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Mechanism for the gas-phase of sulfur vapor with ozone reaction: A theoretical study
Journal of Molecular Structure: THEOCHEM 944 (2010) 110–115
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Journal of Molecular Structure: THEOCHEM journal homepage: www.elsevier.com/locate/theochem
Mechanism for the gas-phase of sulfur vapor with ozone reaction: A theoretical study Moein Goodarzi a, Morteza Vahedpour a,*, Fariba Nazari b a b
Chemistry Department, Zanjan University, Zanjan, Iran Institute for Advanced Studies in Basic Sciences, Zanjan, Iran
a r t i c l e
i n f o
Article history: Received 11 August 2009 Received in revised form 21 December 2009 Accepted 22 December 2009 Available online 13 January 2010 Keywords: Sulfur vapor Ozone Topological analysis of electronic density Potential energy surface
a b s t r a c t The reaction pathways of sulfur vapor with ozone on the singlet potential energy surface have been investigated theoretically at CCSD(T)/6-311++G(3df,3pd)//B3LYP/6-311++G(3df,3pd) level of computation. The calculated results show that the reactants are initially associated with the adduct S–O3 through a barrierless process. Subsequently, via a variety of transformations of isomer S–O3, two kinds of products P1(SO + 3O2) and P2(SO3(D3h)) are obtained. The cleavage and formation of the chemical bonds in the reaction pathways have been discussed using the topological analysis of electronic density. The topological analysis results show that the ring transitional structure region occurs in cis-OSOO ? SO3(Cs) and SO3(Cs) ? SO3(D3h) reaction pathways. Ó 2010 Elsevier B.V. All rights reserved.
1. Introduction The existence of O3 in the atmosphere is important for life on Earth because it absorbs solar radiation with a wavelength between 240 and 320 nm. The largest concentration of ozone is attained at approximately 4.00 1012 molecules/cm3 [1–5]. These molecules form a layer which has 10 km width and between 25 and 35 km height [2]. The applications of ozone in chemical reactions are essential and important. The reaction of ozone with other species is one of the best investigated chemical reactions which have been reported in many researches published in the recent years [6–12]. For example, the potential energy surface of the HO3 ? HO + O2 reaction has been studied using QCISD(T)/CBS level. There exists a cis and trans planer equilibrium geometry for HO3 structure. The cis HO3 is slightly more stable than the trans-HO3 [13]. The principal natural phenomenon which distributes sulfur vapor and gaseous sulfur compounds in atmosphere are volcanoes and those from biological processes that occur on the Earth, in wetlands, and in the oceans. A lot of gaseous sulfur compounds get out during volcanic eruptions which include sulfur vapor, gaseous sulfur compounds and different gases. As we know, the reaction mechanism of S with O3 is ambiguous and the major channels of producing SO + 3O2 and SO3(D3h) have not been identified. Our main objective in this article is the theoretical investigation of the reaction mechanism of S with O3. This reaction is important in atmospheric chemistry, because it forms
* Corresponding author. Fax: +98 241 515 2477. E-mail address: [email protected] (M. Vahedpour). 0166-1280/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.theochem.2009.12.035
SO3 (with D3h symmetry) which is considered as a major factor in the production of acidic rains [14]. The cleavage and formation of the chemical bonds in the reaction pathways have been discussed using the topological analysis of the electronic density. 2. Computational methods The geometries of the reactants, products, intermediates and transition states involved in the reaction are optimized using the density functional theory with the B3LYP [15,16] exchange–correlation functional with 6-31++G(d,p) and 6-311++G(3df,3pd) basis sets and MP2/6-311++G(d,p) [17,18] level. Harmonic vibrational frequencies were obtained at the MP2 level for the verification of the optimized geometries. Transition states were characterized by one imaginary vibrational frequency. The connections between intermediates, transition states and products are confirmed by the intrinsic reaction coordinate (IRC) [19,20] analysis at the MP2 level of theory. A higher level of electronic correlation method, CCSD(T)/ 6-311++G(3df,3pd), is employed in the single-point-energy calculations to improve the accuracy of energetic information on minimum energy path (MEP). All of the calculations are performed with the Gaussian-98 program [21]. Topological analysis was carried out with AIM2000 program [22] and molecular graphs in the reaction pathway of cis-OSOO ? SO3(D3h) were plotted. 3. Results and discussion The optimized geometrical parameters of the reactants, intermediates, transition states (TSs) and products at the B3LYP and
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Fig. 1. Geometries of reactants, intermediates, transition states and products at (a) B3LYP/6-31++G(d,p), (b) B3LYP/6-311++G(3df,3pd) and (c) MP2/6-311++G(d,p) levels (bond lengths in angstrom, bond angles in degree).
MP2 levels, have been shown in Fig. 1. The total energies, ZPEs and relative energies have been listed in Table 1 for the B3LYP, MP2 and CCSD(T) levels, where the molecular energy at the CCSD(T) level is the sum of CCSD(T) energy and the ZPE, which is obtained from the B3LYP/6-311++G(3df,3pd) level. The calculated vibrational frequencies at MP2 level which have been listed in Table 2 show that S–O3, trans-OSOO, cis-OSOO, SO3(Cs) and SO3(D3h) are true minimums on the reaction potential energy surface (PES). Finally, the profile of PES has been depicted in Fig. 2, where the energy of S + O3 has been set to zero as reference.
ecule. The bond length of O–O in S–O3 is 1.31 Å at the MP2 level, which is about 0.03 Å longer compared with parent O3 molecule. The bond length of newly formed S–O is 1.75 Å. S–O3 collision complex has C2V symmetry and its energy is 10.42 kcal/mol less than that of the original reactants and no transition state has been found for the formation of S–O3. This has been confirmed by the point-wise potential energy curve calculated by MP2 level, as shown in Fig. 3. Therefore, the formation of S–O3 with C2V symmetry is barrierless and exothermic. The details of the reaction mechanism are discussed below.
3.1. Initial association 3.2. Isomerization and dissociation pathways We have only considered one stable collision complex (S–O3) between sulfur atom and ozone which is formed through the interaction of the sulfur atom with middle oxygen atom in ozone mol-
It is shown in Fig. 2 that we have two products in five Paths which are summarized as follows:
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Table 1 The total energy (ET), zero-point-energy (ZPE), relative energy (in the parenthesis) and electronic energy (E) obtained at different calculation levels. Species
S + O3 S–O3 Trans-OSOO Cis-OSOO SO3(Cs) SO3(D3h) SO + 3O2 TS1 TS2 TS3 TS4 TS5 TS(6) a b c
B3LYP
MP2/6-311++G(d,p)
CCSD(T)//B3LYP 6-311++G(3df,3pd)
6-31++G(d,p) ETa
6-311++G(3df,3pd) ETa
ETa
ETa
623.4569(0.00) 623.4982(25.92) 623.6567(125.38) 623.6642(130.08) 623.6872(144.51) 623.7607(190.64) 623.6363(112.57) 623.4669(6.27) 623.6231(104.29) 623.6471(119.35) 623.6294(108.24) 623.6322(110.00) 623.4432(8.60)
623.5637(0.00) 623.6088(28.30) 623.7864(139.74) 623.7945(144.83) 623.8267(165.04) 623.9239(226.03) 623.7546(119.79) 623.5755(7.40) 623.7603(123.37) 623.7803(135.92) 623.7633(125.25) 623.7784(134.73) 623.5502(8.47)
622.4932(0.00) 622.5217(17.88) 622.6939(125.94) 622.7096(135.79) 622.7121(137.36) 622.8000(192.52) 622.6680(109.69) 622.4884(3.01) 622.6493(97.95) 622.6611(105.36) 622.6384(91.11) 622.6489(97.70)
622.7211(0.00) 622.7377(10.42) 622.9233(126.88) 622.9313(131.90) 622.9668(154.18) 623.0659(216.37) 622.8916(106.99) 622.7106(6.59) 622.8895(105.67) 622.9156(122.05) 622.8986(111.38) 622.8765(97.52) 622.7048(10.23)
Ea,c
ZPEa,b
622.7284 622.7469 622.9321 622.9407 622.9768 623.0782 622.8979 622.7180 622.8974 622.9239 622.9067 622.8849 622.7110
0.0073 0.0092 0.0088 0.0094 0.0100 0.0123 0.0063 0.0074 0.0079 0.0083 0.0081 0.0084 0.0062
Total energies (ET), zero-point-energy (ZPE), and electronic energy (E) are in Hartree and relative energies in the parenthesis are in kcal/mol. ZPE obtained at the B3LYP/6-311++G(3df,3pd) level. Electronic energy (E) obtained at the CCSD(T) level.
