Theoretical insight into hydroxyl production via H₂O₂ decomposition over the Fe₃O₄(311) surface

Abstract

Fenton's reagent provides a method to produce active hydroxyl radicals (˙OH) for chemical oxidation by mixing iron oxide and hydrogen peroxide, which divides into homogeneous and heterogeneous Fenton's reagent. Heterogeneous Fenton's reagent is fabricated from H₂O₂ and various iron oxide solid materials, such as α-FeOOH, α-Fe₂O₃, and Fe₃O₄. Fe₃O₄ possesses the Fe²⁺/Fe³⁺ mixed valence oxidational state and has been reported to have good catalytic activity. However, the reaction mechanism of H₂O₂ decomposition on Fe₃O₄ surfaces is still unclear. In this work, we performed DFT calculations to investigate the H₂O₂ decomposition mechanisms over the Fe₃O₄(311) surface. There are two iron environments for H₂O₂ adsorption and decomposition on the Fe₃O₄(311) surface, a Fe²⁺/Fe³⁺ environment and a Fe³⁺/Fe³⁺ environment. We found that the H₂O₂ can adsorb on the Fe²⁺/Fe³⁺ environment by molecular adsorption but by dissociative adsorption on the Fe³⁺/Fe³⁺ environment. Our results show that both adsorption structures can produce two OH groups on the Fe₃O₄(311) surface thermodynamically. In addition, based on the electronic property analysis, H₂O₂ on the Fe²⁺/Fe³⁺ environment follows the Haber–Weiss mechanism to form one OH anion and one OH radical. On the other hand, H₂O₂ on the Fe³⁺/Fe³⁺ environment follows the radical mechanism to form two OH radicals. In particular, the OH radical formed on Fe²⁺/Fe³⁺ has energy levels on both sides of the Fermi energy level. It can be expected that this OH radical has good redox activity.

Fenton's reagent provides a method to produce active hydroxyl radicals (˙OH) for chemical oxidation by mixing iron oxide and hydrogen peroxide, which divides into homogeneous and heterogeneous Fenton's reagent.

1. Introduction

Fenton's reagent is a well-known advanced oxidation process (AOP) that can produce reactive oxygen species (ROS), such as hydroxyl radicals (˙OH), peroxyl radical (˙OOH), and superoxide radical (˙O₂).^1–4 Fenton's reagent is usually fabricated by mixing two solutions: a reducing transition metal and hydrogen peroxide. The Fenton-type reagent has been reported as an active catalyst for various reactions such as water treatment,^5,6 methane partial oxidation, and mercury removal. Most AOPs can damage the organic compounds into H₂O, CO₂, and other small molecules by means of hydroxyl radicals (˙OH) because of their strong oxidative ability.⁷ As one of the well-known AOPs, the Fenton reagent shows extraordinary ability for organic decomposition and the least expensive. Moreover, the development of a Fenton reaction can accelerate the application of AOPs for water treatment and purification on an industrial scale.

Conventional homogeneous Fenton reagent composed of hydrogen peroxide (H₂O₂) and ferrous ion (Fe²⁺) for the purpose of producing hydroxyl radicals.⁸ However, there are several drawbacks to the homogeneous Fenton reagent.⁹ For example, homogeneous Fenton reagent needs to react in the narrow pH range, and the aggregation of iron-containing sludge in the reaction can also limit the recycling of catalysts, which can be considered as secondary pollution in the environment.^10,11 Compared to the homogeneous Fenton systems, the heterogeneous iron-based solid catalysts can serve as the other choices for the Fenton reagents, which have been reported in various previous studies.¹² Iron oxides-based catalysts, such as α-FeOOH, α-Fe₂O₃, Fe₃O₄, and FeO,^13–17 possess good catalytic properties in many heterogeneous catalysis reactions, including Fenton reaction¹⁸ and Fischer–Tropsch synthesis.¹⁹ Theoretically, Song et al. has reported the NO oxidation mechanism over α-Fe₂O₃ catalyst by H₂O₂.²⁰ Experimentally, Li et al. have studied the α-FeOOH material as the pCNB degradation catalyst by Fenton-like process.²¹ Furthermore, several investigations have found that the mixed valence oxidational state of iron atoms possess unique catalytic activity towards many heterogeneous catalysis reactions, including Fenton reaction, methane partial oxidation, and mercury oxidation.^10,22–27 Among, magnetite (Fe₃O₄) is one of the iron oxide material that has a Fe²⁺/Fe³⁺ mix valence oxidational state. The bulk magnetite crystal structure was a member of the inverse cubic spinel group with the ferrimagnetic property.^28,29 There are many applications of using magnetite as pigment due to its magnetic properties, such as polishing compounds, cosmetics, medicines, polymer, and rubber filler.^30–32

