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Article Cite This: J. Phys. Chem. A 2018, 122, 1926−1937

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Conflict in the Mechanism and Kinetics of the Barrierless Reaction between SH and NO2 Radicals Ramanpreet Kaur and Vikas* Quantum Chemistry Group, Department of Chemistry & Centre of Advanced Studies in Chemistry, Panjab University, Chandigarh 160014, India S Supporting Information *

ABSTRACT: There are some unsettled issues regarding the mechanism and kinetics of an important atmospheric reaction of NO2 radical with the SH radical. The existing mechanism is based on the formation of HSO and NO radicals, both of which can result only along one barrierless channel. However, the detection of NO radical has never been reported though the formation of HSO radical has been followed in some studies to determine the rate constants. The latter are mainly obtained by monitoring the SH decay, but rate constants are reported to be highly conflicting among the existing studies reporting its value ranging from 10−10 to 10−12 cm3 molecule−1 sec−1. The present work attempts to resolve these issues by exploring various reaction pathways through the global reaction route mapping of the potential energy surface at the level of spin-unrestricted and spin-restricted coupled-cluster and density functional theories. The initial association of two radicals was found to proceed via two barrierless modes: (1) S-N association leading to HSNO2 and, (2) S-O association resulting in HSONO, in particular the cisisomer. The kinetics of the barrierless pathways was investigated through rate constants computed using canonical variational transition state theory (CVTST) along with their temperature and pressure dependence investigated using the master equation. The rate constants calculated using spin-unrestricted methods are found to be in agreement with experimentally observed range of rate constant, and the formation of cis-HSONO (via mode 2) is observed to be the main contributing channel. Contrary to the results of spin-restricted calculations, the barrierless channel (mode 1) leading to the formation of HSNO2 is predicted to involve two bottlenecks when results using spin-unrestricted calculations were analyzed. Notably, the spin-unrestricted calculations predict a prereaction complex for the formation of S-N bond (via mode 1) which has been treated using Miller’s unified transition state theory with a two transition state model. The fate of all the species involved in the reaction is critically evaluated in the present work, and the predictions made can be a subject of further experimental and theoretical studies involving radical− radical reactions.

I. INTRODUCTION The reaction of NO2 radical with SH radical is an important atmospheric process, but the studies reported (both experimental and theoretical) on its mechanism and kinetics are quite conflicting.1−9 The reaction has been studied experimentally by a number of research groups,1−7 and the formation of HSO radical has been considered to be the main channel. The still existing dilemma about the mechanism of this reaction is that HSO radical has been detected experimentally though not yet quantified,4,6 but NO radical has never been reported to be monitored or identified in any of the works which questions the existing mechanism:9

Besides this, there have been some discrepancies in the bimolecular rate constant reported for this radical−radical reaction.1−7 The kinetic studies conducted by Black in 1984,1 using flash photolysis technique and laser-induced fluorescence (LIF),2 determined the value of the rate constant for the SH decay in this reaction to be (3.5 ± 0.4) × 10−11 cm3 molecule−1 sec−1 at 298K, whereas Schoenle et al.,6 in a study using the discharge flow/mass spectroscopy technique, reported the rate constant to be 1.2 × 10−10 cm3 molecule−1 s−1. Several other studies2−5 report the rate constant to be ranging from (2.4 ± 0.2) × 10−11 to (6.7 ± 1.0) × 10−11 cm3 molecule−1 s−1 by either monitoring the SH decay or HSO production. However, the most recent kinetic analysis by Herndon and Ravishankara,7 using FP-LIF, estimated the rate constant at 298K to be (7.0 ± 0.8) × 10−11 cm3 molecule−1 s−1. Notably, this study also detected the contamination by SO radicals which can

Moreover, there have been some speculations whether the formation of HSNO2 and HSONO proceed via barrierless pathways, though none of these isomers have ever been isolated. The present work attempts to resolve this issue. © 2018 American Chemical Society

Received: July 14, 2017 Revised: January 31, 2018 Published: February 1, 2018 1926

DOI: 10.1021/acs.jpca.7b06916 J. Phys. Chem. A 2018, 122, 1926−1937

Article

The Journal of Physical Chemistry A

the downward direction, which can be followed to locate other stationary points along the reaction pathways on the PES. The main algorithm for ADD-f, however, is a scaled hypersphere search (SHS) method.15 Recently,16−22 we had deployed the GRRM method to explore the mechanism and kinetics for the atmospheric reaction of hydroxyl radical with glycolaldehyde, besides revealing chemical pathways for isomerization in exotic radical species, in metastable molecular poly anions as well as stereochemical pathways in chiral molecules. In the present work, initially, a search for equilibrium structures on the singlet PES was carried out through GRRM employing a spin-unrestricted formalism at the DFT/ UBHandHLYP level of density functional theory (DFT)29 using Becke half-and-half Lee−Yang−Parr (BHandHLYP)30 exchange-correlation (XC) functional and 6−31G Gaussian basis set. For a comparison, the initial search was also carried out using the corresponding spin-restricted method. This level of theory is chosen because it is known to provide reliable and faster exploration on the PES of such reaction systems.15,22 The spin-restricted GRRM search was carried around equilibrium structures by following the five largest ADDs. This search provided 64 structures, all the five adducts reported in the study by Resende9 as well as that of Mendez10 have been reproduced along with some new important structures (for the details, see Supporting Information (SI) Figures S1 and S2). Also note that the stationary points obtained on the singlet PES of this radical reaction system were also optimized in their triplet state but found to be dissociating. However, the PES for radical−radical dissociation or association processes obtained by spinrestricted, single reference methods is generally not acceptable because such a PES is likely to describe dissociations into wrong electronic states. For the present system involving the two radical species, the aforementioned PES search using the spin-restricted method will explore only the PES region occupied by the closed-shell species, thereby overlooking the PES region where pathways passing through open-shell species with biradical character are involved. Therefore, the GRRM search was performed using spin-unrestricted UBH&HLYP/6− 31G level of the theory along with molecular orbital (MO) stability check (using the keyword STABLE = OPT) which in fact guarantees obtaining biradical MOs for species having a biradical character.14 Note that this search was carried out around equilibrium structures but by following only two largest ADDs resulted in 12 EQs depicted in SI Figure S3. These includes three key structures, namely, HSNO2, HSONOcis and HSONOtrans, with HSNO2 being the most stable one as was also predicted during search using the spin-restricted method. Therefore, though one may not expect any barrierless pathway being missed during a search using the spin-restricted method, it is likely that high-lying biradical TSs may be involved. However, a search using a multireference method may present a different picture though this is not needed for the present work (see below). For a better comparison of energetic on the PES, the relevant stationary points including reactants, products, intermediates, and transition states obtained were then reoptimized at the DFT/UM06−2X/cc-pVTZ level using Minnesota meta-hybrid XC functional (M06-2X)30 with Dunning’s correlationconsistent basis set cc-pVTZ (for details, see SI Figures S2 and S4). Note that the nature of all the stationary points was verified through a harmonic vibrational (frequency) analysis, and these were characterized as a minimum or a transition state depending on the number of imaginary frequencies (zero for

