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Pathways for the OH + Br # HOBr + Br and HOBr + Br # HBr + BrO Reactions Hongyan Wang, Yudong Qiu, and Henry F. Schaefer J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.5b11524 • Publication Date (Web): 14 Jan 2016 Downloaded from http://pubs.acs.org on January 16, 2016

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The Journal of Physical Chemistry

Pathways for the OH + Br2 → HOBr + Br and HOBr + Br → HBr + BrO Reactions Hongyan Wang,a, b, c* Yudong Qiuc, and Henry F. Schaefer IIIc a

School of Physical Science and Technology, Southwest Jiaotong University b

Key Laboratory of Advanced Technologies of Materials, Ministry of Education of China Chengdu 610031, China

c

Department of Chemistry and Center for Computational Quantum Chemistry, University of Georgia, Athens, Georgia 30602, USA

E-mail: [email protected]

Abstract: The OH radical reaction with Br2 and the subsequent reaction HOBr + Br are of exceptional importance to atmospheric chemistry and environmental chemistry. The entrance complex, transition state, and exit complex for both reactions have been determined using the coupled-cluster method with single, double, and perturbative triple excitations CCSD(T) with correlation consistent basis sets up to size cc-pV5Z and cc-pV5Z-PP. Coupled cluster effects with full triples (CCSDT) and full quadruples (CCSDTQ) are explicitly investigated. Scalar relativistic effects, spin-orbit coupling and zero-point vibrational energy corrections are evaluated. The results from the all-electron basis sets are compared with those from the effective core potential (ECP) pseudopotential (PP) basis sets. The results are consistent. The OH + Br2 reaction is predicted to be exdothermic 4.1±0.5 kcal/mol, compared to experiment, 3.9±0.2 kcal/mol. The entrance complex HO … BrBr is bound by 2.2 ± 0.2 kcal/mol. The transition state lies similarly well below the reactants OH + Br2. The exit complex 1

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HOBr…Br is bound by 2.7±0.6 kcal/mol relative to separated HOBr + Br. The endothermicity of the reaction HOBr + Br → HBr + BrO is 9.6±0.7 kcal/mol, compared with experiment 8.7±0.3 kcal/mol. For the more important reverse (exothermic) HBr + BrO reaction, the entrance complex BrO…HBr is bound by 1.8±0.6 kcal/mol. The barrier for the HBr + BrO reaction is 6.8±0.9 kcal/mol. The exit complex (Br…HOBr) for the HBr + BrO reaction is bound by 1.9±0.2 kcal/mol with respect to the products HOBr + Br.

Key Words: Potential energy profiles, coupled-cluster theory, scalar relativistic effects, spin-orbit coupling, hydroxyl radical reactions, bromine reactions, atmospheric chemistry, environmental chemistry, bromine chemistry, bromine atom reactions, combustion chemistry.

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1. Introduction Due to the fact that bromine is considerably more active in depleting ozone than chlorine, the radical OH reaction with molecular bromine Br2 plays an important role in both atmospheric and combustion chemistry.1 In addition, via the OH + Br2 → HOBr + Br reaction, the products HOBr and Br are also important species relating to brominated flame retardants and waste incineration processes.2 Like the valence isoelectronic OH + Cl2 reaction, the OH + Br2 system has often been the subject of experimental studies. Poulet, Laverdet, and Le Bras firstly reported (1983) the rate constant for the OH + Br2 reaction using electron paramagnetic resonance spectroscopy with laser-induced fluorescence for OH analysis. 3 In their experiments the products HOBr + Br were observed as the unique channel, with the reaction concluded to be exothermic by 9.1 kcal/mol and the rate constant 2.5×1012 cm3 molecule-1 s-1. The same rate constant at room temperature of the OH + Br2 → HOBr + Br reaction was later measured experimentally to be 3.18×1013 by Loewenstein and Anderson (1984);4 2.1×1013 by Boodaghians, Hall, and Wayne (1987); 5 1.19×1013 cm3 molecule-1 s-1 by Gilles, Burkholder, and Ravishankara (1999);6 and 1.1×1013 cm3 molecule-1 s-1 by Bedjanian, Le Bras, and Poulet (1999).7 In 2006, Bryukov, Dellinger, and Knyazev8 investigated the dynamics of the OH + Br2 reaction via a pulsed laser photolysis/pulsed-laser-induced fluorescence technique and added theoretical investigations of the potential energy surface (PES) for the reaction. The reaction enthalpy at 0 K for the pathway OH + Br2 → HOBr + Br were obtained via density functional theory (BH&HLYP) and the CCSD(T)/aug-cc-pVTZ method. However the Bryukov predicted reaction enthalpy at 0 K (-1.8 or -5.6 kcal/mol) is not in 3



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close agreement with experiment (-3.9±0.2 kcal/mol).9 Latter computational study did not examine the reaction HOBr + Br → HBr + BrO or the exit complex for the OH + Br2 → HOBr + Br reaction. The “Gold Standard” CCSD(T) method with correlation consistent basis sets up to cc-pV6Z has recently been successfully applied to the isovalent OH + Cl2 system.10 That reliable theoretical assessment is in excellent agreement with experiment for both the endothermicity and activation energy. In the present research the OH + Br2 reaction will be investigated with high level theoretical methods and compared with the OH + Cl2 system.

2. Methodology High level theoretical methods, namely the partially spin-restricted coupled-cluster single and double substitution method with perturbative treatment of triple excitations RCCSD(T),11-14 as implemented in the Molpro program15 were used here. With this method we determine and characterize the stationary points on the potential energy surface for the OH + Br2 reaction and the subsequent reaction HOBr + Br. The correlation-consistent polarized valence basis sets of Dunning, Kendall, Harrison, Woon, and Peterson, including cc-pVTZ, cc-pVQZ, and cc-pV5Z, are employed to optimize the structures of the reactants, entrance complexes, transition states, exit complexes, and products.16-19 The single reference nature of the stationary points is demonstrated by the fact that the T1 diagnostics and T2 amplitudes in all CCSD(T) computations are smaller than 0.05 and 0.09, respectively. The stationary points are characterized by harmonic vibrational frequency analyses. Spin-restricted Hatree-Fock wavefunctions are used for 4


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both the closed shell and open-shell species throughout this research. The scalar relativistic effects associated with the bromine atom are considered using two different methods. In the first method, the all-electron basis sets cc-pVXZ (X= T, Q, 5) were used for the H, O, and Br atoms, and the scalar-relativistic corrections are evaluated via first-order perturbation theory (including the mass-velocity and Darwin terms) by means of the Pauli Hamiltonian.20-22 In the second method, the effective core potential (ECP) basis sets, cc-pVXZ-PP (X= T, Q, 5),23 which are designed to include scalar relativistic effects, were used for the bromine atom. In the PP basis set for Br, the 10 inner core electrons (1s22s22p6) of Br are replaced by energy-consistent pseudopotential

(PPs),

which

were

adjusted

to

atomic

multi-configurational

Dirac-Hartree-Fock results. In the CCSD(T) studies, the 1s-like MO for oxygen and the 1s22s22p63s23p63d10 like MOs for bromine are frozen, i.e., fully occupied in the coupled cluster treatments. Spin-orbit (SO) computations, based on the corresponding CCSD(T)/cc-pVXZ optimized geometries, were predicted using a multi-configurational self-consistent field (MCSCF) approach, in which spin-orbit matrices are set up and spin-orbit integrals are calculated within CI calculations.24,

