Probing the Potential Energy Profile of the I + (H2O)3 → HI + (H2O)2OH Forward and Reverse Reactions: High Level CCSD(T) Studies with Spin-Orbit Coupling Included

Three different pathways for the atomic iodine plus water trimer reaction I + (H2O)3 → HI + (H2O)2OH were preliminarily examined by the DFT-MPW1K method. Related to previous predictions for the F/Cl/Br + (H2O)3 reactions, three pathways for the I + (H2O)3 reaction are linked in terms of geometry and energetics. To legitimize the results, the “gold standard” CCSD(T) method was employed to investigate the lowest-lying pathway with the correlation-consistent polarized valence basis set up to cc-pVQZ(-PP). According to the CCSD(T)/cc-pVQZ(-PP)//CCSD(T)/cc-pVTZ(-PP) results, the I + (H2O)3 → HI + (H2O)2OH reaction is predicted to be endothermic by 47.0 kcal mol−1. The submerged transition state is predicted to lie 43.7 kcal mol−1 above the separated reactants. The I···(H2O)3 entrance complex lies below the separated reactants by 4.1 kcal mol−1, and spin-orbit coupling has a significant impact on this dissociation energy. The HI···(H2O)2OH exit complex is bound by 4.3 kcal mol−1 in relation to the separated products. Compared with simpler I + (H2O)2 and I + H2O reactions, the I + (H2O)3 reaction is energetically between them in general. It is speculated that the reaction between the iodine atom and the larger water clusters may be energetically analogous to the I + (H2O)3 reaction. The iodine reaction I + (H2O)3 is connected with the analogous valence isoelectronic bromine/chlorine reactions Br/Cl + (H2O)3 but much different from the F + (H2O)3 reaction. Significant difference with other halogen systems, especially for barrier heights, are seen for the iodine systems.


Introduction
Iodine plays important roles in atmospheric and environmental chemistry [1,2]. An iodine atom can deplete tropospheric ozone via I + O 3 → IO + O 2 , exacerbating the ozone hole in the lower stratospheric zone [3][4][5][6]. The forward and reverse reactions of the iodine atom plus water molecule have been the topic of various studies. This is because hydrogen iodide (HI) may be considered as a reservoir of chemically active iodine atoms in the atmosphere. As such, it can regenerate iodine atoms through its reaction with hydroxyl radicals [7][8][9][10][11][12][13]. Studies of the mechanism for the iodine plus water reaction are also important for the kinetics for severe light water reactor accidents [12,14], where the volatile iodine may be released from fuels and react with steam and hydrogen. Following previous studies of the iodine plus water monomer and dimer reactions [13,15], we expand our research to the iodine plus water trimer reaction, I + (H 2 O) 3 → HI + (H 2 O) 2 OH, which is a better model to approach the reaction of iodine with water steam. We also compare the I + (H 2 O) 3 reaction with the valence isoelectronic F/Cl/Br + (H 2 O) 3 reactions [16][17][18] and discuss the main differences between them.

Results and Discussion
From previous research [19][20][21][22][23][24][25], the water trimer (H 2 O) 3 has several isomers, of which the lowest energy isomer is uud-(H 2 O) 3 . Structurally, the uud-(H 2 O) 3 has a six-membered ring structure consisting of three OH bonds (from three different water molecules) joined by three hydrogen bonds, with each OH serving as both electron donor and receptor. The orientations of the three out-of-ring OH bonds in uud-(H 2 O) 3 are "up-up-down" (uud), with respective to the pseudoplanar six-membered ring.
