Download - The dimers of trimethylene sulfide with some hydrogen and halogen bond donors: a theoretical study
The dimers of trimethylene sulfide with some hydrogen and halogen
bond donors: a theoretical study
Ali Ebrahimi*, Hosein Roohi, Sayyed Mostafa Habibi, Ladan Behboodi
Department of Chemistry, Faculty of Science, University of Sistan and Balouchestan, P.O. Box 98135-674, Zahedan, Iran
Received 12 August 2004; revised 29 September 2004; accepted 6 October 2004
Available online 25 November 2004
Abstract
The axial and equatorial conformers of complexes formed by trimethylene sulfide (TMS) and XY (HF, HCl, ClF, and F2) have been
examined with the ab initio calculations. The geometry optimizations and frequency calculations have been performed using the MP2
and B3LYP methods with the 6-311CG(d,p) basis set. In the TMS/HF and TMS/ClF complexes, the MP2 results indicate that the
equatorial conformers are more stable than the axial ones. The results are contrary in the TMS/HCl and TMS/F2 complexes. The
topological properties of electronic charge density have been analyzed employing Bader’s theory of atoms in molecules (AIM). All dimers
(axial and equatorial conformers) have been indicated a bond critical point (BCP) between the X and S atoms of the TMS/XY complexes.
The rBCP, P2rBCP, and HBCP values of the established interactions correspond to the medium HBs. Also, the origin of the change of the bond
strength has been revealed in the axial and equatorial conformers of the complexes using the natural atomic orbitals (NAO) and natural bond
orbitals (NBO) analyses. The changes of total natural atomic orbital occupancies of valence orbitals in ClF and F2 are greater than the HF and
HCl. The most important interaction is LP2/s*XY in all complexes with the exception of TMS/F2. In this complex, the results of the NBO
analysis are different from other complexes and two predicted units are C3H6FSC and FK.
q 2004 Elsevier B.V. All rights reserved.
Keywords: Trimethylene sulfide; Hydrogen bond; Halogen bond; NBO; AIM
1. Introduction
The study of hydrogen bonded systems and other weakly
bonded complexes is a subject of great interest since they
have significant effect on the structure of compounds in the
solid, liquid and gas phases and also affect the mechanisms
of some processes [1]. The hydrogen bond is normally
characterized as relatively weak interaction involving an
electronegative proton donor and an electronegative proton
acceptor [2,3]. A systematic research on the properties of
hydrogen-bonded dimers (B/HX) has been conducted by
Legon and co-workers [4–6]. The conclusions of these
studies have been summarized in a set of empirical rules to
predict the angular geometries. They suggested the
existence of a halogen bond similar to the hydrogen bond
from the close parallelism of the properties of B/XY
0166-1280/$ - see front matter q 2004 Elsevier B.V. All rights reserved.
doi:10.1016/j.theochem.2004.10.015
* Corresponding author. Tel./fax: C98 541 244 6565.
E-mail address: [email protected] (A. Ebrahimi).
corresponding to B/HX. The XY unit is a dihalogen
molecule and the rules of hydrogen bonds have been
extended to the B/XY systems [6,7].
A four membered ring compound such as trimethylene
sulfide (TMS) has nonequavalent lone pairs on the sulfur
atom in the axial and equatorial positions which can act as
proton acceptors (Fig. 1). By this viewpoint, the complexa-
tion of TMS with the hydrogen chloride (TMS/HCl) has
been previously investigated by conducting pulsed-micro-
wave Fourier transform spectroscopy on a jet [8]. Two
different axial and equatorial conformers were detected for
this complex. The axial conformer was more stable than the
equatorial one. The S/H distance in the axial conformer
(w2.28 A) was longer than the other (w2.26 A).
In the present work, the geometrical parameters,
energetic aspects, and relative stability of axial and
equatorial conformers of TMS/XY complexes (XY: HF,
HCl, ClF and F2; see Fig. 1) were investigated using the
ab initio and density functional methods.
Journal of Molecular Structure: THEOCHEM 712 (2004) 159–166
www.elsevier.com/locate/theochem
Fig. 1. Axial and equatorial hydrogen bonded complexes formed between
trimethylene sulfide and XY.
