Journal of Molecular Structure: THEOCHEM 944 (2010) 110–115

Contents lists available at ScienceDirect

Journal of Molecular Structure: THEOCHEM

journal homepage: www.elsevier .com/locate / theochem

Mechanism for the gas-phase of sulfur vapor with ozone reaction: Atheoretical study

Moein Goodarzi a, Morteza Vahedpour a,*, Fariba Nazari b

a Chemistry Department, Zanjan University, Zanjan, Iranb Institute for Advanced Studies in Basic Sciences, Zanjan, Iran

a r t i c l e i n f o

Article history:Received 11 August 2009Received in revised form 21 December 2009Accepted 22 December 2009Available online 13 January 2010

Keywords:Sulfur vaporOzoneTopological analysis of electronic densityPotential energy surface

0166-1280/$ - see front matter � 2010 Elsevier B.V. Adoi:10.1016/j.theochem.2009.12.035

* Corresponding author. Fax: +98 241 515 2477.E-mail address: vahed@znu.ac.ir (M. Vahedpour).

a b s t r a c t

The reaction pathways of sulfur vapor with ozone on the singlet potential energy surface have beeninvestigated theoretically at CCSD(T)/6-311++G(3df,3pd)//B3LYP/6-311++G(3df,3pd) level of computa-tion. The calculated results show that the reactants are initially associated with the adduct S–O3 througha barrierless process. Subsequently, via a variety of transformations of isomer S–O3, two kinds of productsP1(SO + 3O2) and P2(SO3(D3h)) are obtained. The cleavage and formation of the chemical bonds in the reac-tion pathways have been discussed using the topological analysis of electronic density. The topologicalanalysis results show that the ring transitional structure region occurs in cis-OSOO ? SO3(Cs) andSO3(Cs) ? SO3(D3h) reaction pathways.

� 2010 Elsevier B.V. All rights reserved.

1. Introduction SO (with D symmetry) which is considered as a major factor

The existence of O3 in the atmosphere is important for life onEarth because it absorbs solar radiation with a wavelength between240 and 320 nm. The largest concentration of ozone is attained atapproximately 4.00 � 1012 molecules/cm3 [1–5]. These moleculesform a layer which has 10 km width and between 25 and 35 kmheight [2]. The applications of ozone in chemical reactions are essen-tial and important. The reaction of ozone with other species is one ofthe best investigated chemical reactions which have been reportedin many researches published in the recent years [6–12]. For exam-ple, the potential energy surface of the HO3 ? HO + O2 reaction hasbeen studied using QCISD(T)/CBS level. There exists a cis and transplaner equilibrium geometry for HO3 structure. The cis HO3 isslightly more stable than the trans-HO3 [13].

The principal natural phenomenon which distributes sulfur va-por and gaseous sulfur compounds in atmosphere are volcanoesand those from biological processes that occur on the Earth, in wet-lands, and in the oceans. A lot of gaseous sulfur compounds get outduring volcanic eruptions which include sulfur vapor, gaseous sul-fur compounds and different gases.

As we know, the reaction mechanism of S with O3 is ambiguousand the major channels of producing SO + 3O2 and SO3(D3h) havenot been identified. Our main objective in this article is the theo-retical investigation of the reaction mechanism of S with O3. Thisreaction is important in atmospheric chemistry, because it forms

ll rights reserved.

3 3h

in the production of acidic rains [14]. The cleavage and formationof the chemical bonds in the reaction pathways have been dis-cussed using the topological analysis of the electronic density.

2. Computational methods

The geometries of the reactants, products, intermediates andtransition states involved in the reaction are optimized using thedensity functional theory with the B3LYP [15,16] exchange–corre-lation functional with 6-31++G(d,p) and 6-311++G(3df,3pd) basissets and MP2/6-311++G(d,p) [17,18] level. Harmonic vibrationalfrequencies were obtained at the MP2 level for the verification ofthe optimized geometries. Transition states were characterizedby one imaginary vibrational frequency. The connections betweenintermediates, transition states and products are confirmed by theintrinsic reaction coordinate (IRC) [19,20] analysis at the MP2 levelof theory. A higher level of electronic correlation method, CCSD(T)/6-311++G(3df,3pd), is employed in the single-point-energy calcu-lations to improve the accuracy of energetic information on mini-mum energy path (MEP). All of the calculations are performed withthe Gaussian-98 program [21]. Topological analysis was carried outwith AIM2000 program [22] and molecular graphs in the reactionpathway of cis-OSOO ? SO3(D3h) were plotted.

