About the Existence of Organic Oxonium Ions as Mechanistic

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About the Existence of Organic Oxonium Ions as Mechanistic Intermediates in Water Solution Santiago de la Moya Cerero, Hans-Ullrich Siehl, and Antonio García Martínez J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.6b06216 • Publication Date (Web): 23 Aug 2016 Downloaded from http://pubs.acs.org on August 23, 2016

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The Journal of Physical Chemistry

About the Existence of Organic Oxonium Ions as Mechanistic Intermediates in Water Solution Santiago de la Moya Cerero,† Hans-Ullrich Siehl‡ and Antonio García Martínez†,* †Departamento de Química Orgánica I, Facultad de Ciencias Químicas, Universidad Complutense de Madrid, Ciudad Universitaria s/n, E-28040, Madrid, Spain. ‡Abteilung Organische Chemie I, Universität Ulm, Albert Einstein Allee 11, D-89069 Ulm, Germany. *[email protected]

ABSTRACT. This paper is aimed to show overwhelming experimental and theoretical evidences supporting the existence of organic oxonium ions (ROH2+) as mechanistic intermediates in water solution, which should be taken into account when describing important reactions, like hydrations of carbocations or C-O cleavages under acidic conditions. For the hydration reaction of tert-butyl (t-Bu+) cation, we have calculated the reaction rate between the intermediate hydrated cation tBuOH2+ and water, showing that the concerted proton/electron transfer reaction (CPET) is very slow in comparison with experimental data. Much better accordance is achieved by assuming a sequential electron transfer/proton transfer reaction (ETPT). Thus, there is an excellent accordance between the calculated relaxation time (τ = 2.14 ps) for the ETPT process in water and experimentally-determined τ values (1.0-1.5 ps) for related reactions. Moreover, there is also an excellent agreement between the potential energy of activation (ΔVTS≠ = 3.17 kcal/mol) for the proton transfer in gas-phase, computed with the B3LYP/6-31G(d) method following the variational transition state theory (VTST), with the analogous ΔV(QEQ)≠ value (3.09 kcal/mol), calculated using methods based on single electron transfer (SET) reactions.

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INTRODUCTION The determination of reaction intermediates is one of the most important subjects in physical and general organic chemistry.1 One of the most important criterion for establishing a chemical specie as a reaction intermediate is its detection by (statical) infrared spectroscopy, as it was established by one of the most important authorities in this field: Prof. William P. Jencks.2 So, such a species has to be stable enough to have a lifetime of at least a few molecular vibrations under the reaction conditions; i.e., a lifetime greater than 1-0.1 ps.1,2 Jencks also pointed out that if a species cannot fulfill this condition, a mechanism involving it is impossible, and an alternate one is “enforced”. 2 According to differential infrared (DIR) spectroscopy measurements of acidic aqueous solutions, oxonium ions such as hydronium ion (H3O+) and dihydrated proton (H5O2+), also known as Eigen cation and Zundel cation, respectively, do not have lifetimes long enough to exist.3 On this classical background of the theory of organic reactions, Cox rewrote the mechanisms of many organic reactions involving C-O cleavage under acidic conditions as concerted processes, so avoiding the formation of Eigen cation and related alkyl substituted hydronium ions (ROH2+, where R is any alkyl- or aryl-substituted methyl radical, including poly-substituted ones) as intermediates.4,5 Cox also claimed that “thanks to the Grotthuss mechanism of chain transfer along hydrogen bonds, a proton is instantly available anywhere it is needed for reaction”.4,5 Thus, it was strongly assumed that the acidic cleavage of C-O bonds takes place concertedly with the formation of the O-H bond. Consequently, the reverse reaction (i.e., the hydration reaction of a carbocation R+ to give the corresponding alcohol ROH) should also occur concertedly (Mechanism I in Fig 1; note that the proton transfer along the simplest two-water-molecule network represents the Grotthuss mechanism).4,5 In other words, the said hydration should not occur stepped, involving the


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formation of ROH2+, as shown by Mechanism II in Fig. 1. The Cox insight into the hydration of carbocations (i.e., without intermediates) was then fully accepted without any criticism,6, 7 and it continues being accepted as a dogma into the field of the Organic Chemistry.

