I + (H2O)2 → HI + (H2O)OH Forward and Reverse Reactions. CCSD(T

Article pubs.acs.org/JPCB

I + (H2O)2 → HI + (H2O)OH Forward and Reverse Reactions. CCSD(T) Studies Including Spin−Orbit Coupling Hui Wang,† Guoliang Li,*,†,‡,§ Qian-Shu Li,† Yaoming Xie,§ and Henry F. Schaefer, III*,§ †

MOE Key Laboratory of Theoretical Chemistry of the Environment, Center for Computational Quantum Chemistry and Guangzhou Key Laboratory of Materials for Energy Conversion and Storage, School of Chemistry and Environment, South China Normal University, Guangzhou 510006, China § Center for Computational Quantum Chemistry, University of Georgia, Athens, Georgia 30602, United States ‡

ABSTRACT: The potential energy profile for the atomic iodine plus water dimer reaction I + (H2O)2 → HI + (H2O)OH has been explored using the “Gold Standard” CCSD(T) method with quadruple-ζ correlation-consistent basis sets. The corresponding information for the reverse reaction HI + (H2O)OH → I + (H2O)2 is also derived. Both zero-point vibrational energies (ZPVEs) and spin−orbit (SO) coupling are considered, and these notably alter the classical energetics. On the basis of the CCSD(T)/cc-pVQZ-PP results, including ZPVE and SO coupling, the forward reaction is found to be endothermic by 47.4 kcal/ mol, implying a significant exothermicity for the reverse reaction. The entrance complex I···(H2O)2 is bound by 1.8 kcal/mol, and this dissociation energy is significantly affected by SO coupling. The reaction barrier lies 45.1 kcal/mol higher than the reactants. The exit complex HI···(H2O)OH is bound by 3.0 kcal/mol relative to the asymptotic limit. At every level of theory, the reverse reaction HI + (H2O)OH → I + (H2O)2 proceeds without a barrier. Compared with the analogous water monomer reaction I + H2O → HI + OH, the additional water molecule reduces the relative energies of the entrance stationary point, transition state, and exit complex by 3−5 kcal/mol. The I + (H2O)2 reaction is related to the valence isoelectronic bromine and chlorine reactions but is distinctly different from the F + (H2O)2 system.

1. INTRODUCTION The iodine plus water reaction and its reverse reaction are important in atmospheric and environmental chemistry.1−5 It has been reported that iodine may be a critical component of tropospheric photochemistry3 and that iodine, consistent with trends in anthropogenic chlorine and bromine, may also be a factor in determining the widespread current depletion of the lower stratospheric zone.4 Understanding the reaction between iodine and water is also useful for the kinetic study of the role of iodine in severe light water reactor accidents,5 where volatile fission products such as iodine may be released from fuel into a steam−hydrogen atmosphere and react with steam and hydrogen. Given the importance of iodine plus water reactions, it is not surprising that the forward and reverse I + H2O → HI + OH reactions have been the subject of many experimental6−11 and theoretical12−14 studies. Because water dimers are detected under atmospheric conditions15 and studies of the reactions involving the water dimer are important steps from discrete gas-phase water monomers to water polymers to water droplets to liquid water, here we will investigate the reaction between iodine and the water dimer, I + (H2O)2 → HI + (H2O)OH, which, to our knowledge, has not yet been studied. We will investigate the energetics (including the endothermicity, the barrier, and the binding energies for the entrance complex and the exit complex) of this reaction using high-level quantum mechanical © XXXX American Chemical Society

methods. The geometries of all stationary points will also be reported and discussed. Owing to the large amounts of OH radical and water vapor present in the atmosphere, the exothermic reverse reaction HI + (H2O)OH should be even more important, and its energetics can be deduced from those for the forward reaction.

2. THEORETICAL METHODS In this research, two kinds of theoretical methods were used: (1) initially a density functional theory (DFT) method, designated MPW1K, constructed by Truhlar et al.16 and shown to give the best predictions among 49 DFT functionals used for the related F + H2O reaction barrier17 and (2) for our definitive predictions the high-level coupled cluster single and double substitutions method with a perturbative treatment of triple excitations CCSD(T).18−20 The basis sets used here were the Dunning correlationconsistent polarized valence basis sets. For the hydrogen and oxygen atoms, the cc-pVnZ (n = D, T, Q) basis sets21,22 were used. For the iodine atom, the Stuttgart−Cologne effective core potentials (ECPs) and the corresponding correlation-consistent Special Issue: Bruce C. Garrett Festschrift Received: September 22, 2015 Revised: November 11, 2015

A

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Figure 1. Stationary points on the I + (H2O)2 potential energy surface without zero-point vibrational energies (ZPVEs) and spin−orbit (SO) coupling corrections.

