the more reactive

co-solvents of greater or lesser polarity. However, in aqueous

acetone of suﬃcient water content (20% v/v) the mechanism

(triﬂuoromethyl)methyldioxirane, 1b, (Scheme 1) prepared

for sulﬁdes changes to a two-step process in which the inter-

in situ in acetone and triﬂuoroacetone, respectively, by oxidation

mediate sulfonium betaine, 6a, occurs; this then fragments to

of the solvent with peroxomonosulfate, have been the most

give 3 and a molecule of acetone; any subsequent oxidation of

frequently used. Their volatility permits the concentration of

sulfoxide to sulfone remains a concerted process.⁶When the

both dioxiranes by distillation from their respective ketone

oxidation mixtures.³Latterly, both reagents have also been

extracted into, and used in, chloromethane solvents.⁴

dioxirane is 1b, the corresponding betaine intermediate 6b

forms more readily than 6a as the anionic centre is stabilised

by the powerful electron-withdrawing eﬀect of the CF₃group.

As oxidants of sulﬁdes, the dioxiranes display variants of

If formed in chloromethane solvents in which the anionic

two distinct mechanisms. Conversion of a sulﬁde into the

centre is not stabilised by hydrogen bonding, 6b cyclises to

corresponding sulfoxide, 3 (Scheme 1), may occur in a single

another intermediate, the dioxathietane, 7b, that reacts with a

step, via transition state 2, in which the transfer of oxygen

second molecule of 1b to give sulfone 5 and two molecules of

from 1 to the sulﬁde is concerted with elimination of one

MeC(O)CF₃(n = 2) at a rate faster than the initial rate of

reaction of 1b with the sulﬁde.⁷Thus, depending on the

molecule of ketone MeC(O)R₁.^1a,b,5,6Given a stoichiometric

excess of the dioxirane, the resulting sulfoxide, 3, may, in turn,

particular dioxirane and on the composition of the solvent

undergo a comparable, but slower, concerted reaction, via

in which the reaction is performed, the oxidation of a sulﬁde

by one equivalent of a dioxirane can lead to sulfoxide alone, to

Department of Chemistry, University of York, Heslington, York,

UK YO10 5DD. E-mail: ph8@york.ac.uk, jrls1@york.ac.uk

w Electronic supplementary information (ESI) available: 1. Molar

partial oxidation to sulfone alone, or to a mixture of sulfoxide

and sulfone.

There has been relatively little previous investigation of

steric or ring-size eﬀects on the oxidations of sulfur compounds.

Modena and co-workers⁸reported the trends in rate constants,

caused by structural variation of alkyl groups, for the oxidations

of sulﬁdes by H₂O₂/H⁺in aqueous ethanol (6% v/v H₂O) and

absorbances. 2. Connectivity-derived substituent constants for hydro-

carbon moieties; statistical analysis of correlated data. 3. Synthetic

materials. 4. Published rate constants for comparison. See DOI:

10.1039/b9nj00452a

z Present address: Department DMPK & Bio-analysis, AstraZeneca,

AB 221 87, Lund, Sweden. E-mail: ramon.hendrickx@astrazeneca.com

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Scheme 1

of sulfoxides by perbenzoic acid in 50% v/v aqueous dioxane,

the oxidations of the achiral substrates and single constants

were obtained for both processes.

and Ruﬀ and Kucsman⁹have reported oxidations of aralkyl,

dialkyl and cyclic sulﬁdes by periodate ion in 50% aqueous

ethanol in which steric eﬀects are considered.

This paper concludes our investigations into the oxidation

of sulﬁdes and sulfoxides by dimethyldioxirane, 1a; in particular,

the kinetic consequences are described of alkyl moiety variation

in oxidations of alkyl 4-nitrophenyl sulﬁdes and sulfoxides and

dialkyl sulﬁdes and sulfoxides, and of ring-size variation in

cyclic sulﬁdes and sulfoxides, all of which, in acetone, proceed

by concerted mechanisms. In addition, we also describe the

results of MO calculations that give insight into the nature

of the transition states formed by aryl methyl sulﬁdes and

sulfoxides on oxidation by 1a, amplifying prior physical-

organic reasoning.

1.2 Sulﬁdes. The rate constants of the sulﬁdes, k₂(R)_S, vary

with the alkyl group increasing from Me to Et then decreasing,

in the order n-Bu > i-Pr > s-Bu > t-Bu, to values less than

that of Me. This variation suggests that, in the electrophilic

oxidation, the reaction-promoting, electron-donating (+I)

eﬀects of the groups larger than Et are outweighed by their

reaction-hindering steric eﬀects.

Results and discussion

In a ﬁrst attempt to evaluate quantitatively the separate

electronic and steric eﬀects of the alkyl groups we applied the

Taft–Pavelich eqn (1):¹⁰

1

Alkyl 4-nitrophenyl substrates

1.1 Rate constants and alkyl group variation. In Table 1 are

presented the rate constants, measured spectrophotometrically,

for the oxidations of alkyl 4-nitrophenyl sulﬁdes, 8, and

sulfoxides, 9, by dimethyldioxirane, 1a, in acetone. The

procedures for sulﬁde oxidation under second order conditions

and for sulfoxide oxidation under ﬁrst order conditions have

been described previously.^6bThe molar absorbances of

substrates and products required for the former conditions

are given in ESIw 1, Table S1. The sec-butyl sulﬁde, being

racemic, will give a mixture of diasteroisomeric sulfoxides on

oxidation and this mixture, on further oxidation, will give a

racemic sulfone. Neither oxidation behaved diﬀerently from

log [k₂(R)_S/k₂(Me)_S] = r*s*_(T)+ dE_s

(1)

where s*_(T)and E_sare Taft’s polar and steric substituent

constants and r* and d the respective reaction constants (see

ESIw 2, Table S2 for substituent constants); the correlation is

poor: R²= 0.870. The recasting of eqn (1) as eqn (2) which allows

s

variation in the intercept {from [log k₂(Me)_S/dm³mol^ꢁ1^ꢁ1]}

results in a marginal improvement (R²= 0.8895) but the

correlation remains indiﬀerent.

log [k₂(R)_S/dm³mol^ꢁ1^ꢁ1] = r*s*_(T)+ dE_s+ C (2)

s

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Table 1 Rate constants^afor the oxidation of alkyl 4-nitrophenyl sulﬁdes and sulfoxides by 1a in acetone

10^ꢁ2k₂(R)_S/dm³mol^ꢁ1s^ꢁ1

at 291.3 K

10²k_obs(R)_SO/s^ꢁ1

at 294.6 K

k₂(R)_SO/dm³mol^ꢁ1s^ꢁ1

at 294.6 K

R

10³[1a]/mol dm^ꢁ3

Me

Et

i-Pr

n-Bu

s-Bu

t-Bu

5.45 ꢂ 0.11

6.99 ꢂ 0.08

6.54 ꢂ 0.18

6.81 ꢂ 0.22

5.19 ꢂ 0.08

4.86 ꢂ 0.21

4.55 ꢂ 0.18

6.94 ꢂ 0.18

—

6.07 ꢂ 0.12

6.54 ꢂ 0.24

11.0 ꢂ 0.3

5.48 ꢂ 0.13

5.43 ꢂ 0.13

—

5.36 ꢂ 0.16

5.45 ꢂ 0.11

5.35 ꢂ 0.11

8.30 ꢂ 0.54

12.8 ꢂ 0.6

—

11.3 ꢂ 0.6

12.0 ꢂ 0.7

20.5 ꢂ 1.0

a

Uncertainties are 95% conﬁdence intervals.

Since the work of Taft and Pavelich, other scales of both

inductive and steric substituent constants have been proposed

(see ESIw 2, Table S2). A systematic survey of the possible

pairings of the various inductive and steric constants (see ESIw 2,

Table S3) has shown that the sulﬁde data in Table 1 are best

expressed by eqn (3):

the steric eﬀect to be 36% greater than the inductive eﬀect or, put

alternatively, the overall substituent eﬀect of the alkyl groups on

the oxidation of alkyl 4-nitrophenyl sulﬁdes by 1a comprises

a minor electronic component (42.5%) and a major steric

component (57.5%), so quantifying the steric predominance

inferred above.

In our previous work⁶it was inferred that the activation

process for the oxidation of sulﬁdes by 1a is characterised by a

signiﬁcant separation of charge, positive charge increasing on

S with negative charge accumulating on the distal oxygen

atom of 1a (see 10). In a polar aprotic solvent the stabilisation

of these charges depends on the intramolecular interactions of

the diﬀerent substituents and on intermolecular interactions

with solvent dipoles. The alkyl groups, R, being directly

attached to S, are able to stabilise its increased positive charge

by their +I eﬀects. This is indicated by the observation

k₂(Et)_S> k₂(Me)_S. The increase in charge separation on

activation would be expected to cause electrostriction of the

solvent; however, such increased interaction with the solvation

shell is hindered by bulky alkyl groups and hence the transition

states in their cases are deprived of the stabilisation the

interaction would aﬀord. This is shown by the sequence noted

log [k₂(R)_S/dm³mol^ꢁ1

s

^ꢁ1] = rs_I(L)+ dE_s+ C

(3)

where s_I(L)is Levitt and Widing’s inductive scale based on

gas-phase ionisation potentials.¹¹This results in the regression

coeﬃcients and intercept of eqn (4) (R²= 0.9787):

log [k₂(R)_S/dm³mol^ꢁ1

s

^ꢁ1] = ꢁ(10.17 ꢂ 3.94)s_I(L)

+ (0.226 ꢂ 0.065)E_s+ (2.27 ꢂ 0.14)

(4)

It should be noted that, whereas the s_I(L)scale is referred to H,

the E_sscale is referred to Me; the raw regression coeﬃcients

found here cannot therefore be taken as the respective reaction

constants. Even if both scales were referred to a common

standard substituent, the raw coeﬃcients still would not

adequately reﬂect the relative importance of the two substituent

eﬀects because the ranges of the various inductive scales are

considerably less than those of the steric scales (see ESIw 2,

Table S2). This problem can be mitigated by a standardisation

of the data that applies unit normal scaling to the variate and

both explanatory variables (each is assigned a mean value of

zero and a standard deviation of 1).¹²The manipulation also

eliminates the intercept so allowing comparison of coeﬃcients

of substituent constants referred to diﬀerent groups; the

correlation then takes the form of eqn (5),

previously, k₂(Et)_S> k₂(n-Bu)_S> k₂(i-Pr)_S> k₂(s-Bu)_S

>

k₂(t-Bu)_Swhere the increase in a-branching governs the

maximum extent of the hindrance and b-chain-extension within

the primary and secondary examples augments the eﬀect. A

maximum rate constant occurs (for Et) because, as a function

of the ramiﬁcation of alkyl group structure, the steric eﬀect

increases faster than the inductive eﬀect.

{log [k₂(R)_S/dm³mol^ꢁ1

s

^ꢁ1]}_Std= b_Is_I(L)Std+ b_sE_sStd(5)

^ꢁ1]}_Stdis the standardised

in which {log [k₂(R)_S/dm³mol^ꢁ1

s

variate, s_I(L)Stdand E_sStdare the standardised inductive and

steric substituent constants and b_Iand b_sare the corresponding

standardised regression coeﬃcients. Eqn (6) gives their values:

{log [k₂(R)_S/dm³mol^{ꢁ1 ꢁ1}]}_Std

s

1.3 Sulfoxides. Results sharply contrasting with those

above were obtained on attempts to correlate values of log

[k₂(R)_SO/dm³mol^ꢁ1

= ꢁ(1.509 ꢂ 0.444)s_I(L)Std+ (2.054 ꢂ 0.444)E_sStd(6)

s

^ꢁ1] using alkyl inductive and steric

It is seen that the steric eﬀect has the coeﬃcient of larger

absolute magnitude as expected from the trend in the rate

constants. (The signs of the regression coeﬃcients diﬀer

because the s_I(L)values for alkyl groups are negative and their

inductive eﬀects (+I) act to increase the reaction rate whilst

the steric regression coeﬃcient is positive because the alkyl E_s

values are also negative but the steric eﬀects reduce the

reaction rate). The ratio |b_s/b_I| = 2.054/1.509 = 1.36 showing

substituent constants. Paired with any of the scales of inductive

constant (see ESIw 2, Table 2), all steric constants were

statistically insigniﬁcant at the 0.1 level of probability. In

the oxidations by 1a of the alkyl 4-nitrophenyl sulfoxides

examined, the alkyl groups clearly have no eﬀects that are

quantiﬁable by any of their steric substituent constants.