Three different kinds of reaction pathways are predicted when an iodine atom approaches the water trimer (H 2 O) 3 from different directions, as the MPW1K/cc-pVTZ(-PP) results show in Figure S1 in the Supplementary Materials. These pathways are similar in both energetics and structures, just as those for the F/Cl/Br + (H 2 O) 3 reactions. To obtain more reliable predictions, the CCSD(T) method was adopted to further investigate the lowest-lying pathway, with basis sets up to cc-pVTZ(-PP) for geometry optimizations and vibrational frequency analyses and cc-pVQZ(-PP) for single-point energy computations. Thus, the following discussions are based on CCSD(T)/cc-pVTZ(-PP) geometries and vibrational frequencies and the CCSD(T)/cc-pVQZ(-PP)//CCSD(T)/cc-pVTZ(-PP) energetics, unless otherwise specified. Figure 1 shows that the I + (H 2 O) 3 reaction starts with the formation of the entrance complex I···(H 2 O) 3 , in which the I atom is bound to one water molecule, with the other two water molecules loosely linked. The I···(H 2 O) 3 entrance complex is predicted to lie 4.1 kcal mol −1 below the separated I + uud-(H 2 O) 3 reactants.
Molecules 2023, 26, x FOR PEER REVIEW 2 of 8 expand our research to the iodine plus water trimer reaction, I + (H2O)3 → HI + (H2O)2OH, which is a better model to approach the reaction of iodine with water steam. We also compare the I + (H2O)3 reaction with the valence isoelectronic F/Cl/Br + (H2O)3 reactions [16][17][18] and discuss the main differences between them.
Three different kinds of reaction pathways are predicted when an iodine atom approaches the water trimer (H2O)3 from different directions, as the MPW1K/cc-pVTZ(-PP) results show in Figure S1 in the Supplementary Materials. These pathways are similar in both energetics and structures, just as those for the F/Cl/Br + (H2O)3 reactions. To obtain more reliable predictions, the CCSD(T) method was adopted to further investigate the lowest-lying pathway, with basis sets up to cc-pVTZ(-PP) for geometry optimizations and vibrational frequency analyses and cc-pVQZ(-PP) for single-point energy computations. Thus, the following discussions are based on CCSD(T)/cc-pVTZ(-PP) geometries and vibrational frequencies and the CCSD(T)/cc-pVQZ(-PP)//CCSD(T)/cc-pVTZ(-PP) energetics, unless otherwise specified. Figure 1 shows that the I + (H2O)3 reaction starts with the formation of the entrance complex I···(H2O)3, in which the I atom is bound to one water molecule, with the other two water molecules loosely linked. The I···(H2O)3 entrance complex is predicted to lie 4.1 kcal mol −1 below the separated I + uud-(H2O)3 reactants. In the transition state (TS), the forming I-H7 distance is decreased to 1.688 Å, much shorter than that for the I···(H2O)3 entrance complex (3.180 Å), leading to the formation of an eight-membered ring structure containing three conventional OH bonds, one HI bond, three O···H hydrogen bonds and one I···H noncovalent interaction ( Figure 1). The TS In the transition state (TS), the forming I-H7 distance is decreased to 1.688 Å, much shorter than that for the I···(H 2 O) 3 entrance complex (3.180 Å), leading to the formation of an eight-membered ring structure containing three conventional OH bonds, one HI bond, three O···H hydrogen bonds and one I···H noncovalent interaction ( Figure 1). The TS structure has an imaginary vibrational frequency of 307i cm −1 (as shown in Table S1 in the Supplementary Materials), with its normal mode corresponding to simultaneous O1-H7 elongation and I-H7 formation. The energy of the TS is 43.7 kcal mol −1 higher than that of the separated I + uud-(H 2 O) 3 reactants.
The exit complex ud-HI···(H 2 O) 2 OH also has an eight-membered ring structure, with its two out-of-plane OH moieties in "up-down" orientations. The ud-HI···(H 2 O) 2 OH complex is very similar to the TS, differing mainly by the even longer O1-H7 and shorter I-H7 distance ( Figure 1). The covalent I-H7 bond of 1.642 Å in the exit complex ud-HI···(H 2 O) 2 OH is only slightly longer than the 1.619 Å in the free HI molecule. The exit complex ud-HI···(H 2 O) 2 OH lies 42.7 kcal mol −1 energetically above the separated I + uud-(H 2 O) 3 reactants but 4.3 kcal mol −1 below the separated HI + (H 2 O) 2 OH products.
