Cent. Eur. J. Chem. • 11(3) • 2013 • 457-463
DOI: 10.2478/s11532-012-0178-z
Central European Journal of Chemistry
Weak sulfur-sulfur interactions
between chemically-identical atoms
Research Article
Radu Silaghi-Dumitrescu*, Alexandru Lupan
Department of Chemistry and Chemical Engineering,
”Babeş-Bolyai” University, Cluj-Napoca, Romania
Received 12 October 2012; Accepted 20 November 2012
Abstract: Experimentally-known sulfur-sulfur distances shorter than the sum of van der Waals radii and involving two chemically-identical sulfur
atoms are examined at several levels of theory (BP86/6-31G** to CCSD(T)/6-311+G**). None of the theoretical methods predict an
attractive interaction from an energetic point of view, even though molecular orbitals stretching between the two sulfur atoms have been
identified. Most likely, if there is indeed an attractive interaction force between chemically identical sulfur atoms, its value is comparable
to the accuracy of the methods employed here – implying an attractive interaction below 1 kcal/mol. The investigation includes some
simple models of 1,6,12,17-tetrathiacyclodocosa-2,4,13,15-tetrayne which was previously shown to have an S---S interaction involving
two chemically-identical atoms. Attractive interactions calculated for these latter models are shown to arise from S---HC weak bonding,
with the S---S interaction being again repulsive.
Keywords: Sulfur-sulfur interaction • DFT • MP2 • CCSD(T) • Hartree-Fock • Supramolecular chemistry
© Versita Sp. z o.o.
1. Introduction
2. Calculation details
Non-covalent interactions between chemically-identical
atoms are expected to be very weak, with exceptions such
as the aurophilic interactions. Sulfur-sulfur interactions –
in general – have been described experimentally, mainly
as driving forces in the formation of the stack and sheet
structures of the so-called organic metals [1,2]. On the
other hand, sulfur-sulfur interactions involving chemicallyidentical atoms have been poorly emphasized and, at
this time, there is no knowledge about their strength
[3,4]. One convenient method for examining the strength
and nature of weak bonds in supramolecular chemistry
involves computation of their electronic structures with
ab initio methods [5-10]. Here, computational data are
reported on sulfur-sulfur interactions involving identical
sulfur atoms, employing several types of atoms and
attempting to identify the electronic structure factors
controlling these interactions. The findings may in
principle also be relevant for other interactions between
heavier elements, such as the aurophilic interactions
[11-13].
The starting geometry was extracted from the Cambridge
Crystallographic Database, entry XIGPAE based on
reference [3], and is shown in Fig. 1. Energies were
computed with or without geometry optimization, as
specified in the text and Figure/Table legends. The
BP86/6-31G** (density functional theory, DFT), HF/631+G* (Hartree-Fock), MP2/6-31+G* (second order
Møller–Plesset perturbation), HF/6-311+G**, MP2/6311+G**, CCSD/6-311+G** (Coupled Cluster Singles and
Doubles), CCSD(T)/ 6-311+G** (Coupled-Cluster with
Single and Double and Perturbative Triple excitations)
and M06-2X/6-311+G** (DFT) levels of theory were
employed, as indicated in text and Tables, using the
Spartan 06[14] and Gaussian 09 [15] software packages,
with default settings for convergence criteria. Basis set
superposition errors (BSSE) were computed according to
Boys and Bernardi [16]. LC-BP86 calculations [15,17,18]
were also performed, but are not reported in any detail
since the qualitative outcome was essentially identical to
the BP86 case.
* E-mail: [email protected]
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Weak sulfur-sulfur interactions
between chemically-identical atoms
Figure 1.
Structure of a compound exhibiting intermolecular S-S interactions between identical sulfur atoms.