The 4-nitrophenyl and S^d+–O^dꢁmoieties ensure that these

sulfoxides are highly polarised molecules. Our earlier work

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Table 2 Rate constants at various temperatures with derived activation parameters for the oxidation of sec-butyl 4-nitrophenyl sulﬁde and

sulfoxide by 1 in acetone^a

T/K

10^ꢁ2k₂(s-Bu)_S/dm³mol^ꢁ1s^ꢁ1

T/K

k₂(s-Bu)_SO/dm³mol^ꢁ1s^ꢁ1

291.3

294.8

301.1

306.5

5.19 ꢂ 0.08

5.40 ꢂ 0.11

6.56 ꢂ 0.10

8.02 ꢂ 0.20

9.77 ꢂ 0.42

11.3 ꢂ 0.5

—

294.6

301.4

306.5

—

12.0 ꢂ 0.7

20.7 ꢂ 0.8

26.5 ꢂ 0.7

34.2 ꢂ 0.8

43.1 ꢂ 0.9

40.8 ꢂ 10.1

(42.6 ꢂ 3.9)^b

ꢁ84.9 ꢂ 33.0

(ꢁ83.0 ꢂ 13.3)^b

66.2 ꢂ 10.3^c

(67.3 ꢂ 5.6)^bc

312.4

317.5

311.5

317.2

DH^z_S/kJ mol^ꢁ1

23.2 ꢂ 1.7

DH^z_SO/kJ mol^ꢁ1

(22.9 ꢂ 1.9)^b

ꢁ114.0ꢂ 5.5

(ꢁ113.7ꢂ 6.2)^b

57.2ꢂ 2.3^c

DS^z_S/J K^ꢁ1mol^ꢁ1

DG^z_S/kJ mol^ꢁ1

DS^z_SO/J K^ꢁ1mol^ꢁ1

DG^z_SO/kJ mol^ꢁ1

(56.8ꢂ 2.6)^bc

a

b

c

Uncertainties are the 95% conﬁdence intervals. Values for the methyl analogue (data from ref. 6b and Table 1) for comparison. At 298.2 K.

with aryl methyl sulfoxides in mixed solvents⁶showed that, in

acetone–hexane mixtures, the degree of stabilisation of the

ground state by solvation is an important factor in determining

their relative rates of oxidation by 1a and, in aqueous acetone

mixtures, a Kamlet–Taft analysis¹³showed the absolute rate

constants for oxidation of methyl 4-nitrophenyl sulfoxide by

1a to depend only on the polarity of the mixed solvent, as

measured by the parameter p*, and not on the speciﬁc solvating

properties of the aqueous component (a and b). These

observations suggest that interaction between methyl 4-nitro-

phenyl sulfoxide and acetone will result in electrostriction of

the solvent. However, comparable ordering of the solvent-shell

around alkyl 4-nitrophenyl sulfoxides in which the alkyl group

is bulky will be sterically impeded and, consequently, their

ground states are expected to be less stabilised by solvation

than the methyl case.

2 Activation parameters

Table 2 presents the second order rate constants found for the

oxidation of sec-butyl 4-nitrophenyl sulﬁde and sulfoxide at

various temperatures together with the activation parameters

derived via Eyring plots (Fig. 1); activation data for the

methyl analogue^6bare given for comparison. The individual

activation parameters are similar for both alkyl groups but

there are diﬀerences between sulﬁdes on the one hand and

sulfoxides on the other. The enthalpy of activation of the

sulfoxides is larger than that of the sulﬁdes by 10–20 kJ mol^ꢁ1

.

This is consistent with a signiﬁcant diﬀerence, between the two

types of substrate, in the energy of the nucleophilic sulfur lone

pair orbital that attacks 1a. The partial positive charge on

sulfoxidic S confers a greater electronegativity than that of

sulﬁdic S with a resultant relative stabilisation of the sulfoxidic

S lone pair. That this diﬀerence in a ground state property

of the reactants is important, suggests that the transition

states occur relatively early in the reaction coordinates of

both oxidations, consistent with the high reactivity of the

oxidant.

The SO bonds of sulfones are, in general, less polar than

those of sulfoxides and, as a consequence, in transition states

for the concerted oxidation of sulfoxides to sulfones by 1a

there is a dispersal of charge (see 11). It is envisaged that as the

dipolarity of the initial sulfoxide SO bond diminishes, some

negative charge is transferred mainly to the distal oxygen atom

of 1a. There is thus a redistribution of negative charge between

the oxygen centres compensated by positive charge on S. The

activation process for oxidation of a sulfoxide by 1a would

therefore be expected to reduce the prior electrostriction of

solvent caused by the ground state. Two opposed consequences

of the steric eﬀects of bulky alkyl groups can therefore be

envisaged: rate-enhancement, relative to the methyl case,

arising from reduced solvation of the ground state and

rate-retardation arising from hindrance to the solvation of

the transition state (as in the case of sulﬁde oxidation). If these

opposing eﬀects should be similar in magnitude, and hence

cancel, the lack of dependence of observed rate constants upon

steric parameters can be understood (see Sections 2 and 5

below for further discussion).

As bimolecular processes, the oxidations of both types of

substrate result in a loss of entropy on formation of the

corresponding transition state but the loss for the sulﬁdes is

Fig. 1 Comparison of Eyring plots for the oxidation of methyl and

sec-butyl 4-nitrophenyl sulﬁdes and sulfoxides by dimethyldioxirane in

acetone.

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about 30 J K^ꢁ1mol^ꢁ1larger than that for the sulfoxides. The

greater entropy loss for sulﬁdes can be explained by the

ordering inherent in the electrostriction of solvent caused by

the development of a transition state 10 of increased polarity

relative to the reactant 8. Conversely, a lesser entropy loss for

the sulfoxides can be accounted for by the relaxation of

solvent electrostriction between a highly dipolar reactant

ground state 9 and a transition state 11 in which the negative

charge is dispersed.

On similar competition of the two dialkyl sulfoxides the

measured molar ratio of sulfone products led to the relative

rate constant [eqn (8)].

k₂(n-Pr)_2,SO/k₂(t-Bu)_2,SO= (0.34 ꢂ 0.02)

(8)

The net substituent eﬀect here is very diﬀerent from that in the

oxidation of sulﬁdes but the explanation is less clear-cut as its

magnitude (o1) could be explained either by the inductive

eﬀect operating alone or by a combination of the I eﬀect and

steric hindrance with the former predominant. If the mean of

The relative dispositions of the Eyring plots in Fig. 1

illustrate these suggestions. Over the temperature range

examined, the sec-butyl 4-nitrophenyl sulﬁde is less reactive

than its methyl analogue reﬂecting the steric hindrance by the

bulkier alkyl group to the stabilising solvation of the polarised

transition state. By contrast, sec-butyl 4-nitrophenyl sulfoxide

is more reactive than its methyl analogue as a consequence of

the larger +I eﬀect of the sec-butyl group and the fact that the

ground state of the methyl sulfoxide is strongly solvated

relative to its derived transition state, whereas the solvation

diﬀerences between ground and transition state cancel for the

larger group as discussed above.

the Et and n-Bu values, i.e. (12.0 ꢂ 0.43) dm³mol^ꢁ1

s

^ꢁ1, is

taken as an approximation of the rate constant for oxidation

of n-propyl 4-nitrophenyl sulfoxide, k₂(n-Pr)_SO, the relative

rate constant k₂(n-Pr)_SO/k₂(t-Bu)_SOin the 4-nitrophenyl series

is estimated as (0.58 ꢂ 0.04). As the steric eﬀect here was found

to be insigniﬁcant, this ﬁgure represents the ratio of the two

inductive terms. Had the steric eﬀect become signiﬁcant, but

not predominant, in the dialkyl series, the outcome would be a

reduction of both numerator and denominator [in eqn (8)]

with the greater eﬀect in the latter. The expected consequence

would be that k₂(n-Pr)_SO/k₂(t-Bu)_SOo k₂(n-Pr)_2,SO/k₂(t-Bu)_2,SO

.

As this is not the case, the inference is that the steric eﬀect is

insigniﬁcant in the dialkyl series too.

3

Dialkyl substrates

Although the changes in oxidation rate constants of alkyl

4-nitrophenyl substrates that occur as a result of alkyl group

variation have been rationalised, they are relatively small and

it was felt that investigation of the larger changes expected for

dialkyl substrates could provide conﬁrmatory evidence. As

the latter substrates lack the 4-nitrophenyl chromophore

that enabled spectrophotometric monitoring, a protocol of

competitive kinetics was adopted like that used in earlier

Hammett studies of aryl methyl sulﬁdes and sulfoxides.^6a

The substrates selected were (n-Pr)₂S, (n-Pr)₂SO, (t-Bu)₂S

and (t-Bu)₂SO. These choices were convenient not only for

product separation and quantiﬁcation by GC but also on

account of the disparate steric and inductive eﬀects exhibited

by the two alkyl groups (see ESIw 2, Table S2). When the two

sulﬁdes competed in large excess, in acetone solution, for a

limiting amount of 1a, the molar ratio of sulfoxide products

enabled the relative rate constant to be evaluated [eqn (7)].

4

Cyclic substrates

4.1 Rate constants and ring size. With a view to discovering

any eﬀects of ring strain, we have investigated oxidations of

saturated cyclic sulﬁdes and sulfoxides by 1a. Competition

experiments were run from which rate constants were found

for various cyclic sulﬁdes relative to (CH₂)₅S and to (n-Pr)₂S,

and for the corresponding sulfoxides relative to (CH₂)₅SO and

to (n-Pr)₂SO (Table 3). The rate constants of (CH₂)₅S relative

to PhSMe and of (CH₂)₅SO relative to PhSOMe were also

measured [(7.2

ꢂ

0.1) and (2.9

ꢂ

0.1), respectively].

By employing the absolute rate constants of the aromatic

10³dm³mol^ꢁ1s^ꢁ1and

substrates [(2.35

ꢂ

0.24)

ꢃ

(28.6 ꢂ 5.1) dm³mol^ꢁ1

s

^ꢁ1, respectively],^6babsolute second

order rate constants were then evaluated for all the cyclic

substrates and for (n-Pr)₂S and (n-Pr)₂SO. Absolute second

order rate constants for (t-Bu)₂S and (t-Bu)₂SO were derived

from the latter by use of eqn (7) and eqn (8). The second order

constants are presented in Table 4.

k₂(n-Pr)_2,S/k₂(t-Bu)_2,S= (3.96 ꢂ 0.15)

(7)

Fig. 2 shows plots against ring size, x, of the relative rate

constants k(x)_S/k(n-Pr)_2,Sand k(x)_SO/k(n-Pr)_2,SOfor oxidations

by 1a (cf. Table 3) and the corresponding constants for the

oxidation of sulﬁdes by NaIO₄in 50% v/v aqueous ethanol.

The latter data are taken from Ruﬀ and Kucsman⁹apart from

that for the oxidation of thiirane which was measured for this

work (see Experimental). The oxidation of sulfoxides exhibits

a relatively simple sigmoid curve (plot 1) whereas the two

oxidations of sulﬁdes (plots 2 and 3) show a more complex

dependence on ring size with the rate constants passing

through maxima at x = 5. The periodate oxidation involves

an electrophilic attack on S by the oxidant with a concerted

O-atom transfer comparable to oxidation by 1a. The similarity

of the proﬁles found for the two independent sulﬁde oxidations

(for the ﬁve ring sizes in common) is persuasive evidence that

in neither case is the shape accidental but, rather, that both

As both the inductive and steric eﬀects are larger for t-Bu than

for n-Pr, the magnitude of the relative rate constant (>1) is

consistent only with a predominant contribution of steric

hindrance to the net eﬀect of each group. Explained as steric

hindrance of the solvation of the polar transition state, this

accords with the behaviour of the alkyl 4-nitrophenyl sulﬁdes

described above. In the absence of a measured rate constant,

k₂(n-Pr)_S, for the oxidation of n-propyl 4-nitrophenyl sulﬁde,

we interpolate a value of (646⁺⁶⁰⁹

_ꢁ338) dm³mol^ꢁ1s^ꢁ1via eqn (4).

Taking the higher value of k₂(n-Pr)_Sand the lower value of

k₂(t-Bu)_S(Table 1), the upper limit of the relative rate constant

in the 4-nitrophenyl series k₂(n-Pr)_S/k₂(t-Bu)_Sthen becomes

(646 + 609)/(486 ꢁ 21) = 2.7, i.e. o(3.96 ꢂ 0.15); the steric

hindrance in the dialkyl series is consequently greater than that

in the 4-nitrophenyl series as expected.

