Atmospheric Reaction of the HOSO Radical with NO2 - American

ARTICLE pubs.acs.org/JPCA

Atmospheric Reaction of the HOSO Radical with NO2: A Theoretical Study Antonija Lesar* and Anita Tav
car Department of Physical and Organic Chemistry, Institute Jo
zef Stefan, Jamova c. 39, SI-1000 Ljubljana, Slovenia

bS Supporting Information ABSTRACT: The gas-phase reaction between HOSO and NO2 was examined using density functional theory. Geometry optimizations and frequency computations were performed at the B3LYP/6-311++G(2df,2pd) level of theory for all minimum species and transition states. The ground-state potential energy surface, including activation energies and enthalpies, were calculated using the ab initio CBS-QB3 composite method. The results suggest that the addition of HOSO and NO2 leads to two possible intermediates, HOS(O)NO2 and HOS(O)ONO, without any energy barrier. The HOS(O)NO2 easily decomposes into HONO + SO2 through the low energy product complex HONO 3 3 3 SO2, whereas the HOS(O)ONO dissociates to HOSO2 + NO products. This latter dissociation is preferred from the isomerization of the HOS(O)ONO to HOS(NO)O2. Also, HOS(O)NO2 isomerization to HOS(O)ONO is hindered due to the presence of a large energy barrier. From the thermodynamic aspect, the main products in the title reaction are HONO + SO2, whereas HOSO2 + NO are expected as a minor products.

1. INTRODUCTION The hydroxysulfinyl radical HOSO is a key intermediate in the combustion of fuels containing sulfur and is formed by recombination of sulfur dioxide SO2 with an H atom.1 SO2 is also a major ingredient of volcanic emissions and is the primary cause of environmentally damaging acid rain. The HOSO radical was identified experimentally in 1996 by Frank et al.2 in the gas phase and later in matrix isolated studies.3,4 Also, theoretical investigations on the structure, harmonic vibrational frequencies,5 and thermochemistry6 have been reported, whereas little attention has been paid to the reactions of this radical. In the theoretical investigation of the SO2 + HO2 reaction,7 the HOSO + O2 channel was found to be dominant. Rasmussen et al.1 summarized the rate constant modeling studies for the reactions of HOSO with H, O2, and OH. Because HOSO has been found to be relatively stable,8 its subsequent reactions are important for atmospheric chemistry but they are not well characterized. From an atmospheric perspective, the reaction with NOx is very relevant because of the significant abundance of nitrogen oxides in the polluted atmosphere. There is a very recent theoretical study of the SO2/ OH/NO singlet potential energy surface,9 in which the transHONO
SO2 complex, being the global minimum, and the association of HOSO2 + NO resulting in HO(NO)SO2 formation is found to be most favorable process. First evidence for the existence of HO(NO)SO2 (nitrososulfonic acid molecules) was reported in an earlier work by the same authors,10 who carried out an FTIR spectroscopic study of the HONO/SO2 system in low-temperature N2 and Ar matrixes. The main concern of this work is the understanding of the HOSO + NO2 reaction mechanism, including all possible product channels. The products resulting from the reaction of r 2011 American Chemical Society

HOSO with NO2 are not known; several reaction channels are thermodynamically accessible: HOSO þ NO2 f HNO2 þ SO2

ð1aÞ

f HONO þ SO2

ð1bÞ

f HOSO2 þ NO

ð1cÞ

Reactions 1a and 1b can be considered as a transfer of the hydrogen atom from the HOSO radical to either the nitrogen or oxygen atom of the NO2. Moreover, reaction 1b can be represented as a sulfur
nitrogen exchange reaction. One important question is whether stable adducts can be formed in this radical
radical reaction. To clarify the dominant products of the title reaction and possible reaction intermediates, different reaction pathways for the ground-state surface will be investigated with relevant quantum chemical methods. Thus, the purpose of the present work is to study the overall reaction mechanism of the HOSO + NO2 reaction, and for identified intermediates the vibrational and thermodynamic properties will be evaluated.