Figure 1. Concerted Cox mechanism (I) vs. stepped mechanism involving oxonium ion as intermediate (II).

In the present article we show that the concerted Cox mechanism for the hydration of carbocations (Mechanism I in Fig. 1), which is based on the classical theory of the organic reactions,4,5 is neither in accord with recent experimental data, nor with the Marcus Theory (MT) of the kinetics of single electron transfer (SET) processes in polar solvents when applied to organic reactions;20-22 whereas the two-step one, involving the formation of ROH2+ as intermediate (Mechanism II in Fig. 1) fits better to those evidences.

DISCUSSION AND RESULTS Reed et al.8-10 could determine by accurate differential IR spectroscopy (DIR), as well as by previous X-ray data, the structure and properties of the highly symmetrical Stoyanov cation (H13O6+),9 where a proton is solvated by six water molecules, showing that such a cation is the only thermodynamically stable structure in acidic aqueous solutions, 8-9 as pointed out by Cox.4,5


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However, the core of this cation is formed by a fluctuating Eigen/Zundel cation

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8-10

and, hence,

this kind of oxonium ions (hydrated protons) “may exist briefly as kinetically important intermediates in reaction mechanisms, but not as thermodynamically stable entities”.8,11. This conclusion aggress with recent calculations using the molecular dynamics CPMD method, showing Eigen/Zundel-like cations as dominant in acidic aqueous solutions,12 but it is clearly opposite to Cox’s opinion.4,5 On the other hand, it was also concluded by Reed et al. that the proton of the Eigen/Zundel core of the Stoyanov cation is available for the Grotthuss proton-transfer mechanism, but not “instantly”, as believed by Cox,4,5 because the transfer rate depends on the proton hopping through the outer solvation shell.8-10 Therefore, the Stoyanov cation (abbreviated as H+aq in Fig. 1) can be described as a proton center of excess charge (CEC).13 Similarly, ROH2+ can be considered as a CEC formed by the reaction of R+ with water (Fig. 1, Mechanism II). Using ultrafast VIS-IR spectroscopy for the study of the reaction between the photoacid HPTS and acetate, Agmon et al.13,14 could determine that the time needed for the proton transfer between proton CEC and base separated by a water molecule amounts ca. 1 ps, at room temperature.14 By using a similar experimental array applied to the study of proton transfers in ice, Timmer et al.15 arrived to the conclusion that the long-range proton transfer process between acid and base along wires of four water molecules in length, takes place on a very long time- scale of ca. 300 ps (at 270 K), despite the relatively low entropy of the iced water wires. In super-cooled water, the formation of localized H3O+ could be even observed.15 On the other hand, it was also shown by ultrafast IR spectroscopy that the breaking/formation of hydrogen bonds in bulky water, corresponding to the Grotthuss mechanisms in neutral water, occurs on a time scale of ca.10 ps at room temperature. 16-17


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The study of the kinetic of the methanol attack to tetrafluoro-substituted benzhydryl carbocations in methanol solution, conducted by Riedle et al.18 using femtosecond transient spectroscopy and on-the-fly molecular dynamics methods, also affords a very important experimental proof against the concerted mechanism for the hydration reaction. Thus, the found typical reaction trajectory shows that, at ca.1 ps after the photolytic generation of the carbocation, the C-O bond is formed by the attack of a water molecule of the first solvation shell to the carbocation. After the C-O bond formation, proton transfer to neighboring solvent molecules occurs at 1-1.5 ps. These stepped events, observed for the reactions of benzhydryl carbocations with methanol, can be straightforwardly generalized to the hydration reactions of any organic carbocation, R+, since the protonated ethers involved in the former reactions are more acid (ca. 20 times) than the ROH2+ ions involved in the latter ones, whereas water is only 6.31 times more basic than methanol in water at 25ºC.4,5,19 In addition to the just-outlined experimental facts, theoretical support for the formation of ROH2+ cations as intermediates is afforded by the Marcus theory (MT) of SET reactions in polar solvents.20-22 One of the main assumptions of this theory is to consider that the total free energy (G) of the solute/solvent complex is a quadratic (or hyperbolic-cosine23) function of the reaction coordinate (q). Hence, the initial state (IS; q = 0) and the final state (FS; q = 1) of the reaction are given by the minimum energy points of the parabolas corresponding to reactants (R) and products (P), respectively (Fig. 2).