where, R stands for reactants (S and O3), SO and 3O2 products are denoted by P1 and SO3 (with D3h symmetry) by P2. 3.2.1. Formation pathways of P1 [SO + 3O2] There are three feasible pathways to form P1 which can be written as follows:
Path P1 ð1Þ R ! S—O3 ! TS6 ! P1 Path P1 ð2Þ R ! S—O3 ! TS1 ! trans-OSOO ! P1 Path P1 ð3Þ R ! S—O3 ! TS1 ! trans-OSOO ! TS2 ! cis-OSOO ! P1 In the Path P1(1), the initial adduct S–O3 undergoes O2–O3 bond formation and O1–O2 and O1–O3 bonds rupture. This leads to the formation of product P1 via TS6 with energy barrier of 20.65 kcal/ mol. At this step (Path P1(1)), middle oxygen in O3 is absorbed by Table 2 The vibrational frequencies (cm1) of the reactants, intermediates, products and transition states calculated at the MP2 level. Species
Frequencies
O3 S–O3 Trans-OSOO Cis-OSOO SO3(Cs) SO3(D3h) SO 3 O2 TS1 TS2 TS3 TS4 TS5
749 403 203 177 319 421 966 1456 1343i 616i 807i 694i 2804i
1164 500 451 358 426 495
2293 527 565 571 604 495
731 674 616 626 1015
1421 1246 1229 856 1373
1935 6667 4282 1308 1373
266 216 291 301 321
377 241 382 372 403
676 563 835 512 848
1206 1268 1087 955 1231
2636 2420 1175 1187 302
S. It should be noted here that TS6 optimized at B3LYP/6311++G(3df,3pd) level has only one imaginary frequency (473i). In other words, TS6 is a transition state. In spite of numerous attempts, we could not optimize it at the MP2 level. We have checked the T1 diagnostic value of the CCSD(T) method for TS6 structure. The value is 0.11 which is greater than 0.02. This implies that TS6 has a multi-reference character and MP2 method is not reliable. As a result, optimization is done at B3LYP/6311++G(3df,3pd) level which is the most realistic in this case. In Path P1(2), S–O3 undergoes a concerted S4–O2 bond formation and O2–O1 bond rupture to form trans-OSOO via TS1 with energy barrier of 17.01 kcal/mol. Trans-OSOO is easily decomposed to the product P1 by S3–O2 bond rupture without any entrance barrier. In Path P1(3), the formation of trans-OSOO is similar to Path P1(2). The trans-OSOO is 126.88 kcal/mol lower than the total energy of the original reactants. This energy provides the driving force for the formation of cis-OSOO via TS2 by S3–O4 bond rotation around the S3–O2 bond with energy barrier of 21.21 kcal/mol. Finally, cis-OSOO can easily be decomposed to the product P1 by S4–O3 bond rupture without any entrance barrier. For Paths P1(2) and P1(3), the reaction mechanism is the absorption of O3 terminal oxygen by S. Paths P1(1) and P1(2) among these three channels involve fewer intermediates. Also, the energy barrier of S–O3 ? TS1 (in Path P1(2)) is 3.64 kcal/mol lower than that of S–O3 ? TS6 (in Path P1(1)). Therefore, Path P1(2) is expected to be a more feasible channel for product P1 with mechanism of O3 terminal oxygen absorption by S. 3.2.2. Formation pathways of P2 [SO3(D3h)] For product P2 [SO3(D3h)], there are two feasible pathways as follows:
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Fig. 2. The potential energy profile of the title reaction from CCSD(T) calculations based on the B3LYP/6-311++G(3df,3pd) geometries.
Path P2 ð1Þ R ! S—O3 ! TS1 ! trans-OSOO ! TS3 ! SO3 ðCs Þ ! TS5 ! P2 Path P2 ð2Þ R ! S—O3 ! TS1 ! trans-OSOO ! TS2 ! cis-OSOO ! TS4 ! SO3 ðCs Þ ! TS5 ! P2 In Path P2(1), the formation of trans-OSOO is similar to Path P1(2). Trans-OSOO undergoes S3–O1 bond formation to form SO3 (with Cs symmetry) via TS3 with energy barrier of 4.83 kcal/mol. The three-member ring geometry of SO3(CS) is given in Fig. 1. Its energy is 154.18 kcal/mol less than that of the reactants as shown in Fig. 2. Also, SO3(Cs) is transformed to product P2 via TS5 with the energy barrier of 56.66 kcal/mol. In Path P2(2), the formation of cisOSOO is similar to Path P1(3). Cis-OSOO is transformed to SO3(Cs) via TS4 by the formation of S4–O1 bond with energy barrier of 20.52 kcal/mol. Finally, SO3(Cs) is transformed to product P2 via TS5 with energy barrier of 56.66 kcal/mol. Therefore, product P2 is produced via two different channels in which, sulfur atom initially interacts with middle oxygen atom in O3 which is followed by interaction with terminal oxygen atoms in O3. In Path P2(1), the energy barrier of single step trans-OSOO ? SO3(Cs) is 4.83 kcal/mol, while, in Path P2(2), the formation of SO3 is done
in two steps. The energy barriers of the first trans-OSOO ? cisOSOO and the second cis-OSOO ? SO3(Cs) steps are 21.21 and 20.52 kcal/mol, respectively. Therefore, Path P2(1) is expected to be a more feasible channel for P2. According to the reaction pathways obtained in the reaction of S with O3, the most possible reaction pathways of two P1 [SO + 3O2] and P2 [SO3(D3h)] products are listed again:
Path P1 ð2Þ R ! S—O3 ! TS1 ! trans-OSOO ! P1 Path P2 ð1Þ R ! S—O3 ! TS1 ! trans-OSOO ! TS3 ! SO3 ðCs Þ ! TS5 ! P2 The sulfur atom can barrierlessly react with O3 at the middle oxygen site to form intermediate S–O3 followed by isomerization to trans-OSOO which is involved in the Paths P1(2) and P2(1). For the trans-OSOO, there are two pathways. One pathway is the decomposition of the trans-OSOO to product P1 without any entrance barrier [in the Path P1(2)] and the other one is the isomerization of the trans-OSOO to product P2 via TS3 and TS5 [in the Path P2(1)] with energy barriers of 4.83 and 56.66 kcal/mol, respectively. Therefore, Path P1(2) is obviously a more suitable pathway and P1 is a more appropriate product in the reaction of S with O3. 3.3. Topological analysis of electronic density on IRC paths
Fig. 3. Relaxed potential energy curve for the formative process of the adduct S–O3 calculated at the MP2 level.