potentially interfere in the reaction course. Nevertheless, the existing experimental data is highly conflicting with rate constants reported ranging between 10−10 and 10−12 cm3 molecule−1 sec−1, though it has also been attributed to some secondary reactions involved.9 The present work investigates this issue by computing the rate constants along all the possible reaction pathways. As far as the computational studies on the kinetics and mechanism of this reaction are concerned, only a few reports are available.8,9 Stoechlin and Clary8 used an adiabatic capture partial centrifugal sudden approximation to calculate the rate constant with the reported values to be 34.6 and 3.6 × 10−11 cm3 molecule−1 s−1 depending upon whether a dispersion term in the potential is included.8 However, this approximation is only valid for extremely exothermic reactions contrary to the energetics of the present reaction (see later). A comprehensive computational study on the reaction mechanism was performed by Resende9 (see ref 42a for a work by Cameron et al.), while intuitively locating various stationary points (equilibrium structures and transition states) on the singlet potential energy surface (PES) of the reaction system, but no exploration of reaction pathways was carried out to confirm the connectivity between various stationary points. In another report by Mendez et al,10 thermodynamic properties of various isomers of [HNO2S] had also been computationally predicted, in which nine isomers were located. To the best of our knowledge, the present study is the first report which attempts to understand the kinetics of this reaction through advanced rate theories (using spin-unrestricted formalism) while systematically exploring the reaction pathways using global reaction route mapping (GRRM) method,11−22 which will be discussed in detail in the next section. Note that the initial combination of the two radicals (HS and NO2) is believed to be a barrierless process though there may be other reaction pathways which are likely to proceed via transition states with intrinsic energy barrier. In this work, first, all the energetically lower-lying stationary points, including those reported by Resende9 are traced while establishing the connections between them on the singlet PES of the reaction as discussed in the next section. Second, the rate constant along the explored reaction pathways, were investigated using variational transition state theory (VTST)23 and Rice−Ramsperger−Kassell−Marcus (RRKM)24 theory as well as using master equation25 simulations for temperature and pressure dependence of the rate constants as described in the subsequent section. Note that in the present work, the formation of HSNO2, the most stable isomer, is observed to arise from a barrierless process with single transition state using spin-restricted computations, whereas the spin-unrestricted formalism reveal two transition states along this channel (see later). For such a case of multiple transition states, Miller’s unified transition state theory has been utilized for computing the net rate constants.26−28

II. COMPUTATIONAL DETAILS AND METHODOLOGY The PES of the reaction system was systematically explored through a global reaction route mapping (GRRM) method,11−22 which is based on the principle of anharmonic downward distortion following (ADD-f) approach to locate the equilibrium structures (EQs), transition states (TSs), and dissociation channels (DCs). The basic idea in ADD-f is that when a reaction proceeds, the harmonic potential around an equilibrium structure (EQ) suffers an anharmonic distortion in 1927


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Figure 1. Significant connections, both barrierless (depicted in dashed lines) and with barrier (depicted in solid lines) on the singlet PES of the HS• + •NO2 radical−radical reaction. Relative energies (ΔE) (depicted in black) and Gibbs free energy change (ΔG) (depicted in red) including ZPE (in kcal/mol) in parentheses were calculated at the UCCSD(T)/cc-pVTZ//UM06−2X/cc-pVTZ level of the theory w.r.t. separated reactants (R1). The bond distances and angles in structures depicted are in angstroms and degrees, respectively. (For the results using spin-restricted calculations, see SI Figure S5.)

Table 1. Relative Energies (ΔE) and Standard Gibbs Free Energy Change (ΔG), in kcal/mol, w.r.t. Separated Reactants (R1)a for the Relevant Stationary Points on the Singlet PES of the Reaction between HS and NO2 Radicals at the UM06-2X/cc-pVTZ (U-DFT) and UCCSD(T)/cc-pVTZ//DFT/UM06-2X/cc-pVTZ (U-CCSD(T)//U-DFT) Levels of the Theory, Including ZPE Correction Values (Given in Parentheses)b stationary points ΔE (U-DFT) ΔE (U-CCSD(T)//U-DFT) ΔG (U-DFT) ΔG (U-CCSD(T)//U-DFT) harmonic frequencies rotational constants (A,B,C) T1 diagnostics

HSNO2

HSONOtrans

HSONOcis

TS0

TS1

[HSO• + NO•]

−32.55 (4.04) −33.25 −27.26 −23.93 331,399,478 12.98, 5.48, 3.85 0.0156

−31.15 (2.34) −30.06 −24.63 −21.21 134, 203,312 49.60, 3.12, 2.99 0.0158

−31.96 (2.75) −30.71 −25.53 −21.53 282, 314, 344 18.33,4.58, 3.74 0.0170

20.77 (2.37) 19.82 30.00 29.04 i672, 175, 426 22.41, 4.12, 3.48 −

−26.27 (2.21) −22.56 −16.98 −13.27 i209, 248,376 22.25, 3.81,3.5 0.014

−23.37 (0.02) −20.12 −24.46 −21.20 _ _

a The total energy including (ZPE) of R1 at UM06−2X/cc-pVTZ and UCCSD(T)/cc-pVTZ//DFT/UM06−2X/cc-pVTZ levels of the theory are −603.7930 (0.0155) and −603.1446 (0.0155) a.u., respectively, and the total Gibbs free energy of R1 at UM06−2X/cc-pVTZ, UCCSD(T)/ccpVTZ//UDFT/M06−2X/cc-pVTZ level are −603.83484 and −603.18643 au, respectively (1 a.u. = 627.5095 kcal/mol). bThe harmonic frequency values (in cm−1) and rotational constants (in GHz) are given at UM06-2X/cc-pVTZ level. (For results using spin-restricted calculations, see SI Table S1.)

pVTZ level (depicted in Figure 1 using spin-unrestricted calculations, and in SI Figures S5 and S6 using spin-restricted calculations). All the energy values along with standard Gibbs free-energy change, the values of the harmonic frequencies, and the rotational constants for the various species explored along the pathways are reported in Table 1 and SI Table S1. Note that in the present work, only a single reference method like CCSD(T) was utilized, but in the radical−radical systems, a significant multireference character may be expected. To check

EQs and one for TSs). Besides these, 2-point scaled hypersphere search (2PSHS) calculations at the same level of theory were also performed to locate TSs, and the intrinsic reaction coordinate (IRC)32 computations were utilized to confirm the established connection of the located TSs to reactants and intermediates or products. The final refinement of the single-point energy of the species explored along the reaction pathways, was carried out using coupled cluster calculations33 at the UCCSD(T)/cc-pVTZ//UM06−2X/cc1928


