Single solvent molecule effect over S_N2 and E2 competition in the hydroperoxide anion reaction with ethyl-iodide

Abstract

The influence of individual solvent molecules on the dynamics of competing reactions remains largely unexplored for many important chemical systems. Herein, direct dynamics simulations revealed that a single water molecule has multifaceted effects on the reaction between the hydroperoxide anion HOO⁻ and C₂H₅I. The introduction of one water reduced the overall reaction rate and shifted the preference from elimination (E2) to substitution (S_N2) reactions because of the differential solvation effect. Increasing the collision energy lowered the overall reactivity but did not change the S_N2-to-E2 pathway ratio. Notably, the additional water molecules also induced new competing pathways that used HO⁻ as an attacking nucleophile via proton transfer within the nucleophile HOO⁻(H₂O); here, both the HO⁻-E2 and HO⁻-S_N2 trajectories were observed at small percentages. The occurrence of the HO⁻ paths was driven by the extensive proton transfer within the pre-reaction complex well, but was suppressed by the entropy effect and increased barriers. In addition, water molecules complicated the reaction mechanisms, increased the percentage of indirect mechanisms, and affected the dynamic features of proton transfer. As in the solvent-free system, protons were frequently exchanged between the nucleophiles and substrates, whereas in the singly solvated system, proton exchange mainly occurred within the nucleophiles. This work highlights the dynamic role of solvent molecules and may have profound impacts on reaction dynamics, with relevance to organic synthesis and chemistry in biosystems, microdroplets, and aerosols.

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Introduction

In addition to providing a liquid-phase reaction environment, solvents have a profound impact on chemical reactions, such as affecting the reaction kinetics through catalysis^1–5 or inhibition,⁶ altering the product branching ratios,^7–9 and modifying the reaction dynamics.^4,10,11 The influence of the individual solvent molecules on the reaction dynamics has long been a central topic among experimental and theoretical researchers in the fields of atmospheric, physical, and interfacial chemistry.^{1,3,6,7,9,12–19} In particular, the development of crossed-beam imaging experimental techniques and computational simulation powers enables a detailed investigation of the reaction mechanisms and dynamics.^10,20–29 Ion–molecule reactions represent a prevalent category of chemical reactions and can potentially be affected by solvent effects.^10,30–32 However, the dynamic and steric effects caused by the individual solvent molecules remain elusive for numerous critical ion-molecule reactions.

The hydroperoxide anion (HOO⁻), which is the conjugate base of hydrogen peroxide (HOOH), is an important species across diverse fields. For example, in atmospheric chemistry, HOO⁻ participates in reactions that contribute to acid rain formation and ozone consumption.³³ In the cellular biology field, HOO⁻ is involved in the oxidative processes linked to ageing and degenerative diseases since it reacts with lipids and proteins.^34–37 Industrially, HOO⁻ serves as a key oxidant in semiconductor cleaning processes and peroxide bleaching, where it facilitates the breakdown of chromophores to decolorize fabrics.^38–40 Additionally, HOO⁻ likely participates in hydrocarbon oxidation and combustion processes, such as acetylene combustion; here, it reacts with formaldehyde and formic acid.^41,42 Recent advancements in energy storage have also highlighted its importance since shifting the discharge intermediate from superoxide O₂⁻ to HOO⁻ in aprotic Li–O₂ batteries can reduce the byproducts and overpotentials to enhance battery efficiency.⁴³ Due to its multifaceted roles, HOO⁻ needs to be comprehensively understood to advance research in atmospheric science, biochemistry, industrial application, and energy technologies.

The hydrated HOO⁻ ion has garnered great interest for its unique properties.^44–49 Microhydrated HOO⁻ ions, HOO⁻(H₂O)_n, can undergo proton transfer to generate isomers in the form of HO⁻(HOOH)(H₂O)_n−1, where the latter is lower in energy when the number of water molecules n is less than 6.⁴⁸ Hence, when hydrated HOO⁻ ions interact with a substrate, they can behave as dual nucleophiles, similar to CN⁻, such that either HOO⁻ or HO⁻ can act as nucleophiles.^50–53 Previously, direct dynamics simulations of singly hydrated HOO⁻ reacting with CH₃Cl and CH₃I revealed that the HOO⁻ path is dominant and produces CH₃OOH, whereas the HO⁻ path contributes only a minor fraction of the products and produces CH₃OH.^32,54 Calculations have shown that increasing the degree of hydration causes the HO⁻ path to be even less favourable.⁵⁵ Enlarging the substrate from methyl halides to ethyl halides introduces a competing reaction to the S_N2 pathway, namely, elimination reactions (E2).^4,9,56–58 Either HOO⁻ or HO⁻ can serve as the base for the E2 reaction. Interestingly, when singly hydrated HOO⁻ reacts with ethyl halides, the E2 reaction products of the HOO⁻ and HO⁻ paths are identical (Scheme 1) and have similar barriers.⁵⁹ Distinguishing these two product channels by experiment is a formidable task. Therefore, the reaction dynamics need to be investigated using computational simulations.