3. Results and discussion

The optimized geometrical parameters of the reactants, inter-mediates, transition states (TSs) and products at the B3LYP and

Fig. 1. Geometries of reactants, intermediates, transition states and products at (a) B3LYP/6-31++G(d,p), (b) B3LYP/6-311++G(3df,3pd) and (c) MP2/6-311++G(d,p) levels(bond lengths in angstrom, bond angles in degree).

M. Goodarzi et al. / Journal of Molecular Structure: THEOCHEM 944 (2010) 110–115 111

MP2 levels, have been shown in Fig. 1. The total energies, ZPEs andrelative energies have been listed in Table 1 for the B3LYP, MP2 andCCSD(T) levels, where the molecular energy at the CCSD(T) level isthe sum of CCSD(T) energy and the ZPE, which is obtained from theB3LYP/6-311++G(3df,3pd) level. The calculated vibrational fre-quencies at MP2 level which have been listed in Table 2 show thatS–O3, trans-OSOO, cis-OSOO, SO3(Cs) and SO3(D3h) are true mini-mums on the reaction potential energy surface (PES). Finally, theprofile of PES has been depicted in Fig. 2, where the energy ofS + O3 has been set to zero as reference.

3.1. Initial association

We have only considered one stable collision complex (S–O3)between sulfur atom and ozone which is formed through the inter-action of the sulfur atom with middle oxygen atom in ozone mol-

ecule. The bond length of O–O in S–O3 is 1.31 Å at the MP2 level,which is about 0.03 Å longer compared with parent O3 molecule.The bond length of newly formed S–O is 1.75 Å. S–O3 collisioncomplex has C2V symmetry and its energy is 10.42 kcal/mol lessthan that of the original reactants and no transition state has beenfound for the formation of S–O3. This has been confirmed by thepoint-wise potential energy curve calculated by MP2 level, asshown in Fig. 3. Therefore, the formation of S–O3 with C2V symme-try is barrierless and exothermic. The details of the reaction mech-anism are discussed below.

3.2. Isomerization and dissociation pathways

It is shown in Fig. 2 that we have two products in five Pathswhich are summarized as follows:

Table 1The total energy (ET), zero-point-energy (ZPE), relative energy (in the parenthesis) and electronic energy (E) obtained at different calculation levels.

Species B3LYP MP2/6-311++G(d,p) CCSD(T)//B3LYP 6-311++G(3df,3pd) Ea,c ZPEa,b

6-31++G(d,p) 6-311++G(3df,3pd) ETa ET

a

ETa ET

a

S + O3 �623.4569(0.00) �623.5637(0.00) �622.4932(0.00) �622.7211(0.00) �622.7284 0.0073S–O3 �623.4982(�25.92) �623.6088(�28.30) �622.5217(�17.88) �622.7377(�10.42) �622.7469 0.0092Trans-OSOO �623.6567(�125.38) �623.7864(�139.74) �622.6939(�125.94) �622.9233(�126.88) �622.9321 0.0088Cis-OSOO �623.6642(�130.08) �623.7945(�144.83) �622.7096(�135.79) �622.9313(�131.90) �622.9407 0.0094SO3(Cs) �623.6872(�144.51) �623.8267(�165.04) �622.7121(�137.36) �622.9668(�154.18) �622.9768 0.0100SO3(D3h) �623.7607(�190.64) �623.9239(�226.03) �622.8000(�192.52) �623.0659(�216.37) �623.0782 0.0123SO + 3O2 �623.6363(�112.57) �623.7546(�119.79) �622.6680(�109.69) �622.8916(�106.99) �622.8979 0.0063TS1 �623.4669(�6.27) �623.5755(�7.40) �622.4884(3.01) �622.7106(6.59) �622.7180 0.0074TS2 �623.6231(�104.29) �623.7603(�123.37) �622.6493(�97.95) �622.8895(�105.67) �622.8974 0.0079TS3 �623.6471(�119.35) �623.7803(�135.92) �622.6611(�105.36) �622.9156(�122.05) �622.9239 0.0083TS4 �623.6294(�108.24) �623.7633(�125.25) �622.6384(�91.11) �622.8986(�111.38) �622.9067 0.0081TS5 �623.6322(�110.00) �623.7784(�134.73) �622.6489(�97.70) �622.8765(�97.52) �622.8849 0.0084TS(6) �623.4432(8.60) �623.5502(8.47) �622.7048(10.23) �622.7110 0.0062

a Total energies (ET), zero-point-energy (ZPE), and electronic energy (E) are in Hartree and relative energies in the parenthesis are in kcal/mol.b ZPE obtained at the B3LYP/6-311++G(3df,3pd) level.c Electronic energy (E) obtained at the CCSD(T) level.