There are still some challenges for heterogeneous Fenton reagents, such as that the yield to produce the OH radical is low. In addition, the mechanism to produce the OH radical via heterogeneously mixed valence iron oxide catalysts such as Fe₃O₄ of the Fenton reaction is unclear. In literature, there have been proposed two possible mechanisms for the traditional Fenton reaction. The first mechanism had been proposed by Haber and Weiss in the 1930s, named hydroxyl free radical mechanism (Haber–Weiss mechanism),⁸ which involves the formation of hydroxyl radicals (˙OH) in the system with the ferry (Fe²⁺) oxidation. This radical mechanism for the Fenton reaction with the following elementary reactions.Fe²⁺ + H₂O₂ → Fe³⁺ + ˙OH + OH⁻Fe³⁺ + H₂O₂ → Fe²⁺ + ˙OOH + H⁺

Thereafter, another mechanism was proposed by Bray and Gorin in 1932,³³ which generate higher valence Fe complexes such as ferryl (Fe^IV) ion in the Fenton system, as follows:Fe²⁺ + H₂O₂ → Fe^IVO + H₂OFe^IVO + H₂O₂ → Fe²⁺ + H₂O + O₂

As a structure in the spinel family, Fe₃O₄ also possesses stable low-index surfaces, (100), (110), (111) facets,^34–37 and a high-index surface of (311). Some studies have been reported the mercury oxidation mechanism by H₂O₂ over Fe₃O₄(001) and Fe₃O₄(111) surfaces.^27,38 However, even though the low-index facets have relatively low surface energies, Xu et al. have successfully synthesized a polyhedral 50-facet Fe₃O₄ nanocrystal where only one high-index Fe₃O₄(311) facet can stably exist with other low-index facets jointly.³⁹ In their results, there were even 24 high-index (311) facets in that nanocrystal, which is stable and abundant. Thus, Fe₃O₄(311) facet is a stable high-index surface experimentally. Because there was no investigation on the mechanism of the Fenton reaction over the Fe₃O₄(311) surface, in this work, we studied the adsorption and decomposition of H₂O₂ (Fenton reaction) over Fe₃O₄(311) surface using DFT calculations. We also investigated the possible reaction mechanisms of the Fenton reaction on the Fe₃O₄(311) surface. Moreover, we analyzed the electron density difference (EDD) and density of states (DOS) to explore the electronic interaction between H₂O₂/OH and Fe₃O₄(311) surface. To clarify the oxidational states of iron atoms between H₂O₂/OH and Fe₃O₄(311) surface, we also calculated the Bader charge and magnetic moments for the iron atoms on the Fe₃O₄(311) surface.

2. Computational details

The spin-polarized periodic DFT calculations were carried out with the Vienna ab initio simulation package (VASP 5.4.1).^40–43 The generalized gradient approximation (GGA) with the functional proposed by Perdew, Burke and Enzerhof (PBE) exchange-correlation functional⁴⁴ was used together with a plane-wave basis set with a kinetic cutoff energy of 500 eV. The electron ion–core interactions were described by the projector augmented wave (PAW) method.^45,46 In order to correctly describe the itinerant or localized behavior of the Fe 3d-orbital, it is important to account for the strong on-site Coulomb correlations.^47,48 Therefore, in this work, all systems were calculated by using the Hubbard correction term U (GGA + U). We applied the rotationally invariant approach proposed by Dudarev et al. with an effective Hubbard parameter of 4.0 eV for iron, which is the difference between the Coulomb (U) and exchange (J) parameters (U_eff = U − J). The optimized exchange-correlation functional (optB86b-vdW) was considered to determine the effect of van der Waals interactions.⁴⁹

