Activation of the disulfide bond and chalcogen-chalcogen interactions: An experimental (FTICR) and computational study

Article abstract of DOI:10.1002/chem.200600733

Dimethyldisulfide (I) is the simplest model of the biologically relevant family of disubstituted disulfides. The experimental study of its gas-phase protonation has provided, we believe for the first time, a precise value of its gas-phase basicity. This value agrees within 1 kJmol^-1 with the results of G3 calculations. Also obtained for the first time was the reaction rate constant for the bimolecular reaction between I and its protonated form, IH⁺, to yield methanethiol and a dimethyldithiosulfonium ion. This constant is of the order of magnitude of the collision limit. A computational mechanistic study based on the energetic profile of the reaction, completed with Fukui's and Bader's treatments of the reactants and transition states fully rationalizes the regioselectivity of the reaction as well as the existence of a shallow, flat Gibbs energy surface for the reaction. The mechanistic relevance of the chalcogen-chalcogen interaction and the C-H...S bonds has been demonstrated.

Full text of DOI:10.1002/chem.200600733

DOI: 10.1002/chem.200600733
Activation of the Disulfide Bond and Chalcogen–Chalcogen Interactions:
An Experimental (FTICR) and Computational Study
M’Hamed Esseffar,*[a] Rebeca Herrero,[b] Esther Quintanilla,[b] Juan Z. Dµvalos,[b]
Pilar JimØnez,[b] JosØ-Luis M. Abboud,*[b] Manuel YµÇez,[c] and Otilia Mó[c]
Abstract: Dimethyldisulfide (I) is the
simplest model of the biologically rele-
vant family of disubstituted disulfides.
The experimental study of its gas-phase
protonation has provided, we believe
for the first time, a precise value of its
gas-phase basicity. This value agrees
within 1 kJmolꢀ1 with the results of G3
calculations. Also obtained for the first
time was the reaction rate constant for
the bimolecular reaction between I and
its protonated form, IH+, to yield
methanethiol and a dimethyldithiosul-
fonium ion. This constant is of the
order of magnitude of the collision
study based on the energetic profile of
the reaction, completed with Fukuiꢀs
and Baderꢀs treatments of the reactants
and transition states fully rationalizes
the regioselectivity of the reaction as
well as the existence of a shallow, flat
Gibbs energy surface for the reaction.
The mechanistic relevance of the chalc-
limit.
A computational mechanistic
Keywords: basicity · bond activa-
tion · chalcogen–chalcogen interac-
tions · FTICR · gas-phase reactions ·
MP2 calculations
ꢀ
ogen–chalcogen interaction and the C
H···S bonds has been demonstrated.
Introduction
protein folding,[3] it is clear that its activation is relevant
from the fundamental and applied points of view.
Initial experimental studies of the disulfide exchange re-
action [Eq. (1)] in solution,
It has been known for some time that the disulfide group
(S S) is an important constituent of many proteins.
[1–3]
ꢀ
Quite recently, the study of the mechanism of the action of
proton pump inhibitors (PPIs) has revealed that these com-
pounds are prodrugs that inhibit the acid-secreting gastric
(H+,K+)-ATPase by acidic activation to reactive thiophilic
species that form disulfide bonds with one or more cysteines
accessible from the exoplasmic surface of the enzyme.[4] Ir-
respective of the potential relevance of the disulfide bond in
R1SSR1 þ R2SSR2 ! 2R1SSR2
ð1Þ
led us to consider the protonated form of these compounds,
(RSSR)H+ as a key reactive species in this reaction (the
overall process in solution might well be a complex one).[5]
In a classical study by means of ion cyclotron resonance
(ICR)[6] Caserio, Kim and Bonicamp[7] carefully examined
the gas-phase protonation of dimethyldisulfide, CH3SSCH3
(I), by protonated reference bases, BrefH+, see Equation (2).
[a] Prof. Dr. M. Esseffar
DØpartement de Chimie, FacultØ des Sciences (Semlalia)
UniversitØ Cadi Ayyad, Marrakesh (Morocco)
Fax : (+212)24437408
IðgÞ þ BrefHþðgÞ ! IHþðgÞ þ BrefðgÞ
ð2Þ
[b] M.Sc. R. Herrero, Dr. E. Quintanilla, Dr. J. Z. Dµvalos,
Dr. P. JimØnez, Prof. Dr. J.-L. M. Abboud
Instituto de Química Física Rocasolano
CSIC. C/Serrano 119, 28006 Madrid (Spain)
Fax : (+34)915855184
These authors found that IH+ (m/z=95) reacts extremely
fast with the neutral I present in the ICR cell to yield dime-
thyldithiosulfonium ion (II+) (m/z=141), see Equation (3).