112 M. Goodarzi et al. / Journal of Molecular Structure: THEOCHEM 944 (2010) 110–115

where, R stands for reactants (S and O3), SO and 3O2 products aredenoted by P1 and SO3 (with D3h symmetry) by P2.

3.2.1. Formation pathways of P1 [SO + 3O2]There are three feasible pathways to form P1 which can be writ-

ten as follows:

Path P1ð1Þ R! S—O3! TS6! P1

Path P1ð2Þ R! S—O3! TS1! trans-OSOO! P1

Path P1ð3Þ R! S—O3! TS1! trans-OSOO! TS2! cis-OSOO! P1

In the Path P1(1), the initial adduct S–O3 undergoes O2–O3 bondformation and O1–O2 and O1–O3 bonds rupture. This leads to theformation of product P1 via TS6 with energy barrier of 20.65 kcal/mol. At this step (Path P1(1)), middle oxygen in O3 is absorbed by

Table 2The vibrational frequencies (cm�1) of the reactants, intermediates, products andtransition states calculated at the MP2 level.

Species Frequencies

O3 749 1164 2293S–O3 403 500 527 731 1421 1935Trans-OSOO 203 451 565 674 1246 6667Cis-OSOO 177 358 571 616 1229 4282SO3(Cs) 319 426 604 626 856 1308SO3(D3h) 421 495 495 1015 1373 1373SO 9663O2 1456TS1 1343i 266 377 676 1206 2636TS2 616i 216 241 563 1268 2420TS3 807i 291 382 835 1087 1175TS4 694i 301 372 512 955 1187TS5 2804i 321 403 848 1231 302

S. It should be noted here that TS6 optimized at B3LYP/6-311++G(3df,3pd) level has only one imaginary frequency (473i).In other words, TS6 is a transition state. In spite of numerous at-tempts, we could not optimize it at the MP2 level. We havechecked the T1 diagnostic value of the CCSD(T) method for TS6structure. The value is 0.11 which is greater than 0.02. This impliesthat TS6 has a multi-reference character and MP2 method is notreliable. As a result, optimization is done at B3LYP/6-311++G(3df,3pd) level which is the most realistic in this case. InPath P1(2), S–O3 undergoes a concerted S4–O2 bond formationand O2–O1 bond rupture to form trans-OSOO via TS1 with energybarrier of 17.01 kcal/mol. Trans-OSOO is easily decomposed to theproduct P1 by S3–O2 bond rupture without any entrance barrier. InPath P1(3), the formation of trans-OSOO is similar to Path P1(2). Thetrans-OSOO is 126.88 kcal/mol lower than the total energy of theoriginal reactants. This energy provides the driving force for theformation of cis-OSOO via TS2 by S3–O4 bond rotation aroundthe S3–O2 bond with energy barrier of 21.21 kcal/mol. Finally,cis-OSOO can easily be decomposed to the product P1 by S4–O3bond rupture without any entrance barrier. For Paths P1(2) andP1(3), the reaction mechanism is the absorption of O3 terminal oxy-gen by S.

Paths P1(1) and P1(2) among these three channels involve fewerintermediates. Also, the energy barrier of S–O3 ? TS1 (in Path P1(2))is 3.64 kcal/mol lower than that of S–O3 ? TS6 (in Path P1(1)). There-fore, Path P1(2) is expected to be a more feasible channel for productP1 with mechanism of O3 terminal oxygen absorption by S.

3.2.2. Formation pathways of P2 [SO3(D3h)]For product P2 [SO3(D3h)], there are two feasible pathways as

follows:

Fig. 2. The potential energy profile of the title reaction from CCSD(T) calculations based on the B3LYP/6-311++G(3df,3pd) geometries.