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The Journal of Physical Chemistry A this in the explored species along the reaction pathways, T1 diagnostics procedure was applied. As evident in Table 1, the values for T1 diagnostic range between 0.015 and 0.017, which is well within the permissible limit; in fact, the multireference effects are believed to be considerable if T1 > 0.04.34 For the barrierless entrance channel (leading to HSNO2 or HSONO) analyzed using potential energy profiles, depicted in Figures 2a−c (using spin-unrestricted calculations) and in SI Figures S6−S9 (using spin-restricted calculations), a different procedure was adopted in order to locate the position of the loose transition state.35 For this, a set of relaxed scans on the PES was initially performed (with respect to S−N bond distance in HSNO2 and S−O distance in HSONO isomers) at the B3LYP/6−31G level of the theory, which was further improved using M06-2X/cc-pVTZ level of the theory (as depicted in SI Figures S6−S9). Subsequently, the vibrational frequency, calculated with varying bond distances, was obtained using a projected frequency analysis at M06-2X/cc-pVTZ level of the theory. The single point energy at each scan point in relaxed PES (analyzed in SI Figures S6−S9) was further refined at CCSD(T)/cc-pVTZ//M06-2X/cc-pVTZ level of the theory. In order to account for the dispersion effects during PES scan, the basis set superposition error (BSSE) was included using counterpoise method of Boys and Bernardi.36 However, as discussed before, the PES search using spin-restricted method is inappropriate for the open-shell species with biradical character.42b Therefore, these PES scans were also performed using spin-unrestricted formalism, and the scan points are further reoptimized at UM06-2X/cc-pVTZ level of the theory. Their final energy refinement was carried out at UCCSD(T)/ cc-pVTZ//UM06-2X/cc-pVTZ level of the theory by reading the MOs obtained at UHF/cc-pVTZ level (note that STABLE = OPT keyword was utilized again to ensure that the wave function obtained under the spin-unrestricted scheme is stable). All the computations for geometry optimization and vibrational frequencies were performed using GRRM in assistance with Gaussian09 quantum chemistry package.28 These frequencies and energy values were further used in the VTST calculations to find the value of rate constants as discussed in the next section.

III. KINETICS Radical−radical recombination reactions mainly occur through barrierless process. In such cases, energy transfer keeps on occurring through association, dissociation and collisions.37 To realize this, consider a bimolecular reaction between two radicals X• and Y• resulting in an active species XY*: X• + Y • → XY*

(2)

This association step may be followed by a reverse dissociation step, or the active XY* species are stabilized by colliding with some other molecule say M (which can be a stable XY molecule or bath gas):

XY* → X• + Y •

(3)

XY* + M → XY + M*

(4)

Figure 2. Relaxed scan of the potential energy as a function of S−N or S−O distance in the isomer (a) HS-NO2, (b) HSONOtrans, and (c) HSONOcis calculated at the ZPE-corrected UCCSD(T)/cc-pVTZ// UM06−2X/cc-pVTZ level of the theory w.r.t. separated reactants. Note that the transition state species inferred from this figure are not included in Figure 1 which only depicts the species on the PES explored using the initial GRRM search (also see spin-restricted PES scan in SI Figures S7−S10).

However, at the high-pressure limit, XY* molecules are more likely to undergo collisional stabilization rather than redissociation into X• and Y• radicals. The resulting XY molecules can then isomerize into other isomers. For the kinetics analysis of barrierless reactions, for example in the present case, those leading to the formation of HSNO2 1929


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Table 2. CVTST Trial Rate Constants (in cm3 molecule−1 s−1) for the Barrierless Reaction Channel 1: HS• + NO•2 → HSNO2 Calculated Using the Spin-Unrestricted Method, in the Temperature Range of 220−500 K, at 1.01 bar, with Varying S−N Distance (R in Å)a R (Å)

1.875

2.025

2.175

2.325

2.475

2.625

2.925

6.9 × 1016 1.1 × 1012 1.41 × 109 8.32 × 108 5.25 × 105 7.90 × 103 3.53 × 102 6.65 × 10−2 3.075

3.35 × 1013 1.89 × 109 5.23 × 106 3.27 × 104 4.85 × 103 1.19 × 102 7.67 × 10 ° 3.03 × 10−2 3.225

3.14 × 106 2.52 × 103 3.48 × 102 2.47 × 101 2.18 × 10−1 1.48 × 10−2 2.05 × 10−3 3.82 × 10−5 3.375

4.48 × 10−2 5.03 × 10−4 3.36 × 10−5 2.7 × 10−5 1.35 × 10−6 2.45 × 10−7 6.95 × 10−8 5.52 × 10−9 3.525

3.63 × 10−7 2.62 × 10−8 5.39 × 10−9 4.75 × 10−9 8.29 × 10−10 3.09 × 10−10 1.49 × 10−10 3.52 × 10−11 3.675

8.87 × 10−10 1.69 × 10−10 6.22 × 10−11 5.75 × 10−11 1.92 × 10−11 1.04 × 10−11 6.65 × 10−12 2.77 × 10−12 3.825

8.19 × 10−12 3.4 × 10−12 2.01 × 10−12 1.93 × 10−12 1.1 × 10−12 8.05 × 10−13 6.45 × 10−13 4.27 × 10−13 k1 k2 /(k1 + k2)

1.44 × 10−11 5.62 × 10−12 3.2 × 10−12 3.06 × 10−12 1.67 × 10−12 1.19 × 10−12 9.42 × 10−13 6.03 × 10−13

8.01 × 10−13 5.11 × 10−13 3.93 × 10−13 3.85 × 10−13 2.94 × 10−13 2.55 × 10−13 2.33 × 10−13 2.00 × 10−13

1.99 × 10−13 1.61 × 10−13 1.43 × 10−13 1.42 × 10−13 1.27 × 10−13 1.21 × 10−13 1.18 × 10−13 1.16 × 10−13

2.67 × 10−13 2.12 × 10−13 1.86 × 10−13 1.84 × 10−13 1.63 × 10−13 1.54 × 10−13 1.5 × 10−13 1.47 × 10−13

1.85 × 10−13 1.44 × 10−13 1.23 × 10−13 1.22 × 10−13 1.04 × 10−13 9.51 × 10−14 8.99 × 10−14 8.27 × 10−14

T (K) 221 262 295 298 347 383 415 500 R (Å) T (K)

(k1)

221 262 295 298 347 383 415 500

2.65 × 10−12 1.34 × 10−12 8.98 × 10−13 8.7 × 10−13 5.66 × 10−13 4.49 × 10−13 3.82 × 10−13 2.85 × 10−13

(k2) 2.97 × 10−13 2.29 × 10−13 1.98 × 10−13 1.95 × 10−13 1.69 × 10−13 1.59 × 10−13 1.53 × 10−13 1.47 × 10−13

a

The values in bold correspond to loose transition states. The last column list the values obtained following Miller’s unified transition state theory. For rate constants calculated using spin-restricted method, see SI Table S2.