ðCH3ꢀSHꢀSꢀCH3Þþ þ CH3ꢀSꢀSꢀCH3ðgÞ !
ð3Þ
E-mail: iqrla78@iqfr.csic.es
[c] Prof. Dr. M. YµÇez, Prof. Dr. O. Mó
ðCH3ꢀSðSCH3ÞꢀSꢀCH3ÞþðgÞ þ CH3SHðgÞ
Departamento de Química C-9 Universidad Autónoma de Madrid
Canto Blanco, 28049 Madrid (Spain)
In fact, this reaction proceeded so fast after the formation
Supporting information for this article is available on the WWW
under http://www.chemeurj.org/ or from the author.
of IH+ that they could only give a bracketing estimate of
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Chem. Eur. J. 2007, 13, 1796 – 1803

FULL PAPER
the gas-phase basicity (GB) of I,[8] GB(I)=764–
781 kJmolꢀ1.[9]
Relative intensities of the ion signals are taken as directly proportional
to the relative abundances (or partial pressures) of the various ionic spe-
cies. In this study, the temporal evolution of the relative intensities of
ions BrefH+, IH+, and II+ was monitored. The temperature of the cell, as
determined by a platinum resistor was 323 K.[10c,14]
To our knowledge, the determination of GB(I) has not
been attempted again and the mechanism of the reaction in
Equation (3) has not yet been established. On account of
the relevance of the disulfide bond, we have carried out a
systematic experimental study of the reactions in Equa-
tions (2) and (3) by using Fourier Transform Ion Cyclotron
Resonance spectrometry (FTICR) as well as a computation-
al study of both processes.
The ion gauge was calibrated by measuring the rate constant for the reac-
tion in Equation (9)[14]
þ
½CH3OHꢁþC þ CH3OH ! CH3OC þ CH3OH2
ð9Þ
and by considering that for this process the rate constant equals (2.30ꢂ
[10c]
0.29)”10ꢀ9 cm3 moleculeꢀ1 sꢀ1
.
Under the experimental working conditions, PI is constant in each experi-
ment and the reaction in Equation (4) is of pseudo first order. From a
series of experiments involving different pressures of I, k1PI values were
obtained by using the logarithmic form of Equation (6). From the direct
proportionality with PI, they provided values of k1. They were used to de-
termine k2 by means of Equations (7) and (8).
Experimental Section
Materials: n-Butyl trifluoroacetate was obtained from the reaction be-
tween trifluoroacetic anhydride and n-butanol. Its final purification stage
was a distillation through a Perkin–Elmer adiabatic spinning band annu-
lar still (100 theoretical plates). Malononitrile (Fluka) was sublimed
twice. All other products were of commercial origin (Aldrich) and of the
highest purity available.
Figure 1 is a representative plot of the experimental kinetic information
obtained by using ethyl formate, HCOOC2H5, as Bref. Species BrefH+,
IH+, and II+ have m/z values of respectively 75, 95, and 141. The pattern
Gas-phase studies
The FTICR spectrometer: In this work, use was made of a modified
Bruker CMS 47 FTICR mass spectrometer. A detailed description of the
original instrument is given in reference [6d]. It has already been used in
a number of studies.[10] Some salient features are as follows: the spec-
trometer is linked to an Omega Data Station (Ion Spec, CA). The high-
vacuum is provided by a Varian TURBO V550 turbomolecular pump
(550 Lsꢀ1). The magnetic field strength of the superconducting magnet is
4.7 T.
Working conditions: Mixtures of I and a reference base Bref of known
gas-phase basicity were introduced into the high-vacuum section of the
instrument. Typical partial pressures were in the range of 1”10ꢀ8–5”
10ꢀ7 mbar. The average temperature of the cell was approximately 323 K.
The mixture was ionized by electron ionization, using energies in the
range of 12–20 eV and ionic fragments of I and Bref acted as proton sour-
ces (chemical ionization). In all cases, approximately 1”10ꢀ6 mbar of
argon were added. After reaction times of 2–5 s, ions
B
refH+ thus
formed, were isolated by means of ion-selection techniques and reacted
with I for times of up to 120 s (depending on the acidity of BrefH+). It
was established in all cases that the reactions in Equations (2) and/or (3)
were the only observed processes.
Figure 1. Temporal evolution of the relevant ion intensities. Bref
=
HCO2Et. PI =3.3”10ꢀ8 mbar (nominal pressure).