According to the topological analysis of electronic density, in the theory of the Atoms in Molecules (AIM) [23,24], electron density qðrc Þ and Laplacian of the electron density (r2 qðrc Þ) are used to describe the strength and the characteristic of the bond, respectively. The Laplacian (r2 qðrc Þ is the sum of k1, k2 and k3, where ki is the ith eigenvalue of Hessian matrix of the electronic density. If a critical point has two negative and one positive eigenvalues, it is called (3,1) or the bond critical point (BCP). If a critical point has two positive and one negative eigenvalues it is called (3,+1) or the ring critical point (RCP), which indicates that a ring structure exists. The interval from the appearance of the ring to its disappearance is called, ring structure transition region. The k2 eigenvalue of the Hessian matrix of the RCP (the positive curvature lying in the plane) has a tendency to zero ? maximum ? zero. The maximum Hessian matrix k2 of the RCP is called structure transition state (STS). Also, the traditional transition state that is a maximum on energy surface is called, energy transition state (ETS) [12].
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Table 3 Topological properties at BCP and RCP of the ring structure transition region for reaction cis-OSOO ? SO3(D3h) at the MP2 level.
a b c d e f
Bond
Sa,b,c/(amu)1/2 bohr
q
Eigen of the Hessian matrix k1
k2
k3
RCP
S3 = +2.63e S3 = +4.37 S3 = +4.43(STS) S3 = +4.55 S5 = 2.23f
0.1100 0.1373 0.1380 0.1393 0.1245
0.1612 0.2296 0.2313 0.2343 0.2029
0.0464 0.2436 0.2438 0.2436 0.0344
0.3499 0.4154 0.4195 0.4275 0.6027
0.2338 0.4292 0.4320 0.4368 0.4340
O3–O1
Cis-OSOO S3 = +2.63 S3 = +4.37 S3 = +4.43(STS) S3 = +4.55 S5 = 2.23
0.3806 0.2607 0.2331 0.2321 0.2302 0.1246
0.9113 0.5794 0.4920 0.4893 0.4839 0.2038
0.9016 0.5642 0.4734 0.4694 0.4614 0.0344
1.5707 1.2097 1.0990 1.0953 1.0880 1.6243
0.2420 0.0660 0.1332 0.1364 0.1424 0.3780
S–O2
Cis-OSOO S3 = +2.63 S3 = +4.37 S3 = +4.43(STS) S3 = +4.55 S5 = 2.23 SO3(D3h)
0.2785 0.2887 0.2941 0.2942 0.2945 0.2978 0.3021
0.4883 0.5360 0.5505 0.5511 0.5521 0.5640 0.5962
0.4368 0.4795 0.5039 0.5045 0.5056 0.5232 0.4735
1.9633 2.1696 2.2781 2.2809 2.2862 2.3539 2.1740
0.1038 1.1540 1.2232 1.2248 1.2284 1.2664 1.1040
S–O3
Cis-OSOO S3 = +2.63 S3 = +4.37 S3 = +4.43(STS) S3 = +4.55 S5 = 2.23 SO3(D3h)
0.1495 0.2112 0.1897 0.1892 0.1881 0.1995 0.3021
0.2398 0.3281 0.2881 0.2870 0.2850 0.3031 0.5962
0.1659 0.3051 0.2390 0.2371 0.2333 0.2394 0.4735
0.3075 0.4057 0.2688 0.2673 0.2645 0.5150 2.1740
0.0980 0.2272 0.2616 0.2568 0.2536 0.0272 1.1040
S–O1
S3 = +2.63 S3 = +4.37 S3 = +4.43(STS) S3 = +4.55 S5 = 2.23 SO3(D3h)
0.1102 0.1694 0.1715 0.1756 0.2011 0.3021
0.1571 0.2559 0.2586 0.2635 0.3053 0.5962
0.0408 0.2077 0.2104 0.2150 0.2455 0.4735
0.3403 0.2416 0.2357 0.2278 0.5480 2.1714
0.1424 0.2220 0.2332 0.2504 0.0028 1.1040
r2 qd
S, reaction coordinate. ’+’ denotes forward direction of the reaction. ’’ denotes reverse direction of the reaction. r2 q, laplacian of electron density. The formation of the ring structure. The annihilation of the ring structure.
In this context, the topological analysis of electronic density on some points along the cis-OSOO ? SO3(D3h) reaction Path was carried out. The topological characteristics of the BCP and RCP for the reaction are listed in Table 3. Molecular graphs for some points along the IRC paths were plotted and displayed in Fig. 4. Both cis-OSOO and trans-OSOO can be isomerized to SO3(Cs). Then SO3(Cs) is transformed to planar SO3 with D3h symmetry (Fig. 2). So, cis-OSOO ? SO3(D3h) and trans-OSOO ? SO3(D3h) consist of two elementary reactions. We assign the reaction coordinates S3, S4 and S5 to the reaction pathways of cis-OSOO ? SO3(Cs), trans-OSOO ? SO3(Cs) and SO3(Cs) ? SO3(D3h), respectively. As the cis-OSOO ? SO3(D3h) proceeds, in the first step a new bond is formed between S and O1 atom at S3 = +2.63. The formation of this bond creates a three-member ring at S3 = +2.63 and RCP appears. As the reaction progresses, the k2 of Hessian matrix at RCP increases and reaches to the maximum level at S3 = +4.43. After this point, as the reaction proceeds the k2 decreases gradually and a stable intermediate (SO3(Cs)) is formed. Up to now, the threemember ring still exists and at S5 = 2.23, O3–O1 bond has been broken. In the second step, the RCP disappears. Then, the S–O1 bond becomes stronger and stronger, and the product SO3(D3h) is formed. The point of S3 = +4.43 is the so-called STS of the cisOSOO ? SO3(D3h) reaction. The ring structure transition region exists in the two elementary steps of OSOO ? SO3(Cs) and SO3(Cs) ? SO3(D3h). Also, we find out that a ring transition region exists in two elementary steps. The trans-OSOO ? SO3(D3h) process is similar to cis-OSOO ? SO3(D3h). The STS of the process of
Fig. 4. The molecular graphs of cis-OSOO ? SO3(D3h) reaction. (Small represents bond critical point(BCP).) ring critical point(RCP), small
represents
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M. Goodarzi et al. / Journal of Molecular Structure: THEOCHEM 944 (2010) 110–115 Table 4 The thermodynamic data for S + O3 reaction at the MP2 level.
