ORIGINAL RESEARCH

Towards insight into properties and stabilities of complexesof ozone with CO2, CS2 and SCO species

Abdolvahab Seif • Moein Goodarzi

Received: 3 September 2013 / Accepted: 19 October 2013

� Springer Science+Business Media New York 2013

Abstract The MP2 method in combination with the aug-

cc-pVXZ (X = D and T) basis set has been carried out to

examine the complexes between O3 and isostructure spe-

cies of CO2, CS2 and SCO. Two, two and four minima

have been located on the potential energy surfaces of O3–

CO2, O3–CS2 and O3–SCO complexes, respectively. The

results reveal that the stabilization of complexes should be

in the order O3–CS2 [ O3–SCO [ O3–CO2.

Keywords Ozone � Isostructure species �Atmospheric chemistry � MP2

Introduction

By now, the study of noncovalently bonded interactions is

one of the hottest subjects in material world, and has been

studied in numerous pamphlets of such systems [1, 2]. The

complexes formed through these interactions are very

important in many areas, such as atmospheric chemistry

and biochemical procedure.

Ozone (O3) is one of the most interesting species

in the atmosphere. It is incontrovertible that the exis-

tence of O3 in the atmosphere is important for life on

the Earth. Because, it absorbs solar radiation with a

wavelength which influences on our health. In the

troposphere, O3 is a harmful pollutant that causes dam-

age to glaze and respiratory tissues in animals and tis-

sues in plants. It can also act as a chemical oxidant by

adding oxygen atoms to other compounds. The largest

concentration of O3 is attained at approximately

4 9 1012 molecules/cm3 [3–5]. Because of its short-lived

nature, tropospheric O3 does not have strong global

effects, but has very strong radiative forcing effects on

regional scales. In fact, there are regions of the world

where tropospheric O3 has a radiative forcing up to

150 % of carbon dioxide [6].

Atmospheric sulphur chemistry plays an important role

in the Earth’s atmosphere [7, 8]. It is well accepted that

carbon disulphide (CS2) and carbonyl sulphide (SCO) are

two of the major pollutants in the atmosphere [9, 10].

The CS2 molecule gets out during volcanic eruptions

[11]. Swamps are also one of the major sources of this

molecule. The pollutants, which are derived from carbon

disulphide by photolysis, are great threats to human health

and global environment. Its atmospheric quality is greatly

affected by atmospheric particles, on which a lot of het-

erogeneous interactions occur.

The SCO molecule is the most abundant sulphur com-

pound naturally present in the atmosphere. It is emitted

from oceans, volcanoes and deep sea vents. The long

atmospheric lifetime of SCO makes it the major source of

stratospheric sulphate, though sulphur from volcanic

activity can be significant too [12]. As such, it is a sub-

stantial compound in the global sulphur cycle.

In the present work, we report for the first time

detailed examination of the stability and properties of

complexes including O3 molecule with one of CO2, CS2

and SCO molecules. This computational study can

provide valuable information in the atmospheric

chemistry.

A. Seif (&)

Department of Chemistry, Faculty of Science, University of

Kurdistan, Sanandaj, Iran

e-mail: abdolvahabseif@gmail.com

M. Goodarzi

Department of Chemistry, Institute for Advanced Studies in

Basic Sciences (IASBS), Zanjan, Iran

123

Struct Chem

DOI 10.1007/s11224-013-0365-3

Computational method

All calculations have been performed with the GAUSSIAN

03 quantum chemical package [13] using MP2/aug-cc-

pVXZ (X = D and T) level [14] along to the frozen core

approximation. Harmonic vibrational frequency calcula-

tions have been performed at the MP2/aug-cc-pVDZ

computational level to confirm the existence of all com-

plexes as local minima (with the number of imaginary

frequencies NIMAG = 0) and to provide the evaluation of

the zero–point energies (ZPEs).

Despite the complicated nature of O3 upon a multicon-

figuration scheme [15], many reports have focused on the

simple single-configuration types of calculations. In this

regard we can see that MP2, as one of the acceptable

computational levels, has attracted attention to investigate

of O3 complexes [16, 17].

In all complexes, the reported energies correspond to

that corrected from the inherent basis set superposition

error (BSSE) using the full counterpoise method [18].

The molecular electrostatic potential (MEP) on the

electron density isosurface of 0.001 a.u. has been

obtained and depicted using the WFA program [19]. The

atoms in molecules (AIM) methodology [20] have been

used with the AIM2000 [21] programs to analyse the

electron density calculated at the MP2/aug-cc-pVDZ

computational level. The natural bond orbital (NBO)

technique was performed to count the value of charge

transfer occurring at atomic charges using the NBO-3

program [22–24].