The pressures of the neutral species were measured with a Bayard–
Alpert ion gauge. Readings were corrected according to the method of
Bartmess and Georgiadis,[11] by using for each compound, the polarizabil-
shows that the reactions in Equations (2) and (3) are consecutive process-
es, as indicated in reference [5]. A value k1PI of 0.535 sꢀ1 is obtained
from the decay of BrefH+ by using the logarithmic form of Equation (6).
Insertion of this value into Equations (7) and (8) leads to an average
value of k2PI of 0.621 sꢀ1. The curves shown were constructed with these
values. Formal uncertainties on k1 and k2 are estimated at approximately
10 and 17% respectively. In the case of the last three reference bases,
only k1 values can be determined. Uncertainties on these values can be
estimated at 20–30%.
ities, a
(ahc) calculated following Millerꢀs method.[12]
G
Kinetic studies: Elementary processes in Equations (2) and (3) follow
second order kinetics. Let k1 and k2, respectively, stand for their respec-
tive reaction rates. Equations (4) and (5) express this fact:[13]
dPBrefHþ
dt
ð4Þ
ð5Þ
¼ ꢀk1PBrefHþPI
Computational methods: All calculations were performed by using the
programs Gaussian 98 and 03.[17, 18] The gas-phase basicity of I was calcu-
lated at the G3 level of theory[19] to ensure a reliable estimate of this
magnitude. A cheaper approach was used to carry out the theoretical
survey of the potential energy surface (PES) associated with the reaction
in Equation (3) The geometries of all stationary points were optimized at
dPIHþ
dt
¼ k1PBrefHþPIꢀk2PIPIHþ
Equations (6)–(8) follow:
the MP2/6-31G
(d,p) level.[20]
A
PBrefHþ ¼ ðPBrefHþÞinitexpðꢀk1PItÞ
ð6Þ
ð7Þ
In all cases, frequencies were calculated to ensure that the optimized
structural parameters correspond to the equilibrium geometries in the
case of the minima and to a first-order saddle point in the case of transi-
tion states.
ꢀ
ꢁ
k1
ðk2ꢀk1
PIHþ ¼ ðPBrefHþÞinit
½expðꢀk1PItÞꢀexpðꢀk2PItÞꢁ
ꢀ
ꢁ
1
The harmonic vibrational frequencies obtained at this level, corrected ac-
cording to Radom scale factors,[21] were used to obtain the zero-point vi-
PIIþ ¼ ðPBrefHþÞinit
½k2expð1ꢀk1PItÞꢀk1expð1ꢀk2PItÞꢁ
ð8Þ
ðk2ꢀk1Þ
Chem. Eur. J. 2007, 13, 1796 – 1803
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1797

J.-L. M. Abboud, M. Esseffar et al.
brational energies (ZPE), thermal correction to enthalpy (TCH) and en-
Consider the proton transfer between two bases, M and
the reference base Bref, respectively, Equation (10):
tropies (Smꢃ).
In all cases, the intrinsic reaction coordinate (IRC)[22] path was construct-
ed to check the energetic profile connecting each transition structure to
the two associated minima of the proposed mechanism.
M þ ½BrefHꢁþ ! ½MHꢁþ þ Bref
DrGmꢃð10Þ
ð10Þ
The MP2/6-31G
311+G
(d,p) level.[22] Finally, single-point energy calculations at the MP2/
6-311+G
(3df,2p) level were performed on these optimized structures.[23]
Electrophilic and nucleophilic Fukui functions[24] condensed to atoms
were evaluated from single-point calculations performed on the ground-
state structures of molecules as optimized at the same level of theory.
Fukui functions were evaluated by using the coefficients of the frontier
molecular orbitals (FMOs) involved in the reaction and the overlap
matrix.
The global electrophilicity,[25] w=(m2/2h), is defined in terms of the chem-
ical potential m and the chemical hardness h.[26] Both quantities may be
expressed in terms of the one-electron energies of the HOMO and
LUMO molecular orbitals, eH and eL, as m=(eH +eL)/2 and h=(eLꢀeH).[27]
A
Some years ago, Bouchoux and co-workers[29] drew attention
to the fact that a correlation of the form of Equation (11) is
observed between the experimental rate constant for this re-
action, k, and the standard Gibbs energy change for reaction
(10), DrGmꢃ(10).
ACHTREUNG
ACHTREUNG
k
kcoll
1
1 ¼
¼
ð11Þ
1 þ exp½ðDrGmꢃð10Þ þ DrGꢃaÞ=RTꢁ
In this expression, kcoll stands for the collision rate constant
and DrGꢃa is an apparent activation energy for Equation (10).
