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Mechanism and kinetics for the reaction of O(3P) with DMSO: A theoretical study

Debasish Mandal, Sabyasachi Bagchi, Abhijit K. Das ⇑

Department of Spectroscopy, Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700 032, India

a r t i c l e i n f o

Article history:

Received 27 June 2012In final form 4 September 2012

Available online 18 September 2012

a b s t r a c t

Mechanism and kinetics for the reaction of DMSO with O( 3P) have been investigated by M06-2X/MG3S,CBS-QB3 and G4MP2 methods. Four possible reaction pathways are identified. Among them, the O(3P)

addition to S-atom followed by CH3 elimination is almost exclusive. Four pre-reactive complexes havebeen located. AIM theory is used to determine the nature of interactions in these complexes. Consideringthe formation of pre-reactive complex, the rate constant for major pathway is calculated using transitionstate theory applied to a two-step mechanism. Enthalpies of formation at 298.15 K (Df H 298.15) have beencalculated using the composite CBS-QB3, G4MP2 and G3B3 methods.

2012 Elsevier B.V. All rights reserved.

1. Introduction

Dimethyl sulfoxide (DMSO) is an important atmospheric org-ano-sulfur compound. It is observed in marine atmosphere [1–3]and is a key intermediate species of dimethyl sulfide (DMS) oxida-tion [4], which is considered to be the main biogenic source of reactive sulfur in the atmosphere [5]. DMSO has also been indenti-

fied in laboratory [6,7] as well as in other field [8]. AtmosphericDMSO is mainly produced by the OH initiated oxidation of DMS.Due to such environmental importance, many gas phase experi-mental and theoretical investigations into the reaction of DMSOwith OH, NO3 and O3 are reported [9–13]. The experimental andtheoretical studies of the reaction of DMSO with chlorine atomhave also been performed [13,14]. In the reactions of DMSO withOH or with Cl, the –CH3 elimination pathway is the most probableone that produces a potentially important atmospheric radical,CH3SO2. In this context the reaction of DMSO with oxygen atommay be an important source of the CH3SO2 radical. Two extensiveexperimental studies were performed for the kinetics analysis of the title reaction [15,16]. Pope et al. [15] presented a temperaturedependent kinetics study of the reaction of O(3P) with DMSO and

the pressure independent rate constant for the reaction was re-ported to be 7.48 1012 cm3 molecule1 s1 at 298 K. In anotherinvestigation, Riffault et al. [16] studied the kinetics of the abovereaction and predicted the rate constant (1.0 ± 0.2) 1011 cm3

molecule1 s1 at the same temperature. The CH3 radical and SO2

are the exclusive products obtained from the reaction. Althoughthe values for the above mentioned rate constants are not perfectlyidentical, both results would be similar if the experimental uncer-tainty is considered. Despite such atmospheric importance, notheoretical study has been reported to explore the mechanism

and kinetics of the DMSO + O(3P) reaction. The oxygen atom, oneof the key reactive species in the atmosphere, reacts with DMSOthrough the following probable ways:

Oð3PÞ þ ðCH3Þ2SO!TS1

CH3SCH3 þ O2 ðR1Þ

!TS2

OHþ CH3SðOÞCH2 ðR2Þ

!TS3

CH3SO2 þ CH3 ðR3Þ

!TS4

CH3SOþ CH3O ðR4Þ

Some other pathways proposed previously are characterized by thereaction or decomposition of these initially formed products.

The main objective of the present Letter is to investigate thecomplete reaction mechanism and kinetics of O(3P) atom withDMSO. Usually in environmental atom–molecule reaction, the ini-tial adduct formation is very important. Accordingly extensivesearches for the pre-reactive complexes have been performedand finally they are characterized by the quantum theory of atomsin molecules (AIM) analysis. We then proceed to investigate the

reaction mechanism using advanced density functional theory(DFT) and high-level composite methods. Based on the mechanism,rate constants have been calculated using the conventional transi-tion state theory (TST) including the Eckart tunneling correction.Besides, thermochemical studies have been performed using vari-ous composite methods to analyze the stability of the species in-volved in the reaction.

2. Computational details

The structures have been optimized by DFT with M06-2X [17]in conjunction with MG3S [18] basis set. The M06-2X is a hybridmeta-DFT functional with a high percentage of HF exchange which

0009-2614/$ - see front matter 2012 Elsevier B.V. All rights reserved.http://dx.doi.org/10.1016/j.cplett.2012.09.002

⇑ Corresponding author. Fax: +91 33 24732805.

