theoretical studies on sox (x = 1–3) formation in the reaction of ch3so radical with o3

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Journal of Molecular Structure: THEOCHEM 847 (2007) 52–58

Theoretical studies on SOx (x = 1–3) formation in the reactionof CH3SO radical with O3

Xiaoyan Li a,b, Lingpeng Meng b, Shijun Zheng b,*

a Department of Chemistry, Graduate School, Chinese Academy of Sciences, Beijing 100049, Chinab Institute of Computational Quantum Chemistry, College of Chemistry, Hebei Normal University, Yuhua Road, Shijiazhuang 050016, China

Received 12 May 2007; received in revised form 28 August 2007; accepted 29 August 2007Available online 14 September 2007

Abstract

The reaction of CH3SO radical with O3 has been studied at MP2/6-311++G (2df, p) level. Geometries of the reactants, tran-sition states (TS) and products have been optimized and the transition states are found for the first time. The breakage andformation of the chemical bonds in the reaction have been discussed by the topological analysis of electronic density. The follow-ing conclusions were obtained: Because the reaction has relative high energy barriers, the CH3SO can be oxidized by O3 at hightemperature. The major oxidized products, SO2 and SO3, are the precursor substance of acid rain. Furthermore, OSOO fi SO3

(D3h) reaction consists of two elementary reaction, the topological analysis of electron density results show that the ring transi-tional structure region exists not only in OSOO fi SO3 (Cs) process but also in SO3 (Cs) fi SO3 (D3h) process. It is the first timewe found a ring transitional structure exists in two elementary reactions. And there are two kinds of S–O bond characters indifferent SO3 isomers.� 2007 Elsevier B.V. All rights reserved.

Keywords: CH3SO radical; CH3SO2 radical; Topological analysis of electronic density; Structure transition region

1. Introduction

Dimethyl sulfide (DMS), CH3SCH3, is the largest natu-ral contributor to sulfur in the troposphere [1], and itsatmospheric oxidation has been suggested to play animportant role in the formation of clouds by producingnew sulfate particles which act as cloud condensationnuclei (CCN) [2]. On the basis of laboratory kinetic andend product analysis studies, it has been postulated thatone of the possible key intermediate in DMS oxidationmechanism is the methylsulfonyl radical (CH3SO2) [3–5].It may be formed in reactions of CH3SO radical withNO2 and O3 [6]. By now the mechanism for the reactionof CH3SO with O3 has been studied less extensively. Mostof previous studies focus on the spectra of reactants anddynamics properties of the reaction [7–10]. Borrssenko

0166-1280/$ - see front matter � 2007 Elsevier B.V. All rights reserved.

doi:10.1016/j.theochem.2007.08.038

* Corresponding author. Tel./fax: +86 311 86269217.E-mail address: [email protected] (S. Zheng).

et al. have studied the reactions mechanism of CH3SO withNO2 and O3 by using Laser pulsed photolysis/LIF and dis-charge flow mass spectrometry techniques [11]. They pro-posed that the reactions mechanism of CH3SO with O3 issimilar to that of with NO2:

CH3SOþO3 ! CH3 þ SO2 þO2 ðaÞ! CH3SO2 þO2 ðbÞ

Up to now, the reaction mechanism of CH3SO with O3 isambiguous and the major channels of producing SO2 andSO3 have not been identified. In this paper, we carry outtheoretical studies on the reaction mechanism of CH3SOwith O3, the significance of this reaction in the formationof acid rain are investigated, the breakage and formationof the bonds in the process of CH3SO2 fi CH3OSO andOSOO fi SO3 are also discussed according the AIM theory[12]. We hope that our computations may provide useful

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X. Li et al. / Journal of Molecular Structure: THEOCHEM 847 (2007) 52–58 53

information for understanding the properties of CH3SOradical and stimulate further studies on it.