Table 1. Harmonic Vibrational Frequencies (ω, in cm−1) and ZPVEs (in kcal/mol) for the Stationary Points of the I + (H2O)2 → HI + (H2O)OH Reaction along with the Experimental Frequencies for Comparisona ZPVE

ΔZPVE

(H2O)2 entrance complex TS exit complex (H2O)OH HI HI + (H2O)OH

29.26 30.52 25.60 25.87 21.30 3.33 24.63

0.00 1.26 −3.66 −3.39

(H2O)2 entrance complex TS exit complex (H2O)OH HI HI + (H2O)OH

29.15 30.28 25.60 25.85 21.04 3.31 24.34

(H2O)2 (H2O)OH HI HI + (H2O)OH

29.14 20.95 3.32 24.27

(H2O)2 (H2O)OHg (H2O)OHh HIi

3.30

ω CCSD(T)/cc-pVDZ-PP 3915, 3902, 3814, 3900, 3862, 3800, 3901, 3802, 3453, 3907, 3804, 3547, 3920, 3816, 3640, 2326

3781, 3661, 1689, 2248, 1685,

1724, 1686, 650, 396, 192, 173, 153, 84 1716, 1689, 785, 460, 362, 331, 224, 218, 155, 124, 64 1475, 933, 708, 499, 429, 372, 259, 228, 95, 68, 491i 1687, 713, 621, 358, 293, 239, 235, 222, 106, 63, 54 607, 579, 248, 217, 185

CCSD(T)/cc-pVTZ-PP 3933, 3918, 3832, 3913, 3885, 3808, 3915, 3814, 3508, 3918, 3810, 3557, 3941, 3838, 3654, 2314

3775, 3663, 1769, 2211, 1664,

1695, 1665, 627, 370, 184, 144, 138, 110 1687, 1667, 755, 423, 335, 304, 211, 200, 134, 128, 65 1669, 844, 639, 414, 392, 340, 236, 212, 96, 60, 266i 1666, 751, 519, 343, 326, 251, 235, 212, 121, 97, 66 635, 456, 195, 172, 158

−4.63 0.00 1.13 −3.55 −3.30

−4.81 0.00

CCSD(T)/cc-pVQZ-PP 3940, 3924, 3836, 3769, 1683, 1658, 622, 363, 183, 146, 134, 129 3948, 3842, 3650, 1656, 625, 430, 191, 160, 150 2320

−4.87 Experiment 3745,b 3735,c 3660,c 3601,c 1616,d 1599,d 523,d 311,d 143,e 108,f 103,f 88f 3728, 3663, 3472, 1599 3711−3743, 3635, 3454, 1593 2309

a

The experimental observed are fundamental frequencies not harmonic. bNear-infrared spectra from ref 29. cInfrared spectra from ref 30. dMidinfrared spectra in a Ne matrix from ref 31. eTerahertz laser vibration−rotation tunneling spectra from ref 32. fTerahertz laser vibration−rotation tunneling spectra from ref 33. gIn a Ne matrix from ref 35. hIn an Ar matrix from ref 36. iFrom ref 37. B

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Figure 2. ZPVE and SO coupling effects on the energetics of the I + (H2O)2 reaction. The classical energetics (the electronic energies not including either ZPVE or SO coupling corrections) are based on the CCSD(T)/cc-pVQZ-PP level of theory.