E-mail address: [email protected] (A.K. Das).

Chemical Physics Letters 551 (2012) 31–37

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S2 in the supporting information. Figure 2 depicts the CBS-QB3 po-tential energy profile. All the product complexes are in triplet state.

3.2.1. Channel R1

In channel R1, oxygen elimination leads to the production of P1(CH3SCH3 and O2) through the transition state, TS1. In TS1, O–Odistance is 1.57 Å and the breaking S–O bond distance increasesby 0.31 Å from the reactant. It possesses an imaginary frequency

of 1329.44 cm1

responsible for the stretching of S–O bond. Inspite of the exothermicity of the product formation (33.69 kcal/

mol), these channels are expected to be less important due tohigher barrier of 29.64 kcal/mol. However, CH3SCH3 formed in thisroute may be responsible for the production of CH2S throughfurther decomposition and it takes place via TS5. This route isnot shown in the PES to avoid complexity.

3.2.2. Channel R2

In R2, the direct H-abstraction takes place and P2 (CH3SOCH2 +

OH) is formed. These routes are slightly exothermic (1.15 kcal/mol). Since the DMSO contains three distinct H-atoms, there are

Figure 1. Optimized structures with geometrical parameters and molecular graphs calculated at the M06-2X/MG3S level for all the pre-reactive complexes involved in thereaction of O(3P) with DMSO.

Table 2

Zero point energies (ZPE), hS 2i and T 1 diagnostic values, Relative energy, enthalpy and free energy in kcal/mol calculated at M062X/MG3S level for all the species involved in the

reaction of O(3P) with DMSO.

Species ZPE hS 2i T 1 DE DH DG

R{DMSO+ O(3P)} 50.13 0.0, 2.000 0.016, 0.007 0.00 0.00 0.00A1 51.08 2.0001 0.035 5.19 5.44 1.69A2 50.80 2.000 0.019 4.24 4.47 2.35A3 50.74 2.000 0.017 2.76 2.87 3.53A4 50.48 2.000 0.027 2.26 2.47 3.97TS1 49.66 2.0004 0.041 32.73 32.39 39.30TS2a 46.04 2.0001 0.026 7.09 6.64 13.64TS2b 45.80 2.0001 0.02 8.84 8.45 15.13TS2c 46.45 2.0001 0.027 5.50 4.93 12.36TS3 49.68 2.0002 0.034 1.10 0.54 8.47TS4 49.70 2.0006 0.033 17.51 17.20 24.08TS5 + O2 44.37 0.0, 2.001 0.019, 0.017 68.22 68.66 64.92P1: CH3SCH3 + O2 50.48 0.0, 2.001 0.008 37.03 36.91 39.32P2: CH3SOCH2 + OH 46.51 0.75, 0.75 0.024, 0.010 0.86 0.14 2.52

P3: CH3SO2 + CH3 47.45 0.75, 0.75 0.021, 0.007 37.03 36.49 39.02P4: CH3SO+CH3O 47.86 0.75, 0.75 0.025, 0.018 40.05 39.64 44.86P5: CH4 + CH2S + O2 46.49 0.0, 0.0, 0.0 0.006, 0.019 15.88 14.52 26.21P6: CH3 + CH3 + SO2 93.01 0.75, 0.0 0.023 19.52 17.45 30.37

D. Mandal et al./ Chemical Physics Letters 551 (2012) 31–37 33



three possibilities for H-abstraction reactions. The abstraction of each of the three distincthydrogens of DMSO by O(3P) is consideredin channels R2a, R2b and R2c. The TSs involved in these pathwaysare TS2a, TS2b and TS2c, respectively. The natures of these threetransition states are comparable. TS2a possesses the activation en-ergy of 8.50 kcal/mol, and in TS2a, the forming O–H and the break-ingH–Cbond distances are1.20and 1.30 Å,respectively. The barrierof activation, 10.23 kcal/mol, for TS2b is highest among all the H-abstraction channels.TS2c possesses 7.32 kcal/mol barrier of activa-

tion, whichis slightly lower than theother two. In TS2c,the formingand breaking bond lengths are 1.23 and 1.28 Å, respectively. The

imaginary frequencies responsible for the H-shifts in TS2a, TS2band TS2c are 1687.22, 1697.26 and 1664.88 cm1, respectively.

