Computational study on the multi-channel mechanism

Computational study on the multi-channel mechanism of disulfur and ozone reaction

Moein Goodarzi & Morteza Vahedpour

Structural Chemistry Computational and Experimental Studies of Chemical and Biological Systems ISSN 1040-0400 Volume 23 Number 5 Struct Chem (2012) 23:1599-1607 DOI 10.1007/s11224-012-9967-4

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Author's personal copy Struct Chem (2012) 23:1599–1607 DOI 10.1007/s11224-012-9967-4

ORIGINAL RESEARCH

Computational study on the multi-channel mechanism of disulfur and ozone reaction Moein Goodarzi • Morteza Vahedpour

Received: 24 September 2011 / Accepted: 30 January 2012 / Published online: 24 February 2012 Ó Springer Science+Business Media, LLC 2012

Abstract The reaction mechanism of disulfur (S2) and O3 on the triplet and singlet potential energy surfaces has been investigated theoretically at the B3LYP/6-311 ? G(3df) and G3B3 levels. The definite mechanism has not been obtained for the S2 ? O3 reaction on the triplet potential energy surface while one stable collision complex, IN1 (S-cyclicSOOO), has been considered between S2 and O3 reactants on the singlet potential energy surface. Through variety of IN1 transformations, three kinds products S ? SO3(D3h), SSO ? O2, and SO2 ? SO are obtained. The results show that the S2 ? O3 reaction proceeds on the singlet potential energy surface to produce SSO ? O2 as main product. The rate constant of S2 ? O3 ? SSO ? O2 reaction is small value of 2.71 9 10-20 cm3 molecule-1 s-1 under atmospheric conditions. Therefore, S2 molecule reacts with O3 at the high temperatures. Keywords

Disulfur  Ozone  Mechanism  G3B3

Introduction In the stratosphere, the existence of O3 is important for life on the Earth because it absorbs solar radiation with a wavelength between 240 and 320 nm within a region of 10–50 km altitudes. The largest concentration of ozone is attained at approximately 4.00 9 1012 molecules/cm3 [1–3]. In the troposphere, ozone is a harmful pollutant that causes damage to lung tissue and plants, and it can also act as a chemical oxidant by adding oxygen atoms to other compounds. Because of severe reaction of ozone with other M. Goodarzi (&)  M. Vahedpour Department of Chemistry, Zanjan University, Zanjan, Iran e-mail: [email protected]

molecules, high levels of ozone are toxic to living system. The role and application of ozone in chemical reactions are essential and well known. So, countless papers can be found for the reaction of ozone with other species [4–9]. Atmospheric sulfur chemistry plays an important role in the Earth’s atmosphere [10, 11]. The S2 molecule is one of the gaseous sulfur compounds that exists in the Earth’s atmosphere and gets out during volcanic eruptions. Also, we can find S2 molecules at various natural and industrial plasmas which contain sulfur compounds. For example, emission and absorption of S2 molecules have been observed in the Jupiter’s atmosphere [12] and its satellite Io. [13] They are also observed in the atmospheres of some comets [14]. In industrial conditions, S2 molecules can be seen in reactive ion etching process using SF6 molecules [15]. Sulfur lamps contain S2 molecules as an important ingredient [16]. Diatomic sulfur, S2, has been the subject of many theoretical and spectroscopic investigations for a long period of time [17–19]. The reaction mechanism of S2 ? O3 has never been studied, theoretically. Therefore, our main objective in this article is to reveal the details of the S2 ? O3 reaction mechanism, theoretically and to compare these results with those of the experiments.