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13)
Step of reaction
DE (kcal/mol)
DH (kcal/mol)
TDS (kcal/mol)
DG (kcal/mol)
S + O3 ? S–O3 S–O3 ? TS1 TS1 ? trans-OSOO Trans-OSOO ? P1 Trans-OSOO ? TS2 TS2 ? cis-OSOO Cis-OSOO ? P1 Cis-OSOO ? TS4 TS4 ? SO3(Cs) SO3(Cs) ? TS5 TS5 ? P2 Trans-OSOO ? TS3 TS3 ? SO3(Cs) S + O3 ? P2 S + O3 ? P1
18.261 20.959 128.828 16.755 28.050 37.776 26.481 44.490 46.247 39.470 94.817 20.394 31.878 192.959 109.375
18.888 20.959 128.828 17.319 28.050 37.776 27.046 44.490 46.185 39.408 94.817 20.394 31.815 193.587 109.438
8.058 0.172 0.069 7.467 0.154 0.117 17.508 0.457 0.098 0.173 0.046 0.366 0.082 8.319 2.004
10.856 20.833 128.891 9.840 27.861 37.902 9.569 44.930 46.060 39.596 94.754 20.708 31.878 185.241 111.446
trans-OSOO ? SO3(D3h) is very close to the one that we had in the process of cis-OSOO ? SO3(D3h). 3.4. Topological analysis of the S–O bond in the SO3 isomerization The topological analysis of the electronic density was performed for S–O bond in the SO3 isomerization. The topological characteristics in the BCP’s of three S–O bonds and one O–O bond are listed in Table 3. According to the theory of AIM, the Laplacian of the electron density (r2 qðrc Þ) describes the characteristic of the bond. In general, when r2 qðrc Þ < 0 the bond is covalent, but when r2 qðrc Þ > 0 the bond belongs to the electrostatic interaction. The r2 qðrc Þ values in Table 3 indicate that the ionic character of the S–O2 bond is strong, and as the process proceeds, the ionic characteristic does not have an obvious change. From the emergence to the disappearance of the ring structure, the r2 qðrc Þ of S–O3 and S–O1 bonds are negative. This indicates that in the structure transition regions, S–O3 and S–O1 bonds have distinct covalent characteristics. After the transition state region, the covalent characteristics of two bonds become weak. The difference between S–O3 and S–O1 is that the covalent characteristic of S–O3 bond becomes weaker and weaker as the process proceeds, and finally it becomes ionic. However, the covalent characteristic of S–O1 is strengthened in the transition state region and then it becomes weaker and weaker when O3–O1 bond is broken. Three S–O bonds show ionic characteristics in the last product, SO3, which has D3h symmetry. 4. The thermodynamic data in the S and O3 reaction process The change of thermodynamic characteristics for each reaction channel is the difference between the corresponding thermodynamic properties of the products and the reactants. The thermodynamic data is corrected by ZPE for S + O3 reaction .The calculated relative internal energies, enthalpies, Gibbs free energies and entropies of all steps of the reactions in gas-phase at atmospheric pressure and temperature of 298.15 K, have been summarized in Table 4. These data show that, DH and DG for the channels (1), (3), (6), (9), (11) and (13) are negative. This means that they are exothermic and exergonic. DH and DG for the channels (2), (4), (5), (7), (8), (10) and (12) are positive, which implies that they are endothermic and endergonic. Finally, the S + O3 ? P1 and S + O3 ? P2 reactions are exothermic and exergonic (DH < 0 and DG < 0). 5. Conclusion Details of the reaction pathways of the S + O3 on the singlet potential energy surface have been characterized with CCSD(T) energies, based on B3LYP/6-311++G(3df,3pd) geometries. The studied
reaction is most likely initiated by sulfur atom that is attached to middle oxygen atom in ozone to form adduct S–O3 with no barrier. Subsequently, through a variety of transformations of isomer S–O3, two kinds of products P1 (SO + 3O2) and P2 (SO3(D3h)) are obtained. Product P1 is a more suitable product which is generated by one middle oxygen absorption channel and two terminal oxygen absorption channels. According to the energy profile, product P2 is less favorable than the product P1. Product P2 is produced via two different channels. In these two channels, sulfur atom initially interacts with middle oxygen atom in O3 which is followed by interaction with terminal oxygen atoms of O3. The topological analysis shows that the ring transitional structure region occurs in cis-OSOO ? SO3(Cs) and SO3(Cs) ? SO3(D3h) reaction pathways. Finally, the S + O3 ? P1 and S + O3 ? P2 reactions are exothermic and exergonic (DH < 0 and DG < 0) at atmospheric pressure and temperature of 298.15 K in the gas-phase. Acknowledgements This project was supported by the Zanjan University and M. Vahedpour would like to thank Dr. Ghanbari for the English improvement and research vice president of Zanjan University, Dr. Rashtch, for his financial supporting. References [1] A.A. Fonseca, M.A. Campinho, G. Arbilla, Quı´m. Nova 19 (1996) 361. [2] D.L. Baulch, R.A. Cox, P.J. Crutzen, R.F. Hampson Jr., J.A. Kerr, J. Troe, R.T. Watson, J. Phys. Chem. Ref. Data 11 (1982) 32. [3] V.W.J.H. Kirchhoff, Queimadas na Amazoˆnia e Efeito Estufa, Contexto, Sa~o Paulo, Brasil, 1992. [4] V.W.J.H. Kirchhoff, J. Geophys. Res. 93 (1988) 1469. [5] R.P. Wayne, Chemistry of Atmospheres, second ed., Oxford Science Publications, Oxford, 1991. [6] L. Yang, D. Fang, J. Mol. Struct.: Theochem. 671 (2004) 141. [7] Z.F. Xu, M.C. Lin, Chem. Phys. Lett. 440 (2007) 12. [8] J. Peiró-García, L. Nebot-Gil, Chem. Phys. Lett. 391 (2004) 195. [9] G.D. Petris, A. Cartoni, M. Rosi, A. Troiani, Chem. Phys. Lett. 410 (2005) 377. [10] A.J.C. Varandas, L. Zhang, Chem. Phys. Lett. 385 (2004) 409. [11] B. Makiabadi, H. Roohi, Chem. Phys. Lett. 460 (2008) 72. [12] J. Peiró-García, L. Nebot-Gil, Chem. Phys. Chem. 4 (2003) 843. [13] H.G. Yu, A.J.C. Varandas, Chem. Phys. Lett. 334 (2001) 173. [14] X. Li, L. Meng, S. Zheng, J. Mol. Struct.: Theochem. 847 (2007) 52. [15] A.D. Becke, J. Chem. Phys. 97 (1992) 9173. [16] C. Lee, W. Yang, R.G. Parr, Phys. Rev. 37 (1988) 785. [17] M.J. Frisch, M. Head-Gordon, J.A. Pople, Chem. Phys. Lett. 166 (1990) 275. [18] M.J. Frisch, M. Head-Gordon, J.A. Pople, Chem. Phys. Lett. 166 (1990) 281. [19] C. Gonzalez, H.B. Schlegel, J. Chem. Phys. 90 (1989) 2154. [20] C. Gonzalez, H.B. Schlegel, J. Phys. Chem. 94 (1990) 5523. [21] M.J. Frisch et al., Gaussian 98, Revision A.7, Gaussian, Inc., Pittsburgh, PA, 1998. [22] F.J. Biegler-Kônìng, R. Derdau, D. Bayles, R.F.W. Bader, AIM2000, Version 1, 2000. [23] R.F.W. Bader, Atoms in Molecules – A Quantum Theory, Oxford University Press, Oxford, 1990. [24] R.F.W. Bader, Chem. Rev. 91 (1991) 893.