25

All the MCSCF and CI computations utilize the

full-valence active space, i.e., 21 electrons in 13 spatial orbitals (21e, 13o) for the tetra-atomic entrance and exit complexes and transition states; (7e,5o) for OH; (7e, 4o) for Br; (13e, 8o) for BrO; and (14e, 9o) for HOBr. For the MCSCF computations the usual frozen-core approach is employed. The SO computations employ the Breit−Pauli operator in the interacting-states approach. 26

The SO orbitals are obtained by

diagonalizing the effective Fock operator. The three lowest-energy non-SO doublet

5



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electronic states are computed for all the stationary points and transition states, in which the SO eigenstates are obtained by diagonalizing the 6 × 6 SO matrices. All these MCSCF, and SO computations are performed with the Molpro package.13 The final relative energies were obtained using the focal-point analysis (FPA) approach of Allen and coworkers.27,28 The core-valence cc-pVXZ (X= T, Q, 5) basis sets were utilized for extrapolation to the complete basis set (CBS) limit, employing the three-parameter exponential function for the HF energy (Eq. 1) and two-parameter polynomial formula for electron correlation energies (Eq. 2). We note that the basis set superposition error (BSSE) arising from the incompleteness of the basis sets is greatly reduced if not eliminated in this treatment. = + = 3, 4, 5

(1)

+ = 4, 5 =

(2)

Higher order correlation effects, including coupled cluster theory with full single, double, and triple excitations (CCSDT), as well as quadruple excitations (CCSDTQ)29, were treated by the focal point additivity scheme. The MRCC program of Kállay 30 , 31 interfaced with Molpro was used to obtain the unrestricted coupled-cluster energies. The final energies were appended by zero-point vibrational energy corrections (∆ZPVE) computed at CCSD(T)/cc-pV5Z level, and relativistic corrections (∆rel) at HF/cc-pV5Z level, as well as spin-orbit corrections (∆SO) determined with MRCI/cc-pV5Z.

3. Results and Discussions 3.1 Stationary Point Geometries The reactants, entrance complexes, transition states, exit complexes, and products 6


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were optimized with the CCSD(T) method for the reactions (Figures 1-4)

OH + Br2  → HOBr + Br

(A)

HOBr + Br  → HBr + BrO

(B)

On the HOBrBr potential energy surface (PES), a total of four complexes and two transition states (TSA, TSB) were predicted by the CCSD(T) method. The optimized energies E (hartree), harmonic vibrational frequencies ω (cm-1), and zero-point vibrational energies for all the stationary points are reported in Table 1 and 2. The CCSD(T) geometries using the all-electron basis set cc-pVXZ and the effective core potential basis set cc-pVXZ-PP (X=T, Q, 5) are almost the same. The entrance complex A (H-O…Br-Br) and transition state A (Figure 1 and 2) are found to analogous to those for the OH + Cl2 system.10 The OH radical approaches Br2 at an angle 110 degrees, i.e., the H-O and Br-Br moieties are not collinear. The entrance complex H-O…Br-Br in the reactant valley is coplanar. The resulting equilibrium O…Br distance is 2.928 Å (O…Cl distance 2.924 Å in H-O…Cl-Cl) with the CCSD(T)/cc-pVQZ method.

The scalar

relativistic effects shorten the O…Br distance from 2.912 Å (5Z) to 2.870 Å with the cc-pV5Z-PP basis set. In the transition state (TSA) for Reaction A, the O…Br linkage twists out of the plane to dihedral angle 67○ , with an imaginary vibrational frequency of 220i cm-1 (cc-pVTZ)/ 206i cm-1 (cc-pVTZ-PP), 184i cm-1 (cc-pVQZ)/ 168i cm-1 (cc-pVQZ-PP), and 176i cm-1 (cc-pV5Z)/ 156i cm-1 (cc-pV5Z-PP). The corresponding twisting normal mode leads to Exit Complex A, namely Br…H-O-Br in the product valley with a nonlinear Br… H-O arrangment. This is qualitatively different from the analogous 7



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chlorine system.10 In the latter case the Cl…H-O-Cl moiety has a collinear Cl…H-O structure. The Br…H and Br…Br connections with distances 2.625 Å and 2.945 Å (cc-pV5Z) or 2.632 Å and 2.932 Å (cc-pV5Z-PP) in Exit Complex A break to yield the separated products HOBr and Br. For Reaction B (structures seen in Figure 3 and 4), namely HOBr + Br, the entrance complex B and Exit Complex B are analogous to the valence isoelectronic HOCl + Cl system. However our transition state TSB is not coplanar, in distinction from HOCl + Cl system. The resulting equilibrium H…Br distance in the entrance complex B is 2.600 Å (cc-pVQZ) or 2.594 Å (cc-pVQZ-PP), longer than the analogous H…Cl distance 2.459 Å in H-O…Cl-Cl with the CCSD(T)/cc-pVQZ method. The angle ∠Br-O-H is 103 ○ (cc-pVQZ and

cc-pVQZ-PP),while ∠Cl-O-H is 107○(cc-pVQZ) in valence

isoelectronic entrance complex Cl-O-H…Cl. Following the Br…H vibrational coordinate, we find transition state TSB, which has a dihedral angle 88○out of the plane, different from TSB on the analogous HOCl + Cl reaction potential energy surface. In the chlorine case the ClHOCl transition state is coplanar, and the Cl-H-O moiety is collinear. The transition state TSB has a large imaginary vibrational frequency of 1778i cm-1 (cc-pVTZ)/ 1741i cm-1 (cc-pVTZ-PP), 1759i cm-1 (cc-pVQZ)/1706i cm-1 (cc-pVQZ-PP) or 1755i cm-1 (cc-pV5Z) /1716i cm-1 (cc-pV5Z-PP). This normal mode leads to Exit Complex B, namely Br-O…H-Br with O…H distance 2.054 Å(cc-pV5Z)/ 2.051 Å(cc-pV5Z-PP). Subsequently the O…H bond is broken, leading to products BrO and HBr.

8


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3.2 Energetics i. Classical Energetics Relative energies with and without relativistic effects (REL), spin-orbit, and zero-point vibrational energy (ZPVE) corrections for all stationary points of both reactions are reported in Figures 5-8. The analogous energies with relativistic effects (REL), spin-orbit, and zero-point vibrational energy (ZPVE) corrections are given in parentheses. The cc-pVXZ and cc-pVXZ-PP (X = T, Q, 5) basis sets give the same relative energy ordering. Reaction A is predicted to be exothermic by 4.6, 4.0, and 3.7 kcal/mol with the cc-pVTZ, cc-pVQZ, and cc-pV5Z basis sets; and 4.7, 4.0, and 3.7 kcal/mol with the cc-pVTZ-PP, cc-pVQZ-PP, and cc-pV5Z-PP basis sets, respectively, without any corrections. The results from the cc-pVXZ and cc-pVXZ-PP (X = T, Q, 5) are thus very consistent. The entrance complex H-O…Br-Br is predicted to lie 2.7/2.8, 2.6/2.7, 2.5/2.7 kcal/mol below the separated reactants OH + Br2 with the cc-pVXZ/cc-pVXZ-PP(X = T, Q, 5) basis sets. Transition state A lies at every level of theory above the energy of entrance complex A. The energy barrier is sensitive to the different basis sets. The predicted classical reaction barrier height (with respect to separated reactants) is very small, i.e., 0.7/0.3, -0.4/-0.9, and -0.7/-1.2 kcal/mol, respectively, with the TZ/TZ-PP, QZ/QZ-PP, and 5Z/5Z-PP basis sets. The barrier is predicted to lie below the energy of the reactants with both the QZ/QZ-PP, and 5Z/5Z-PP basis sets. This differs from the isovalent OH + Cl2 reaction, where the barrier is located 3.8, 2.2, and 1.2 kcal/mol above the reactants with the cc-pVTZ, cc-pVQZ, and cc-pV5Z basis sets. The Reaction A exit complex