Separating HI from the ud-HI···(H 2 O) 2 OH exit complex leads to the reaction products HI and ud-(H 2 O) 2 OH. The two out-of-plane OH bonds of ud-(H 2 O) 2 OH are in the "updown" orientations with respect to the pseudo six-membered ring plane. Compared with separated I + uud-(H 2 O) 3 reactants, the HI + ud-(H 2 O) 2 OH products lie 47.0 kcal mol −1 above. Thus, the I + (H 2 O) 3 → HI + (H 2 O) 2 OH reaction is significantly endothermic.
For the possible chemistry applications of this PES, we also considered the relative Gibbs free energies for the lowest-energy pathway of the I + (H 2 O) 3 → HI + (H 2 O) 2 OH reaction at various conditions, as shown in Table S2. It appears that the different temperatures and pressures have little effect on the relative Gibbs free energies.
The harmonic vibrational frequencies and zero-point energies (ZPE) for the stationary points of the I + (H 2 O) 3 → HI + (H 2 O) 2 OH reaction using the CCSD(T)/cc-pVTZ(-PP) method are shown in Table S1 of the Supplementary Materials. As seen from Table S1, our computational frequencies for (H 2 O) 3 and (H 2 O) 2 OH agree with existing experimental values [26][27][28]. Especially, our theoretical H-I stretching frequency of 2314 cm −1 is very close to the experimental frequency of 2309 cm −1 [29]. The ZPE values given in Table S1 can be used to correct the energies of the stationary points. Including the ZPE corrections, the relative energies of the entrance complex, TS, exit complex and products for the I + (H 2 O) 3 → HI + (H 2 O) 2 OH reaction become −4.1, 38.9, 38.3 and 41.7 kcal mol −1 , respectively.
Spin-orbit coupling (SOC) effects also need to be considered in iodine-containing systems. In this research, the Breit-Pauli operator implemented in the MOLPRO program package is employed to provide SOC corrections, starting with the full valence complete active space self-consistent field (CASSCF) wave functions, using cc-pVQZ(-PP) basis sets [30,31]. For the reactant (I atom), entrance complex, TS, exit complex, and product [(H 2 O) 2 OH] in the lowest-energy pathways of the I + (H 2 O) 3 reaction (Figure 1), our CASSCF SOC corrections are predicted to be 2425, 1229, 0.6, 0.1 and 4 cm −1 (or 6.9, 3.5, 0.0, 0.0, and 0.0 kcal mol −1 ), respectively. The SOC correction of 2425 cm −1 obtained herein for the I( 2 P) atom is in reasonable agreement with the experimental value of 2534 (= 7603/3) cm −1 [32]. With both ZPE and SOC corrections, the relative energies of the entrance complex, TS, exit complex and products for the I + (H 2 O) 3 Figure 2. The trimer complex I···(H 2 O) 3 is bound by 4.1 kcal mol −1 (two new noncovalent interactions form but one is broken) lower than the binding energy of 6.0 kcal mol −1 (two new noncovalent interactions form) for the water dimer complex I···(H 2 O) 2 but higher than that of 3.3 kcal mol −1 (one new noncovalent interaction forms) for the water monomer complex I···H 2 O. At the transition state, the relative energy of 43.7 kcal mol −1 for the water trimer reaction I + (H 2 O) 3 is between those for the water dimer reaction (42.0 kcal mol −1 ) and water monomer reaction (44.9 kcal mol −1 ). A similar case occurs for the exit complex. For the separated products, the relative energy for the water trimer reaction (47.0 kcal mol −1 ) is somewhat higher than that for the water dimer reaction (45.4 kcal mol −1 ) and that for the water monomer reaction (46.1 kcal mol −1 ). With some exceptions, the water trimer reaction I + (H 2 O) 3 looks energetically between the water dimer reaction I + (H 2 O) 2 and the water monomer reaction I + H 2 O. the water trimer reaction I + (H2O)3 is between those for the water dimer reaction (42.0 kcal mol −1 ) and water