M. Goodarzi et al. / Journal of Molecular Structure: THEOCHEM 944 (2010) 110–115 113

Path P2ð1Þ R! S—O3 ! TS1! trans-OSOO! TS3! SO3ðCsÞ! TS5! P2

Path P2ð2Þ R! S—O3 ! TS1! trans-OSOO! TS2! cis-OSOO! TS4! SO3ðCsÞ ! TS5! P2

In Path P2(1), the formation of trans-OSOO is similar to PathP1(2). Trans-OSOO undergoes S3–O1 bond formation to form SO3

(with Cs symmetry) via TS3 with energy barrier of 4.83 kcal/mol.The three-member ring geometry of SO3(CS) is given in Fig. 1. Itsenergy is 154.18 kcal/mol less than that of the reactants as shownin Fig. 2. Also, SO3(Cs) is transformed to product P2 via TS5 with theenergy barrier of 56.66 kcal/mol. In Path P2(2), the formation of cis-OSOO is similar to Path P1(3). Cis-OSOO is transformed to SO3(Cs)via TS4 by the formation of S4–O1 bond with energy barrier of20.52 kcal/mol. Finally, SO3(Cs) is transformed to product P2 viaTS5 with energy barrier of 56.66 kcal/mol. Therefore, product P2

is produced via two different channels in which, sulfur atom ini-tially interacts with middle oxygen atom in O3 which is followedby interaction with terminal oxygen atoms in O3. In Path P2(1),the energy barrier of single step trans-OSOO ? SO3(Cs) is4.83 kcal/mol, while, in Path P2(2), the formation of SO3 is done

Fig. 3. Relaxed potential energy curve for the formative process of the adduct S–O3

calculated at the MP2 level.

in two steps. The energy barriers of the first trans-OSOO ? cis-OSOO and the second cis-OSOO ? SO3(Cs) steps are 21.21 and20.52 kcal/mol, respectively. Therefore, Path P2(1) is expected tobe a more feasible channel for P2.

According to the reaction pathways obtained in the reaction of Swith O3, the most possible reaction pathways of two P1 [SO + 3O2]and P2 [SO3(D3h)] products are listed again:

Path P1ð2Þ R! S—O3 ! TS1! trans-OSOO! P1

Path P2ð1Þ R! S—O3 ! TS1! trans-OSOO! TS3! SO3ðCsÞ ! TS5! P2

The sulfur atom can barrierlessly react with O3 at the middleoxygen site to form intermediate S–O3 followed by isomerizationto trans-OSOO which is involved in the Paths P1(2) and P2(1). Forthe trans-OSOO, there are two pathways. One pathway is thedecomposition of the trans-OSOO to product P1 without any en-trance barrier [in the Path P1(2)] and the other one is the isomeri-zation of the trans-OSOO to product P2 via TS3 and TS5 [in the PathP2(1)] with energy barriers of 4.83 and 56.66 kcal/mol, respec-tively. Therefore, Path P1(2) is obviously a more suitable pathwayand P1 is a more appropriate product in the reaction of S with O3.

3.3. Topological analysis of electronic density on IRC paths

According to the topological analysis of electronic density, inthe theory of the Atoms in Molecules (AIM) [23,24], electron den-sity qðrcÞ and Laplacian of the electron density (r2qðrcÞ) are usedto describe the strength and the characteristic of the bond, respec-tively. The Laplacian (r2qðrcÞ is the sum of k1, k2 and k3, where ki isthe ith eigenvalue of Hessian matrix of the electronic density. If acritical point has two negative and one positive eigenvalues, it iscalled (3,�1) or the bond critical point (BCP). If a critical pointhas two positive and one negative eigenvalues it is called (3,+1)or the ring critical point (RCP), which indicates that a ring structureexists. The interval from the appearance of the ring to its disap-pearance is called, ring structure transition region. The k2 eigen-value of the Hessian matrix of the RCP (the positive curvaturelying in the plane) has a tendency to zero ? maximum ? zero.The maximum Hessian matrix k2 of the RCP is called structure tran-sition state (STS). Also, the traditional transition state that is amaximum on energy surface is called, energy transition state(ETS) [12].

Fig. 4. The molecular graphs of cis-OSOO ? SO3(D3h) reaction. (Small representsring critical point(RCP), small represents bond critical point(BCP).)

Table 3Topological properties at BCP and RCP of the ring structure transition region for reaction cis-OSOO ? SO3(D3h) at the MP2 level.