Br … H-O-Br

is

predicted

to

lie

8.1

kcal/mol(cc-pV5Z)

9


or

8.2


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kcal/mol(cc-pV5Z-PP) below the separated reactants OH + Br2; and 4.4 kcal/mol (cc-pV5Z) or 4.5 kcal/mol(cc-pV5Z-PP) below the separated products HOBr+Br. Reaction B (Figure 6), HOBr + Br → HBr + BrO, is predicted to be endothermic by 12.4/13.2, 12.0/12.7, and 11.8/12.5 kcal/mol with the cc-pVXZ/cc-pVXZ-PP (X = T, Q, 5) basis sets, respectively, without any corrections. Analogous to the HOCl + Cl system, the Reaction B barrier heights 20.8/21.1, 20.3/20.6, and 20.2/20.4 kcal/mol with the TZ/TZ-PP, QZ/QZ-PP, and 5Z/5Z-PP basis sets, are much higher than those for the above-discussed Reaction A, OH + Br2. Transition State B is predicted to lie 22.4 kcal/mol higher in energy than Entrance Complex B (Br…H-O-Br) at the CCSD(T)/ cc-pV5Z level. Entrance Complex B lies 2.2 kcal/mol below the separated reactants with both 5Z and 5Z-PP basis sets. Exit Complex B, BrH…OBr, lies 8.9/9.6, 8.6/9.3 and 8.5/9.2 kcal/mol above the reactants HOBr + Br. The same Exit Complex B falls 3.5/3.6, 3.4 and 3.3 kcal/mol below the separated products HBr + BrO with the TZ/TZ-PP, QZ/QZ-PP, and 5Z/5Z-PP basis sets. Since the reaction HOBr + Br is so endothermic, it is likely to be important for room temperature experiments. For the reverse exothermic reaction HBr + BrO, the predicted classical barrier is 8.4 kcal/mol, an energy much more achievable under atomaspheric conditions.

ii. Scalar Relativistic Effects. In general, the scalar relativistic effects include: the Darwin term (relativistic fluctuations of an electron about its mean position) and mass-velocity corrections 10


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(relativistic increase in the mass of an electron with its velocity approaching the speed of light). Table 3 shows the mass-velocity correction (Em-v), Darwin term correction (ED) and the contribution of the scalar relativistic effects in the nonrelativistic total energy for each stationary point of our two reactions. The scalar relativistic contribution for OH radical is very small, only 0.07% of the total energy. However, because of the heavier Br atom, the contribution of the scalar relativistic effects to the nonrelativistic total energies for Br, Br2 and HBr are larger (1.21%). The contributions of the scalar relativistic effects for the other bromine-including stationary points are 1.18% or 1.19%. The scalar relativistic corrections to the entrance complexes A and B, transition states A and B, and exit complexes A and B are, in kcal/mol, -0.17/-0.02, -0.52/0.30, -0.24/0.64 respectively with the cc-pV5Z basis sets (Table 4). Incorporating the scalar relativistic corrections, the exothermicity of Reaction A is -4.86, -3.95, or -3.73 kcal/mol and the Reaction A barrier heigh is 0.07, -1.03, or -1.26 kcal/mol respectively, with the cc-pVTZ, cc-pVQZ, and cc-pV5Z basis sets. For Reaction B, the scalar relativistic corrected endothermicities are 12.82, 12.62, or 12.52 kcal/mol, and the classical barrier heights are 21.09, 20.50, or 20.51 kcal/mol, predicted with the cc-pVTZ, cc-pVQZ, and cc-pV5Z basis sets, respectively. Thus the relative energy ordering of the stationary points is not changed by the scalar relativistic energy corrections. The results obtained using the relativistic effective core potentials cc-pVXZ-pp (X = T, Q, 5) agree well with the above-discussed relative energies of the stationary points corrected perturbatively for the scalar relativistic effects (Table 4). The reaction energy using relativistic effective core potentials is -4.68, -3.98, or -3.71 kcal/mol for reaction A and 13.13, 12.67, or 12.53 kcal/mol for reaction B. The barrier heights obtained using

11



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relativistic effective core potentials are 0.25, -0.93, or -1.22 kcal/mol for the reaction A and 21.10, 20.55, or 20.45 kcal/mol for Reaction B, predicted with the cc-pVXZ-pp (X = T, Q, 5) basis sets, respectively. The reaction energies and the barrier heights from the two methods are similar for the two reactions studied here.

iii. Spin-Orbit Effects. Spin−orbit coupling involves the interaction of the spin magnetic moment of an electron with the magnetic field induced by its own orbital motion. Our spin-orbit predictions are summarized in Table 5. The SO correction is defined as the difference between the SO and non-SO ground state electronic energies, i.e., ∆SO = ESO(ground state) - Enon-SO(ground state). The theoretical spin-orbital constants of OH, Br and BrO at the MCSCF/cc-pV5Z level are 137, 3200 and 723 cm-1, respectively, which agree reasonably with the corresponding experimental SO constants [139.7 (OH)32, 3685.24 (Br)33, and 967.98(BrO)34 cm-1]. These SO corrections for OH, Br and BrO from MCSCF with the cc-pV5Z or cc-pV5Z-PP basis sets are -0.20/-0.20, 3.05/3.24, -1.05/-1.10 kcal/mol, respectively. These predictions agree reasonably with the corresponding experimental SO splittings [0.20 (OH),35 3.51 (Br), and 1.39 (BrO) kcal/mol]. The SO correction for Br is of course larger than that for the Cl atom. The theoretical SO corrections lower the OH+Br2, Br+HOBr, and HBr+BrO asymptotes by -0.20/-0.20, 3.05/3.24, -1.05/-1.10 kcal/mol with cc-pV5Z or cc-pV5Z-PP basis sets, respectively. For Reaction A, the SO correction of the Entrance Complex HO…BrBr and the transition state TSA are small, i.e., -0.04/-0.04

and -0.03/-0.04 kcal/mol with the

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MCSCF/cc-pV5Z or cc-pV5Z-PP methods, respectively. The TSA barrier height and the relative energy of the HO…BrBr entrance complex thus increase by about 0.17/0.16 and 0.16/0.16 kcal/mol, because the SO correction lowers the reactant asymptote and has little effect on the energies of the Entrance Complex A. The SO correction of the exit Br…HOBr complex is quenched to -0.88/-0.97 kcal/mol with the MCSCF/cc-pV5Z or cc-pV5Z-PP methods, which are much less than that of the Br atom. This can be contrasted with the exit Cl…HOCl complex, where the SO correction for the exit Cl…HOCl complex (-0.76 kcal/mol), with its 2.47 Å Cl…H equilibrium distance, is almost the same as that of the Cl atom (-0.78 kcal/mol).