Results and discussion

The stabilization energies of the complexes in the

present work were calculated as the difference between

the energy of the complex and the sum of the ener-

gies of the isolated monomers in their minimum

configuration.

To determine the structural complexes, the different

orientations of CO2, CS2 and SCO species to O3 molecule

have been chosen. The b, c and d nomenclatures stand for

complexes of O3–CO2, O3–CS2 and O3–SCO, respec-

tively. Notice that the numbering that has been used in

nomenclature conform to the ordering of binding energy

(corrected with BSSE) at the MP2/aug-cc-pVTZ//MP2/

aug-cc-pVDZ level. In the present work, our results have

been accommodated within three sections. The first on

monomers and its characterizations have been discussed.

The second on the analyses of the dimers clustering and at

last the evaluation of the AIM and NBO analyses are

discussed.

Monomers

The O3 molecule has C2V symmetry, whereas other iso-

structure species are belonging to the more symmetrical

groups, CO2 and CS2 molecules have D?h symmetry and

SCO one has C?v symmetry.

The electronic feature of the monomers, which is of the

topmost interest in the study of non-covalent interactions,

is the MEP on the 0.001 a.u. electron density isosurface.

The 0.001 a.u. isosurface has been famed, since it has been

shown to resemble the experimental van der Waals surface

[25]. To identify basic and acidic sites for possible inter-

molecular interactions, the MEP is very useful implement.

To understanding of a more detailed of the electrostatic

characterization, it is worth to mention the presence of four

minima in the MEP of the O3 molecule, each twin of them

for lateral oxygen atoms. Figure 1 shows that O3 molecule

has two major regions on its electrostatic profile. Blue

colour indicates the high density of the presence of elec-

trons, whereas red refers to deficiency of the presence of

electrons. This approach mainly exists for other studied

monomers, CO2, CS2 and SCO. Minima for each of CO2

and CS2 (D?h) species and also for SCO (C?v) are shown

in Fig. 1. According to electrostatic potential profiles of

monomers along interaction, it is worth to underscore three

of the following points:

(a) According to the electrostatic potential profile of O3,

it seems that the surrounding of central oxygen atom

is mainly positive.

(b) Comparing profiles of CO2 and CS2 monomers reveal

that the substitution of both O-atoms in CO2 mono-

mer by S-atoms causes diminishing of deficiency

upon central atom and towards it to lateral atoms.

This treatment can be attributed to the decreasing of

electronegativity of S-atoms. Thus, the S-atoms of

CS2 are more positive than the O-atoms of CO2.

(c) The profile of SCO monomer shows that the head of

O-atom is much more negative than that of S-atom.

Heterodimers

O3–CO2 complexes

Figure 2 shows that association of CO2 monomer leads to

two minima, b1 and b2. b1 complex is formed when just

one of O-atoms of CO2 molecule attacks to both terminal O

atoms of O3. The distances of O���O interaction are 2.973

and 2.966 A at the MP2/aug-cc-pVDZ level. Table 1

shows that the binding energy of b1 complex (after BSSE

correction) is 8.32 kJ/mol at the MP2/aug-cc-pVTZ//MP2/

aug-cc-pVDZ level.

Struct Chem

123

b2 complex was found on the PES of O3–CO2 system.

This complex is formed through a linkage between terminal

O-atom of O3 and C-atom of CO2 (O���C interaction) with

bond length of 2.951 A at the MP2/aug-cc-pVDZ level. The

binding energy of this complex (corrected with BSSE) is

5.22 kJ/mol at the MP2/aug-cc-pVTZ//MP2/aug-cc-pVDZ

level.

These results show that b1 complex is 3.10 kJ/mol more

stable than b2 one. Note that our results are calculated at

the room situation. Hence, differences of temperature and

pressure, particularly in the atmosphere, may influence this

result.

O3–CS2 complexes

Similar to prior system, two minima, c1 and c2, were

located on the PES of O3–CS2 system as shown in Fig. 2.

c1 is the most stable complexes among all obtained com-

plexes for O3–CO2, O3–CS2 and O3–SCO systems. c1 is

12.04 kJ/mol more stable than initial reactants of O3 and CS2

Fig. 1 Molecular electrostatic

potential on the 0.001 a.u.

electron density isosurface of

monomers a O3, b CO2, c CS2

and d SCO

Table 1 Stabilization energies (kJ/mol) of O3–CO2, O3–CS2 and O3–SCO systems at the MP2 level