2. Computational methods

The geometries of reactants, transition states, productsand some points on the potential energy surface werelocated by MP2/6-311++G (2df, p) calculations. Vibra-tional frequencies were computed for the stationarypoints characterization and zero-point energies (ZPE)

106.8 1.4764

1.7982 1.2792

116.9

CH3SO O3

1.8053

107.31.4578

122.2

58.4

1.8254 1

2.0723

CH3SO2 TS2

1.7968

1.4680 1.3109104.9 110.6 1.80541.3096

1.4696 108.9

113.7

cis-OSOO

trans-OSOO

1.4388

113.4

1.6570 1.4403

120.9 1.5263

1.5962

SO3 (Cs) TS5

Fig. 1. Geometries of reactants, intermediate, transition states and

corrections were included. The reaction paths were tracedout by intrinsic reaction coordinate (IRC) [13]. Computa-tions were performed using GAUSSIAN 98 program[14]. Topological analyses were carried out with GTA-2000 program, which we developed and registered atQCPE (register number QCPE-661) [15]. Moleculargraph in the reaction of CH3SO2 fi CH3OSO and Gradi-ent path of the electronic density along the IRC ofSO + O2 fi SO3 (Fig. 3) were also plotted by programGTA-2000.

1.2238

106.0

1.6706

116.4

2.3850

1.8187

105.7

TS1

.5503

1.4300116.0

111.3

1.6509

1.4736

CH3OSO

1.4450

1.4525123.295.0

1.5360

1.4736113.3 1.6274

97.8 1.3201

TS4

120.0

1.4351

SO3 (D3h)

TS3

products (bond lengths in angstrom, bond angles in degree).

-80

-60

-40

-20

0

20

40

60

8066.3

-10 -5 5 10 15

-587.52

-587.50

-587.48

-587.46

-587.44

-587.42

-587.40 IRC pathway ETS Structure Transition Region STS)

CH3SO2

TS2

CH3 OSO

E(a.u)E(kcal/mol)

-51.5

-9.4

-72.3

-15.5

-66.8

0.0

TS2

CH3+SO

2

CH3OSO

CH3O+SO

CH3SO

2+O

2

TS1

CH3SO+O

3

0

Fig. 2. The potential energy curves of the CH3SO + O3 reaction.

Table 1Topological properties at BCP and RCP of the ring transition region forreaction CH3SO2 fi CH3OSO

Bond S q Eigenvalues of Hessian matrix $2q

k1 k2 k3

54 X. Li et al. / Journal of Molecular Structure: THEOCHEM 847 (2007) 52–58

3. Results and discussion

3.1. Potential energy curves on IRC paths

The geometry parameters of the reactants, transitionstates and products on the reaction potential energy surfacewere optimized and shown in Fig. 1. The transition statesare found for the first time.

Because singlet-state is the ground-state of O3, the wholereactions proceed on doublet-state potential energy surface(PES). The reaction potential energy surface, as shown inFig. 2, consists of two reaction steps. Firstly, the terminalO atom of O3 attacks S atom of CH3SO and formsCH3SO2 and O2 via TS1. The relative energy of TS1 is66.3 kcal/mol higher than that of the products is66.8 kcal/mol lower than the reactants. Because the reac-tion has relative high energy barrier, the CH3SO can be

E(a.u.)

-77.0

35.3

-12.4

29.5

41.3

7.20.0

TS5

SO3(D3h)

SO3(Cs)

cis-OSOO

trs-OSOO TS4

TS3

IRC pathwaythe first ETSthe second ETSSTSStructure Transitation Region

Fig. 3. The potential energy curves of the OSOO fi SO3 reaction (theitalic numbers are relative energy (kcal/mol)).

oxidized by O3 at high temperature. Secondly, CH3SO2

via two pathways to yield SOx (x = 1–2). One pathway isCH3SO2 decomposes to CH3 and SO2 directly, the otheris CH3SO2 isomerizes to CH3OSO via TS2, and thenCH3OSO decomposes to CH3O and SO.