Bond Sa,b,c/(amu)1/2 bohr q Eigen of the Hessian matrix r2qd

k1 k2 k3

RCP S3 = +2.63e 0.1100 �0.1612 0.0464 0.3499 0.2338S3 = +4.37 0.1373 �0.2296 0.2436 0.4154 0.4292S3 = +4.43(STS) 0.1380 �0.2313 0.2438 0.4195 0.4320S3 = +4.55 0.1393 �0.2343 0.2436 0.4275 0.4368S5 = �2.23f 0.1245 �0.2029 0.0344 0.6027 0.4340

O3–O1 Cis-OSOO 0.3806 �0.9113 �0.9016 1.5707 0.2420S3 = +2.63 0.2607 �0.5794 �0.5642 1.2097 0.0660S3 = +4.37 0.2331 �0.4920 �0.4734 1.0990 0.1332S3 = +4.43(STS) 0.2321 �0.4893 �0.4694 1.0953 0.1364S3 = +4.55 0.2302 �0.4839 �0.4614 1.0880 0.1424S5 = �2.23 0.1246 �0.2038 �0.0344 1.6243 0.3780

S–O2 Cis-OSOO 0.2785 �0.4883 �0.4368 1.9633 0.1038S3 = +2.63 0.2887 �0.5360 �0.4795 2.1696 1.1540S3 = +4.37 0.2941 �0.5505 �0.5039 2.2781 1.2232S3 = +4.43(STS) 0.2942 �0.5511 �0.5045 2.2809 1.2248S3 = +4.55 0.2945 �0.5521 �0.5056 2.2862 1.2284S5 = �2.23 0.2978 �0.5640 �0.5232 2.3539 1.2664SO3(D3h) 0.3021 �0.5962 �0.4735 2.1740 1.1040

S–O3 Cis-OSOO 0.1495 �0.2398 �0.1659 0.3075 �0.0980S3 = +2.63 0.2112 �0.3281 �0.3051 0.4057 �0.2272S3 = +4.37 0.1897 �0.2881 �0.2390 0.2688 �0.2616S3 = +4.43(STS) 0.1892 �0.2870 �0.2371 0.2673 �0.2568S3 = +4.55 0.1881 �0.2850 �0.2333 0.2645 �0.2536S5 = �2.23 0.1995 �0.3031 �0.2394 0.5150 �0.0272SO3(D3h) 0.3021 �0.5962 �0.4735 2.1740 1.1040

S–O1 S3 = +2.63 0.1102 �0.1571 �0.0408 0.3403 0.1424S3 = +4.37 0.1694 �0.2559 �0.2077 0.2416 �0.2220S3 = +4.43(STS) 0.1715 �0.2586 �0.2104 0.2357 �0.2332S3 = +4.55 0.1756 �0.2635 �0.2150 0.2278 �0.2504S5 = �2.23 0.2011 �0.3053 �0.2455 0.5480 �0.0028SO3(D3h) 0.3021 �0.5962 �0.4735 2.1714 1.1040

a S, reaction coordinate.b ’+’ denotes forward direction of the reaction.c ’�’ denotes reverse direction of the reaction.d r2q, laplacian of electron density.e The formation of the ring structure.f The annihilation of the ring structure.

114 M. Goodarzi et al. / Journal of Molecular Structure: THEOCHEM 944 (2010) 110–115

In this context, the topological analysis of electronic density onsome points along the cis-OSOO ? SO3(D3h) reaction Path was car-ried out. The topological characteristics of the BCP and RCP for thereaction are listed in Table 3. Molecular graphs for some pointsalong the IRC paths were plotted and displayed in Fig. 4. Bothcis-OSOO and trans-OSOO can be isomerized to SO3(Cs). ThenSO3(Cs) is transformed to planar SO3 with D3h symmetry (Fig. 2).So, cis-OSOO ? SO3(D3h) and trans-OSOO ? SO3(D3h) consist oftwo elementary reactions. We assign the reaction coordinates S3,S4 and S5 to the reaction pathways of cis-OSOO ? SO3(Cs),trans-OSOO ? SO3(Cs) and SO3(Cs) ? SO3(D3h), respectively. Asthe cis-OSOO ? SO3(D3h) proceeds, in the first step a new bond isformed between S and O1 atom at S3 = +2.63. The formation of thisbond creates a three-member ring at S3 = +2.63 and RCP appears.As the reaction progresses, the k2 of Hessian matrix at RCP in-creases and reaches to the maximum level at S3 = +4.43. After thispoint, as the reaction proceeds the k2 decreases gradually and astable intermediate (SO3(Cs)) is formed. Up to now, the three-member ring still exists and at S5 = �2.23, O3–O1 bond has beenbroken. In the second step, the RCP disappears. Then, the S–O1bond becomes stronger and stronger, and the product SO3(D3h) isformed. The point of S3 = +4.43 is the so-called STS of the cis-OSOO ? SO3(D3h) reaction. The ring structure transition region ex-ists in the two elementary steps of OSOO ? SO3(Cs) andSO3(Cs) ? SO3(D3h). Also, we find out that a ring transition regionexists in two elementary steps. The trans-OSOO ? SO3(D3h) pro-cess is similar to cis-OSOO ? SO3(D3h). The STS of the process of