A. Ebrahimi et al. / Journal of Molecular Structure: THEOCHEM 712 (2004) 159–166160
The nature of the interactions of the axial and equatorial
conformers has been studied here by means of Bader’s
theory of atoms in molecules (AIM) [9]. Such analysis was
employed because of the electronic density at the bond
critical point (BCP), rBCP, and its Laplacian, P2rBCP,
obtained by AIM analysis may be very useful parameters for
the estimation of relative strength of hydrogen bonds [10].
The AIM analysis does not reveal the origin of the change of
the bond strength in the H-bonding [11]. To overcome this
difficulty the natural atomic orbital (NAO) and the natural
bond orbital (NBO) analyses were employed [12]. These
methods have been successfully applied to analyze the
hydrogen bonded complexes in terms of orbital interactions
[13–15].
2. Methods
The geometries of monomers (TMS and XY) and
complexes (TMS/XY) were optimized with the GAUS-
SIAN-98 program package [16] using the 6-311CG(d,p) [17]
basis set and the hybrid Hartree–Fock-density functional
method (Becke3LYP) [18] and Post-Hartree–Fock at the
second order Møller–Plesset (MP2) level [19].
The nature of the monomers and their complexes as a
potential energy minimum was established at the B3LYP/6-
311CG(d,p) and MP2/6-311CG(d,p) levels by verifying
that all the corresponding frequencies are positive. Addition
to the interaction energies, a corrected interaction energy
excluding the inherent basis set superposition error (BSSE)
was evaluated. The BSSE was calculated using the Boys-
Bernardi counterpoise technique [20].
The topological properties of the electronic charge density
and the atomic charges were characterized using the atoms in
molecules methodology (AIM) with the AIM2000 program
package [21] on the wave functions obtained at MP2/6-
311CG(d,p) level. Most of these calculations were not
possible with default settings; to meet the Poincare-Hopf
criterion, additional critical points were sought with the
decrement of stepsize. A correct topology of the gradient
vector field is the first necessary condition to confirm the
presence of a hydrogen bond [22]. In addition, there are other
criteria. Two criteria are connected to the electron density
(rBCP) and Laplacian (P2rBCP) of the electron density
which evaluated at the H-bond critical point. The typical
ranges of rBCP and P2rBCP for H-bonding are 0.002–
0.035 e/a03 and 0.020–0.139 e/a0
5, respectively.
The NAO and NBO analyses were carried out on the
MP2/6-311CG(d,p) wave functions obtained for the
MP2/6-311CG(d,p) geometries using the NBO package
[23] included in the GAUSSIAN-98 suite of programs.
These analyses were carried out to understand some
effective factors on the weak interactions and the nature of
lone pairs.
3. Results and discussion
3.1. Geometries
The potential energy surfaces of the TMS/XY com-
plexes were explored at the B3LYP/6-311CG(d,p) and
MP2/6-311CG(d,p) levels of theory. Two minima struc-
tures corresponding to the axial and equatorial conformers
(experimentally detected for TMS/HCl, 2) were located
and characterized by computing the Hessian matrixes which
had only positive eigenvalues. The optimized structures
show Cs symmetry in all cases. The most important
geometrical parameters of the complexes, XY ligands, and
TMS molecule calculated using the above methods are
reported in Table 1. The S/H bond lengths of the axial and
equatorial conformers of complex 2 are 2.219 and 2.207 A
at the B3LYP/6-311CG(d,p) level, and 2.304 and 2.282 A
at the MP2/6-311CG(d,p) level, respectively. The exper-
imental data (2.28 and 2.26 A) of these conformers are in a
good agreement with the computed structural parameters,
especially at the MP2/6-311CG(d,p) level. Hence, this
level expects to provide reliable geometries for all
complexes. This point becomes more evident when one
considers the uncertainties associated with the experimental
distances and angles [8]. As can be seen from Table 1, the
calculated S/X bond length in the axial conformer is
greater than the equatorial one in all complexes with the
exception of 3. Therefore, if the S/X bond length is a
measure of bond power, this bond in the axial conformer
will be weaker than the equatorial one.
In addition, the deviations of the YXS angle from 1808 in
the equatorial conformers are larger than the axial ones. In
the following complexes, the order of deviations from 1808
(4–148) are as follow
2O1z4O3
Thus, nonlinearity in the halogen-bonded systems is
smaller than the hydrogen-bonded systems.
Furthermore, the XSCaCa dihedral angle is close to 908
and the deviations from 908 is expressed as follow
3O1O2O4
to express this behavior, some responsible factors will be
represented later by the NBO and AIM analyses.