Table 3. Same as Table S2 but for the Barrierless Reaction Channel 2: HS• + NO•2 → HSONOcis Calculated Using the SpinUnrestricted Method, in the Temperature Range of 220−500 K, at 1.01 bar, with Varying S−O Distance (R in Å)a R(Å)

1.81

1.96

2.11

2.26

2.31

2.36

2.41

4.76 × 1016 9.27 × 1011 1.37 × 109 8.16 × 108 6.13 × 105 1.03 × 104 5.04 × 102 1.15 × 100 2.56

3.75 × 1010 6.62 × 106 3.69 × 104 2.44 × 102 7.99 × 101 3.11 × 100 2.84 × 10−1 2.32 × 10−2 2.71

7.91 × 101 2.87 × 10−1 9.81 × 10−1 7.48 × 10−2 1.79 × 10−4 2.16 × 10−5 4.52 × 10−6 1.95 × 10−7 2.86

1.38 × 10 −6 8.54 × 10 −8 1.61 × 10 −8 1.41 × 10 −8 2.26 × 10 −9 8.07 × 10 −10 3.79 × 10 −10 8.49 × 10 −11 3.01

9.40 × 10 −9 1.27 × 10 −9 3.84 × 10 −10 3.50 × 10 −10 9.44 × 10 −11 4.54 × 10 −11 2.66 × 10 −11 9.37 × 10 −12 3.31

3.88 × 10 −10 8.61 × 10 −11 3.50 × 10 −11 3.25 × 10 −11 1.22 × 10 −11 7.05 × 10 −12 4.75 × 10 −12 2.21 × 10 −12 3.46

2.54 × 1013 1.44 × 109 4.03 × 106 2.52 × 106 3.79 × 104 9.43 × 102 6.14 × 100 2.50 × 10−2 3.61

2.92 × 1010 5.91 × 106 3.61 × 105 2.40 × 104 8.76 × 101 3.64 × 100 3.48 × 10−1 3.15 × 10−3

2.75 × 10−2 4.58 × 10−4 4.00 × 10−5 3.29 × 10−5 2.30 × 10−6 5.19 × 10−7 1.75 × 10−7 2.04 × 10−8

T (K) 221 262 295 298 347 383 415 500 R(Å) T (K) 221 262 295 298 347 383 415 500 a

1.14 × 1015 3.64 × 1010 7.19 × 107 4.37 × 107 4.50 × 104 9.02 × 102 5.01 × 102 1.47 × 10−2

8.17 × 1014 2.86 × 1010 5.98 × 107 3.65 × 107 4.02 × 104 8.38 × 102 4.79 × 101 1.50 × 10−1

6.48 × 1013 3.54 × 109 9.74 × 106 6.08 × 106 9.08 × 103 2.25 × 102 1.47 × 101 6.07 × 10−2

1.16 × 1012 1.31 × 108 5.60 × 105 3.63 × 105 8.90 × 102 2.94 × 101 2.37 × 100 1.51 × 10−2

2.78 × 1010 5.65 × 106 3.45 × 105 2.30 × 104 8.38 × 101 3.48 × 100 3.33 × 10−1 3.01 × 10−3

For rate constants calculated using spin-restricted method, see SI Table S3.

considered, which using the conventional TST, can be written as

and HSONO as depicted in Figures 1 and 2, the conventional transition state theory (TST) cannot be applied, unlike the reactions with intrinsic potential energy barrier. In order to calculate the rate constant for the barrierless step, the position of any loose transition state involved along the pathway needs to be determined (see later). Also note that in such cases, either the unimolecular dissociation rate constant or the bimolecular recombination rate constant can be considered because the two are related to each other by an equilibrium constant.31 In the present work, unimolecular rate constants have been

k(T ) = σ

⎛ E − E Reactant ⎞ kBT QTS ⎟, exp⎜ − TS ⎝ ⎠ h Q Reactant RT

(5)

where σ represents symmetry number referring to reaction path degeneracy (taken as 1 in the present work), kB, h, R, and T are Boltzmann’s constant, Planck’s constant, universal gas constant and temperature, respectively. QReactant and QTS in eq 5 are the overall partition functions per unit volume for reactant and 1930


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Table 4. Same as Table 2 but for the Barrierless Reaction Channel: HS• + NO•2 → HSONOtrans Calculated Using the SpinUnrestricted Method, in the Temperature Range of 220−500 K, at 1.01 bar, with Varying S−O Distance (R in Å)a R(Å)

1.778

1.928

2.078

2.228

2.378

2.678

2.828

2.978

T (K) 221 262 295 298 347 383 415 500 a

1.49 2.81 1.58 6.01 9.28 4.53 1.59 1.73

× × × × × × × ×

1042 1033 1028 1027 1021 1018 1016 1011

7.58 2.32 6.92 3.01 2.92 4.05 3.07 1.56

× × × × × × × ×

1030 1023 1018 1018 1013 1010 108 104

7.15 1.82 7.87 4.24 8.00 6.05 1.62 1.08

× × × × × × × ×

1018 1013 109 109 105 103 102 10−1

4.91 1.13 7.37 4.93 1.90 8.12 7.88 7.20

× × × × × × × ×

109 106 103 103 101 10−1 10−2 10−4

7.56 8.66 5.95 4.81 2.54 4.82 1.42 1.25

× × × × × × × ×

10−2 10−4 10−5 10−5 10−6 10−7 10−7 10−8

7.1 4.41 3.37 3.3 2.53 2.22 2.04 1.81

× × × × × × × ×

10‑13 10‑13 10‑13 10‑13 10‑13 10‑13 10‑13 10‑13

1.81 1.43 1.26 1.25 1.13 1.09 1.08 1.11

× × × × × × × ×

10−13 10−13 10−13 10−13 10−13 10−13 10−13 10−13

1.45 1.22 1.12 1.12 1.06 1.05 1.06 1.15

× × × × × × × ×

10−13 10−13 10−13 10−13 10−13 10−13 10−13 10−13

For rate constants calculated using spin-restricted method, see SI Table S2.

transition state, respectively, whereas EReactant and ETS are the ZPE-corrected energies of the reactant and the transition state, respectively. As discussed in the previous section, to locate the loose transition state, a relaxed potential-energy scan over the reaction coordinate (the bond being formed/dissociated) was carried out initially at UB3LYP/6-31G level of the theory followed by further energy refinement and projected vibrational frequency analysis at the UCCSD(T)/cc-pVTZ//UM06-2X/ cc-pVTZ level of theory at each scan point to obtain the values of partition functions. For a comparison, the restricted calculations were also carried out at B3LYP/6-31G followed by refinement at BSSE corrected CCSD(T)/cc-pVTZ//M062X/cc-pVTZ level of theory. Subsequently, at each scan-point, the trial canonical variational TST (CVTST) rate constant is calculated using eq 5. The point which corresponds to the minimum trial CVTST rate constant corresponds to the structure of loose transition state. This procedure is also repeated at different temperatures, because the minimum value of CVTST is likely to change with temperature; therefore, the position of loose transition state may vary with temperature. Note that the aforementioned trial rate constants were calculated by deploying a procedure implemented in MultiWell package of kinetic analysis.38 In this procedure, the trial CVTST rate constants are calculated at each fixed bond length structure, obtained through the relaxed potential-energy scan over the bond being formed/dissociated. An option referred to as THERMO in MultiWell package utilizes the molecular properties such as heat of formation at 0K and degrees of freedom (including vibrational and rotational) at all the fixed distances in the system to calculate the trial rate constants, ktrial (r, T, V = 0) at different temperatures (T) assuming the potential V(r) = 0 at distance r. Actual trial rate constant, ktrial (r, T) at any temperature T can then be given as ⎛ V (r ) ⎞ k trial(r , T ) = k trial(r , T , V = 0)*exp⎜ − ⎟ ⎝ kT ⎠

utilized where the internal-energy dependent unimolecular rate constants were computed using23,24 k(E) =