3.2.3. Channel R3

R3 is the most important and almost unique reaction pathwayfor the reaction of O(3P) with DMSO. This is a typical O(3P) additionto S-atom followed by CH3 elimination, though it occurs in a sin-gle-step concerted fashion. In channel R3, the addition of O(3P)atom to the S atom of DMSO occurs via the TS3. The breaking of

the S–C bond leads to the formation of P3 (CH3SO2 + CH3). In R3,the sufficiently stable pre-reactive complex, A1, has an important

Table 3

The Relative energy, enthalpy and free energy in kcal/mol calculated at CBS-QB3 and G4MP2 levels for all the species involved in the reaction of O( 3P) with DMSO.

Species CBS-QB3 G4MP2

DE DH DG DE DH DG

R{DMSO + O(3P)} 0.00 0.00 0.00 0.00 0.00 0.00A1 3.12 3.35 3.63 3.63 3.85 3.11A2 1.27 1.58 5.54 3.61 3.94 3.27A3 0.99 1.16 5.33 3.33 3.50 3.06A4 0.80 1.47 6.34 3.33 3.50 3.06TS1 29.64 29.18 36.03 29.88 29.40 36.51TS2a 8.51 7.94 15.39 8.46 7.92 15.30TS2b 10.23 9.77 16.86 10.06 9.63 16.61TS2c 7.32 6.70 14.29 7.65 7.02 14.66TS3 0.01 0.43 7.13 0.42 0.10 7.72TS4 17.38 17.20 23.63 18.19 17.69 24.98TS5+O2 71.50 71.42 69.40 71.73 72.20 68.39P1: CH3SCH3 + O2 33.70 33.61 35.59 32.11 32.01 34.05P2: CH3SOCH2 + OH 1.15 0.46 2.81 3.04 2.38 4.66P3: CH3SO2 + CH3 41.29 40.81 43.22 40.89 40.40 42.84P4: CH3SO+CH3O 37.67 37.61 41.81 37.88 37.82 42.02P5: CH4 + CH2S + O2 15.94 14.72 26.14 14.55 13.31 24.77P6: CH3 + CH3 + SO2 25.01 23.12 35.70 25.59 23.66 36.32

Figure 2. CBS-QB3 potential energy surface for the reaction of O(3P) with DMSO.

34 D. Mandal et al. / Chemical Physics Letters 551 (2012) 31–37



role. From the IRC calculation of TS3, it is very clear that the sepa-rated reactants go to the transition state via A1. The minimum en-ergy path for this reaction is presented in Figure S2 in thesupplementary material. TS3 occurs at lower energy than the sep-arated reactants in the PES, but with respect to A1 it possesses3.06 kcal/mol barrier of activation. In TS3, the forming S–O bond(Wiberg bond index value 0.72) distance is 1.68 Å, and the elimi-nating methyl group is situated 2.10 Å away from the S atom of DMSO. The production of P3 is spontaneous by 43.22 kcal/mol freeenergy. According to the previous study, the major reaction chan-nel for the title reaction is the 2CH3 + SO2 product formation path-way. Our computation also provides similar outcomes as theinitially obtained product CH3SO2 can further decompose to CH3

and SO2 by breaking of the C–S bond and this channel exists ondoublet surface. We have tried to find the TS for this decomposi-tion and after several attempts it is established that the processis truly barrier-less. The related relaxed potential energy scan ob-tained by increasing the C–S distance is presented in figure S3 inthe supplementary material.

3.2.4. Channel R4

Besides the S-site, the carbon atom in the methyl of DMSO canalso be attacked by O(3P) atom. In R4, O(3P) atom is added to thecarbon atom of DMSO followed by the breaking of the C–S bondwhich leads to the formation of P4 (CH3SO+CH3O). The TS in-volved in this substitution step is TS4 with rather high barrierheight of 17.38 kcal/mol. The product P4 is about 37.67 kcal/molenergetically lower than the reactants. Apparently, this elementarysubstitution channel is not important to the overall reactions.