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Table 3 Relative rate constants for the oxidation of cyclic sulﬁdes and sulfoxides by dimethyldioxirane in acetone at 293 K

Ring size, x

[k(x)/k(6)]_S

[k(x)/k(n-Pr)₂]_S

Ring size, x

[k(x)/k(6)]_SO

[k(x)/k(n-Pr)₂]_SO

3

4

5

6

0.14 ꢂ 0.02

0.81 ꢂ 0.02

1.71 ꢂ 0.04

1.00 ꢂ 0.00

0.99 ꢂ 0.02

2.32 ꢂ 0.10

1.57 ꢂ 0.04

0.09 ꢂ 0.01

0.52 ꢂ 0.02

1.08 ꢂ 0.04

0.64 ꢂ 0.02

0.63 ꢂ 0.02

1.48 ꢂ 0.07

1.00 ꢂ 0.00

3

4

5

6

0.17 ꢂ 0.01

0.23 ꢂ 0.01

0.36 ꢂ 0.01

1.00 ꢂ 0.00

2.39 ꢂ 0.11

2.50 ꢂ 0.09

1.57 ꢂ 0.05

0.11 ꢂ 0.01

0.15 ꢂ 0.01

0.23 ꢂ 0.01

0.64 ꢂ 0.02

1.52 ꢂ 0.08

1.59 ꢂ 0.08

1.00 ꢂ 0.00

7

8

(n-Pr)₂S

8

(n-Pr)₂SO

Table 4 Second order rate constants for the oxidation of cyclic and

other sulﬁdes and sulfoxides by dimethyldioxirane in acetone at 293 K

Table 5 Comparison of conventional ring strain energies of cyclo-

alkanes and cyclic sulﬁdes^a

10^ꢁ3k₂(x)_S/

10^ꢁ1k₂(x)_SO

/

Cycloalkane^b

Cyclic sulﬁde^c

Ring size, x

dm³mol^ꢁ1s^ꢁ1

Ring size, x

dm³mol^ꢁ1s^ꢁ1

E_RS(conv)/kJ mol^ꢁ1

Ring size, x

3

4

5

6

7

8

2.37 ꢂ 0.42

13.7 ꢂ 1.5

28.9 ꢂ 3.1

16.9 ꢂ 1.7

16.8 ꢂ 1.8

39.1 ꢂ 4.4

26.6 ꢂ 2.8

6.72 ꢂ 0.75

3

4

5

6

7

8

1.41 ꢂ 0.27

1.91 ꢂ 0.36

2.99 ꢂ 0.55

8.29 ꢂ 1.51

19.8 ꢂ 3.7

20.7 ꢂ 3.8

13.0 ꢂ 2.4

38.2 ꢂ 7.4

3

4

5

6

7

8

9

115.1

110.9

25.9

0.0

25.9

40.2

52.7

83.3

82.5

8.4

ꢁ0.8

—

(n-Pr)₂S

(t-Bu)₂S

(n-Pr)₂SO

(t-Bu)₂SO

—

a

b

Data are from tables in ch. 7 of ref. 14. Table 39. Table 41.

c

molecular orbital calculations carried out by means of the

Gaussian 98 suite of programs.¹⁵Using the B3-LYP/6-31G*

level of density functional theory (DFT),^16,17the geometries of

the 3- to 8-membered cyclic sulﬁdes, sulfoxides and sulfones

were fully optimised without geometry constraints. The validity

of this method in producing accurate results for these types of

S-containing substrate, for the oxidant 1a [and for their

derived transition states (see later)] has been well established.^18–24

The energies calculated were treated in the manner of Dudev

and Lim.²⁵The ring strain E_rsof an x-membered cyclic

compound relative to an r-membered cyclic reference compound

of the same type is given by eqn (9),

E_rs= E_xꢁ E_rꢁ (x ꢁ r)E_CH(9)

where E_xand E_rare the energies of the two compared cyclic

2

Fig. 2 Variation with ring size of the rate constants for oxidations of

cyclic sulﬁdes and sulfoxides relative to (n-Pr)₂S and (n-Pr)₂SO,

respectively. Plot 1 (ﬁlled squares) sulfoxides oxidised by dimethyl-

dioxirane in acetone at 293 K; plot 2 (open circles) sulﬁdes oxidised by

dimethyldioxirane in acetone at 293 K; plot 3 (open diamonds) sulﬁdes

oxidised by NaIO₄in 50% v/v aqueous ethanol at 298 K; + is the

reference point for all plots.

compounds and E_CHis the energy of a strain-free CH₂

2

fragment, (x ꢁ r) of which diﬀerentiate the two rings. The

value of E_CHwas taken as the diﬀerence in energy between the

2

all-trans-conformers of hexane and pentane. The ring strain of

a monocyclic compound can also be expressed relative to an

acyclic reference with the same number of like, contiguous

non-H atoms; in this case, it is given by eqn (10),

oxidations respond in essentially the same way to a ring

size-dependent property.

E_rs= E_cycloꢁ E_acyclo+ E_2H

(10)

where E_2H= 2E_C–Hꢁ E_C–Ccompensates for the C–C bond

lost and the two C–H bonds gained between the cyclic

compound and its acyclic reference. The latter two energies

were deﬁned by eqn (11) and eqn (12), respectively. The

fragment energies cited in eqn (9)–(12) are given in Table 6.

4.2 Ring strain. For the compounds of present interest

conventional, thermochemically-derived ring strain energies

are limited to cyclic sulﬁdes with ring sizes of 3–6, inclusive.¹⁴

Table 5 compares the conventional ring strain energies of these

sulﬁdes with those of the corresponding cycloalkanes; the

smaller E_rs(conv)values found for the sulﬁdes relative to

cycloalkanes of the same ring size are ascribed to the fact that

C–S are longer than C–C bonds.¹⁴

ꢄ

E_C–H= E_{CH CH}ꢁ E_{CH CH}

(11)

(12)

3

2

ꢄ

E_C–C= E_{CH CH}ꢁ 2E_CH

3

Owing to the lack of available heat of formation data for

cyclic sulfoxides and sulfones we have obtained theoretical

ring strain values for sulﬁdes, sulfoxides and sulfones via

Table 7 gives the results of calculations of the total energies

and derived ring strain energies for cyclic sulﬁdes of ring

sizes 3–8, relative to that in the 6-membered cyclic sulﬁde.

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Table 6 Fragment energies (B3-LYP/6-31G* DFT) for ring strain evaluation

Antecedent species

E/Hartrees per particle

10^ꢁ5E/kJ mol^ꢁ1

Fragment energies/kJ mol^ꢁ1

All-trans-CH₃(CH₂)₄CH₃

All-trans-CH₃(CH₂)₃CH₃

ꢁ237.085 51

ꢁ197.771 78

ꢁ6.224 54

ꢁ5.192 38

E_CH

ꢁ1.032 16 ꢃ 10⁵

2

CH₃CH₃

CH₃CH₂

ꢁ79.830 42

ꢁ79.157 87

ꢁ39.838 29

ꢁ2.095 90

ꢁ2.078 24

ꢁ1.045 93

ꢄ

CH₃

E_C–H

E_C–C

E_2H

ꢁ1.765 74 ꢃ 10³

ꢁ4.038 79 ꢃ 10²

ꢁ3.127 60 ꢃ 10³

Table 7 Total energies for cyclic sulﬁdes and derived ring strain

energies relative to that of C₅H₁₀

and cycloalkanes (cf. Table 5),¹⁴against ring size. It is clear

that, despite the disparity in magnitude between the DFT

energies on the one hand and heats of atomisation used in the

calculation of conventional values¹⁴on the other (2–3 orders

of magnitude), the agreement between the theoretical and

thermochemical values for sulﬁdes is quite good for the four

ring sizes in common; indeed, they are linearly related:

E_rs(DFT)S= 0.9147 ꢃ E_rs(conv)Swith R²= 0.998. Equally,

for the 6- to 8-membered rings, the comparability of E_rs(DFT)S

values with E_{rs(conv)Cycloalk}is also close. These agreements give

conﬁdence in the values of E_rs(DFT)obtained for the cyclic

sulﬁdes and the sulfoxides and sulfones for which there are no

thermochemical values. Ring strain energies for all three

families of heterocycle, now relative to the acyclic references

(n-Pr)₂S, (n-Pr)₂SO and (n-Pr)₂SO₂, as appropriate, are given

in Table 8. Also given are the changes in ring strain on

oxidation of sulﬁdes to sulfoxides, DE_rs(I), and of sulfoxides

to sulfones, DE_rs(II).

S

Ring size, x

10^ꢁ6ꢃ E_(x)DFT/kJ mol^ꢁ1

E_rs(DFT)S/kJ mol^ꢁ1a

3

4

5

6

7

8

ꢁ1.251 77

ꢁ1.354 98

ꢁ1.458 27

ꢁ1.561 49

ꢁ1.664 68

ꢁ1.767 88

74.23

77.37

7.10

0.00

30.03

43.30

Calculated as E_(x)DFT+ 1.56149 ꢃ 10⁶ꢁ (x ꢁ 6) ꢃ 1.03216 ꢃ 10⁵

cf. eqn (9) and Table 6.

a

4.3 Sulfoxides. Both k(7)_SO/k(n-Pr)_2,SOand k(8)_SO

/

k(n-Pr)_2,SO> 1 (cf. Table 3 and Fig. 2, plot 1), i.e. the

7- and 8-membered cyclic sulfoxides are more reactive than

the unstrained acyclic reference compound (n-Pr)₂SO on reaction

with 1a. In Sections 1.2 and 3 above it was shown that the

oxidation of sulfoxides by 1a is insensitive to the steric eﬀects

of alkyl substituents on S. Furthermore, in cyclic sulfoxides

the conformational freedom of the carbon ligands on S is

restricted relative to that in dialkyl sulfoxides, it is therefore

unlikely that the ring structure, as such, will exert any

signiﬁcant steric inﬂuence on oxidation for ring sizes r8.

The polymethylene chains in (CH₂)₆SO and (CH₂)₇SO are

expected to exert inductive eﬀects similar to that of two

n-propyl groups (see ESIw 2.2 and Table S5) so the fact that

these cyclic sulfoxides react 50% faster than the acyclic

comparator does not arise from signiﬁcantly enhanced inductive

promotion. However, the values of DE_rs(II) in Table 8 show

Fig. 3 Variation with ring size, x, of ring strain energies relative to

the six-membered ring for cycloalkanes and cyclic sulﬁdes. Plot 1

(open circles) thermochemically-derived values for cycloalkanes; plot 2

(open squares) thermochemically-derived values for sulﬁdes; plot 3

(ﬁlled diamonds) theoretically-derived (DFT) values for sulﬁdes.

In Fig. 3 the values of E_rs(DFT)Sare plotted, together with

thermochemically-derived E_rs(conv)values for cyclic sulﬁdes

Table 8 Ring strain energies, E_rs(DFT), for cyclic sulﬁdes, sulfoxides and sulfones calculated relative to the corresponding acyclic di-(n-propyl)

reference compound

Ring size, x

E_rs(DFT)S/kJ mol^ꢁ1

E_rs(DFT)SO/kJ mol^ꢁ1

DE_rs(I)/kJ mol^ꢁ1a

DE_rs(II)/kJ mol^ꢁ1a

2

3

4

5

6

7

8

105.5

108.7

38.4

31.3

61.3

74.6

118.3

100.3

47.4

36.5

66.3

84.7

212.2

115.5

56.3

35.7

60.0

74.3

12.8

ꢁ8.4

9.0

5.2

5.0

93.9

15.2

8.9

ꢁ0.8

ꢁ6.3

ꢁ10.4

10.1

a

DE_rs(I) = E_rs(DFT)SOꢁ E_rs(DFT)Sand DE_rs(II) = E_rs(DFT)SOꢁ E_rs(DFT)SO

.

2

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that whilst there is a large increase in ring strain between

thiirane 1-oxide, (CH₂)₂SO, and its derived sulfone, for larger

rings the magnitudes of the corresponding increases decline

with increasing ring size and eventually become negative, i.e.

ring strain is signiﬁcantly reduced on oxidation of sulfoxide to

sulfone for x Z 7. If the activation energies for the oxidation

were sensitive to these changes in ring strain, the behaviour of

k(x)_SO/k(n-Pr)_2,SOas a function of ring size can be understood:

the smaller rings are oxidised more slowly than the acyclic

reference because reaction increases ring strain but, for x Z 7,

the relief of ring strain enhances the relative rates of oxidation.

With the exception of the 3-membered system, there is

a linear correlation, ‘fair’ by Exner’s criterion,²⁶between

Table 9 Frontier orbital energies (B3-LYP/6-31G* DFT)

Frontier orbital

energy/eV

F = [1/(E_HOMOꢁ

E_LUMO)]/eV^ꢁ1

Reactant

LUMO

Dimethyldioxirane, 1a

ꢁ0.4773

HOMO

(CH₂)₂S,

(CH₂)₃S

(CH₂)₄S

(CH₂)₅S

(CH₂)₆S

(CH₂)₇S

(n-Pr)₂S

ꢁ6.1354

ꢁ5.8736

ꢁ5.7517

ꢁ5.8137

ꢁ5.7767

ꢁ5.7435

ꢁ5.7685

ꢁ0.1767

ꢁ0.1853

ꢁ0.1896

ꢁ0.1874

ꢁ0.1887

ꢁ0.1899

ꢁ0.1889

log [k₂(x)_SO/dm³mol^ꢁ1

s

^ꢁ1] and the change in ring strain

particularly relevant for reactions that proceed via early

transition states. major determinant of reactivity is

[eqn (13)] (see ESIw 2, Table S7 for statistical detail),

A

the reciprocal of the frontier-orbital energy diﬀerence, i.e.