Computational methods All the calculations are performed with the Gaussian 03 program [20]. In our previous works, we investigated the reaction mechanism for some sulfur compounds in gas phase [9, 21, 22]. In present study, we have pursued the same trend for the level of calculations and basis set in the reaction mechanism of S2 ? O3. Therefore, the geometries of the reactants, products, intermediates (INs) and

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transition states (TSs) involved in the title reaction are optimized using the B3LYP [23, 24] level with 6-311 ? G(3df) basis set. To obtain more reliable results, energy calculations have been performed on all species at the G3B3 [25, 26] level. The nature of the stationary points is determined according to the number of negative eigenvalues of Hessian matrix at the B3LYP level. Any reactants, products and INs possess all real frequencies and any TSs have one imaginary frequency. Connections between the reactants, INs, TSs and products are confirmed by the intrinsic reaction coordinate (IRC) [27] analysis at the B3LYP level. Finally, the counterpoise procedure (CP) [28] is used to correct the interaction energy for the basis set superposition error (BSSE).

change (3S2 ? 1S2). The optimized geometries of the reactants, INs, TSs and products involved in the 1S2 ? O3 reaction at the B3LYP level are shown in Figs. 1 and 2. Also, the experimental values of the structural parameters of some species are shown in Fig. 1. There are good agreements between the theoretical structural parameters at the B3LYP level and those of the experiments. To make our discussion easier, the 3S2 ? O3 energy is set to zero as reference. The total energies and relative energies have been listed in Table 1 for the B3LYP and G3B3 levels. The calculated vibrational frequencies at the B3LYP level have been listed in Table 2. Finally, by means of the TSs and their connected INs or products at the G3B3 level, a schematic PES for S2 ? O3 reaction is plotted in Fig. 3.

Results and discussions

Initial association

The ground state of disulfur (S2) and ozone (O3) reactants are triplet (3S2) and singlet (1O3), respectively. Therefore, the 3S2 ? 1O3 reaction progresses on the triplet potential energy surface (PES). In spite of numerous attempts, one definite mechanism has not been obtained for the 3 S2 ? 1O3 reaction on the triplet PES. Therefore, calculations have been pursued on the singlet excited PES. Disulfur (3S2) reactant first is excited to the singlet state (1S2), when it approaches the terminal oxygen atoms of O3 to form adduct IN1 (S-cyclicSOOO) on the singlet PES. Therefore, the initial step (adduct formation) involves the activation energy 15.8 kcal/mol due to spin multiplicity

One stable collision complex, IN1 (S-cyclicSOOO), has been considered between disulfur (1S2) and ozone (O3) on the singlet PES. The atoms of ozone terminal oxygen approach one of the S atoms of S2, which leads to one suitable intermediate, i.e., the four-membered ring IN1. Figure 1 shows that the bond length of O–O in IN1 is ˚ at the B3LYP level, which is about 0.201 A ˚ longer 1.452 A than that in parent O3 molecule. The bond length of newly ˚ . The four-membered ring IN1 has formed S–O is 1.735 A Cs symmetry and lies 12.8 kcal/mol below the original reactants (3S2 ? O3) at the G3B3 level. This energy contains basis set superposition error (BSSE). The BSSE value

Fig. 1 The optimized structures of the reactants, products, and intermediates at the B3LYP level (bond lengths in angstrom and bond angles in degree. The values in square parentheses are in experiment)

IN1

IN5

O3

123

3

O2

IN2

IN3

IN6

SO 3(D3h)

1

O2

3

S2

1

S2

IN4

SSO

1

SO

SO 2

3

SO

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Fig. 2 The optimized structures of the transition states at the B3LYP level (bond lengths are in angstrom)

TS1

TS5

TS2

TS6

TS9

TS3

TS4

TS7

TS8

TS10

Table 1 The total energies (ET) and relative energies (in the parenthesis) obtained in the S2 ? O3 reaction Species

B3LYP EaT

G3B3 Ea,b T

Species

B3LYP EaT

G3B3 Ea,b T

S2 (3Rg ) ? O3

-1021.9222

-1021.4067 (0.0)

IN5

-1022.0863

-1021.5795 (-108.4)

1

S2 ( Dg) ? O3

-1021.8863

-1021.3815 (15.8)

IN6

-1022.1054

-1021.5945 (-117.9)

S (3P) ? SO3(D3h)

-1022.0585

-1021.5500 (-89.9)

TS1

-1021.9273

-1021.4070 (-0.2)

S (1D) ? SO3(D3h)

-1021.9972

-1021.5071 (-63.0)

TS2

-1021.9180

-1021.4080 (-0.8)

SSO ? O2 (3Rg)

-1022.0488

-1021.5289 (-76.7)