Table 1
The most important geometrical parameters of the axial and equatorial conformers at the MP2/6-311CG(d,p) and B3LYP/6-311CG(d,p) levels in the
complexes
HF HCl ClF F2
MP2
SX 2.180 2.176 2.304 2.282 2.497 2.504 2.058 2.049
XY 0.935 0.934 1.296 1.296 1.804 1.796 1.794 1.790
YXS 169.587 165.866 167.708 160.577 176.071 174.236 168.186 168.635
XSCaCa 92.053 94.122 90.989 89.712 93.449 96.501 86.057 89.756
YHa 3.445 3.118 3.712 3.133 4.401 4.199 3.638 3.358
YHb 2.861 4.753 3.058 4.619 3.979 5.867 2.897 4.795
SCb 2.420 2.417 2.423 2.418 2.428 2.416 2.428 2.418
CaSCa 76.00 75.995 76.323 76.132 76.737 76.328 77.02 76.884
XYa 0.9166 1.2731 1.6727 1.4167
SCba 2.410
CaSCaa 76.02
B3LYP
SX 2.156 2.143 2.219 2.207 2.508 2.500 1.959 1.957
XY 0.9470 0.9465 1.325 1.326 1.820 1.818 1.803 1.796
YXS 171.299 169.242 173.154 170.144 177.371 176.12 171.546 172.06
XSCaCa 94.636 96.035 94.404 94.897 96.258 98.242 90.860 93.555
YHa 3.472 3.257 3.782 3.511 4.504 4.349 3.777 3.576
YHb 3.344 4.685 3.675 4.916 4.477 5.792 3.342 4.794
SCb 2.454 2.453 2.456 2.452 2.458 2.454 2.445 2.457
CaSCa 76.404 76.472 76.667 76.469 76.6427 76.667 76.543 77.058
XYa 0.9222 1.2867 1.6788 1.4087
SCba 2.449
CaSCaa 76.59
Bond lenthes in angestromes (A) and bond angles in degrees.a Corresponding to the monomers. In each case, first and second columns correspond to the axial and equatorial conformers, respectively.
A. Ebrahimi et al. / Journal of Molecular Structure: THEOCHEM 712 (2004) 159–166 161
The X–Y bond length increases in all cases on
complexation. These changes in the axial conformers are
usually greater than the equatorial conformers. In addition,
approximately same changes occur in the S–Cb bond length
and also C–S–C bond angle. In different complexes, the
average change of the CSC angle is as follow
4O3O2O1
A summery of the changes of C–H, S–C, and C–C bond
lengths on complexation are given in Table 2 (see Scheme 1
for the numbering). In each complex, more bond lengths are
changed for the more stable conformer. Some of these
changes will be interpreted in the NBO section.
The most important geometrical aspects obtained at the
B3LYP/6-311CG(d,p) level (which are different from
the corresponding values at the MP2/6-311CG(d,p) level)
Table 2
The changes of C–H, S–C, and C–C bond lengths on complexation
HF HCl
C3–H7 K0.001 – K0.001 –
C3–H8 – K0.001 – –
C2–H5 – K0.001 – –
C4–H9 – K0.001 – –
C2–H6 K0.001 K0.001 K0.001 –
C4–H10 K0.001 K0.001 K0.001 –
C–S 0.004 0.004 0.003 0.003
C–C – – 0.001 –
–, means no change. In each case, first and second columns correspond to the ax
are mentioned as the following points: (1) The S/H bond
length in the equatorial conformer is shorter than the axial
one in the TMS/HCl complex. (2) The deviations of
the YXS angles from 1808 (3–108) are lesser. (3) The
average values of the XSCaCa dihedral angles are greater.
(4) The Y–Hb distances of the axial conformers obtained
using the B3LYP method are approximately 0.45–0.62 A
greater than the MP2 method.
3.2. Relative stability of conformers
The frequency calculations were performed to investi-
gate the relative stability of the axial and equatorial
conformers at the MP2/6-311CG(d,p) level of theory at
298.15 K and 1 atm. The electronic energies (Ee) of the
equatorial conformers relative to the axial ones are reported
ClF F2
K0.003 K0.001 K0.004 K0.001
K0.001 K0.001 K0.002 K0.002
K0.001 K0.001 K0.001 –
K0.001 K0.001 K0.001 –
K0.001 K0.001 – K0.002
K0.001 K0.001 – K0.002
– K0.001 K0.009 K0.010
0.002 0.001 0.003 0.003
ial and equatorial conformers, respectively.