This apparent activation energy is expected to be small and
independent of the base Bref. DrGmꢃ(10) is the difference be-
tween the gas-phase basicities of Bref and M, DrGmꢃ(10)=
Results and Discussion
GB
process.
Although the reaction in Equation (10) occurs at a low
A
Experimental results
We summarize in Table 1 the experimental values of k1
and k2 obtained as indicated above.
pressure and thus under single-collision conditions in which
a temperature cannot be maintained by gas collisions, Bou-
choux et al.[29] ascribed an effective temperature, T*, to the
collision complex, in a manner similar to that of Cooks[30] in
the kinetic method. An effective temperature of about
550 K appears to describe adequately most experimental re-
sults. Bouchoux and co-workers parameterized Equa-
tion (11) in terms of parameters that depend only on the
properties of M and not on the nature of the base and thus
suggested the use of Equation (12) as a general expression
for the study of the relationship between 1 and DrGmꢃ(10).
Table 1. Kinetic results pertaining to the protonation of I.
[a]
[a,b,c]
[a,d]
[a]
[a,d]
Bref
GB
[Bref
]
k1
11norm
k2
H2O
660.0
694.1
733.8
764.8
768.4
773.9
777.5
784.8[f]
790.7
2.58ꢂ0.26
1.00
1.00
0.87ꢂ0.15
0.87ꢂ0.15
0.82ꢂ0.14
0.93ꢂ0.16
0.93ꢂ0.16
0.86ꢂ0.15
CH2(CN)2
CF3CO2nBu
n-C4H9CHO
HCO2Et
HCO2nPr
c-C3H5CN
CH3COCH3
CH3CO2Me
Average k2
1.55ꢂ0.16
1.30ꢂ0.13
0.987
0.819
0.530
0.198
0.116
1.05ꢂ0.11
0.842ꢂ0.084
0.284ꢂ0.028
0.189ꢂ0.019
0.028ꢂ0.006
0.011ꢂ0.003
[e]
–
–
–
[e]
0.0162
0.0080
[e]
0.87ꢂ0.12[g]
a
a
[a] Defined in the text. [b] In kJmolꢀ1. [c] From reference [9]. [d] In units
of 10ꢀ9 cm3 moleculeꢀ1 sꢀ1. [e] See text. [f] See ref. [28]. [g] Uncertainty
taken as three standard deviations.
1 ¼
¼
1 þ exp½bðDrGmꢃð9Þ þ cÞꢁ 1 þ exp½bðGBðBrefÞꢀGBðMÞ þ cÞꢁ
ð12Þ
It was found that in general, the normalization factor a
equals (0.90ꢂ0.05) and b=1/RT* amounts to (3.8ꢂ
1.0) kJꢀ1 mol. c=DrGꢃa is in the range of 2.5–6.0 kJmolꢀ1.
Let us assume that GB(M) is unknown. Fitting the experi-
mental 1 values for the proton transfer from series of pro-
tonated reference bases, BrefH+, to M through Equation (12)
provides a means for its determination. This method has
been quite successful, particularly when standard methods
fail.[29b]
As expected, the rate of proton transfer from BrefH+ to I
depends on GB
A
of GB(Bref), a consequence of the fact that neither Bref nor
ACHTREUNG
BrefH+ participate in the reaction in Equation (3). This is
also consistent with the efficient thermalization of IH+(g)
prior to the reaction. On going from H2O to HCO2nPr, the
ratio k2/k1 varies from 0.34 to 3.0. For bases stronger than
the latter, the ratio is even larger. The protonation of I
being the rate-determining step, no reliable k2 values can
then be extracted from these experimental data.
Figure 2 is a plot of the normalized value of 11 =k1/kcoll
,
namely 11norm against GB
ACHTREUNG
constant, we took a value of 2.66”10ꢀ9 cm3 moleculeꢀ1 sꢀ1,
as estimated by means of the ADO theory.[16] 11norm is simply
the ratio between the value of 11 for any of the studied reac-
tions and that for the fastest reaction (that with H3O+ in
Even prior to a theoretical discussion of these processes,
some important results can be obtained from the above.