TS3

-1021.9290

-1021.3692 (23.5)

SSO ? O2 (1Dg)

-1021.9875

-1021.4828 (-47.7)

TS4

-1021.9138

-1021.4168 (-6.3)

SO2 ? SO (3R-)

-1022.1333

-1021.6187 (-133.0)

TS5

-1021.9631

-1021.4626 (-35.1)

1

SO2 ? SO ( D)

-1022.0879

-1021.5847 (-111.7)

TS6

-1021.9091

-1021.3860 (13.0)

IN1

-1021.9385

-1021.4271 (-12.8)

TS7

-1021.9527

-1021.3906 (10.1)

IN2

-1021.9712

-1021.4651 (-36.7)

TS8

-1021.9985

-1021.4421 (-22.2)

IN3 IN4

-1022.0111 -1022.0121

-1021.5010 (-59.2) -1021.5099 (-64.8)

TS9 TS10

-1022.0074 -1022.0743

-1021.5005 (-58.9) -1021.5648 (-99.2)

a

The total energies (ET) are in hartree and ET = Eelec ? ENN ? EZPE

b

The relative energies (in the parenthesis) are in kcal/mol

for IN1 is 1.6 kcal/mol. Subsequently, three kinds of products are obtained via variety of IN1 transformations. The details of the reaction mechanism are discussed below.

Path P1 3 S2 þ O3 ! 1 S2 þ O3 ! IN1 ! IN2 ! IN4 ! 1 S þ SO3 ðD3h Þ ! 3 S þ SO3 ðD3h Þ

Formation path of S ? SO3(D3h)

In path P1, IN1 intermediate undergoes 1S–3O and 2S–4O bonds formation and 3O–4O bond rupture process to form IN2 intermediate through TS2 with the energy barrier 12.0 kcal/mol as shown in Fig. 3. IN2 intermediate

From Fig. 3, we find out that only one path is possible to form S ? SO3(D3h) product. It can be written as follows:

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lies 36.7 kcal/mol below 3S2 ? O3 reactants and can transform to IN4 intermediate via TS4 by 1S–3O bond rupture with the energy barrier 30.4 kcal/mol. IN4 intermediate lies 64.8 and 28.1 kcal/mol below 3S2 ? O3 reactants and IN2 intermediate, respectively. IN4 intermediate can decompose into 1S ? SO3(D3h) product via TS8 through 1S–2S and 3O–4O bonds rupture with the energy barrier 42.6 kcal/mol at the G3B3 level. Finally, 1S would relax to the triplet ground state (3S) to form the final product of 3S ? SO3(D3h). Formation paths of SSO ? O2 For SSO ? O2 product, there are three possible paths as follows: Path P2 3 S2 þ O3 ! 1 S2 þ O3 ! IN1 ! SSO þ 1 O2 ! SSO þ 3 O2

Path P3 3 S2 þ O3 ! 1 S2 þ O3 ! IN1 ! IN2 ! SSO þ 1 O2 ! SSO þ 3 O2 Path P4 3 S2 þ O3 ! 1 S2 þ O3 ! IN1 ! IN2 ! IN4 ! SSO þ 1 O2 ! SSO þ 3 O2 In path P2, IN1 intermediate can directly decompose into SSO ? 1O2 product via TS1 with the energy barrier 12.6 kcal/mol at the G3B3 level. In this step, 4O–3O and 2S–5O bonds rupture. In path P3, the formation of the IN2 intermediate is similar to path P1. Subsequently, IN2 intermediate, similar to IN1, can directly transform to SSO ? 1O2 product via TS6 with the energy barrier 49.7 kcal/mol. In path P4, the formation of the IN4 intermediate is similar to path P1. IN4 intermediate can decompose into SSO ? 1O2 via TS7 with the energy barrier 74.9 kcal/mol.