‡ T ‡ m‡ σext ge 1 G (E − E0 ) ‡ ge h ρ (E ) m σext

(7)

where ‡ refers to the TS. In eq 7, m, σext, ge, and h refer to the number of optical isomers, external rotation symmetry number, electronic degeneracy, and Planck’s constant, respectively. The density of states of the reactant molecule is taken as ρ(E) with energy E, and ET0 being the reaction threshold energy including the zero-point-energy and centrifugal corrections at temperature T. The term G‡ (E − ET0 ) is the sum of states of the transition state. Besides these, Miller’s unified transition state theory has been utilized to deal with the barrierless channels involving more than one transition state (observed along mode 1, see next section). For instance, in a two-TS model, if the microcanonical rate constants corresponding to the two transition states are k1(E) and k2(E), then the net effective rate constant can reliably be estimated as:27,28 keff (E) =

k1(E)k 2(E) k1(E) + k 2(E)

(8)

where ki’s are calculated using parameters of eq 7 as: ki(E) =

‡ T ‡ m‡ σext ge 1 G (E − E0i − ⟨ΔEJi⟩) ‡ ge h m σext ρ (E )

(9)

(ET0i)

In eq 9, a critical energy is taken into account for the ith CVTST rate constant, and the difference between the rotational energy (due to adiabatic external rotations) of reactant and transition state is accounted in an average way through ⟨ΔEJi⟩.27 Further, the master equation simulations (as implemented in MultiWell package) were carried out to study the temperature and pressure dependence of the rate constants for mode 1 (as discussed in the next section). As a prerequisite for these calculations, the Lennard-Jones parameters, in terms of size (σ in Å) and energy (∈/kB in K), for He bath gas were taken to be 2.5Å and 10.0K, respectively,39 and for the other isomers, these parameters were calculated through the method of Stiel and Thodos,40 taking, σ = 0.785Vc1/3 and ∈ = 0.897Tc, where Joback method41 was used to calculate the critical volume Vc and the critical temperature Tc, which comes out to be 171.5 cm3/mol and 660.7 K, respectively, with the final values of σ and ∈ taken to be 4.36 Å and 592.65K, respectively. The biexponential model i.e., Type 1,38 was used as the collisional

(6)

Note that in eq 6, trial CVTST rate constants are multiplied by an exponential term to take care of the potential energy V(r). The potential energy used for the rate constants reported in the Tables 2−4 is calculated at the ZPE-corrected UCCSD(T)/ccpVTZ//UM06−2X/cc-pVTZ level of the theory, whereas for the rate constants reported in SI Tables S2−S5, corresponding results from spin-restricted calculations are used. To obtain the rate constants for the isomerization pathways involving TSs, MultiWell’s procedure using RRKM theory was 1931


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formation of HSONOtrans and HON(S)Ocis from HSNO2 via respective transition states TS0 and TS4 seems to be kinetically infeasible because of the high activation barrier involved. Note that the formation of SNO + OH (product set P3) results from HON(S)Otrans, the formation of which requires HON(S)Ocis. Other than these two pathways, a third reaction channel was also explored, in which there is an interconversion of HSONOtrans into SON(O)H via TS2 leading to the formation of HNO + SO (product set P2). This pathway is highly improbable since it is thermodynamically as well as kinetically hindered (see later). Therefore, similar to the prediction using spin-unrestricted calculations, the spin-restricted method also predict the involvement of only two main channels, mode 1 and 2, with the latter resulting in HSO and NO radicals from HSONO, which are discussed below in detail one by one. At first sight, the barrierless mode (1), being thermodynamically more stable, is expected to be very fast and hence can be assumed to play an important role in the reaction kinetics; however, note that HSNO2 is still not reported to be isolated in any of the experimental studies known so far. In order to locate the loose transition states along the barrierless channels and to analyze the effect of species with biradical character, the relaxed PES scan using spin-unrestricted method (along with MO stability check) was carried out as described in the previous sections. These PES profiles, at the UCCSD(T)/cc-pVTZ //M06-2X/cc-pVTZ level of the theory, are provided in Figure 2. Note that in order to locate the position of the loose transition state along mode 1, the relaxed PES scan was carried out over the S−N bond being formed in HSNO2, by varying the S−N distance from 1.9Å to 4.2Å at intervals of 0.15 Å so as to explore the region where the potential energy curves may become nearly flat, as depicted in Figure 2a at the spinunrestricted UCCSD(T)//UDFT level of theory. From this figure, it can be seen that the slope of the PES approaches zero at about 3.1 Å followed by a shallow well at about 3.2 Å. The depth of this well is ∼0.7 kcal/mol. This, however, indicates that at the S−N distance of ∼ 3.2 Å, the system behaves as a biradical prereaction complex (PRC), for which the loose transition state occurs at an intermolecular distance of 3.075 Å as evident in Figure 2a, which converts the PRC into HSNO2. Hence, the outer loose transition state (the one corresponding to the intermolecular distance of 3.525 Å) is the transition state which transforms the separated reactants into the PRC. It means that although there is no real barrier for the formation of the PRC, further formation of HSNO2 takes place through a barrier of 0.73 kcal/mol. Hence, contrary to a pure barrierless channel, the spin-unrestricted calculations predict two bottlenecks involved in the formation of HSNO2. However, the corresponding PES scan using the spinrestricted method (given in SI Figure S7) predicts this interaction between the two radicals along mode 1 to be completely barrierless as evident from the slope of PES, which approaches zero at about 3.38 Å. In this case, the interaction of the SH radical with NO2 radical was further analyzed through harmonic vibrational frequency analysis as depicted in SI Figure S11, which shows the variation of logarithm of vibrational frequencies orthogonal to the reaction path at the relaxed scan points. It is evident that there is a sudden decrease in the value of lowest vibrational frequency corresponding to the normal mode in which there is simultaneous movement of SH as well as NO2 toward each other. Comparing the PES scan with that obtained using spin-unrestricted method, a sharp contrast in the net behavior (in terms of the detection of the loose

energy transfer model, and the energy transfer parameter was considered to be independent of energy and was assumed to be 200 cm−1.

IV. RESULTS AND DISCUSSION The only theoretical investigation of this reaction by Resende9 revealed that the association reaction of the SH radical with NO2 radical can occur mainly through two channels: (i) through the formation of S−N bond, (ii) through the formation of S−O bond (which can further result into two types of isomers, discussed later in this section).9 In this previous study, five important adducts were reported, all of which have been reproduced in the present work. The important connections along the reaction pathways explored on the singlet potential energy surface using spin-unrestricted and spin-restricted calculations are shown in Figure 1 and SI Figure S5, respectively. The relative energy values of the stationary points, corresponding T1 diagnostic (to check the multireference character), vibrational frequencies, and rotational constants are given in Table 1 and SI Table S1, respectively, for the spinunrestricted and spin-restricted case. The optimized structures of stationary points and the respective Cartesian coordinates are also provided in the Supporting Information. Initially, the mercaptyl radical may form adduct with the NO2 via two modes along barrierless pathways: along mode 1, S atom of HS combine with N of NO2 which results in the formation of HSNO2, whereas along mode 2, it combines with O atom of NO2 resulting in the formation of HSONO: mode 1: HS• + NO•2 → HSNO2

(10)

mode 2: HS• + ONO• → HSONO(trans or cis)