Scheme 1 S_N2 and E2 reaction pathways of the HOO⁻(H₂O) + CH₃CH₂X reactions.

In this work, we performed direct dynamics simulations on CH₃CH₂I reacting with HOO⁻ and HOO⁻(H₂O) in the gas phase to reveal the role of a single water molecule in the reaction dynamics. The key questions we explored are as follows: What is the effect of one water molecule on (1) the reaction kinetics, i.e., the rate constants; (2) the competition between S_N2 and E2 reactions, i.e., their ratio and atomic-level mechanism; and (3) the competition between the HOO⁻ and HO⁻ pathways? (4) What is the role of collision energy? The simulations focus on the microhydrated HOO⁻ ions and reveal that the solvent molecules not only affect the competition between the different pathways but also influence the dynamic behaviour of chemical reactions. These findings provide valuable theoretical guidance for the environment, energy, and synthesis chemistry.

Computational methods

Direct dynamics simulations were performed at the CAM-B3LYP/6-31+G(d,p)&ECP level of theory using the VENUS/NWChem program.^60–62 The 6-31+G(d,p) basis set was used for the H, C, and O atoms, and the LANL2DZdp basis set and effective core potential (ECP) were used for iodine. The choice of this method was based on the accuracy of the structure and reaction enthalpy (ESI Note and Tables S1–S3†). The initial distance between CH₃CH₂I and HOO⁻ or HO⁻(HOOH) was 15 Å, and the collision energy (E_coll) was 0.04 eV (equivalent to 300 K) and 1.0 eV. The vibrational and rotational temperatures of the reactants were 300 K, and the vibrational and rotational energies were sampled for their respective Boltzmann distributions. At an E_coll of 0.04 eV, the trajectories were calculated at a fixed impact parameter b of 0, 1, 3, 5, 7, 9, 11, 13, and 15 Å; here, the reaction probability was zero at the maximum b under investigation, namely, b_max. At E_coll = 1.0 eV, the impact parameter b was 0, 1, 3, 5, 7, and 9 Å for the HOO⁻ system, and b was 0, 1, 3, 5, and 7 Å for the HO⁻(HOOH) system. For each b, approximately 100–120 trajectories were simulated, resulting in a total of 3178 trajectories. Considering the computational efficiency, the trajectories were integrated by the velocity Verlet method⁶³ with a 1.0 fs time step.

Results and discussion

Overall reactivity

The reactivities of CH₃CH₂I with HOO⁻ and HO⁻(HOOH) at collision energies of 0.04 eV and 1.0 eV were evaluated by plotting the opacity functions P_r(b) versus the impact parameter b for the total reaction and different product channels, i.e., the HOO⁻-S_N2, HO⁻-S_N2, HOO⁻-E2, and HO⁻-E2 pathways (Fig. 1). In comparison, increasing the collision energy decreases both the maximum impact parameter b_max and the reaction probability at each b, i.e., P_r(b), which together lower the overall reactivity. For example, for the unsolvated HOO⁻ + CH₃CH₂I reaction, the value of b_max decreases from 15.0 Å at an E_coll of 0.04 eV to 9 Å at 1.0 eV; P_r(b) at b = 1 Å decreases from 0.89 at 0.04 eV to 0.23 at 1.0 eV. Evaluating the total integral cross sections (ICSs) σ_r via the formula provides an σ_r value of 452.8 ± 7.6 Ų at 0.04 eV and a much smaller value of 17.7 ± 1.9 Ų at 1.0 eV. The corresponding reaction rate constants of k(E_coll, T_v, T_r) = v(E_coll)σ(E_coll, T_v, T_r) are (23.8 ± 0.4) and (4.7 ± 0.5) × 10⁻¹⁰ cm³ mol⁻¹ s⁻¹. These results indicate that increasing E_coll from 0.04 to 1.0 eV reduces the rate constant by a factor of 4.

Fig. 1 Opacity functions P_r(b) of the different pathways for CH₃CH₂I reacting with (a and c) HOO⁻ and (b and d) HO⁻(HOOH) at collision energies of 0.04 eV (top) and 1.0 eV (bottom).