4. Thermochemistry

All the species involved in the reaction of O(3P) with DMSO areimportant as they can exist in the environment. So, thermochemi-cal analysis is very important for the determination of the stability

of the species. The most important thermochemical parameter,namely, the standard enthalpy of formation at 298.15 K(Df H 298.15) is computed using M062X/MG3S, CBS-QB3, G4MP2,G3B3 electronic energies and the results are collected in Table 4.As there is lack of earlier experimental or theoretical informationon Df H 298.15 for most of the species involved in this Letter, theaccuracy of the method is ensured by comparing the calculated en-thalpy of formation values with the existing literature for O2, OH,CH3, CH2S, CH4, SO2, CH3O, CH3SCH3, and DMSO and good agree-ment is observed for all the methods. TheDf H 298.15 values are alsocalculated for the TSs involved in the title reaction. From the valuesin Table 4, it is obvious that A1 is the most probable one to formthan the other pre-reactive complexes, and also, TS3 is the mostfavorable than other TSs. Comparing with the experimental values,it appears that the CBS-QB3 method is more reliable than G3B3 andG4MP2 methods. Although the M062X/MG3S values deviateslightly from the experimental values compared to the values ob-tained by other composite methods, this methodology works quiteefficiently for the investigated system. These results can be usedfor the determination of stability of the species in atmosphere.

5. Kinetics

It is observed from the PES that R3 is the most favorable andalmost exclusive reaction path for the reactions of O(3P) withDMSO. Therefore, the kinetics of this pathway is investigated verycarefully. We assume that this pathway proceeds via a two-stepmechanism. The first step involves a fast pre-equilibrium (K eq)

between the reactants and the pre-reactive complex, and thesecond step having rate constant k2 is the addition of O(3P) atom

with simultaneous methyl elimination. The schematic representa-tions are as follows:

Step1 :

DMSOþ Oð

3

PÞ $ A1

Step2 : A1 ! P4ðCH3SO2 þ CH3Þ

The first step is barrier-less and involves fast pre-equilibriumbetween the reactants and pre-reactive complex. If k1 and k1

are the forward and reverse rate constants for the first step andk2 is that for the second step, after steady state analysis the effec-tive rate constant can be calculated by the following equation:

ktot ¼ k1k2

k1 k2

Assuming k2 << k1, the above equation can be written as

ktot ¼ k1

k1k2

ktot ¼ keqk2

where keq is the equilibrium constant of the first step. keq can beestimated by basic statistical thermodynamic equation

keq ¼ req

Q RCQ OQ DMSO

exp

ðE RC E O E DMSOÞ

kbT

where Q O and Q DMSO are the partition functions for the reactantsand Q RC is that for the pre-reactive complex. E RC, E O, and E DMSO

denote the total energy (ZPVE corrected) of the pre-reactivecomplex, O(3P) and DMSO, respectively. The constant, r, is thesymmetry factor counting the number of possible identical reactionpath. The kb and T are the Boltzmann constant and the absolute

temperature, respectively. The rate for the second step can be eval-uated using the conventional TST equation [36]

Table 4

Standard enthalpies of formation at 298.15 K in kcal/mol calculated using M062X/

MG3S, CBS-QB3, G4MP2 and G3B3 energies for all the species involved in the reaction

of O(3P) with DMSO.

Species D f H

298:15

M062X/MG3S CBS-QB3 G4MP2 G3B3 Exp

O2 1.03 0.58 1.50 0.17 0.00a

OH 10.07 8.95 8.70 8.49 8.93

b

CH3 36.64 35.56 34.95 34.38 34.82b

CH4 15.26 17.72 17.54 17.79 17.89b

CH2S 29.93 27.08 26.28 27.67 27.41 ± 1.91c

SO2 62.57 70.76 70.01 68.03 70.94b

CH3O 3.81 4.46 4.61 4.65 4.1 ± 1d

CH3SO 15.29 18.58 18.88 15.89CH3SO2 44.97 52.88 51.80 48.10CH3SCH3 7.72 9.53 9.96 8.16 8.96 ± 0.48e

CH3SOCH2 17.95 14.09 12.47 15.98DMSO 31.40 36.06 36.01 33.65 35.97± 0.36f

A1 22.72 20.14 19.69 21.98A2 23.69 21.92 19.61 22.41A3 25.30 22.34 20.05 22.98A4 25.69 22.02 20.05 23.29TS1 60.55 52.67 52.95 53.55TS2a 34.80 31.44 31.46 33.39TS2b 36.61 33.27 33.18 35.31

TS2c 33.10 30.20 30.57 32.36TS3 28.70 23.06 23.45 26.25TS4 45.36 40.70 41.24 48.00TS5 97.84 95.49 94.24 96.42

a Ref. [30].b Ref. [31].c Ref. [32].d Ref. [33].e Ref. [34].f Ref. [35].




k ¼ krkbT

h

Q TSQ RC

exp

ðE TS E RCÞ

kbT

where Q TS and E RC are the partition function and energy of the tran-

sition state, respectively andj is thetunnelingfactor that originatesfrom quantum mechanical tunneling through the potential energybarrier along the reaction coordinate.

