Performance of edges on carbon for the catalytic hydroxylation of benzene to phenol

Abstract

Carbon catalyst is regarded as an efficient and environment-friendly material for the direct oxidation of benzene to phenol. However, the essence and detailed performances of the active sites are still unclear at the molecular level. In the present study, the role of typical defect sites on carbon for benzene hydroxylation to phenol with hydrogen peroxide as the oxidant was theoretically investigated at M06-2x/6-311++G(d, p) level in acetonitrile solution. The carbon with defect sites was modeled with armchair and zigzag edges. The turnover frequency analysis indicated that the rate-controlling step was associated with the HO–OH bond cleavage in the H₂O₂ moiety for the formation of hydroxyl radical. For both the armchair and zigzag edges on carbon material, the defect site plays an essential role in the hydroxyl radical formation from H₂O₂. In the presence of water, the defect site of carbon could readily be hydrated, where the zigzag defect site could be more easily hydrated to hydroquinone than the defect armchair site. Furthermore, the zigzag defect carbon exhibits better catalytic performance than the armchair defect carbon. Based on activation strain analysis, there is a stronger stabilizing transition state interaction in the zigzag defect carbon than that in the defect armchair carbon, which arises from a narrower HOMO–LUMO gap. The present study could shed some light on the essence and function of active sites on carbon for the benzene hydroxylation to phenol.

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1. Introduction

Recently, the transformation of benzene into oxygen-containing aromatic compounds such as phenol under mild conditions has been one of the most active topics in both applied and fundamental catalytic research.¹ Benzene is a very important bulk chemical in the energy and industry fields, and the C–H bond is one of the most stable to be activated. Phenol, as a crucial bulk commodity chemical, is currently produced in industry by a three-step cumene process, which has drawbacks such as high pollution, high-energy consumption, and relatively low selectivity towards phenol.² To address these issues, a direct one-step benzene oxidation approach with H₂O₂ as the oxidizer is highly desired.³

The development of innovative catalytic technologies to transform benzene into phenol is attracting increasing interest. In this process, many catalysts including Fe-containing zeolite, palladium membrane, titanium-containing mesoporous molecular sieves, modified titanium silicalite, vanadium-substituted phosphomolybdate, and metal-free activated carbon (AC) have been developed.^4–17 Among them, carbon-based catalysts were reported as environment-friendly and promising catalysts with hydrogen peroxide as the oxidant because of its physical properties and surface functional groups.^6–17 However, less information is available regarding the reaction mechanism and the essence of the active sites owing to the complex surface structure (e.g., oxygenated groups, curved sp²-hybridized carbon surface, defects, or graphene layers) and the presence of metal impurities.^6,7,18–20 Ma et al. demonstrated that the nitric acid treated graphene acts as an excellent catalyst, in which the outstanding catalytic performance has been attributed to the appropriate H₂O₂ activation rate, good benzene adsorption ability, and consequently the balanced kinetic control over the oxidation reaction of the novel catalyst.⁷ Su et al. successfully identified the armchair defect as one type of active defect, which is responsible for the formation of active oxygen species.⁶ Despite the present research situation and existing issues, how the defect on AC, as an active site, exhibits the catalytic performance remains elusive at the molecular level.

Commonly, the functionalized carbon materials include the oxygenated groups (e.g., C=O, O=C–O, and C–OH) and defects. Another aspect of the carbon materials chemistry, which is often overlooked, is the dependence of the chemical and physical properties of the material under consideration on its spin state (i.e. multiplicity).²¹ Carbon materials depend on the presence of certain active sites on their surface, and their accessibility, which will permit the interface reaction. Two distinct types of sites can be considered in this structure: the basal plane sites and the edge plane sites. The edge plane sites are usually considered as chemically/electrochemically active sites, whereas the basal plane sites are relatively inactive.²² Unsaturated carbon atoms can chemisorb oxygen, water or compounds such as ammonia, generating some groups on the carbon surface that can act as active sites in different reactions. Among these surface groups, oxygenated groups are of great importance since they are the most abundant and consequently can modify the behaviour of the AC.²³ AC can promote hydrogen peroxide decomposition through the formation of hydroxyl radicals.^24–26 In general, basic or reduced AC promotes faster hydrogen peroxide decomposition, whereas the presence of surface oxygen groups inhibits the reaction.^26–28 Bahamonde et al. proposed that the surface of AC promotes H₂O₂ decomposition to an extent depending on related-structural features and on the amount and nature of surface oxygen groups; also, a lower ordering of the carbon structure with less developed graphene layers leads to a higher decomposition rate due to higher surface concentration of unpaired electron active sites. In ACs with a similar structural ordering, the presence of acidic surface oxygen groups inhibits the decomposition of hydrogen peroxide.²⁹ Despite the heightened effort to probe the reaction mechanism, a clear understanding of the role of active sites on carbon materials is lacking for the catalytic hydroxylation of benzene to phenol with H₂O₂, particularly for the formation of the hydroxyl radicals from H₂O₂ on the carbon materials at the molecular level.