Adding one water molecule to the nucleophile barely affects the value of b_max but lowers P_r(b). For example, at b = 1.0 Å and E_coll = 0.04 eV, the total P_r(b) decreases from 0.89 for the unsolvated system to 0.49 for the singly solvated system. As a result, this leads to a decrease in the cross-section and reaction rate constant. For the singly solvated HO⁻(HOOH) + CH₃CH₂I system, σ_r is 209.2 ± 8.0 Ų at 0.04 eV and 7.5 ± 1.0 Ų at 1.0 eV, and the respective rate constants k are (9.3 ± 0.4) and (1.7 ± 0.2) × 10⁻¹⁰ cm³ mol⁻¹ s⁻¹. Taken together, adding one water to the system decreases the rate constant by factors of 1.6 and 1.8 at E_coll of 0.04 and 1.0 eV, respectively.

Product channels

The S_N2 and E2 reactions compete with each other during the reaction process. For the unsolvated system, both the HOO⁻-S_N2 and the HOO⁻-E2 pathways occur throughout the range of b from 0 to b_max. Notably, the E2 pathway remains dominant over the S_N2 pathway at each b (Fig. 1a and c). The branching ratio derived from the ICSs for E2 : S_N2 is 60.4 : 39.6 at 0.04 eV and 62.7 : 37.3 at 1.0 eV (Fig. 2a and c). These results show that increasing E_coll slightly enhances the advantage of E2 over S_N2 reactions, even though the overall reactivity is reduced.

Fig. 2 Branching ratios of the HOO⁻-S_N2 (blue), HOO⁻-E2 (red), HO⁻-S_N2 (green) and HO⁻-E2 (orange) pathways for CH₃CH₂I reacting with (a and c) HOO⁻ and (b and d) HO⁻(HOOH) at collision energies of 0.04 eV (top) and 1.0 eV (bottom).

The addition of one water molecule to the system introduces significant changes in the products and their ratios, in addition to affecting the reactivity. At an E_coll of 0.04 eV, in addition to the normal HOO⁻-S_N2 and E2 pathways, additional pathways are observed owing to proton transfer within the nucleophile. One is the HO⁻-S_N2 pathway; here, HO⁻ behaves as the attacking nucleophile and generates CH₃OH + H₂O₂ + I⁻, and this reaction occurs at b values of 1, 3, 5, 7, 9, and 11 Å. The other is the HO⁻-E2 pathway, which generates the same products as normal HOO⁻-E2, i.e., C₂H₄ + H₂O₂ + H₂O + I⁻, but the attacking base is HO⁻. This reaction occurs at b values of 0, 1, 3, 7, 9 and 13 Å. However, both pathways are quite rare, where the HO⁻-S_N2 and HO⁻-E2 paths account for 2.2% and 2.6%, respectively, of the overall products. At an E_coll of 1.0 eV, only the HO⁻-E2 pathway is observed, with a minor contribution of 6.8%. Nevertheless, the observation of these HO⁻-attacking trajectories highlights the unique role of water molecules in shaping the reaction dynamics.^32,54

Furthermore, the solvated products, i.e., I⁻(H₂O) and I⁻(HOOH), are observed in both the S_N2 and E2 reaction trajectories. Although the calculated reaction energies are more negative for the solvated products than for the separated products (Fig. S1†), the unsolvated product I⁻ ions dominate over the solvated I⁻(solvent) ions. In comparison, the reaction energy of the CH₃OOH + I⁻(H₂O) products is −47.8 kcal mol⁻¹, and this value is 11.4 kcal mol⁻¹ lower than that of the CH₃OOH + I⁻ + H₂O products; the reaction energy of the C₂H₄ + I⁻(H₂O) + H₂O₂ products is −22.7 kcal mol⁻¹, and this value is 11.4 kcal mol⁻¹ lower than that of the C₂H₄ + I⁻ + H₂O + H₂O₂ products. At an E_coll of 0.04 eV, the simulated product anion ratio I⁻ : I⁻(solvent) is approximately 97 : 3, highlighting that solvated pathways are suppressed because of the dynamic nature of the reactions in the gas phase; these results are consistent with previous experimental and theoretical works.^8,22,30,64 When the collision energy is increased to 1.0 eV, no solvated ions are found. Halogen-bonded complexes, either [C₂H₅⋯I⋯OOH]⁻ or [C₂H₅⋯I⋯OOH]⁻(H₂O), are observed in both solvent-free and singly solvated systems and are less than 1%.