cc-pVnZ-PP (n = D, T, Q) basis sets23 of Peterson and coworker were employed. With these ECPs, the 28 inner core electrons (1s22s22p63s23p63d10) of iodine were embodied in the energy-consistent pseudopotentials, which were adjusted to atomic multiconfigurational Dirac−Hartree−Fock results.23 The I + (H2O)2 potential energy surface was initially explored using the MPW1K/cc-pVQZ-PP method. All of the stationary points were fully optimized and characterized via harmonic vibrational frequency analyses, with the minima having all real frequencies and the transition state possessing only one imaginary frequency. The intrinsic reaction coordinate (IRC)24−26 analyses were performed at the same level to confirm that the transition state connects the designated entrance and exit complexes. All of these DFT-MPW1K computations were carried out with the Gaussian 09 program suite.27 The theoretically more sophisticated geometry optimizations were performed at the CCSD(T)/cc-pVnZ-PP (n = D, T, Q) levels of theory, and vibrational frequency analyses were carried out up to the CCSD(T)/cc-pVTZ-PP level. In these CCSD(T) computations, the 1s-like core for oxygen and the 4s4p4d-like core for iodine were frozen. All of the CCSD(T) computations were undertaken using the CFOUR program.28

I···(H2O)2 is formed by interaction between the iodine atom and mainly one of the water molecules of the water dimer, with the second water molecule more loosely connected. At the transition state, the O2−H4 bond length (1.622 Å) is much longer than that in the water dimer (0.949 Å). For the exit complex HI···(H2O)OH, the I−H4 bond distance (1.626 Å) is close to the bond length of isolated hydrogen iodide (1.604 Å). The DFT barrier (energy difference between reactants and the transition state) for the I + (H2O)2 reaction is predicted to be 38.2 kcal/mol. Our high-level CCSD(T) studies predict that the I + (H2O)2 → HI + (H2O)OH reaction is endothermic by 41.2 (cc-pVDZPP), 44.8 (cc-pVTZ-PP), or 45.4 (cc-pVQZ-PP) kcal/mol, in which good convergence is seen with respect to basis set size. From the most reliable CCSD(T)/cc-pVQZ-PP method, the I···(H2O)2 entrance complex is predicted to lie 6.0 kcal/mol below the reactants I + (H2O)2. The HI···(H2O)OH exit complex lies 40.8 kcal/mol above the reactants I + (H2O)2 and 4.6 kcal/mol lower than separated products HI + (H2O)OH. The reacton barrier is predicted to be 42.0 kcal/mol. The harmonic vibrational frequencies for the stationary points of the I + (H2O)2 → HI + (H2O)OH reaction computed using the CCSD(T) method are reported in Table 1. It is seen that our predicted frequencies for (H2O)2, (H2O)OH, and HI are in general concurrence with the existing experimental results, 29−37 with the understanding that computed harmonic frequencies will somewhat overestimate the anharmonic experimental ones. The transition state found in this research has an imaginary vibrational frequency of 491i cm−1 (cc-pVDZ-PP) or 266i (cc-pVTZ-PP) cm−1, with the corresponding normal mode showing simultaneous I−H4 bond formation and O2−H4 bond rupture as the reaction proceeds toward HI + (H2O)OH. For the I + (H2O)2 → HI + (H2O)OH reaction, we report stationary point zero-point vibrational energies (ZPVEs) in

3. RESULTS AND DISCUSSION Figure 1 shows geometrical parameters and relative energies for the five stationary points of the I + (H2O)2 → HI + (H2O)OH reaction with the MPW1K/cc−PVQZ-PP and CCSD(T)/ccpVnZ-PP (n = D, T, Q) methods. The MPW1K/cc−PVQZ-PP method predicts that the I + (H2O)2 → HI + (H2O)OH reaction is endothermic by 41.4 kcal/mol. The forward reaction begins with the barrierless formation of an entrance complex I···(H2O)2, occurring before the transition state, followed by the formation of an exit complex HI···(H2O)OH and the release of the products HI + (H2O)OH. The entrance complex C

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Figure 3. Comparison of the stationary points on the potential energy profiles for the I + (H2O)2 reaction with those of the Br + (H2O)2, Cl + (H2O)2, F + (H2O)2, and I + H2O reactions at the CCSD(T)/cc-pVQZ(-PP) level of theory. The ZPVE and SO coupling corrections are not included.