F = 1/(E_HOMOꢁ E_LUMO) where E_HOMOis the energy of

the highest occupied molecular orbital of the nucleophilic

reactant and E_LUMOis the energy of the lowest unoccupied

orbital of the electrophilic reactant. This term represents a

stabilisation attenuating the larger, ﬁlled-orbital repulsions

that give rise to the energy of activation of the reaction.

Table 9 reports the relevant frontier-orbital energies for the

reaction of cyclic sulﬁdes with 1a and Fig. 4 compares log

log [k₂(x)_SO/dm³mol^ꢁ1

s

^ꢁ1] = 1.915 ꢁ 0.044DE_rs(II) (13)

The deviation of the point for (CH₂)₂SO from the correlation

line is such that eqn (13) underestimates k₂(x)_SOby more than

two orders of magnitude. Later (see Section 5.1) we shall ﬁnd

that ring strain change between the reactant and product

ground state does not, alone, fully explain the behaviour of

4- to 6-membered cyclic sulfoxides.

[k₂(x)_S/dm³mol^ꢁ1^ꢁ1] with F/eV^ꢁ1

s .

4.4 Sulﬁdes. Although the steric eﬀects of bulky alkyl

groups were found to outweigh their +I eﬀects on the

oxidation of alkyl 4-nitrophenyl and dialkyl sulﬁdes by 1a

(see Sections 1.1 and 3 above), it is unlikely that, in similar

oxidations, the polymethylene chains in 4- to 8-membered

cyclic sulﬁdes will exert steric eﬀects that are much diﬀerent

from each other, the reason being that the steric₀eﬀects of

linear alkyl groups are essentially constant [e.g. E_s= ꢁ0.31

for n-Pr, n-Bu and n-Pe²⁷(see ESIw 2, Table S2)] and the cyclic

structure restricts the conformational freedom, and hence the

capacity for hindrance, of the polymethylene chain relative to

that of linear alkyl groups. Also, the inductive eﬀect is

expected to increase regularly with the length of polymethylene

chain, similar to that of linear alkyl groups¹¹(see ESIw 2.2 and

Table S5). The irregular variation of k(x)_S/k(n-Pr)_2,Swith ring

size (see Table 6 and Fig. 2) cannot therefore be accounted for

in terms of steric and inductive eﬀects either alone or in

combination. Furthermore, the ﬁnding that both k(5)_S/k(n-Pr)_2,S

and k(8)_S/k(n-Pr)_2,S> 1 shows that these relative rate

constants are not inﬂuenced by the change in ring strain on

oxidation for, after the 3-membered ring, the 5- and 8-membered

rings have the largest positive values of DE_rs(I) (see Table 8).

As DE_rsvalues measure the diﬀerence in ring strain between a

substrate and its oxidation product, a relationship between

oxidation rate constants and DE_rsvalues implies the transition

state to have developed some product-character; such was the

case with the oxidation of sulfoxides. The lack of relationship

between oxidation rate constants and DE_rs(I) therefore implies

product-character to be poorly developed in the case of sulﬁde

oxidation: the transition states for sulﬁde oxidation evidently

occur earlier in their reaction coordinate than those of

sulfoxide oxidation [though the latter still occur relatively

early, see Section 2 and later 6.2]. The frontier-orbital approach

to the explanation of reactivity²⁸considers transition states

in terms of the reactants’ orbital interactions and hence is

It is clear that there is an inverse relationship between the

two. The order of reactivity of the cyclic sulﬁdes predicted by

the frontier-orbital term is k₂(8)_S> k₂(5)_S> k₂(7)_S

k₂(n-Pr)_2,S> k₂(6)_S> k₂(4)_S> k₂(3)_S. The experimental

order is k₂(8)_S> k₂(5)_S> k₂(n-Pr)_2,S> k₂(7)_SE k₂(6)_S

E

>

k₂(4)_S> k₂(3)_S, i.e. only k₂(7) is out of sequence, being less

than predicted. In view of the expected similarity of +I eﬀects

(see ESIw 2, Table S5) and of steric eﬀects for (CH₂)₆and

(n-Pr)₂(see ESIw 2.3) and independence of the ring strain given

Fig. 4 Plot 1 (open squares), variation with ring size, x, of log k₂(x)_S

for the oxidation of cyclic sulﬁdes by dimethyldioxirane in acetone at

293 K; the ﬁlled square is the value for (n-Pr)₂S. Plot 2 (open circles),

variation with ring size of F/eV^ꢁ1, the reciprocal of the diﬀerence in

corresponding frontier orbital energies; the ﬁlled circle is the value for

(n-Pr)₂S.

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by eqn (10), k₂(7)_Sis less than expected. The reason is not

obvious but the similar behaviour of the value of k₂(7)_Sfor

oxidation by periodate⁹(Fig. 2) indicates the eﬀect to be real.

5

Overall correlation of reactivities

Here we seek to correlate the reactivities towards 1a of all the

substrates examined in our previous and present work (i.e. aryl

methyl, dialkyl, alkyl 4-nitrophenyl and cyclic sulﬁdes and

sulfoxides) and to identify the parameters required to do so.

The data used are the logarithms of rate constants reported

previously^6bor given above (Table 1 and Table 4) for reactions

in acetone at 293 ꢂ 2 K, and the explanatory variables we have

0

conside₀red are: Ss* and SE_s, respectively, the sum of the s*

and E_svalues of the two carbon ligands on S; q_S/e, the

Mulliken charge²⁹at S (e = 1.602 177 ꢃ10^ꢁ19C); F/eV^ꢁ1

,

the inverse of the diﬀerence between the energy of the HOMO

2

of the substrate and the LUMO of 1a; c_{S H}, the square of the

3p_zcomponent of the HOMO at S, taken as a measure of

electron density at the reaction centre; and DE_rs/kJ mol^ꢁ1, the

change in ring strain, if any, between the reactant and the

product. The s* values for 3- and 4-substituted-phenyl groups

were calculated by means of an algorithm from ref. 30, those

for alkyl groups and the polymethylene chain in cyclic

substrates were calculated from the carbon connectivity as

Fig. 5 (a) Plot of log [k₂/dm³mol^ꢁ1s^ꢁ1] for aryl methyl, and dialkyl,

sulﬁdes and sulfoxides versus values calculated for the aryl methyl

compounds by eqn (14). (b) Plot of log [k₂/dm³mol^ꢁ1^ꢁ1] for all the

s

sulﬁdes studied versus values calculated by eqn (16); the deﬁnition of

0

described in ESIw 2; E_svalues are taken from Dubois and

the line excludes (CH₂)₂S.

co-workers,²⁷or assumed (see ESIw 2.3), and the quantum

2

mechanical parameters, q_S/e, F/eV^ꢁ1and c_{S H}are from our

percentage weightings of the two parameters are q_S/e, 80.6%

and Ss*, 19.4% (see ESIw 2, Table S7). The line of eqn (14)

provides a reference against which other data may be compared.

For example, Fig. 5a also includes points for the dialkyl

sulﬁdes (n-Pr)₂S and (t-Bu)₂S and the corresponding sulfoxides.

The points for the two sulfoxides and for (n-Pr)₂S lie close to

the line but that for (t-Bu)₂S does not. If the close-lying points

are included in the correlation, eqn (14) is modiﬁed to eqn (15).

calculations at the B3-LYP/6-31G* level of density functional

theory as are the DE_rsvalues already given in Table 8 (see ESIw 2,

Table S6). A probability level not greater than 0.01 was

speciﬁed for each explanatory variable. Correlations using

the raw variables were run with, and without, an intercept.

In general, those obtained with an intercept are statistically

the more precise and require fewer variables; none involved

2

_{S H}. Since the variables have widely diﬀering ranges and are

c

log [k₂/dm³mol^ꢁ1s^ꢁ1

]

= 4.324 ꢁ 3.086q_S/e ꢁ 0.922Ss*

calc

not referred to a common standard, the chemical signiﬁcance of

the intercept is unclear but this uncertainty is circumvented by

standardisation of the variables and reactivity data [cf. discussion

of eqn (5)]¹²(see ESIw 2, Table S7 for statistical detail).

Previous work showed that oxidations, in acetone solution,

of methyl 3- and 4-substituted-phenyl sulﬁdes and sulfoxides

by 1a, though diﬀering in rate constants by 2–3 orders of

magnitude, exhibit very similar Hammett reaction constants.^5,6

As a consequence, a common Hammett plot produces two

essentially parallel lines separated by 2–3 ordinate units and

the same is true if s* values for the substituted-phenyl groups

are used, as these are proportional to the Hammett s_mand s_p

constants.³¹Fig. 5a shows the logarithms of the rate constants

of aryl methyl sulﬁdes and sulfoxides plotted against calculated

values given by eqn (14). The data for the two subsets are

accommodated by a single line, spanning 2–3 ordinate units:

(15)

When this regression is standardised, the percentage weightings

of the two parameters in the correlation are q_S/e, 70.0% and

Ss*, 30.0% (see ESIw 2, Table S7). The non-correlation of the

point for (t-Bu)₂S conﬁrms the conclusion in Section 3 that the

oxidation of bulky dialkyl sulﬁdes is sterically inhibited

whereas the correlation of the point for (t-Bu)₂SO conﬁrms

the contrary for bulky sulfoxides.

Fig. 5b is the plot of the values of log [k₂/dm³mol^ꢁ1s^ꢁ1] for

the oxidation of all the sulﬁdes that we have considered versus

the calculated value given by eqn (16):

log [k₂/dm³mol^ꢁ1s^ꢁ1

]

calc

= 2.991 ꢁ 0.648Ss* + 0.289SE_sꢁ 7.190F/eV^ꢁ1(16)

0

On standardisation, the percentage weightings of the variables

0

log [k₂/dm³mol^ꢁ1s^ꢁ1

]

= 4.336 ꢁ 3.061q_S/e ꢁ 0.949Ss*

in the correlation are found to be Ss*, 51.7%; SE_s, 36.4%

calc

and F/eV^ꢁ1, 11.9%. This line is essentially equivalent to that

in Fig. 5a in the collinearity of the data for ArSMe and

(n-Pr)₂S but the point for (t-Bu)₂S is now also correlated on

(14)

This result implies that the diﬀerence in reactivity, towards 1a

in solution, between the sulﬁdes and sulfoxides arises from

variation, within a single mechanism, of the polarity of the

sulfur function. When the regression is standardised,¹²the

0

account of the inclusion of SE_s. Also well correlated are the

points for the alkyl 4-nitrophenyl sulﬁdes for which the

importance of the steric eﬀect of the alkyl group was found

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above (see Section 1.2). Among the cyclic sulﬁdes, the only

seriously deviant point is that due to (CH₂)₂S (not included in

the deﬁnition of the line) but the remainder lie close to the line

near the point for (n-Pr)₂S. This clustering justiﬁes the values

envisaged: rate-enhancement, relative to the methyl case, arising

from hindered solvation of the substrates’ ground states and

rate-retardation arising from hindered solvation of their

transition states. These opposing eﬀects were suggested to be

similar in magnitude and hence to cancel. The correlation by

eqn (17) implies the rate-enhancing term to be marginally

bigger in the extended data set. Although DE_rsis signiﬁcant, it

is insuﬃcient to ensure correlation of (CH₂)_3–5SO (cf. 4.3).

Fig. 6b shows the variation of log [k₂/dm³mol^ꢁ1s^ꢁ1] for all

of our substrates as a function of calculated values given

by eqn (18); the percentage weightings of the standardised

variables allow comparison of their relative importance as

follows: q_S/e, 60.9%; Ss*, 31.2% and DE_rs, 7.9%. The deﬁnition

of the line excludes the points for (t-Bu)₂S, (CH₂)₂S and

(CH₂)_3ꢁ5SO. Eqn (18) is thus a reﬁnement of eqn (15) accom-

modating the change in ring strain of the included cyclic

compounds [the points for (CH₂)₆SO and (CH₂)₇SO coincide].

0

of Ss* and SE_sassigned to polymethylene chain, (CH₂)_3–7

(see ESIw 2.2 and 2.3) and the absence of dependence on DE_rs

conﬁrms the inference that cyclic sulﬁde oxidation is independent

of ring strain change. The correlation also implies the frontier-

orbital term F/eV^ꢁ1to be signiﬁcant for sulﬁdes generally and

not just for the cyclic sulﬁdes for which it was inferred in

Section 4.4 above.