3. Results and discussion
3.1. Non-covalent interaction between two
chemically-identical sulfur atoms in a Sn
complex
Fig. 1 illustrates the structure of a compound exhibiting
a sulfur-sulfur distance of 3.4561(7) Å [3] between two
identical molecules found within the crystallographic
cell, shorter than the sum of their van der Waals radii,
3.630 Å. The only other close contacts, also shown in
Fig. 1, are two 3.033 Å distances between each sulfur
and a methyl proton; these sulfur-hydrogen distances
are 0.018 Å longer than the respective sum of van der
Waals radii. Under these conditions, unless the two
molecules are forced in this particular geometry by
crystal packing forces involving other parts of the dimer,
one reason why the two sulfur atoms would be sitting
closer to each other by 0.173 Å compared to the sum
of their van der Waals radii, would be an attractive force
between the two atoms.
Fig. 2 illustrates the electron density resulting from
an electronic structure calculation (single-point, BP86/631G**) using the experimentally-known geometry,
truncated by reducing the phenyl rings to methyl groups,
and the bipyridyl units to pyridyl. It can be seen that the
only region of continuous electron density connecting
the two molecules is the sulfur-sulfur axis.
Figure 2.
Electron density computed for a truncated version of the
experimental structure shown in Fig. 1 (Isovalue=0.008;
BP86/6-31G**, single-point calculation on crystal
structure coordinates).
Fig. 3 illustrates the one frontier molecular orbital
which was found to correlate with the electron density in
Fig. 2, extending between the two sulfur atoms. It can be
seen that this molecular orbital has strong contributions
from the p orbitals belonging to the two sulfur atoms;
these p orbitals thus appear to engage in a π-type
interaction. One may therefore speculate that it is this
molecular orbital (or the respective p-p orbital interaction)
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R. Silaghi-Dumitrescu, A. Lupan
Figure 3.
Two views (perpendicular to each other) of the HOMO-5
orbital of the system shown in Fig. 2 (BP86/6-31G**,
single-point calculation on crystal structure coordinates).
antibonding orbitals in Figs. 3 and 4 reveals that the
antibonding orbital has slightly less contribution from
the sulfur orbitals of interest, compared to the bonding
orbital (calculated coefficients from the respective sulfur
pz orbitals are 0.50 in HOMO-5 and 0.34 in HOMO).
Geometry optimization of the structure shown in
Fig. 2 resulted in almost negligible changes in geometry.
Significantly, however, the S---S distance marked in
Fig. 1 to be 3.456 Å became 3.749 (longer than the sum
of the corresponding van der Waals radii) while the S---H
distances marked in Fig. 1 at 3.033 Å became 2.953 Å,
shorter than the respective sum of van der Waals radii.
Thus, according to the level of theory employed by us,
and contrary to experiment, the forces holding the dimer
together would be S---H and not S---S. This conclusion
should be regarded cautiously, as it relies on the ability
of density functional methods to very accurately predict
relative energies of weak forces of different types – and
in this respect our result may indeed be a manifestation
of methodological imperfections. Another parameter
that is slightly affected by geometry optimization is
the S---Sn distance between atoms belonging to
the two units: this distance elongates from 4.085 to
4.232 Å upon geometry optimization, suggesting that a
possible electrostatic attraction between the two atoms
is also not among the key forces holding the dimer
together.
To further probe the energetics of the S---S
interaction in the system illustrated in Fig. 2, the two
monomers were moved with respect to each other,
to S---S distances of 3.50 Å, 4.00 Å and 6.00 Å, and
the energies of the resulting systems were calculated
without geometry optimization. These ‘elongated’
geometries were all more stable than the experimental
one by 1.00, 8.72 and 2.89 kcal mol-1, respectively,
suggesting that there is no force whose energy would be
accurately predicted by DFT and which would be able to
hold the two dimers at the distances seen in the crystal
structures.
3.2. H2S dimers
Figure 4.