For the total energy calculations, the Brillouin zone integrations for the pristine and defect system were performed using the 2 × 2 × 1 based on the Monkhorst–Pack k-points scheme⁵⁰ for all structural configuration relaxations. The convergence threshold was set to be 10⁻⁵ eV for electronic optimization and the force convergence was set to be 0.02 eV Å⁻¹ for structural optimization. The adsorption energy (E_ads) of adsorbate was defined as following equation:E_ads = E_Total − E_surf. − E_Moleculewhere E_Total is the total energy of the surface together with the adsorbate, E_surf. is the total energy of the surface, and E_molecule is the total energy of the free molecule in gas-phase. Therefore, a negative adsorption energy illustrated a thermodynamically-favored exothermic adsorption process. An 8 × 8 × 1 k-point grid was used to calculate electronic density difference (EDD), Bader charge analysis, and density of state (DOS) with the same cutoff energy. The climbing image nudged elastic band (CI-NEB) method⁵¹ and dimer method was applied to find transition states and minimum energy path of all reactions. The vibrational frequencies analysis was performed for validating the optimized and transition state structures.

The bulk Fe₃O₄ was adopted the conventional Fe₃O₄ unit cell comprising 56 atoms (Fe₂₄O₃₂). For the Fe₃O₄ bulk calculations, 8 × 8 × 8 k-mesh of a grid density was employed. The optimized lattice parameters of bulk Fe₃O₄ were a = b = c = 8.396 Å and α = β = γ = 90°. The result of the calculation is in good agreement well with the experimental data (a = b = c = 8.394 Å and α = β = γ = 90°).⁵² The bulk magnetite crystal structure was inverse cubic spinel with ferrimagnet property, the structure comprises the tetrahedral iron site and octahedral iron site with different oxidation number, and the O anions form a close-packed face-centered cubic (fcc) sublattice, as shown in Fig. S1(a).† Moreover, the tetrahedral and octahedral iron sites were performed by two magnetic sub-lattices in the opposite direction to form a typical inverse spinel structure as [Fe³⁺]_tet[Fe³⁺, Fe²⁺]_octO₄. During the calculation, the initial atomic spin magnetic moments were m_s = −5 μ_B and 4 μ_B for the tetrahedral iron and the octahedral iron sites, respectively. After structure optimization, the magnetic moment per formula unit was calculated to be 4.0 μ_B, which lies close to experiment data (4.05 μ_B).³² The magnetic moments of Fe³⁺ and Fe²⁺ in the tetrahedral iron and the octahedral iron atoms were with the antiparallel alignment, creating the ferrimagnetic character. Fig. S1(b)† shows the structure of the Fe₃O₄(311) surface by constructing four molecular layer models with the bottom two layers being fully fixed. The simulated XRD pattern of Fe₃O₄ bulk structure is drawn in Fig. S1(c),† which is in a good agreement with the experimental observation.⁵³

3. Results and discussion

3.1. Adsorption of H₂O₂ molecule

Fig. 1 shows the adsorption configuration of H₂O₂ on the Fe₃O₄(311) surface. There are two possible adsorption structures of H₂O₂ on the Fe₃O₄(311) surface: (1) molecular adsorption (Fig. 1(a)) and (2) dissociative adsorption (Fig. 1(b)). In the H₂O₂ molecular adsorption structure, the H₂O₂ adsorbs on the Fe_tet site via one OH to form the Fe–O bond, while the other OH end of H₂O₂ points to the lattice oxygen to form the hydrogen bond instead of forming the Fe–O bond between the adjacent Fe_oct site, as can be seen in Fig. 1(a). The adsorption energy of the H₂O₂ molecular adsorption is −1.17 eV. Moreover, the molecule geometry of H₂O₂ distorts seriously after adsorption that the two OH bonds within the molecule point to the different lattice oxygen atoms and form the hydrogen bonding with the distances of 1.66 Å and 1.47 Å, respectively. It results in the O–H bonds within the molecule elongated from 0.98 Å (free H₂O₂) to 1.016 and 1.061 Å, respectively. In the dissociative adsorption of H₂O₂, the H₂O₂ adsorbs on the two adjacent Fe_oct sites to form two Fe–O bonds, with the whole O–O bond being paralleled to the bridge of two octahedral iron sites, and one O–H bond directly dissociates to form OOH group, as can be seen in Fig. 1(b). The adsorption energy of H₂O₂ dissociative adsorption is −1.56 eV. The O–O bond of the OOH is elongated from 1.472 Å (in free H₂O₂) to 1.483 Å, as listed in Table 1.