To study the role of specific groups and defects, two model catalysts with armchair and zigzag edges were constructed to mimic carbon with oxygenated groups (e.g., C=O and C–OH) and/or defects. Herein, we report the catalytic mechanism for the benzene catalytic hydroxylation to phenol on carbon in acetonitrile solution. The goals are as follows: (a) to ascertain the catalytic nature of the defect on carbon materials for hydrogen peroxide decomposition, (b) to gain a deep insight into determining the transition state (TDTS) and the intermediate (TDI) of the turnover frequency (TOF), (c) to elucidate the role of an active defect on carbon, and (d) to compare the catalytic performance of armchair and zigzag edges.

2. Computational details

All calculations were performed with the Gaussian 09 program package.³⁰ A polarized continuum model (PCM-SMD) was utilized to simulate the solvent effect of acetonitrile.^31,32 Geometry optimizations were run to locate all the stationary points and transition states (TSs) using the M06-2x density functional theory method with the 6-311++G(d, p) basis set for all atoms, namely, M06-2x/6-311++G(d, p).^33,34 For the reaction pathway analysis, every transition structure has only one imaginary frequency; the connections between transition states and corresponding intermediates were verified through intrinsic reaction coordinate (IRC) calculations.^35,36 The natural charges, dominant occupancies of natural bond orbitals, and dominant stabilization energies E(2) between donors and acceptors for some species have been analysed with the help of the natural bond orbital (NBO) analysis.^37,38 Unless otherwise mentioned, the Gibbs free energy of formation (ΔG) is relative to the initial ground state reactants obtained at the M06-2x/6-311++G(d, p) level in acetonitrile solution under atmospheric pressure and experimental temperature (1.0 atm and 343 K).⁸

The turnover frequency (TOF) of the catalytic cycle determines the efficiency of the catalyst. Based on the transition state theory, TOF can be calculated by eqn (i) and (ii),^39–42 in which δE (the energetic span)^43,44 is defined as the energy difference between the summit and trough of the catalytic cycle.

where k_B is the Boltzmann constant, T is the absolute temperature, and h is the Planck's constant. G_TDTS and G_TDI are the Gibbs free energies of the TOF determining transition state (TDTS) and the TOF determining intermediate (TDI), and ΔG_r is the global free energy of the entire cycle. The rate constants k(T) were evaluated according to the conventional transition state theory (TST) k′(T), including tunneling correction κ(T), as mentioned in our previous study.⁴⁵

3. Results and discussion

Based on the functionalized carbon materials with the oxygenated groups (e.g., C=O and C–OH) and/or defects, we designed two carbon models with armchair and zigzag edges, namely, hydroquinone, semiquinone, quinone, and defect, denoted as a/z-2OH, a/z-OH–O, a/z-2O, a/z-O, respectively, to simulate the active sites. The optimized geometric structures for the active sites in acetonitrile solution are depicted in Fig. S1 in the ESI.† Herein, we studied the catalytic roles of the above active sites for the formation of hydroxyl radical and subsequently phenol in acetonitrile solution.

3.1 Formation of hydroxyl radical from hydrogen peroxide

3.1.1 The formation of ˙OH from H₂O₂ in the absence of catalyst. The geometric structures and Gibbs free energy relative to the singlet ground state H₂O₂ for the H₂O₂ decomposition in acetonitrile solution are shown in Fig. S2 (see ESI†) and denoted as P-S2. As depicted in Fig. S2,† the reaction pathway P-S2 possesses the energy height of the highest point (EHHP) of 225.0 kJ mol⁻¹ with the spin flip of H₂O₂ from the singlet ground state to the triplet excited state. Such high EHHP makes its self-decomposition kinetically difficult without the action of catalyst.