Moreover, the additional water molecules shift the preference between the S_N2 and E2 pathways compared with the solvent-free case (Fig. 2b and d). For the singly solvated system, at an E_coll of 0.04 eV, the HOO⁻-S_N2 path has a higher P_r(b) than the HOO⁻-E2 path from b of 0 to 5 Å, and they have similar P_r(b) values at b values of 7 to 13 Å. At an E_coll of 1.0 eV, the HOO⁻-S_N2 path has a higher P_r(b) at b values of 1 and 5 Å. The resulting branching ratios of E2 : S_N2 are approximately 46 : 54 under both collision energies. Considering only the HOO⁻ pathways, i.e., excluding the HO⁻ pathways, S_N2 is also preferred over E2. The phenomenon that solvent molecules promote a portion of the S_N2 path has also been observed in F⁻(CH₃OH) + CH₃CH₂Br reactions.^4,5 Why does a single water molecule shift the preference between the S_N2 and E2 pathways in the studied system? To answer this question, we analysed the potential energy profiles, the atomistic mechanisms and the dynamics of water molecules in the following section.

Potential energy profiles

The potential energy profile of each S_N2 and E2 pathway (Fig. 3) displays a double-well shape, where a central transition state (TS) connects a shallow well of pre-reaction complex (RC) and a deep well of the postreaction complex (PC). All S_N2 and E2 reactions are highly exoergic, and the S_N2 products are more exoergic.

Fig. 3 Potential energy profile of CH₃CH₂I reacting with HOO⁻ and HO⁻(HOOH). (a) refers to the backside attack HOO⁻-S_N2 pathway (blue); (b) refers to the backside attack HO⁻-S_N2 pathway (green); (c) refers to the antisymmetric HOO⁻-E2 pathway (red); (c’) refers to the syn-symmetric HOO⁻-E2 pathway (pink); (d) refers to the antisymmetric HO⁻-E2 pathway (orange). Energy values (in kcal mol⁻¹) excluding zero-point energy corrections are in normal text, and the values of Gibbs free energy at 298.15 K are in parentheses.

For the unsolvated system, both the back-side S_N2 pathway (denoted as a) and the anti-E2 pathway (denoted as c) share the same pre-reaction complex (denoted as 0aRC), with a relative energy of −18.3 kcal mol⁻¹ with respect to reactants HOO⁻ + C₂H₅I. The relative energies of the transition states of the S_N2 pathway (0aTS, −17.9 kcal mol⁻¹) and the anti-E2 pathway (0cTS, −17.7 kcal mol⁻¹) exceed that of 0aRC by less than 1 kcal mol⁻¹. These results indicate that overcoming both barriers is easy. When the E2 reaction proceeds via a syn-E2 mechanism, the HOO⁻ group abstracts the H^β atom from the same side of leaving group I, and its transition state (0c′TS) is much greater in energy, with a value of −7.4 kcal mol⁻¹ with respect to the reactants. The halogen complex [C₂H₅⋯I⋯OOH]⁻ (−19.0 kcal mol⁻¹) has a similar energy as 0aRC.

One water molecule is added to the HOO⁻ anion to form HO⁻(HOOH), and HOO⁻(H₂O) is 29.1 kcal mol⁻¹ exoergic. Starting from HO⁻(HOOH) + C₂H₅I, the reaction energies of the HOO⁻-S_N2, HO⁻-S_N2, and E2 pathways are −36.4, −30.0, and −11.3 kcal mol⁻¹, respectively. The HOO⁻-S_N2 and HOO⁻-E2 pathways share the same RC, i.e., 1aRC, and the HO⁻-S_N2 (denoted as b) and HO⁻-E2 pathways (denoted as d) share the same RC, denoted as 1bRC. The nomenclatures of TS and PC use the a, b, c, and d annotations. The pre-reaction complex for the HO⁻ path (1bRC, −14.3 kcal mol⁻¹) is slightly more stable than that for the HOO⁻ path (1aRC, −13.0 kcal mol⁻¹), as observed for the reaction with CH₃Cl/CH₃I.^32,54 Nevertheless, the transition states of the HO⁻ paths are higher in energy than that for the HOO⁻-path (either the S_N2 path or the E2 path). Arranged in ascending order of transition state energies, the order of pathways is HOO⁻-S_N2 < HO⁻-S_N2 < HOO⁻-E2(anti) < HO⁻-E2(anti). The energies are −9.4, −7.1, −6.2, and −4.0 kcal mol⁻¹ for 1aTS, 1bTS, 1cTS, and 1dTS, respectively. When the free energies are compared, the transition state of HO⁻-S_N2 has the highest free energy among these four TSs. As expected, the syn-E2 path has an even higher transition state, 1c′TS, whose relative energy is 2.7 kcal mol⁻¹ in electronic energy and 9.6 kcal mol⁻¹ in free energy.