HOMO orbital of the system shown in Fig. 2 (BP86/631G**, single-point calculation on crystal structure
coordinates).
that draws the two sulfur atoms closer than the sum of
their van der Waals radii. One counterargument may
be that the corresponding antibonding orbital (Fig. 4)
is also occupied, which may be expected to cancel the
interaction; however, comparison of the bonding and
In order to allow treatment of the S---S sulfur interaction
at levels higher than those employed in Figs. 2-4, the
monomers were reduced to simple hydrogen sulfide
units (2×H2S), preserving the positions of the sulfur
atoms and the orientations of their bonds to the values
seen in the crystal structure. This simple system was
then treated at the CCSD/6-311+G** level. The two H2S
moieties were then moved away from each other while
maintaining a constant distance between their respective
planes. This elongation was carried out to a point where
the S-S distance was longer by 0.1 Å than in the starting
structure. At this point, the energy computed with
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Weak sulfur-sulfur interactions
between chemically-identical atoms
CCSD/6-311+G** (without geometry optimization) was
still lower than that computed in the crystal structure-like
geometry, by 0.48 kcal mol-1.
3.3. Dimethyl thioether units
Figure 5.
Dimer of dimethyl thioether, employed for computations
shown in Table 1.
Figure 6.
Simple models of the columnar structure of 1,6,12,17tetrathiacyclodocosa-2,4,13,15-tetrayne in the solid
state; heavy-atom positions correspond to the crystal
structure [19,20], while the positions of the hydrogens
are geometry-optimized. Dashed lines represent
potential non-covalent interactions. “Bonding energies”
are obtained using MP2/6-311+G**, and represent
differences in energy between structures shown here
and hypothetical non-equilibrium structures obtained
by simple elongation of the S-S distance along the S-S
axis, from the equilibrium distance of 3.473 Å to 3.872 Å
(arbitrarily chosen to be somewhat longer than the sum
of van der Waals radii).
Figure 7.
Electrostatic potential surface for the dimer shown in
Fig. 6 (methyl groups included; isocontour 0.009).
To further explore the possibility of weak sulfur-sulfur
interactions, the model shown in Fig. 5 was employed,
with two dimethyl thioether units and featuring all 6
heavy atoms in the same plane. The sulfur-sulfur
distance was set to various values and the energy was
computed (without geometry optimization) as shown in
Table 1 with DFT, Hartree-Fock and MP2 methods, and
with two different basis sets. For each of the methods,
the relative energies are seen to increase constantly
upon going from a S---S distance of 4 Å to 3 Å, without
evidence of local minima at distances similar to the
ones in the crystal structure described in Fig. 1. Notably,
among the methods that agree upon the non-existence
of an attractive S---S interaction between the chemically
identical sulfurs in Fig. 5, are MP2, CCSD(T), and M062X. In conjunction with the large basis sets employed
here, these methods would be expected to identify
non-covalent interactions at least qualitatively if not
quantitatively. As expected, BSSE corrections lead to
even larger repulsive energies.
3.4. S---S attractive interactions between
chemically-identical
sulfur
atoms
previously identified by computations
S---S weak interactions between chemically identical
sulfur atoms have also been discussed for compounds
of the 1,6,12,17-tetrathiacyclodocosa-2,4,13,15-tetrayne
type, including computational approaches [19,20]. Fig. 6
illustrates a previously-used model for these compounds
[19,20], a dimer of ethyl-methyl thioether for which
Fig. 6 indeed shows attractive interaction in line with
previous calculations for this model [19,20]. However,
Fig. 6 also shows that the removal of methyl groups from
sulfur, which in turn means removal of the S---H(methyl)
interactions while leaving the two identical sulfurs at the
same distance, changes the sign of the bonding energy.
This implies that S---H interactions are responsible for the
attractive forces holding the dimer together in the crystal
structure. Presumably, their nature is largely electrostatic.
An electrostatic potential surface for the dimer
model of Fig. 6 (methyl groups included) is shown in
Fig. 7, confirming that higher electron density is located
along the S---S axis than along the S---H axes. Together
with Fig. 6, this may be interpreted to mean that the two
S---H interactions, largely electrostatic, hold the dimer
together and force the two sulfur atoms to sit closer to
each other than the sum of their van der Waals radii.
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R. Silaghi-Dumitrescu, A. Lupan
Table 1.
Relative energies of the dimethyl thioether, computed at several levels of theory. For each method, the lowest-energy geometries are
set as arbitrary references. Energy values were obtained on models built as described in the text, varying the S---S distance and then
computing energies without further geometry optimization.