Contents lists available at ScienceDirect
Journal of Molecular Structure: THEOCHEM journal homepage: www.elsevier.com/locate/theochem
Mechanism for the gas-phase of sulfur vapor with ozone reaction: A theoretical study Moein Goodarzi a, Morteza Vahedpour a,*, Fariba Nazari b a b
Chemistry Department, Zanjan University, Zanjan, Iran Institute for Advanced Studies in Basic Sciences, Zanjan, Iran
a r t i c l e
i n f o
Article history: Received 11 August 2009 Received in revised form 21 December 2009 Accepted 22 December 2009 Available online 13 January 2010 Keywords: Sulfur vapor Ozone Topological analysis of electronic density Potential energy surface
a b s t r a c t The reaction pathways of sulfur vapor with ozone on the singlet potential energy surface have been investigated theoretically at CCSD(T)/6-311++G(3df,3pd)//B3LYP/6-311++G(3df,3pd) level of computation. The calculated results show that the reactants are initially associated with the adduct S–O3 through a barrierless process. Subsequently, via a variety of transformations of isomer S–O3, two kinds of products P1(SO + 3O2) and P2(SO3(D3h)) are obtained. The cleavage and formation of the chemical bonds in the reaction pathways have been discussed using the topological analysis of electronic density. The topological analysis results show that the ring transitional structure region occurs in cis-OSOO ? SO3(Cs) and SO3(Cs) ? SO3(D3h) reaction pathways. Ó 2010 Elsevier B.V. All rights reserved.
1. Introduction The existence of O3 in the atmosphere is important for life on Earth because it absorbs solar radiation with a wavelength between 240 and 320 nm. The largest concentration of ozone is attained at approximately 4.00 1012 molecules/cm3 [1–5]. These molecules form a layer which has 10 km width and between 25 and 35 km height [2]. The applications of ozone in chemical reactions are essential and important. The reaction of ozone with other species is one of the best investigated chemical reactions which have been reported in many researches published in the recent years [6–12]. For example, the potential energy surface of the HO3 ? HO + O2 reaction has been studied using QCISD(T)/CBS level. There exists a cis and trans planer equilibrium geometry for HO3 structure. The cis HO3 is slightly more stable than the trans-HO3 [13]. The principal natural phenomenon which distributes sulfur vapor and gaseous sulfur compounds in atmosphere are volcanoes and those from biological processes that occur on the Earth, in wetlands, and in the oceans. A lot of gaseous sulfur compounds get out during volcanic eruptions which include sulfur vapor, gaseous sulfur compounds and different gases. As we know, the reaction mechanism of S with O3 is ambiguous and the major channels of producing SO + 3O2 and SO3(D3h) have not been identified. Our main objective in this article is the theoretical investigation of the reaction mechanism of S with O3. This reaction is important in atmospheric chemistry, because it forms
* Corresponding author. Fax: +98 241 515 2477. E-mail address: [email protected] (M. Vahedpour). 0166-1280/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.theochem.2009.12.035
SO3 (with D3h symmetry) which is considered as a major factor in the production of acidic rains [14]. The cleavage and formation of the chemical bonds in the reaction pathways have been discussed using the topological analysis of the electronic density. 2. Computational methods The geometries of the reactants, products, intermediates and transition states involved in the reaction are optimized using the density functional theory with the B3LYP [15,16] exchange–correlation functional with 6-31++G(d,p) and 6-311++G(3df,3pd) basis sets and MP2/6-311++G(d,p) [17,18] level. Harmonic vibrational frequencies were obtained at the MP2 level for the verification of the optimized geometries. Transition states were characterized by one imaginary vibrational frequency. The connections between intermediates, transition states and products are confirmed by the intrinsic reaction coordinate (IRC) [19,20] analysis at the MP2 level of theory. A higher level of electronic correlation method, CCSD(T)/ 6-311++G(3df,3pd), is employed in the single-point-energy calculations to improve the accuracy of energetic information on minimum energy path (MEP). All of the calculations are performed with the Gaussian-98 program [21]. Topological analysis was carried out with AIM2000 program [22] and molecular graphs in the reaction pathway of cis-OSOO ? SO3(D3h) were plotted. 3. Results and discussion The optimized geometrical parameters of the reactants, intermediates, transition states (TSs) and products at the B3LYP and
M. Goodarzi et al. / Journal of Molecular Structure: THEOCHEM 944 (2010) 110–115
111
Fig. 1. Geometries of reactants, intermediates, transition states and products at (a) B3LYP/6-31++G(d,p), (b) B3LYP/6-311++G(3df,3pd) and (c) MP2/6-311++G(d,p) levels (bond lengths in angstrom, bond angles in degree).
MP2 levels, have been shown in Fig. 1. The total energies, ZPEs and relative energies have been listed in Table 1 for the B3LYP, MP2 and CCSD(T) levels, where the molecular energy at the CCSD(T) level is the sum of CCSD(T) energy and the ZPE, which is obtained from the B3LYP/6-311++G(3df,3pd) level. The calculated vibrational frequencies at MP2 level which have been listed in Table 2 show that S–O3, trans-OSOO, cis-OSOO, SO3(Cs) and SO3(D3h) are true minimums on the reaction potential energy surface (PES). Finally, the profile of PES has been depicted in Fig. 2, where the energy of S + O3 has been set to zero as reference.
ecule. The bond length of O–O in S–O3 is 1.31 Å at the MP2 level, which is about 0.03 Å longer compared with parent O3 molecule. The bond length of newly formed S–O is 1.75 Å. S–O3 collision complex has C2V symmetry and its energy is 10.42 kcal/mol less than that of the original reactants and no transition state has been found for the formation of S–O3. This has been confirmed by the point-wise potential energy curve calculated by MP2 level, as shown in Fig. 3. Therefore, the formation of S–O3 with C2V symmetry is barrierless and exothermic. The details of the reaction mechanism are discussed below.
3.1. Initial association 3.2. Isomerization and dissociation pathways We have only considered one stable collision complex (S–O3) between sulfur atom and ozone which is formed through the interaction of the sulfur atom with middle oxygen atom in ozone mol-
It is shown in Fig. 2 that we have two products in five Paths which are summarized as follows:
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Table 1 The total energy (ET), zero-point-energy (ZPE), relative energy (in the parenthesis) and electronic energy (E) obtained at different calculation levels. Species
S + O3 S–O3 Trans-OSOO Cis-OSOO SO3(Cs) SO3(D3h) SO + 3O2 TS1 TS2 TS3 TS4 TS5 TS(6) a b c
B3LYP
MP2/6-311++G(d,p)
CCSD(T)//B3LYP 6-311++G(3df,3pd)
6-31++G(d,p) ETa
6-311++G(3df,3pd) ETa
ETa
ETa
623.4569(0.00) 623.4982(25.92) 623.6567(125.38) 623.6642(130.08) 623.6872(144.51) 623.7607(190.64) 623.6363(112.57) 623.4669(6.27) 623.6231(104.29) 623.6471(119.35) 623.6294(108.24) 623.6322(110.00) 623.4432(8.60)
623.5637(0.00) 623.6088(28.30) 623.7864(139.74) 623.7945(144.83) 623.8267(165.04) 623.9239(226.03) 623.7546(119.79) 623.5755(7.40) 623.7603(123.37) 623.7803(135.92) 623.7633(125.25) 623.7784(134.73) 623.5502(8.47)
622.4932(0.00) 622.5217(17.88) 622.6939(125.94) 622.7096(135.79) 622.7121(137.36) 622.8000(192.52) 622.6680(109.69) 622.4884(3.01) 622.6493(97.95) 622.6611(105.36) 622.6384(91.11) 622.6489(97.70)
622.7211(0.00) 622.7377(10.42) 622.9233(126.88) 622.9313(131.90) 622.9668(154.18) 623.0659(216.37) 622.8916(106.99) 622.7106(6.59) 622.8895(105.67) 622.9156(122.05) 622.8986(111.38) 622.8765(97.52) 622.7048(10.23)
Ea,c
ZPEa,b
622.7284 622.7469 622.9321 622.9407 622.9768 623.0782 622.8979 622.7180 622.8974 622.9239 622.9067 622.8849 622.7110
0.0073 0.0092 0.0088 0.0094 0.0100 0.0123 0.0063 0.0074 0.0079 0.0083 0.0081 0.0084 0.0062
Total energies (ET), zero-point-energy (ZPE), and electronic energy (E) are in Hartree and relative energies in the parenthesis are in kcal/mol. ZPE obtained at the B3LYP/6-311++G(3df,3pd) level. Electronic energy (E) obtained at the CCSD(T) level.