SO and SO2 can be oxidized by Ox (x = 1–2) to formstraight-chain OSOO [16,17]. The straight-chain OSOOhas two isomers: one is cis-OSOO and the other istrans-OSOO. As shown in Fig. 3: there are two steps in theisomerization reaction of OSOO to the last product SO3

RCP �0.33 0.0948 �0.1359 0.0165 0.3400 0.2206ETS 0.0967 �0.1366 0.0948 0.2242 0.1824+0.04 0.0965 �0.1356 0.0981 0.2123 0.1748+0.05 0.0964 �0.1354 0.0982 0.2107 0.1735+0.06 (STS) 0.0964 �0.1353 0.0982 0.2092 0.1721+0.07 0.0963 �0.1350 0.098 0.2079 0.1709+0.37 0.0928 �0.1222 0.0124 0.2243 0.1145

C–S �0.33 0.1160 �0.1598 �0.1366 0.2360 �0.0604ETS 0.1045 �0.1381 �0.0981 0.2414 0.0052+0.04 0.1024 �0.1345 �0.0900 0.2419 0.0174+0.05 0.1021 �0.1339 �0.0886 0.2419 0.0194+0.06 (STS) 0.1018 �0.1334 �0.0873 0.2420 0.0213+0.07 0.1015 �0.1328 �0.0858 0.2420 0.0234+0.37 0.0928 �0.1206 �0.0118 0.2318 0.0994

C–O1 �0.33 0.0948 �0.1371 �0.0154 0.3687 0.2162ETS 0.1049 �0.1590 �0.0821 0.3839 0.1428+0.04 0.1070 �0.1633 �0.0901 0.3820 0.1286+0.05 0.1074 �0.1639 �0.0914 0.3816 0.1263+0.06 (STS) 0.1077 �0.1647 �0.0927 0.3812 0.1238+0.07 0.1081 �0.1654 �0.0940 0.3807 0.1213+0.37 0.1195 �0.1875 �0.1305 0.3616 0.0436

Table 2Topological properties at BCP and RCP of the ring structure transition region for reaction cis-OSOO fi SO3

Bond S q Eigenvalues of Hessian matrix $2q

k1 k2 k3

RCP S3 = +2.6 0.0992 �0.1394 0.0347 0.3874 0.2827S3 = +4.7 0.1405 �0.2327 0.2891 0.4575 0.5139S3 = +4.8 (STS) 0.1415 �0.2352 0.2893 0.4631 0.5172S3 = +4.9 0.1424 �0.2372 0.2889 0.4685 0.5202S5 = �3.7 0.1195 �0.1960 0.0541 0.6573 0.5154

O3–O4 S3 = +2.5 0.2366 �0.5281 �0.5116 1.2518 0.2121S3 = +2.6 0.2369 �0.5279 �0.5127 1.2526 0.2120S3 = +4.7 0.2344 �0.5120 �0.4873 1.2417 0.2424S3 = +4.8 (STS) 0.2335 �0.5094 �0.4830 1.2381 0.2457S3 = +4.9 0.2326 �0.5068 �0.4688 1.2345 0.2589S5 = �3.7 0.1201 �0.2012 �0.0529 0.6998 0.4457

S–O2 OSOO 0.2730 �0.4239 �0.3973 1.7398 0.9816S3 = +2.5 0.2877 �0.4868 �0.4487 2.0599 1.1244S3 = +2.6 0.2878 �0.4868 �0.4492 2.0598 1.1238S3 = +4.7 0.2911 �0.4931 �0.4616 2.0846 1.1299S3 = +4.8 (STS) 0.2911 �0.4936 �0.4622 2.0869 1.1311S3 = +4.9 0.2913 �0.4942 �0.4627 2.0896 1.1327S5 = �3.7 0.2928 �0.5000 �0.4712 2.1045 1.1333S5 = �3.6 0.2927 �0.4994 �0.4714 2.1003 1.1297SO3 (D3h) 0.2960 �0.5242 �0.4237 1.9810 1.0331

S–O3 OSOO 0.2027 �0.3258 �0.2195 0.3502 �0.1951S3 = +2.5 0.2154 �0.3384 �0.3144 0.4698 �0.1830S3 = +2.6 0.1978 �0.2977 �0.2680 0.3042 �0.2615S3 = +4.7 0.1965 �0.2962 �0.2657 0.3046 �0.2573S3 = +4.8 (STS) 0.1951 �0.2947 �0.2636 0.3058 �0.2525S3 = +4.9 0.2157 �0.3186 �0.2821 0.4964 �0.1043S5 = �3.7 0.2167 �0.3208 �0.2843 0.5188 �0.0863SO3 (D3h) 0.2960 �0.5242 �0.4237 1.9810 1.0331

