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Theoretical study on the mechanism of S2 + O2 reaction
Chemical Physics Letters 497 (2010) 1–6
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Theoretical study on the mechanism of S2 + O2 reaction Moein Goodarzi a, Morteza Vahedpour a,*, Fariba Nazari b a b
Department of Chemistry, Zanjan University, Zanjan, Iran Department of Chemistry, Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan 45137-66731, Iran
a r t i c l e
i n f o
Article history: Received 2 December 2009 In final form 28 July 2010 Available online 30 July 2010
a b s t r a c t The reaction pathways of disulfur (S2) with oxygen (O2) on the triplet and singlet potential energy surfaces have been investigated at the G3B3//B3LYP/6-311++G(3df,3pd) level. The calculated results reveal that P2(trans-1OSSO), P3(cis-1OSSO) and P4(3S + 1SO2) produce only on the singlet energy potential surface while, P1(3SO + 3SO) produces on the both triplet and singlet surfaces. No intersystem crossing has been found between triplet and singlet surfaces and the energy barriers of the triplet surface are much lower than singlet surface. Therefore, S2 + O2 reaction proceeds only on triplet surface to produce P1(3SO + 3SO). Ó 2010 Elsevier B.V. All rights reserved.
1. Introduction Atmospheric sulfur chemistry has an important role in atmosphere of the Earth [1,2]. The SO molecule is one of the gaseous sulfur compounds that exist in atmosphere of the Earth and only is available in the gaseous phase [3]. Gaseous SO and other sulfur oxides are formed when sulfur is burnt in low pressure pure oxygen. Two SO units can join via the sulfur atoms in a cis or trans configuration, Lovas et al. observed disulfur dioxide in a microwave discharge of SO2 [4]. In their experiments, S2O2 is a cis-bent, planner chain O–S–S–O, with C2v symmetry. The bond lengths indicate that the S–O bonds are double bonds and the S–S bond has partial double bond character. The structure was calculated by obtaining r0(S–S) = 2.024(6) Å for the S–S bond length. Other parameters are r0(S–O) = 1.458(2) Å and \SSO = 112.7(5)° [4]. Many theoretical studies have been performed on S2O2 [5–8], although, only the cisplanar form of disulfur dioxide has been experimentally observed and confirmed. The theoretical studies of Marsden and Smith [5] show that a trigonal planar form of S2O2 (Fig. 1, 1IN7), similar to the structure of SO3, is more stable than cis-OSSO, energetically. Nevertheless, due to the relatively high energies of the molecular products, Lovas et al. did not observe trigonal planar form of S2O2 in the microwave discharge spectra. Also, Marsden and Smith show that the energy of trans-OSSO is very close to its corresponding cis form. Clements et al. [9] have indicated that geometries of cis-OSSO and trigonal planar (1IN7) at the B3LYP level differ from those calculated and optimized by Marsden and Smith at the SCF level. The largest difference between two calculations is the S–S bond length which is increased from 1.931 Å (at the SCF level) to 2.069 Å (at the B3LYP level) for the trigonal isomer, and from 1.866 Å (at the SCF level) to 1.912 Å (at the B3LYP level) for the
* Corresponding author. Fax: +98 241 5152477. E-mail address: [email protected] (M. Vahedpour). 0009-2614/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2010.07.084
cis-OSSO isomer. The S–S bond length value in the cis-OSSO isomer at the B3LYP level matches more closely to the experimental value of 2.025 Å [4,9]. The disulfur (S2) is another of the gaseous sulfur compounds that exist in atmosphere of the Earth. Also, we can find S2 molecules at various natural and industrial plasmas containing sulfur compounds. For example, emission and absorption of S2 molecules have been observed in the atmosphere of Jupiter [10] and its satellite Io [11]. They are also observed in the atmosphere of some comets [12]. In industrial condition, S2 molecules can be seen in reactive ion etching process using SF6 molecules [13]. Sulfur lamps contain S2 molecules as an important component [14]. Diatomic sulfur, S2, has been subject of many theoretical and spectroscopic investigations for long time [15–17]. The reaction of disulfur with oxygen has not been investigated, and in this Letter, we carry out the theoretical study of S2 + O2 reaction on the triplet and singlet potential energy surfaces (PES). Our main objective in this Letter is to reveal the details of the reaction mechanism, to explain the formation and decomposition of trans-1OSSO and cis-1OSSO complexes, and provide further information about gaseous phase reaction of S2 + O2 on the triplet and singlet surfaces. 2. Computational details All the calculations are performed with the GAUSSIAN 03 program [18]. The geometrical parameters of the reactants, products, intermediates (denoted as INs), and transition states (denoted as TSs) involved in the S2 + O2 reaction are fully optimized using density functional theory with the Becke 3-parameter hybrid exchange [19] and Lee–Yang–Parr [20] correlation density functional (B3LYP) in conjunction with the 6-311++G(3df,3pd) basis set. Clements et al. via computation at the B3LYP/6-311+G(d) level showed that the structural parameters in the cis-1OSSO molecule
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M. Goodarzi et al. / Chemical Physics Letters 497 (2010) 1–6
Fig. 1. Geometries of reactants, products, intermediates and transition states optimized at the B3LYP level. The values in square parentheses are from experiment (Ref. [4] for 1 cis-OSSO). Bond distances are in angstrom and angles are in degree.
are more closely to the experimental values [9]. To obtain more reliable relative energies, we have applied a larger basis set (6311++G(3df,3pd)) in the present calculations. Single-point calculations are performed on all species at the G3B3 [21,22] level using the B3LYP optimized geometries. The optimized geometries are characterized by harmonic analysis, and the nature of the stationary points is determined according to the number of negative eigenvalues of the Hessian matrix at the B3LYP level. Any reactant, product and intermediate possess all real frequencies and any transition state has only one imaginary frequency. Connections between reactants, intermediates, transitions states and products are confirmed by intrinsic reaction coordinate (IRC) [23,24] analysis at the B3LYP level. The counterpoise (CP) procedure [25] is used to correct the interaction energy for basis set superposition error (BSSE), and the CCSD [26,27] method is used
to calculate the T1 diagnostic values for the structures. Finally, the CASSCF [28,29] method is used to give some computational evidences that the results are sufficiently correct at the B3LYP level.
3. Results and discussion The optimized geometries of the reactants, intermediates, transition states and products involved in the S2 + O2 reaction at the B3LYP level are shown in Fig. 1. To simplify our discussion, the energy of reactant 3S2 + 3O2 (denoted as R1) is set to be zero for reference. Also, the reactant 1S2 + 1O2 is denoted as R2. The total energies and relative energies have been listed in Table 1 for the B3LYP and G3B3//B3LYP levels. The calculated vibrational frequencies at the B3LYP level have been listed in Table 2 show that all of
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M. Goodarzi et al. / Chemical Physics Letters 497 (2010) 1–6 Table 1 The total energies (ET), relative energies (in the parenthesis) and T1 diagnostic values obtained in the S2 + O2 reaction. Species
ETa
T1b diagnostic
B3LYP 3
S2 + 3O2 (R1) 1 S2 + 1O2 (R2) 1 IN1 1 IN2 1 IN3 1 IN4 1 IN5 1 IN6 1 IN7 P1(3SO + 3SO) 1 SO + 1SO P2(trans-1OSSO) P3(cis-1OSSO) a
ETa
Species
G3B3//B3LYP
946.8073 946.7101 946.7712 946.7831 946.6504 946.8422 946.8511 946.8696 946.8967 946.8488 946.7578 946.8825 956.8871
946.3362 946.2649 946.3241 946.3385 946.1896 946.3880 946.3980 946.4174 946.4452 946.3820 946.3139 946.4243 946.4291
(0.00) (44.74) (7.59) ( 1.44) (91.99) ( 32.51) ( 38.78) ( 50.95) ( 68.40) ( 28.74) (13.99) ( 55.28) ( 58.30)
T1b diagnostic
B3LYP P4(3S + 1SO2) 1 S + 1SO2 1 TS1 1 TS2 1 TS3 1 TS4 1 TS5 1 TS6 1 TS7 1 TS8 1 TS9 3 TS1 3 TS2
0.0142 0.0140 0.0282 0.0474 0.0378 0.0221 0.0189
0.0247 0.0245
G3B3//B3LYP
946.8434 946.7821 946.6294 946.6247 946.6904 946.8351 946.8379 946.8230 946.8199 946.8395 946.8191 946.7347 946.7455
946.3901 946.3473 946.1439 946.1718 946.2305 946.3737 946.3852 946.3068 946.3699 946.3736 946.3721 946.2659 946.2772
( 33.82) ( 6.97) (120.67) (103.16) (66.33) ( 23.53) ( 30.75) (18.45) ( 21.15) ( 23.47) ( 22.53) (44.11) (37.02)
0.0649 0.0366 0.0685 0.0355 0.0562 0.0591 0.0529 0.0368 0.0336 0.0528 0.0373
The total energies (ET) are in hartree and relative energies (in the parenthesis) are in kcal/mol. T1 diagnostic values obtained from CCSD/6-311++G(3df,3pd)//B3LYP level.
b
Table 2 The vibrational frequencies (cm
1
) of the reactants, intermediates, products and transition states calculated at the B3LYP level.