Because the exit complex

Br…HOBr with nonlinear Br…H-O, in which the Br…Br distance 2.945 Å (5Z) or 2.932 Å (5Z-PP) is slightly longer than the Br-Br distance 2.294 Å(5Z) or 2.292 Å (5Z-PP) in the Br2 molecule. For Reaction B, HOBr + Br → HBr + BrO, the SO corrections for the entrance complex Br-O-H…Br, the transition state TSB and the exit complex BrH…OBr are -3.08/-3.27, -0.19/-0.20, -0.54/-0.64 kcal/mol with MCSCF/cc-pV5Z or cc-pV5Z-PP method, significantly larger than for the analogous HOCl + Cl system. The energies of both HOBr + Br and Br-O-H…Br decrease by 3.05/3.24 and 3.08/3.27 kcal/mol with MCSCF/cc-pV5Z or cc-pV5Z-PP method, since the SO effect is larger for Br than for OH. The SO correction for the entrance complex Br-O-H…Br (-3.08/-3.27 kcal/mol), with its 2.59 Å Br…H equilibrium distance, is almost the same as that of the Br atom (-3.05/-3.24 kcal/mol), which is analogous to the isovalent HOCl + Cl system. The TSB energy increases by 2.86/3.04 kcal/mol relative to reactants HOBr + Br with the MRCI/cc-pV5Z 13



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or cc-pV5Z-PP methods. Finally, the relative energy of the HBr + BrO product channel decreases by about 2.00/2.14 kcal/mol with MRCI/cc-pV5Z or cc-pV5Z-PP method, because the SO splitting of BrO is larger than that for OH.

iv. Energetics with Zero-Point Vibration Considering the zero-point vibrational energy (ZPVE) corrections (Table 6), the endothermicity of Reaction A is -2.31/-2.42, -1.76/-1.74, or -1.47/-1.47 kcal/mol, respectively, with the cc-pVXZ/cc-pVXZ-PP (X=T, Q, 5) basis sets. It is seen that the ZPVE corrections shift the endothermicity from -3.7 kcal/mol to -1.5 kcal/mol. The ZPVE corrections increase the CCSD(T) classical barrier for Reaction A to 2.19/1.72, 1.03/0.43, and 0.66/0.10 kcal/mol, respectively, for the TZ/TZ-PP, QZ/QZ-PP, and 5Z/5Z-PP basis sets. Therefore the effect of ZPVE on the barrier changes the classical barrier from -0.74/-1.22 kcal/mol to 0.66/0.10 kcal/mol. The origin of this change lies with the facts that (a) the OH frequencies of the isolated diatomic and the OH frequency at TSA are the same to within 13 cm-1; and (b) the frequency of isolated Br2 is only 325 cm-1, much less than the sum of the other four real TSA frequencies (673, 292, 261, and 89 cm-1). Tables 1 and 2 show that the ZPVE of OH + Br2 (5.8 kcal/mol) is less than that of TSA (7.2 kcal/mol). For Reaction B, the predicted ZPVE corrected endothermicity is 9.11/9.85, 8.75/9.42, or 8.59/9.28 kcal/mol, with the cc-pVXZ/cc-pVXZ-PP (X=T, Q, 5) basis sets, respectively. The ZPVE correction for the reaction energy with cc-pV5Z is larger than with cc-pV5Z-PP, namely from (11.8-8.6) = 3.2 kcal/mol (cc-pV5Z) to (11.5-9.3) = 2.2 kcal/mol (cc-pV5Z-PP). This change is due to the departure of the large OH stretching

14


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frequency (for reactant HOBr 3804 cm-1) from the products HBr + BrO. The Reaction B classical barrier height with the ZPVE correction is 17.3/17.6, 16.8/17.0, or 16.7/17.0 kcal/mol with our three correlation consistent basis sets (Table 6). For this barrier, the ZPVE reduces the magnitude by 3.49 kcal/mol (cc-pV5Z) or 3.51 kcal/mol (cc-pV5Z-PP). The ZPVE correction for all-electron basis set is the same for the ECP basis set. Due to the absence of anharmonicity in our zero-point computations, the ZPVE corrections are perhaps as much as 10% too big. Even so, these zero-point corrections to the energetics are large.

v. Final Computations For our final energetic predictions we use the full CCSDT and CCSDTQ methods described at the end of the Methodology section above. These final relative energies for the stationary points of Reaction A and B are determined via focal point analyses (Tables 7 and 8). Small energy differences (< 0.3 kcal/mol) between the CCSDTQ/cc-pV5Z and CCSDTQ/CBS results indicate reasonable convergence with respect to the size of basis sets. Moreover, the small CCSDTQ contributions are indicative of reasonable convergence toward higher excitation effects in coupled cluster theory. For the OH + Br2 reaction, the final energies relative to the reactants, are −2.17 (entrance complex), −2.56 (transition state), −6.83 (exit complex), and −4.10 kcal/mol (products) at the CCSDTQ/CBS

level

of

theory

appended

by

corrections

including

∆ZPVE

[CCSD(T)/cc-pV5Z], ∆REL [HF/cc-pV5Z], and ∆SO [MRCI/cc-pV5Z]. The largest change in the CCSDT and CCSDTQ energetics compared to the CCSD(T) results occurs for the transition state for OH + Br2 → HOBr + Br. There full triples

15



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lowers the barrier height by 0.92 kcal/mol compared to the reactants, and by 0.91 kcal/mol compared to the entrance complex. As a result, the TSA becomes lower in energy than the entrance complex. The full CCSDTQ method reduces the barrier by a further 0.33 kcal/mol relative to reactants and 0.32 kcal/mol relative to the entrance complex. Perhaps the full CCSDTQ/cc-pV5Z optimizations (not currently feasible) would place the entrance complex again below the transition state. For now we must say that the entrance well may not exist, i.e., the reactants may go straight downhill to the exit complex Br-O-H…Br. For Reaction B (Table 8), the energies relative to HOBr + Br are determined to be −1.92 (entrance complex), +16.46 (transition state), +7.84 (exit complex), and +9.65 kcal/mol (products), at the CCSDTQ/CBS focal point level of theory. The large energy barrier and endothermicity suggest that the forward path of Reaction B is thermally unfavorable. However, the more important exothermic reverse reaction, HBr + BrO → HOBr + Br, has the barrier height of 6.8 kcal/mol, based on our computations. The experimental thermochemical energetics (in kcal/mol) pertinent to this research are listed in Table 9, in which all results are from the Active Thermochemical Tables (ATcT version 1.112) of Ruscic and coworkers,9,

36-38

and private communications. The

experimental exothermicity of the reaction OH + Br2 → HOBr + Br (−3.90 ± 0.19 kcal/mol) is in agreement with our theoretically predicted results (−4.10 kcal/mol). For Reaction B, HOBr + Br → HBr + BrO, the theoretically computed endothermicity (9.65 kcal/mol) is in fair agreement with the experimental result (8.7 ± 0.3 kcal/mol).

4. Conclusions 16


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The reaction of OH and Br2 to produce HOBr and Br, and subsequent reaction HOBr + Br → HBr + BrO, have been investigated using state-of-the-art high level coupled cluster methods. The geometries of all stationary points are optimized at CCSD(T)/cc-pV5Z level of theory, and the energies are determined at CCSDTQ/CBS level using the focal point analysis of Allen and coworkers. The final exothermicity of the reaction OH + Br2 → HOBr + Br is predicted to be −4.1±0.5 kcal/mol, in agreement with experimental results derived from the Active Thermochemical Tables of Ruscic and coworkers.9 For the reaction HOBr + Br → HBr + BrO, our computations show a large barrier of 16.5±0.9 kcal/mol, and an endothermicity of 9.6±0.7 kcal/mol. The ECP computations show results consistent with conventional all-electron basis sets. Among the additional corrections, the ZPVE and spin-orbit effects are important in determining accurate energetics. In comparison, the relativistic corrections are generally smaller.