In Fig. 6a are plotted the values of log [k₂/dm³mol^ꢁ1s^ꢁ1

]

for the oxidation of all the sulfoxides we have investigated as a

function of calculated values given by eqn (17):

log [k₂/dm³mol^ꢁ1s^ꢁ1

]

calc

0

= 1.857 ꢁ 0.967Ss* ꢁ 0.0056DE_rsꢁ 0.0576SE_s

(17)

log [k₂/dm³mol^ꢁ1s^ꢁ1

]

calc

In deﬁning the line, the points for the three cyclic sulfoxides

(CH₂)_3–5SO are excluded so ensuring the points for ArSOMe

and the two dialkyl sulfoxides are collinear as in Fig. 5a. The

points for the remaining 3-, 7- and 8-membered cyclic sulfoxides

are well correlated as are those of the alkyl 4-nitrophenyl

sulfoxides. Standardisation leads to the following weightings

of the variables in the correlation: Ss*, 76.1%; DE_rs, 16.6%

and SE_s, 7.3%. Interestingly, not only is SE_ssigniﬁcant but

here its negative coeﬃcient implies the reaction rate to be

sterically accelerated. This contrasts with the situation in

Sections 1.3 and 3 above where, in considering, separately,

the limited subsets of alkyl 4-nitrophenyl sulfoxides and

dialkyl sulfoxides, there was no evidence of any alkyl steric

eﬀect. In explaining this apparent lack, two opposed

consequences of the steric eﬀects of bulky alkyl groups were

= 4.287 ꢁ 3.027q_S/e ꢁ 0.928Ss* ꢁ 0.00885DE_rs(18)

If the data for (t-Bu)₂S are included in the correlation, SE_s

becomes signiﬁcant at a level of probability o0.01, with a

positive coeﬃcient [eqn (19)] and the following percentage

weightings of the standardised variables: q_S/e, 59.0%; Ss*,

0

25.9%; DE_rs, 9.0% and SE_s, 6.0%.

log [k₂/dm³mol^ꢁ1s^ꢁ1

]

calc

= 4.375 ꢁ 2.961q_S/e ꢁ 0.753Ss* ꢁ 0.01027DE_rs+ 0.110SE_s⁰

(19)

However, the precision deteriorates relative to eqn (18) (see

ESIw 2, Table S7). The added point still does not fall on the

line and, as a consequence of the diﬀerent signs of the

0

coeﬃcient of SE_sfor the sulﬁde and sulfoxide subsets discerned

above, points for other t-Bu derivatives are displaced from the

line and the strict collinearity of the ArSMe and ArSOMe

subsets is also lost. Eqn (19) is not therefore an improvement

on eqn (18).

5.1 Non-correlated points. The correlation line in Fig. 6b

[eqn (18)] overestimates log [k₂/dm³mol^{ꢁ1 ꢁ1}] for (t-Bu)₂S

s

and (CH₂)₂S by similar amounts. As seen above, the cause is

steric for (t-Bu)₂S but this cannot be the case for (CH₂)₂S

which has the least encumbered sulfur centre of all the substrates.

Nor can the non-correlation be reasonably explained in terms

of Ss*: it would require a value 5–6 times greater than that

used (1.0–1.2 rather than 0.2, see ESIw 2.2) to correlate the

point by eqn (16) and eqn (18) [see also ESIw 2, comments on

Table S7, eqn (S24)]. Evidently, the three-membered cyclic

sulﬁde is unique and not directly comparable with the remaining

cyclic sulﬁdes in its reaction with 1a. Given this fact, we

investigated the eﬀect of removing the (correlated) point for

the 3-membered cyclic sulfoxide, (CH₂)₂SO, from the deﬁnition

of the line in Fig. 6a to see whether the non-correlated points

for (CH₂)_3–5SO are then brought into line. To a certain extent

this is the case: all the sulfoxides, excluding (CH₂)₂SO, are

correlated but the correlation is poorer than eqn (17) [see ESIw 2,

Fig. 6 (a) Plot of log [k₂/dm³mol^ꢁ1s^ꢁ1] for all the sulfoxides studied

versus values calculated by eqn (17); the deﬁnition of the line excludes

(CH₂)_3–5SO. (b) Plot of log [k₂/dm³mol^ꢁ1s^ꢁ1] for all the sulﬁdes and

sulfoxides studied versus values calculated by eqn (18); the deﬁnition of

the line excludes (t-Bu)₂S, (CH₂)₂S and (CH₂)_3–5SO.

comments on Table S7, eqn (S25)] and log [k₂/dm³mol^ꢁ1s^ꢁ1

for (CH₂)₂SO is then underestimated by almost 3 orders of

]

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magnitude similar to the case with eqn (13). If the point for

(CH₂)₂SO is also excluded from the deﬁnition of eqn (18),

those for (CH₂)_3–5SO are not better correlated than when it is

included. Eqn (18) thus represents the best overall correlation

of the full data set with the minimum number of exclusions

(5 out of 45). The displacement of the points for the 4- to

6-membered cyclic sulfoxides from the correlation line is

greater the smaller is the ring. There is clearly a ring-size eﬀect

which is not adequately expressed by DE_rs, the diﬀerence in

ring strain between the ground states of the reactant and

product. Presumably, the displacements have their origin in

a transition state property such as increased eclipsing strain

within the ring caused by the proximity of the oxidant; the

degree of such strain would be expected to depend on the

ﬂexibility of the polymethylene chain and hence be greater

the smaller the ring size. We have not, however, performed the

calculations on the transition states of the oxidations of cyclic

sulfoxides by 1a which could support or disprove this hypothesis.

found (see Section 6.2 below). Each SO bond lowers the

molecular enthalpy ostensibly by a similar amount irrespective

of whether it is a sulfoxide or sulfone bond: for the tabulated

compounds the mean enthalpy of sulfonic SO bonds exceeds

that of sulfoxidic SO bonds by only 0.05% but, because the

calculated enthalpies are so large, this nevertheless corresponds

to

a greater exothermicity of sulfonic SO bonds of

B104 kJ mol^ꢁ1. The Mulliken charges on S and O are more

obviously characteristic of the species. The increment in

positive charge on S when sulﬁde is oxidised to sulfoxide is

about twice as large as that when sulfoxide is oxidised to

sulfone and the negative charge on each sulfonic O atom is less

by 0.09e relative to that on the O of its sulfoxide precursor.

The bond lengths show variations consistent with these charge

variations: sulfonic SO bonds are shorter than sulfoxidic SO

bonds owing to their less dipolar, more double-bonded, character.

The variation in molecular dipole moments is more

complex. The Mulliken charges at S for the unsubstituted

compounds show that consecutive oxidations of the sulfur

function will result in an increasing polarisation of the

attached aromatic ring, a fact conveniently expressed by the

Hammett s_pconstants^31aof the sulfur functional groups:

s_p(SMe) = 0, s_p(SOMe) = 0.49 and s_p(SO₂Me) = 0.72.

Although individual molecular geometry has a key role in

determining the precise molecular dipole moment, the pattern

of the tabulated values, where the substituent X is an electron-

withdrawing group, may be largely explained on the assumption

that the transfer of polarisation by the p-system of the

aromatic ring is responsible for the major part of the variation

between 4-substituted structures. In Fig. 7 the dipole moments

of Table 10 are plotted versus Hammett’s s_p(X), now taken as

an index of the substituents’ electronic character.

6

Calculations on the reactants, products and transition states

in the oxidation of aryl methyl sulﬁdes and sulfoxides by 1a

Calculations of the optimised ground state geometries of the

reactants and products of the oxidations of aryl methyl

sulﬁdes and sulfoxides were performed using the Gaussian

98 suite of programs, revision A.3¹⁵and the B3-LYP/6-31G*

level of density functional theory;^16,17the transition state

calculations employed revision A.7.³²The eﬀects of solvation

(by acetone) were simulated at the B3-LYP/6-31G* level by

single point self consistent reaction ﬁeld (SCRF) calculations

with Tomasi’s polarised continuum model³³(PCM) using the

gas-phase B3-LYP/6-31G*-optimised geometries. The output

of all calculations was visualised, as appropriate, using the

program Molekel.³⁴

A substituent with s_p(X) = s_p(SOMe) would negate the

polarisation due to the SOMe group and reduce the dipole

moment to zero. As s_p(Cl) = 0.23 (i.e. 0 o s_p(Cl) o 0.49),^31a

the dipole moment of 4-chlorophenyl methyl sulfoxide is

reduced relative to PhSOMe but to a value greater than zero.

Similar reasoning may be applied to 4-chlorophenyl methyl

6.1 Reactants and products. In Table 10 are given

enthalpies and other descriptors of the ground states of

compounds that are reactants or products of oxidations by

1a for which optimised transition state structures have been

Table 10 Enthalpies and other characteristics of the optimised ground state structures of various methyl 4-substituted-phenyl sulfur compounds,

their oxidant and co-product as calculated using B3-LYP/6-31G* DFT

Enthalpy,

10^ꢁ6H1/kJ mol^ꢁ1a

Mulliken charge

q_S/e^b

Mulliken charge

q_Oso/e^b

Bond length

r_S–O/A^c

Molecular dipole

moment, m/D^d

Species

4-MeOPhSMe (syn)

(anti)

4-MeOPhSOMe (syn)

(anti)

PhSMe

ꢁ2.059105

ꢁ2.059104

ꢁ2.256477

ꢁ2.256476

ꢁ1.758427

ꢁ1.955794

ꢁ2.153265

ꢁ2.295350

ꢁ2.492707

ꢁ3.162460

ꢁ3.359930

ꢁ2.197974

ꢁ2.395440

ꢁ0.704349

ꢁ0.507139

0.127

0.126

0.762

0.760

0.133

0.765

1.098

0.168

0.780

0.771

1.100

0.778

1.104

—

ꢁ0.635

—

ꢁ0.631

ꢁ0.540

—

ꢁ0.619

ꢁ0.628

ꢁ0.537

ꢁ0.622

ꢁ0.532

ꢁ0.318^e

ꢁ0.426^e

—

1.514

—

1.513

1.471

—

1.511

1.513

1.471

1.511

1.470

—

2.676

0.871

3.800

5.276

1.413

3.917

5.137

5.459

4.191

3.218

4.009

4.124

3.701

3.373

2.816

PhSOMe

PhSO₂Me

4-O₂NPhSMe

4-O₂NPhSOMe

4-ClPhSOMe

4-ClPhSO₂Me

4-NCPhSOMe

4-NCPhSO₂Me

Me₂CO₂, 1a

Me₂CQO

—

a

b

Sum of total electronic and thermal enthalpies at 298.15 K and 1 atmosphere, corrected for zero-point energy. e = 1.602177 ꢃ 10^ꢁ19C.

c

d

e

1 A = 10^ꢁ10m. 1 D = 3.336 ꢃ 10^ꢁ30C m. Mulliken charge on oxygen.

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moment (Table 10). The dipole moment of syn 4-methoxy-

phenyl methyl sulfoxide seems anomalous in being slightly less

than that of PhSOMe: a substituent which is an electron donor

is expected to enhance the ring polarisation produced by the

SOMe group (see structure 13) as occurs with the anti-

conformer. This no doubt occurs because the orientation of

the O–Me bond dipole modulates the net ring-polarisation

pattern. In the case of 4-methoxyphenyl methyl sulﬁde, neither

substituent is electron withdrawing [s_p(OMe) = ꢁ0.27,

s_p(SMe) = 0].^31aThe dipole moment calculated for the

syn-conformer is close to the sum of the experimental values

for PhOMe and PhSMe [1.38 D (gas phase)^35aand 1.38 D

(benzene),^35brespectively] suggesting that it is determined by

an order of electronegativities, within the molecule, of O > C > S

and that minor polarisations of the ring induced by the

heteroatoms are not countervailing but coincident. Structure

14 shows the syn-conformation found for 4-methoxyphenyl

methyl sulﬁde as a stick diagram (in which O is red, S is yellow,

C is green and H is white); the associated molecular electro-

static potential (MEP) illustrates the distribution of charge.³⁴

By contrast, the dipole moment of only 0.871 D calculated for

the anti-conformer shows the sensitivity of the measure to the

rotameric state of the molecule when the ring is not strongly

polarised.

Fig. 7 Molecular dipole moments calculated for 4-X-substituted-

phenyl methyl sulﬁdes, sulfoxides and sulfones plotted against s_p(X).