S–O4 S3 = +2.5S3 = +2.6 0.1103 �0.1585 �0.0344 0.3496 0.1567S3 = +4.7 0.1799 �0.2767 �0.2450 0.3490 �0.1727S3 = +4.8 (STS) 0.1838 �0.2818 �0.2500 0.3346 �0.1972S3 = +4.9 0.1874 �0.2862 �0.2545 0.3220 �0.2187S5 = �3.7 0.2018 �0.2957 �0.2626 0.3199 �0.2384S5 = �3.6 0.2016 �0.2955 �0.2627 0.3196 �0.2386SO3 (D3h) 0.2960 �0.5242 �0.4237 1.9810 1.0331


which has D3h symmetry. Firstly, cis-OSOO and trans-OSOO via TS3 and TS4 isomerizes to SO3 (Cs), respectively;then SO3 (Cs) via TS5 transforms to the product SO3 (D3h).In this process, the energy barriers are low; therefore, isom-erization reaction of OSOO to SO3 occurs easily. The prod-uct, SO3 with D3h symmetry, is the precursor substance ofacid rain.

Our computational results provide some informationabout SOx (x = 1–3) formation in the atmospheric oxida-tion of DMS. The IRC pathway gives the theoretical evi-dence that CH3SO is a key intermediate in DMSoxidation process; the reaction of CH3SO with O3 maythe major path of CH3SO oxidation, this reaction playsan important role in the formation of acid rain.

3.2. Topological analysis of electronic density on IRC paths

According to the topological analysis of electronic den-sity in the theory of AIM [18,19], electron density q(rc) is

used to describe the strength of a bond and Laplacian ofthe electron density ($2q(rc)) describes the characteristicof the bond. The Laplacian $2q(rc) is the sum of k1, k2

and k3, ki is one of the eigenvalues of Hessian matrix ofelectronic density. If a critical point has two negativeand one positive eigenvalue, it is called (3, �1) or thebond critical point (BCP). If a critical point has two posi-tive and one negative eigenvalue, it is called (3, +1) or thering critical point (RCP), which indicate that a ring struc-ture exists. From the ring’s appearance to its disappear-ance calls ‘structure transition regions’, the k2 eigenvalueof the Hessian matrix of the RCP (the positive curvaturelying in the plane) has the trend of zero fi maxi-mum fi zero. We call the maximum Hessian matrix k2

of the RCP as STS and the traditional transition statethat is the maximum on energy surface as ‘energy transi-tion state (ETS)’.

The topological analyses of electronic density on somepoints along the CH3SO2 fi CH3OSO and OSOO fi SO3


reaction path were carried out. The topological propertiesat BCP and RCP for the reactions are listed in Tables 1and 2, respectively. Molecular graphs, contour maps ofelectronic density and gradient paths of density surfacefor some points along the IRC paths were plotted and dis-played in Figs. 4 and 5, respectively.

For the reaction of CH3SO2 fi CH3OSO, the topologi-cal properties at BCP are listed in Table 1 and moleculargraphs are shown in Fig. 4. In this process, from CH3SO2

to TS2, S–O6 bond becomes weaker and weaker and thebond path becomes more bent. At S = �0.33, C, S andO6 forms a ring structure, a RCP appears. The k2 of Hes-sian matrix at BCP increases and reaches the maximum atS = +0.06. After this point the k2 decreases gradually. Thepoint of S = +0.06 is the so-called STS in the reaction. Atthe point S = +0.38, the C–S bond has been broken andthe RCP disappeared. And then the C–O6 bond becomesstronger and stronger, and the product CH3OSO forms.Furthermore, the process of CH3SO2 fi CH3OSO is exo-thermic and the STS (S = +0.06) appears after the ETS(S = 0.00). This is accordance with our previous conclusionof ‘STS appears after ETS in exothermic reaction’ [20,21].

CH3 2SO S=-0.3

ETS(S=0.00) STS(S=

S=+0.38

(small represents bond critical point, sm

Fig. 4. The molecular graphs of C

Because this process is a less exothermic reaction, theSTS is near the ETS.