2. COMPUTATIONAL METHODS The electronic structure calculations in this study were performed with the GAUSSIAN 03 program.11 Optimized geometries and corresponding energies for reactants, reactive intermediates, products, and transition states were determined using the Becke three-parameter nonlocal exchange functional12 Received: December 15, 2010 Revised: September 2, 2011 Published: September 06, 2011 11008

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Figure 1. Reaction scheme for the HOSO + NO2 reaction.

with the nonlocal correlation of Lee, Yang, and Parr (B3LYP).13,14 The B3LYP method has proved to be an economical and accurate computational model for obtaining reliable results and has been employed widely. Preliminary searches of stationary points were carried out using the 6-311G(d) basis set and the results from these calculations were reoptimized with the 6-311++G(2df,2pd) basis set. The eigenvalue following method was used in the transition state optimizations. The spin contamination was monitored for all species, the ÆS2æ showed insignificant deviation from the expectation value of 0.75 for open shell species. The harmonic and anharmonic frequencies of all species were computed at the same level of theory, to characterize the nature of the stationary points and to determine zero point energies. Furthermore, an IRC procedure15 was used to follow the reaction path in both directions from the transition states to the corresponding reactant and product structures, with a step size of 0.1 amu1/2 bohr. The final energies of the stationary points were improved using the CBS-QB3 level16 of theory. Additionally, for the purpose of comparison, the critical points on the potential energy surface were evaluated also by the G2MP2 method.17 The heats of formation of HOS(O)NO2, HOS(O)ONO, and HOS(NO)O2 were evaluated also at the CBS-QB3 level of theory, which is estimated to be accurate to 0.87 kcal mol
1, by following the procedure based on atomization energies as outlined by Curtiss et al.18

3. RESULTS AND DISCUSSION The stationary points on the ground state potential energy surface were located and characterized at the B3LYP/6-311 +G(2df,2pd) level of theory. The possible reaction channels 1a
1c are schematically illustrated in Figure 1. The optimized structure of the stable intermediates are shown in Figure 2, and the transition state structures are given in Figure 3. The harmonic and anharmonic vibrational frequencies, together with the IR intensities for the adducts (Table SI-1), the harmonic vibrational frequencies for the transition states (Table SI-2), and the zero-point corrected relative energies of the HOS(O)ONO conformers and conformational transition states (Table SI-3) are available in the Supporting Information. The transition states are confirmed to have only one imaginary vibrational frequency. Table 1 summarizes the zero-point corrected relative energies (relative to the reactants HOSO + NO2) of all the species relevant for the different reaction channels of the B3LYP/ 6-311+G(2df,2pd) and CBS-QB3 methods, and the subsequent discussion and the overall energy profiles shown in Figure 4 refer to the CBS-QB3 values. G2(MP2) energies of particular critical points on the potential energy surface were calculated and included in Table 1. MP2(Full)/6-31G(d) geometries used in these computations closely coincide with B3LYP geometries. Table 1 involves the relative Gibbs free energies evaluated at the CBS-QB3 level of calculations. Figure 5 displays the part of the