Fig. 1. Side and top views of optimized adsorption structures of H₂O₂ on the Fe₃O₄(311) surface by different adsorption configurations of (a) molecular adsorption and (b) dissociative adsorption. Purple, red, and white spheres represent Fe, O, and H atoms, respectively. The deep red color represents the oxygen of H₂O₂ while the light red color is the oxygen of Fe₃O₄(311) surface.

The adsorption energy and geometrical parameters of H₂O₂via different adsorption configurations on the Fe₃O₄(311) surface.

Adsorption type	E ads (eV)	O–O bond length (Å)	O–H1 bond length (Å)	O–H2 bond length (Å)
Gas phase	—	1.472	0.98	0.98
Molecular adsorption	−1.17	1.475	1.016	1.061
Dissociate adsorption	−1.57	1.483	2.135	0.983

3.2. The activation of H₂O₂ on Fe₃O₄

To understand the reaction mechanism of H₂O₂ decomposition, we calculated the energy barrier and reaction energy of each reaction step from both adsorption structures of H₂O₂ on the Fe₃O₄(311) surface. Two cleave aspects are considered in either molecular adsorption of H₂O₂ or dissociative adsorption of H₂O₂: (1) O–O bond-breaking into the OH group; (2) O–H bond-breaking into the OOH group. The following steps show the possible mechanisms for the molecular adsorption of H₂O₂ on the Fe₃O₄(311) surface:

H₂O₂ → 2OH 1

H₂O₂ → OOH + H 2

OOH → OH + O 3

In eqn (1), the reaction barrier is 0.76 eV of that the H₂O₂ molecule cleaves the O–O bond to form two OH groups on one Fe_tet site and one Fe_oct site, and the reaction energy of this reaction is significant exothermic by 1.44 eV. Fig. S2(a)† depicts the structures of the initial state, transition state, and final state of this reaction. In eqn (2), the pathway starts from the deprotonation of H₂O₂ to deliver one hydrogen atom to the lattice oxygen, then forming an OOH group and the surface hydroxyl group. The oxygen atoms of the OOH group are separately adsorbed on both Fe_tet and Fe_oct, as shown in Fig. S2(b).† The calculated energy barrier of this reaction is 0.52 eV by a slight endothermicity of 0.22 eV. Comparing the pathways via O–O bond breaking and deprotonation, the reaction in the former is more thermodynamically favorable to produce the two OH groups, but it has larger activation energy for O–O bond scission, whereas the reaction in the latter possesses a smaller energy barrier to form the OOH group.

When the decomposition reaction starts from the dissociative adsorption of H₂O₂ (H + OOH), the reaction can also divide into O–O bond breaking and OH deprotonation reactions. The first pathway is the O–O bond decomposition of OOH to form O atom and OH group on two Fe_oct sites of the surface. The calculated energy barrier and reaction energy of this elementary step (OOH → O + OH) is 0.24 eV and 0.20 eV, respectively. The activated O–O bond length in the transition state structure is 1.70 Å, and the intermediate state will form a hydrogen bonding interaction between the O atom and OH group with a distance of 1.86 Å after dissociation, as shown in Fig. S3(a).† However, the dissociated O atom is unstable so that this O atom can attract the atomic H of the surface hydroxyl group to form another OH group on the Fe_oct2 site via the hydrogen bonding networks, which results in a large exothermic reaction by 1.44 eV due to the stability of forming two OH groups. The second pathway is that deprotonation from OOH to transfer one H atom to the lattice oxygen to form dioxygen on the two octahedral iron sites, as shown in Fig. S3(b).† This process is a thermal neutral process with an activation energy of 0.79 eV. This result demonstrates that the most favorable pathway from the decomposition reaction of the dissociative adsorption of H₂O₂ is to produce two OH groups on the Fe₃O₄(311) surface. Table 2 summarizes the calculated reaction energy and activated barriers of the elementary steps of the O–O bond and O–H bond dissociation of H₂O₂ on Fe₃O₄(311) surface. Fig. 2 depicts the potential energy profiles for H₂O₂ decomposition on different sites over Fe₃O₄(311) surface. Our results show that it is thermodynamically favorable to produce the two hydroxyl groups on the Fe₃O₄(311) surface from both molecular adsorption and dissociative adsorption.