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Figure 2. Diabatic (TS) and adiabatic crossing (red line) of the MT parabolas. For adiabatic reactions, the tunneling rate is proportional to 2H.

In the two-sphere model of the outer-shell MT, the charge is transferred gradually along q.20 This assumption is, however, against the indivisible quantum nature of the electron. Thus, in the case of diabatic inner-shell reactions, the SET process (electron jumping) occurs at the cross point of the R and P parabolas, which represents the transition state (TS) of the reaction.20,22 Therefore, accordingly to the MT, the activation free energy (ΔG≠) for SET reactions in polar solvents is a nonlinear function of the free energy of reaction (ΔG) and the barrier height for ΔG = 0, called the intrinsic reaction barrier (Λ), as shown by Eq. 1.24-28 The Λ value is related to the most popular reorganization energy (λ) by the expression: Λ = λ/4.

20-28

Others and we have used Eq 1

successfully for the computation of reaction barriers for the hydration of several carbocations.24-28 ΔG ≠ = Λ [1  (ΔG/4Λ)2]

(Eq. 1)

For adiabatic reactions, the TS are tunneled and the reaction profile is different (red line in Fig. 2). The adiabaticity of a reaction is measured by the overlapping (coupling) Hamiltonian (H) between the IS and FS at the TS (Fig. 2).29-31 When the coupling H is strong, the reaction is adiabatic. Most organic reactions follows adiabatic mechanisms,29,30 because bonds are formed or broken at the TS, whereas diabatic reactions are limited to certain hydrogen and proton transfer processes.30,31


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In the case of the hydration of carbocations at the molecular level, the required (macroscopic) polarization of the solvent at the TS, when the electron is yet located at the electron-donating water molecule (see TS1 in Fig. 3), as well as the reorganization of the reactants at the TS does have to occur simultaneously, since both conditions are needed for the SET.32 As a result, the formation of the C-O bond by the SET process does not take place concertedly with the proton transfer from water to the solvent shell, as it was assumed by Cox,4,5 but consecutively by the proton transfer from the intermediate ROH2+ (FS in Fig. 3), as shown by Mechanism II in Fig. 1. The FS is formed by the shortening of the C-O bond from TS2. Such an exergonic decay process should occur in the time scale of a molecular vibration ( is the average variance of the quadratic energygap between the IS and FS, which was calculated to be 8.10 (kcal/mol)2 at 298 K (see Supporting Information).

𝜆i =

(Eq. 4)

2R𝑇

The reorganization energies (λ0ET = 0.99 eV and λ0PT = 1.71x10-3 eV) were calculated according to Eqs. 5 and 6, respectively. As a result, global λ amounts 1.29 eV. 𝑒2

𝜆𝐸𝑇 0 = 4𝜋𝜀 (𝜀 0

𝜆𝑃𝑇 0 =

1 4𝜋𝜀0

1 𝑜𝑝

1

1

(Eq. 5)

− 𝜀 ) 2𝑎 𝑠

𝜀 −1

𝜀𝑜𝑝 −1

(𝜇𝐼𝑆 −𝜇𝐹𝑆 )2

𝑠

𝑜𝑝

𝑎3

[(2𝜀𝑠 +1) − (2𝜀

)] +1

(Eq. 6)

In Eqs. 5 and 6, 𝜀0 is the vacuum permeability, whereas 𝜀𝑜𝑝 = 1.78 and 𝜀𝑠 = 80.0 are the optical and static dielectric constants in water, respectively. Parameter 𝑎 is the radius of the IS equivalent sphere, and it was determined to amount 4.0 Å by using the SCRF=DIPOLE//B3LYP/6-31G(d) method implemented in GAUSSIAN 98,40 On the other hand, 𝜇𝐼𝑆 and 𝜇𝐹𝑆 are the dipole moments of the IS and FS and were determined to amount 4.290 D and 3.456 D, respectively, by using also the B3LYP/6-31G(d) method. Calculating coupling constant C, and determining the adiabaticity of the CPET reaction between t-BuOH2+ and water. In our opinion, one of the more important contributions of the seminal work of Costentin et al.31 is the derive of a very simple procedure for the determination of constant C, as a function of the