Species
Frequencies
1
170 162 302 155 152 265 344 138 185 712 716 1634 1645 1157
IN1 1 IN2 1 IN3 1 IN4 1 IN5 1 IN6 1 IN7 cis-1OSSO trans-1OSSO 1 S2 3 S2 1 O2 3 O2 3 SO
205 359 387 188 335 414 407 285 194
369 464 472 374 516 442 469 475 342
629 592 517 692 647 559 667 491 581
714 734 721 719 747 805 1181 1139 1130
1054 1106 895 1254 1254 1272 1373 1192 1159
intermediates (INs) are true minimum on the reaction potential energy surfaces, and any transition state has only one imaginary frequency. Finally, by means of the transition states and their connected intermediates or products at the G3B3//B3LYP level, a schematic PES for S2 + O2 reaction on the triplet and singlet potential energy surfaces are plotted in Fig. 2. The geometries of 3TS2 and 1IN2 are very similar except for the bond length of 4S–1O. Therefore, the existence of the minimum energy crossing point (MECP) between the triplet and singlet potential energy surfaces has been investigated. In order to obtain the MECP, the potential energy surfaces for 3TS2 and 1IN2 are plotted through the variation of bond length of 4S–1O at the B3LYP level. Fig. 3 shows that there is no intersystem crossing between the triplet and singlet potential energy surfaces.
Species
Frequencies
1
1157 519 548 i 554 i 977 i 202 i 224 i 576 i 611 i 382 i 626 i 846 i 307 i
SO 1 SO2 1 TS1 1 TS2 1 TS3 1 TS4 1 TS5 1 TS6 1 TS7 1 TS8 1 TS9 3 TS1 3 TS2
1179 253 212 187 227 234 215 222 285 254 239 199
1378 292 305 239 343 391 424 317 307 375 324 424
483 474 390 511 581 476 475 562 462 482 520
713 632 689 939 810 796 856 836 1028 668 631
905 872 1051 1272 1264 1272 1200 1225 1293 782 873
of newly formed S–O is 1.665 Å. In the intermediate 1IN2, the bonds length of S–S and O–O are 1.877 and 1.294 Å, respectively, which bond of S–S is about 0.027 Å lower and bond of O–O is about 0.091 Å longer than the parent 1S2 and 1O2 molecules, respectively. The bond length of newly formed S–O is 1.685 Å. The intermediate 1IN1 is 7.59 kcal/mol above the original reactants, while the intermediate 1IN2 is 1.44 kcal/mol below the original reactants (3S2 + 3O2) at the B3LYP level. The BSSE values for the intermediates 1IN1 and 1IN2 energies are 1.11 and 1.09 kcal/mol at the B3LYP level, respectively. No transition state has been found for their formation. So, the formation of 1IN1 or 1IN2 is a barrierless process. Subsequently, via variety of transformations of 1IN1 or 1 IN2, four kinds of products are obtained. The details of the reaction mechanism on the triplet and singlet potential energy surfaces will be discussed in below.
3.1. Initial association In spite of numerous attempts, no stable collision complex has been found on the triplet potential energy surface while, two stable collision complexes, 1IN1 (trans-1SSOO) and 1IN2 (cis-1SSOO), have been considered between disulfur (1S2) and oxygen (1O2) on the singlet potential energy surface. Both complexes are formed via one of the sulfur atoms in 1S2 molecule which is associated with one of the oxygen atoms in 1O2 molecule with the main frames being trans and cis. In the intermediate 1IN1, the bonds length of S–S and O–O are 1.889 and 1.312 Å at the B3LYP level, respectively, which bond of S–S is about 0.015 Å lower and bond of O–O is about 0.109 Å longer in compare to 1S2 and 1O2 molecules, respectively. The bond length
1
IN5 P2
1
IN1
1
1
IN3
1
IN4
IN6 P3
1
S2 + O2 1
IN7
1
IN2
P3
3
TS1
3
P1
1
3
S2 + O2
P1 3
TS2
P1
P4
4
M. Goodarzi et al. / Chemical Physics Letters 497 (2010) 1–6
Fig. 2. Potential energy profile of the S2 + O2 reaction at the G3B3//B3LYP level.
3.3. Formation pathways of P1(3SO + 3SO) For product P1(3SO + 3SO), there are six possible pathways as follows: Path Path Path Path Path Path
Fig. 3. Potential energy surfaces (exclude ZPE) of triplet 3TS2 and singlet 1IN2 for the variation of the bond length 4S–1O at the B3LYP level.
3.2. Isomerization and dissociation pathways on the triplet and singlet potential energy surfaces Our calculations led to the identification of a complex mechanism for the reaction between S2 with O2 on the triplet and singlet potential energy surfaces which can be summarized in the following schemes: where, P1, P2, P3 and P4 stand for the products 3SO + 3SO, trans-1OSSO, cis-1OSSO and 3S + 1SO2, respectively. For the R2 (1S2 + 1O2) reactant, comprehensive calculations has been carried out on singlet potential energy surface. For the R1 (3S2 + 3O2) reactant, there are three potential energy surfaces, one singlet, one triplet, and one quintet. In present work, quintet potential energy surface has not been investigated and singlet surface has been overlooked for R1 (3S2 + 3O2) reactant because there is high energy barriers on the singlet surface. Therefore, we have focused our calculations only on triplet potential energy surface for R1 (3S2 + 3O2) reactant.