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conformational potential energy surface of the HOS(O)ONO isomer limited to those conformers involved in Figure 4. The CBS-QB3 calculated heats of formation of the HOS(O)NO2, HOS(O)ONO, and HOS(NO)O2 are listed in Table 2. Figures 2 and 3 make clear also the denotations of the intermediates used in subsequent text and in Figures 4 and 5. 3.1. Formation of Initial Adducts. The formation of an intermediate or an adduct involves the addition of NO2 to HOSO and can proceed in two directions. The first addition process is described as the approach of both radicals along the S
N reaction coordinate and leads to the formation of the HOS(O)NO2 intermediate. As confirmed by the relax scan calculations of the S
N bond, there is no energy barrier. Because the first step is radical
radical association, the barrierless process has been expected. The formed bond is 2.068 Å long, the S
N bond energy is calculated to be 21.9 kcal mol
1. The other HOSO + NO2 addition occurs along the S
O coordinate, and it is also a barrierless process resulting in the HOS(O)ONO intermediate. Twelve conformational structures have been characterized on the conformational potential energy surface of this intermediate. They are classified by four dihedral angles: τ1(HOSO), τ2(OSON), τ3(OSOO), and τ4(SONO). Dihedral angles of approximately 0, 90, and 180 refer to cis (c), perp (p), and trans (t), respectively. Among these conformational forms the lowest energy structure is the cppt conformation labeled as the HOS(O)ONO-L structure, whereas the tptc structural form, HOS(O)ONO-A, is the highest energy conformer, lying 7.0 kcal mol
1 above the L form. The vibrational frequencies listed in Table SI-1 of the Supporting Information are all positive for each isomer and conformer, confirming that these structures are stable minima. 3.2. Reaction Pathways of HOS(O)NO2. HOS(O)NO2 undergoes dissociation into HONO + SO2. In this process the H-atom migrates through the five-center transition state TS-PC to the product complex HONO 3 3 3 SO2-PC. The H
O bond in the HOSO part is elongated to 1.145 Å in the TS-PC, and the formed H
O bond is 1.295 Å. The S
N bond of the transition state is slightly compressed with regard to the HOS(O)NO2 and is lengthened to 3.813 Å in the complex. Vibrational frequency analysis of TS-PC indicates one imaginary frequency of 827i cm
1. The activation barrier is only 1 kcal mol
1, and the complex is 19.6 kcal mol
1 lower in energy than the HOS(O)NO2. The dissociation of the complex to the t-HONO + SO2 products is barrierless and requires an energy of 3.8 kcal mol
1. The overall HOSO + NO2 f t-HONO + SO2 reaction is exothermic with a large energy difference of 37.7 kcal mol
1. However, this reaction channel is energetically favorable and might be the main reaction path. An inspection of the relative Gibbs free energies from Table 1 for this pathway shows that this reaction channel is spontaneous. Furthermore, it can be considered either as an exchange reaction of the sulfur from HOSO by the nitrogen resulting in t-HONO or as hydrogen atom abstraction from HOSO by NO2. These findings are similar to that reported by Poggi and Francisco19 for the HOCO + NO2 reaction, where the exchange of carbon and nitrogen centers occurs. Both S
N and C
N exchange reactions are predicted to be the major reaction route. We considered the decomposition channel from HOS(O)NO2 resulting in the HOSO2 + NO products; no transition state was found for this pathway. On the other hand, the HOS(O)NO2 transforms to the HOS(O)ONO isomer. The transition states TS-H, TS-J, TS-E, and TS-L are found to represent the conversion of the HOS(O)NO2 to the different 11009

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Figure 2. Structure of the intermediates involved in the HOSO + NO2 reaction. Bond lengths are in Å.

conformeric forms of the HOS(O)ONO isomer, i.e., H, J, E, and L forms. The energy barriers of 28.8, 31.0, 30.6, and 29.6 kcal mol
1, respectively, are above the reactant energy level, suggesting that the conversions are inefficient. As expected, their structures are similar, all of them are three-center transition states including the S
N bond breaking and S
O bond forming. The difference is related to the orientation of the ONO part with respect to HOSO moiety, which leads to the different structural

conformers of the HOS(O)ONO isomer. It is evident that simultaneous S
N bond breaking and S
O bond forming in the isomerization transition states require more energy than only S
N bond breaking or only S
O bond forming. 3.3. Conformational Isomerizations of HOS(O)ONO. Although HOS(O)ONO isomer formation is a barrierless process, the first-order saddle point TS-A is characterized at the entrance of the association reaction. The TS-A structure exhibits 11010

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Figure 3. Transition state structures involved in the HOSO + NO2 reaction. Bond lengths are in Å.

a relatively early character with an imaginary frequency of 177i cm
1. In the four-center structure the bond distances from the S atom to either of the O atoms of the NO2 moiety approach 2.4 Å. IRC calculations confirmed the connection of TS-A with the maximum energy conformer of the HOS(O)ONO isomer, i.e., the HOS(O)ONO-A structure. This conformer can easily interconvert to a minimum energy HOS(O)ONO-L structure or

to the other conformers. The conformers are labeled as HOS(O)ONO followed by capital letters from A to L. Actually, twelve conformeric forms (Figure SI-1, Supporting Information) are interconnected between themselves with thirteen transition states (Figure SI-2, Supporting Information) resulting from the OH rotation around the S
O1 bond, the NO rotation around the N
O3 bond, and the NO2 rotation around the S
O3 bond. 11011