Scheme 1. The numbering of atoms of trimethylene sulfide.
A. Ebrahimi et al. / Journal of Molecular Structure: THEOCHEM 712 (2004) 159–166162
in the first row of Table 3. The relative energies corrected
for the zero point energies (ZPE), thermal energies,
enthalpies, and Gibbs free energies are given in the next
rows. The basis set superposition errors (BSSE) were
estimated by means of the counterpoise procedure (CP). In
each case, the data in the right column correspond to the
corrected values excluding the basis set superposition error.
As can be observed from Table 3, the predicted relative
stabilities with the BSSE correction and without it are equal
for all complexes with the exception of the complex 3. In the
complex 1, the equatorial conformer is more stable than the
axial one. In this complex, DG and DH values are negative
and positive, respectively, for the conversion of the axial
form to the equatorial one. Thus, DSO0 and jDHj!jTDSj.
Therefore, the entropic factor controls the stability of the
equatorial conformer relative to the axial one. In the
complex 3, the equatorial form is also more stable than
the axial form (see Table 3). Thus, the relative stability of
conformers can be interpreted in the same way.
In the complex 2, for the same conversion, DG and DH
values are positive and negative, respectively. Hence,
DS!0 and jDHj!jTDSj. Contrary to the previous com-
plexes (1 and 3), the entropic factor controls the stability of
the axial conformer in comparison with the equatorial one.
Therefore, the relative stability of two conformers changes
at low-temperatures.
In the complex 4, for the same conversion, DG and DH
values are positive and DGODH. Thus, DS!0 and both
enthalpic and entropic factors control the stability of axial
conformer in comparison with the equatorial one. In this
case, the relative stability of two conformers does not
change at low-temperatures.
Table 3
The stabilization energies (Ee), zero point energies (ZPE), thermal energies, enthalp
the axial ones
HF HCl
DEe 0.872 0.711 0.003 K0.28
D(EeCZPE) 0.693 0.532 0.179 K0.11
DE 0.853 0.693 0.089 K0.20
DH 0.853 0.693 0.089 K0.20
DG K0.194 K0.355 0.743 0.45
In each case, the data of right column correspond to CP-corrected values.
3.3. Atoms in molecules analysis
Bader’s theory is a very useful tool to analyze the
hydrogen-bridges [24]. This theory may also be applied to
the halogen-bridges.
For all dimers, the topological analysis of electron
density by AIM approach at the MP2/6-311CG(d,p) level
shows one bond critical point (BCP) between the X atom of
the XY monomer (HB donor; HB stands for the hydrogen
and halogen bonds) and the S atom of TMS (HB acceptor).
The representative molecular graphs of the axial and
equatorial conformers of the complexes 1 and 2 are shown
in Fig. 2. The bond critical points (small black spheres), ring
critical points (small gray spheres) and bond paths are
illustrated in these molecular graphs. The obtained results
for the electron density (rBCP), its Laplacian (P2rBCP),
energy density (HBCP), and ellipticity (3BCP) at the S/X
bond critical points are reported in Table 4. As can be seen,
there is a good relationship between rBCP (or HBCP) values
at the S/X bond critical points and the lengths (see
Table 1) of these bonds. In all cases, the S/X bond is
longer in the conformer with the smaller rBCP or more
negative HBCP. The S/X bond length in the axial
conformer of HF, HCl, and F2 cases is greater than the
equatorial conformer [2.180(2.176), 2.304(2.282),
2.058(2.049) A] and on the contrary for ClF case
[2.497(2.504) A]. The data in the parentheses correspond
to the equatorial conformers. Also, rBCP value at the S/X
critical point of the axial conformer of HF, HCl, and F2
cases is smaller than the equatorial one [r!10K2 values are
283(293), 253(259), and 805(817) au] and on the contrary
for ClF case [564(549) au]. On the other hand, the absolute
value of HBCP at the S/X critical point of the axial
conformer of mentioned cases is also smaller than the
equatorial conformer [KHBCP!10K4 values are 18(26),
9(11), 82(84) au] and on the contrary for ClF case [71(65)].