Calculated reaction barriers (E_a in eV), reaction energies (ΔE in eV), and imaginary frequencies (IMF, cm⁻¹) for elementary reactions of H₂O₂ decomposition on the Fe₃O₄(311) surface.

Elementary steps	E a	ΔE	IMF (cm−1)
Molecular adsorption
H2O2(gas) → H2O2*	—	−1.17
H2O2* → 2OH*	0.76	−1.44	i424
H2O2* → H* + OOH*	0.52	0.22	i493
Dissociate adsorption
H2O2*(gas) → H* + OOH*	—	−1.57
H* + OOH* → H* + O* + OH*	0.24	0.20	i641
H* + O* + OH*→ 2OH*	—	−1.44
H* + OOH* → OO* + 2H*	0.79	0.002	i943

Fig. 2. The potential energy profiles of the decomposition of H₂O₂ on the Fe₃O₄(311) surface via (a) H₂O₂ molecular adsorption and (b) H₂O₂ dissociative adsorption.

3.3. Solvent effect

To realistically simulate the effect of the catalytic environment on Fenton's reaction, we carried out the implicit solvent model by using VASPsol.^54,55 The implicit solvent effect of water was adopted in this work, where the corresponding dielectric constant of water was 78.3553. As listed in Table S1,† the reaction barriers of either O–O bond breaking or O–H bond breaking of the H₂O₂ molecule in an aqueous solution become smaller than that of the H₂O₂ molecule in the vacuum, which is contributed by the solvent effects. Besides, the OH groups production is still the most thermodynamically favorable pathway via O–O bond breaking of the H₂O₂ on the Fe₃O₄(311) surface, as shown in Fig. S4.† Thus, with/without the solvent effect, the reaction trend of H₂O₂ decomposition on the Fe₃O₄(311) surface is similar.

3.4. Electronic property analysis

3.4.1. H₂O₂ molecular adsorption

To analyze the interactions between H₂O₂ and Fe atoms upon adsorption on Fe₃O₄(311) surface, we calculate the electron density difference (EDD) and density of states (DOS). Fig. 3(a) and (b)† show the different views of 2D EDD contour plots of H₂O₂ molecular adsorption. Fig. 3(a) illustrates the accumulation of electron region between the OH group and Fe_tet site, representing that the oxygen donates electrons to the iron atom to form a dative bond between oxygen and iron atom. On the other hand, Fig. 3(b) shows the cutting plane along with the other H atom and the O–O bond (H_t–O–O), which displays the electron density accumulation (red contour) between the OH group and the lattice O. This EDD plot in Fig. 3(b) indicates that the H₂O₂ donates the electron transfer from the lattice O to the OH group via the hydrogen bonding interaction. In addition, Fig. 4(a) shows the PDOS diagram of the H₂O₂ molecule before and after its adsorption. One can observe that the spin up and spin down of the peaks of H₂O₂ is getting splitting after adsorption. Moreover, as can be seen in Fig. S5(a) and (b),† the projected d orbitals of Fe_tet and Fe_oct atoms show that the d orbitals of Fe_tet have obviously changed, and the peak is getting broad. In comparison, the peaks of the Fe_oct changed slightly after H₂O₂ adsorption. Additionally, the d orbitals of the Fe_tet atom have an overlap with the p orbitals of H₂O₂ around −0.50 eV, reflecting the dative bond between H₂O₂ and Fe_tet atom.