The gas-phase basicity of I: As mentioned earlier, GB(I) has
been estimated to lie in the 764–781 kJmolꢀ1 range.[9] Using
data from Table 1, it is possible to get a more precise value.
our case). 11norm =(k1/kcoll)/
C
)
.
max
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Chem. Eur. J. 2007, 13, 1796 – 1803

Chalcogen–Chalcogen Interactions
FULL PAPER
finity (1.8 eV) is also quite consistent with the experimental
value (1.75 eV).[9d]
Mechanism of the reaction in Equation (3): The fast reac-
tion between I and IH+ suggests the existence of an ener-
getically favorable interaction between these two reagents
prior to the bond-making–bond-breaking steps. Dispersion,
ion-dipole and ion-induced dipole interactions are important
contributors, but as we indicate below, more “specific” inter-
actions probably exist:
Global and local electrophilicity analysis: In Table 2, the
static global properties of neutral and protonated I are dis-
played. The electronic chemical potential[9] of
I (m=
Figure 2. Thermokinetic plot for the reaction in Equation (2). Error bars
for GB
(Bref) values and 11norm are taken as 2 kJmolꢀ1 and as 10–30% (de-
A
Table 2. Electronic chemical potential (m), chemical hardness (h), and
global electrophilicity (w) of species I and IH+.[a]
pending on Bref, see Table 1), respectively.
Species
HOMO
LUMO
m
h
w
I
ꢀ0.3505
ꢀ0.5675
0.0665
ꢀ0.1098
ꢀ0.1420
ꢀ0.3386
0.4170
0.4578
0.66
3.41
proton transfer from protonated bases with GBs in the
range of 660–734 kJmolꢀ1 takes place at essentially collision
rate.
IH+
[a] All values in hartree.
A referee has rightly observed that the determination of
pressures is subject to considerable uncertainties and that
the same applies to the estimation of kcoll by means of the
ADO model (or even its improved versions). Here, these
drawbacks are considerably reduced because 11norm involves
relative values. Furthermore, under these conditions, the
comparison of the largest experimental rate constants and
the computed kcoll is useful because it might reveal the exis-
tence of eventual complicating factors in the protonation
process (none found here).
Fitting of 11norm through Equation (11) yields values of
(769.25ꢂ0.23) kJmolꢀ1 and (0.293ꢂ0.018) kJꢀ1 mol for
GB(I) and b, respectively. The latter corresponds to an ef-
fective temperature of (410ꢂ30) K.
ꢀ0.1425 hartree) is higher than that of IH+ (m=
ꢀ0.3386 hartree). As expected, the electron flow will take
place from I to IH+.
The electrophilicity values (w) of I and IH+, are 0.66 and
3.41 hartree, respectively. According to the absolute scale of
electrophilicity[25] based on w indexes, I and IH+ may be
classified as moderate and strong electrophiles, respective-
ly.[31]
Analysis of I and IH+ by means of Fukui functions[24]
(Table 3) allows us to explain the regioselectivity of the
polar process. The largest values of Fukui nucleophilic and
Table 3. Values of the nucleophilic, fꢀk, and electrophilic, fþk, Fukui func-
tions for I and IH+.
2) k2 versus the collision rate constant: ADO theory[16] pro-
vides an estimate of the collision rate constant for the pro-
cess in Equation (3) of 1.54”10ꢀ9 cm3 moleculeꢀ1 sꢀ1. The
ratio k2/kcoll thus equals (0.56ꢂ0.14).
Species
Indexes
S1
S2
I
fꢀk
0.460
S3
0.605
0.460
S4
0.538
IH+
fꢀk
Computational treatment and discussion
GB(I): As mentioned above, we have carried out a study at
the G3 level of species I and IH+. The raw results are pre-
sented in Table S1 of the Supporting Information. They
yield a value for GB(I) of 768.1 kJmolꢀ1, a result agreeing
within approximately 1 kJmolꢀ1 with the experimental
value.
electrophilic functions correspond to sulfur atoms S1(S2)
(fꢀk =0.460) and S3 (fþk =0.605), respectively (see Figure 4
for the numbering of atoms). Therefore, the latter will be
the preferred site for a nucleophilic attack.
Energies: The calculated nuclear-plus-electronic energies,
zero-point vibrational energies (ZPE), thermal corrections,
and entropy values of the relevant species are summarized
in Table S2 of the Supporting Information. Table 4 lists their
relative nuclear-plus-electronic energies, DEm, enthalpies,
DHmꢃ, and Gibbs energies, DGmꢃ, relative to the separate re-
agents.
Ionization energies and electron affinities: Koopmanꢀs theo-
rem allows the use of the HOMO and LUMO energies ob-
tained in this study to estimate the ionization energy of I.
We find a value of 9.5 eV, in reasonable agreement with the
experimental vertical ionization energies reported in the lit-
erature (8.97–9.0 eV range).[9b,c] The estimated electron af-
Chem. Eur. J. 2007, 13, 1796 – 1803
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1799

J.-L. M. Abboud, M. Esseffar et al.