3.1.2 Formation of ˙OH from H₂O₂ on both hydroquinone and semiquinone active sites. The geometric structures and relative Gibbs free energy relative to the ground state reactants ¹a-2OH/¹z-2OH + H₂O₂ for the H₂O₂ decomposition in acetonitrile solution are shown in Fig. S3 and S4 (see ESI†) and denoted as Pa-S3, Pz-S3, Pa-S4, and Pz-S4. As depicted in Fig. S3 and S4,† these reaction pathways Pa-S3, Pz-S3, Pa-S4, and Pz-S4 involve the EHHPs of 276.4, 246.6, 231.5, and 292.1 kJ mol⁻¹, respectively. Compared with the blank P-S2, both hydroquinone and semiquinone do not exhibit any catalytic activity toward the decomposition of H₂O₂ because of their higher EHHPs.

3.1.3 Formation of ˙OH from H₂O₂ on defect active site. The geometric structures and Gibbs free energy relative to the ground state reactants ¹a-O/¹z-O + H₂O₂ for the H₂O₂ decomposition on the armchair and zigzag models of carbon materials in acetonitrile solution are depicted in Fig. 1 and denoted as P1-a and P1-z.

Fig. 1 The geometric structures (a) and the schematic energy diagrams (b) with the relative Gibbs free energy (G_r, kJ mol⁻¹) relative to the triplet state reactants ³a-O/³z-O + H₂O₂ for the H₂O₂ decomposition in two models of carbon in acetonitrile solution. For clarity, hydrogen atoms on carbon are not shown. Bond lengths are reported in Å.

As shown in Fig. 1, for the defect armchair model of carbon, a-O, the singlet state ¹a-O is located 50.2 kJ mol⁻¹ above the ground triplet state ³a-O. Then, for P1-a, the minimal energy reaction pathway (MERP) should start at the ground triplet state. At the beginning, H₂O₂ interacts with ³a-O through H-bonding, forming a molecular complex ³a-1-IM1. Next, the O–O bond homolytic cleavage of the H₂O₂ moiety takes place via a linear three-membered transition state ³a-1-TS1, resulting in a ˙OH-containing molecular complex ³a-1-IM2. Finally, ³a-1-IM2 sets the ˙OH radical free, leaving behind the o-semiquinone ²a-OH–O. The reaction pathway P1-a possesses the EHHP of 85.4 kJ mol⁻¹ at ³a-1-TS1.

As depicted in Fig. 1, for the defect zigzag model of carbon, z-O, the singlet state ¹z-O lies 52.1 kJ mol⁻¹ above the ground triplet state ³z-O. Therefore, for P1-z, the MERP should begin at the ground triplet state. Initially, H₂O₂ interacts with ³z-O through H-bonding, generating a molecular complex ³z-1-IM1. Then, the O–O bond homolytic cleavage of H₂O₂ moiety occurs via a linear three-membered transition state ³z-1-TS1 with an intramolecular H-bonding, leading to a ˙OH-containing molecular complex ³z-1-IM2. Finally, ³z-1-IM3 liberates the ˙OH radical, leaving behind the m-semiquinone ²z-OH–O. The reaction pathway P1-z comprises an EHHP of 78.4 kJ mol⁻¹ at ³z-1-TS1.

Upon comparing with the reaction pathways P-S2, Pa-S3, Pa-S4, and P1-a in the absence of catalyst, it could be noted that the reaction pathways P1-a and P1-z over the armchair and zigzag defect carbon models are kinetically more preferable because of their lower EHHP (85.4 and 78.4 vs. 225.0, 276.4, and 231.5 kJ mol⁻¹, respectively). This indicates that both the armchair and zigzag defect carbon models should exhibit superior catalytic performance toward the H₂O₂ decomposition. Moreover, compared with P1-a, P1-z is kinetically more favourable because of its lower EHHP (78.4 vs. 85.4 kJ mol⁻¹). This can be attributed to the fact that there is one intramolecular H-bonding in ³z-1-TS1 and not in ³a-1-TS1.

3.2 Formation of phenol from benzene and hydroxyl radical

3.2.1 Reaction of hydroxyl radical with benzene. The geometric structures and the Gibbs free energies (G_r) of different species for the reaction of hydroxyl radical with benzene in acetonitrile solution are depicted in Fig. 2.

Fig. 2 The geometric structures and the schematic energy diagrams with the relative Gibbs free energy (G_r, kJ mol⁻¹) relative to different species for the reaction of hydroxyl radical with benzene in acetonitrile solution. For clarity, hydrogen atoms on carbon are not shown. Bond lengths are reported in Å.