All kinetic calculations have been performed using the TheRateprogram [37]. In these calculations, overall rotations are treatedclassically and vibrations are treated quantum mechanically with-in the harmonic approximation except for the modes correspond-ing to the internal rotations of the CH3 groups, which are treatedas hindered rotations using the method of Ayala et al. [38].

The corrections for quantum-mechanical tunneling have beentaken into account by Eckart’s formalism[39]. The rate coefficientsobtained by this procedure, which was applied to previous investi-gation [40] also, show a good agreement with the reported experi-mental values. The rate coefficients are calculated using the

electronic energy obtained from the M062X/MG3S method andtwo high levels composite CBS-QB3 and G4MP2 methods. The ap-plied methods give consistent results, summarized in Table 5, forallthe channels.It is worthmentioning here that theratesof therestof the channels with respect to R3 are negligible, therefore, thebranching ratio is not so sensitive to the reaction pathways andR3 represents almostoverall rate of the reaction.A symmetry factorof 2 is used for the rate calculation of R3, as there are two identicalleaving (methyl) groups. The values for rate constants for R3 at298 k calculated by M062X/MG3S, CBS-QB3 and G4MP2 are4.37 1013, 2.79 1011 and 1.31 1012 cm3 molecule1 s1,respectively. CBS-QB3 produces most accurate results comparedto experimental findings, although all rate constants are in agree-ment with previous experimental values [15,16] and exist within

the reported experimental error limits.For the other three paths, as the pre-reactive complexes have noeffect, the free energy difference between TS and separated reac-tants should reflect the real kinetics and the rate constant are cal-culated by the conventional TST equation. The values for thementioned rate constants are 1.22 1032, 1.01 1015,4.14 1024 cm3 molecule1 s1 for R1, R2 and R4, respectively.

6. Conclusions

Quantum chemical methods and reaction kinetics theories areapplied to investigate the atmospheric reaction of O(3P) atom withDMSO. A complete potential energy profile is constructed forunderstandingthe comprehensivereactionmechanismand thereaf-

ter the kinetics for the title reaction is explored. The conventionaltransition state theory calculations of atom–molecule reactions

have been performed to verify the experimentally observed valuesfor the rate coefficients. The AIManalysis is also presented to deter-mine the nature of interaction in the pre-reactive complexes.Although four possible channels are identified, the CH3SO2 + CH3

production channel, an S-addition/elimination path, is almostexclusive. The result shows good agreement with previous findings.The rate constants evaluated at 298 k are of the order of 1011 cm3

molecule1 s1. Thermochemical parameters (Df H

298.15

) of all thespecies involved in the title reaction are predicted using theM062X/MG3S, CBS-QB3, G3B3 and G4MP2 methods. The values ob-tained by CBS-QB3 method deviate less from experimental data.

Acknowledgement

D.M. is very much grateful to the CSIR, Government of India forproviding Research Fellowships. S.B. is thankful to NSEC, Kolkatafor allowing him to work at IACS. Thanks also are due to thereviewers for their valuable suggestions.

Appendix A. Supplementary data

The optimized structures and their Cartesian coordinates, ZPVE,thermochemical parameters, frequencies, MEP and relaxed PESscan image and the Wiberg bond indices for TS3 are presented insupporting information. Supplementary data associated with thisLetter can be found, in the online version, at http://dx.doi.org/10.1016/j.cplett.2012.09.002 .

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Table 5

The equlibirium constant (K eq, cm3 mol1) of the first step and the rate constants (k2,

s1) of the second step and the total rate constant (ktot, cm3 mol1 s1) for all the

pathways of the reaction of O(3P) with DMSO calculated at 298 K.

Method Reaction K eq K 2 K tot

M062X-MG3S R1 6.94 1035

R2 1.60 1014

R3 2.68 1021 1.63 108 4.37 1013

R4 3.28 1024

CBS-QB3 R1 1.22 1032

R2 1.01 1015

R3 8.19 1023 3.41 1010 2.79 1011

R4 4.14 1024

G4MP2 R1 8.06 1033

R2 4.15 1020

R3 1.90 1022 7.02 109 1.31 1012

R4 1.05 1024

36 D. Mandal et al. / Chemical Physics Letters 551 (2012) 31–37







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