In these complexes, the established interactions show the
amount of rBCP around 10K2 au, positive P2rBCP, and
negative tiny amount of HBCP. According to the classifi-
cation of Rozas et al. [25], these values correspond to the
medium HBs (complexes 1 and 2). The S/X distances (see
Table 1) are smaller than the sum of the van der Waals radii
(the van der Waals radii of the hydrogen, fluorine, chlorine,
and sulfur atoms are 1.20, 1.47, 1.89, and 1.80 A,
ies, and Gibbs free energies (kJ/mol) of the equatorial conformers relative to
ClF F2
8 1.72 0.358 6.67 4.56
2 1.63 0.261 6.06 3.95
1 1.71 0.342 6.43 4.32
1 1.71 0.342 6.43 4.32
3 0.95 K0.419 4.61 2.50
Fig. 2. Molecular graphs for the axial and equatorial conformers of (a)
TMS/HF (1) and (b) TMS/HCl (2). Small black spheres, small gray
spheres, and lines correspond to the bond critical points (BCP), ring critical
points (RCP) and bond paths, respectively.
A. Ebrahimi et al. / Journal of Molecular Structure: THEOCHEM 712 (2004) 159–166 163
respectively). This is compatible with a HB interaction. It is
pointed out that the value of P2rBCP is greater than
0.139 au in the complex 4.
Also, the ellipticity values of the equatorial conformers
are greater than the axial ones in all complexes. Thus, the
bond curvature of the equatorial conformers is greater than
the axial ones.
It is necessary to mention that in the axial conformer of
the complex 2, it is seen an additional BCP between Cl and
Hb (see Fig. 2b). For this critical point, the values of rBCP,
P2rBCP, and HBCP are 0.0052, 0.0184, and 0.0010 au,
respectively. This is a weak interaction but it seems to be
Table 4
The values of electron density (rBCP), Laplacian (P2rBCP), energy density
(HBCP), and ellipticity (3) calculated at the S/X bond critical points
rBCP P2rBCP- HBCP 3BCP
HF a 0.0283 0.0662 0.0018 0.0086
e 0.0293 0.0611 0.0026 0.0175
HCl a 0.0253 0.0488 0.0009 0.0074
e 0.0259 0.0509 0.0011 0.0234
ClF a 0.0564 0.0992 0.0071 0.0103
e 0.0549 0.1000 0.0065 0.0140
F2 a 0.0805 0.2255 0.0082 0.0111
e 0.0817 0.2296 0.0084 0.0286
All quantities are in atomic units.
important in the more stability of the axial conformer with
respect to the equatorial one.
3.4. Natural atomic orbital and natural bond
orbital analyses
3.4.1. Natural atomic orbital analysis
Some results of the natural atomic orbital analysis are
collected in Table 5. In the complex 1, the total natural
atomic orbital occupancies of valence orbitals of hydrogen
and fluorine atoms approximately increase by 0.008 and
0.04 e in each conformer. Also, in the complexes 3 and 4,
the total natural atomic orbital occupancies of valence
orbitals of X and Y atoms increase on complexation. These
changes are greater than the changes in the complex 1. This
property approximately decreases by 0.008 e and increases
by 0.06 e on the H and Cl atoms of the complex 2,
respectively. On the other hand, the natural charges on the X
atoms in the complexes 1–4 alter by 0.015, 0.001, 0.20 and
0.50 au, respectively. The changes in the complexes 1 and 2
are less than the others.
Furthermore, the total natural atomic orbital occupancy
of valence orbitals of S atom changes on complexation. This
occupancy increases very small (by 0.001 and 0.008 e in the
axial and equatorial conformers, respectively) in the
complex 1 and decreases by 0.016 and 0.012 e in the axial
and equatorial conformers of complex 2, respectively. Also,
the total occupancy of valence orbitals of S atom increases
in the complexes 3 and 4 by 0.215 and 0.550 e for the axial
conformers and 0.204 and 0.556 e for the equatorial ones,
respectively. Thus, it is expected that the charge transfer
effect in the complexes 3 and 4 is stronger than the
complexes 1 and 2.
Furthermore, complexation increases the natural charges
on Ha and Hb (Table 5). The changes on Hb are greater than
Ha. In addition, the increasing of natural charges on the
axial conformers is greater than the equatorial conformers.
Thus, in each case, the hydrogen atom that is closer to the
XY unit suffers a bigger change.