Assuming a Boltzmann distribution of these four pathways and according to the calculated free energies of the TSs, the thermal ratio at 300 K of HOO⁻-S_N2 : HOO⁻-E2 is 19.5 : 80.5 for the unsolvated system, and the thermal ratio of HOO⁻-S_N2 : HO⁻-S_N2 : HOO⁻-E2 : HO⁻-E2 is 87.9 : 0.1 : 11.7 : 0.3 for the singly solvated system. At an E_coll of 0.04 eV, corresponding to a temperature of 300 K, the ratios given by direct dynamic simulations are 39.6 : 60.4 and 51.8 : 2.2 : 43.4 : 2.6. The thermal distribution predictions (based on stationary point calculations) and dynamic simulation results are consistent in that the HOO⁻-E2 path is dominant under unsolvated conditions, whereas the HOO⁻-S_N2 path is dominant under singly solvated conditions. Notably, the simulations provide a much higher percentage of the HOO⁻-E2 path, differing by 20–30%, and a slightly higher percentage of the HO⁻ paths. These results highlighted the dynamic characteristics of the reaction process. The dynamic preference of the E2 product channel has also been observed in the F⁻(CH₃OH) + C₂H₅Br reaction,^4,5 where the dominant pathway given by simulation becomes the E2 path instead of the S_N2 path, which was predicted by the thermal distribution. The atomistic mechanisms discussed in the next section provide a detailed picture of the dynamic characteristics.

Atomistic mechanisms

Different types of mechanisms were observed by tracking the animations of each reactive trajectory. The distribution of the mechanisms is shown in Fig. 4. The mechanisms are classified into direct and indirect mechanisms, depending on whether intermediates are formed during the trajectory.^20,65 For the unsolvated system, the reaction mechanism is primarily direct. At an E_coll of 0.04 eV, the direct HOO⁻-S_N2 mechanism accounts for 24.2%, and the direct HOO⁻-E2 mechanism accounts for 40.4%; at an E_coll of 1.0 eV, the corresponding values are 34.2% and 57.8%, respectively. As expected, a higher collision energy leads to more direct trajectories. For both the HOO⁻-S_N2 and E2 pathways, both direct stripping (DS) and direct rebound (DR) mechanisms were observed, where the former is more common. The features of these mechanisms have been described in previous works,^20,65,66 and representative animations are presented in the ESI Movies.† The addition of one water molecule increases the percentage of indirect mechanisms. For the singly hydrated system, at an E_coll of 0.04 eV, the indirect HOO⁻-S_N2 mechanism accounts for 40.5%, and the indirect HOO⁻-E2 mechanism accounts for 29.8%; at an E_coll of 1.0 eV, the corresponding values are 22.2% and 21.8%, respectively. These values are much higher than the corresponding values from the unsolvated system, which are 15.4, 20.0, 3.1, and 4.9% (Fig. 4). The distributions of the product I⁻ ion velocity scattering angle are shown in Fig. S2,† where the indirect mechanism shows isotropic scattering.

Fig. 4 Distributions of the reaction mechanisms for the S_N2 and E2 pathways for CH₃CH₂I reacting with (a and b) HOO⁻ and (c and d) HO⁻(HOOH) at collision energies of 0.04 and 1.0 eV. Note: For unsolvated systems, the 0aRC mechanism involves α-elimination and H^α-exchange mechanisms.

For both unsolvated and singly solvated systems, the observed indirect mechanisms include the formation of various intermediates and roundabout (Ra) mechanisms, where the latter contribute less than 3%. Previous reports of roundabout mechanisms of E2 reactions were limited to F⁻ nucleophiles;^5,56,67,68 this work extends the roundabout mechanism to HOO⁻ and HO⁻(HOOH) reactions.