Table 2 The vibrational frequencies (cm-1) of the reactants, intermediates, products and transition states calculated at the B3LYP level Species

Frequencies

IN1

60

165

287

524

573

713

750

906

919

IN2

205

254

354

393

489

608

739

902

1,006

IN3

128

228

388

430

448

680

690

814

1,271

IN4

256

316

413

438

589

660

739

993

1,324

IN5

72

278

405

544

585

689

719

768

1,293

IN6

97

120

299

309

462

547

674

1,176

1,211

O3

753

1,213

1,265

O2 (1Dg)

1,633

1,076

1,399

1,400

O2 (3Rg)

1,644

S2 (1Dg)

712

S2 (3Rg) SSO

716 382

688

1,196

SO3(D3h)

495

524

525

SO2

519

1,179

1,378

SO (1D) 3

-

1,157

SO ( R )

1,157

TS1

545 i

107

236

343

385

581

741

774

1,023

TS2

424 i

156

227

351

386

553

760

830

1,021

TS3

357 i

201

251

333

388

598

685

901

971

TS4

526 i

185

241

356

389

527

748

936

1,065

TS5

602 i

228

257

339

440

581

716

868

1,019

TS6

446 i

136

180

283

394

478

556

986

1,006

TS7

415 i

195

249

317

414

618

727

955

1,288

TS8

519 i

157

323

430

443

586

848

999

1,345

TS9

549 i

152

255

398

421

444

741

812

1,267

TS10

326 i

186

311

431

542

637

716

820

1253

The vibrational frequencies are without any scaling factors i Symbols stand for imaginary frequencies

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Fig. 3 The potential energy profile of the S2 ? O3 reaction at the G3B3 level

In these three paths (P2, P3, and P4), at the end product, 1O2 would relax to the triplet ground state (3O2) to form the final product of SSO ? 3O2. Formation paths of SO2 ? SO There are two possible paths to produce SO2 ? SO, which can be written as follows: Path P5 3 S2 þ O3 ! 1 S2 þ O3 ! IN1 ! IN2 ! IN3 ! SO2 þ 1 SO ! SO2 þ 3 SO Path P6 3 S2 þ O3 ! 1 S2 þ O3 ! IN1 ! IN2 ! IN5 ! IN6 ! SO2 þ 1 SO ! SO2 þ 3 SO In paths P5 and P6, the formation of IN2 intermediate is similar to path P1. In path P5, IN2 intermediate undergoes 1S–3O and 2S–5O bonds rupture and 1S–5O bond formation process to produce the IN3 intermediate via TS3. The energy barrier for IN2 ? IN3 conversion is 60.2 kcal/mol. Finally, IN3 intermediate can be decomposed to SO2 ? 1SO via TS9 with the energy barriers 0.3 kcal/mol. In the IN3 ? SO2 ? 1SO conversion, 1S–2S and 4O–5O bonds rupture and SO2 ? 1SO product appears. In path P6, IN2 intermediate lies 36.7 kcal/mol below 3 S2 ? O3 reactants and undergoes 1S–2S and 4O–5O bonds rupture and 1S–5O bond formation process to form the IN5 intermediate via TS5 with the energy barrier

1.6 kcal/mol. IN5 intermediate is 108.4 kcal/mol lower than the total energy of 3S2 ? O3 original reactants. This energy provides the driving force for the formation of IN6 intermediate via TS10 by 1S–3O bond rupture with the energy barrier 9.2 kcal/mol. Finally, IN6 intermediate can be directly decomposed to SO2 ? 1SO through the 1S–3O bond rupture without any transition states. For these two paths (P5 and P6), at the end product, 1SO would relax to the triplet ground state (3SO) to produce SO2 ? 3SO. Based on the obtained paths from S2 and O3 reaction on singlet PES, the most possible reaction paths of the three products of S ? SO3(D3h), SSO ? O2 and SO2 ? SO are listed below: Path P1 3 S2 þ O3 ! 1 S2 þ O3 ! IN1 ! IN2 ! IN4 ! 1 S þ SO3 ðD3h Þ ! 3 S þ SO3 ðD3h Þ Path P2 3 S2 þ O3 ! 1 S2 þ O3 ! IN1 ! SSO þ 1 O2 ! SSO þ 3 O2 PathP6 3 S2 þ O3 ! 1 S2 þ O3 ! IN1 ! IN2 ! IN5 ! IN6 ! SO2 þ 1 SO ! SO2 þ 3 SO In these three paths, the barrier energy 42.6 kcal/mol (IN4 ? 1S ? SO3(D3h)) in path P1 is much higher than 12.6 kcal/mol (IN1 ? SSO ? 1O2) and 12.0 kcal/mol