Acknowledgments We are indebted to Dr. Branko Ruscic (reference 36-38) for his illumination of experimental thermochemistry. H.Y. Wang is grateful for financial support from the China Scholarship Council, the China National Science Foundation (Grants 11174237 and 11404268), the Sichuan Province Applied Science and Technology Project (Grant 2013JY0035), and the Fundamental Research Funds for the Central Universities (2682014ZT30 and 2682015QM04). Y. Q. and H.F.S. are supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Chemical Sciences Division, Combustion Research Program, Grant DE-FG02-97ER14748.

17



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FIGURE CAPTIONS Figure 1. Optimized geometries of the reactants, entrance complex, transition state, exit complex, and products for Reaction A, namely OH + Br2 → HOBr + Br. The distances (in Å) from top to bottom are from the cc-pVTZ, cc-pVQZ, and cc-pV5Z all-electron basis sets, respectively, with the CCSD(T) method. Figure 2. Optimized geometries of the reactants, entrance complex, transition state, exit complex, and products for Reaction A, namely OH + Br2 → HOBr + Br. The distances (in Å) from top to bottom are from the cc-pVTZ-PP, cc-pVQZ-PP, and cc-pV5Z-PP effective core potential basis sets, respectively, with the CCSD(T) method. Figure 3. Optimized geometries of the reactants, entrance complex, transition state, exit complex, and products for Reaction B, namely HOBr +Br → HBr + BrO. The distances (in Å) from top to bottom are from the cc-pVTZ, cc-pVQZ, and cc-pV5Z all-electron basis sets, respectively, with the CCSD(T) method. Figure 4. Optimized geometries of the reactants, entrance complex, transition state, exit complex, and products for Reaction B, namely HOBr +Br → HBr + BrO. The distances (in Å) from top to bottom are from the cc-pVTZ-PP, cc-pVQZ-PP, and cc-pV5Z-PP effective core potential basis sets, respectively, with the CCSD(T) method. Figure 5. Schematic energy diagram for Reaction A, namely OH + Br2 → HOBr +Br from the cc-pVTZ, cc-pVQZ, and cc-pV5Z all-electron basis sets with the CCSD(T) method. The predictions in parentheses include ZPVE, relativistic, and 23



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

spin-orbit corrections. Figure 6. Schematic energy diagram for Reaction B, namely HOBr +Br → HBr + BrO from the cc-pVTZ, cc-pVQZ, and cc-pV5Z all-electron basis sets with the CCSD(T) method. The predictions in parentheses include ZPVE, relativistic and spin-orbit corrections. Figure 7. Schematic energy diagram for Reaction A, namely OH + Br2 → HOBr + Br from the cc-pVTZ-PP, cc-pVQZ-PP, and cc-pV5Z-PP effective core potential basis sets with the CCSD(T) method. The predictions in parentheses include ZPVE, relativistic and spin-orbit corrections. Figure 8. Schematic energy diagram for Reaction B, namely HOBr +Br → HBr + BrO from the cc-pVTZ-PP, cc-pVQZ-PP, and cc-pV5Z-PP effective core potential basis sets with the CCSD(T) method. The predictions in parentheses include ZPVE, relativistic, and spin-orbit corrections.

24


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Figure 1. Optimized geometries of the reactants, entrance complex, transition state, exit complex, and products for Reaction A, namely OH + Br2 → HOBr + Br. The distances (in Å) from top to bottom are from the cc-pVTZ, cc-pVQZ, and cc-pV5Z all-electron basis sets, respectively, with the CCSD(T) method. 25



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 2. Optimized geometries of the reactants, entrance complex, transition state, exit complex, and products for Reaction A, namely OH + Br2 → HOBr + Br. The distances (in Å) from top to bottom are from the cc-pVTZ-PP, cc-pVQZ-PP, and cc-pV5Z-PP effective core potential basis sets respectively, with the CCSD(T) method 26


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Figure 3. Optimized geometries of the reactants, entrance complex, transition state, exit complex, and products for Reaction B, namely HOBr +Br → HBr + BrO. The distances (in Å) from top to bottom are from the cc-pVTZ, cc-pVQZ, and cc-pV5Z all-electron basis sets, respectively, with the CCSD(T) method. 27



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Figure 4. Optimized geometries of the reactants, entrance complex, transition state, exit complex, and products for Reaction B, namely HOBr +Br → HBr + BrO. The distances (in Å) from top to bottom are from the cc-pVTZ-PP, cc-pVQZ-PP, and cc-pV5Z-PP effective core potential basis sets respectively, with the CCSD(T) method.

28


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Figure 5. Schematic energy diagram for Reaction A, namely OH + Br2 → HOBr +Br from the cc-pVTZ, cc-pVQZ, and cc-pV5Z all-electron basis sets with the CCSD(T) method. The predictions in parentheses include ZPVE, relativistic, and spin-orbit corrections.

29



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Figure 6. Schematic energy diagram for Reaction B, namely HOBr +Br → HBr + BrO from the cc-pVTZ, cc-pVQZ, and cc-pV5Z all-electron basis sets with the CCSD(T) method. The predictions in parentheses include ZPVE, relativistic and spin-orbit corrections.

30


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Figure 7. Schematic energy diagram for Reaction A, namely OH + Br2 → HOBr + Br from the cc-pVTZ-PP, cc-pVQZ-PP, and cc-pV5Z-PP effective core potential basis sets with the CCSD(T) method. The predictions in parentheses include ZPVE, relativistic and spin-orbit corrections.

31



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Figure 8. Schematic energy diagram for Reaction B, namely HOBr +Br → HBr + BrO from the cc-pVTZ-PP, cc-pVQZ-PP, and cc-pV5Z-PP effective core potential basis sets with the CCSD(T) method. The predictions in parentheses include ZPVE, relativistic, and spin-orbit corrections.

32


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Table 1. Total energies (E, in hartrees), harmonic vibrational frequencies (ω, in cm−1) and zero point vibrational energies (ZPVE, in kcal/mol) for each stationary point of the reactions: OH + Br2 → HOBr + Br and HOBr + Br → HBr + BrO. All results are from the CCSD(T) method with the three specified all-electron basis sets.

OH

E

ω ZPVE

Br2

E

ω ZPVE E

Entrance A

ω ZPVE

cc-pVTZ -75.63756 3745 5.35

cc-pVQZ -75.66144 3750 5.36

cc-pV5Z -75.66941 3747 5.36

-5145.27919 317 0.45

-5145.32319 324 0.46

-5145.33696 325 0.47

-5220.92103 46, 50, 92, 218, 313, 3733 6.30

-5220.98869 46, 47, 89, 213, 319, 3736 6.23

-5221.01034 43, 46, 92, 215, 321, 3734 6.23

-5220.98532 184i, 97, 288, 291, 685, 3742 7.29

-5221.00756 176i, 89, 261, 292, 673, 3739 7.23

-5220.92839 62, 108, 216, 629, 1249, 3729 8.57

-5220.99722 83, 117, 226, 638, 1243, 3709 8.60

-5221.01925 91, 121, 231, 642, 1249, 3698 8.62

-2648.32165 628, 1209, 3813 8.08

-2648.36934 636, 1198, 3810 8.07

-2648.38479 639, 1199, 3804 8.07

E

TSA

-5220.91569 220i, 104, 277, 287, 725, 3742 ZPVE 7.34

ω

E Exit A

ω ZPVE E

HOBr

ω ZPVE

33



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Page 34 of 45

Br

E

-2572.60239

-2572.62166

-2572.62749

E Entrance B

ω

-5220.92710 26, 96, 177, 630, 1237, 3770 8.45

-5220.99436 25, 93, 174, 638, 1226, 3759 8.42

-5221.01575 23, 95, 185, 641, 1226, 3750 8.43

ZPVE E

TSB

-5220.89086 -5220.95865 -5220.98011 1778i, 93, 417, 655, 884, 1146 1759i, 89, 417, 659, 877, 1153 1755i, 89, 419, 663, 867, 1156 ZPVE 4.57 4.57 4.57