For both the S_N2 and E2 pathways, the dominant indirect mechanism is the formation of the HOO⁻⋯C₂H₅I complex (0aRC) for the unsolvated system at both E_coll values and the singly solvated system at an E_coll of 1.0 eV. The dominant indirect mechanism becomes the formation of the (H₂O)HOO⁻⋯C₂H₅I complex (1aRC) for the singly solvated system at an E_coll of 0.04 eV. In addition, the mechanism of the singly solvated system was complicated by the participation of multiple intermediates, including 0aRC, 1aRC, 1bRC, and 1aPC. To demonstrate the indirect mechanisms, we provide snapshots of representative trajectories in Fig. 5. Fig. 5a shows an indirect HOO⁻-S_N2 trajectory that is trapped in the pre-reaction complex 1aRC well for approximately 4 ps before the products are formed. Fig. 5c displays an indirect HOO⁻-E2 trajectory that is trapped in the 1aRC well for ∼9 ps. Then, the HOO⁻(H₂O) group abstracts the H^β atom from the opposite side of leaving group I; specifically the anti-E2 mechanism occurs, and E2 products are formed. The lifetimes of pre-reaction complexes 1aRC were analysed by plotting ln[N(t)/N(0)] versus time (t) for the trajectories, where N(0) refers to the number of trajectories that experienced the formation of RCs and N(t) refers to the number of trajectories whose lifetimes of RCs are no less than t (Fig. S3†). The resulting dissociation rate constant of 1aRC is 0.13 ps⁻¹ for the S_N2 path and 0.16 ps⁻¹ for the E2 path. Consequently, the corresponding half-lives of 1aRC are 5.33 and 4.33 ps; these results indicate that the reaction system was trapped in the pre-reaction complex well.

Fig. 5 Snapshots of the representative trajectories showing the indirect mechanism of the HOO⁻(H₂O) + CH₃CH₂I reaction. The distance between the C^α atom and I atom r(C^α-I) (purple), the distance between the C^α atom and the attacking O atom r(C^α–O) (green), and the distance between H^β and the attacking O atom r(H^β–O) (orange) are shown as a function of time. (a) HOO⁻-S_N2 pathway, (b) HO⁻-S_N2 pathway, (c) HOO⁻-E2 pathway, (d) HO⁻-E2 pathway.

In addition to the anti-E2 mechanism, we also observed trajectories that follow the syn-E2 mechanism (Fig. S4b†). Owing to the higher transition states (Fig. 3) and greater steric hindrance than those of the anti-E2 paths, the syn-E2 trajectories constitute only a small portion of all E2 trajectories. For the unsolvated system, the fraction of syn-E2 trajectories is approximately 3% and 8% at E_coll values of 0.04 and 1.0 eV; for the singly solvated system, the corresponding fractions are 0.9% and 0.

In the abovementioned anti-E2 and syn-E2 trajectories, the nucleophile first abstracts H^β from the substrate CH₃CH₂I. For the unsolvated system at an E_coll of 1.0 eV, the E2 trajectories may be initiated by a nucleophile abstracting a H^α atom. As shown in Fig. S5b,† HOO⁻ initially abstracts an H^α atom from the CH₃CH₂I substrate to form HOOH, followed by the C–I bond breaking, and then the substrate becomes CH₃CH. Thereafter, the substrate goes through an H^β-transfer transition state (EαTS) to generate CH₂=CH₂. This mechanism is called α-elimination (Eα) in previous simulations of F⁻ + CH₃CH₂Br reactions,⁵ and this name is adopted here. The barrier of EαTS is as high as 7.9 kcal mol⁻¹ (Fig. S6†); thus, this mechanism is highly unfavourable and is observed only at an E_coll of 1.0 eV and accounts for 2.2% of the HOO⁻-E2 path.

In addition, the trajectories that experience the formation of 0aRC sometimes involve hydrogen exchange (HE) between the nucleophile HOO⁻ and substrates, as observed in both the S_N2 and E2 pathways (Fig. S7b and S5c†). Similar to the first step of the Eα mechanism, the nucleophile initially abstracts an H^α atom from the CH₃CH₂I substrate. The newly formed HOOH moiety transfers an H atom to C^α simultaneously or after a period, and then, the system reforms the CH₃CH₂I and HOO⁻ parts. This H-atom can be either the same H^α or the H that originally belonged to the nucleophile HOO⁻. For the latter case, a transition state was located with a high barrier of 9.5 kcal mol⁻¹. Proton exchange may occur several times within a trajectory. These multiple types of hydrogen exchange trajectories are presented in Fig. S5 and S7.† Overall, these trajectories account for 0.36% (2.17%) of the S_N2 reactions and 0.63% (0.12%) of the E2 reactions at an E_coll of 0.04 eV (1.0 eV). Notably, the H^α-abstraction may generate CH₃CHI⁻ + HOOH products. The product channel is 48.6 endothermic and was not observed during our simulation. However, a trace amount of CH₃CHCl⁻ was observed in previous simulations of F⁻/HO⁻ + CH₃CH₂Cl.^69,70