(11)

Mode 1 is likely to occur through a barrierless process resulting in the formation of HSNO 2 with binding energy of − 33.25kcal/mol as predicted at UCCSD(T)/cc-pVTZ// UM06-2X/cc-pVTZ level of the theory. This is readily feasible because of the presence of the unpaired electron on S- and Natomic centers of the reactants. Along mode 2, another barrierless process leads to the formation of HSONO, which though is thermodynamically slightly less stable than HSNO2 as evident in Figure 1. Therefore, mode 1 thermodynamically dominates over mode 2, which means that initially the formation of HSNO2 is more likely; however, it can isomerize into a trans-isomer HSONOtrans via transition state TS0 as shown in Figure 1. The trans-isomer, HSONOtrans, may further isomerize to cis-isomer HSONOcis via transition state TS1, but the formation of HSONOtrans from HSNO2 via respective transition states TS0 seems to be kinetically infeasible because of high activation barrier involved. Overall, two main channels (via mode 1 and 2) may be involved in this reaction, and only mode 2 can result in the formation of HSO and NO radicals via cis- or trans-HSONO. Note that the spin-restricted calculations also reveal that mode 1 thermodynamically dominates over mode 2, which means that initially the formation of HSNO2 is more likely which; however, can isomerize into a trans-isomer HSONOtrans via transition state TS0 or to a relatively less stable HON(S)Ocis via TS4 shown in SI Figure S5. The trans-isomer of HSONOtrans may isomerize to cis-isomer HSONOcis(a) via transition state TS1 or to HON(S)Otrans via TS5. The cisisomer HSONOcis(a) can further isomerize to another cis-isomer HSONOcis(b) via TS3, albeit these can also result from barrierless channels depicted in SI Figure S5. However, the 1932


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HSONOcis, and HSONOtrans, were calculated at different temperatures as described in the previous section. As evident in Table 2, the minimum trial rate constant for mode (1) leading to the formation of HSNO2 at 298K is found to be 1.22 × 10−13 cm3 molecule−1 sec−1 calculated using Miller’s unified transition state theory with a two-TS model27,28 because along this mode two bottlenecks are predicted to be involved. This calculated effective rate constant as well as the rate constants (k1 and k2) corresponding to the two loose transitions states are significantly lower than the experimentally observed rate constant (found to be between 10−10-10−12 cm3 molecule−1 sec−1), thereby, ruling out contribution of mode 1 toward the reaction rates. The rate constant for the formation of trans-HSONO isomer is also found to be the order of 10−13 cm3 molecule−1 sec−1 at 298 K as evident in Table 4, ruling out involvement of this channel as well. Moreover this channel is predicted to involve a barrier at ∼ 3.43Å. However, using the spin-unrestricted analysis of HSONOcis, as evident in Figures 2c, we found that with conformational changes, an isomer similar to HSONOcis(a) isomer (predicted using spin-restricted calculations) can form through barrierless channel when the distance between HS and NO2 radical approaches 2.36 Å as also discussed before. Therefore the rate constants were also calculated for it in the distance range of 1.81−2.36 Å as analyzed in Table 3, and the minimum rate constant value for this association at 298 K is found to be 3.25 × 10−11 cm3 molecule−1 sec−1, which is in excellent agreement with the experimental reported range of rate constants. Note that although the isomer HSONOcis(a) could not be traced directly in the spin-unrestricted GRRM search, but the sudden change in the geometry of HSONOcis at distance 2.36 Å reveals HSONOcis(a) as evident in Figure 2c. However, for the formation of other cis-isomer HSONOcis(b), around the intermolecular distance 2.41Å, a barrier of about 12 kcal/mol is involved as evident in Figure 2c. This may be the reason that it has never been detected in any of the experimental studies irrespective of reaction temperature, which is another important result from the present work. The spin-restricted calculations also predict the formation of isomer HSONOcis(b) to involve a high barrier as can be seen in SI Figures S9 and S10. However, if only the spin-restricted calculations have to be believed, then as evident from SI Table S2, it can be seen that the rate constant at S−N distance of 3.38 Å is 1.84 × 10−13 cm3 molecule−1 sec−1. However, in range of S−N distance of 2.78− 2.98Å, the trial CVTST rate constant varies between 10−10 and 10−12 cm3 molecule−1 sec−1 at 298K, similar to that reported in the experimental studies. Note that these S−N distances lie toward HS-NO2 and therefore might be influential. Moreover, the position of the loose transition state shifts to the lower interatomic distances with an increase in the temperature (see text below). On the other hand, the minimum CVTST rate constants listed in SI Table S3 corresponding to both the cisisomers of HSONO are found to be the same, which is 1.79 × 10−19 cm3 molecule−1 sec−1 at S−O distance 4.19 Å, whereas the rate constant for the trans-isomer is 4.70 × 10−31 cm3 molecule−1 sec−1 (depicted in SI Table S4), which is too low for this mode to be operative. However, note that at S−O distance of 3.8 Å, which lies toward the HSONOcis(a) or cis(b), the rate constant is 1.38 × 10−12 cm3 molecule−1 sec−1 at 298 K, which may also contribute to the experimentally observed rate constants. However, note that while using results from spinrestricted calculations, one has to make all these arbitrary

transition state) is quite evident, and overall the two energy profiles seems quite different, in particular, involving two bottlenecks along mode 1. On the similar lines, the other barrierless mode (2), in which HS radical approaches toward NO2 radical through the oxygen atom, was investigated. This mode is also relevant from the point of view that the dissociation of the isomer (HSONO) formed along this mode may lead to the products HSO and NO, note that only the former has been detected experimentally. Similar to the case of HSNO2, the relaxed PES scan was carried out but over the S−O bond in cis- and trans-isomers of HSONO, as depicted in the corresponding potential energy profiles in Figure 2b,c at the UCCSD(T)// DFT level. Figure 2b, related to HSONOtrans, shows that the PES curve becomes flat around 2.83 Å corresponding to separated reactants. The corresponding PES obtained using the spin-restricted method is given in SI Figure S8. Here also, the formation of HSONOtrans is predicted completely different by the two spin formalisms. It should be noted that the rate constants calculated for this channel through spin-restricted calculations (see later) were found to be too low to make any significant contribution to the net reaction rate. However, the spin-unrestricted method reveals this channel to involve a small barrier of height 1.48 kcal/mol when the distance between the reactants approaches 3.42 Å as evident from Figure 2b (depicting biradical species near the entrance channel).42b In fact, these relaxed scans followed by the VTST rate constant calculations (see later) reveal that both the channels (1 and 2) are competing, although the existence of two bottlenecks (predicted by the spin-unrestricted calculations) for the formation of HSNO2 may be the reason for its nonexistence despite it being the thermodynamically most stable isomer, which is actually in accordance with the experimental studies. However, the formation of cis-isomer, HSONOcis, is somewhat unusual, as depicted in Figures 2c using spin-unrestricted calculations and in SI Figures S9 and S10 using spin-restricted calculations. After a careful analysis, it can be concluded that this channel also show a typical behavior of a barrierless process. Note that in Figure 2c, it can be seen that at the S−O distance of about 2.36 Å, the geometry of the system changes dramatically shifting between isomers similar to cis(a) and cis(b) observed using spin-restricted calculations, which may falsely lead to the conclusion that there is actually a barrier. At distances less than 2.36 Å, the sulfur atom of SH radical points toward the oxygen atom, say O(1), but when the distance between S-O(1) approaches 2.36Å, S atom points toward O(2) of NO2. Clearly, the species at 2.36 Å corresponds to the separated reactants. The reason for this unconventional behavior along the S−O association as compared with the S− N association can be explained as follows: It can be expected that when SH radical begins to interact with the oxygen atom of NO2, the two oxygen atoms compete with each other for association with sulfur atom. For instance, if the SH radical is approaching the oxygen atom O(1), then as soon as the distance between them comes close to 2.3 Å, the other oxygen atom O(2) will be in a position so as to attract the SH radical toward itself and vice-versa. Therefore, contrary to what is expected, it can be concluded that mode 2 may lead to HSO and NO radicals through barrierless channels involving cis- and trans-HSONO. To further confirm this fact, the CVTST rate constants listed in Tables 2−4 (using the spin-unrestricted method) and SI Tables S2−S5 (using the spin-restricted method), for the channels corresponding to HSNO 2 , 1933