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potential-energy barrier high (ΔV≠), which is in turn dependent on the distance Q. Thus, the shorter Q, the higher is the vibrational coupling between IS and FS and, hence, the probability of tunneling. The key of the Costentin procedure is the modeling of the proton tunneling barrier by triangular approximation. Within this model, C(Q) is expressed by Eq. 7. 3

8√2 ℎ𝜈0≠ Δ𝑉 ≠ (𝑄) 1 2 √ C(𝑄) = ℎ𝜈0≠ exp [− ( − ) ] 3 Δ𝑉 ≠ ℎ𝜈0≠ 2

(Eq. 7)

The O-H frequency in the TS, 𝜈0≠ = 3387.61 cm-1, was calculated from the difference in zero point energies (Δ𝑍𝑃𝐸) between TS and IS (Δ𝑍𝑃𝐸 = (ℎ𝜈0≠ − ℎ𝜈0 )/2 = -0.10 eV). Hence, ℎ𝜈0≠ = 0.12 eV. The frequency analysis of the IS allows the determination of ℎ𝜈0 = 0.32 eV. On the other hand, the potential energy of activation, Δ𝑉 ≠ (𝑄) = 0.134 eV, as defined in Fig. 5, was calculated according to Eq. 8, where 𝑓0≠ = 4𝜋 2 𝑐 2 𝜈0≠2 𝑚𝑝 (6828.37 N/m) is the force constant of the proton 0 (𝐼𝑆) 0 (𝐹𝑆) well 𝑑𝑂𝐻 (1.041 Å) and 𝑑𝑂𝐻 (1.437 Å) are the equilibrium O-H distances in the IS and

FS, respectively, and Q was assumed to be the equilibrium distance between the involved oxygen atoms (QE= 2.548 Å).31 Δ𝑉 ≠ (𝑄) =

𝑓0≠ 4

0 (𝐼𝑆)−𝑑0 (𝐹𝑆) 𝑄−𝑑𝑂𝐻 𝑂𝐻

(

2

2

)

(Eq. 8)

All the required distances were computed from the fully optimized structures using the B3LYP/631G(d) procedure. Substituting all these values in Eq. 7, affords C(QE) = 0.02. From the calculated equilibrium coupling constant and the reorganization energy (λ), the probability (𝑝) of proton and electron tunneled transfers at the TS results to be 0.39 eV, according to Eq. (3). The so-obtained p value allows the calculation of the transmission coefficient as χ = 0.56, according to Eq. 2. This value is significant higher than the corresponding to the homogeneous proton transfer in the case of aminophenols (χ = 0.004)31 and, hence, the global reaction can be considered as adiabatic, although χ has not reached the unit value.31


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Figure 5. Potential energy (V) profiles (red line in the case of adiabatic reactions) of the concerted proton and electron transfers at the TS of the reaction between ROH2+ and water. At the TS, the solvated IS and FS are isoenergetic. ΔV≠ is the potential energy of activation for the tunneled CPET reaction.

Calculating the reaction rate. The product of χ by the collision frequency Z = 1.13x1012 M-1s-1 affords a pre-exponential term of 5.31x1011 M-1s-1. The product of the pre-exponential term by the quadratic Marcus-Hush term, a variation of Eq. 1, affords Eq. 9 allowing the calculation of the pseudo-unimolecular reaction rate of the CPET reaction, 𝑘CPET . 𝑘CPET = 𝜒𝑍 exp [−

𝜆 4R𝑇

(1 −

𝛥𝐺 2 𝜆

) −

∆𝑍𝑃𝐸 R𝑇

]

(Eq. 9)