Table 4. MP2/6-311+G
C
(d,p)
nuclear-plus-elec-
The reaction involves the initial formation of a reactive
complex, Rc, 65.4 kJmolꢀ1 more stable than the separate re-
actants (in terms of DHmꢃ). This complex then overcomes the
first transition state, TS1, leading to the intermediate INT
and further evolves leading to a second intermediate, a
product complex Pc, via a second transition state, TS2. Pc is
practically an adduct of II+ and methyl mercaptan. Inspec-
tion of Figure 4 reveals that the first step corresponds to the
nucleophilic attack of S2 of the neutral molecule on S3 of
the protonated one to give the ionic reactive complex. The
Species
DEm
TDSmꢃ
DGmꢃ
I+IH+
0.0
ꢀ34.2
ꢀ36.3
ꢀ33.3
ꢀ38.0
ꢀ34.6
ꢀ1.6
0.0
Rc[b]
ꢀ68.20
ꢀ49.20
ꢀ79.79
ꢀ60.75
ꢀ80.92
ꢀ42.76
ꢀ31.2
ꢀ11.4
ꢀ43.0
ꢀ21.0
ꢀ42.9
ꢀ42.7
TS1
INT[c]
TS2
Pc[d]
II+ +MeSH
ꢀ
second step corresponds to the breaking of the S3 S4 bond
[a] All values in kJmolꢀ1
[d] Product complex.
ꢀ
and the formation of the S2 S3 bond. This step appears to
be the key process of the reaction allowing the formation of
ꢀ
Pc through the formation of a new S S bond. Pc further de-
The computed energetics profile of the reaction is repre-
sented in Figure 3. The structures of the various species in-
volved are given in Figure 4.
composes leading to the departure of methanethiol and the
formation of II+. The feeble activation Gibbs energies asso-
ciated with TS1 and TS2 favor the rapid evolution of the
system. This reaction pattern is formally similar to that of
cationic SN2 reactions[32] and is consistent with the experi-
mental kinetic results presented above. These results can be
compared to those obtained in our studies involving the
formal transfer of methyl groups in the gas phase.[10c] The ac-
tivation Gibbs energies for these processes are much higher
than those involved in the formal transfer of the thiomethyl
group, relevant in this study.
The standard entropies for these species are strongly neg-
ative (in the range of ꢀ111.3 to ꢀ127.6 Jmolꢀ1 Kꢀ1) with re-
spect to the separate reagents, and they are responsible for
the increase in the Gibbs energy of all the stationary points.
The exception corresponds to
Figure 3. Enthalpy and Gibbs energy profiles for the reaction of I and
IH+ as computed at the MP2/6-311+G(d,p) level. Values in kJmolꢀ1
.
A
the separate products in which
it is only of ꢀ1.3 Jmolꢀ1 Kꢀ1.
Physically, the main contribu-
tion to these entropic effects
originates in the loss of the
translational entropy of the var-
ious systems with respect to the
separate reagents. This entropy
is recovered once the products
separate.
At this point, we can look
back at the fact that the rate
constant k2 is roughly half of
the collision rate. The reactive
complex Rc is formed by the
encounter of I and IH+ orient-
ed in such a way that they
allow the reaction in Equa-
tion (3). However, this is not
the only energetically favored
encounter. IH+ and I can also
interact leading to a hydrogen-
bonded complex (say between
S4–H+ and S1 or S2, Figure 4).
A simple model, such as ADO,
indicates that the collision fre-
quencies for the two processes
Figure 4. Structures optimized at the MP2/6-311+G
of I and IH+. Bond lengths in Š.