Both of cis-OSOO and trans-OSOO can isomerizes toSO3 (Cs) and then SO3 (Cs) transformed to SO3 (D3h), seeFig. 3 and 5. So cis-OSOO fi SO3 (D3h) and trans-OSOO fi SO3 (D3h) consists of two elementary reactions.We assign S3, S4 and S5 as reaction coordinates for pro-cesses of cis-OSOO fi SO3 (Cs), trans-OSOO fi SO3 (Cs)and SO3 (Cs) fi SO3 (D3h), respectively. In the first stepof the cis-OSOO fi SO3, as the process proceeds a newbond is formed between S and O4 atoms at S3 = +2.6.S–O3–O4 three-membered ring is formed at this point. AtS3 = +5.6, a stable intermediate SO3 (Cs) forms. By now,the three-membered ring still exists and it disappears atS5 = �3.7 in the second step. The ring structure transitionregion exists in the two elementary steps of OSOO fi SO3

(Cs) and SO3 (Cs) fi SO3 (D3h). It is the first time that wefound a ring transition region exists in two elementarysteps. The trans-OSOO fi SO3 process is similar with cis-OSOO fi SO3. The STS’s in the processes of trans-OSOO fi SO3 (D3h) is very near to that of in the processof cis-OSOO fi SO3 (D3h).

4 S=-0.33

+0.06) S=+0.37

CH3OSO

all represents ring critical point)

H3SO2 fi CH3OSO reaction.

Fig. 5. The contour maps of electronic density and gradient path of density surface of cis-OSOO fi SO3 reaction. +, represents nuclear of atomic; m,represents bond critical point; d, represents ring critical point.


3.3. Topological analysis of the S–O bond

The topological analysis of electronic density was per-formed for S–O bond in the SO3 isomerization. The topo-logical properties at the BCP’s of three S–O bonds and oneO–O bond are also listed in Table 2. According to the the-ory of AIM [18,19], the Laplacian of the electron density($2q(rc)) describes the characteristic of the bond. In gen-eral, $2q(rc) < 0, the bond is covalent, as $2q(rc) > 0, thebond belongs to the electrostatic interaction. The $2q(rc)values in Table 2 indicate that the ionic character of theS–O2 bond is strong, and as the process proceeds, the ioniccharacteristic has not obvious change. From the emergenceto the disappearance of the ring structure, the $2q(rc) ofS–O3 and S–O4 are negative. This indicates that in thestructure transition regions, S–O3 and S–O4 have distinctcovalent characteristic. After the transition state region,the covalent characteristics of the two bonds become weak.The difference between S–O3 and S–O4 is that the covalentcharacteristic of S–O3 becomes weaker and weaker as the

process proceeds, at last it becomes ionic; however, thecovalent characteristic of S–O4 is strengthen in the transi-tion state region, then it becomes weaker and weaker afterO3–O4 bond was broken. All three S–O bonds show ioniccharacteristic in the last product SO3 which has D3h

symmetry.

4. Conclusions

(1) The reaction mechanisms and the geometries of tran-sition states of CH3SO + O3 reaction are reported forthe first time.

(2) Because the reaction has relative high energy barrier,the CH3SO can be oxidized by O3 at high tempera-ture. The major oxidized products, SO2 and SO3,are the precursor substance of acid rain.

(3) The process of CH3SO2 fi CH3OSO is exothermic,the ring STS appears after the ETS, it is in accor-dance with our former conclusion.


(4) A ring transitional structure region exists not only inOSOO fi SO3 (Cs) process but also in SO3

(Cs) fi SO3 (D3h) process. It is the first time that wefound a ring structure transitional region exists intwo elementary reactions.

(5) There are two kinds of S–O bonds in different SO3

isomers, one is ionic and the other is covalent.

Acknowledgements

This project was supported by the National Natural Sci-ence Foundation of China (Contract Nos. 20573032,20503035) and the Natural Science Foundation of HebeiProvince (Contract No. B2006000137). Li Xiaoyan wouldlike to thank the Chinese Academy of Sciences for a schol-arship for the period of this work.

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theoretical studies on sox (x = 1–3) formation in the reaction of ch3so radical with o3

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