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(IN1 ? IN2) in paths P2 and P6, respectively. Therefore, paths P2 and P6 are the most feasible reaction paths on the singlet PES. It is necessary to say that in the investigation of reaction mechanism, there are two path categories. They are forward (in orientation of the products formation) and backward (in orientation of the reactants formation) paths. In this study, we have argued only forward paths to explain the formation of different products that is our main objective. Therefore, backward paths have been not argued in text and they can continue through Fig. 3.

Comparative study of the theory of the reaction heat with the experiments The heat of 3S2 ? O3 ? SSO ? 3O2 reaction (DH) have been directly reported at room temperature, experimentally [29] (DH = -77.7 kcal/mol). The heat of 3S2 ? O3 ? SSO ? 3O2 reaction is -76.6 kcal/mol at the G3B3 level which is in good agreement with the experiment (-77.7 kcal/mol) at room temperature. The heat of 3S2 ? O3 ? SO2 ? 3SO and 3S2 ? O3 ? 3S ? SO3 reactions have been not directly reported at room temperature, experimentally. Therefore, we have used from Hess’s law to calculate the experimental DH value of 3S2 ? O3 ? SO2 ? 3SO and 3S2 ? O3 ? 3S ? SO3 reactions by experimental DH values of listed reactions in Table 3. The result of these calculations shows that the experimental DH of 3S2 ? O3 ? SO2 ? 3SO and 3S2? O3 ? 3S ? SO3 reactions should be -133.5 and -92.7 kcal/mol, respectively [29, 30]. As shown in Table 3, DH value of 3S2 ? O3 ? SO2 ? 3SO (-133.1 kcal/mol) and 3S2? O3 ? 3 S ? SO3 (-90.2 kcal/mol) reaction at the G3B3 level is in good agreement with those of experiment.

Comparative study of the triplet–singlet S2, S, O2, and SO gaps at the G3B3 level with the experiment data The triplet–singlet S2, S, O2, and SO gaps at the G3B3 level and experiment have been listed in Table 4. The experi1 3 1 mental values for the S2(3Rg ) ? S2( Dg), S( P) ? S( D) 1 and O2(3Rg ) ? O2( Dg) gaps are 14.3 [31], 26.4 [32], and 22.7 [33] kcal/mol, respectively. The theoretical values for 1 3 1 the S2(3Rg ) ? S2( Dg) (15.8 kcal/mol) and S( P) ? S( D) (26.9 kcal/mol) gaps at the G3B3 level are in very good agreement with those of experiment while, the triplet–singlet O2 gap (29.0 kcal/mol) at the G3B3 level is in relatively good agreement with that of experiment (22.7 kcal/mol). As far as we know, no experimental value has been not reported for SO(3R-) ? SO(1D) gap to compare with theoretical value of 21.3 kcal/mol at the G3B3 level. Calculation of the rate constants Based on the obtained results from S2 and O3 reaction, paths P2 and P6 are the most feasible reaction paths on the Table 4 The triplet–singlet S2, S, O2, and SO gaps reported at the theory and experiment G3B3 levela,b

Expa

1 S2 (3Rg ) ? S2 ( Dg)

15.8

14.3c

S (3P) ? S (1D)

26.9

26.4d

29.0

22.7e

O2 (3Rg) 3 -

1

? O2 ( Dg) 1

SO ( R ) ? SO ( D) a

21.3

The energies are in kcal/mol

b

This work

c

Ref. [31]

d

Ref. [32]

e

Ref. [33]

Table 3 The values of reaction heat (DH) reported at the G3B3 level and experiment DHa,b