ACHTREUNG
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Chalcogen–Chalcogen Interactions
FULL PAPER
Table 5. Evolution of the S–S interatomic distances (d, in Š), along the reaction path at the MP2/6-311+G
ACHTREUNG
density, H(r) at the bond and ring critical points, bcp and rcp, respectively. All values in a.u. at the MP2/6-31+G
A
ACHTREUNG
Species
Rc
TS1
INT
TS2
Pc
II+
d(S1
2.07
2.07
2.07
2.08
2.08
2.06
ꢀ
S2)
1(S1 S2), H(S1
0.1412, ꢀ0.0767
0.1417, ꢀ0.0771
0.1421, ꢀ0.0776
0.1397, ꢀ0.0753
0.1397, ꢀ0.0753
0.1404, ꢀ0.0765
ꢀ
ꢀ
S2)
S3)
S3)
S4)
d(S2
4.17
3.95
3.72
2.37
2.08
2.08
ꢀ
S3)
1(S2 S3), H(S2
–, –
4.95
–, –
2.08
0.1372, ꢀ0.0738
0.0093, 0.0078
0.0089, 0.0011
0.0077, 0.0011
–, –
0.0088, 0.0011
3.54
0.0077, 0.0010
2.09
0.0054, 0.0009
4.24
–, –
2.09
0.1350, ꢀ0.0722
0.0772, ꢀ0.0195
0.1399, ꢀ0.0758
0.1396, ꢀ0.0754
ꢀ
ꢀ
d(S1
3.75
3.36
–, –
3.70
–
–
ꢀ
S3)
1(S1 S3), H(S1
–, –
2.53
0.0563, ꢀ0.0091
–, –
–
–, –
–, –
–, –
–, –
ꢀ
ꢀ
d(S3
ꢀ
S4)
1(S3 S4), H(S3
0.1345, ꢀ0.0718
ꢀ
ꢀ
1(S1
H(S1
ꢀ
S4)
ꢀ
S4)
1(S2 S4), H(S2
0.0100, 0.0011
ꢀ
ꢀ
S4)
1(S2-H-(C-S3)), H(S2-H-(C-S3))
rcp(S1-S2-S3), H(S1-S2-S3)
1(S1-H-(C-S3)), H
rcp(S1-H-C-S4), H(S1-H-C-S4)
rcp(S2-H-C-S3), H(S2-H-C-S3)
rcp(S1-H-C-S3-S2), H
0.0059, 0.0010
0.0070, 0.0012
0.0055, 0.0012
0.0055, 0.0012
0.0058, 0.0011
0.0053, 0.0011
0.0046, 0.0075
–
–
–, –
0.0043, 0.0007
–, –
–
–
0.0064[a], 0.0012[a]
–
–
–, –
–
0.0070[b], 0.0014[b]
0.0063[b], 0.0013[b]
0.0048[c], 0.0008[c]
–, –
0.0144, 0.0010
–, –
–
–, –
(S1-H-(C-S3))
0.0110, 0.0022
0.0052[d], 0.0011[d]
(S1-H-C-S3-S2)
[a] 1(S4-H-C-S3). [b] 1(S1-H-C-S3). [c] rcp(S2-H-C-S3-S4). [d] rcp(S2-S4-H-C-S3)
.
+
ꢀ
ꢀ
should be roughly the same. However, extensive exploration
of the potential-energy surface of these systems carried out
during the initial stages of this work, failed to show that
they could lead to the reaction in Equation (3) at a low en-
ergetic cost. This explains why under the low working pres-
sures, these complexes dissociate and approximately half of
the total encounters do not lead to II+.
S1 S2 (or S2 S3) in II . 3) The existence of several bcps in-
volving a hydrogen atom of a methyl group and the nearest
sulfur atom. Here again, the largest value of 1 appears in
the TS2 structure. We have also located a ring critical point
(rcp), nicely indicating the existence of an unconventional
hydrogen bond stabilizing this transition state (Figure 5).
Geometries: The structures of the TSs and the intermediates
corresponding to the reaction channel are displayed in
Figure 4. The evolution of the S2–S3 and S3–S4 bond distan-
ces on going from the first adduct to the final intermediate
are summarized in Table 5.
It can be seen that the S2–S3 distance varies from 4.17 Š,
in Rc to 2.08 Š, in Pc, indicating the S–S bond-making via
TS1 and TS2. At the same time, the distance S3–S4 varies
from 2.08, in Rc to 3.70 Š in Pc, indicating a bond-breaking
via the same TSs. A closer look at the geometrical structures
shows that TS2 is the main bond-making–bond-breaking
process while TS1 constitutes an orientation transition state.
Somewhat surprisingly, however, the standard Gibbs ener-
gies of activation involved in the formation of TS2 and TS1
are practically the same. An inspection of the topological
analysis of the charge density of the species involved in the
reaction pathway by means of the atoms in molecules
(AIM) theory,[33] may offer some clues to understanding this
question. The bond critical points (bcps) of the different sta-
tionary points along the PES are given in Table 5. Several
conclusions can be drawn from this table. Firstly, the values
of the charge density at the bond critical points exhibit a
good correlation with the bond distances: the shorter the
bond, the larger the 1 value. Secondly, as regards 1(r), fur-
ther important points must be mentioned: 1) The fact that
the 1 values are relatively low in the case of TS1 indicates
that it is effectively an orientation TS. 2) Among the 1
values corresponding to the making–breaking bonds, only
those of TS2 are relatively high. Therefore, 1(r)s for the
Figure 5. Molecular graph for TS2. Red dots are bcps. The yellow dot is
ꢀ
the rcp pertaining to the five-membered structure. The C H bonds are
ꢀ
not represented, except in the case of S1 HCS3.