As shown in Fig. 2, from benzene and the above released hydroxyl radical, there are two reaction pathways, i.e., formation of hydroxybenzene radical and benzene radical denoted as P2-HB and P2-B, respectively. For P2-HB, the hydroxyl radical initially interacts with benzene, generating a molecular complex ²2-IM1. Next, the C–O bond forms via a linear two-membered ²2-HB-TS1, resulting in hydroxybenzene radical (Ph(H)OH). The P2-HB involves an EHHP of 54.8 kJ mol⁻¹ at ²2-HB-TS1. Alternatively, for P2-B, from ²2-IM1, the C–H bond cleavage occurs via a quasilinear three-membered ²2-B-TS1, producing a H₂O-containing molecular complex ²2-B-IM2. Finally, ²2-B-IM2 releases the free water molecule, leaving behind the benzene radical. The P2-B possesses an EHHP of 60.5 kJ mol⁻¹ at ²2-B-TS1.

As compared to P2-B, P2-HB is kinetically more favourable because of its lower EHHP (54.8 vs. 60.5 kJ mol⁻¹). This indicates that the hydroxybenzene radical should be more feasibly generated than benzene radical in the reaction of hydroxyl radical with benzene.

3.2.2 Phenol formation from hydroxybenzene radical on semiquinone. There are two types of oxygen atoms, i.e., those present in hydroxyl and carbonyl groups, on the resultant semiquinone of carbon. Therefore, the hydroxybenzene radical could attack these two types of oxygen atoms.

The geometric structures and the schematic energy diagrams for the hydroxybenzene radical attacking the oxygen atom of hydroxyl and carbonyl groups on the armchair and zigzag semiquinones of carbon in acetonitrile solution are shown in Fig. 3 and 4 and denoted as P3-a, P3-z, P4-a, and P4-z.

Fig. 3 The geometric structures (a) and the schematic energy diagrams (b) with the relative Gibbs free energy (G_r, kJ mol⁻¹) relative to the hydroxybenzene radical attacking the oxygen atom of hydroxyl group on the armchair and zigzag semiquinones of carbon in acetonitrile solution. For clarity, hydrogen atoms on carbon are not shown. Bond lengths are reported in Å.

Fig. 4 The geometric structures (a) and the schematic energy diagrams (b) with the relative Gibbs free energy (G_r, kJ mol⁻¹) relative to the hydroxybenzene radical attacking the oxygen atom of carbonyl group on the armchair and zigzag semiquinones of carbon in acetonitrile solution. For clarity, hydrogen atoms on carbon are not shown. Bond lengths are reported in Å.

As depicted in Fig. 3, for P3-a and P3-z, at the beginning, the Ph(H)OH radical interacts with the oxygen atom of hydroxyl group in semiquinone ²a-OH-O or ²z-OH-O, forming a molecular complex ³a-3-IM1 or ³z-3-IM1, respectively. Next, C–H bond cleavage takes place via a rectangular five-membered ¹a-3-TS1 or ¹z-3-TS1, producing a phenol- and H₂O-containing molecular complex ¹a-3-IM2 or ¹z-3-IM2, respectively. Then, ¹a-3-IM2 or ¹z-3-IM2 liberates the free phenol and H₂O molecules, regenerating the defect armchair ¹a-O or ¹z-O, respectively. Finally, the singlet–triplet spin-crossing should take place via the minimum energy crossing point (MECP) between ¹a-O and ³a-O or between ¹z-O and ³z-O, regenerating the defect armchair ³a-O or zigzag ³z-O, respectively. The reaction pathways, P3-a and P3-z, possess EHHPs of 92.3 and 97.9 kJ mol⁻¹ at ¹a-3-TS1 or ¹z-3-TS1 for the C–H bond cleavage, respectively.

As shown in Fig. 4, for P4-a and P4-z, as mentioned earlier, the Ph(H)OH radical initially interacts with the oxygen atom of the carbonyl group in semiquinone ²a-OH–O or ²z-OH–O, generating a molecular complex ³a-3-IM1 or ³z-3-IM1, respectively. Next, the C–H bond cleavage occurs via a rectangular five-membered ¹a-4-TS1 or ¹z-4-TS1, producing a phenol-containing molecular complex ¹a-4-IM2 or ¹z-4-IM2, respectively. Following this, the molecular complex ¹a-4-IM2 or ¹z-4-IM2 releases the free phenol molecule, setting aside the armchair ¹a-2OH or zigzag ¹z-2OH, respectively. Then, the singlet–triplet spin-crossing should occur via MECP between ¹a-2OH and ³a-2OH or between ¹z-2OH and ³z-2OH. Subsequently, from ³a-2OH or ³z-2OH, a [1,4]-H shift or a [1,5]-H shift takes place via a five-membered ring ³a-4-TS2 or via a six-membered ring ³z-4-TS2, forming a H₂O-containing molecular complex ³a-4-IM3 or ³z-4-IM3, respectively. Finally, the complex ³a-4-IM3 or ³z-4-IM3 set the H₂O molecule free, recovering the defect armchair ³a-O or zigzag ³z-O, respectively. The reaction pathways P4-a and P4-z possess EHHPs of 181.4 and 130.4 kJ mol⁻¹ at ¹a-4-TS2 and ¹z-4-TS2 for the C–O and O–H bond cleavages, respectively.