Interestingly, these α-elimination and H^α-exchange mechanisms were not observed in the singly hydrated system. This can be understood by comparing the proton affinities (PAs). The PA of HOO⁻ is 375.9 kcal mol⁻¹, and the PA of HO⁻(HOOH) is 357.0 kcal mol; thus, the abstraction of either H^α or H^β from CH₃CH₂I by HO⁻(HOOH) is more difficult than that by HOO⁻. Instead, the proton transfer between the nucleophiles and substrates is completely suppressed by proton transfer within the singly solvated nucleophile HO⁻(HOOH). Representative trajectory snapshots are shown in Fig. S8 and S9.†

For the water-induced HO⁻-S_N2 and HO⁻-E2 pathways, Fig. 5b and d show that these trajectories also experience a long time (approximately 6–7 ps) within the pre-reaction complex well; here, the nucleophile group strongly interconverts between HOO⁻(H₂O) and HO⁻(HOOH). The singly solvated pre-reaction complexes (H₂O)HOO⁻⋯C₂H₅I (1aRC) and (HOOH)HO⁻⋯C₂H₅I (1bRC) are close in energy, and the latter is approximately 1 kcal mol⁻¹ more stable. However, tracking the trajectories within the well indicates that the system prefers to stay in the configuration of (H₂O)HOO⁻⋯C₂H₅I. For example, for a representative HO⁻-S_N2 trajectory (Fig. 5b) and considering the time within the pre-reaction complex well, the system adopts the (H₂O)HOO⁻⋯C₂H₅I configuration 69% of the time, and this value is 73% for a representative HO⁻-E2 trajectory (Fig. 5d). The more stable (HOOH)HO⁻⋯C₂H₅I configuration only accounts for 31% and 27%, respectively. A detailed analysis is provided in Fig. S10.† This occurs because the symmetric structure of (HOOH)HO⁻ in 1bRC can easily be disturbed during the dynamic reaction process, namely, the entropy effect. Hence, the lower probability of the HO⁻ configurations within the well and the higher barrier both lead to the suppression of the HO⁻ paths, both S_N2 and E2. Nevertheless, the simulated HO⁻ paths have a slightly greater portion than those predicted by the thermal distribution at 300 K; these results indicate the dynamic effects of proton transfer during the reaction processes.

Finally, we investigated the reason for the suppression of the thermodynamically favoured solvated product I⁻(solvent) by the I⁻ product from the simulation. To understand this, we plotted the time at which the H₂O molecule departed from the system against the formation time of CH₃CH₂OOH for the HOO⁻-S_N2 pathway and against the formation time of CH₂=CH₂ for the HOO⁻-E2 pathway (Fig. 6). At E_coll = 0.04 eV, the formation of CH₃CH₂OOH or CH₂=CH₂ simultaneously occurred with the departure of H₂O, mostly within 20 ps. As E_coll increased to 1.0 eV, the majority of S_N2 reactions occurred within 5 ps, whereas the H₂O molecules were removed much earlier, mainly before 2.5 ps. Similarly, the E2 reactions occurred within ∼4 ps, and the H₂O molecules were removed before 2.0 ps. With a time width of ±250 fs centred on the unit slope line, the percentages of the trajectories for S_N2 and E2 were 65.2% and 71.5%, respectively, at E_coll = 0.04 eV, and the corresponding values decreased to 46.0% and 41.4%, respectively, at E_coll = 1.0 eV. The above analysis, together with the mechanism analysis, indicated that a large portion of the collision energy and/or the reaction exothermicity were transferred to the relative translational energy of the solvent and the remaining parts. Consequently, solvated products were rarely observed.

Fig. 6 Water-leaving time as a function of CH₃CH₂OOH (left) and CH₂=CH₂ (right) formation time for the HOO⁻(H₂O) + CH₃CH₂I reaction at 0.04 (top) and 1.0 eV (bottom) collision energies.

Conclusions

In this work, the effect of a single water molecule on the reaction between the hydroperoxide anion and ethyl iodide was investigated by direct dynamics simulation. The introduction of one water molecule had multiple effects. First, it lowered the overall reactivity; here, the rate constant was reduced by 61% and 63% in comparison to that of the solvent-free reaction, under the considered collision energies of 0.04 and 1.0 eV. Second, it changed the preference between the competing S_N2 and E2 reactions. The S_N2-to-E2 ratio was approximately 40 : 60 for the solvent-free system, and this ratio changed to approximately 54 : 46 for the single-solvation system under both E_coll values. A single solvent shifted the preference from E2 to S_N2 because of the differential solvation effect that led to a higher barrier for the E2 path than for the S_N2 path. However, the dynamical simulations resulted in more E2 trajectories than what was predicted by the potential energy profiles. Increasing E_coll did not affect the S_N2-to-E2 ratio but lowered the overall reactivity by 82%.