The 1 values at the bcp (0.014 a.u.) and at the rcp
(0.011 a.u.) strongly suggest that the interaction is signifi-
cant. Furthermore, the energy density, H(r), which identifies
regions of the space wherein the electronic charge is locally
depleted (H(r)>0), as in hydrogen bonds or ionic bonds, or
built up (H(r)<0)), as in covalent linkages, is positive at the
ꢀ
S2 S3 bond of TS1, indicating that this interaction is weak
and essentially electrostatic. Conversely, it is negative for
the same linkage in TS2, indicating that already in the tran-
sition state the S2–S3 and S3–S4 interactions have a non-
negligible covalent character. The overall molecular graph
for TS2 is presented in Figure 5. The combination of the S–S
interactions and these hydrogen bonds efficiently stabilizes
TS2.
ꢀ
ꢀ
bonds S2 S3 and S3 S4 are roughly half of those for bonds
Chem. Eur. J. 2007, 13, 1796 – 1803
ꢁ 2007 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
www.chemeurj.org
1801

J.-L. M. Abboud, M. Esseffar et al.
Equilibria: Further conclusions can be extracted from the
above:
Conclusion
The experimental study of the gas-phase protonation of di-
methyldisulfide has provided, we believe for the first time, a
rather precise value of its gas-phase basicity (the accuracy is
possibly lower). This value agrees to within 1 kJmolꢀ1 with
the results of G3 calculations.
Also obtained for the first time was the reaction rate con-
stant for the bimolecular reaction between neutral and pro-
tonated dimethyldisulfide to yield methanethiol and dime-
thyldithiosulfonium ion. This constant is of the order of
magnitude of the collision limit. A computational mechanis-
tic study based on the energetic profile of the reaction, com-
pleted with Fukuiꢀs and Baderꢀs treatments of the reactants
and transition states fully rationalizes the regioselectivity of
the reaction as well as the existence of a shallow, flat Gibbs
energy surface for the reaction. The mechanistic relevance
1) The low activation barriers separating species Rc, INT
and Pc should allow their fast interconversion. More pre-
cisely, we might consider the reactions in Equations (13)
Rc ! INT
DrGmꢃð13ÞKpð13Þ
ð13Þ
and (14):
INT ! Pc
DrGmꢃð14ÞKpð14Þ
ð14Þ
From the data given in Table 4, we obtain DrGmꢃ(13)=
ꢀ11.7 and DrGmꢃ(14)=ꢀ11.6 kJmolꢀ1. Then, Kp(13)ꢄ
Kp(14)=1.1”102. The equilibrium in Equation (15) is
pressure dependent:
ꢀ
of the chalcogen–chalcogen interaction and the C H···S
bonds has been demonstrated.
Pc ! IIþ þ MeSH
DrGmꢃð15Þ Kpð15Þ
ð15Þ
For this process, DrGmꢃ(15)=ꢀ3.1 kJmolꢀ1 and Kp(15)=
3.5.[34] It is clear, therefore, that under pressures of the
order of 1 atm or higher, one could observe an equili-
brating mixture of species II+, MeSH, Pc, and INT. In
our experiments, this is not the case, simply because the
very low working pressure shifts the reaction in Equation
(15) to the right.
Acknowledgements
This work was supported by grants BQU2003-05827 and BQU2003-00894
of the Spanish DGIYT, and by the Project MADRISOLAR. Ref.:
S-0505/PPQ/0225 of the Comunidad Autónoma de Madrid. Support from
a joint CNRST (Morocco)–CSIC (Spain) project is also gratefully ac-
knowledged. Valuable comments by the referees are most appreciated.
2) Going back to the global and local electrophilicity analy-
sis, we see that the formation of Rc and its evolution to-
wards INT is driven by the nucleophilic attack of a S
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ꢀ
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can be viewed as a consequence of a nucleophilic attack
ꢀ
of the sulfur atom of MeSH on an activated S S bond of
+
ꢀ
II . In both cases, S S bonds are activated by an elec-
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ꢀ
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ꢁ 2007 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
Chem. Eur. J. 2007, 13, 1796 – 1803

Chalcogen–Chalcogen Interactions
FULL PAPER
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Received: May 25, 2006
Published online: November 24, 2006
Chem. Eur. J. 2007, 13, 1796 – 1803
ꢁ 2007 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
www.chemeurj.org
1803