ω

E Exit B

ω ZPVE E

BrO

ω ZPVE E

HBr

ω ZPVE

-5220.90993 27, 110, 275, 365, 717, 2567 5.77

-5220.97723 25, 116, 268, 362, 728, 2556 5.76

-5220.99868 28, 118, 263, 361, 732, 2553 5.76

-2647.65705 707 1.01

-2647.70246 718 1.03

-2647.71739 723 1.03

-2573.24728 2660 3.80

-2573.26944 2661 3.80

-2573.27605 2657 3.80

34


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Table 2. Total energies (E, in hartrees), harmonic vibrational frequencies (ω, in cm−1) and zero point vibrational energies (ZPVE, in kcal/mol) for each stationary point of the reactions: OH + Br2 → HOBr + Br and HOBr + Br → HBr + BrO. All results are from the CCSD(T) method with the three specified effective core potentials (ECP) basis sets. The analogous results for the OH radical appear in Table 1.

Br2

E

ω ZPVE E

Entrance A

ω ZPVE

cc-pVTZ-PP -831.37189 317 0.45

cc-pVQZ-PP -831.41307 323 0.46

cc-pV5Z-PP -831.42653 324 0.46

-907.01390 48, 50, 93, 225, 313, 3733 6.24

-907.07887 46, 48, 91, 220, 318, 3736 6.24

-907.10021 47, 51, 96, 230, 319, 3733 6.33

-907.07599 168i, 87, 258, 291, 649, 3740 7.18

-907.09788 156i, 81, 248, 295, 634, 3738 6.90

-907.08724 84, 123, 222, 635, 1242, 3707 8.60

-907.10898 82, 116, 206, 631, 1227, 3708 8.53

E

TSA

-907.00905 206i, 99, 2769, 280, 696, 3740 ZPVE 7.28

ω

E Exit A

ω ZPVE E

HOBr

ω ZPVE

Br

E

-907.02135 62, 107, 215, 627, 1244, 3731 8.56 -491.36775 627, 1205, 3811 8.07

-491.41386 634, 1198, 3808 8.06

-415.64915

-415.66700 35


-491.42914 637, 1195, 3805 8.06 -415.67270


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48

E Entrance B

ω ZPVE

-907.01994 26, 91, 171, 629, 1233, 3770 8.42

-907.08421 24, 92, 168, 635, 1223, 3757 8.40

E

TSB

-906.98328 -907.04810 1741i, 92, 418, 655, 865, 1141 1706i, 94, 425, 659, 872, 1148 ZPVE 4.53 4.57

ω

E Exit B

ω ZPVE E

BrO

ω ZPVE E

HBr

ω ZPVE

Page 36 of 45

-907.10530 22, 93, 180, 640, 1223, 3752 8.42 -907.06926 1716i, 88, 418, 663, 863, 1150 4.55

-907.00159 26, 113, 266, 360, 715, 2561 5.74

-907.06600 28, 118, 272, 369, 724, 2546 5.76

-907.08713 27, 116, 265, 365, 728, 2541 5.74

-490.70293 704 1.01

-490.74683 714 1.02

-490.76156 720 1.03

-416.29305 2648 3.79

-416.31384 2650 3.79

-416.32032 2647 3.78

36


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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 3. Mass-velocity corrections (EM-V) and Darwin term corrections (ED) to the energies of each stationary point of the two reactions: OH + Br2 → HOBr + Br and HOBr + Br → HBr + BrO. EREL is the sum of these two contributions. The final row labeled EREL/E is the ratio of the relativistic corrects to the nonrelativistic total energy. cc-pVTZ OH + Br2 → HOBr + Br EM-V -0.25228 ED 0.20044 OH EREL -0.05184 EREL/E 0.07%

cc-pVQZ

cc-pV5Z

-0.25626 0.20427 -0.05199 0.07%

-0.25771 0.20571 -0.05200 0.07%

EM-V ED EREL EREL/E

-234.36187 172.10873 -62.25314 1.21%

-234.56721 172.31133 -62.25588 1.21%

-235.14979 172.89063 -62.25912 1.21%

Entrance A

EM-V ED EREL EREL/E

-234.61523 172.30993 -62.30529 1.19%

-234.82448 172.51632 -62.30816 1.19%

-235.40851 173.09707 -62.31143 1.19%

TSA

EM-V ED EREL EREL/E

-234.61753 172.31161 -62.30592 1.19%

-234.82659 172.51776 -62.30882 1.19%

-235.41029 173.09830 -62.31199 1.19%

Exit A

EM-V ED EREL EREL/E

-234.61555 172.31010 -62.30545 1.19%

-234.82506 172.51677 -62.30829 1.19%

-235.40913 173.09759 -62.31154 1.19%

HOBr

EM-V ED EREL EREL/E

-117.43200 86.25427 -31.17773 1.18%

-117.53848 86.35940 -31.17908 1.18%

-117.83127 86.65055 -31.18072 1.18%

Br

EM-V ED EREL EREL/E

-117.18345 86.05576 -31.12769 1.21%

-117.28563 86.15690 -31.12872 1.21%

-117.57718 86.44671 -31.13047 1.21%

Br2

37



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Page 38 of 45

cc-pVTZ HOBr + Br → HBr + BrO EM-V -234.61498 ED 172.30975 Entrance B EREL -62.30523 EREL/E 1.19%

cc-pVQZ

cc-pV5Z

-234.82415 172.51627 -62.30788 1.19%

-235.40832 173.09713 -62.31119 1.19%

TSB

EM-V ED EREL EREL/E

-234.61187 172.30688 -62.30499 1.19%

-234.82069 172.51320 -62.30749 1.19%

-235.40464 173.09395 -62.31069 1.19%

Exit B

EM-V ED EREL EREL/E

-234.61058 172.30584 -62.30474 1.19%

-234.81877 172.51187 -62.30691 1.19%

-235.40281 173.09267 -62.31014 1.19%

BrO

EM-V ED EREL EREL/E

-117.43245 86.25440 -31.17805 1.18%

-117.53882 86.35948 -31.17934 1.18%

-117.83163 86.65065 -31.18098 1.18%

HBr

EM-V ED EREL EREL/E

-117.17816 86.05149 -31.12667 1.21%

-117.27983 86.15238 -31.12745 1.21%

-117.57120 86.44209 -31.12910 1.21%

38


Page 39 of 45

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48


Table 4. Relative energies for the two reactions: OH + Br2 → HOBr + Br and

HOBr + Br → HBr + BrO. The quantity

∆REL gives the contributions to relativistic effects from the mass-velocity and Darwin term corrections. The quantity ∆E+∆REL adds ∆REL to the all-electron nonrelativistic relative energies The quantity ∆EECP gives relative energies with relativistic effects treated with the effective core potentials basis sets. ∆E+∆REL (kcal/mol) ∆EECP (kcal/mol) ∆REL (kcal/mol) cc-pVTZ cc-pVQZ cc-pV5Z cc-pVTZ cc-pVQZ cc-pV5Z cc-pVTZ -PP cc-pVQZ -PP cc-pV5Z -PP OH + Br2 → HOBr + Br OH+Br2 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Entrance A -0.20 -0.18 -0.17 -2.88 -2.73 -2.66 -2.79 -2.74 -2.68 TSA -0.59 -0.59 -0.52 0.07 -1.03 -1.26 0.25 -0.93 -1.22 Exit A -0.29 -0.26 -0.24 -7.59 -8.16 -8.32 -7.47 -7.99 -8.18 HOBr+Br -0.28 0.05 -0.02 -4.86 -3.95 -3.73 -4.68 -3.98 -3.71 HOBr + Br → HBr + BrO HOBr+Br 0.00 Entrance B 0.12 TSB 0.27 Exit B 0.43 HBr+BrO 0.45