3.4.2. Natural bond orbital analysis
Some results of the natural bond orbital analysis are
collected in Tables 6 and 7. The NBO analysis of TMS
indicate two lone pairs (LP) on the S atom; one of them is a
sp0.42 hybrid orbital (LP1, 70.51% s character and 29.45% p
character) and the other is approximately a pure p orbital
(LP2, 0.72% s character and 99.99% p character). The
occupancies of these orbitals are 1.99716 and 1.94812 e,
respectively. The most important donor–acceptor inter-
actions (above 0.5 kcal/mol threshold limit) of lone pairs
with other orbitals are LP2/[s*C3H8 (0.69), s*
C2H5 (2.94),
s*C2H6 (7.07), s*
C4H9 (2.94), s*C4H10 (7.07)]. The data in
the parentheses are stabilization energies (kcal/mol).
It seems that the bond length of C3–H8 to be smaller than
C3–H7 and the bond lengths of C2–H6 and C4–H10 to be
Table 5
The total natural atomic orbital occupancies of valence orbitals and the natural charges of atoms
Occupancy Natural charge Occupancy Natural charge
XZH, YZF XZCl, YZF
X 0.4580 0.4550 0.5234 0.5280 7.3635 7.3588 K0.4482 K0.4433
Y 7.5127 7.5106 K0.5841 K0.5822 6.7833 6.7681 0.1239 0.1390
S 5.7358 5.7429 0.1722 0.1643 5.5191 5.5306 0.3853 0.3738
Hb 0.7830 0.7959 0.2104 0.1976 0.7743 0.7891 0.2194 0.2046
Ha 0.7894 0.7932 0.2041 0.1994 0.7771 0.7801 0.2160 0.2119
Xa 0.4481 0.5407 6.5743 0.3369
Ya 7.4714 K0.5412 7.2619 K0.3369
XZH, YZCl XZF, YZF
X 0.7374 0.7366 0.2407 0.2432 7.1315 7.1256 K0.4913 K0.4878
Y 7.2145 7.2127 K0.3039 K0.3023 7.4199 7.4163 K0.2185 K0.2130
S 5.7184 5.7224 0.1888 0.1844 5.1848 5.1782 0.7248 0.7305
Hb 0.7846 0.7967 0.2084 0.1968 0.7509 0.7825 0.2431 0.2114
Ha 0.7918 0.7945 0.2016 0.1975 0.7600 0.7491 0.2337 0.2437
Xa 0.7447 0.2417 6.9358 0.0000
Ya 7.1544 K0.2417 6.9358 0.0000
Sa 5.7345 0.1689
Hba 0.8032 0.7963 0.1899 0.1969
Haa 0.7976 0.8048 0.1957 0.1876
a Corresponding to the monomers. In each case, first and second columns correspond to the axial and equatorial conformers, respectively.
A. Ebrahimi et al. / Journal of Molecular Structure: THEOCHEM 712 (2004) 159–166164
lesser than C2–H5 and C4–H9, respectively. The optimized
bond lengths are in agreement with these expectations.
The above mentioned interactions slightly decrease on
complexation. In addition, other interactions should be
considered from LPS to some antibonding and Rydberg
(RY*) orbitals. The most important interactions emerge from
LP1 and LP2 to s*XY (Table 7). For example, the axial
conformer of complex 1 shows LP1/s*HF and LP2/s*
HF
interactions with the energy of 1.05 and 21.85 kcal/mol.
Also, the corresponding interaction energies in the equatorial
conformer are 1.91 and 24.83 kcal/mol, respectively. In this
complex, the occupancy of s*HF in the axial and equatorial
conformers are 0.04765 and 0.05034 e. It is pointed out that
the equatorial conformer is more stable than the axial one at
the MP2/6-311CG(d,p) level (298.15 K and 1.0 atm). As
can be seen from Table 7, in the axial and equatorial
conformers of the complex 2, the energy of LP2/s*HCl
interaction is equal to 19.76 and 19.05 kcal/mol, respect-
ively. Contrary to the complex 1, the axial conformer of
complex 2 is more stable than the equatorial one at the MP2/
6-311CG(d,p) level at the same temperature and pressure.