P1(1): P1(2): P1(3): P1(4): P1(5): P1(6):
R1 ? P1 R2 ? 1IN1 ? 1IN3 ? 1IN4 ? 1IN6 ? P2 ? P1 R2 ? 1IN1 ? 1IN3 ? 1IN4 ? 1IN5 ? 1IN6 ? P2 ? P1 R2 ? 1IN2 ? P3 ? P1 R2 ? 1IN1 ? 1IN3 ? 1IN4 ? 1IN6 ? P3 ? P1 R2 ? 1IN1 ? 1IN3 ? 1IN4 ? 1IN5 ? 1IN6 ? P3 ? P1
In Path P1(1), reactants 3S2 and 3O2 (R1) are directly transformed into the product P1 via 3TS1 and 3TS2 with the energy barriers of 44.11 and 37.02 kcal/mol, respectively. In this Path, O–O and S–S bands in the reactants (3S2 + 3O2) rupture and two new bands of S–O form. In Path P1(2), 1IN1 undergoes 4S–2O bond formation and 4S–3S bond rupture process to form 1IN3 via 1TS1 with the energy barrier of 113.08 kcal/mol. Fig. 2 shows that the energy of 1IN1 is 84.40 kcal/mol lower than 1IN3. So, 1IN1 ? 1IN3 conversion is infeasible energetically and in ordinary condition this step is difficult to be carried out. The intermediate 1IN3 is transformed to 1IN4 via 1TS2 by 4S–1O bond formation and 3O–1O bond rupture. The energy barrier for 1IN3 ? 1IN4 conversion is 11.17 kcal/mol. The intermediate 1IN4 is 32.51 kcal/mol below the original reactants (3S2 + 3O2) and can be transformed to 1IN6 via 1TS5 by 4S–1S bond formation. The energy barrier for 1IN4 ? 1IN6 conversion is 1.76 kcal/mol. Finally, 1IN6 is transformed to the product P2(trans-1OSSO) via 1TS8 by 2S–1O bond rupture with the energy barrier of 27.48 kcal/mol. In Path P1(3), the formation of 1IN4 is similar to Path P1(2). The straight-chain SOSO has two isomers: one is 1IN4 (trans-1SOSO) and the other is 1IN5 (cis-1SOSO) which is 6.27 kcal/mol more stable than 1IN4. The intermediate 1IN4 is transformed to 1IN5 via 1 TS4 with the energy barrier of 8.98 kcal/mol. The intermediate 1 IN5 is 38.78 kcal/mol below the original reactants (3S2 + 3O2) and can be transformed to 1IN6 via 1TS6 by 4S–2S bond formation. The energy barrier for 1IN5 ? 1IN6 conversion is 57.23 kcal/mol which 55.47 kcal/mol is higher than 1IN4 ? 1IN6 conversion in
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M. Goodarzi et al. / Chemical Physics Letters 497 (2010) 1–6
Path P1(2). Finally, 1IN6 is transformed to the product P2(trans-1OSSO) via 1TS8 by 2S–1O bond rupture with the energy barrier of 27.48 kcal/mol. In Path P1(4), the intermediate 1IN2 can directly be transformed to product P3(cis-1OSSO) via 1TS3 by 2O–1O bond rupture and 4S– 1O bond formation. The energy barrier for 1IN2 ? P3 conversion is 67.77 kcal/mol. In Paths P1(5) and P1(6), the formation of 1IN6 is similar to Paths P1(2) and P1(3), respectively. In these two Paths, 1IN6 is transformed to the product P3(cis-1OSSO) via 1TS7 by 2S–1O bond rupture with the energy barrier of 29.80 kcal/mol. In Paths P1(2), P1(3), P1(4), P1(5) and P1(6), the products P2(trans-1OSSO) and P3(cis-1OSSO) are the complexes between two SO units which are indicated by the long bonds of 4S–2S and 4S–3S, respectively. In these five possible pathways, the products P2(trans-1OSSO) and P3(cis-1OSSO) directly can be decomposed to 1 SO + 1SO by 4S–2S and 4S–3S bonds rupture without any transition state, respectively. The product 1SO + 1SO is 69.27 and 72.29 kcal/mol above P2(trans-1OSSO) and P3(cis-1OSSO), respectively. So, the decomposition of them to the product 1SO + 1SO is difficult to carry out in ordinary condition. Subsequently, 1SO + 1SO would relax to ground triplet state (P1(3SO + 3SO)). In Fig. 2, relaxation pathway of 1SO to 3SO (1SO + 1SO ? P1(3SO + 3SO)) has been shown by different line rather than the triplet and singlet lines. For these six reaction Paths, the most competitive one should be Path P1(1) because the energy barrier of 37.02 kcal/mol (R1 ? P1) in Path P1(1) is much lower than, 113.08 kcal/mol (1IN1 ? 1IN3) in Paths P1(2), P1(3), P1(5) and P1(6) and 67.77 (1IN2 ? P3) kcal/ mol in Path P1(4), Therefore, Path P1(1) is the most suitable pathway for the product P1(3SO + 3SO) on the triplet potential energy surface. 3.4. Formation pathways of P2(trans-1OSSO) and P3(cis-1OSSO) For products P2(trans-1OSSO) and P3(cis-1OSSO), there are five possible pathways as follows: Path Path Path Path Path
P2(1): P2(2): P3(1): P3(2): P3(3):
R2 ? 1IN1 ? 1IN3 ? 1IN4 ? 1IN6 ? P2 R2 ? 1IN1 ? 1IN3 ? 1IN4 ? 1IN5 ? 1IN6 ? P2 R2 ? 1IN2 ? P3 R2 ? 1IN1 ? 1IN3 ? 1IN4 ? 1IN6 ? P3 R2 ? 1IN1 ? 1IN3 ? 1IN4 ? 1IN5 ? 1IN6 ? P3
The product P2(trans-1OSSO) produces through two Paths P2(1) and P2(2) which are similar to Paths P1(2) and P1(3), respectively. The product P3(cis-1OSSO) produces through three Paths P3(1), P3(2) and P3(3) which are similar to Paths P1(4), P1(5) and P1(6), respectively. For these five possible pathways, the energy barrier of 113.08 kcal/mol (1IN1 ? 1IN3) in Paths P2(1), P2(2), P3(2), and P3(3) and 67.77 kcal/mol (1IN2 ? P3) in Path P3(1) are very high. So, in ordinary condition, these steps are difficult to be carried out. These results show that in the reaction of S2 + O2, there is no favorable pathway for the formation of the products P2(trans-1OSSO) and P3(cis-1OSSO).
28.42 kcal/mol. The intermediate 1IN7 is the complexes between atomic sulfur and SO2 molecule which are indicated by the bond of 4S–3S. In these two possible pathways, the intermediate 1IN7 directly can be decomposed to 1S + 1SO2 by 4S–3S bond rupture without any transition state. The product 1S + 1SO2 is 61.43 kcal/ mol above the intermediate 1IN7. So, the decomposition of the intermediate 1IN7 to the product 1S + 1SO2 is difficult to carry out in ordinary condition. Subsequently, 1S would relax to ground triplet state 3S to produce P4(3S + 1SO2). In Fig. 2, relaxation pathway of 1 S to 3S (1S + 1SO2 ? P4(3S + 1SO2)) has been shown by different line rather than the triplet and singlet lines. For these two possible pathways, the energy barrier of 113.08 kcal/mol (1IN1 ? 1IN3) are very high. So, in ordinary condition, these steps are difficult to be carried out. These results show that in the reaction of S2 + O2, there is no favorable pathway for the formation of the product P4(3S + 1SO2). The calculated results reveal that P2(trans-1OSSO), P3(cis-1OSSO) and P4(3S + 1SO2) are only produced on the singlet potential energy surface through the very high energy barriers while, P1(3SO + 3SO) produces on the triplet and singlet potential energy surfaces. The energy barriers of the triplet surface are much lower than singlet surface as shown in Fig. 2. Therefore, S2 + O2 reaction proceeds only with triplet surfaces to produce P1(3SO + 3SO) through Path P1(1).
3.6. Theoretical and experimental evidences for the accuracy of applied methodologies As shown in Table 1, the T1 diagnostic values for the some of the structures are greater than 0.045 [30]. We present below reasons to confirm the accuracy of the calculations at the B3LYP and G3B3//B3LYP levels.
3.6.1. Experimental data comparison with the B3LYP and G3B3//B3LYP levels data As shown in Table 3, for 3S2 + 3O2 ? 3SO + 3SO reaction, the heat of reaction (DH) at the B3LYP and G3B3//B3LYP levels are 25.98 and 28.80 kcal/mol, respectively. These two values are in the range of experimental value (DH = 27.82) [31] but the heat of reaction at the G3B3//B3LYP level is in better agreement with the experiment. For the 3S2 + 3O2 ? 3S + 1SO2 reaction, the heat of reaction at the B3LYP level (DH = 22.84) is not in good agreement with experiment (DH = 35.42) [31], while the heat of reaction of value at the G3B3//B3LYP level (DH = 34.07) is in good agreement with experiment. These results show that single-point calculations at the G3B3//B3LYP level have been amended the heat of reaction of values at the B3LYP level and these values are in good agreement with experiment. Lovas et al. observed disulfur dioxide experimentally [4]. In their experiments S2O2 is a cis-bent planner chain, O–S–S–O, with C2v symmetry. As shown in Fig. 1, for cis-OSSO product, the structural parameters at the B3LYP level are in good agreement with those in the experiment.
3.5. Formation pathways of P4(3S + 1SO2) For product P4(3S + 1SO2), there are two possible pathways as follows: Path P4(1): R2 ? 1IN1 ? 1IN3 ? 1IN4 ? 1IN6 ? 1IN7 ? P4 Path P4(2): R2 ? 1IN1 ? 1IN3 ? 1IN4 ? 1IN5 ? 1IN6 ? 1IN7 ? P4 1
In Paths P4(1) and P4(2), the formation of IN6 is similar to Paths P1(2) and P1(3), respectively. In these two Paths, the intermediate 1 IN6 is transformed to 1IN7 via 1TS9 with the energy barrier of
Table 3 The heat of reaction of values for the 3S2 + 3O2 ? 3SO + 3SO and 3S2 + 3O2 ? 3S + 1SO2 reactions. Reaction
DH B3LYP
3
S2 + 3O2 ? 3SO + 3SO 3 S2 + 3O2 ? 3S + 1SO2
25.98 22.84
G3B3//B3LYP 28.80 34.07
The energies are in kcal/mol. The temperature is 298 K at the theory and experiment.