Sulﬁdes, open squares; sulfoxides, open circles; sulfones, ﬁlled

diamonds.

sulfone where the Cl substituent reduces the dipole moment to

a value between those of PhSO₂Me and the chlorinated

sulfoxide. Both the CN and NO₂groups have values of

s_p> 0.49 (i.e. 0.66 and 0.78, respectively);^31athe ring

polarisation in the corresponding sulfoxides will therefore be

reversed relative to that in the unsubstituted sulfoxide. The

dipole moments of the two substituted sulfoxides are then not

directly comparable with that of the unsubstituted molecule

but they are expected to be less than those of PhNO₂and

PhCN, which is the case (experimental gas-phase values 4.17 D

and 4.23 D, respectively).^35aSince s_p(SOMe) o s_p(CN) o

s_p(SO₂Me), a reversal of ring polarisation is expected between

4-cyanophenyl methyl sulfoxide and its derived sulfone. The

ring of the sulfone is therefore polarised in the same sense as

that of 4-chlorophenyl methyl sulfone (see Fig. 7) but, as

s_p(CN) > s_p(Cl), the cyano-sulfone has the smaller dipole

moment. Methyl 4-nitrophenyl sulﬁde exhibits a molecular

dipole moment larger than PhNO₂owing to the direct

conjugation between the ring substituents represented by 12

[here the electronic eﬀect of the SMe group is better represented

by s_p⁺(ꢁ0.6)³⁶than by s_p(0)]; on oxidation, this conjugation

is lost and the SOMe group attenuates the polarisation due to

the NO₂group.

In order to investigate the diﬀerences between sulﬁdes and

sulfoxides in more detail a natural bond order (NBO) analysis

was carried out for PhSMe and PhSOMe within the Gaussian 98

package utilising Gaussian NBO version 3.1.³⁷Details for S

are given in Table 11. The non-equivalence of the sulﬁdic lone

pairs is evident. The pair of higher energy is in an atomic

3p_z-orbital which accords with the geometry found for the aryl

methyl sulﬁdes in which the S–Me bond is coplanar with the

aromatic ring (see 14) so allowing stabilising overlap of

the lone pair with the aromatic p-system. [This is expressed in

the corresponding molecular orbital of PhSMe in which the

coeﬃcient at S of the HOMO, c_S,H, is 0.541 whereas those for

saturated sulﬁdes, in general, exceed 0.6 (see ESIw 2, Table S6

2

for values of c_{S H}for aryl methyl, dialkyl and cyclic sulﬁdes).]

4-OMe is a net electron donor [s_p(OMe) o 0] and, furthermore,

rotation about the ring-C–O_Mebond allows the lone pair of

OMe to conjugate with the aromatic p-system in two coplanar

conformations that give rise to syn and anti conformers when

the ring also carries another unsymmetrical group. Thus both

4-methoxyphenyl methyl sulfoxide and sulﬁde exhibit syn–anti

conformers which lie close in energy but diﬀer in dipole

Given that, for PhSMe, the 3p_z-orbital is occupied by the

lone pair of higher energy, the three hybrid orbitals formed

by the 3s, 3p_xand 3p_yorbitals accommodate the lone pair

of lower energy and contribute to the bonds to C.

The orbital of the latter lone pair accounts for 66.9% of

the 3s orbital and 33.1% of the two 3p orbitals, the S–C_Ph

and S–C_Mebonds thus account for 17.6% and 15.8% of

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Table 11 Natural bond order analysis at sulfur

NBO percentage

Electronic character percentage

S

C

O

s

p

d

Energy/eV

Angle/1

PhSMe

1st S lone pair

2nd S lone pair

S–C_Ph

ꢁ6.31

ꢁ16.54

—

45.44

46.88

—

54.56

53.12

—

0.00

99.96

33.09

81.63

83.44

—

0.04

0.02

0.75

0.68

—

66.89

17.61

15.85

—

S–C_Me

+C_PhSC_Me

PhSOMe

S lone pair

S–C_Ph

S–C_Me

S–O

+C_PhSC_Me

+C_PhSO

+C_MeSO

103.62

ꢁ14.72

—

64.08

—

96.28

107.20

106.89

52.33

15.28

14.27

18.98

—

47.64

83.67

84.71

80.00

—

0.03

1.05

1.03

1.02

—

44.86

46.25

35.92

—

55.14

53.75

—

s-character and 81.6% and 83.4% p-character, respectively,

which confers a C_PhSC_Meangle of 103.61. The polarisation of

each bond to S is indicated by the NBO percentages.

On oxidation of PhSMe to PhSOMe, the sulﬁdic second

lone pair orbital, on becoming the sulfoxidic lone pair orbital,

undergoes a reduction in s- and an increase in p-character

with a concomitant increase in energy by almost 2 eV

(Table 11). The reaction of the ﬁrst lone pair in the oxidation

of a sulﬁde thus potentiates the nucleophilic character of

the second lone pair. The change in hybridisation of the lone

pair entrains corresponding changes in the contributions of

S to the bonds to its C and O ligands which narrow the

C

_PhSC_Meangle to 96.31 while according the CSO angles values

B1071. It is the resultant pyramidal disposition of the sulfur

ligands, rather than delocalisation of the lone pair, that

sterically determines the conformation adopted by PhSOMe

(see 15): the oxygen and Me groups are positioned so as

to minimise their interaction with ortho-H atoms of the

aromatic ring. Equally, the pyramidal geometry at S and the

single-bond character of the sulfoxidic bond also prevents

mesomeric delocalisation of aromatic p-electrons on to the

SOMe group.³⁸

The transition state structures were very similar to those

found by the same authors. At the reaction centre the transition

state 16 formed by PhSMe and 1a was characterised by the

following angles (the values²⁴for the transition state formed by

Me₂S and 1a are given in parentheses for comparison): +SOO,

169.161 (168.541); +SOC, 126.111 (125.921). Avoidance of the

lone pairs on O by the nucleophile reduces +SOO from 1801.

It is also apparent in 16 that activation involves the rotation of

the SMe group from co-planarity with the ring (cf. 14) so

decoupling the S lone pair from conjugation with the aromatic

p-system. In transition state 17 formed by PhSOMe and 1a the

geometry of the nucleophile is closer to that of its ground state

15 as the S lone pair is not conjugated. The angles at the

reaction centre are similar to those found²⁴in the transition

state formed by Me₂SO and 1a +SOO, 172.801 (172.561);

+SOC, 129.391 (128.431).

The reaction enthalpies, D_rH1, show that the oxidation of a

sulfoxide to sulfone is more exothermic than the oxidation of a

sulﬁde to a sulfoxide by B104 kJ mol^ꢁ1, consistent with the

molecular enthalpy diﬀerences noted in Table 10. In addition,

it is clear that in both oxidations the exothermicity increases

the more electron-donating is the substituent; on the other

hand, the trend in the enthalpies of activation, DH^z, is the

opposite. The enthalpy data together thus constitute examples

of the Bell–Evans–Polanyi principle:³⁹for each class of

substrate, the stronger the bond being formed, the lower is

6.2 Transition states. Transition states were located by a

scanning procedure in which the distance between the S atom

of a substrate and the proximal O atom of the oxidant was

varied stepwise between 3 A and 1.5 A. At each ﬁxed separa-

tion, the geometry was optimised by the B3-LYP/6-31G*

method, so generating a separation-dependent potential energy

curve exhibiting a maximum at the approximate separation

of the moieties in the required transition state. This distance

was then used as the starting point for optimising the geometry

of the transition state. All the transition state structures

were found to be ﬁrst order saddle-points on the potential

energy surface characterised by a single imaginary frequency

which, on visualisation using the Molekel program,³⁴corres-

ponded in every case to a vibration between the sulfur atom

and the proximal oxygen of the oxidant. The method was

validated by repeating, with excellent agreement, B3-LYP/6-31G*

calculations that had been reported by Baboul and

co-workers²⁴for the oxidation of H₂S and H₂SO by dioxirane

(see Table 12).

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Table 12 Reaction energetics and key features of the transition states formed by various substrates on oxidation by 1a as calculated by

B3-LYP/6-31G* DFT

Substrate

D_rH1/kJ mol^ꢁ1a

DH^z/kJ mol^ꢁ1b

r^z_(S–Op)/A^c

r^z_(Op–Od)/A^d

r^z_(C–Op)/A^e

x^f

m/D^g

4-MeOPhSMe

PhSMe

4-O₂NPhSMe

PhSOMe

ꢁ162.6

33.2

40.9

56.9

37.2

39.4

43.3

2.022

2.011

1.986

2.032

2.019

2.003

1.888

1.933

1.930

1.935

1.946

1.885

1.889

1.894

2.017

1.902

1.482

1.487

1.506

1.475

1.482

1.491

1.520

1.457

0.455

0.463

0.481

0.403

0.411

0.421

0.572

0.456

5.986

6.453

6.020

5.246

3.765

3.374

6.922

3.012

ꢁ157.5

ꢁ146.9

ꢁ261.7

4-ClPhSOMe

4-NCPhSOMe

H₂S^h

ꢁ260.3

ꢁ256.5

ꢁ73.3 (ꢁ73.2)ⁱ

81.0 (81.2)ⁱ

44.9 (44.8)ⁱ

H₂SO^h

ꢁ228.3 (ꢁ228.4)ⁱ

a

Standard enthalpy of reaction, calculated as the diﬀerence between the sum of combined electronic and thermal enthalpies of the products at

b

298.15 K and 1 atmosphere, corrected for zero point energy, and the sum of the similar entropies of the substrate and oxidant. Enthalpy of

activation, calculated as the diﬀerence between the combined electronic and thermal enthalpies of the transition state at 298.15 K and 1

c

atmosphere, corrected for zero point energy, and the sum of the similar entropies of the substrate and oxidant. The length of the partial bond

d

between the S atom of the substrate and the proximal (transferred) O atom of the oxidant. The length of the partial bond between the proximal

e

and distal O atoms of the oxidant. The length of the partial bond between the ring-C and the proximal O atoms of the oxidant. The extent of

f

g

reaction at the transition state calculated by eqn (20). The gas-phase dipole moment of the transition state. The oxidant was dioxirane instead

h

i

of dimethyldioxirane. Derived from values reported by Baboul and co-workers in kcal mol^ꢁ1(ref. 24).

the activation barrier to its formation and vice versa. In

general, the gas-phase oxidations of sulfoxides exhibit lower

activation energy barriers than the oxidation of sulﬁdes, a

result that has also been obtained with other levels of theory.^24,40

For the O-atom transfer, the extent of reaction, x, may be

deﬁned by eqn (20):⁴¹

eqn (21) and eqn (22). As expected, the less reactive sulﬁdes do

show the reaction constant of larger absolute magnitude.

log [k₂(X)/k₂(H)]_S= ꢁ3.7s_p, R²= 0.986

log [k₂(X)/k₂(H)]_SO= ꢁ1.9s_p, R²= 0.996

(21)

(22)

z

r_{ðOpꢅꢅꢅOdÞ}ꢁ r_ð^R_OpꢁOdÞ

Table 13 gives additional calculated data concerning gas-phase

transition states. On formation of transition states with 1a

there are large percentage increases in the Mulliken charges on

sulﬁdic S together with increases in negative charge on the O

atoms of the dioxirane moiety, especially the distal O atom.

These increases are responsible for the large dipole moments

found for the sulﬁde-derived transition states (Table 12). The

sulfoxides show similar charge changes on the proximal O

atom to those of the sulﬁdes on transition state formation but

the changes at S and the distal O atom are smaller consistent

with their lesser dipole moments (Table 12) and the negative

charges on the sulfoxidic O atoms decrease due to their

transformation into sulfonic O atoms. The increases in charge

separation in transition states formed by both sulﬁdes and

sulfoxides indicate that the formation of the S–O bond and

breakage of the O–O bond are further advanced than the

changes to C–O bonds and that the asynchrony is more

marked for sulﬁdes than sulfoxides. Comparison of changes

to bond lengths bears this out: the percentage extensions of the

O–O bond length of the dimethyldioxirane moiety are 4–5 fold

greater than the corresponding changes to the C–O bond

lengths in the oxidation of both sulﬁdes and sulfoxides. The

S–O bond lengths in transition states formed by both sulﬁdes

and sulfoxides average 2.01 A (Table 12) but, expressed as

percentage extensions of S–O bonds in the reaction products,

they appear diﬀerent because sulfonic bonds are shorter than

sulfoxidic bonds (Table 10); the important point is that the

relatively short partial bond length, however expressed,

indicates signiﬁcant S–O bonding in both types of transition

state. The extent of O–O bond cleavage in transition states

that are sulﬁde-derived indicates that even in the gas phase, the

distribution of charge and bonding has a tendency towards the

sulfonium betaine structure 6a (Scheme 1).

x ¼

ð20Þ

z

ðr_{ðOpꢅꢅꢅOdÞ}ꢁ r^R_ðOpꢁOdÞÞ þ ðr_{ðSꢅꢅꢅOpÞ}ꢁ r_ð^P_SꢁOpÞ

Þ

in which r^z

is the length of the partial bond between

(Opꢅ ꢅ ꢅOd)

the proximal and distal O atoms in the dimethyldioxirane

moiety of the transition state; r^R

is the length of the

(OpꢁOd)

Op–Od bond in the reactant (oxidant), i.e. 1.506 A; r^z_{(Sꢅ ꢅ ꢅOp)}is

the length of the partial bond between S and the proximal O

atom in the transition state and r^P_(S–Op)is the length of the SO

bond in the product (see Table 10). The values of x tabulated

for the aryl methyl substrates indicate that, in the gas phase,

both oxidations have relatively early transition states (x o 0.5),

as in solution (see Section 2, above); that in each class, the

more reactive substrates manifest the earlier transition states

and that the transition states for sulfoxide oxidation occur

earlier in their reaction coordinate than those of sulﬁde

oxidation (x_SOo x_S). The behaviour of the substrates and

their derived transition states, summarised in Table 12, thus

accords with the Hammond postulate:³⁹the more exothermic

a reaction, the more its transition state resembles the reactants

in energy and geometry.