Reaction

G3B3 level 3

S2 ? O3 ? SSO ? 3O2

3

3

3

Exp

-76.6e

-77.7c

3

S2 ? O2 ? SO ? SO 3

CS ? SSO ? OCS ? S2 3

OCS ? SO ? CS ? SO2 Net: 3S2 ? O3 ? SO2 ? 3SO

-133.1e

DHa,b

Reaction

-27.6

c

-56.6

d

28.4

d

-133.5f

3

S2 ? O3 ? SSO ? 3O2 3

The values of reaction heat (DH) are in kcal/mol The temperature is 298.15 K at the theory and experiment

c

Ref. [29]

d

Ref. [30]

e

This work

f

Obtained in terms of Hess’s law

123

-76.6e

-77.7c 77.1d

3

-36.0d

CS ? SO ? OCS ? S 3

-63.5d

OCS ? O2 ? CO ? SO2 CO ? SSO ? OCS ? 3SO 3

Net: S2 ? O3 ? S ? SO3 a

Exp

OCS ? SO2 ? CS ? SO3

3

b

G3B3 level

7.4d e

-90.2

-92.7f

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singlet PES. Therefore, the rate constants have been calculated only for these two paths by the RRKM (RiceRamsperger-Kassel-Marcus) [34, 35] and VTST (Variational Transition State Theory) [36] theories implemented in the SSUMES (Steady-State Unimolecular MasterEquation Solver) [37] and GPOP (Gaussian POst Processor) [38] programs. The path P2 of S2 ? O3 reaction includes the transfer of O3 terminal O-atom to S2 molecule. As shown in Scheme 1, O3 molecule reacts with S2 to produce the energized complex IN1*. The forward and backward rate constants of barrier-less and bimolecular conversion of S2 ? O3 ? IN1* have been denoted by k1 and k-1, respectively. Subsequently, IN1* transforms to final product of SSO ? O2 through TS1. The forward rate constant of unimolecular conversion of IN1* ? SSO ? O2 has been denoted by k2. The following equation has been used for the calculation of the overall rate constant of path P2 (denoted as kT2) through the individual rate constants of k1, k-1 and k2.

denoted by k3, k4, and k5 and backward rate constants of these conversions have been denoted by k-3, k-4, and k-5, respectively. Finally, k6 stands for the forward rate constant of IN6* ? SO ? SO2 conversion. In our previous works [9, 21], we have used from these two programs to calculate the rate constant of multi-step reactions. In present study, the same trend has been pursued for the calculation of the rate constant of paths P2 and P6. The following equation has been used for calculation of the overall rate constant of path P6 (denoted as kT6) through the individual rate constants. kT6 ¼ k1

k3 k4 k5 k6 k1 þ k3 k3 þ k4 k4 þ k5 k5 þ k6

2 where k1kþk is the possibility of the reaction progression in 2 IN1* ? SSO ? O2 conversion. The S2 ? O3 reaction mechanism in path P6 is oxygen abstraction and sulfur insertion. As shown in Scheme 2, the mechanism of path P6 is more complex than path P2. By starting from IN1*, there are three energized intermediates IN2*, IN5*, and IN6* in path P6 to produce final product of SO ? SO2. In path P6, the forward rate constants of IN1* ? IN2*, IN2* ? IN5*, and IN5* ? IN6* conversions have been

3 5 6 4 where k1kþk ; k3kþk ; k4kþk , and k5kþk are the possibilities 3 4 5 6 for reaction progression in IN1* ? IN2*, IN2* ? IN5*, IN5* ? IN6*, and IN6* ? SO ? SO2 conversions, respectively. For the multi-channel reaction of S2 ? O3, the calculated overall rate constants for paths P2 and P6 are denoted as kT2 and kT6, respectively. The overall rate constants for the S2 ? O3 reaction is denoted as kT, kT = kT2 ? kT6. The branching ratios for paths P2 and P6 are kT2/kT and kT6/kT, respectively. Table 5 shows the overall rate constant for paths P2 and P6 and S2 ? O3 reaction and the branching ratios at the temperature range of 200–1,400 K. As shown in Table 5, the value of kT2 is bigger than kT6. Also, the branching ratios variation of kT2/kT is from 100 to 60% while, kT6/kT is from 0 to 40% at the temperature range of 200–1,400 K. Therefore, the path P2 is more suitable than path P6 on the singlet PES. The overall rate