Experiment 27.82 35.42
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M. Goodarzi et al. / Chemical Physics Letters 497 (2010) 1–6
3.6.2. Comparative study of the structural parameters at the B3LYP and CASSCF(6, 8) levels for some of the intermediates Due to hardware limitation, we can examine only some of the calculations via CASSCF(6, 8) to give some computational evidences that the results are sufficiently correct at the B3LYP level. In the CASSCF calculations, the active space has been selected based on natural bond orbital analysis (NBO). As shown in Fig. 1S of the supplementary data, for cis-OSSO product the structural parameters at the CASSCF(6, 8)/6-31+G(d) level are in good agreement with those in the experiment. Therefore, this active space (6, 8) is suitable for the investigation of reaction mechanism. As a representative, we have selected the intermediates 1IN1, 1IN4, 1 IN5, 1IN6 and 1IN7 and the product cis-1OSSO and optimized those at the B3LYP and CASSCF(6,8) levels by basis set 6-31+G(d). Fig. 1S of the supplementary data shows that, the structural parameters at the B3LYP level are in good agreement with the structural parameters at the CASSCF(6, 8) level. Subsequently, to obtain reliable relative energies, single-point calculations at the G3B3 level have been carried out using the B3LYP optimized geometries. 3.6.3. Comparative study with previous work Murakami et al. [32] have investigated the reaction of S + SO2 theoretically and experimentally on the triplet and singlet potential energy surfaces. They have optimized all the structural parameters at the B3LYP level and have carried out single-point calculations at the G2M (CC1) level by using the B3LYP optimized geometries. In present work, we have investigated the reaction mechanism of S2 + O2 in the triplet and singlet potential energy surfaces which is isoelectronic with the reaction of S + SO2 because, both the reactions have the same number and similar atoms. Therefore, it is possible which in mechanism of S2 + O2 and S + SO2 reactions similar intermediates and transition states have been found. In S + SO2 reaction, intermediates which Murakami et al. have found on the singlet potential surface are exactly the intermediates 1IN5, 1IN6, 1IN7 and cis-1OSSO in present work (S2 + O2). Also, transition states TS5, TS6X and TS7X in S + SO2 reaction are exactly the transition states 1TS9, 1TS6 and 1TS7 in present work (S2 + O2), respectively. Therefore, the mechanism of S2 + O2 (present work) and S + SO2 (Murakami et al.) reactions have some of similar intermediates and transition states. In S + SO2 reaction, Murakami et al. have relied to optimized structures at the B3LYP level and have carried out single-point calculations at the G2M (CC1) level using the B3LYP optimized geometries to obtain reliable relative energies of each stationary point on the PES. These results show that single-point calculations at the high levels of theory using the B3LYP optimized geometries is suitable for investigation of S2 + O2 and S + SO2 reactions mechanism. Also, Wen-Kai et al. [33] previously was investigated the ground state isomers of S2O2 using the B3LYP method with different basis sets. Therefore, Wen-Kai et al. have relied to optimized structures at the B3LYP level. 4. Conclusion Details of the reaction pathways of S2 + O2 on the triplet and singlet potential energy surfaces have been characterized at the
G3B3//B3LYP/6-311++G(3df,3pd) level. In spite of numerous attempts, any stable collision complex has not been found on the triplet potential energy surface. While, two stable collision complexes, 1IN1 (trans-1SSOO) and 1IN2 (cis-1SSOO), have been considered on the singlet potential energy surface. No intersystem crossing has been shown between triplet and singlet surfaces. The calculated results reveal that P2(trans-1OSSO), P3(cis-1OSSO) and P4(3S + 1SO2) produce only on the singlet energy potential surface while, P1(3SO + 3SO) produces on the triplet and singlet energy potential surfaces. The energy barriers of the triplet surface are much lower than singlet surface. Therefore, S2 + O2 reaction proceeds only with triplet energy potential surfaces to produce P1(3SO + 3SO). Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.cplett.2010.07.084. References [1] J. Farquhar, H. Bao, M. Thiemens, Science 289 (2000) 756. [2] K.S. Habicht, M. Gade, B. Thamdrup, P. Berg, D.E. Canfield, Science 298 (2002) 2372. [3] N.N. Greenwood, A. Earnshaw, Chemistry of the Elements, second edn., Butterworth–Heinemann, Oxford, 1997. [4] F.J. Lovas, E. Tiemann, D.R. Johnson, J. Chem. Phys. 60 (1974) 5005. [5] C.J. Marsden, B.J. Smith, Chem. Phys. 141 (1990) 335. [6] C.D. Paulse, R.A. Poirier, R. Wellington Davis, Chem. Phys. Lett. 172 (1990) 43. [7] P. Mathies, F.O. Sladky, B.M. Rode, J. Mol. Struct. (THEOCHEM) 7 (1982) 335. [8] I. Mayer, M. Révész, Inorg. Chim. Acta 77 (1983) L205. [9] T.G. Clements, H.-J. Deyerl, R.E. Continetti, J. Phys. Chem. A 106 (2002) 279. [10] K.S. Noll et al., Science 267 (1995) 1307. [11] P. Geissler, A. McEwen, C. Porco, D. Strobel, J. Saur, J. Ajello, R. West, Icarus 172 (2004) 127. [12] S.J. Kim, M.F. A’Hearn, D.D. Wellnitz, R. Meier, Y.S. Lee, Icarus 166 (2003) 157. [13] L. St-Onge, N. Sadeghi, J.P. Booth, J. Margot, C. Barbeau, J. Appl. Phys. 78 (1995) 6957. [14] C.W. Johnston, H.W.P. van der Heijden, A. Hartgers, K. Garloff, J. van Dijk, J.J.A.M. van der Mullen, J. Phys. D: Appl. Phys. 37 (2004) 211. [15] G. Herzberg, Molecular Spectra and Molecular Structure: Spectra of Diatomic Molecules, vol. 1, Van Nostrand Reinhold, New York, 1950. [16] W.C. Swope, Y.P. Lee, H.F. Schaefer III, J. Chem. Phys. 70 (1979) 947. [17] R.P. Saxon, B. Liu, J. Chem. Phys. 73 (1980) 5174. [18] M.J. Frisch et al., GAUSSIAN 03, Revision B.03, Gaussian Inc., Pittsburgh, PA, 2003. [19] A.D. Becke, J. Chem. Phys. 98 (1993) 1372. [20] C. Lee, W. Yang, R.G. Parr, Phys. Rev. B 37 (1988) 785. [21] L.A. Curtiss, K. Raghavachari, P.C. Redfern, V. Rassolov, J.A.J. Pople, Chem. Phys. 109 (1998) 7764. [22] A.G. Boboul, L.A. Curtiss, P.C. Redfern, K.J. Raghavachari, Chem. Phys. 110 (1999) 7650. [23] C. Gonzalez, H.B. Schlegel, J. Chem. Phys. 90 (1989) 2154. [24] C. Gonzalez, H.B. Schlegel, J. Phys. Chem. 94 (1990) 5523. [25] S.F. Boys, F. Bernardi, Mol. Phys. 19 (1970) 553. [26] J. Cizek, Adv. Chem. Phys. 14 (1969) 35. [27] G.E. Scuseria, C.L. Janssen, H.F. Schaefer III, J. Chem. Phys. 89 (1988) 7382. [28] D. Hegarty, M.A. Robb, Mol. Phys. 38 (1979) 1795. [29] R.H.E. Eade, M.A. Robb, Chem. Phys. Lett. 83 (1981) 362. [30] J.C. Rienstra-Kiracofe, W.D. Allen, H.F. Schaefer III, J. Phys. Chem. A 104 (2000) 9823. [31] K. Schofield, Combust. Flame 124 (2001) 137. [32] Y. Murakami et al., J. Phys. Chem. A 107 (2003) 10996. [33] C. Wen-Kai, L. Jun-Qian, Z. Yong-Fan, D. Kai-Ning, L. Yi, Chinese J. Struct. Chem. 23 (2004) 469.