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Figure 3. Logarithm of trial CVTST rate constants (listed in Tables 2−4) for (a) mode 1 leading to the formation of HSNO2, (b) mode 2 leading to the formation of HSONOtrans, (c and d) mode 2 leading to the formation of HSONOcis at temperatures 221, 298, 500, and 1000 K.

methods. At each temperature, simulations were carried out, for example for mode 1, in the pressure range of 0.001−2 bar, which resulted in the fractional yields. The latter were further used as weighting factor with limiting CVTST rate constants to estimate the pressure-dependence as analyzed in Figure 4 (and in SI Figure S12 using the spin-restricted method). As observed in the case of the spin-unrestricted case, the formation of HSONO dominates the formation of HSNO2, and therefore, the variation in the rate constants for both the HSONO isomers, cis- as well as trans-, was analyzed as shown in Figure 4. It is clear from the figure that the formation of cis-HSONO dominates the formation of trans-analogue at low temperatures and pressures. However, in the temperature range of 1000 K, when the reaction is carried out at high pressure, trans-HSONO may be formed in preference to the cis-HSONO. Contrary to this, in the case of spin-restricted analysis presented in SI Figure S12, mode 1 is observed to be the most feasible reaction channel than the mode 2 leading to cis-HSONO. As evident, at low pressure, the rate constants exhibit significant departure from the conventional Arrhenius behavior with the reaction rate for the barrierless pathway (via mode 1), becoming temperature-independent, particularly at low temperatures and pressures, which is in agreement with the findings by Friedl et al.,2 that the reaction shows no pressure dependence in the range of 2−8 Torr of He bath gas. However, note that only the

assumptions in order to arrive at the experimentally observed rates. The temperature dependence of the rate constants for all the aforementioned channels is further analyzed in Figure 3 (using spin-unrestricted calculations) and in SI Figure S12 (using spinrestricted calculations). At each temperature, the minimum value of the rate constant corresponds to the position of the loose transition state at that temperature. Figure 3a clearly reveals the presence of two transition states in the formation of the isomer HSNO2 in the temperature range of 221−1000 K, confirming the analysis presented before, contrary to that observed using spin-restricted calculations. A step-like feature seen in this figure actually depicts two minima corresponding to two TSs, which has also been predicted in a study on HO +OClO reaction system.27 Furthermore, the variations seen in Figure 3c are due to conformational change in the cis-HSONO isomer as observed along potential energy profile analyzed in Figure 2c. However, no such abrupt variation is visible in Figure 3d, which actually corresponds to the barrierless channel leading to an isomer similar to cis(a) isomer of HSONO observed in spin-restricted calculations (note the difference in the range of S-O distances in Figure 3c,d). The pressure dependence of the rate constants corresponding to different modes was also analyzed through the master equation simulations using both spin-unrestricted and spin-restricted 1934


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Figure 1 and SI Figure S5. The isomerization rate constants for these pathways, provided in SI Table S6, were calculated using RRKM theory through MultiWell package. Note that RRKM theory was chosen for the present work in order to additionally check if there is some competing reaction path, passing through the saddle point, which may be contributing toward the overall rate constant observed besides the main contribution to the rate constants being from the barrierless pathways. The rate constants for isomerization of HSONO between its cis- and trans- isomers are found to be quite high indicating that the three isomers cis(a), cis(b), and trans are readily interconvertible. Note that all of these three may readily dissociate into HSO and NO as evident from Gibbs free-energy profile in SI Figure S6. However, the rate constant for conversion of HSNO2 to HON(S)Ocis is relatively quite low (6.27 × 10−7 sec−1), whereas the two geometric isomers HON(S)Ocis and HON(S)Otrans are readily interconvertible with a rate of ∼107 sec−1. Note that so far, no attempt has been made to identify these isomers experimentally.

Figure 4. Arrhenius plots for the rate constants calculated for the entrance channels corresponding to the formation of cis-HSONO and trans-HSONO at different pressures.

V. CONCLUSIONS Finally, from the aforementioned analysis of rate constants using spin-unrestricted calculations, it seems that the formation of HSNO2 can be ruled out because of the presence of two bottlenecks: one connecting the separated reactants to the prereaction complex (PRC) and the second connecting the PRC to HSNO2. The formation of HSONO, in particular cisisomer, seems to be the most feasible barrierless channel in the course of this radical−radical reaction, which in fact can ultimately result in the production of HSO radical, which is further substantiated by the fact that the rate constant of 3.25 × 10−11 cm3 molecule−1 sec−1 at 298K computed for this channel is found to be in excellent agreement with the experimentally observed range of rate constants. This is contrary to the results of spin-restricted calculations which remain inconclusive about the reaction mechanism, and to arrive at the rate constant in agreement with the experimental results using this, one has to assume several other processes as outlined at the end of the previous section. Therefore, the results using spin-unrestricted method seem to settle the conflicts about the mechanism and kinetics of this radical−radical reaction, though a multireference quantum-mechanical method may reveal some other interesting facets of this reaction.

negative-temperature dependence of the overall rate constant has been experimentally reported,4 as clearly predicted for the cis-HSONO in Figure 4 using spin-unrestricted calculations. It is quite clear that whereas the rate constants for mode 2 calculated using spin-unrestricted methods are found to be in agreement with the experimental rate constants, the spinrestricted methods are unable to find a definite answer to the issues outlined in the beginning. The latter predicts that the production of HSNO2 is more likely though the formation of HSONO, in particular cis-isomers, both cis-(a) and cis-(b), cannot be dismissed, which in fact can ultimately result in the production of HSO and NO radicals as revealed by the spinunrestricted computations. Note that if it is presumed that the HSO radical, which has been reported to be detected in insignificant amounts, results from secondary processes in the experimental setup then the fate of HSNO2 remains unanswered if spin-restricted computations have to be believed. To the contrary, if it is presumed that the HSO radical results from cis-HSONO, then the fate of NO radical remains unanswered. However, there is no ambiguity in deciding the fate of various species involved. Note that in all the experimental studies, H2S has been used to generate HS radical, which means the system contains H radicals as well. Therefore, there is high possibility that the H radical reacts with HSNO2 to regenerate NO2 and H2S. Therefore, the rate of this reaction may also contribute toward the overall rate, and hence, the fate of HSNO2 is self-evident. On the other hand, if the formation of cis-HSONO is also assumed to be another barrierless channel in the title reaction, though with relatively slower rate than that in the case of HSNO2 as explained before, then the HSO radical would have been formed in insignificant amounts, which is actually the case observed experimentally.3−6,9 The NO radical, resulting from the same channel, should also be formed in insignificant amounts, but it is likely to get oxidized to regenerate the NO2 radical. Any secondary reaction proposed for the formation of HSO radicals are hence ruled out, but all these require a detailed experimental input which is missing from the studies reported so far. Besides the aforementioned barrierless pathways, the PES of the reaction system may also involve several isomerization pathways with a finite energy barrier passing through respective TSs depicted in