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The Journal of Physical Chemistry A The corresponding energy barriers range from 0.3 to 7.3 kcal mol
1. The complete listing of the zero-point corrected relative energies (relative to the reactants HOSO + NO2) are provided in Table SI-3 of the Supporting Information. Figure 5 illustrates the part of the conformational potential energy surface of the HOS(O)ONO isomer, where only those conformers related to the overall energy profile of HOSO + NO2 (presented in Figure 4) are shown. From the figure it can be clearly seen that the transformation of the maximum energy form A to the minimum energy form L is accompanied by an energy barrier of only 1.5 kcal mol
1; otherwise, the energy barriers extend by 0.3 kcal mol
1 to 4.8 kcal mol
1. The dissociation of the HOS(O)ONO isomer to the HOSO2 + NO products requires the energy extend from 6.6 to 13.6 kcal mol
1 for maximum and minimum energy conformers, respectively. Although the dissociations are endothermic processes, the HOSO2 + NO products still lie below the reactant asymptote by 16.4 kcal mol
1, making this product channel likely. 3.4. HOS(O)ONO Isomerization to HOS(NO)O2. The conformers HOS(O)ONO-E and HOS(O)ONO-L can overcome the TS-N barrier, resulting in the HOS(NO)O2 isomer, where the NO is transferred from the sulfur-bonded oxygen atom O3 to the sulfur atom. The HOS(O)ONO conformer is converted to HOS(NO)O2 with a cis orientation of the OH and NO groups with regard to the S
N bond. The N
O bond breaking in the three-center TS-N is elongated to 2.016 Å and the formed S
N bond is 2.380 Å long. The magnitude of the imaginary frequency is 163i cm
1. The energy barriers for the isomerizations HOS(O)ONO-E T c-HOS(NO)O2 and HOS(O)ONO-L T c-HOS(NO)O2 are 13.5 and 17.4 kcal mol
1, respectively. In any case, the isomerization is energetically less appropriate than direct dissociation to the HOSO2 + NO products by 3.8 kcal mol
1. Nitrososulfonic acid HOS(NO)O2 is the only species identified in the experiment on photolysis of the matrix HONO/SO2 system. The IR spectra are reported for nitrogen and argon matrixes,10 the experimental values are included in Table SI-1 (Supporting Information) for comparison. One can see that the agreement between B3LYP/6-311+G(2df,2pd) anharmonic frequencies and experimental data are satisfactorily, in any case, better than those of MP2/6-311++G(3df,3pd) harmonic frequencies reported by Wierzejewska and Olbert-Majkut.10 For example, the relatively intense frequency ν(OH)/N2(Ar) is 3502 cm
1 (3549 cm
1) compared to 3583 (3794) cm
1 for the cis form and 3573 (3795) cm
1 for the trans form at the B3LYP (MP2) levels of calculation. 3.5. Reaction Pathways of HOS(NO)O2. As presented above, the isomerization of HOS(O)ONO results in c-HOS(NO)O2. The NO group is almost freely rotated along the S
N bond, leading to the gauche conformer, g-HOS(NO)O2, or to the trans conformer, t-HOS(NO)O2. The geometrical parameters of conformers and the transition state TS-ct (shown on Figure SI-2, Supporting Information) are very similar, the only difference is related to the O4
NSO2 dihedral angle. Thus, the low imaginary frequency of 90i cm
1 corresponds to NO torsion. The barrier height of the TS-ct and the energy separation between the cis and trans structural forms are insignificant, only 0.6 and 0.5 kcal mol
1, respectively. Either conformer can directly dissociate to the HOSO2 + NO products, being 16.4 kcal mol
1 lower in energy than the reactants. The S
N bond dissociation energies of the HOS(NO)O2 conformers are calculated to be 16.8, 16.9, and 17.3 kcal mol
1 for the cis, gauche, and trans forms, respectively. Because the HOSO + NO2 f HOSO2 + NO reaction is moderately exothermic, there is a question concerning the