monomer reaction (44.9 kcal mol −1 ). A similar case occurs for the exit complex. For the separated products, the relative energy for the water trimer reaction (47.0 kcal mol −1 ) is somewhat higher than that for the water dimer reaction (45.4 kcal mol −1 ) and that for the water monomer reaction (46.1 kcal mol −1 ). With some exceptions, the water trimer reaction I + (H2O)3 looks energetically between the water dimer reaction I + (H2O)2 and the water monomer reaction I + H2O. We also compare the potential energy profile of the I + (H2O)3 reaction with those for the Br + (H2O)3, Cl + (H2O)3 and F + (H2O)3 reactions. All five stationary points for the four reactions are geometrically related [16][17][18], while the landscape profiles of the four reactions are quantitatively different, as shown in Figure 3. The entrance well for I···(H2O)3 lies below the reactants by 4.1 kcal mol −1 , slightly shallower than the 4.7 kcal mol −1 for bromine, 5.3 kcal mol −1 for chlorine, and 7.1 kcal mol −1 for fluorine. The relative energies of the other stationary points (i.e., the transition state, exit complex and products) display significant differences. Taking the transition state as an example, the relative energy of 43.7 kcal mol −1 for the I + (H2O)3 reaction is much higher than that of 29.  We also compare the potential energy profile of the I + (H 2 O) 3 reaction with those for the Br + (H 2 O) 3 , Cl + (H 2 O) 3 and F + (H 2 O) 3 reactions. All five stationary points for the four reactions are geometrically related [16][17][18], while the landscape profiles of the four reactions are quantitatively different, as shown in Figure 3. The entrance well for I···(H 2 O) 3 lies below the reactants by 4.1 kcal mol −1 , slightly shallower than the 4.7 kcal mol −1 for bromine, 5.3 kcal mol −1 for chlorine, and 7.1 kcal mol −1 for fluorine. The relative energies of the other stationary points (i.e., the transition state, exit complex and products) display significant differences. Taking the transition state as an example, the relative energy of 43.7 kcal mol −1 for the I + (H 2 O) 3 reaction is much higher than that of 29.

Computational Methods
Our preliminary computational method employed in this research is similar to that successfully used for the water dimer reaction of I + (H2O)2 [15], namely MPW1K, a density functional theory (DFT) method constructed by Truhlar et al. [33] MPW1K gave the best predictions among 49 DFT functionals used for the related F + H2O reaction barrier [34]. Our more reliable theoretical results come from the "gold standard" CCSD(T), the coupled-cluster single and double substitution method with a perturbative treatment of triple excitations [35][36][37].
In conjunction with the MPW1K and CCSD(T) methods, the correlation-consistent polarized valence basis sets (cc-pVnZ) of Dunning et al. were used. For the hydrogen and oxygen atoms, the cc-pVnZ (n = D, T, Q) basis sets [38,39] were utilized. For the iodine atom, the Stuttgart-Cologne pseudopotential (PP) and the corresponding cc-pVnZ-PP (n = D, T, Q) basis sets [40] of Peterson et al. were employed. The PP method replaces 28 inner core electrons (1s 2 2s 2 2p 6 3s 2 3p 6 3d 10 ) of the iodine atom with an effective core potential.
The low energy pathways of the I + (H2O)3 reaction were firstly investigated at the MPW1K/cc-pVTZ(-PP) level of theory, using the Gaussian 16 program suite [41]. All of the stationary points involved were fully optimized and characterized via harmonic vibrational frequency analyses. Intrinsic reaction coordinate (IRC) [42][43][44] analyses were also performed with this method to ascertain that the transition state connects the designated entrance and exit complexes.