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Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett
Theoretical study on the mechanism of S2 + O2 reaction Moein Goodarzi a, Morteza Vahedpour a,*, Fariba Nazari b a b
Department of Chemistry, Zanjan University, Zanjan, Iran Department of Chemistry, Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan 45137-66731, Iran
a r t i c l e
i n f o
Article history: Received 2 December 2009 In final form 28 July 2010 Available online 30 July 2010
a b s t r a c t The reaction pathways of disulfur (S2) with oxygen (O2) on the triplet and singlet potential energy surfaces have been investigated at the G3B3//B3LYP/6-311++G(3df,3pd) level. The calculated results reveal that P2(trans-1OSSO), P3(cis-1OSSO) and P4(3S + 1SO2) produce only on the singlet energy potential surface while, P1(3SO + 3SO) produces on the both triplet and singlet surfaces. No intersystem crossing has been found between triplet and singlet surfaces and the energy barriers of the triplet surface are much lower than singlet surface. Therefore, S2 + O2 reaction proceeds only on triplet surface to produce P1(3SO + 3SO). Ó 2010 Elsevier B.V. All rights reserved.
1. Introduction Atmospheric sulfur chemistry has an important role in atmosphere of the Earth [1,2]. The SO molecule is one of the gaseous sulfur compounds that exist in atmosphere of the Earth and only is available in the gaseous phase [3]. Gaseous SO and other sulfur oxides are formed when sulfur is burnt in low pressure pure oxygen. Two SO units can join via the sulfur atoms in a cis or trans configuration, Lovas et al. observed disulfur dioxide in a microwave discharge of SO2 [4]. In their experiments, S2O2 is a cis-bent, planner chain O–S–S–O, with C2v symmetry. The bond lengths indicate that the S–O bonds are double bonds and the S–S bond has partial double bond character. The structure was calculated by obtaining r0(S–S) = 2.024(6) Å for the S–S bond length. Other parameters are r0(S–O) = 1.458(2) Å and \SSO = 112.7(5)° [4]. Many theoretical studies have been performed on S2O2 [5–8], although, only the cisplanar form of disulfur dioxide has been experimentally observed and confirmed. The theoretical studies of Marsden and Smith [5] show that a trigonal planar form of S2O2 (Fig. 1, 1IN7), similar to the structure of SO3, is more stable than cis-OSSO, energetically. Nevertheless, due to the relatively high energies of the molecular products, Lovas et al. did not observe trigonal planar form of S2O2 in the microwave discharge spectra. Also, Marsden and Smith show that the energy of trans-OSSO is very close to its corresponding cis form. Clements et al. [9] have indicated that geometries of cis-OSSO and trigonal planar (1IN7) at the B3LYP level differ from those calculated and optimized by Marsden and Smith at the SCF level. The largest difference between two calculations is the S–S bond length which is increased from 1.931 Å (at the SCF level) to 2.069 Å (at the B3LYP level) for the trigonal isomer, and from 1.866 Å (at the SCF level) to 1.912 Å (at the B3LYP level) for the
* Corresponding author. Fax: +98 241 5152477. E-mail address: [email protected] (M. Vahedpour). 0009-2614/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2010.07.084
cis-OSSO isomer. The S–S bond length value in the cis-OSSO isomer at the B3LYP level matches more closely to the experimental value of 2.025 Å [4,9]. The disulfur (S2) is another of the gaseous sulfur compounds that exist in atmosphere of the Earth. Also, we can find S2 molecules at various natural and industrial plasmas containing sulfur compounds. For example, emission and absorption of S2 molecules have been observed in the atmosphere of Jupiter [10] and its satellite Io [11]. They are also observed in the atmosphere of some comets [12]. In industrial condition, S2 molecules can be seen in reactive ion etching process using SF6 molecules [13]. Sulfur lamps contain S2 molecules as an important component [14]. Diatomic sulfur, S2, has been subject of many theoretical and spectroscopic investigations for long time [15–17]. The reaction of disulfur with oxygen has not been investigated, and in this Letter, we carry out the theoretical study of S2 + O2 reaction on the triplet and singlet potential energy surfaces (PES). Our main objective in this Letter is to reveal the details of the reaction mechanism, to explain the formation and decomposition of trans-1OSSO and cis-1OSSO complexes, and provide further information about gaseous phase reaction of S2 + O2 on the triplet and singlet surfaces. 2. Computational details All the calculations are performed with the GAUSSIAN 03 program [18]. The geometrical parameters of the reactants, products, intermediates (denoted as INs), and transition states (denoted as TSs) involved in the S2 + O2 reaction are fully optimized using density functional theory with the Becke 3-parameter hybrid exchange [19] and Lee–Yang–Parr [20] correlation density functional (B3LYP) in conjunction with the 6-311++G(3df,3pd) basis set. Clements et al. via computation at the B3LYP/6-311+G(d) level showed that the structural parameters in the cis-1OSSO molecule
2
M. Goodarzi et al. / Chemical Physics Letters 497 (2010) 1–6
Fig. 1. Geometries of reactants, products, intermediates and transition states optimized at the B3LYP level. The values in square parentheses are from experiment (Ref. [4] for 1 cis-OSSO). Bond distances are in angstrom and angles are in degree.
are more closely to the experimental values [9]. To obtain more reliable relative energies, we have applied a larger basis set (6311++G(3df,3pd)) in the present calculations. Single-point calculations are performed on all species at the G3B3 [21,22] level using the B3LYP optimized geometries. The optimized geometries are characterized by harmonic analysis, and the nature of the stationary points is determined according to the number of negative eigenvalues of the Hessian matrix at the B3LYP level. Any reactant, product and intermediate possess all real frequencies and any transition state has only one imaginary frequency. Connections between reactants, intermediates, transitions states and products are confirmed by intrinsic reaction coordinate (IRC) [23,24] analysis at the B3LYP level. The counterpoise (CP) procedure [25] is used to correct the interaction energy for basis set superposition error (BSSE), and the CCSD [26,27] method is used
to calculate the T1 diagnostic values for the structures. Finally, the CASSCF [28,29] method is used to give some computational evidences that the results are sufficiently correct at the B3LYP level.
3. Results and discussion The optimized geometries of the reactants, intermediates, transition states and products involved in the S2 + O2 reaction at the B3LYP level are shown in Fig. 1. To simplify our discussion, the energy of reactant 3S2 + 3O2 (denoted as R1) is set to be zero for reference. Also, the reactant 1S2 + 1O2 is denoted as R2. The total energies and relative energies have been listed in Table 1 for the B3LYP and G3B3//B3LYP levels. The calculated vibrational frequencies at the B3LYP level have been listed in Table 2 show that all of
3
M. Goodarzi et al. / Chemical Physics Letters 497 (2010) 1–6 Table 1 The total energies (ET), relative energies (in the parenthesis) and T1 diagnostic values obtained in the S2 + O2 reaction. Species
ETa
T1b diagnostic
B3LYP 3
S2 + 3O2 (R1) 1 S2 + 1O2 (R2) 1 IN1 1 IN2 1 IN3 1 IN4 1 IN5 1 IN6 1 IN7 P1(3SO + 3SO) 1 SO + 1SO P2(trans-1OSSO) P3(cis-1OSSO) a
ETa
Species
G3B3//B3LYP
946.8073 946.7101 946.7712 946.7831 946.6504 946.8422 946.8511 946.8696 946.8967 946.8488 946.7578 946.8825 956.8871
946.3362 946.2649 946.3241 946.3385 946.1896 946.3880 946.3980 946.4174 946.4452 946.3820 946.3139 946.4243 946.4291
(0.00) (44.74) (7.59) ( 1.44) (91.99) ( 32.51) ( 38.78) ( 50.95) ( 68.40) ( 28.74) (13.99) ( 55.28) ( 58.30)
T1b diagnostic
B3LYP P4(3S + 1SO2) 1 S + 1SO2 1 TS1 1 TS2 1 TS3 1 TS4 1 TS5 1 TS6 1 TS7 1 TS8 1 TS9 3 TS1 3 TS2
0.0142 0.0140 0.0282 0.0474 0.0378 0.0221 0.0189
0.0247 0.0245
G3B3//B3LYP
946.8434 946.7821 946.6294 946.6247 946.6904 946.8351 946.8379 946.8230 946.8199 946.8395 946.8191 946.7347 946.7455
946.3901 946.3473 946.1439 946.1718 946.2305 946.3737 946.3852 946.3068 946.3699 946.3736 946.3721 946.2659 946.2772
( 33.82) ( 6.97) (120.67) (103.16) (66.33) ( 23.53) ( 30.75) (18.45) ( 21.15) ( 23.47) ( 22.53) (44.11) (37.02)
0.0649 0.0366 0.0685 0.0355 0.0562 0.0591 0.0529 0.0368 0.0336 0.0528 0.0373
The total energies (ET) are in hartree and relative energies (in the parenthesis) are in kcal/mol. T1 diagnostic values obtained from CCSD/6-311++G(3df,3pd)//B3LYP level.
b
Table 2 The vibrational frequencies (cm
1
) of the reactants, intermediates, products and transition states calculated at the B3LYP level.