Fig. 3. The 2D electron density difference diagrams of (a) Fe_tet–OH–O plane, and (b) Fe_tet–O–O plane of H₂O₂ molecular adsorption, and (c) H₂O₂ dissociative adsorption. The isosurface level is 0.002|e|/bohr³. Brown, red, and white spheres represent Fe, O, and H atoms, respectively.

Fig. 4. The PDOS plots of (a) H₂O₂ before and after molecular adsorption, (b) H₂O₂ before and after dissociative adsorption, (c) OH groups from the decomposition of H₂O₂ molecular adsorption, and (d) OH groups from the decomposition of H₂O₂ dissociative adsorption. The dotted line is the Fermi level.

3.4.2. H₂O₂ dissociative adsorption

Fig. 3(c) shows the 2D EDD plot of the OOH group of the H₂O₂ dissociative adsorption configuration, and the cutting plane is along the bridge between two Fe_oct atoms and the O–O bond (Fe_oct–O–O–Fe_oct). The blue contour around the OOH group reveals that the OOH group loses electrons electron. There is also a broad electron density accumulation (red contour) around the bound OOH and two Fe_oct atoms, and the region around the OOH group, which indicates the strong electron interactions between Fe atoms and the OOH group. The strong electronic interactions mean that the OOH can form a dative chemical bond with the Fe atoms.

Further, the PDOS plots, as shown in Fig. 4(b), demonstrated that the peaks of the OOH (from the dissociative adsorption of H₂O₂) has a significant splitting on both spin up and spin down, reflecting the strong radical property of the OOH group. The peaks around −1.50 eV and −1.00 eV belong to α-HOMO and β-HOMO, respectively, as well as the peak around 0.50 eV represents the LUMO of the OOH group before adsorption (black line in Fig. 4(b)). For the dissociative adsorption configuration of H₂O₂, the peaks of the OOH group (red line in Fig. 4(a)) display a broad region above Fermi level energy to 3.00 eV, but the peaks around 0.50 eV disappear. It reflects that the OOH group can gain electrons from the Fe atoms. After dissociative adsorption configuration of H₂O₂, the peaks still show a notable splitting on both spin up and spin down, representing the strong radical property of the OOH group. Besides, as can be seen in Fig. S5(c) and (d),† the d orbital of the Fe_oct2 atom shows a more remarkable change than that of the Fe_oct1 atom before and after OOH group formation, indicating the strong interaction between the Fe_oct2 atom and the OOH group.

3.4.3. OH on the Fe_tet/Fe_oct of the Fe₃O₄(311) surface

According to the calculated results, both molecular adsorption of H₂O₂ and dissociative adsorption of H₂O₂ can produce two OH groups on either Fe_oct or Fe_tet atoms of the Fe₃O₄(311) surface. Because Fenton's reaction involves the redox reaction, we did the electronic property analysis to understand the electronic and magnetic properties after H₂O₂ decomposition. Fig. S6(a) and (b)† show the EDD plots of the adsorption of the OH group on the Fe_oct and Fe_tet sites after H₂O₂ decomposition, respectively. It shows wide regions of electron density accumulation (red lines) between the OH group and either Fe_tet or Fe_oct atoms, which shows the electron transferred from the OH group to the Fe atoms. Fig. 4(c) represents the PDOS of the OH groups on the Fe_tet and Fe_oct sites after H₂O₂ decomposition. For the OH on the Fe_oct atom, there are peaks with similar intensity on both sides of the Fermi level, indicating that the oxygen atom on OH has unpaired electrons after H₂O₂ decomposition. Since the peaks are close to the Fermi level, we can expect that the OH group on the Fe_oct atom should be very active. Besides, it can be observed from Fig. S7(a)† that the DOS distribution of Fe_tet changes significantly before and after adsorption, whereas from Fig. S7(b)† that the DOS distribution of Fe_oct is very similar after H₂O₂ decomposition. The changes of the DOS distribution of Fe_tet implies that Fe_tet²⁺ might have been oxidized to Fe_tet³⁺.