where, R stands for reactants (S and O3), SO and 3O2 products are denoted by P1 and SO3 (with D3h symmetry) by P2. 3.2.1. Formation pathways of P1 [SO + 3O2] There are three feasible pathways to form P1 which can be written as follows:
Path P1 ð1Þ R ! S—O3 ! TS6 ! P1 Path P1 ð2Þ R ! S—O3 ! TS1 ! trans-OSOO ! P1 Path P1 ð3Þ R ! S—O3 ! TS1 ! trans-OSOO ! TS2 ! cis-OSOO ! P1 In the Path P1(1), the initial adduct S–O3 undergoes O2–O3 bond formation and O1–O2 and O1–O3 bonds rupture. This leads to the formation of product P1 via TS6 with energy barrier of 20.65 kcal/ mol. At this step (Path P1(1)), middle oxygen in O3 is absorbed by Table 2 The vibrational frequencies (cm1) of the reactants, intermediates, products and transition states calculated at the MP2 level. Species
Frequencies
O3 S–O3 Trans-OSOO Cis-OSOO SO3(Cs) SO3(D3h) SO 3 O2 TS1 TS2 TS3 TS4 TS5
749 403 203 177 319 421 966 1456 1343i 616i 807i 694i 2804i
1164 500 451 358 426 495
2293 527 565 571 604 495
731 674 616 626 1015
1421 1246 1229 856 1373
1935 6667 4282 1308 1373
266 216 291 301 321
377 241 382 372 403
676 563 835 512 848
1206 1268 1087 955 1231
2636 2420 1175 1187 302
S. It should be noted here that TS6 optimized at B3LYP/6311++G(3df,3pd) level has only one imaginary frequency (473i). In other words, TS6 is a transition state. In spite of numerous attempts, we could not optimize it at the MP2 level. We have checked the T1 diagnostic value of the CCSD(T) method for TS6 structure. The value is 0.11 which is greater than 0.02. This implies that TS6 has a multi-reference character and MP2 method is not reliable. As a result, optimization is done at B3LYP/6311++G(3df,3pd) level which is the most realistic in this case. In Path P1(2), S–O3 undergoes a concerted S4–O2 bond formation and O2–O1 bond rupture to form trans-OSOO via TS1 with energy barrier of 17.01 kcal/mol. Trans-OSOO is easily decomposed to the product P1 by S3–O2 bond rupture without any entrance barrier. In Path P1(3), the formation of trans-OSOO is similar to Path P1(2). The trans-OSOO is 126.88 kcal/mol lower than the total energy of the original reactants. This energy provides the driving force for the formation of cis-OSOO via TS2 by S3–O4 bond rotation around the S3–O2 bond with energy barrier of 21.21 kcal/mol. Finally, cis-OSOO can easily be decomposed to the product P1 by S4–O3 bond rupture without any entrance barrier. For Paths P1(2) and P1(3), the reaction mechanism is the absorption of O3 terminal oxygen by S. Paths P1(1) and P1(2) among these three channels involve fewer intermediates. Also, the energy barrier of S–O3 ? TS1 (in Path P1(2)) is 3.64 kcal/mol lower than that of S–O3 ? TS6 (in Path P1(1)). Therefore, Path P1(2) is expected to be a more feasible channel for product P1 with mechanism of O3 terminal oxygen absorption by S. 3.2.2. Formation pathways of P2 [SO3(D3h)] For product P2 [SO3(D3h)], there are two feasible pathways as follows:
M. Goodarzi et al. / Journal of Molecular Structure: THEOCHEM 944 (2010) 110–115
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Fig. 2. The potential energy profile of the title reaction from CCSD(T) calculations based on the B3LYP/6-311++G(3df,3pd) geometries.
Path P2 ð1Þ R ! S—O3 ! TS1 ! trans-OSOO ! TS3 ! SO3 ðCs Þ ! TS5 ! P2 Path P2 ð2Þ R ! S—O3 ! TS1 ! trans-OSOO ! TS2 ! cis-OSOO ! TS4 ! SO3 ðCs Þ ! TS5 ! P2 In Path P2(1), the formation of trans-OSOO is similar to Path P1(2). Trans-OSOO undergoes S3–O1 bond formation to form SO3 (with Cs symmetry) via TS3 with energy barrier of 4.83 kcal/mol. The three-member ring geometry of SO3(CS) is given in Fig. 1. Its energy is 154.18 kcal/mol less than that of the reactants as shown in Fig. 2. Also, SO3(Cs) is transformed to product P2 via TS5 with the energy barrier of 56.66 kcal/mol. In Path P2(2), the formation of cisOSOO is similar to Path P1(3). Cis-OSOO is transformed to SO3(Cs) via TS4 by the formation of S4–O1 bond with energy barrier of 20.52 kcal/mol. Finally, SO3(Cs) is transformed to product P2 via TS5 with energy barrier of 56.66 kcal/mol. Therefore, product P2 is produced via two different channels in which, sulfur atom initially interacts with middle oxygen atom in O3 which is followed by interaction with terminal oxygen atoms in O3. In Path P2(1), the energy barrier of single step trans-OSOO ? SO3(Cs) is 4.83 kcal/mol, while, in Path P2(2), the formation of SO3 is done
in two steps. The energy barriers of the first trans-OSOO ? cisOSOO and the second cis-OSOO ? SO3(Cs) steps are 21.21 and 20.52 kcal/mol, respectively. Therefore, Path P2(1) is expected to be a more feasible channel for P2. According to the reaction pathways obtained in the reaction of S with O3, the most possible reaction pathways of two P1 [SO + 3O2] and P2 [SO3(D3h)] products are listed again:
Path P1 ð2Þ R ! S—O3 ! TS1 ! trans-OSOO ! P1 Path P2 ð1Þ R ! S—O3 ! TS1 ! trans-OSOO ! TS3 ! SO3 ðCs Þ ! TS5 ! P2 The sulfur atom can barrierlessly react with O3 at the middle oxygen site to form intermediate S–O3 followed by isomerization to trans-OSOO which is involved in the Paths P1(2) and P2(1). For the trans-OSOO, there are two pathways. One pathway is the decomposition of the trans-OSOO to product P1 without any entrance barrier [in the Path P1(2)] and the other one is the isomerization of the trans-OSOO to product P2 via TS3 and TS5 [in the Path P2(1)] with energy barriers of 4.83 and 56.66 kcal/mol, respectively. Therefore, Path P1(2) is obviously a more suitable pathway and P1 is a more appropriate product in the reaction of S with O3. 3.3. Topological analysis of electronic density on IRC paths
Fig. 3. Relaxed potential energy curve for the formative process of the adduct S–O3 calculated at the MP2 level.