Species
Frequencies
1
170 162 302 155 152 265 344 138 185 712 716 1634 1645 1157
IN1 1 IN2 1 IN3 1 IN4 1 IN5 1 IN6 1 IN7 cis-1OSSO trans-1OSSO 1 S2 3 S2 1 O2 3 O2 3 SO
205 359 387 188 335 414 407 285 194
369 464 472 374 516 442 469 475 342
629 592 517 692 647 559 667 491 581
714 734 721 719 747 805 1181 1139 1130
1054 1106 895 1254 1254 1272 1373 1192 1159
intermediates (INs) are true minimum on the reaction potential energy surfaces, and any transition state has only one imaginary frequency. Finally, by means of the transition states and their connected intermediates or products at the G3B3//B3LYP level, a schematic PES for S2 + O2 reaction on the triplet and singlet potential energy surfaces are plotted in Fig. 2. The geometries of 3TS2 and 1IN2 are very similar except for the bond length of 4S–1O. Therefore, the existence of the minimum energy crossing point (MECP) between the triplet and singlet potential energy surfaces has been investigated. In order to obtain the MECP, the potential energy surfaces for 3TS2 and 1IN2 are plotted through the variation of bond length of 4S–1O at the B3LYP level. Fig. 3 shows that there is no intersystem crossing between the triplet and singlet potential energy surfaces.
Species
Frequencies
1
1157 519 548 i 554 i 977 i 202 i 224 i 576 i 611 i 382 i 626 i 846 i 307 i
SO 1 SO2 1 TS1 1 TS2 1 TS3 1 TS4 1 TS5 1 TS6 1 TS7 1 TS8 1 TS9 3 TS1 3 TS2
1179 253 212 187 227 234 215 222 285 254 239 199
1378 292 305 239 343 391 424 317 307 375 324 424
483 474 390 511 581 476 475 562 462 482 520
713 632 689 939 810 796 856 836 1028 668 631
905 872 1051 1272 1264 1272 1200 1225 1293 782 873
of newly formed S–O is 1.665 Å. In the intermediate 1IN2, the bonds length of S–S and O–O are 1.877 and 1.294 Å, respectively, which bond of S–S is about 0.027 Å lower and bond of O–O is about 0.091 Å longer than the parent 1S2 and 1O2 molecules, respectively. The bond length of newly formed S–O is 1.685 Å. The intermediate 1IN1 is 7.59 kcal/mol above the original reactants, while the intermediate 1IN2 is 1.44 kcal/mol below the original reactants (3S2 + 3O2) at the B3LYP level. The BSSE values for the intermediates 1IN1 and 1IN2 energies are 1.11 and 1.09 kcal/mol at the B3LYP level, respectively. No transition state has been found for their formation. So, the formation of 1IN1 or 1IN2 is a barrierless process. Subsequently, via variety of transformations of 1IN1 or 1 IN2, four kinds of products are obtained. The details of the reaction mechanism on the triplet and singlet potential energy surfaces will be discussed in below.
3.1. Initial association In spite of numerous attempts, no stable collision complex has been found on the triplet potential energy surface while, two stable collision complexes, 1IN1 (trans-1SSOO) and 1IN2 (cis-1SSOO), have been considered between disulfur (1S2) and oxygen (1O2) on the singlet potential energy surface. Both complexes are formed via one of the sulfur atoms in 1S2 molecule which is associated with one of the oxygen atoms in 1O2 molecule with the main frames being trans and cis. In the intermediate 1IN1, the bonds length of S–S and O–O are 1.889 and 1.312 Å at the B3LYP level, respectively, which bond of S–S is about 0.015 Å lower and bond of O–O is about 0.109 Å longer in compare to 1S2 and 1O2 molecules, respectively. The bond length
1
IN5 P2
1
IN1
1
1
IN3
1
IN4
IN6 P3
1
S2 + O2 1
IN7
1
IN2
P3
3
TS1
3
P1
1
3
S2 + O2
P1 3
TS2
P1
P4
4
M. Goodarzi et al. / Chemical Physics Letters 497 (2010) 1–6
Fig. 2. Potential energy profile of the S2 + O2 reaction at the G3B3//B3LYP level.
3.3. Formation pathways of P1(3SO + 3SO) For product P1(3SO + 3SO), there are six possible pathways as follows: Path Path Path Path Path Path
Fig. 3. Potential energy surfaces (exclude ZPE) of triplet 3TS2 and singlet 1IN2 for the variation of the bond length 4S–1O at the B3LYP level.
3.2. Isomerization and dissociation pathways on the triplet and singlet potential energy surfaces Our calculations led to the identification of a complex mechanism for the reaction between S2 with O2 on the triplet and singlet potential energy surfaces which can be summarized in the following schemes: where, P1, P2, P3 and P4 stand for the products 3SO + 3SO, trans-1OSSO, cis-1OSSO and 3S + 1SO2, respectively. For the R2 (1S2 + 1O2) reactant, comprehensive calculations has been carried out on singlet potential energy surface. For the R1 (3S2 + 3O2) reactant, there are three potential energy surfaces, one singlet, one triplet, and one quintet. In present work, quintet potential energy surface has not been investigated and singlet surface has been overlooked for R1 (3S2 + 3O2) reactant because there is high energy barriers on the singlet surface. Therefore, we have focused our calculations only on triplet potential energy surface for R1 (3S2 + 3O2) reactant.