Complexes MP2/aug-cc-pVDZ MP2/aug-cc-pVTZ//MP2/aug-cc-pVDZ

EI EI ? BSSE EI ? BSSE ? ZPE EI EI ? BSSE

b1 -11.88 [-9.58] -6.87, 42 % [-3.26,65 %] -0.42 -10.84 -8.32

b2 -7.83 -4.40 1.19 -6.84 -5.22

c1 -14.78 [-16.91] -8.83, 40 % [-1.54, 90 %] -4.42 -15.23 -12.04

c2 -14.23 -8.88 -4.25 -14.55 -11.64

d1 -12.53 [-12.11] -7.59, 39 % [-1.79, 85 %] -2.08 -12.60 -10.03

d2 -12.70 -7.45 -1.94 -12.57 -9.81

d3 -8.06 -4.55 -0.10 -7.44 -5.68

d4 -7.74 -4.36 0.11 -7.17 -5.46

The values of in square brackets are at the MP2/6-311??G(d,p) level [23]. The BSSE contributions to the raw interaction energy are in

percentage form

Struct Chem

123

at the MP2/aug-cc-pVTZ//MP2/aug-cc-pVDZ level. In c1

complex, all three O-atoms of O3 present in intermolecular

interactions. Two of them have been emanated from the

connection of terminal oxygen atoms of O3 monomer with one

of S-atoms of CS2 monomer, with interaction distance of

3.256 A. The third interaction, with bond length of 3.061 A is

formed through the linkage of central O-atom of O3 to C-atom

of CS2 monomer. Note that interaction of central O-atom of O3

with C-atom of CS2 monomer appeals only in the c1 complex.

C2 is the second stable complexes among all obtained

complexes for O3–CO2, O3–CS2 and O3–SCO systems

which is formed through two interactions, O���S (3.113 A)

and O���C (2.968 A). The binding energy of this complex,

approaching to c1 complex, is 11.64 kJ/mol (corrected

with BSSE) at the MP2/aug-cc-pVTZ//MP2/aug-cc-pVDZ

level.

O3–SCO complexes

The latest system, considered in this work, has four minima

as shown in Fig. 1.

d1 complex is the most stable complex in the O3–SCO

system. In this complex, both terminal O-atoms of O3

molecule approach SCO molecule to form two interactions

of O���S (3.173 A) and O���C (2.916 A). As shown in

Table 1, the binding energy d1 complex is 10.03 kJ/mol at

the MP2/aug-cc-pVTZ//MP2/aug-cc-pVDZ level (cor-

rected with BSSE).

The second most stable complexes in the O3–SCO

system are d2 including two similar interactions of O���Cwith bond length 3.045 A at the MP2/aug-cc-pVDZ level.

The third and fourth minima located on the PES of this

system are d3 and d4, respectively. Although these two

Fig. 2 The representation of molecular graph of the minima obtained at the MP2/aug-cc-pVDZ level, b O3–CO2, c O3–CS2 and d O3–SCO

systems. The red and yellow dots represent the position of the bond and ring critical points, respectively

Struct Chem

123

complexes are very similar to each other, they have been

differed on the orientation of oxygen and sulphur atoms of

SCO towards the O3 monomer. It is mentionable that both

of them include one O���C interaction, in which O���Cinteraction of d3 complex is only 0.008 A shorter than that

of d4 complex. The computation of binding energies for

them shows that they should be 5.68 and 5.46 kJ/mol at the

MP2/aug-cc-pVTZ//MP2/aug-cc-pVDZ level, respectively.

The d3 and d4 complexes are the most unstable complexes

in the O3–SCO system.

Note that Venayagamoorthy and Ford [26] have recently

done molecular orbital studies of the vibrational spectra on

the complexes between O3 and each of CO2, CS2 and SCO

monomers at the MP2/6-311??G(d,p) level. They have

only reported the most stable complex for each of O3–CO2,

O3–CS2 and O3–SCO systems which are b1, c1 and d1,

respectively. As shown in Table 1, the reported binding

energy by Venayagamoorthy and Ford for b1, c1 and d1

complexes (at the MP2/6-311??G(d,p) level) are in good

agreement with those of the present work (without BSSE)

at the MP2/aug-cc-pVDZ level. While, comparison of the

corrected binding energy with BSSE shows that energy

values at the MP2/aug-cc-pVDZ level (in the present work)

are very different from those of MP2/6-311??G(d,p) level

(by Venayagamoorthy and Ford [26]). The values of BSSE

in both the present and the previous works are gathered in

Table 1.

It should be noted that the binding energies with the

Dunning basis sets are considerably larger than those of the

earlier work using a fairly large pople- type basis set.

As result, the binding energy of all complexes obtained

in the O3–CO2, O3–CS2 and O3–SCO systems can organize

in the order c1 [ c2 [ d1 [ d2 [ b1 [ d3 [ d4 [ b2.

This means that the most stable complexes belong to O3–

CS2 system. Therefore, this system plays more prodigious

role, from the atmospheric point of view.