To further understand the redox reaction before and after H₂O₂ decomposition on the Fe₃O₄(311) surface, we calculated the Bader charge and magnetic moments of iron ions and the fragments of H₂O₂ during the reaction. The calculated Bader charge values and magnetic moment values of iron ions are similar before and after the adsorption of H₂O₂. After the adsorption of H₂O₂, the calculated Bader charge values of Fe_tet and Fe_oct are around 1.36 and 1.67|e|, respectively, and the calculated magnetic moment values of both Fe_tet and Fe_oct atoms are around 3.804 and 4.243 μ_B, respectively. The results indicate that the oxidational state of Fe_tet and Fe_oct atoms upon H₂O₂ adsorption is Fe²⁺ and Fe³⁺, respectively. Furthermore, after the H₂O₂ decomposition to OH groups, the calculated Bader charge value of both Fe_tet and Fe_oct atoms become 1.69 and 1.71|e|, respectively, and the calculated magnetic moment of both Fe_tet and Fe_oct atoms become 4.249 and 4.234 μ_B, respectively, as listed in Table 3. The changes in Bader charge and the magnetic moment suggest that the Fe_tet is oxidized from Fe²⁺ to Fe³⁺, while the Fe_oct is maintained at Fe³⁺. The calculated results indicate that the OH group on the Fe_tet will be reduced to the OH⁻ anion, while the one on the Fe_oct will be an OH radical, which is consistent with the prediction of DOS analysis. Therefore, we predict that the Fe_tet and Fe_oct atoms may be the ferrous ion (Fe²⁺) and ferric ion (Fe³⁺) initially and then the Fe_tet can be oxidized to Fe³⁺ after H₂O₂ decomposition, in agreement with the prediction from PDOS analysis. As a result, we predict that this redox mechanism follows the Haber–Weiss mechanism of the Fenton's reaction as the following equations:H₂O₂ → ˙OH + ˙OHFe_tet²⁺ + ˙OH → Fe_tet³⁺ + OH⁻Fe_oct³⁺ + ˙OH → Fe_oct³⁺ + ˙OH

Calculated Bader charge and magnetization for Fe atoms, H₂O₂, and OH groups before and after H₂O₂ decomposition. The positive and negative values of the Bader charge represent the loss and gain electrons, respectively.

Species	Bader charge	Magnetization	Species	Bader charge	magnetization
Free surface			Free surface
Fetet	1.32	3.782	Feoct1	1.68	4.248
Feoct	1.67	4.240	Feoct2	1.69	4.262
Molecular adsorption			Dissociative adsorption
Fetet	1.36	3.804	Feoct1	1.73	4.258
Feoct	1.67	4.243	Feoct2	1.71	4.276
H2O2	−0.012	—	H–OOH	−0.09	—
OH on the Fetet/Feoct			OH on the Feoct1/Feoct2
Fetet	1.69	4.249	Feoct1	1.69	4.258
Feoct	1.71	4.234	Feoct2	1.70	4.278
OH–Fetet	−0.47	—	OH–Feoct1	−0.50	—
OH–Feoct	−0.51	—	OH–Feoct2	−0.45	—

3.4.4. OH on the Fe_oct1/Fe_oct2 of the Fe₃O₄(311) surface

After the decomposition of the H₂O₂ to two OH groups on the Fe_oct1 and Fe_oct2 atoms, we also investigated the electronic interaction between these OH groups and the Fe_oct atoms via EDD, PDOS, Bader charge and magnetization analyses. Fig. S6(c) and (d)† show the EDD contour plots from the different perspective cutting planes of these two OH groups. These EDD plots display a wide region with electron density accumulation (red color) between the OH group and either Fe_oct1 or Fe_oct2 atoms, demonstrating the OH group has a strong interaction with either Fe_oct1 or Fe_oct2 atoms. In Fig. 4(d), the peaks of OH groups show a little split, which also denotes the radical character for these OH groups. Besides, the PDOS of the d orbital of either Fe_oct1 atom or Fe_oct2 atom display only slightly changes before and after H₂O₂ decomposition, as shown in Fig. S7(c) and (d).† This result implies that the redox reactivity between OH groups and Fe_oct1/Fe_oct2 atoms is weak.