Method
BP86/6-31G**
HF/6-31+G*
MP2/6-31+G*
HF/6-311+G**
MP2/6-311+G**
M06-2X/6-311+G**
CCSD(T)/6-311+G**
S---S
distance
Energy
(hartree)
ΔE
(kcal mol-1)
EBSSEcorr
(hartree)
ΔEBSSEcorr
(kcal mol-1)
3.00
-956.1663400
9.04
-956.02555605
9.59
3.30
-956.1748400
3.71
-956.03438715
4.05
3.50
-956.1777200
1.90
-956.03746663
2.12
3.70
-956.1792600
0.93
-956.03917901
1.05
4.00
-956.1807500
0.00
-956.04084494
0.00
3.00
-953.4092016
13.68
-953.40876461
13.86
3.30
-953.4217015
5.84
-953.42145286
5.90
3.50
-953.4261951
3.02
-953.42595347
3.08
3.70
-953.4286617
1.47
-953.42846561
1.50
4.00
-953.4310074
0.00
-953.43085949
0.00
3.00
-954.1966585
9.10
-954.19298382
10.71
3.30
-954.2056242
3.47
-954.20320261
4.29
3.50
-954.2085079
1.66
-954.20662428
2.15
3.70
-954.2099408
0.76
-954.20843458
1.01
4.00
-954.2111584
0.00
-954.21004653
0.00
3.00
-953.5022454
13.67
-953.50154492
13.91
3.30
-953.5147430
5.83
-953.51423832
5.94
3.50
-953.5190879
3.10
-953.51875761
3.11
3.70
-953.5217051
1.46
-953.52129320
1.52
4.00
-953.5240319
0.00
-953.52370794
0.00
3.00
-954.4058074
9.07
-954.40263361
10.24
3.30
-954.4149077
3.36
-954.41246167
4.07
3.50
-954.4177702
1.56
-954.41573331
2.02
3.70
-954.4191712
0.68
-954.41745328
0.94
4.00
-954.4202587
0.00
-954.41894916
0.00
3.00
-955.9043790
8.24
-955.90371459
8.47
3.30
-955.9128880
2.90
-955.91238452
3.03
3.50
-955.9153151
1.38
-955.91490495
1.45
3.70
-955.9164995
0.64
-955.91614613
0.67
4.00
-955.9175171
0.00
-955.91721403
0.00
3.00
-954.4951590
9.96
-954.52479556
10.67
3.30
-954.5050173
3.77
-954.53502746
4.25
3.50
-954.5081809
1.79
-954.53844364
2.10
3.70
-954.5097621
0.79
-954.54023970
0.98
4.00
-954.5110279
0.00
-954.54179522
0.00
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Weak sulfur-sulfur interactions
between chemically-identical atoms
4. Conclusions
Experimentally-known sulfur-sulfur distances shorter
than the sum of van der Waals radii involving two
chemically-identical sulfur atoms have been examined
here at several levels of theory and with several
models. None of the theoretical methods examined
here were able to predict this interaction from an
energy point of view, although molecular orbitals
may be identified and used to rationalize the short
sulfur-sulfur distance. Most likely, if there is indeed an
attractive interaction force between chemically-identical
sulfur atoms, its value is comparable tothe accuracy
of the methods employed here (i.e., up to CCSD(T)/6311+G**) – implying an interaction force well below
1 kcal mol-1.
Figure 8.
Sulfur-sulfur-related molecular orbitals for the dimer
shown in Fig. 6.
Fig. 8 shows molecular orbitals for the dimer shown
in Fig. 6, illustrating the interaction between the two
sulfur centers. HOMO-5 has a bonding character and
may be taken as evidence of bonding between the two
sulfurs; however, since its corresponding antibonding
orbital, HOMO-4, is also filled with electrons, the net
result should be no bonding between the two sulfurs –
at least not involving these orbitals.
Acknowledgments
Financial support from the Romanian National Council for
Scientific Research (grant PCCE 312/2008), and helpful
discussions from Drs. Luminita Silaghi-Dumitrescu,
Monica M. Venter (with Prof. Kieran C. Molloy), and
Matei-Maria Uta are gratefully acknowledged.
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