a value of 0.5 kcal/mol was obtained by Feller, Peterson, de Jong, and Dixon for the SO coupling of the closed-shell HI,42 which will slightly lower the relative energy of products. In order to further understand the water dimer reaction I + (H2O)2 → HI + (H2O)OH, we compare it with the water monomer reaction I + H2O → HI + OH.14 Structurally, the entrance complex I···(H2O)2 (Figure 1) looks much like the monomer entrance complex I···H2O (Figure 1 in ref 14) loosely associated with a second water molecule. However, the binding energy of the dimer complex is predicted to be 6.0 kcal/mol classically, while the analogous monomer complex binding energy is only 3.3 kcal/mol, as shown in Figure 3. Thus, the second H2O enhances the I···H2O dissociation energy by 2.7 kcal/mol, which may be the result of the extra interaction between the iodine atom and the H7 atom of the second H2O. The predicted I···H and I···O internuclear separations for the dimer complex are consistently less than those for the analogous monomer complex. The I···O distance in the dimer complex is 2.853 Å, which is shorter than the analogous I···O distance of 3.012 Å in the monomer complex; the I···H distances for the dimer complex are 3.063 and 3.257 Å, while that for the monomer complex is 3.381 Å. Obviously, the iodine atom is more strongly bound to (H2O)2 than to H2O. Considering the two transition states, the second H2O reduces the barrier for the water dimer I + (H2O)2 → HI + (H2O)OH reaction compared to that for the water monomer I + H2O → HI + OH reaction by (44.9 − 42.0) = 2.9 kcal/mol. In terms of their structures, the water dimer transition state is essentially that of a water monomer transition state loosely attached to a second water molecule (H7H6O3). However, unlike the entrance complexes, the distances between the iodine atom and the H atom being abstracted (1.656 Å, Figure 1) in the water dimer transition state is longer than that in the water monomer transition state (1.646 Å), which may be a

Table 1, and these allow us to correct the classical energies. Because the ZPVE corrections from different basis sets are close to each other, we use the ZPVEs from the CCSD(T)/ccpVTZ-PP method. After ZPVE corrections, the CCSD(T)/ccpVQZ-PP predicted relative energies (purple entries) become −4.9 (entrance complex), 38.4 (transition state), 37.5 (exit complex), and 40.6 kcal/mol (products), respectively, as shown in Figure 2. For iodine-incorporating systems, relativistic effects must be carefully examined. Relativistic effects for the iodine core electrons have been incorporated in this research using scalar relativistic pseudopotentials. The latter were constructed exploiting quasirelativistic Hartree−Fock or Dirac−Hartree− Fock results.38 However, spin−orbit (SO) coupling effects associated primarily with the iodine valence electrons may also be consequential. Herein, we adopt a rigorous theoretical motif using the Breit−Pauli operator to provide SO coupling corrections.39 The MOLPRO program package40 was chosen for this purpose, using the full valence complete active space self-consistent field (CASSCF) wave functions, in which ccpVQZ-PP basis sets were used. The active spaces utilized comprise the full-valence electrons and orbitals, that is, 23 electrons in 16 spatial orbitals (23e, 16o) for the entrance and exit complexes and transition states, (7e, 4o) for the iodine atom, and (15e, 11o) for (H2O)OH. Our theoretical CASSCF SO corrections are predicted to be 2425 (iodine atom), 1324 (entrance complex), 58 (transition state), 7 (exit complex), and 34 cm−1 [(H2O)OH], or 6.9, 3.8, 0.2, 0.0, and 0.1 kcal/mol, respectively. The SO correction for I(2P) of 2425 cm−1 obtained here is in reasonable agreement with experiment (7603/3 = 2534 cm−1).41 As Figure 2 demonstrates, including both ZPVE and SO coupling, the CCSD(T)/cc-pVQZ-PP relative energies (red entries) become −1.8 (entrance complex), 45.1 (transition state), 44.4 (exit complex), and 47.4 kcal/mol (products), respectively. It should be noted that D

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the second H2O in the water dimer reaction I + (H2O)2 → HI + (H2O)OH lowers each stationary point relative to separated I + (H2O)2. Compared with the valence isoelectronic F + (H2O)2, Cl + (H2O)2, and Br + (H2O)2 systems, the I + (H2O)2 reaction is somewhat similar to the Br + (H2O)2 and Cl + (H2O)2 reactions but significantly different from the F + (H2O)2 reaction because the fluorine reaction is exothermic and is barrierless from the F + (H2O)2 side.