For the lowest-energy pathway of the I + (H2O)3 reaction, the CCSD(T)/cc-pVnZ(-PP) (n = D, T, Q) computations were performed, using the CFOUR program [45]. This allowed us to enhance the reliabilities of the geometries, energies and vibrational frequencies of the stationary points involved. In all CCSD(T) computations, the 1s-like MO for oxygen

Computational Methods
Our preliminary computational method employed in this research is similar to that successfully used for the water dimer reaction of I + (H 2 O) 2 [15], namely MPW1K, a density functional theory (DFT) method constructed by Truhlar et al. [33] MPW1K gave the best predictions among 49 DFT functionals used for the related F + H 2 O reaction barrier [34]. Our more reliable theoretical results come from the "gold standard" CCSD(T), the coupledcluster single and double substitution method with a perturbative treatment of triple excitations [35][36][37].
In conjunction with the MPW1K and CCSD(T) methods, the correlation-consistent polarized valence basis sets (cc-pVnZ) of Dunning et al. were used. For the hydrogen and oxygen atoms, the cc-pVnZ (n = D, T, Q) basis sets [38,39] were utilized. For the iodine atom, the Stuttgart-Cologne pseudopotential (PP) and the corresponding cc-pVnZ-PP (n = D, T, Q) basis sets [40] of Peterson et al. were employed. The PP method replaces 28 inner core electrons (1s 2 2s 2 2p 6 3s 2 3p 6 3d 10 ) of the iodine atom with an effective core potential.
The low energy pathways of the I + (H 2 O) 3 reaction were firstly investigated at the MPW1K/cc-pVTZ(-PP) level of theory, using the Gaussian 16 program suite [41]. All of the stationary points involved were fully optimized and characterized via harmonic vibrational frequency analyses. Intrinsic reaction coordinate (IRC) [42][43][44] analyses were also performed with this method to ascertain that the transition state connects the designated entrance and exit complexes.
For the lowest-energy pathway of the I + (H 2 O) 3 reaction, the CCSD(T)/cc-pVnZ(-PP) (n = D, T, Q) computations were performed, using the CFOUR program [45]. This allowed us to enhance the reliabilities of the geometries, energies and vibrational frequencies of the stationary points involved. In all CCSD(T) computations, the 1s-like MO for oxygen and the 4s4p4d-like MOs for iodine were frozen, i.e., doubly occupied. Restricted Hartree-Fock orbitals were used for all closed shell systems, while unrestricted orbitals were employed for the open-shell species.

Conclusions
Low energy pathways of the I + (H 2 O) 3 → HI + (H 2 O) 2 OH reaction were explored using the "gold standard" CCSD(T) method. The Dunning correlation-consistent basis sets as large as cc-pVTZ(-PP) are used for the geometry optimizations and vibrational frequency analyses and cc-pVQZ(-PP) for the single-point energy determinations. Based on our CCSD(T)/cc-pVQZ(-PP)//CCSD(T)/cc-pVTZ(-PP) computations, the I + (H 2 O) 3 → HI + (H 2 O) 2 OH reaction is significantly endothermic by 47.0 kcal mol −1 . The submerged (compared to products) transition state lies 43.7 kcal mol −1 above the separated reactants, indicating there is no energy needed for the reverse reaction. Including zero-point energy and spin-orbit coupling corrections, the relative energies of the entrance complex, transition state, exit complex and products for the I + (H 2 O) 3 2 reaction. This indicates that the second water molecule lowers the barrier of the water monomer reaction, but the third water molecule has almost no effect on the barrier. Thus, it is plausible that larger water clusters may behave energetically like the water trimer when reacting with an iodine atom. Of course, more research is necessary to prove this prediction. The

Data Availability Statement:
The data presented in this study are available upon request from the corresponding authors.