According to the topological analysis of electronic density, in the theory of the Atoms in Molecules (AIM) [23,24], electron density qðrc Þ and Laplacian of the electron density (r2 qðrc Þ) are used to describe the strength and the characteristic of the bond, respectively. The Laplacian (r2 qðrc Þ is the sum of k1, k2 and k3, where ki is the ith eigenvalue of Hessian matrix of the electronic density. If a critical point has two negative and one positive eigenvalues, it is called (3,1) or the bond critical point (BCP). If a critical point has two positive and one negative eigenvalues it is called (3,+1) or the ring critical point (RCP), which indicates that a ring structure exists. The interval from the appearance of the ring to its disappearance is called, ring structure transition region. The k2 eigenvalue of the Hessian matrix of the RCP (the positive curvature lying in the plane) has a tendency to zero ? maximum ? zero. The maximum Hessian matrix k2 of the RCP is called structure transition state (STS). Also, the traditional transition state that is a maximum on energy surface is called, energy transition state (ETS) [12].
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Table 3 Topological properties at BCP and RCP of the ring structure transition region for reaction cis-OSOO ? SO3(D3h) at the MP2 level.
a b c d e f
Bond
Sa,b,c/(amu)1/2 bohr
q
Eigen of the Hessian matrix k1
k2
k3
RCP
S3 = +2.63e S3 = +4.37 S3 = +4.43(STS) S3 = +4.55 S5 = 2.23f
0.1100 0.1373 0.1380 0.1393 0.1245
0.1612 0.2296 0.2313 0.2343 0.2029
0.0464 0.2436 0.2438 0.2436 0.0344
0.3499 0.4154 0.4195 0.4275 0.6027
0.2338 0.4292 0.4320 0.4368 0.4340
O3–O1
Cis-OSOO S3 = +2.63 S3 = +4.37 S3 = +4.43(STS) S3 = +4.55 S5 = 2.23
0.3806 0.2607 0.2331 0.2321 0.2302 0.1246
0.9113 0.5794 0.4920 0.4893 0.4839 0.2038
0.9016 0.5642 0.4734 0.4694 0.4614 0.0344
1.5707 1.2097 1.0990 1.0953 1.0880 1.6243
0.2420 0.0660 0.1332 0.1364 0.1424 0.3780
S–O2
Cis-OSOO S3 = +2.63 S3 = +4.37 S3 = +4.43(STS) S3 = +4.55 S5 = 2.23 SO3(D3h)
0.2785 0.2887 0.2941 0.2942 0.2945 0.2978 0.3021
0.4883 0.5360 0.5505 0.5511 0.5521 0.5640 0.5962
0.4368 0.4795 0.5039 0.5045 0.5056 0.5232 0.4735
1.9633 2.1696 2.2781 2.2809 2.2862 2.3539 2.1740
0.1038 1.1540 1.2232 1.2248 1.2284 1.2664 1.1040
S–O3
Cis-OSOO S3 = +2.63 S3 = +4.37 S3 = +4.43(STS) S3 = +4.55 S5 = 2.23 SO3(D3h)
0.1495 0.2112 0.1897 0.1892 0.1881 0.1995 0.3021
0.2398 0.3281 0.2881 0.2870 0.2850 0.3031 0.5962
0.1659 0.3051 0.2390 0.2371 0.2333 0.2394 0.4735
0.3075 0.4057 0.2688 0.2673 0.2645 0.5150 2.1740
0.0980 0.2272 0.2616 0.2568 0.2536 0.0272 1.1040
S–O1
S3 = +2.63 S3 = +4.37 S3 = +4.43(STS) S3 = +4.55 S5 = 2.23 SO3(D3h)
0.1102 0.1694 0.1715 0.1756 0.2011 0.3021
0.1571 0.2559 0.2586 0.2635 0.3053 0.5962
0.0408 0.2077 0.2104 0.2150 0.2455 0.4735
0.3403 0.2416 0.2357 0.2278 0.5480 2.1714
0.1424 0.2220 0.2332 0.2504 0.0028 1.1040
r2 qd
S, reaction coordinate. ’+’ denotes forward direction of the reaction. ’’ denotes reverse direction of the reaction. r2 q, laplacian of electron density. The formation of the ring structure. The annihilation of the ring structure.
In this context, the topological analysis of electronic density on some points along the cis-OSOO ? SO3(D3h) reaction Path was carried out. The topological characteristics of the BCP and RCP for the reaction are listed in Table 3. Molecular graphs for some points along the IRC paths were plotted and displayed in Fig. 4. Both cis-OSOO and trans-OSOO can be isomerized to SO3(Cs). Then SO3(Cs) is transformed to planar SO3 with D3h symmetry (Fig. 2). So, cis-OSOO ? SO3(D3h) and trans-OSOO ? SO3(D3h) consist of two elementary reactions. We assign the reaction coordinates S3, S4 and S5 to the reaction pathways of cis-OSOO ? SO3(Cs), trans-OSOO ? SO3(Cs) and SO3(Cs) ? SO3(D3h), respectively. As the cis-OSOO ? SO3(D3h) proceeds, in the first step a new bond is formed between S and O1 atom at S3 = +2.63. The formation of this bond creates a three-member ring at S3 = +2.63 and RCP appears. As the reaction progresses, the k2 of Hessian matrix at RCP increases and reaches to the maximum level at S3 = +4.43. After this point, as the reaction proceeds the k2 decreases gradually and a stable intermediate (SO3(Cs)) is formed. Up to now, the threemember ring still exists and at S5 = 2.23, O3–O1 bond has been broken. In the second step, the RCP disappears. Then, the S–O1 bond becomes stronger and stronger, and the product SO3(D3h) is formed. The point of S3 = +4.43 is the so-called STS of the cisOSOO ? SO3(D3h) reaction. The ring structure transition region exists in the two elementary steps of OSOO ? SO3(Cs) and SO3(Cs) ? SO3(D3h). Also, we find out that a ring transition region exists in two elementary steps. The trans-OSOO ? SO3(D3h) process is similar to cis-OSOO ? SO3(D3h). The STS of the process of
Fig. 4. The molecular graphs of cis-OSOO ? SO3(D3h) reaction. (Small represents bond critical point(BCP).) ring critical point(RCP), small
represents
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M. Goodarzi et al. / Journal of Molecular Structure: THEOCHEM 944 (2010) 110–115 Table 4 The thermodynamic data for S + O3 reaction at the MP2 level.