An expected consequence of ‘Hammond behaviour’ is that,

in the same reaction conditions, on comparing the reactivities

of diﬀerent substrates, the reactivity–selectivity principle

should apply; e.g. in Hammett correlations, the more reactive

substrates should give reaction constants of smaller absolute

magnitude than the less reactive. On the reasonable assumption

that, for gas-phase bimolecular processes, the entropy of

activation diﬀerences will be negligible, log [k₂(X)/k₂(H)]_S

and log [k₂(X)/k₂(H)]_SOcan be evaluated from the calculated

activation enthalpies for sulﬁdes and sulfoxides given in

Table 12; these give the (three-point) Hammett correlations

ꢀc

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Table 13 Percentage changes in Mulliken charges and bond lengths in transition states^a

b

c

d

e

f

g

h

i

Substrate

Dq_S

Dq_Op

Dq_Od

Dq_Oso

Dr_SOp

Dr_(Op–Od)

Dr_COp

Dr_COd

4-MeOPhSMe

PhSMe

4-O₂NPhSMe

PhSOMe

4-ClPhSOMe

4-NCPhSOMe

239.4

232.3

180.8

25.6

45.9

47.2

50.6

49.1

50.6

52.5

63.5

63.2

61.6

55.0

54.4

53.8

—

ꢁ11.7

ꢁ11.6

33.2

32.9

31.4

38.1

37.3

36.3

28.3

28.5

29.2

25.2

25.4

25.8

5.6

6.0

7.3

5.1

5.6

6.3

ꢁ5.6

ꢁ5.7

ꢁ6.1

ꢁ4.9

ꢁ3.4

ꢁ5.2

a

Percentages are calculated relative to the ground state parameter in each case; positive values are increases and negative values are decreases in

b

c

d

the absolute magnitude of the parameter. Increase in positive charge on S. Increase in negative charge on the proximal O atom of 1a. Increase

f

in negative charge on the distal O atom of 1a. Decrease in negative charge on the sulfoxidic O atom. Extension in the length of the product

e

g

h

i

S–O bond. Increase in the O–O bond length of 1a. Increase in length of the C to proximal O bond of 1a. Decrease in length of the C to

distal O bond of 1a.

6.3 Modelling transition state solvation. The Hammett

reaction constants for sulﬁdes and sulfoxides, ꢁ3.7 and ꢁ1.9,

respectively, found above from calculations for gas-phase

reactions, contrast with the experimental values of ꢁ0.76

and ꢁ0.78 found for sulﬁdes and sulfoxides, respectively, for

reactions in acetone solution;^6amoreover, the sulfoxides were

found to be less reactive than sulﬁdes.^6bIn order to gain

insight into these diﬀerences, the eﬀects of solvation by

acetone were simulated at the B3-LYP/6-31G* level by single

point self-consistent reaction ﬁeld (SCRF) calculations with

Tomasi’s polarised continuum model³³(PCM) using the gas-

phase B3-LYP/6-31G* optimised geometries as implemented

in Gaussian 98. Caution is required in the interpretation of

these results as they relate to single point calculations on the

optimised gas-phase structures and not to re-optimisations in

the simulated medium; for this reason no bond lengths or

derived x values for the solution phase are given. In view of the

inversion in relative reactivity of sulﬁdes and sulfoxides between

the theoretical gas phase and the experimental solution phase,

the PCM calculations investigated the inﬂuence of the medium

on the activation barriers to the oxidations of PhSMe and

PhSOMe by 1a.

activation enthalpies and in the phase-transfer enthalpies of

their initial states eqn (24):

{[DH^z] ꢁ [DH^z] } = {[DH^z] ꢁ [DH^z] }

s SO

s S

g SO

g S

+ {[D_g-s(H1)_IS]_SOꢁ [D_g-s(H1)_IS]_S}

(24)

Since the sulfoxide has the lower gas-phase activation barrier

(Table 14a), the inversion in relative reactivity found for

reaction in solution (where [DH^z] > [DH^z] ) must arise

s SO

s S

from a positive diﬀerence in the phase-transfer enthalpies of

their initial states out-weighing the negative diﬀerence in their

gas-phase activation enthalpies. As the initial states each

comprise one mole of 1a and one mole of substrate, the

diﬀerence in the phase-transfer enthalpies stems from the

diﬀerence in ground state solvation of the two substrates:

the inversion in relative reactivity of PhSMe and PhSOMe

between the two phases occurs because solvation of the

sulfoxide is more exothermic than that of the sulﬁde.

This conclusion depends on the equality of D_g-s(H1)_TSfor

these two substrates and it is relevant to enquire why this

should occur. At ﬁrst sight, it might be expected that the

transition state diﬀerence [D_g-s(H1)_{TS SO}

]

ꢁ [D_g-s(H1)_{TS S}

]

should be greater than zero, as in the case of the initial-state

diﬀerence, owing to solvation of the S⁺–O^ꢁbond, but this

ignores the large increase in charge separation on passage from

the ground state to the transition state in the case of the

sulﬁde. As shown in Table 14b, the percentage increase in

Mulliken positive charge on S is 232% for the gas phase rising

to 329% in solution with corresponding negative charge

increases of 63.2% and 74.5% on the distal oxygen atom.

There is thus an increase of B100% in the positive charge on S

and B10% in the negative charge on distal O on transfer of

the transition state from the gas phase to solution. This change

in charge distribution is reﬂected in the dipole moments

(Table 14c). Comparison of the changes in dipole moments

shows increases for both substrates on transfer from the gas to

solution phase with the greater increase for the sulfoxide, i.e.

Table 14a gives relevant enthalpy changes. For a reaction in

a particular phase, the datum from which the enthalpy of

reaction, D_rH1, and the enthalpy of activation, DH^z, are

measured is, of course, the total enthalpy of the reactants in

their ground states (the initial state, IS); on the other hand, the

datum for the enthalpies of transfer of any state from the gas

phase to solution in acetone is the total enthalpy of the

particular state in the gas phase. Fig. 8 illustrates how the

absolute magnitudes of these enthalpy changes are related.

For both substrates, the enthalpy of activation for reaction in

solution, DH^z, is given, in terms of absolute magnitudes, by

s

eqn (23).

DH^z= DH^z+ D_g-s(H1)_ISꢁ D_g-s(H1)_TS

(23)

s

g

D

_S-SOD_g-s(m_IS)/D is +0.40. This is consistent with the larger

The attenuation of the gas-phase activation enthalpy DH^zto

magnitude of D_g-s(H1)_IScalculated for the sulfoxide. The

transition states also show an increase in dipole moment on

transfer from the gas to solution phase, consistent with their

stabilisation by solvation but, in the case of the sulfoxide-

derived transition state, the increase is smaller than that of

the sulﬁde-derived transition state, i.e. D_S-SOD_g-s(m_TS)/D is

g

the solution value thus depends on the magnitudes of the

phase-transfer enthalpies of the initial and transition states.

Fortuitously, for both substrates, the phase-transfer enthalpies

of the transition state, D_g-s(H1)_TS, are equal, hence their

relative reactivity depends on the diﬀerence in their gas-phase

ꢀc

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Fig. 8 Enthalpy changes calculated for oxidations by dimethyldioxirane (a) PhSMe; (b) PhSOMe.

negative (ꢁ0.44) by a similar amount to the positive diﬀerence

found for the initial state. The solvation of the relatively

enhanced dipole of the sulﬁde-derived transition state will there-

fore negate that of the S⁺–O^ꢁbond in the sulfoxide-derived

In terms of absolute magnitudes, the ﬁrst diﬀerence is negative

(Table 14a) and it is probable that the second diﬀerence is

positive for many pairs of substrates (as in the case for

PhSOMe and PhSMe) on account of the polarity of the

S⁺–O^ꢁbond but, in cases of direct conjugation between

SMe and a 4-substituent of ꢁM type, it may be that the dipole

moment of the sulﬁde is greater than that of the like-substituted

sulfoxide (see 12 and Table 10) with the possibility that

[D_g-s(H1)_IS]_S> [D_g-s(H1)_IS]_SOand the second diﬀerence

may then be negative. On activation, sulﬁdes show the greater

changes in Mulliken charges (Table 13) thus, notwithstanding

the zero value of the third diﬀerence for PhSMe and PhSOMe,

transition state so reducing [D_g-s(H1)_{TS SO}

zero. It does not necessarily follow, however, that the comparable

diﬀerence is zero for all other ArSMe and ArSOMe.

]

ꢁ [D_g-s(H1)_TS]_Sto

In solution, the aryl methyl sulfoxides are less reactive towards

1a than the corresponding sulﬁdes [e.g. values of k₂(X)_S/k₂(X)_SO

lie in the range 81–86]^6bi.e. [DH^z] > [DH^z] hence the in-

s SO

s S

equality (25), comprising three diﬀerences, follows from eqn (23).

{[DH^z] ꢁ [DH^z] } + {[D_g-s(H1)_IS]_SOꢁ [D_g-s(H1)_IS]_S}

g SO

g S

it is probable, generally, that [D_g-s(H1)_TS]_S> [D_g-s(H1)_{TS SO}

]

ꢁ {[D_g-s(H1)_{TS SO}

]

ꢁ [D_g-s(H1)_TS]_S} > 0 (25)

and the third diﬀerence makes a positive contribution to the

ꢀc

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Table 14 (a) Comparison of various enthalpies for reactions of PhSMe and PhSOMe with 1a in the gas phase and acetone solution as calculated

by B3-LYP/6-31G* DFT. (b) Comparison of changes in Mulliken charges in the transition states of the reactions of PhSMe and PhSOMe with 1a

in the gas phase and in acetone solution as calculated by B3-LYP/6-31G* DFT. (c) Comparison of the molecular dipole moments of PhSMe and

PhSOMe and their derived transition states with 1a and of their changes on transfer from the gas phase to acetone solution and on oxidation

(a) Reactants

Phase

D_rH1/kJ mol^ꢁ1a

DH^z/kJ mol^ꢁ1b

D

_g-s(H1)_IS/kJ mol^ꢁ1c

D

_g-s(H1)_TS/kJ mol^ꢁ1d

D

_g-s(H1)_FS/kJ mol^ꢁ1e

PhSMe + 1a

PhSOMe + 1a

Gaseous

Solution

Gaseous

Solution

ꢁ157.5

ꢁ162.3

ꢁ261.7

ꢁ270.4

40.9

30.4

37.2

31.9

—

ꢁ16.9

—

ꢁ27.3

—

ꢁ21.7

—

ꢁ22.1

—

ꢁ27.3

—

ꢁ30.7

(b) Reactants

Phase

Dq_S/e^f

Percent^g

Dq_Op/e^h

Percentⁱ

Dq_Od/e^j

Percent^k

Dq_Oso/e^l

Percent^m

PhSMe + 1a

PhSOMe + 1a

Gaseous

0.309

0.362

0.196

0.205

232

329

25.6

27.0

ꢁ0.150

ꢁ0.137

ꢁ0.156

ꢁ0.143

47.2

41.0

49.1

42.8

ꢁ0.201

ꢁ0.249

ꢁ0.175

ꢁ0.212

63.2

74.5

55.0

63.5

—

0.074

0.086

—

Solution

Gaseous

Solution

ꢁ11.7

ꢁ13.2

(c) Substrate

Phase

m

_IS/Dⁿ

D

_g-s(m_IS)/Dⁿ

D_S-SO

D

_g-s(m_IS)/Dⁿ

m

_TS/D

D_g-s(m_TS)/D

D_S-SO

D

_g-s(m_TS)/D

PhSMe

PhSOMe

Gaseous

Solution

Gaseous

Solution

1.413

1.733

3.917

4.641

—

0.404

6.453

8.401

5.246

6.758

—

ꢁ0.436

0.320

—

0.724

1.948

—

1.512

a

Standard enthalpy of reaction, calculated as the diﬀerence between the sum of combined electronic and thermal enthalpies of the products at

b

298.15 K and 1 atmosphere, corrected for zero point energy, and the sum of the similar entropies of the substrate and oxidant. Enthalpy of

activation, calculated as the diﬀerence between the combined electronic and thermal enthalpies of the transition state at 298.15 K and 1

c

atmosphere, corrected for zero point energy, and the sum of the similar entropies of the substrate and oxidant. Change in combined standard

d

enthalpies of the initial state (reactants) on transfer from the gas phase to solution in acetone. Change in standard enthalpy of the transition state

e

on transfer from the gas phase to solution in acetone. Change in combined standard enthalpies of the ﬁnal state (products) on transfer from the

f

gas phase to solution in acetone. Change relative to the ground state value of the organo-sulfur substrate (PhSMe: q_Sg= 0.133e, q_Ss= 0.110e;

g

h

PhSOMe: q_Sg= 0.765e, q_Ss= 0.759e). Percentage increase in positive charge on S. Change relative to an O atom of 1a (q_Og= ꢁ0.318e,

i

j

q

_Os= ꢁ0.334e). Percentage increase in negative charge on the proximal O atom of 1a. Change relative to an O atom of 1a (q_Og= ꢁ0.318e, q_Os