Table 4The thermodynamic data for S + O3 reaction at the MP2 level.

Step of reaction DE (kcal/mol) DH (kcal/mol) TDS (kcal/mol) DG (kcal/mol)

(1) S + O3 ? S–O3 �18.261 �18.888 �8.058 �10.856(2) S–O3 ? TS1 20.959 20.959 0.172 20.833(3) TS1 ? trans-OSOO �128.828 �128.828 0.069 �128.891(4) Trans-OSOO ? P1 16.755 17.319 7.467 9.840(5) Trans-OSOO ? TS2 28.050 28.050 0.154 27.861(6) TS2 ? cis-OSOO �37.776 �37.776 0.117 �37.902(7) Cis-OSOO ? P1 26.481 27.046 17.508 9.569(8) Cis-OSOO ? TS4 44.490 44.490 �0.457 44.930(9) TS4 ? SO3(Cs) �46.247 �46.185 �0.098 �46.060(10) SO3(Cs) ? TS5 39.470 39.408 �0.173 39.596(11) TS5 ? P2 �94.817 �94.817 �0.046 �94.754(12) Trans-OSOO ? TS3 20.394 20.394 �0.366 20.708(13) TS3 ? SO3(Cs) �31.878 �31.815 0.082 �31.878

S + O3 ? P2 �192.959 �193.587 �8.319 �185.241S + O3 ? P1 �109.375 �109.438 2.004 �111.446

M. Goodarzi et al. / Journal of Molecular Structure: THEOCHEM 944 (2010) 110–115 115

trans-OSOO ? SO3(D3h) is very close to the one that we had in theprocess of cis-OSOO ? SO3(D3h).

3.4. Topological analysis of the S–O bond in the SO3 isomerization

The topological analysis of the electronic density was performedfor S–O bond in the SO3 isomerization. The topological characteris-tics in the BCP’s of three S–O bonds and one O–O bond are listed inTable 3. According to the theory of AIM, the Laplacian of the electrondensity (r2qðrcÞ) describes the characteristic of the bond. In general,when r2qðrcÞ < 0 the bond is covalent, but when r2qðrcÞ > 0 thebond belongs to the electrostatic interaction. Ther2qðrcÞ values inTable 3 indicate that the ionic character of the S–O2 bond is strong,and as the process proceeds, the ionic characteristic does not havean obvious change. From the emergence to the disappearance ofthe ring structure, ther2qðrcÞ of S–O3 and S–O1 bonds are negative.This indicates that in the structure transition regions, S–O3 and S–O1bonds have distinct covalent characteristics. After the transitionstate region, the covalent characteristics of two bonds become weak.The difference between S–O3 and S–O1 is that the covalent charac-teristic of S–O3 bond becomes weaker and weaker as the processproceeds, and finally it becomes ionic. However, the covalent charac-teristic of S–O1 is strengthened in the transition state region andthen it becomes weaker and weaker when O3–O1 bond is broken.Three S–O bonds show ionic characteristics in the last product,SO3, which has D3h symmetry.

4. The thermodynamic data in the S and O3 reaction process

The change of thermodynamic characteristics for each reactionchannel is the difference between the corresponding thermody-namic properties of the products and the reactants. The thermody-namic data is corrected by ZPE for S + O3 reaction .The calculatedrelative internal energies, enthalpies, Gibbs free energies and entro-pies of all steps of the reactions in gas-phase at atmospheric pressureand temperature of 298.15 K, have been summarized in Table 4.These data show that, DH and DG for the channels (1), (3), (6), (9),(11) and (13) are negative. This means that they are exothermicand exergonic. DH and DG for the channels (2), (4), (5), (7), (8),(10) and (12) are positive, which implies that they are endothermicand endergonic. Finally, the S + O3 ? P1 and S + O3 ? P2 reactionsare exothermic and exergonic (DH < 0 and DG < 0).

