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DFT STUDY OF THE ENTIRE REACTION CYCLE OF H2O2 DECOMPOSITION AND O2 GENERATION CATALYZED BY FENTON REAGENT

The reaction cycle of H2O2 decomposition and O2 generation catalyzed by Fenton reagent was studied using density functional theory calculations. A four-stage mechanism for the oxygen production and the Fe 2+ regeneration in the Fenton reaction is proposed based on the obtained results. The transition state for each step of the entire reaction cycle was localized and verified by intrinsic reaction coordinate analysis. It is shown that the O-O bond cleavage of coordinated H2O2 at the first step of reaction does not lead to a free HO ● radical. Instead, a highly reactive intermediate [Fe IV (H2O)4(OH)2] 2+ with two HO ● radicals “trapped” in the complex is formed with the energy barrier of 15 kcal/mol. The result of the next two reaction steps is the formation of the two HO2 ● radicals which can react on the triplet energy surface in order to produce O2 in the triplet ground state and a H2O2 molecule.


Introduction
The Fenton reaction is known for a long time since Fenton, H.H. (1894) first observed the oxidation of tartaric acid by a mixture of iron sulphate and hydrogen peroxide. However, intensive discussions about the mechanism of this reaction and the nature of the active oxidizing intermediates continue to this day. In the 30s of the last century, almost simultaneously, two alternative models of this reaction were proposed in the literature, the so-called radical and nonradical mechanisms.
According to the first one, proposed by Haber, F. and Weiss, J. [1] and subsequently modified by Barb, W.G. et al. [2], the reaction of Fe(II) with hydrogen peroxide in an aqueous solution leads to the formation of free HO • and HO 2 • radicals as active intermediates in reactions (Eqs. (1)(2)(3)(4)(5)): Fe 2+ + HO • → Fe 3+ + OH - (5) It was assumed that the hydroxyl free radical HO • is the oxidative intermediate, whereas the HO 2 • radical is the key intermediate in the O 2 production.
The second mechanism proposed by Bray, W.C. and Gorin, M.H. [3] involves the formation of the highly reactive ferryl-oxo complex Fe IV O 2+ (Eqs. (6,7) Since then, a great number of studies have been performed to elucidate the mechanism of these reactions and to determine whether the hydroxyl radical or another strongly oxidizing species are formed during the oxidation of Fe(II). The nature of these species is still a subject of controversy, since the direct experimental detection of intermediates is problematic because of their very short lifetime. So, experimental studies only indirectly confirm either one or the other reaction mechanism.
Some scientists consider that hydroxyl radicals in either "free" or "caged" form are the major oxidizing agent in the Fenton reaction [4][5][6][7][8]. The radical pathway seems to be preferable also in the case of many catalytic systems based on other transition metals (the so-called non-ferrous Fenton catalysts) [9,10]. Another group of scientists supports an alternative mechanism in which the ferryl ion is regarded as the main oxidant in Fenton's reaction [11][12][13][14][15][16][17][18]. Some papers discuss that, depending on the experimental conditions, either a radical or nonradical reaction mechanism can be implemented [19][20][21]. A more complete discussion of the various points of view on the mechanisms of Fenton's reaction can also be found in a number of reviews [21][22][23][24][25].
Since, as already mentioned, the experimental identification of intermediates in the Fenton reaction is almost impossible because of their extremely short lifetime, a theoretical study of possible reaction paths can be helpful in understanding the mechanisms of this reaction. One such study based on the density functional theory (DFT) calculations was carried out by the group of Baerends, E.J. et al. [26][27][28]. In their thorough works [26,27] the authors have analyzed the possible mechanism for the oxygen evolution in the Fenton reaction assuming the formation of a ferryl-oxo complex as the key active intermediate. However, in our opinion, some aspects of the entire reaction cycle remain unclear (namely the localization of the transition states, the determination of the barriers heights and the reaction coordinates at every stage of reaction cycle). The authors start their study from the primary intermediate [Fe II (H 2 O) 5 H 2 O 2 ] which is formed by exchange of a water molecule in the hydration shell of the hexa-aqua-Fe 2+ complex by H 2 O 2 . At the same time, the first bond dissociation energy of ferrous hexa-aqua complex was found to be rather high, 24.5 kcal/mol [26]. The very process of exchange of the water molecule with the hydrogen peroxide, however, is not described.
In the present paper, using DFT calculations, we propose a possible alternative mechanism of the entire reaction cycle for the catalytic decomposition of hydrogen peroxide and the concomitant evolution of O 2 , as well as the regeneration of the Fe(II) catalyst in the Fenton reaction. We consider here the processes occurring in the first solvation shell of the Fe 2+ ion. There are a number of studies in which it is reported that the first solvation shell of Fe 2+ consists of six water molecules [29], so we start with the hexa-aqua-Fe 2+ complex.
We assume that the entire reaction cycle may proceed in the following four steps (i)-(iv).
The summary of the reaction cycle is: 6 ] 2+ . In the calculations it is assumed an excess of hydrogen peroxide over Fe 2+ ions, since oxygen evolution is actually observed experimentally under such conditions.