It can also be seen another donor acceptor interactions from
Table 6
The occupancies (in e) of the most interest NBOs
HF HCl
sXYa 0.048 0.050 0.051 0.048
LP1(S) 1.995 sp0.5 1.992 sp0.46 1.995 sp0.51 1.992 sp0.4
LP2(S) 1.906 sp20.12 1.911 sp26.60 1.900 sp20.25 1.906 sp50
LP1(Y) 1.999 sp0.35 1.999 sp0.37 1.998 sp0.36 1.999 sp0.2
LP2(Y) 1.998 sp 1.998 sp 1.998 sp 1.998 sp
LP3(Y) 1.998 sp99.99 1.998 sp67.03 1.998 sp10.79 1.998 sp42
a Corresponding to the LP4(F). The occupancies of LP1(S) and LP2(S) in TMS a
sp99.99, respectively. In each case, first and second columns correspond to the ax
one unit to other and it is expected that these interactions to be
so important in the relative stability of conformers.
Furthermore, in the complex 1, there are interactions from
LP and sCS orbitals of the S atom to RY* orbitals of the H and
F atoms. Also, there are some donor–acceptor interactions
from HF to TMS. For example, it can be seen an interaction
from sHF to s*C3H7 (above 0.05 kcal/mol threshold limit) in
the axial form which cannot be seen in the equatorial
conformer and also complex 2. Instead of that, one LPCl/s*C3H7 and four LPCl/s*(C2H5, C2H6, C4H9, C4H10) inter-
actions (above 0.05 kcal/mol threshold limit) are seen in the
axial and equatorial conformers, respectively.
Furthermore, in the complex 3, the most important
interactions between two monomers are LP1/s*ClF (3.54
and 3.89 kcal/mol in the axial and equatorial conformers,
respectively), LP2/s*ClF (84.79 and 79.66 kcal/mol in the
axial and equatorial conformers, respectively), and several
LPCl/(s*CH and s*CS). Because of the small difference
in the stability of the axial and equatorial conformers and
also the complexity of interactions, it is difficult to attribute
the relative stabilities of conformers of complex 3 to a
specific interaction.
ClF F2
0.249 0.233 0.515 0.5224 1.995 sp0.59 1.990 sp0.59 1.997 sp0.45 1.994 sp0.55
.56 1.699 sp10.83 1.717 sp10.81 1.486a sp44.50 1.474a sp44.89
5 2.000 sp0.10 2.000 sp0.10 2.000 sp 2.000 sp
1.998 sp 1.998 sp 2.000 sp0.28 2.000 sp7.60
.05 1.998 sp99.99 1.998 sp99.99 1.999 sp4.16 2.000 sp0.16
re 1.997 and 1.948 e, respectively. The hybridization of these are sp0.42 and
ial and equatorial conformers, respectively.
Table 7
Most important second-order perturbative estimates of donor–acceptor interactions energies (kcal/mol)
HF HCl ClF F2a
LP1/s*XY 1.05 1.91 1.44 1.98 3.54 3.89 5.15 1.65
LP1/RY*X 0.27 0.23 1.18 1.18 6.14 6.59 2.53 5.51
LP2/s*XY 21.85 24.83 19.76 19.05 84.79 79.66 218.11 224.25
a Corresponding to the LPi (F)/s*SF, interaction where iZ2,3,4. This interaction is lower than threshold limit (0.05 kcal/mol) for iZ1. In each case, first
and second columns correspond to the axial and equatorial conformers, respectively.
A. Ebrahimi et al. / Journal of Molecular Structure: THEOCHEM 712 (2004) 159–166 165
It is necessary to mention that the results of the NBO
analysis of the complex 4 are different from other
complexes (see Tables 6 and 7). Two predicted units are
C3H6FSC and FK. Four lone pairs are predicted on the FK
unit. The occupancies of these orbitals are reported in
Table 6. As can be seen, the occupancy of LP4 is lower than
the others (1.48622 and 1.47426 e in the axial and equatorial
forms, respectively). In this complex, the most important
donor–acceptor interaction is LP4/s*CS (the interaction
energies are 218.11 and 224.25 kcal/mol in the axial and
equatorial conformers, respectively). The extent of inter-
action energies of the axial and equatorial conformers are in
agreement with the S–F bond length and the stability of
conformers (Table 7).
In all complexes, some C–H bond lengths decrease and
the rest of them do not change on complexation (Table 2).
Although, donor–acceptor interactions between the C–H
bonding and antibonding orbitals and other orbitals change
on complexation but it is so difficult to attribute the
decreasing of the C–H bond length to a specific interaction.