The calculated Bader charge values have slight changes on both Fe_oct1 and Fe_oct2 atoms before and after O–O decomposition, where the value of Fe_oct1 atom changes from 1.68|e| to 1.73|e|, and the value of Fe_oct2 atom from 1.69|e| becomes 1.71|e|. The calculated magnetic moment values of both Fe_oct1 and Fe_oct2 atoms remain around 4.25 μ_B before and after O–O decomposition. These results indicate that both Fe_oct1 and Fe_oct2 atoms are the ferric ions (Fe³⁺) initially and the Fe atoms will get hardly further oxidized after forming the OH group on these Fe atoms. Thus, the OH groups on these ferric ions (Fe³⁺) also possess a radical character after H₂O₂ decomposition. The calculated Bader charge and magnetic moment values are listed in Table 3.

Finally, in a comparison of two mechanisms of H₂O₂ decomposition on the Fe₃O₄(311) surface, we found that it can occur a redox reaction between H₂O₂ and Fe₃O₄(311) surface when H₂O₂ adsorbed on both Fe_tet and Fe_oct sites. The mechanism obeys the Haber–Weiss mechanism to produce one OH anion and one OH radical, which has a strong redox activity. On the other hand, while H₂O₂ adsorbed on two Fe_oct sites, H₂O₂ can dissociate into two OH radicals without oxidizing the Fe_oct atoms, which is the radical mechanism of H₂O₂ decomposition. Based on these results, we could predict that the active OH radicals would be the surface abundant species on the Fe₃O₄(311) surface. Moreover, the calculated desorption energies of OH radicals are 2.84 eV and 2.94 eV at Fe_tet²⁺/Fe_oct³⁺ and Fe_oct³⁺/Fe_oct³⁺ sites, respectively. The desorption energy indicated that the hydroxyl radicals might be challenging to desorb from the Fe₃O₄(311) surface. Therefore, in our study, we predict that the surface OH groups might go through surface heterogeneous oxidation reactions.

4. Conclusions

In this work, we have employed DFT calculations to study the H₂O₂ adsorption and the decomposition mechanism on the Fe₃O₄(311) surface. Fe₃O₄(311) surface possesses a mixed valence (Fe²⁺/Fe³⁺) state so that there are two possible adsorption sites for H₂O₂ adsorption. When H₂O₂ adsorbs on the Fe_tet²⁺/Fe_oct³⁺ sites, the adsorption structure is molecular adsorption, whereas the adsorption structure of H₂O₂ on Fe_oct³⁺/Fe_oct³⁺ sites becomes dissociative adsorption (OOH + H). We found that the molecular adsorption of H₂O₂ can proceed O–H or O–O bond scission to form OOH or 2OH on the Fe₃O₄(311) surface, respectively. The O–H and O–O bond dissociation is kinetic control and thermodynamic control of the decomposition reaction for the molecular adsorption of H₂O₂, respectively. On the contrary, the dissociative adsorption of H₂O₂ only prefers to go through the O–O bond scission to produce 2OH on the Fe₃O₄(311) surface with a small energy barrier of 0.24 eV. In addition, according to various electronic property calculations, DOS, EDD, Bader charge, and magnetic moments, we observed that the reaction from H₂O₂ to 2OH on the Fe_tet²⁺/Fe_oct³⁺ sites obeys the Haber–Weiss mechanism of the Fenton reaction. The Fe_tet²⁺ site can be oxidized to Fe_tet³⁺ while the other Fe_oct³⁺ site maintains its original oxidation state. Thus, the 2OH formed from the molecular adsorption of H₂O₂ is a composition of OH anion and OH radical. On the contrary, the 2OH produced from the dissociative adsorption of H₂O₂ is two radicals because the Fe_oct³⁺/Fe_oct³⁺ sites did not change their oxidation states, which belongs to the radical mechanism. Compared to two mechanisms, it can produce an active OH radical on the surface via either the Haber–Weiss mechanism or radical mechanism, where the oxidation state of Fe on the Fe₃O₄(311) surface can stay at Fe³⁺ instead of further oxidation. As a result, our results predict that these OH radicals from the Fenton-like reaction of H₂O₂ on the Fe₃O₄(311) surface might be a candidate of oxidant for other heterogeneous catalysis reactions.

Conflicts of interest

There are no conflicts to declare.