Computational details
The density functional theory (DFT) calculations of all the species involved in reaction steps (i)-(iv) were performed with the quantumchemical program suite PRIRODA 06 [30][31][32], designed for the study of complex molecular systems by the density functional theory. The quantum-chemical code employed expansion of the electron density in an auxiliary basis set to accelerate evaluation of the Coulomb and exchange-correlation terms [30,31]. The generalized gradient approximation (GGA) with the functional proposed by Perdew, J.P., Burke, K. and Enzerhof, M. (PBE) [33] was used for treating both the exchange and correlation. The geometrical parameters for reactants, products, and transition states were fully optimized, using the all-electron correlationconsistent double-ζ polarized quality basis sets (implemented in the PRIRODA 06 package as the basis set L1, which is analogous to Dunning's basis sets cc-pVDZ [34]). For each species, the harmonic vibrational frequencies were calculated in order to validate the nature of stationary points: all positive frequencies for equilibrium structures and one imaginary frequency for transition states. After the transition state for each of the reaction steps (i)-(iv) was localized and verified to be a first-order saddle point, an intrinsic reaction coordinate (IRC) calculations were carried out to find out whether the founded transition state leads to the correct reactants and products.
Step (i) [ Numerous calculations of the structure and properties of chemical compounds and the mechanisms of chemical reactions, performed using the PRIRODA 06 code, demonstrate the acceptability of the chosen calculation scheme for studying our systems (see, e.g. references in work [34]).

Hexa-aqua Fe II complex [Fe II (H 2 O) 6 ] 2+ study
To verify the accuracy of the method used, we performed calculations on the Fe(II)-aqua complex in both the low-spin (S= 0) and high-spin (S= 2) states and compared the results with the data available in the literature. The minimum energy nuclear configuration of the ferrous complex in the S= 0 state has T h symmetry with the six water molecules at the vertices of the octahedron around the iron (Figure 1(a)). All the highest triply-degenerate t g molecular orbitals (MO) are fully occupied giving rise the 1 A 1g ground state. The six Fe-O bond lengths are equal to 2.01 Å compared with 2.03 Å obtained in [26]. In the high-spin (S= 2) electron configuration (t g ) 4 (e g ) 2 the ground state of Fe 2+ (H 2 O) 6 is a triply degenerate 5 T g term. The doubly degenerate 5 E g state lays ~20 kcal/mol higher in energy [29]. In this 5 T g state, the T h nuclear configuration is unstable with respect to both the doubly degenerate tetragonal (e g type) and the triply degenerate trigonal (t g type) displacements. This is the so-called T g (e g +t g ) Jahn-Teller problem. Calculations show that in the present case the most active Jahn-Teller non-totally symmetric coordinate is the Q Θ one (e g type), and the absolute minimum of energy is achieved at the nuclear configuration of D 2h symmetry ( Figure 1 Fe-O bonds respectively. This result agrees with the data from the works [26,29], and with experimental data [35]. Thus, the ground state of the considered [Fe II (H 2 O) 6 ] 2+ complex is the high-spin electronic state (S= 2) with the nuclear configuration of D 2h symmetry; the low-spin state (S= 0) is 29.6 kcal/mol higher in energy than the high-spin one.

Reaction path from ([Fe II (H 2 O) 6 ] 2+ to [Fe IV (H 2 O) 4 (OH) 2 ] 2+ (step (i))
Consider the first step (i) of the entire reaction cycle in which the hydrogen peroxide molecule approaches the Fe(II)-aqua complex in such a way that its oxygen atoms "look at" the two hydrogen atoms of adjacent water molecules. We found that in this case the stable complex [Fe II (H 2 O) 6 -H 2 O 2 ] 2+ with two hydrogen bonds is formed (complex 1 in Figure 2); the energy of stabilization is equal to 29.87 kcal/mol.
The transition state for this step with one imaginary frequency 918.94i cm -1 was localized (complex TS-i in Figure 2). The transition vector indicates that the molecular motion of this frequency is dominated by the transfer of a hydrogen atom H 1 from O 3 to O 1 and by the out-of-plane displacement of H 2 . Besides that, the torsion motion involving the four oxygen atoms also takes place. It is seen that geometry of TS-i complex differs significantly from that of the reactants. Immediately after the transition state TS-i the vibrational motion of the complex corresponds to the displacement of the hydrogen atom H 2 (involved in the second hydrogen bond) towards the oxygen atom O 2 . This, in turn, leads to further elongation and breaking of the O 1 -O 2 bond.
The result of the first step (i) is the formation of the complex [Fe IV (H 2 O) 4 (OH) 2 ] 2+ with four water molecules and two OH radicals "trapped" in the complex, and two water molecules in the second coordination sphere (complex 2 in Figure 2). During the step (i) of reaction, the oxidation state of iron changes from Fe(II) to Fe(IV