5. Conclusion

Details of the reaction pathways of the S + O3 on the singlet po-tential energy surface have been characterized with CCSD(T) ener-gies, based on B3LYP/6-311++G(3df,3pd) geometries. The studied

reaction is most likely initiated by sulfur atom that is attached tomiddle oxygen atom in ozone to form adduct S–O3 with no barrier.Subsequently, through a variety of transformations of isomer S–O3,two kinds of products P1 (SO + 3O2) and P2 (SO3(D3h)) are obtained.Product P1 is a more suitable product which is generated by onemiddle oxygen absorption channel and two terminal oxygenabsorption channels. According to the energy profile, product P2

is less favorable than the product P1. Product P2 is produced viatwo different channels. In these two channels, sulfur atom initiallyinteracts with middle oxygen atom in O3 which is followed byinteraction with terminal oxygen atoms of O3. The topologicalanalysis shows that the ring transitional structure region occursin cis-OSOO ? SO3(Cs) and SO3(Cs) ? SO3(D3h) reaction pathways.Finally, the S + O3 ? P1 and S + O3 ? P2 reactions are exothermicand exergonic (DH < 0 and DG < 0) at atmospheric pressure andtemperature of 298.15 K in the gas-phase.

Acknowledgements

This project was supported by the Zanjan University and M.Vahedpour would like to thank Dr. Ghanbari for the Englishimprovement and research vice president of Zanjan University,Dr. Rashtch, for his financial supporting.

References

[1] A.A. Fonseca, M.A. Campinho, G. Arbilla, Quım. Nova 19 (1996) 361.[2] D.L. Baulch, R.A. Cox, P.J. Crutzen, R.F. Hampson Jr., J.A. Kerr, J. Troe, R.T.

Watson, J. Phys. Chem. Ref. Data 11 (1982) 32.[3] V.W.J.H. Kirchhoff, Queimadas na Amazonia e Efeito Estufa, Contexto, Sa~o

Paulo, Brasil, 1992.[4] V.W.J.H. Kirchhoff, J. Geophys. Res. 93 (1988) 1469.[5] R.P. Wayne, Chemistry of Atmospheres, second ed., Oxford Science

Publications, Oxford, 1991.[6] L. Yang, D. Fang, J. Mol. Struct.: Theochem. 671 (2004) 141.[7] Z.F. Xu, M.C. Lin, Chem. Phys. Lett. 440 (2007) 12.[8] J. Peiró-García, L. Nebot-Gil, Chem. Phys. Lett. 391 (2004) 195.[9] G.D. Petris, A. Cartoni, M. Rosi, A. Troiani, Chem. Phys. Lett. 410 (2005) 377.

[10] A.J.C. Varandas, L. Zhang, Chem. Phys. Lett. 385 (2004) 409.[11] B. Makiabadi, H. Roohi, Chem. Phys. Lett. 460 (2008) 72.[12] J. Peiró-García, L. Nebot-Gil, Chem. Phys. Chem. 4 (2003) 843.[13] H.G. Yu, A.J.C. Varandas, Chem. Phys. Lett. 334 (2001) 173.[14] X. Li, L. Meng, S. Zheng, J. Mol. Struct.: Theochem. 847 (2007) 52.[15] A.D. Becke, J. Chem. Phys. 97 (1992) 9173.[16] C. Lee, W. Yang, R.G. Parr, Phys. Rev. 37 (1988) 785.[17] M.J. Frisch, M. Head-Gordon, J.A. Pople, Chem. Phys. Lett. 166 (1990) 275.[18] M.J. Frisch, M. Head-Gordon, J.A. Pople, Chem. Phys. Lett. 166 (1990) 281.[19] C. Gonzalez, H.B. Schlegel, J. Chem. Phys. 90 (1989) 2154.[20] C. Gonzalez, H.B. Schlegel, J. Phys. Chem. 94 (1990) 5523.[21] M.J. Frisch et al., Gaussian 98, Revision A.7, Gaussian, Inc., Pittsburgh, PA, 1998.[22] F.J. Biegler-Kônìng, R. Derdau, D. Bayles, R.F.W. Bader, AIM2000, Version 1,

2000.[23] R.F.W. Bader, Atoms in Molecules – A Quantum Theory, Oxford University

Press, Oxford, 1990.[24] R.F.W. Bader, Chem. Rev. 91 (1991) 893.