0.00 -0.05 0.19 0.56 0.63

0.00 0.00 0.32 0.66 0.70

0.00 -1.79 21.09 9.29 12.82

0.00 -2.16 20.50 9.20 12.62

0.00 -2.17 20.51 9.20 12.52

39


0.00 -1.90 21.10 9.61 13.13

0.00 -2.11 20.55 9.31 12.67

0.00 -2.17 20.45 9.24 12.53


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48

Page 40 of 45

Table 5. Spin-orbit corrections (in kcal/mol) for the stationary points of the two reactions: OH + Br2 → HOBr + Br and HOBr + Br → HBr + BrO from the multi-reference configuration interaction method. ∆SO is the absolute value of the spin-orbital correction, while ∆*SO is the spin-orbit correction relative to the reactants. cc-pVTZ ∆SO ∆*SO OH + Br2 → HOBr + Br OH+Br2 -0.19 0.00 Entrance A -0.03 0.16 TSA -0.06 0.13 Exit A -1.13 -0.94 HOBr+Br -3.04 -2.85

cc-pVQZ ∆SO ∆*SO

cc-pV5Z ∆SO ∆*SO

cc-pVTZ-PP ∆SO ∆*SO

cc-pVQZ-PP ∆SO ∆*SO

cc-pV5Z-PP ∆SO ∆*SO

-0.19 -0.04 -0.04 -0.93 -3.04

0.00 0.15 0.15 -0.74 -2.85

-0.20 -0.04 -0.03 -0.88 -3.05

0.00 0.16 0.17 -0.68 -2.85

-0.19 -0.03 -0.06 -1.28 -3.22

0.00 0.16 0.13 -1.09 -3.03

-0.19 -0.03 -0.05 -1.02 -3.23

0.00 0.16 0.15 -0.83 -3.04

-0.20 -0.04 -0.04 -0.97 -3.24

0.00 0.16 0.16 -0.77 -3.04

HOBr + Br → HBr + BrO HOBr+Br -3.04 Entrance B -3.06 TSB -0.18 Exit B -0.60 HBr+BrO -0.91

-3.04 -3.07 -0.18 -0.69 -1.04

0.00 -0.03 2.86 2.35 2.00

-3.05 -3.08 -0.19 -0.54 -1.05

0.00 -0.03 2.86 2.51 2.00

-3.22 -3.25 -0.19 -0.66 -0.96

0.00 -0.03 3.03 2.56 2.26

-3.23 -3.27 -0.20 -0.73 -1.09

0.00 -0.04 3.03 2.50 2.14

-3.24 -3.27 -0.20 -0.64 -1.10

0.00 -0.03 3.04 2.60 2.14

0.00 -0.02 2.86 2.44 2.13

40


Page 41 of 45

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48


Table 6. Zero-point vibrational contributions to the energetics of the two reactions: OH + Br2 → HOBr + Br and HOBr + Br → HBr + BrO. The columns labeled ∆ZPVE (in kcal/mol) give the ZPVE energies relative to that of the reactants. The columns labeled ∆E+∆ZPVE (in kcal/mol) give the energies (relative to reactants) including total energies and ZPVE corrections.

cc-pVTZ cc-pVQZ ∆ZPVE ∆E+∆ZPVE ∆ZPVE ∆E+∆ZPVE OH + Br2 → HOBr + Br OH+Br2 0.00 0.00 0.00 0.00 Entrance A 0.49 -2.19 0.40 -2.15 TSA 1.53 2.19 1.47 1.03 Exit A 2.76 -4.54 2.77 -5.13 HOBr+Br 2.27 -2.31 2.24 -1.76 HOBr + Br → HBr + BrO HOBr+Br 0.00 0.00 Entrance B 0.37 -1.54 TSB -3.51 17.31 Exit B -2.31 6.55 HBr+BrO -3.26 9.11

0.00 0.36 -3.50 -2.30 -3.24

0.00 -1.75 16.81 6.34 8.75

cc-pV5Z ∆ZPVE ∆E+∆ZPVE

cc-pVTZ-PP ∆ZPVE ∆E+∆ZPVE

cc-pVQZ-PP ∆ZPVE ∆E+∆ZPVE

cc-pV5Z-PP ∆ZPVE ∆E+∆ZPVE

0.00 0.41 1.40 2.80 2.24

0.00 -2.08 0.66 -5.28 -1.47

0.00 0.43 1.47 2.75 2.26

0.00 -2.36 1.72 -4.72 -2.42

0.00 0.42 1.36 2.78 2.24

0.00 -2.32 0.43 -5.21 -1.74

0.00 0.51 1.32 2.72 2.24

0.00 -2.17 0.10 -5.46 -1.47

0.00 0.37 -3.49 -2.30 -3.23

0.00 -1.80 16.70 6.24 8.59

0.00 0.36 -3.54 -2.33 -3.28

0.00 -1.54 17.56 7.28 9.85

0.00 0.34 -3.49 -2.30 -3.25

0.00 -1.77 17.06 7.01 9.42

0.00 0.36 -3.51 -2.32 -3.25

0.00 -1.81 15.47 6.92 9.28

41



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Page 42 of 45

Table 7. Focal point analysis of the relative energies (∆E, kcal mol−1) for the stationary points on the pathway of Reaction A. All stationary point geometries used here were optimized with the RCCSD(T)/cc-pV5Z method. Each entry except the ROHF results is from a single energy computation, all made in the unrestricted formulation. Basis Set

∆E[ROHF]

δ[MP2]

δ[CCSD]

δ[CCSD(T)]

δ[CCSDT]

δ[CCSDTQ]

∆E[CCSDTQ]

(a) OH + Br2 → Entrance A cc-pVDZ

−2.26

−1.47

+0.31

−0.22

−0.02

−0.01

[−3.68]

cc-pVTZ

−0.96

−1.87

+0.46

−0.32

−0.01

[−0.01]

[−2.71]

cc-pVQZ

−0.55

−2.11

+0.48

−0.38

[−0.01]

[−0.01]

[−2.59]

cc-pV5Z

−0.39

−2.16

+0.45

−0.40

[−0.01]

[−0.01]

[−2.53]

CBS limit

[−0.33]

[−2.21]

[+0.42]

[−0.42]

[−0.01]

[−0.01]

[−2.57]

∆E = −2.57 + 0.41 − 0.17 + 0.16 =

−2.17 kcal mol

−1

(b) OH + Br2 → TSA cc-pVDZ

+12.48

-8.11

-1.13

-1.77

-0.87

−0.33

[+0.27]

cc-pVTZ

+13.48

-10.45

-0.91

-2.47

-0.92

[−0.33]

[-1.59]

cc-pVQZ

+13.61

-11.41

-0.95

-2.79

[-0.92]

[−0.33]