AIM and NBO

Because of the presence of intermolecular interaction, it is

important to know the nature of interaction meticulously.

Thus, the usage of the Badar’s theory within AIM analysis

can be beneficial to analyse of interactions, especially weak

interactions. According to this theory, which is capable of

the topological analysis of the electron density, those points

of space where the gradient is hollow are characterized.

Three main kinds of these hollowed gradients, the so-called

critical points, are bond critical points, BCP (3, -1), ring

critical points, RCP (3, ?1) and cage critical points, CCP

(3, ?3). Note that the number (3) and sign (-1, ?1 and

?3) of the eigenvalues of these critical points have been

calculated after the solution of Hessian matrixes. The most

interested critical point, BCP, is located along a maximum

electron density trajectory that connects two atoms, known

as bond path.

These BCPs present electron density values between

0.0073 and 0.0103 a.u. and Laplacians between 0.0265 and

0.0356 a.u. as shown in Table 2. In Fig. 2, the corre-

sponding critical points and bond path of the three systems

are portrayed showing a diversity of complex graph forms.

The GC/VC ratio, being GC and VC the kinetic and potential

energy density at BCP, respectively, has been used as a

measure of the covalency in non-covalent interactions.

Values greater than 1 generally indicates a non-covalent

interaction without covalent character, while ratios smaller

than 1 are stating of the covalent nature of the interaction

[27]. The values of this quantity are around 1.2 that indi-

cates non-covalent nature of the interactions.

The small electron density, positive values of r2q and

-GC/VC \ 1 indicate that all intermolecular interactions

are weak interactions of non-covalent without any covalent

characters.

The electron density for each dataset shows a good

correlations between interatomic distance of the atoms

involved and qBCP (a.u.) and r2qBCP (a.u.). However,

previous reports have shown that this correlation should be

exponential (Fig. 3) [28, 29]. Thus, as the intermolecular

distance of the interacting atoms decreases, the values of

qBCP and r2qBCP increases.

The charge transfer values upon the formation of the

complexes are listed in Table 3. It is interest that the

maximum value of this quantity among all complexes is

belonging to the most stable complexes, c1 (0.009). Also,

O3 molecule has the role of an acceptor in O3–CS2, O3–

SCO systems, while it is a donor in O3–CO2 systems. The

Table 2 Interatomic distances (A) and bond critical point data (a.u.)

calculated at the MP2/aug-cc-pVDZ level

Complexes Interaction Interaction

distance

q r2q -G/V

b1 O���O 2.973 0.0087 0.0351 1.1616

O���O 2.966 0.0088 0.0356 1.1605

b2 O���C 2.951 0.0088 0.0324 1.2495

c1 O���S 3.256 0.0079 0.0265 1.1383

O���C 3.061 0.0074 0.0300 1.2037

O���S 3.256 0.0079 0.0265 1.1381

c2 O���C 2.968 0.0092 0.0317 1.1792

O���S 3.113 0.0103 0.0323 1.1113

d1 O���S 3.173 0.0094 0.0294 1.1112

O���C 2.916 0.0093 0.0332 1.2019

d2 O���C 3.045 0.0081 0.0291 1.2024

O���C 3.045 0.0081 0.0291 1.2023

d3 O���C 3.071 0.0074 0.0292 1.2474

d4 O���C 3.079 0.0073 0.0295 1.2438

Struct Chem

123

values of dipole momentum of complexes were listed in the

latest column of this table. These values are in range of

0.550–1.365 D. It should be noted that the minimum value

of dipole momentum among all systems is belong to the

most stable complexes c1 (0.550 D).

Conclusions

Ab initio calculations have been performed at the MP2/

aug-cc-pVDZ and MP2/aug-cc-pVTZ//MP2/aug-cc-pVDZ

levels to analyse the complexes at the O3–CO2, O3–CS2

and O3–SCO systems. The results can be summed as

follows:

(a) Our calculations reveal that the stability of three

systems can be organized in the order O3–CS2 [ O3–

SCO [ O3–CO2. The stability energies are in range

5.22–12.04 kJ/mol at the MP2/aug-cc-pVTZ//MP2/

aug-cc-pVDZ level.

(b) All possible interactions (regarding AIM analysis)

among atoms of monomers have been found in the

present work. Note that interaction of central O-atom

of O3 with C-atom of CS2 monomer appeals only in

the c1 complex.

(c) Based on AIM analysis, the small electron density,

positive values of r2qBCP and -GC/VC [ 1 indicates

that all intermolecular interactions in O3–CO2, O3–

CS2 and O3–SCO systems are weak interactions of

non-covalent with no covalent characters.

(d) The maximum value of charge transfer and the

minimum value of dipole momentum obtained are

belonging to the most stable complexes among three

systems.

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Struct Chem

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