P1(1): P1(2): P1(3): P1(4): P1(5): P1(6):
R1 ? P1 R2 ? 1IN1 ? 1IN3 ? 1IN4 ? 1IN6 ? P2 ? P1 R2 ? 1IN1 ? 1IN3 ? 1IN4 ? 1IN5 ? 1IN6 ? P2 ? P1 R2 ? 1IN2 ? P3 ? P1 R2 ? 1IN1 ? 1IN3 ? 1IN4 ? 1IN6 ? P3 ? P1 R2 ? 1IN1 ? 1IN3 ? 1IN4 ? 1IN5 ? 1IN6 ? P3 ? P1
In Path P1(1), reactants 3S2 and 3O2 (R1) are directly transformed into the product P1 via 3TS1 and 3TS2 with the energy barriers of 44.11 and 37.02 kcal/mol, respectively. In this Path, O–O and S–S bands in the reactants (3S2 + 3O2) rupture and two new bands of S–O form. In Path P1(2), 1IN1 undergoes 4S–2O bond formation and 4S–3S bond rupture process to form 1IN3 via 1TS1 with the energy barrier of 113.08 kcal/mol. Fig. 2 shows that the energy of 1IN1 is 84.40 kcal/mol lower than 1IN3. So, 1IN1 ? 1IN3 conversion is infeasible energetically and in ordinary condition this step is difficult to be carried out. The intermediate 1IN3 is transformed to 1IN4 via 1TS2 by 4S–1O bond formation and 3O–1O bond rupture. The energy barrier for 1IN3 ? 1IN4 conversion is 11.17 kcal/mol. The intermediate 1IN4 is 32.51 kcal/mol below the original reactants (3S2 + 3O2) and can be transformed to 1IN6 via 1TS5 by 4S–1S bond formation. The energy barrier for 1IN4 ? 1IN6 conversion is 1.76 kcal/mol. Finally, 1IN6 is transformed to the product P2(trans-1OSSO) via 1TS8 by 2S–1O bond rupture with the energy barrier of 27.48 kcal/mol. In Path P1(3), the formation of 1IN4 is similar to Path P1(2). The straight-chain SOSO has two isomers: one is 1IN4 (trans-1SOSO) and the other is 1IN5 (cis-1SOSO) which is 6.27 kcal/mol more stable than 1IN4. The intermediate 1IN4 is transformed to 1IN5 via 1 TS4 with the energy barrier of 8.98 kcal/mol. The intermediate 1 IN5 is 38.78 kcal/mol below the original reactants (3S2 + 3O2) and can be transformed to 1IN6 via 1TS6 by 4S–2S bond formation. The energy barrier for 1IN5 ? 1IN6 conversion is 57.23 kcal/mol which 55.47 kcal/mol is higher than 1IN4 ? 1IN6 conversion in
5
M. Goodarzi et al. / Chemical Physics Letters 497 (2010) 1–6
Path P1(2). Finally, 1IN6 is transformed to the product P2(trans-1OSSO) via 1TS8 by 2S–1O bond rupture with the energy barrier of 27.48 kcal/mol. In Path P1(4), the intermediate 1IN2 can directly be transformed to product P3(cis-1OSSO) via 1TS3 by 2O–1O bond rupture and 4S– 1O bond formation. The energy barrier for 1IN2 ? P3 conversion is 67.77 kcal/mol. In Paths P1(5) and P1(6), the formation of 1IN6 is similar to Paths P1(2) and P1(3), respectively. In these two Paths, 1IN6 is transformed to the product P3(cis-1OSSO) via 1TS7 by 2S–1O bond rupture with the energy barrier of 29.80 kcal/mol. In Paths P1(2), P1(3), P1(4), P1(5) and P1(6), the products P2(trans-1OSSO) and P3(cis-1OSSO) are the complexes between two SO units which are indicated by the long bonds of 4S–2S and 4S–3S, respectively. In these five possible pathways, the products P2(trans-1OSSO) and P3(cis-1OSSO) directly can be decomposed to 1 SO + 1SO by 4S–2S and 4S–3S bonds rupture without any transition state, respectively. The product 1SO + 1SO is 69.27 and 72.29 kcal/mol above P2(trans-1OSSO) and P3(cis-1OSSO), respectively. So, the decomposition of them to the product 1SO + 1SO is difficult to carry out in ordinary condition. Subsequently, 1SO + 1SO would relax to ground triplet state (P1(3SO + 3SO)). In Fig. 2, relaxation pathway of 1SO to 3SO (1SO + 1SO ? P1(3SO + 3SO)) has been shown by different line rather than the triplet and singlet lines. For these six reaction Paths, the most competitive one should be Path P1(1) because the energy barrier of 37.02 kcal/mol (R1 ? P1) in Path P1(1) is much lower than, 113.08 kcal/mol (1IN1 ? 1IN3) in Paths P1(2), P1(3), P1(5) and P1(6) and 67.77 (1IN2 ? P3) kcal/ mol in Path P1(4), Therefore, Path P1(1) is the most suitable pathway for the product P1(3SO + 3SO) on the triplet potential energy surface. 3.4. Formation pathways of P2(trans-1OSSO) and P3(cis-1OSSO) For products P2(trans-1OSSO) and P3(cis-1OSSO), there are five possible pathways as follows: Path Path Path Path Path
P2(1): P2(2): P3(1): P3(2): P3(3):
R2 ? 1IN1 ? 1IN3 ? 1IN4 ? 1IN6 ? P2 R2 ? 1IN1 ? 1IN3 ? 1IN4 ? 1IN5 ? 1IN6 ? P2 R2 ? 1IN2 ? P3 R2 ? 1IN1 ? 1IN3 ? 1IN4 ? 1IN6 ? P3 R2 ? 1IN1 ? 1IN3 ? 1IN4 ? 1IN5 ? 1IN6 ? P3
The product P2(trans-1OSSO) produces through two Paths P2(1) and P2(2) which are similar to Paths P1(2) and P1(3), respectively. The product P3(cis-1OSSO) produces through three Paths P3(1), P3(2) and P3(3) which are similar to Paths P1(4), P1(5) and P1(6), respectively. For these five possible pathways, the energy barrier of 113.08 kcal/mol (1IN1 ? 1IN3) in Paths P2(1), P2(2), P3(2), and P3(3) and 67.77 kcal/mol (1IN2 ? P3) in Path P3(1) are very high. So, in ordinary condition, these steps are difficult to be carried out. These results show that in the reaction of S2 + O2, there is no favorable pathway for the formation of the products P2(trans-1OSSO) and P3(cis-1OSSO).
28.42 kcal/mol. The intermediate 1IN7 is the complexes between atomic sulfur and SO2 molecule which are indicated by the bond of 4S–3S. In these two possible pathways, the intermediate 1IN7 directly can be decomposed to 1S + 1SO2 by 4S–3S bond rupture without any transition state. The product 1S + 1SO2 is 61.43 kcal/ mol above the intermediate 1IN7. So, the decomposition of the intermediate 1IN7 to the product 1S + 1SO2 is difficult to carry out in ordinary condition. Subsequently, 1S would relax to ground triplet state 3S to produce P4(3S + 1SO2). In Fig. 2, relaxation pathway of 1 S to 3S (1S + 1SO2 ? P4(3S + 1SO2)) has been shown by different line rather than the triplet and singlet lines. For these two possible pathways, the energy barrier of 113.08 kcal/mol (1IN1 ? 1IN3) are very high. So, in ordinary condition, these steps are difficult to be carried out. These results show that in the reaction of S2 + O2, there is no favorable pathway for the formation of the product P4(3S + 1SO2). The calculated results reveal that P2(trans-1OSSO), P3(cis-1OSSO) and P4(3S + 1SO2) are only produced on the singlet potential energy surface through the very high energy barriers while, P1(3SO + 3SO) produces on the triplet and singlet potential energy surfaces. The energy barriers of the triplet surface are much lower than singlet surface as shown in Fig. 2. Therefore, S2 + O2 reaction proceeds only with triplet surfaces to produce P1(3SO + 3SO) through Path P1(1).
3.6. Theoretical and experimental evidences for the accuracy of applied methodologies As shown in Table 1, the T1 diagnostic values for the some of the structures are greater than 0.045 [30]. We present below reasons to confirm the accuracy of the calculations at the B3LYP and G3B3//B3LYP levels.
3.6.1. Experimental data comparison with the B3LYP and G3B3//B3LYP levels data As shown in Table 3, for 3S2 + 3O2 ? 3SO + 3SO reaction, the heat of reaction (DH) at the B3LYP and G3B3//B3LYP levels are 25.98 and 28.80 kcal/mol, respectively. These two values are in the range of experimental value (DH = 27.82) [31] but the heat of reaction at the G3B3//B3LYP level is in better agreement with the experiment. For the 3S2 + 3O2 ? 3S + 1SO2 reaction, the heat of reaction at the B3LYP level (DH = 22.84) is not in good agreement with experiment (DH = 35.42) [31], while the heat of reaction of value at the G3B3//B3LYP level (DH = 34.07) is in good agreement with experiment. These results show that single-point calculations at the G3B3//B3LYP level have been amended the heat of reaction of values at the B3LYP level and these values are in good agreement with experiment. Lovas et al. observed disulfur dioxide experimentally [4]. In their experiments S2O2 is a cis-bent planner chain, O–S–S–O, with C2v symmetry. As shown in Fig. 1, for cis-OSSO product, the structural parameters at the B3LYP level are in good agreement with those in the experiment.
3.5. Formation pathways of P4(3S + 1SO2) For product P4(3S + 1SO2), there are two possible pathways as follows: Path P4(1): R2 ? 1IN1 ? 1IN3 ? 1IN4 ? 1IN6 ? 1IN7 ? P4 Path P4(2): R2 ? 1IN1 ? 1IN3 ? 1IN4 ? 1IN5 ? 1IN6 ? 1IN7 ? P4 1
In Paths P4(1) and P4(2), the formation of IN6 is similar to Paths P1(2) and P1(3), respectively. In these two Paths, the intermediate 1 IN6 is transformed to 1IN7 via 1TS9 with the energy barrier of
Table 3 The heat of reaction of values for the 3S2 + 3O2 ? 3SO + 3SO and 3S2 + 3O2 ? 3S + 1SO2 reactions. Reaction
DH B3LYP
3
S2 + 3O2 ? 3SO + 3SO 3 S2 + 3O2 ? 3S + 1SO2
25.98 22.84
G3B3//B3LYP 28.80 34.07
The energies are in kcal/mol. The temperature is 298 K at the theory and experiment.