Scheme 1 The details of S2 ? O3 ? SSO ? O2 conversion

Scheme 2 The details of S2 ? O3 ? SO ? SO2 conversion

kT2 ¼ k1

k2 k1 þ k2

Table 5 The overall rate constants for path P2 (kT2) and path P6 (kT6) and overall rate constants for S2 ? O3 reaction (kT) [in cm3 molecule-1 s-1] and the branching ratios (kT2/kT and kT6/kT) calculated at the temperature range of 200–1,400 K kT6

kT

kT2/kT

kT6/kT

T (K)

kT2

200

1.40 9 10-23

5.73 9 10-33

1.40 9 10-23

1.00 9 1000

298

-20

-27

-20

00

1.07 9 10-7

00

2.71 9 10

2.94 9 10

2.71 9 10

1.00 9 10

409 500

-17

2.24 9 10 2.21 9 10-16

-23

8.81 9 10 4.39 9 10-20

2.24 9 10 2.21 9 10-16

1.00 9 10 1.00 9 1000

3.93 9 10-6 1.99 9 10-4

600

1.35 9 10-16

0.80 9 10-17

1.43 9 10-16

9.44 9 10-1

5.59 9 10-2

800

-15

-16

-15

-1

1.40 9 10-1

-1

2.40 9 10-1

-1

4.00 9 10-1

1,000 1,400

1.52 9 10

-15

7.47 9 10

-14

5.72 9 10

2.47 9 10

-15

2.36 9 10

-14

3.81 9 10

-17

4.09 9 10-10

1.76 9 10

-15

9.82 9 10

-14

9.53 9 10

8.64 9 10 7.61 9 10 6.00 9 10

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constant value of the path P2 (kT2) is 2.71 9 10-20 cm3 molecule-1 s-1 under atmospheric conditions. This small value for rate constant shows that S2 and O3 react at the high temperatures. To our knowledge, there is no direct experimental investigation to report the rate constant of S2 ? O3 reaction under atmospheric conditions. Hills et al. [29] have investigated kinetics of S2 ? O3 reaction at the temperature of 409 K, experimentally. The theoretical value for the rate constant of path P2 at the temperature of 409 K (2.24 9 10-17 cm3 molecule-1 s-1) is in relatively good agreement with that of Hills et al. [29] (4.00 9 10-15 cm3 molecule-1 s-1).

Conclusions In spite of numerous attempts, no mechanism has been obtained for the 3S2 ? O3 reaction on the triplet PES. Therefore, the details of theoretical investigation on the singlet PES of 1S2 ? O3 reaction has been carried out at the B3LYP/6-311 ? G(3df) and G3B3 levels. Disulfur (3S2) reactant is first excited to the singlet state (1S2), when it approaches the terminal oxygen atoms of O3 to form adduct IN1 (S-cyclicSOOO) on the singlet PES. Through variety of IN1 (S-cyclicSOOO) transformations, three kinds of products S ? SO3(D3h), SSO ? O2 and SO2 ? SO are obtained. The most possible reaction paths of the three products of S ? SO3(D3h), SSO ? O2, and SO2 ? SO are P1, P2, and P6, respectively. The barrier energy 42.6 kcal/mol (IN4 ? 1S ? SO3(D3h)) in path P1 is much higher than 12.6 kcal/mol (IN1 ? SSO ? 1O2) and 12.0 kcal/mol (IN1 ? IN2) in paths P2 and P6, respectively. Therefore, paths P2 and P6 are the most feasible paths of S2 ? O3 reaction on the singlet PES. The rate constant values of paths P2 (donated as k1) and P6 (donated as k2) show that k1 is bigger than k2. Also, the branching ratios variation of k1/k is from 100 to 60% while, k2/k is from 0 to 40% at the temperature range of 200–1,400 K. Therefore, the results show that the S2 ? O3 reaction proceeds on the singlet PES to produce SSO ? O2 through path P2. The rate constant of S2 ? O3 ? SSO ? O2 reaction through path P2 is small value of 2.71 9 10-20 cm3 molecule-1 s-1 under atmospheric conditions. Therefore, S2 reacts with O3 at the high temperatures.

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