Third, the extra water molecules facilitated new pathways via proton transfer between HOO⁻(H₂O) and HO⁻(HOOH), thus leading to the HO⁻-S_N2 and HO⁻-E2 paths, in addition to the traditional HOO⁻-S_N2 and HOO⁻-E2 paths, where the latter two paths were dominant. The percentages of HOO⁻-S_N2, HOO⁻-E2, HO⁻-S_N2, and HO⁻-E2 paths were 51.8%, 43.4%, 2.2%, and 2.6%, respectively, at an E_coll of 0.04 eV and 54.6%, 38.6%, 0, and 6.8%, respectively, at an E_coll of 1.0 eV. Extensive proton transfer within the pre-reaction complex well drove the occurrence of the HO⁻ paths. However, the lower probability of HO⁻ configurations that caused by the entropy effect and the relatively higher barrier led to their low percentages. We anticipate that the solvent molecule inducing new pathways is not an isolated case, especially for protic solvents such as H₂O, NH₃, and CH₃OH. However, such studies are quite limited so far. Singly-solvated anions like OH⁻(H₂O), NH₂⁻(NH₃), and CH₃O⁻(CH₃OH) experience extensive proton exchange, but generate the same type of anions. Anions like F⁻(H₂O), HO⁻(NH₃), HOO⁻(NH₃), and CH₃O⁻(H₂O) can generate new nucleophiles through proton transfer, but they are usually higher in energy. Their dynamics remain to be explored in the future.

Fourth, the introduction of one water molecule complicated the reaction mechanisms, increased the percentage of indirect mechanism, and affected the dynamical feature of proton transfer. For the solvent-free system, proton transfer occurred between nucleophiles and substrates; for example, α-elimination and H^α-exchange mechanisms were observed. In contrast, for the singly solvated system, proton transfer mainly occurred within the nucleophile, i.e., the configurations shifted between (H₂O)HOO⁻⋯C₂H₅I and (HOOH)HO⁻⋯C₂H₅I. Finally, solvated products were observed for the singly solvated reactions, but at a very low percentage of 3%. This occurred because a large portion of the collision energy and/or the reaction exothermicity were transferred to the translation of the products.

To conclude, this work revealed that for the HOO⁻ + C₂H₅I reaction, a single water molecule affected more than the reactivity and competition between the S_N2 and E2 reactions. It also induced new competing pathways that used HO⁻ as an attacking nucleophile via proton transfer and complicated the reaction mechanisms. These dynamic roles of the individual solvent molecules observed in this work could reveal new facets of reaction dynamics relevant to organic synthesis, biochemistry,^71,72 microdroplet chemistry,^73–76 and chemistry in aerosols.^77–80

Data availability

Data are in ESI.†

Author contributions

J. X. designed the research. X. Wu performed the computations, analyzed the data, prepared the figures and tables, and wrote the draft of the paper. C. Z. edited the paper. J. X. and J. S. F. supervised the research and edited the paper.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This work was supported by the National Key Research and Development Program of China (2024YFA1509602), the National Natural Science Foundation of China (no. 22273004), and the Teli Fellowship and the Innovation Foundation (no. 2021CX01026) from the Beijing Institute of Technology, China.

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Footnote

† Electronic supplementary information (ESI) available: Direct rebound mechanism of the HOO⁻-S_N2 path (Video S1); direct stripping mechanism of the HOO⁻-S_N2 path (Video S2); direct rebound mechanism of the HOO⁻-E2 path (Video S3); direct stripping mechanism of the HOO⁻-E2 path (Video S4); indirect mechanism, roundabout mechanism of the HOO⁻-S_N2 path (Video S5); indirect mechanism of the H-exchange of the HOO⁻-S_N2 path (Video S6); indirect mechanism of the HOO⁻-anti-E2 path (Video S7); indirect mechanism of the HOO⁻-syn-E2 path (Video S8); indirect mechanism of the α-elimination of the HOO⁻-E2 path (Video S9); indirect mechanism of the HO⁻-S_N2 path (Video S10); indirect mechanism of the HO⁻-E2 path (Video S11). See DOI: https://doi.org/10.1039/d5sc04298d

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