The [Fe IV (H 2 O) 4 (OH) 2 ] 2+ and H 2 O 2 interaction (step (ii))
The  A shortening of the O 1 -O 2 bond in the hydrogen peroxide molecule up to 1.37 Å is also observed (TS-ii in Figure 3). The calculated activation energy of this reaction is only 0.63 kcal/mol, and the energy gain is 1.7 kcal/mol, which means that the reaction is exothermic.
As a result of this reaction, the intermediate complex [Fe III (H 2 O) 5 -OH] 2+ (complex 4, Figure 3) is formed, and a HO 2 • free radical is released.

Regeneration of initial [Fe II (H 2 O) 6 ] 2+ catalyst (step (iii))
In its turn, in excess of hydrogen peroxide, the complex [Fe III (H 2 O) 5  The product of this reaction is the complex 6 ( Figure 4)

→ HOOH + O 2 (step (iv))
Thus, as a result of the first three stages of the process under consideration, the initial complex [Fe II (H 2 O) 6 ] 2+ is restored, and two hydroperoxyl radicals HO 2 • are formed. The gas-phase bimolecular self-reaction of HO 2 • has been the subject of numerous experimental [38][39][40] and theoretical [41][42][43][44][45] studies because it plays an important role in the atmospheric chemistry [46,47]. It was shown that the most favourable channel of this interaction is the step (iv) HO   Two HO 2 • radicals in their ground electronic state ( 2 A′′) can form a common H 2 O 4 system either in the singlet or in the triplet spin state. Since we are interested in the products of the step (iv) of reaction, in their electronic ground state, namely H 2 O 2 ( 1 A) and O 2 ( 3 Σ g -), all calculations for the reactants, intermediates, products and the transition state of this reaction were performed for the triplet spin states. Calculations show that the most stable structure of the intermediate H 2 O 4 in its triplet spin state is a doubly hydrogen-bonded planar six-member ring of C 2h symmetry (complex 7 in Figure 5). This complex is formed from two HO 2 • radicals without any energy barrier; relative to the reagents, its stabilization energy is 15.7 kcal/mol. The lengths of two equal hydrogen bonds are 1.58 Å, the HOO bond angles are equal to 103.9°. These results agree rather well with the data from other studies [42][43][44][45].
The transition state for dissociation of the intermediate complex H 2 O 4 to the products was localized (TS-iv in Figure 5), which is only 1.07 kcal/mol higher than the stable triplet intermediate H 2 O 4 structure (7).    16.20°. Besides that, the torsion motion involving the four oxygen atoms also takes place.
As a result of the reaction step (iv), we obtain the hydrogen-bonded complex H 2 O 2 -O 2 which is 23.21 kcal/mol lower than the TS-iv structure. The total energy gain of the reaction is 35.14 kcal/mol compared to the experimental value of 38.28 kcal/mol [51].

The summary reaction cycle for the hydrogen peroxide decomposition, the Fe 2+ regeneration and the molecular oxygen production
Thus, as a result the above four steps we have the summary reaction cycle for the hydrogen peroxide decomposition and the molecular oxygen production:  Figure 6 illustrates the general process of hydrogen peroxide decomposition and the molecular oxygen generation in the Fenton reaction. This process consists of four steps, each of which passes through a transition state (TS-i, TS-ii, TS-iii, and TS-iv in Figure 6). The initial step, . During the last, step (iv) of the reaction, (7)→(TS-iv)→(8), the interaction of the two HO 2 • radicals gives an oxygen molecule in its ground triplet state and a hydrogen peroxide molecule.
It can be seen that the entire reaction cycle is an energetically favourable process with an energy gain of 43.8 kcal/mol, so that the above four-stage reaction mechanism seems reasonable.
In the present paper, we considered the processes occurring in the first solvation shell of the Fe 2+ ion. The role of the solvent effect will be the subject of further research.

Conclusions
A consistent picture of the entire reaction cycle of hydrogen peroxide decomposition and the molecular oxygen generation in the Fenton reaction is provided by means of DFT calculations. The proposed four-stage mechanism assumes implicitly an excess of hydrogen peroxide over Fe 2+ ions, since oxygen evolution is actually observed experimentally under such conditions. The transition states for all steps of the reaction cycle were localized and verified by intrinsic reaction coordinate analysis.
Starting ). It is shown that the entire reaction cycle is an energetically favourable process with an energy gain of 43.8 kcal/mol.