Also, the interactions between two parts of the complexes
indirectly affect the interactions in the TMS unit in
comparison with the lone TMS. For example, in the
complex 1, the interactions from sC3H8 to RY*s and s*s
increase on complexation (the energy of sC3H8/s*CS
interaction is 1.16, 1.20, and 1.19 kcal/mol in the monomer,
axial, and equatorial conformers, respectively). On the other
hand, the interactions to s*C3H8 decrease (the energy of
sCS/s*C3H8 interaction is 4.67, 4.38, and 4.45 kcal/mol in
the monomer, axial, and equatorial conformers, respect-
ively). The occupancy of sC3H8 (s*C3H8) is 1.99 (0.02), 1.99
(0.02), and 1.99 (0.01) e in the monomer, axial, and
equatorial conformers, respectively. In this complex, the
change of the C3–H8 bond length in the axial and equatorial
conformers is discussable with the changes in the above
interactions. In the complex 2, the changes of these
interactions are small so that the occupancies of sC3H8
and s*C3H8 tend to be approximately constant. The
occupancy of sC3H8 (s*C3H8) is 1.99 (0.02) and 1.99
(0.02) e in the axial and equatorial conformers, respectively.
As a result, the C3–H8 bond length does not change on
complexation. In the complex 3, the occupancy of sC3H8
(s*C3H8) is 1.99 (0.01) e in both axial and equatorial
conformers. Thus, the C3–H8 bond length changes on
complexation. The changes of other C–H bonds can be
discussed the same as C3–H8.
4. Conclusions
The relative stability, geometric and energetic aspects of
the axial and equatorial conformers of the TMS/XY
complexes (XY: HF, HCl, ClF and F2) were investigated
using the MP2 and B3LYP (only geometric aspects)
methods. In the MP2 method, for all complexes with the
exception of 3, the calculated S/X bond length in the axial
conformer is greater than the equatorial one. In addition, in
the complexes 1 and 3, the equatorial conformer is more
stable than the axial conformer. On the contrary, in the
complexes 2 and 4, the axial conformer is more stable than
the equatorial one.
The topological analysis of the electron density by AIM
approach at the MP2/6-311CG(d,p) level shows one BCP
between the X and S atoms of all TMS/XY complexes. In
these complexes, established interactions show positive
P2rBCP, tiny negative HBCP, and about 10K2 au for rBCP.
These values correspond to the medium HBs. In each
complex, the S/X bond is longer in the conformer with the
smaller rBCP (or more negative HBCP). In the axial
conformer of complex 2, an additional BCP is seen between
Cl and only one Hb (Fig. 2).
The relative stability of conformers and many of changes
in the geometrical parameters are discussable by the NAO
and NBO analyses. In all complexes, with the exception of
2, the total natural atomic orbital occupancies of valence
orbitals of the X and Y atoms increase on complexation.
These changes in 3 and 4 are greater than 1 and 2.
Furthermore, the total natural atomic orbital occupancy of
valence orbitals of S atom changes on complexation. These
changes in 3 and 4 are also greater than 1 and 2. Thus, it is
expected that the effect of charge transfer in the complexes 3
and 4 is stronger than the complexes 1 and 2.
The most important donor–acceptor interaction in the
axial conformer of the complex 1 is LP2/s*HF with the
energy of 21.85 kcal/mol. The corresponding interaction
energy in the equatorial conformer is 24.83 kcal/mol
(Table 7). This is in agreement with the relative stability of
conformers at the MP2/6-311CG(d,p) level (298.15 K and
1.0 atm). In the axial and equatorial conformers of the
complex 2, the interaction energy of LP2/s*HCl is equal to
19.76 and 19.05 kcal/mol, respectively. This is consistent
with the relative stability of conformers. In the complex 3, the
most important interaction between two monomers is LP2/s*ClF (84.79 and 79.66 kcal/mol in the axial and equatorial
conformers, respectively). Because of the small difference in
A. Ebrahimi et al. / Journal of Molecular Structure: THEOCHEM 712 (2004) 159–166166
the stability of the axial and equatorial conformers and also
the complexity of the interactions, it is difficult to attribute
the relative stability of conformers of the complex 3 to a
specific interaction. In the complex 4, the results of the NBO
analysis are different from other complexes. In this case, two
predicted units are C3H6FSC and FK.
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