result of the interactions between the iodine atom and the nonabstracting H7 atom. The water dimer exit complex HI···(H2O)OH dissociation energy is greater (4.6 kcal/mol with respect to the products) than the analogous H2O complex (2.1 kcal/mol compared to the separated HI + OH; see ref 14). Consistent with these energetics, the H4···O2 separation for the dimer exit complex (2.139 Å) is notably less than that for the analogous monomer (2.295 Å). It is also instructive to compare the I + (H2O)2 reaction with the analogous Br + (H2O)2, Cl + (H2O)2, and F + (H2O)2 reactions.43−45 Structurally, the five stationary points for the I + (H2O)2 reaction (Figure 1) are qualitatively related to those for the Br + (H2O)2 (ref 43), Cl + (H2O)2 (ref 44), and F + (H2O)2 reactions (ref 45). Energetically, the landscape profiles for these four reactions are also shown in Figure 3. With the CCSD(T)/cc-pVQZ(-PP) method, the entrance well for I··· (H2O)2, lying 6.0 kcal/mol (classically) below the reactants, is less strongly bound than the corresponding 6.5 kcal/mol for bromine, 6.8 kcal/mol for chlorine, and 7.3 kcal/mol for fluorine. However, the relative energies of the final three stationary points (transition state, exit complex, and products) for the I + (H2O)2 reaction are much higher than those for the Br + (H2O)2 reaction (by 14−15 kcal/mol), the Cl + (H2O)2 reaction (by 25−30 kcal/mol), and the F + (H2O)2 reaction (by 45−68 kcal/mol). These significant energy differences may in large part be credited to the dissociation energy order HI (70.5 kcal/mol) < HBr (86.5 kcal/mol) < HCl (102.2 kcal/ mol) < HF (134.9 kcal/mol).37 Specifically, the I + (H2O)2 → HI + (H2O)OH reaction is predicted to be endothermic by 45.4 kcal/mol (classically) with the CCSD(T)/cc-pVQZ-PP method. This energy decreases to 31.7 kcal/mol for the Br + (H2O)2 reaction, further decreases to 17.7 kcal/mol for the Cl + (H2O)2 reaction, and becomes exothermic (by 16.2 kcal/ mol) for the F + (H2O)2 reaction, as shown in Figure 3. Thus, the F + (H2O)2 reaction is qualitatively different from the other three reactions; the F + (H2O)2 reaction is an exothermic reaction with a transition state but no barrier with respect to the reactants, while the I + (H2O)2, Br + (H2O)2, and Cl + (H2O)2 reactions go uphill energetically, with transition states but no barriers relative to products.

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. Phone: 1-706-542-2067 (H.F.S.). *E-mail: [email protected]. Phone: 86-20-39310255 (G.L.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The research in China was supported by the Guangdong Province Universities and Colleges Pearl River Scholar Funded Scheme (2012) and the National Natural Science Foundation of China (21273082). The study leave of G.L. at the University of Georgia was supported by the National Foundation for Study Abroad from the China Scholarships Council (201308440320). The research at the University of Georgia was supported by the U.S. Department of Energy, Basic Energy Sciences, Chemical Sciences Division, Gas Phase Chemical Physics Program.

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REFERENCES

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4. CONCLUSIONS The reaction between the iodine atom and (H2O)2 has been investigated using initially the DFT-MPW1K method and then the much more reliable CCSD(T) approach with Dunning correlation-consistent basis sets as large as cc-pVQZ-PP. On the basis of the most reliable CCSD(T)/cc-pVQZ-PP results (excluding ZPVE or SO effects), the I + (H2O)2 → HI + (H2O)OH reaction is found to be significantly endothermic, by 45.4 kcal/mol. The transition state lies at 42.0 kcal/mol, suggesting that the reverse reaction is barrierless. We predict the presence of an entrance complex (6.0 kcal/mol below the reactants) and an exit complex (4.6 kcal/mol lower in energy than the products). Both ZPVE and SO coupling effects are found to make notable alterations to the predicted classical energetics. When ZPVE and SO coupling are incorporated, the energies relative to separated I + (H2O)2 become −1.8 kcal/ mol [I···(H2O)2], 45.1 kcal/mol [saddle point], 44.4 kcal/mol [HI···(H2O)OH], and 47.4 kcal/mol [separated HI + (H2O)OH]. The potential energy profile for the exothermic reverse reaction can be derived from the above infomation. With respect to the monomer reaction I + H2O → HI + OH, E

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DOI: 10.1021/acs.jpcb.5b09253 J. Phys. Chem. B XXXX, XXX, XXX−XXX