By applying Eq. 9, where ∆𝐺 =12.0 kcal/mol is the free energy of reaction in water, calculated with the PCM solvation model implemented in GAUSSIAN program suite, a kCPET value of 6.74x1011 s-1 is obtained. This value is much higher than the experimental rate constant for the hydration of t-Bu+ (kw = 1010 s-1),38 showing that the proton transfer rate is the fast step of the global reaction. However, the corresponding relaxation time (τ = 14.6 ps) is significantly higher than the experimentally determined τ (ca. 1 ps) for the proton transfer by a water molecule,14 as


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well as to the needed time (1.0-1.5 ps) for the proton transfer from the protonated (substituted) benzhydryl alcohol to the neighboring solvent molecules.18 This situation is not unexpected, since it is known that for some simple proton transfer reactions,35, 36

the concerted proton transfer does have a Franck-Condon "drag", slowing down the global CPET

reaction. Thus, the pyridine/pyridinium concerted CPET reaction is much slower (kCPET = 5.6x104 s-1) than the consecutive electron transfer/proton transfer reaction (ETPT), whose reaction rate was calculated to be 2.4x108 s-1.35,36 In order to clear up this situation, we have calculated a kETPT value of 4.68x1012 s-1 for the sequential proton transfer reaction between t-BuOH2+ and H2O, using the Costentin formalism31 and assuming λ =𝜆𝐸𝑇 0 , and hence χ ETPT = 0.60, according to Eq 2 and Eq 3. It should be noted that the so-calculated kETPT value represents an upper limit of the rate constant, because the equivalence between λ and 𝜆𝐸𝑇 0 supposes that the electron transfer takes place at the IS complex (see Fig. 4). However, this value is in excellent accord with experimental data, because the corresponding τ (2.14 ps) is very similar to experimentally determined τ values (ca. 1.0-1.5 ps) for related proton transfer reactions in acidic water at room temperature.14,18 Computing the free energy barrier for the proton transfer between t-BuOH3+ and H2O. We have computed the free energy barrier (∆GTS≠) in the gas-phase for the proton transfer reaction between t-BuOH2+ and water by using the variational transition state theory (VTST).41 The TS was determined as the annihilation point of the 2nd derivative of the potential energy curve (PEC), obtained by scanning the O-H distance from the IS. The so-determined TS structure, occurring at 1.287 Å (see Fig.6), shows one imaginary frequency (see Supporting Information).


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2nd. derivative of the PEC


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150000 100000 50000 0 1

1,1

-50000

1,2

1,3

1,4

1,5

O-H distante (in Å)

Figure 6. 2nd derivative of the PEC obtained by scanning the O-H distance (in Å) from the IS. The annihilation point occurs at 1.287 Å.

The so-computed ∆GTS≠ value in gas-phase (3.71 kcal/mol, at 298 K) is slightly higher than the corresponding value for ΔVTS≠ (3.17 kcal/mol), the total energy of activation in gas-phase including thermal corrections. Both values are in excellent agreement with the calculated ΔV(QEQ)≠ (3.09 kcal/mol) value, taking into account that the error in this type of computations amounts to ca. 1 kcal/mol.25 The free-energy barrier in water for the proton transfer reaction (∆GET≠(w) = 0.17 kcal/mol) was calculated from the kETPT value ( 4.68x1012 s-1) using the Eyring equation (Eq. 10), with its usual pre-exponential term. 𝑘𝐸𝑇𝑃𝑇 =

𝑘𝐵 𝑇 ℎ

exp (−

∆𝐺 ≠ 𝐸𝑇 (𝑤) 𝑅𝑇

)

(10)

From the experimental rate constant for the hydration of t-Bu+ (kw = 1010 s-1 in water at 298 K), 38 a global ΔG≠ barrier of 3.81 kcal/mol was calculated according to Eq 10, which is much higher than the corresponding proton transfer step (∆GET≠(w) = 0.17 kcal/mol). For related reactions involving thermodynamically less-stable carbocations (e.g., norbornyl bridgehead carbocations), even lower ΔG≠ barriers (ca. 0.02 kcal/mol) were calculated by using Eq 1 for the global hydration