[-2.79]

cc-pV5Z

+13.75

-11.71

-1.03

-2.91

[-0.92]

[−0.33]

[-3.15]

CBS limit

[+13.82]

[-12.02]

[-1.12]

[-3.04]

[-0.92]

[−0.33]

[-3.61]

∆E = −3.61 + 1.40 − 0.52 + 0.17 = −2.56 kcal mol

−1

(c) OH + Br2 → Exit A cc-pVDZ

+13.75

−21.59

+4.92

-1.65

-0.02

-0.24

[-4.83]

cc-pVTZ

+13.58

−24.49

+6.02

-2.44

+0.06

[-0.24]

[-7.52]

cc-pVQZ

+13.41

−25.12

+6.27

-2.66

[+0.06]

[-0.24]

[-8.26]

cc-pV5Z

+13.48

−25.40

+6.34

-2.71

[+0.06]

[-0.24]

[-8.47]

CBS limit

[+13.53]

[−25.70]

[+6.41]

[-2.77]

[+0.06]

[-0.24]

[-8.71]

∆E = −8.71 + 2.80 − 0.24 − 0.68 = −6.83 kcal mol

−1

(d) OH + Br2 → HOBr + Br cc-pVDZ

+8.23

-15.55

+4.16

-0.86

+0.07

-0.16

[-4.10]

cc-pVTZ

+8.09

-16.15

+4.56

-1.10

+0.13

[-0.16]

[-4.63]

cc-pVQZ

+7.96

-15.67

+4.74

-1.04

[+0.13]

[-0.16]

[-4.05]

cc-pV5Z

+8.01

-15.55

+4.80

-0.99

[+0.13]

[-0.16]

[-3.76]

CBS limit

[+8.04]

[-15.41]

[+4.87]

[-0.93]

[+0.13]

[−0.16]

[-3.47]

−1

∆E = −3.47 + 2.24 − 0.02 − 2.85 = −4.10 kcal mol / Experiment is 3.9 ± 0.2 kcal mol

−1

The symbol δ denotes the increment in the relative energy with respect to the preceding level of theory in the hierarchy HF→MP2→CCSD→CCSD(T) →CCSDT→CCSDTQ. Square brackets signify results obtained from basis set extrapolations or additivity assumptions. Each final ∆E is the sum of ∆E[CCSDTQ/CBS], ∆ZPVE[CCSD(T)/cc-pV5Z], ∆REL[HF/cc-pV5Z], ∆SO[MRCI/cc-pV5Z], as listed in order in the summation lines.

42


Page 43 of 45

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 8. Focal point analysis of the relative energies (∆E, kcal mol−1) for the stationary points on the pathway of Reaction B. All stationary point geometries used here were optimized with the RCCSD(T)/cc-pV5Z method. Each entry except the ROHF results is from a single energy computation, all made in the unrestricted formulation. Basis Set

∆E[ROHF]

δ[MP2]

δ[CCSD]

δ[CCSD(T)]

δ[CCSDT]

δ[CCSDTQ]

∆E[CCSDTQ]

(a) HOBr + Br → Entrance B cc-pVDZ

−0.51

−1.30

+0.26

−0.17

−0.00

−0.01

[−1.73]

cc-pVTZ

−0.15

−1.94

+0.48

−0.29

+0.01

[−0.01]

[−1.92]

cc-pVQZ

−0.10

−2.18

+0.52

−0.35

[+0.01]

[−0.01]

[−2.11]

cc-pV5Z

−0.07

−2.25

+0.52

−0.37

[+0.01]

[−0.01]

[−2.17]

CBS limit

[−0.06]

[−2.33]

[+0.52]

[−0.40]

[+0.01]

[−0.01]

[−2.26]

∆E = −2.26 + 0.37 + 0.00 − 0.03 = −1.92 kcal mol

−1

(b) HOBr + Br → TSB cc-pVDZ

+39.30

-10.61

-5.19

-3.02

-0.52

-0.36

[+19.61]

cc-pVTZ

+38.84

-9.84

-6.06

-4.10

-0.42

[-0.36]

[+18.06]

cc-pVQZ

+39.04

-10.16

-6.34

-4.47

[-0.42]

[-0.36]

[+17.29]

cc-pV5Z

+39.20

-10.25

-6.49

-4.60

[-0.42]

[-0.36]

[+17.09]

CBS limit

[+39.27]

[-10.35]

[-6.64]

[-4.73]

[-0.42]

[-0.36]

[+16.77]

∆E = +16.77 − 3.49 + 0.32 + 2.86 = +16.46 kcal mol

−1

(c) HOBr + Br → Exit B cc-pVDZ

+12.17

+4.89

-7.35

-1.03

-0.46

-0.04

[+8.17]

cc-pVTZ

+12.06

+5.51

-8.16

-1.29

-0.56

[-0.04]

[+7.51]

cc-pVQZ

+12.32

+5.52

-8.64

-1.45

[-0.56]

[-0.04]

[+7.13]

cc-pV5Z

+12.44

+5.55

-8.88

-1.52

[-0.56]

[-0.04]

[+6.97]

CBS limit

[+12.49]

[+5.58]

[-9.13]

[-1.60]

[-0.56]

[-0.04]

[+6.73]

∆E = +6.97 − 2.30 + 0.66 + 2.51 = +7.84 kcal mol

−1

(d) HOBr + Br → HBr + BrO cc-pVDZ

+12.91

+8.19

-7.45

-0.61

-0.45

+0.01

[+12.60]

cc-pVTZ

+11.60

+9.37

-8.55

-0.68

-0.57

[+0.01]

[+11.18]

cc-pVQZ

+11.60

+9.52

-9.11

-0.79

[-0.57]

[+0.01]

[+10.65]

cc-pV5Z

+11.62

+9.60

-9.38

-0.85

[-0.57]

[+0.01]

[+10.43]

CBS limit

[+11.63]

[+9.68]

[-9.66]

[-0.92]

[-0.57]

[+0.01]

[+10.18]

−1

∆E = +10.18 − 3.23 + 0.70 + 2.00 = +9.65 kcal mol / Experiment is 8.7 ± 0.3 kcal mol

−1

The symbol δ denotes the increment in the relative energy with respect to the preceding level of theory in the hierarchy HF→MP2→CCSD→CCSD(T) →CCSDT→CCSDTQ. Square brackets signify results obtained from basis set extrapolations or additivity assumptions. Each final ∆E is the sum of ∆E[CCSDTQ/CBS], ∆ZPVE[CCSD(T)/cc-pV5Z], ∆REL[HF/cc-pV5Z], ∆SO[MRCI/cc-pV5Z], as listed in order in the summation lines.

43



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Table 9. Experimental thermochemical energetics (in kcal/mol) pertinent to this research. All results are from the Active Thermochemical Table (ver. 1.112) of Ruscic and coworkers,9, 36-38 and private communication. ∆fH(0K)

OH

8.90±0.01

∆fH(0K)

Br2

10.92±0.03

∆fH(0K)

HOBr

-12.26±0.13

∆fH(0K)

Br

28.18±0.02

∆fH(0K)

HBr

-6.69±0.04

∆fH(0K)

BrO

31.34±0.07

∆fH(0K)

OH + Br2 → HOBr + Br

-3.90±0.19

∆fH(0K) HOBr + Br → HBr + BrO

8.73±0.26

44


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Relative Energies (kcal/mol)

Page 45 of 45

0.0 -2.2

-2.6 -4.1 -6.8

TOC Graphic

45


Pathways for the OH + Br2 â HOBr + ... - ACS Publications

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