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: ebrahimi@hamoon.usb.ac.ir (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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