14

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reaction. 25 Contrarily, in the case of more stable carbocations, such as benzylic-like carbocations, significantly higher barriers were experimentally determined (2.15-13.08 kcal/mol).26 Hence, in the case of the hydration of more stable carbocations the formation of the intermediate R-OH2+ seems to be the slow step, due to the very high intramolecular reorganization energy (λi) needed for the first step (see Mechanism II in Fig. 2) in the case of the hydration of π-delocalized carbocations.26-28

CONCLUSIONS From the exposed experimental and theoretical facts, the following conclusions can be easily arrived: (1) The reaction of carbocations with water is a two-step process involving the formation of oxonium ions (ROH2+) as intermediates. In the case of the hydration of t-Bu+, the first step is the rate limiting one. (2) The concept of intermediate should not be only limited to species with a life-time determinable by IR spectroscopy, and quantum-mechanical (also kinetically) “enforced” intermediates, such as ROH2+ cations, should be recognized as reasonable intermediates in proposals of organic reactions mechanisms, independently of their lifetimes, as it occurs in the case of short-lived photochemical intermediates.42 (3) We are aware that reactions assumed to follow “two-electrons processes are very much part of the paradigm of Organic Chemistry”,30 but this paradigm is for a long time challenged by suggestions of alternative mechanisms involving SET reactions.30,43-46 Hence, all the concerted mechanisms for acidic C-O cleavage reactions, as well as for the carbocation hydrations reactions proposed by Cox4,5 (i.e., involving curved arrows for proton transfer reactions) are probably


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wrong, because according to the MT and other quantum mechanical electron transfer theories the electrons are transferred only one to one.30,43-46 Moreover, the formation of continuous water wires, needed for a collective proton transfer (soliton mechanisms), is an energetically disfavored process mainly due to the low entropy of the wire structures.47 Hence, the Grotthuss proton transfer reaction is by no means “instantaneous”,13-18,39,47,48 as wrongly assumed by Cox.4,5 On the other hand, we are convinced that, nowadays, Grothuss himself would not qualify his pioneering proton propagation mechanism49 as instantaneous. (4) There is an excellent agreement between the reaction barrier, ΔVTS≠, computed according to the VTST, and the calculated ΔV(QEQ)≠ value using the triangular approximation.31 Moreover, there is an excellent accordance between the calculated relaxation time (τ = 2.14 ps) for the ETPT process and experimentally-determined τ values (1.0-1.5 ps) for related reactions.

AUTHOR INFORMATION Notes The authors declare no competing financial interests.

ACKNOWLEDGMENT Financial support from MINECO (MAT2014-51937-C3-2-P) and UCM are gratefully acknowledged.

SUPPORTING INFORMATION Gaussian output parameters of key computed reaction states, as well as key mathematic operations related to the conducted energy calculations.


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(2)

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(3)

Jiang, J.-C.; Wang, Y.-S.; Chang, H.-C.; Lin, S.H.; Lee, Y.T.; Niedner-Schatteburg, G.; Chang, H.-C. Infrared Spectra of H+(H2O)5-8 Clusters: Evidence for Symmetric Proton Hydration. J. Am. Chem. Soc. 2000, 122, 1398-1410.

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Cox, R. A. A Greatly Under-Appreciated Fundamental Principle of Physical Organic Chemistry. Int. J. Mol. Sci. 2011, 12, 8316-8332.

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Cox, R. A.; Buncel, E. Three Different Mechanisms for Azo-Ether Hydrolyses in Aqueous Acid. Can. J. Chem. 2012, 90, 791-797.

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Silverstein, T. P. The Solvated Proton is NOT H3O+! J. Chem. Educ. 2011, 88, 875, and references cited therein.

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Reed, C. Myths about the Proton. The Nature of H+ in Condensed Media. Acc. Chem. Res. 2013, 46, 2567-2575.

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Stoyanov, E. S.; Stoyanova, I. V.; Reed, C. A. The Structure of the Hydrogen Ion (Haq+) in Water. J. Am. Chem. Soc. 2010, 132, 1484-1485.


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TABLE OF CONTENTS GRAPHICS

Experimental and theoretical evidences support the existence of organic oxonium ions as mechanistic intermediates in water solution


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About the Existence of Organic Oxonium Ions as Mechanistic

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