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13)
Step of reaction
DE (kcal/mol)
DH (kcal/mol)
TDS (kcal/mol)
DG (kcal/mol)
S + O3 ? S–O3 S–O3 ? TS1 TS1 ? trans-OSOO Trans-OSOO ? P1 Trans-OSOO ? TS2 TS2 ? cis-OSOO Cis-OSOO ? P1 Cis-OSOO ? TS4 TS4 ? SO3(Cs) SO3(Cs) ? TS5 TS5 ? P2 Trans-OSOO ? TS3 TS3 ? SO3(Cs) S + O3 ? P2 S + O3 ? P1
18.261 20.959 128.828 16.755 28.050 37.776 26.481 44.490 46.247 39.470 94.817 20.394 31.878 192.959 109.375
18.888 20.959 128.828 17.319 28.050 37.776 27.046 44.490 46.185 39.408 94.817 20.394 31.815 193.587 109.438
8.058 0.172 0.069 7.467 0.154 0.117 17.508 0.457 0.098 0.173 0.046 0.366 0.082 8.319 2.004
10.856 20.833 128.891 9.840 27.861 37.902 9.569 44.930 46.060 39.596 94.754 20.708 31.878 185.241 111.446
trans-OSOO ? SO3(D3h) is very close to the one that we had in the process of cis-OSOO ? SO3(D3h). 3.4. Topological analysis of the S–O bond in the SO3 isomerization The topological analysis of the electronic density was performed for S–O bond in the SO3 isomerization. The topological characteristics in the BCP’s of three S–O bonds and one O–O bond are listed in Table 3. According to the theory of AIM, the Laplacian of the electron density (r2 qðrc Þ) describes the characteristic of the bond. In general, when r2 qðrc Þ < 0 the bond is covalent, but when r2 qðrc Þ > 0 the bond belongs to the electrostatic interaction. The r2 qðrc Þ values in Table 3 indicate that the ionic character of the S–O2 bond is strong, and as the process proceeds, the ionic characteristic does not have an obvious change. From the emergence to the disappearance of the ring structure, the r2 qðrc Þ of S–O3 and S–O1 bonds are negative. This indicates that in the structure transition regions, S–O3 and S–O1 bonds have distinct covalent characteristics. After the transition state region, the covalent characteristics of two bonds become weak. The difference between S–O3 and S–O1 is that the covalent characteristic of S–O3 bond becomes weaker and weaker as the process proceeds, and finally it becomes ionic. However, the covalent characteristic of S–O1 is strengthened in the transition state region and then it becomes weaker and weaker when O3–O1 bond is broken. Three S–O bonds show ionic characteristics in the last product, SO3, which has D3h symmetry. 4. The thermodynamic data in the S and O3 reaction process The change of thermodynamic characteristics for each reaction channel is the difference between the corresponding thermodynamic properties of the products and the reactants. The thermodynamic data is corrected by ZPE for S + O3 reaction .The calculated relative internal energies, enthalpies, Gibbs free energies and entropies of all steps of the reactions in gas-phase at atmospheric pressure and temperature of 298.15 K, have been summarized in Table 4. These data show that, DH and DG for the channels (1), (3), (6), (9), (11) and (13) are negative. This means that they are exothermic and exergonic. DH and DG for the channels (2), (4), (5), (7), (8), (10) and (12) are positive, which implies that they are endothermic and endergonic. Finally, the S + O3 ? P1 and S + O3 ? P2 reactions are exothermic and exergonic (DH < 0 and DG < 0). 5. Conclusion Details of the reaction pathways of the S + O3 on the singlet potential energy surface have been characterized with CCSD(T) energies, based on B3LYP/6-311++G(3df,3pd) geometries. The studied
reaction is most likely initiated by sulfur atom that is attached to middle oxygen atom in ozone to form adduct S–O3 with no barrier. Subsequently, through a variety of transformations of isomer S–O3, two kinds of products P1 (SO + 3O2) and P2 (SO3(D3h)) are obtained. Product P1 is a more suitable product which is generated by one middle oxygen absorption channel and two terminal oxygen absorption channels. According to the energy profile, product P2 is less favorable than the product P1. Product P2 is produced via two different channels. In these two channels, sulfur atom initially interacts with middle oxygen atom in O3 which is followed by interaction with terminal oxygen atoms of O3. The topological analysis shows that the ring transitional structure region occurs in cis-OSOO ? SO3(Cs) and SO3(Cs) ? SO3(D3h) reaction pathways. Finally, the S + O3 ? P1 and S + O3 ? P2 reactions are exothermic and exergonic (DH < 0 and DG < 0) at atmospheric pressure and temperature of 298.15 K in the gas-phase. Acknowledgements This project was supported by the Zanjan University and M. Vahedpour would like to thank Dr. Ghanbari for the English improvement and research vice president of Zanjan University, Dr. Rashtch, for his financial supporting. References [1] A.A. Fonseca, M.A. Campinho, G. Arbilla, Quı´m. Nova 19 (1996) 361. [2] D.L. Baulch, R.A. Cox, P.J. Crutzen, R.F. Hampson Jr., J.A. Kerr, J. Troe, R.T. Watson, J. Phys. Chem. Ref. Data 11 (1982) 32. [3] V.W.J.H. Kirchhoff, Queimadas na Amazoˆnia e Efeito Estufa, Contexto, Sa~o Paulo, Brasil, 1992. [4] V.W.J.H. Kirchhoff, J. Geophys. Res. 93 (1988) 1469. [5] R.P. Wayne, Chemistry of Atmospheres, second ed., Oxford Science Publications, Oxford, 1991. [6] L. Yang, D. Fang, J. Mol. Struct.: Theochem. 671 (2004) 141. [7] Z.F. Xu, M.C. Lin, Chem. Phys. Lett. 440 (2007) 12. [8] J. Peiró-García, L. Nebot-Gil, Chem. Phys. Lett. 391 (2004) 195. [9] G.D. Petris, A. Cartoni, M. Rosi, A. Troiani, Chem. Phys. Lett. 410 (2005) 377. [10] A.J.C. Varandas, L. Zhang, Chem. Phys. Lett. 385 (2004) 409. [11] B. Makiabadi, H. Roohi, Chem. Phys. Lett. 460 (2008) 72. [12] J. Peiró-García, L. Nebot-Gil, Chem. Phys. Chem. 4 (2003) 843. [13] H.G. Yu, A.J.C. Varandas, Chem. Phys. Lett. 334 (2001) 173. [14] X. Li, L. Meng, S. Zheng, J. Mol. Struct.: Theochem. 847 (2007) 52. [15] A.D. Becke, J. Chem. Phys. 97 (1992) 9173. [16] C. Lee, W. Yang, R.G. Parr, Phys. Rev. 37 (1988) 785. [17] M.J. Frisch, M. Head-Gordon, J.A. Pople, Chem. Phys. Lett. 166 (1990) 275. [18] M.J. Frisch, M. Head-Gordon, J.A. Pople, Chem. Phys. Lett. 166 (1990) 281. [19] C. Gonzalez, H.B. Schlegel, J. Chem. Phys. 90 (1989) 2154. [20] C. Gonzalez, H.B. Schlegel, J. Phys. Chem. 94 (1990) 5523. [21] M.J. Frisch et al., Gaussian 98, Revision A.7, Gaussian, Inc., Pittsburgh, PA, 1998. [22] F.J. Biegler-Kônìng, R. Derdau, D. Bayles, R.F.W. Bader, AIM2000, Version 1, 2000. [23] R.F.W. Bader, Atoms in Molecules – A Quantum Theory, Oxford University Press, Oxford, 1990. [24] R.F.W. Bader, Chem. Rev. 91 (1991) 893.