=

k

l

ꢁ0.334e). Percentage increase in negative charge on the distal O atom of 1a. Change relative to the sulfoxidic O atom of PhSOMe (q_Oso,g= ꢁ0.631e,

m

n

q_Oso,s= ꢁ0.653e). Percentage decrease in negative charge on the sulfoxidic O atom of PhSOMe. Here the initial state excludes 1a.

inequality. The value of k₂(NO₂)_S/k₂(NO₂)_SOis 85.7,^6bthe

largest ratio observed for any substituent. If the second

diﬀerence in inequality (25) is negative for this ꢁM substituent,

the negative sum of the ﬁrst two diﬀerences is clearly more

than compensated by a positive third diﬀerence. The reversal

of relative reactivity of sulfoxides and sulﬁdes towards 1a

between the gas and solution phases thus stems from a

combination of factors, the principal of which are a greater

ground state stabilisation by solvation in the case of sulfoxides

due to their polar S⁺–O^ꢁbonds and a greater transition state

stabilisation by solvation in the case of sulﬁdes, the latter made

possible by the enhanced charge separation that develops as a

consequence of more asynchronous bond scission.

atom of 1a and the ordinate represents decrease in the distance

between the S atom and the proximal O atom of 1a. The lower

left corner (origin) corresponds to the reactants in their ground

state and is thus an energy minimum; the upper right corner

corresponds to the products in their ground states and is also

an energy minimum. Four pathways between reactants and

products are indicated (two two-step paths aa⁰, bb⁰and two

concerted paths c and d). Change along the abscissa (path a) is

accompanied by a steep increase in energy followed by a

shallow decrease as 1a undergoes fragmentation to acetone

and the high-energy intermediate oxene. Change along the

ordinate (path b) also marks an increase in energy followed by

a shallow decrease as the charges of the intermediate sulfonium

betaine separate. Concerted reaction coordinates pass directly

from the lower left to the upper right. If all the bonding

changes were to occur in synchrony (at the same rate), the

saddle-point of the synchronous transition state, TS_syn, would

occur in the centre of the diagonal (path c, x = 0.500).

However, our calculations have shown that formation of the

S–O bond and breaking of the O–O bond are in advance of the

changes to bonding at C, hence the saddle-point of the

6.4 Anti-Hammond behaviour. Above (Section 6.2),

calculations showed that in the gas phase the oxidations of

sulﬁdes and sulfoxides by 1a exhibit Hammond behaviour.

The inversion of relative reactivity in solution therefore must

result from a switch to ‘anti-Hammond’ behaviour by at least

one of them; such a switch is usually explained in terms of

factors that displace a transition state away from the reaction

coordinate between reactants and products.³⁹

asynchronous transition state, TS_asyn

, occurs displaced

towards the upper left corner and at a distance less than

half-way along the reaction coordinate, path d (x = 0.463,

Table 12). Our previous studies of the reaction in acetone

solution⁶have shown that the introduction of an aqueous

component to the solvent increases the betaine-like character

Fig. 9 is a qualitative potential energy-surface (PES)

diagram^39,42for the gas-phase oxidation of PhSMe by 1a;

the actual energy coordinate is not given explicitly being

perpendicular to the page. The abscissa represents decrease

in the bond length between the ring-C atom and the distal O

ꢀc

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their +I eﬀects, assist the development of a transition state

which is more polarised than the reactants but, sterically, they

hinder its solvation; for bulky groups the hindrance outweighs

the stabilisation.

2. The rate constants for the oxidation of alkyl 4-nitrophenyl

and dialkyl sulfoxides by 1a are also sensitive to the +I eﬀects

of alkyl groups as both ground states and transition states are

polar. The polarity of both states leads to their solvation but

this is hindered by bulky alkyl groups. Hindrance to solvation

of the ground state is rate-enhancing whereas hindrance to

that of the transition state is rate-inhibiting. For the subsets of

alkyl 4-nitrophenyl sulfoxides and dialkyl sulfoxides these

hindering factors cancel but, when the range of sulfoxides is

expanded to include other aryl methyl sulfoxides and cyclic

sulfoxides, a steric acceleration of oxidation may be discerned

statistically.

Fig. 9 Qualitative potential energy-surface diagram for the oxidation

3. Comparisons of activation parameters show that, on

oxidation by 1a, alkyl 4-nitrophenyl sulﬁdes exhibit lower

activation enthalpies than sulfoxides owing to the diﬀerence

in energy of their nucleophilic sulfur lone pairs. Activation

entropy diﬀerences between sulﬁdes and sulfoxides reﬂect the

diﬀerence in the solvation patterns for the two oxidations.

4. The oxidation of saturated cyclic sulﬁdes by 1a is

independent of ring strain energies and the pattern of rate

constants is well accounted for in frontier orbital terms. By

contrast, rate constants for the oxidation of analogous

cyclic sulfoxides show a dependence on the change in ring

strain energy between reactant and product but there is

also statistical evidence that an additional ring size-

dependent factor aﬀects the transition states for 4- to

6-membered rings.

of PhSMe by dimethyldioxirane.

of the transition state by lone pair donation at S and hydrogen

bonding at O so enhancing the anti-Hammond behaviour: the

absolute magnitude of the Hammett reaction constant is

increased (from ꢁ0.76 in acetone to ꢁ1.33 in 5% v/v aqueous

acetone) and a decrease in the value of x is expected.

Ultimately, with the addition of suﬃcient water (20% v/v),

the betaine 6a is suﬃciently stabilised to occur as a real

reaction intermediate (path bb⁰). In terms of Fig. 9, speciﬁc

aqueous solvation of the betaine converts the shallow energy

minimum of the upper left corner into a deeper minimum with

the energy maximum between the two left-hand corners

decreasing and receding towards the origin.

The PES diagram for the gas-phase oxidation of PhSOMe

by 1a is similar to Fig. 9: the bonding changes are asynchronous

(x = 0.403, Table 12). However, the changes on transfer of the

reaction to acetone solution diﬀer from those of PhSMe.

Although the gas-phase TS_asynhas some betaine-like character,

the response of the PES to solvent variation is diﬀerent.

Solvation of the polar S⁺–O^ꢁbond results in a deepening of

the energy minimum at the origin, a change which will shift

TS_asynalong the reaction coordinate towards the products

with an associated increase in the magnitude of x, i.e. Hammond-

behaviour. Experimentally, a 20% v/v addition of water has

scant eﬀect on the Hammett reaction constant (it is reduced in

magnitude from ꢁ0.78 to ꢁ0.70)^6aand there is no speciﬁc

stabilisation to produce a real sulfoxonium betaine intermediate,

PhS⁺(O)OCMe₂O^ꢁ.^6bThe upper left corner of the diagram

stays high in energy relative to the saddle-point of TS_asynand

the reaction remains concerted. Owing to the mentioned

limitations of our PCM calculations we cannot give modiﬁed

x values but in Section 4.4 we inferred that, in solution, sulﬁdes

manifest earlier transition states than sulfoxides (i.e. x_So x_SO).

The modelling of the eﬀect of solvation by acetone thus

strongly supports the inferences drawn from our present and

prior experimental mechanistic studies.

5. Calculations at the B3-LYP/6-31G* level of density

functional theory have been performed on a range of

4-substituted-phenyl alkyl, dialkyl and cyclic sulﬁdes and

sulfoxides. The reactivities of 40 of these have been correlated

using a combination of quantum mechanical and empirical

parameters (Mulliken charge on S, q_S; substituent eﬀects, Ss*;

and ring strain diﬀerences between reactant and product,

DE_rs). Sulﬁdes and sulfoxides must b₀e treated separately in

order to account for steric eﬀects, SE_sand the reciprocals of

the frontier orbital energy diﬀerences, F/eV, are relevant only

to sulﬁdes.

6. Calculations at the B3-LYP/6-31G* level of density

functional theory have been performed for the transition states

formed by three aryl methyl sulﬁdes and three aryl methyl

sulfoxides on oxidation by 1a and the nature of charge

and bonding changes explored. For both types of substrate,

formation of the S–O bond and scission of the O–O bond

occur ahead of bonding changes at C but these changes are

more marked for sulﬁde-derived transition states. The calculations

indicate sulfoxides to be more reactive than sulﬁdes in the

gas phase.

7. The application of Tomasi’s PCM model to the gas-phase

transition state structures allows simulation of solvation by

acetone. It is shown how solvation accentuates diﬀerences

between sulﬁdes and sulfoxides by inducing anti-Hammond

behaviour in the former, and inverting their relative reactivity.

The calculations give strong support to the conclusions

reached by physical-organic reasoning.

Conclusions

1. The rate constants for the oxidation of alkyl 4-nitrophenyl

and dialkyl sulﬁdes by 1a are sensitive to variation in alkyl

group structure. In both series of sulﬁdes alkyl groups, by

ꢀc

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(25% v/v H₂O) was added an aqueous solution of NaIO₄

(1.0 cm³, 4.5 ꢃ 10^ꢁ3mol dm^ꢁ3). After shaking, the mixture

was allowed to stand overnight (ca. 16 h) at 298 K and the

sulfoxide product ratio was then found by GC with 1,4-

dibromobenzene as internal standard and used to evaluate

k(3)_S/k(6)_Sas previously described.^6aThe oxidation was

repeated 3 times and the average value of k(3)_S/k(6)_Sfound

to be (0.43 ꢂ 0.03). This value together with those for k₂(6)_S

Experimental

Instrumental methods

Our previous papers⁶give details of the instrumentation and

procedures used in the characterisation of reactants and

products. The procedures include the determination by GC

of relative rate constants from the product ratios of competitive

oxidations of sulﬁdes and sulfoxides by 1a, and the spectro-

photometric determination of absolute rate constants for the

oxidations of substrates bearing a 4-nitrophenyl chromophore

under both pseudo-ﬁrst order and second order conditions.

and k₂(n-Pr)_2,S[0.399 dm³mol^ꢁ1s^ꢁ1and 0.237 dm³mol^ꢁ1s^ꢁ1

,

respectively (cf. ESIw 4, Table S8)],⁹allows evaluation of

k(3)_S/k(n-Pr)_2,Sfor periodate oxidation as 0.72 (see Fig. 2)

and also k₂(3)_Sas 0.17 dm³mol^ꢁ1s^ꢁ1

.

Acquired materials

Acknowledgements

Organic solvents were supplied by Fisher and were of

analytical or HPLC grade. Methyl phenyl sulﬁde, its 4-nitro-

derivative, ethylene sulﬁde (thiirane), tetramethylene sulﬁde

(tetrahydrothiophen, thiolane), pentamethylene sulﬁde (thiane),

di-(n-propyl) sulﬁde, di-(tert-butyl) sulﬁde and other reagents

were purchased in the highest available purity (Aldrich, Fluka

or Lancaster); liquid sulﬁdes were distilled before use. Methyl

phenyl sulfoxide and sulfone (Aldrich) were further puriﬁed by

column chromatography (silica, 10% v/v acetone in CH₂Cl₂).

The water used was deionised.

We thank AstraZeneca for a studentship (RAAJH) and

Dr A. M. Davis and Dr N. Gensmantel for their interest

and encouragement. We are grateful to Professor J. E. McGrady

for the provision of facilities, help and advice with the DFT

calculations and to Dr A. C. Whitwood for advice and help

with IT.

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84 | New J. Chem., 2010, 34, 65–84

Article Doi

A kinetic investigation, supported by theoretical calculations, of steric and ring strain effects on the oxidation of sulfides and sulfoxides by dimethyldioxirane in acetone

DOI: 10.1039/b9nj00452a

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