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Table 1. Relative Energies (ΔE0, kcal mol
1) and Gibbs Free Energies (ΔG, kcal mol
1) of Reactants, Intermediates, Transition States, and Products in the HOSO + NO2 Reaction ΔE0 species

B3LYP

CBS-QB3

ΔG G2MP2

CBS-QB3

HOSO+NO2

0

0

0

0

HOS(O)NO2


16.2


21.9


23.8


9.8

PC


30.0


41.5


42.9


33.1

HOS(O)ONO-A


14.8


23.0


26.3


10.9

HOS(O)ONO-E HOS(O)ONO-F


16.2
17.2


26.1
26.3


14.8
14.6

HOS(O)ONO-G


14.4


26.4


14.6

HOS(O)ONO-H


17.0


28.0


16.3

HOS(O)ONO-I


18.0


28.4


17.0

HOS(O)ONO-J


19.4


29.9

HOS(O)ONO-L


19.5


30.0


31.6


18.4

c-HOS(NO)SO2


18.3


33.2


32.9


21.5

t-HOS(NO)SO2 g-HOS(NO)SO2


18.8
18.2


33.7
33.3


33.3


22.0
21.6

TS-PC


22.6


8.4


18.8


15.6


20.9

TS-A


2.9


6.4

5.8

TS-H

12.2

6.9

18.7

TS-J

12.4

9.1

20.9

TS-E

12.6

8.7

20.7

TS-L

12.0

7.7

TS-N TS-ct


5.4
17.6


12.6
32.6

19.6
14.8
32.5


0.8
20.3

TS-c

1.0


4.7


7.3

7.2

TS-t


1.4


6.9


9.4

5.1

TS-1


10.1


23.3


11.8

TS-2


15.5


25.2


13.1

TS-3


13.0


22.4


10.1

TS-4


16.6


26.5


15.0

TS-5 TS-6


13.8
12.9


24.8
21.5


12.9
9.7

TS-7


14.7


25.2


5.7


16.4


14.5


14.9

c-HONO+SO2


26.9


37.3


38.5


36.5

t-HONO+SO2


27.6


37.7


39.1


36.9

HOSO2+NO


13.3

decomposition of the HOSO2. Calculations showed that the HOSO2 radical is stable to decomposition into HO + SO2 by 26.9 kcal mol
1, implying that the HO + SO2 + NO final products are not expected. When we considered the other decomposition pathways for the HOS(NO)O2, two three-center transition states were identified. The TS-c connects the c-HOS(NO)O2 and the c-HONO + SO2 end products, whereas t-HONO + SO2 is formed from t-HOS(NO)O2 passing through the TS-t transition state. In TS-c and TS-t the S
N bonds (2.434 Å) and the S
O(H) bonds (1.998 Å, oxygen of the OH group) are significantly elongated compared to the corresponding intermediates (2.055 and 1.625 Å, respectively). In both TSs the bond distance from the O(H) to the N(O) becomes nearly the same, approximately 1.98 Å, as the distance from the O(H) to the S atom. Thus, the TSs resemble an OH weak bond to the SO2 or to the NO. Further progress of 11012

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Figure 4. CBS-QB3 energy profile of the HOSO + NO2 reaction. The minimum energy pathway is shown by a green dashed line. (To make the figure more clear, only the L conformer is connected with the HOSO2 + NO products, although each conformer can dissociate to these products.)

Table 2. CBS-QB3 Calculated Atomization Energies (ΔH0at, kcal mol
1) and Heats of Formation (ΔH0f , kcal mol
1) of Intermediates Involved in the HOSO + NO2 Reaction ΔH0at,0 species

Figure 5. Part of the conformational potential energy surface of the HOS(O)ONO isomer (see Figure 2 for labeling of conformers).