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.7b06916. Figures S1−S4 depicting the structures of relevant EQs obtained during different GRRM search and their optimized geometries; Figures S5 and S6 depicting the important connections using spin-restricted calculations; Figures S7−S10 representing the relaxed scans of relevant isomers; Figure S11 depicting logarithm of vibrational frequencies for mode 1; Figure S12 depicting Arrhenius plots obtained using spin-restricted calculations; Table S1 listing the relative energies and other parameters of all the stationary points; Tables S2−S4 for the microcanonical rate constant of different reaction modes using spin-restricted calculations; Table S5 listing rate constants at different temperatures and pressures for mode 1; Table S6 summarizing the RRKM unimolecular 1935


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(14) Maeda, S.; Ohno, K. A new global reaction route map on the potential energy surface of H2CO with unrestricted level. Chem. Phys. Lett. 2008, 460, 55−58. (15) Maeda, S.; Ohno, K.; Morokuma, K. Systematic exploration of the mechanism of chemical reactions: the global reaction route mapping (GRRM) strategy using the ADDF and AFIR methods. Phys. Chem. Chem. Phys. 2013, 15, 3683−3701. (16) Kaur, G.; Vikas. On the mechanism of intramolecular nitrogenatom hopping in the carbon chain of C6N radical: A Plausible 3c−4e crossover Π Long-Bond. J. Comput. Chem. 2014, 35, 1568−1576. (17) Kaur, R.; Vikas. Mechanisms for the inversion of chirality: global reaction route mapping of stereochemical pathways in a probable chiral extraterrestrial molecule, 2- aminopropionitrile. J. Chem. Phys. 2015, 142, 074307. (18) Kaur, G.; Vikas. Exploring water catalysis in the reaction of thioformic acid with hydroxyl radical: a global reaction route mapping perspective. RSC Adv. 2015, 5, 82587−82604. (19) Sangwan, P.; Vikas. Exploring the metastability and the pathways for polyanionic isomerization in the dianions and trianions of doubly- and triply-deprotonated benzene. Theor. Chem. Acc. 2015, 134, 99. (20) Kaur, R.; Vikas. Exploring the role of a single water molecule in the tropospheric reaction of glycolaldehyde with an OH radical: a mechanistic and kinetics study. RSC Adv. 2016, 6, 29080−29098. (21) Vikas; Sangwan, P.; Kaur, R. Chemical pathways for polyanionic isomerisation in the metastable anions of tetra-deprotonated naphthalene: An intra-molecular inter-ring proton-transfer. Phys. Chem. Chem. Phys. 2017, 19, 11571. (22) Kaur, R.; Vikas. From nitrogen inversion in amines to stereoinversion in aminium salts: role of a single water molecule. Theor. Chem. Acc. 2017, 136, 1−16. (23) Forst, W. Unimolecular Reaction: A Concise Introduction; Cambridge University Press: Cambridge, U.K., 2003. (24) Baer, T.; Hase, W. L. Unimolecular Reaction Dynamics: Theory and Experiments: Theory and Experiments; Oxford University Press: Oxford, U.K., 1996. (25) Miller, J. A.; Klippenstein, S. J. Master equation methods in gas phase chemical kinetics. J. Phys. Chem. A 2006, 110, 10528−10544. (26) Miller, W. H. Unified statistical model for “complex” and “direct” reaction mechanisms. J. Chem. Phys. 1976, 65, 2216−2223. (27) Yang, L.; Sonk, J. A.; Barker, J. R. HO + OClO reaction system: featuring a barrierless entrance channel with two transition states. J. Phys. Chem. A 2015, 119, 5723−5731. (28) Greenwald, E. E.; North, S. W.; Georgievskii, Y.; Klippenstein, S. J. A two transition state model for radical-molecule reactions: a case study of the addition of OH to C2H4. J. Phys. Chem. A 2005, 109, 6031−6044. (29) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A. et al. Gaussian 09, Revision D.01; Gaussian, Inc.: Wallingford, 2013. (30) Becke, A. D. A new mixing of Hartree−Fock and local densityfunctional theories. J. Chem. Phys. 1993, 98, 1372−1377. (31) Zhao, Y.; Truhlar, D. G. The M06 suite of density functionals for main group thermochemistry, thermochemical kinetics, noncovalent interactions, excited states, And transition elements: two new functionals and systematic testing Of four M06-class functionals and 12 other functional. Theor. Chem. Acc. 2008, 120, 215−241. (32) Page, M.; McIver, J. W., Jr On evaluating the reaction path Hamiltonian. J. Chem. Phys. 1988, 88, 922−935. (33) Raghavachari, K.; Trucks, G. W.; Pople, J. A.; Head-Gordon, M. A fifth-order perturbation comparison of electron correlation theories. Chem. Phys. Lett. 1989, 157, 479−483. (34) Rienstra-Kiracofe, J. C.; Allen, W. D.; Schaefer, H. F. The C2H5 + o2 reaction mechanism: high-level ab initio characterizations. J. Phys. Chem. A 2000, 104, 9823−9840. (35) Yang, L.; Liu, J-Y.; Luo, C.; Barker, J. R. Theoretical study on the kinetics of the reaction CH2Br + NO2. J. Phys. Chem. A 2014, 118, 3313−3318.

rate constants for the isomerization pathways with intrinsic energy barrier; and Cartesian coordinates (in Å), energy and zero-point vibrational energy (ZPVE) of key equilibrium structures (EQs) obtained at UM06− 2X/cc-pVTZ level of the theory are also provided (PDF)

AUTHOR INFORMATION

Corresponding Author

*E-mails: [email protected], [email protected]. Phone: +919855712099, +91-172-2534408. ORCID

Vikas: 0000-0002-3901-5205 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS One of the authors, RK, thanks Council of Scientific and Industrial Research (CSIR), New Delhi (India) for providing financial support in the form of SRF(NET) fellowship. The authors are also grateful to Prof. Koichi Ohno for providing GRRM program, Prof. John R. Barker for Multiwell-2016, and to the Department of Chemistry, Panjab University, Chandigarh for providing other computational software and resources. Prof. T. S. Dibble (from ESF, SUNY) pointed out refs 42a and 42b after reading the Just Accepted Manuscript version of the paper, emphasizing the necessity for the critical evaluation of character of transition state species in such reactions.

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