Experiment 27.82 35.42
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3.6.2. Comparative study of the structural parameters at the B3LYP and CASSCF(6, 8) levels for some of the intermediates Due to hardware limitation, we can examine only some of the calculations via CASSCF(6, 8) to give some computational evidences that the results are sufficiently correct at the B3LYP level. In the CASSCF calculations, the active space has been selected based on natural bond orbital analysis (NBO). As shown in Fig. 1S of the supplementary data, for cis-OSSO product the structural parameters at the CASSCF(6, 8)/6-31+G(d) level are in good agreement with those in the experiment. Therefore, this active space (6, 8) is suitable for the investigation of reaction mechanism. As a representative, we have selected the intermediates 1IN1, 1IN4, 1 IN5, 1IN6 and 1IN7 and the product cis-1OSSO and optimized those at the B3LYP and CASSCF(6,8) levels by basis set 6-31+G(d). Fig. 1S of the supplementary data shows that, the structural parameters at the B3LYP level are in good agreement with the structural parameters at the CASSCF(6, 8) level. Subsequently, to obtain reliable relative energies, single-point calculations at the G3B3 level have been carried out using the B3LYP optimized geometries. 3.6.3. Comparative study with previous work Murakami et al. [32] have investigated the reaction of S + SO2 theoretically and experimentally on the triplet and singlet potential energy surfaces. They have optimized all the structural parameters at the B3LYP level and have carried out single-point calculations at the G2M (CC1) level by using the B3LYP optimized geometries. In present work, we have investigated the reaction mechanism of S2 + O2 in the triplet and singlet potential energy surfaces which is isoelectronic with the reaction of S + SO2 because, both the reactions have the same number and similar atoms. Therefore, it is possible which in mechanism of S2 + O2 and S + SO2 reactions similar intermediates and transition states have been found. In S + SO2 reaction, intermediates which Murakami et al. have found on the singlet potential surface are exactly the intermediates 1IN5, 1IN6, 1IN7 and cis-1OSSO in present work (S2 + O2). Also, transition states TS5, TS6X and TS7X in S + SO2 reaction are exactly the transition states 1TS9, 1TS6 and 1TS7 in present work (S2 + O2), respectively. Therefore, the mechanism of S2 + O2 (present work) and S + SO2 (Murakami et al.) reactions have some of similar intermediates and transition states. In S + SO2 reaction, Murakami et al. have relied to optimized structures at the B3LYP level and have carried out single-point calculations at the G2M (CC1) level using the B3LYP optimized geometries to obtain reliable relative energies of each stationary point on the PES. These results show that single-point calculations at the high levels of theory using the B3LYP optimized geometries is suitable for investigation of S2 + O2 and S + SO2 reactions mechanism. Also, Wen-Kai et al. [33] previously was investigated the ground state isomers of S2O2 using the B3LYP method with different basis sets. Therefore, Wen-Kai et al. have relied to optimized structures at the B3LYP level. 4. Conclusion Details of the reaction pathways of S2 + O2 on the triplet and singlet potential energy surfaces have been characterized at the
G3B3//B3LYP/6-311++G(3df,3pd) level. In spite of numerous attempts, any stable collision complex has not been found on the triplet potential energy surface. While, two stable collision complexes, 1IN1 (trans-1SSOO) and 1IN2 (cis-1SSOO), have been considered on the singlet potential energy surface. No intersystem crossing has been shown between triplet and singlet surfaces. The calculated results reveal that P2(trans-1OSSO), P3(cis-1OSSO) and P4(3S + 1SO2) produce only on the singlet energy potential surface while, P1(3SO + 3SO) produces on the triplet and singlet energy potential surfaces. The energy barriers of the triplet surface are much lower than singlet surface. Therefore, S2 + O2 reaction proceeds only with triplet energy potential surfaces to produce P1(3SO + 3SO). Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.cplett.2010.07.084. References [1] J. Farquhar, H. Bao, M. Thiemens, Science 289 (2000) 756. [2] K.S. Habicht, M. Gade, B. Thamdrup, P. Berg, D.E. Canfield, Science 298 (2002) 2372. [3] N.N. Greenwood, A. Earnshaw, Chemistry of the Elements, second edn., Butterworth–Heinemann, Oxford, 1997. [4] F.J. Lovas, E. Tiemann, D.R. Johnson, J. Chem. Phys. 60 (1974) 5005. [5] C.J. Marsden, B.J. Smith, Chem. Phys. 141 (1990) 335. [6] C.D. Paulse, R.A. Poirier, R. Wellington Davis, Chem. Phys. Lett. 172 (1990) 43. [7] P. Mathies, F.O. Sladky, B.M. Rode, J. Mol. Struct. (THEOCHEM) 7 (1982) 335. [8] I. Mayer, M. Révész, Inorg. Chim. Acta 77 (1983) L205. [9] T.G. Clements, H.-J. Deyerl, R.E. Continetti, J. Phys. Chem. A 106 (2002) 279. [10] K.S. Noll et al., Science 267 (1995) 1307. [11] P. Geissler, A. McEwen, C. Porco, D. Strobel, J. Saur, J. Ajello, R. West, Icarus 172 (2004) 127. [12] S.J. Kim, M.F. A’Hearn, D.D. Wellnitz, R. Meier, Y.S. Lee, Icarus 166 (2003) 157. [13] L. St-Onge, N. Sadeghi, J.P. Booth, J. Margot, C. Barbeau, J. Appl. Phys. 78 (1995) 6957. [14] C.W. Johnston, H.W.P. van der Heijden, A. Hartgers, K. Garloff, J. van Dijk, J.J.A.M. van der Mullen, J. Phys. D: Appl. Phys. 37 (2004) 211. [15] G. Herzberg, Molecular Spectra and Molecular Structure: Spectra of Diatomic Molecules, vol. 1, Van Nostrand Reinhold, New York, 1950. [16] W.C. Swope, Y.P. Lee, H.F. Schaefer III, J. Chem. Phys. 70 (1979) 947. [17] R.P. Saxon, B. Liu, J. Chem. Phys. 73 (1980) 5174. [18] M.J. Frisch et al., GAUSSIAN 03, Revision B.03, Gaussian Inc., Pittsburgh, PA, 2003. [19] A.D. Becke, J. Chem. Phys. 98 (1993) 1372. [20] C. Lee, W. Yang, R.G. Parr, Phys. Rev. B 37 (1988) 785. [21] L.A. Curtiss, K. Raghavachari, P.C. Redfern, V. Rassolov, J.A.J. Pople, Chem. Phys. 109 (1998) 7764. [22] A.G. Boboul, L.A. Curtiss, P.C. Redfern, K.J. Raghavachari, Chem. Phys. 110 (1999) 7650. [23] C. Gonzalez, H.B. Schlegel, J. Chem. Phys. 90 (1989) 2154. [24] C. Gonzalez, H.B. Schlegel, J. Phys. Chem. 94 (1990) 5523. [25] S.F. Boys, F. Bernardi, Mol. Phys. 19 (1970) 553. [26] J. Cizek, Adv. Chem. Phys. 14 (1969) 35. [27] G.E. Scuseria, C.L. Janssen, H.F. Schaefer III, J. Chem. Phys. 89 (1988) 7382. [28] D. Hegarty, M.A. Robb, Mol. Phys. 38 (1979) 1795. [29] R.H.E. Eade, M.A. Robb, Chem. Phys. Lett. 83 (1981) 362. [30] J.C. Rienstra-Kiracofe, W.D. Allen, H.F. Schaefer III, J. Phys. Chem. A 104 (2000) 9823. [31] K. Schofield, Combust. Flame 124 (2001) 137. [32] Y. Murakami et al., J. Phys. Chem. A 107 (2003) 10996. [33] C. Wen-Kai, L. Jun-Qian, Z. Yong-Fan, D. Kai-Ning, L. Yi, Chinese J. Struct. Chem. 23 (2004) 469.