these reaction pathways involves breaking the S
N and S
O bonds and forming a new N
O bond. In other words, these pathways can be attributed to OH transfer from the sulfur atom to the nitrogen atom. The vibrational frequency analysis shows that the TS-c and TS-t are first-order saddle points with imaginary frequency modes of 325i and 305i cm
1, respectively. Although the energy barriers of 28.5 and 26.8 kcal mol
1 are quite high, both still lie below the reactant HOSO + NO2 energy level, making the processes possible. To summarize, the HONO + SO2 products dominate in the reaction of the HOSO radical with NO2. The low energy pathway happens via HOS(O)NO2 formation and then proceeds through rearrangement to the product complex HONO 3 3 3 SO2 and its final dissociation. The same products can be generated also in another subchannel; namely, if any HOS(NO)O2 is formed by the isomeriztion of the HOS(O)ONO, then it will probably dissociate to the HONO + SO2 products. This subchannel is of minor importance for HONO + SO2 production because of the significant energy barrier for isomerization and the even higher energy barrier in the exit channel. It should be noted that the energy levels of both transition states are still below the reactants energy levels, making the processes feasible. Furthermore, it was

ΔH0at,298

ΔH0at,0

ΔH0at,298

ΔH0f,0

ΔH0f,298

HOS(O)NO2


539.1


544.9


73.4


71.9

HOS(O)ONO-A HOS(O)ONO-L


540.2
547.2


545.8
552.6


74.5
81.5


72.8
79.5

c-HOS(NO)O2


550.5


555.9


84.7


82.8

t-HOS(NO)O2


551.0


556.4


85.2


83.4

found that the HOSO2 + NO products can be produced either by direct decomposition of the HOS(O)ONO isomer or through its isomerization to HOS(NO)O2, followed by its subsequent dissociation. Compared with the HONO + SO2 products, these second products are energetically less convenient because the HOSO2 + NO energy level is higher than the HONO + SO2 energy level by as much as 21.3 kcal mol
1. Finally, it is worth comparing the conclusions resulting from the present calculations with that of the SO2/OH/NO potential energy surface at the MP2/6-311++G(2d,2p) level of theory reported in the literature.10 Because different levels of calculations have been used, some qualitative conclusions can be drawn. It should be noted that the CBS-QB3 energies used here are more accurate and reliable than the MP2 energies. Inspection of the corresponding energy profiles leads to the following similarities. First, the HONO 3 3 3 SO2 product complex is the global minimum on the PES and the structure is similar to the transHONO
SO2 complex global minimum calculated by Wierzejewska and Olbert-Majkut.10 Furthermore, the transition states TS-c and TS-t for OH transfer from the sulfur atom to the nitrogen atom connecting the HOS(NO)O2 adduct and the HONO + SO2 products coincide with those of the TSR
2c and TSR
2t related to the SO2/OH/NO PES. Next, the structure of the TS-A 11013

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The Journal of Physical Chemistry A resembles the TSR
3 from the mentioned study, where TSR
3 is operative in the formation of the HOSO
NO2 complex from HOSO2 + NO. The HOSO
NO2 complex from that study is consistent with our HOS(O)ONO-A adduct, but our calculations confirmed that the TS-A connects the HOSO + NO2 reactants and the HOS(O)ONO-A adduct. We demonstrated that the HOS(O)ONO adduct has twelve conformeric configurations with a flat conformational potential energy surface and also that the two HOS(O)ONO conformers can isomerize to HOS(NO)O2. Another important finding regarding the HOSO + NO2 reaction is the existence of the HOS(O)NO2 association adduct, which through the transition state TS-PC easily transforms to the HONO 3 3 3 SO2 product complex. 3.6. Thermodynamic Stability of the Intermediates. The heat of formation of the intermediates involved in the HOSO + NO2 reaction were calculated via atomization reactions using the CBS-QB3 compound method and known heats of formation of the elements. The experimental heats of formation at 0 K for the atoms18 used in the calculations are as follows: the H atom, ΔH0f,0 = 51.63 ( 0.001 kcal mol
1; the N atom, ΔH0f,0 = 112.53 ( 0.02 kcal mol
1; the O atom, ΔH0f,0 = 58.99 ( 0.02 kcal mol
1; the S atom, ΔH0f,0 = 65.66 ( 0.06 kcal mol
1. The heats of formation at 298 K were evaluated from the 0 K values by including thermal contribution corrections.18 The calculated atomization energies and heats of formation at 0 and 298 K for HOSONO2, HOS(O)ONO-A, HOS(O)ONO-L, c-HOS(NO)O2, and t-HOS(NO)O2 are summarized in Table 2. The applicability of the CBS-QB3 composite method to the current system of interest containing sulfur as the third-row atom was tested by the heat of formation computation for the HOSO radical.20 The CBS-QB3 calculated value of
58.2 kcal mol
1 coincides well with the very recent highly accurate result of
58.0 kcal mol
1 reported by Wheeler et al.8 from systematically extrapolated ab initio energies, accounting for electron correlation primarily through CCSDT(Q) theory and corrections for core
electron correlation, harmonic and anharmonic ZPE, and non-Born
Oppenheimer and scalar relativistic effects. For HOS(O)NO2, the heat of formation at 0 K is predicted to be
73.4 kcal mol
1 at the CBS-QB3 level of theory. The maximum energy conformer of the HOS(O)ONO isomer, the HOS(O)ONO-A structure (with
74.5 kcal mol
1 heat of formation), is somewhat more stable than the HOS(O)NO2 and the HOS(O)ONO-L structure, as the minimum energy conformer (with a
81.5 kcal mol
1 heat of formation) is more stable by 7.0 kcal mol
1 than the HOS(O)ONO-A. The c-HOS(NO)O2 structure (with a
84.7 kcal mol
1 heat of formation) is only 0.5 kcal mol
1 higher in energy than the t-HOS(NO)O2 structure (with a
85.2 kcal mol
1 heat of formation) and possesses the lowest energy and, thus, the highest stability. However, the HOS(O)NO2, HOS(O)ONO, and HOS(NO)O2 intermediates are thermodynamically very stable; their relative stabilities vary by 11.8 kcal mol
1. The heat of formation data support the following ordering of isomers or conformers HOS(O)NO2 < HOS(O)ONO-A < HOS(O)ONO-L < c-HOS(NO)O2 < t-HOS(NO)O2, which is consistent with the results provided by the relative energy calculations.

4. CONCLUSION The present calculations indicate that in the association reaction of the HOSO radical with NO2, HOS(O)NO2 and HOS(O)ONO are formed directly in a barrierless exothermic

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process. The HOS(O)ONO isomer possesses many conformeric forms in the energy range of 7.0 kcal mol
1. The conformers can be easily transformed to one another, the energy barriers extend up to 7.3 kcal mol
1. The HOS(O)NO2 T HOS(O)ONO isomerization is accompanied by energy barriers of about 30 and 39 kcal mol
1 for forward and backward isomerizations, respectively. Although the HOS(O)NO2 isomer is quite stable against the reactant radicals (21.9 kcal mol
1), the required energy for thermal dissociation to the HOSO2 + NO radicals amounts to only 5.5 kcal mol
1. On the other hand, HOS(O)NO2 can very easily convert to the lower energy HONO 3 3 3 SO2 intermolecular product complex (
41.5 kcal mol
1) with S
N bond dissociation energy of only 3.8 kcal mol
1. Thus, the conversion of the HOSO + NO2 radicals to the HONO and SO2 radicals, i.e., a hydrogen abstraction reaction mechanism, is predicted to be thermodynamically very feasible and it presents the dominant reaction pathway. The dissociation of the HOS(O)ONO to the HOSO2 + NO products is an endothermic process (6.6
13.6 kcal mol
1), but the products energy level is still below the reactant asymptote, making this product channel likely.

’ ASSOCIATED CONTENT

bS

Supporting Information. Table SI-1 contains the harmonic and anharmonic vibrational frequencies, together with IR intensities for the adducts, whereas the harmonic vibrational frequencies for transition states are summarized in Table SI-2. Zero-point corrected relative energies (relative to the reactants HOSO + NO2) of the HOS(O)ONO conformers and conformational transition states are presented in Table SI-3, and their optimized structures of the HOS(O)ONO and conformational transition states are given in Figure SI-1 and Figure SI-2, respectively. This information is available free of charge via the Internet at http://pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*Fax: +386 1 477 38 22. E-mail: e-mail:[email protected].

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