Compared with P4-a and P4-z, P3-a and P3-z are kinetically more favourable, because of their lower EHHP (92.3 and 97.9 vs. 181.4 and 130.4 kJ mol⁻¹, respectively). This indicates that the intermolecular H-shift for the H₂O formation both in ¹a-3-TS1 and ¹z-3-TS1 is kinetically favourable than the intramolecular H-shift for the H₂O formation both in ³a-4-TS2 and ³z-4-TS2, respectively. In other words, for the regeneration of the carbon catalyst, the intermolecular dehydration is superior to the intramolecular dehydration. This phenomena is similar to that reported for the dehydration of fructose.⁴⁶

3.3 Branched reactions

3.3.1 Conversion of hydroquinone to semiquinone by hydroxyl radical. The geometric structures and the schematic energy diagrams for the conversion of hydroquinone to semiquinone with the armchair and zigzag carbon oxidized by hydroxyl in acetonitrile solution are shown in Fig. 5 and denoted as P5-a and P5-z, respectively.

Fig. 5 The geometric structures (a) and the schematic energy diagrams (b) with the relative Gibbs free energy (G_r, kJ mol⁻¹) relative to the conversion of hydroquinone to semiquinone with the armchair and zigzag carbon oxidized by hydroxyl in acetonitrile solution. For clarity, hydrogen atoms on carbon are not shown. Bond lengths are reported in Å.

As mentioned earlier, the hydroxyl radical can be easily formed from H₂O₂ on the defect active sites ³a-O or ³z-O. As shown in Fig. 5, once the hydroxyl radical is produced, it could trigger the interconversion from hydroquinone to semiquinone and to quinone of carbon.

For P5-a or P5-z, from hydroquinone to semiquinone oxidized by hydroxyl radical, the hydroxyl radical initially interacts with hydroquinone on the armchair or zigzag carbon. Next, the O–H bond cleavage occurs via a linear-like three-membered ²a-5-TS1 or ²z-5-TS1, resulting in a H₂O-containing molecular complex, ²a-5-IM2 or ²z-5-IM2, respectively. Finally, ²a-5-IM2 or ²z-5-IM2 releases the free water molecule, leaving behind the semiquinone ²a-OH-O or ²z-OH-O. The reaction pathway P5-a or P5-z includes an EHHP of 33.5 or 7.5 kJ mol⁻¹ at ²a-5-TS1 or ²z-5-TS1, respectively. Such a low EHHP oxidizes hydroquinone readily to semiquinone via hydroxyl radical.

In short, once hydroquinone is generated, it could be readily oxidized to semiquinone and consume the hydroxyl radical.

3.3.2 Conversion of semiquinone to quinone by hydroxyl radical. The geometric structures and the schematic energy diagrams from semiquinone to quinone with the armchair and zigzag carbon oxidized by hydroxyl in acetonitrile solution are depicted in Fig. 6 and denoted as P6-a and P6-z, respectively.

Fig. 6 The geometric structures (a) and the schematic energy diagrams (b) with the relative Gibbs free energy (G_r, kJ mol⁻¹) relative to the reaction from semiquinone to quinone with the armchair and zigzag carbon oxidized by hydroxyl in acetonitrile solution. For clarity, hydrogen atoms on carbon are not shown. Bond lengths are reported in Å.

As shown in Fig. 6, for P6-a, initially, hydroxyl radical attacks the carbon atom of the –COH group on semiquinone, forming a molecular complex ³a-6-IM1. Next, C–O bond formation takes place via a three-membered ring ³a-6-TS1, leading to a dihydroxyl-containing complex ³a-6-IM2. Next, the triplet–singlet spin-crossing could occur via MECP between ³a-6-IM2 and ¹a-6-IM2, resulting in the ground-state ¹a-6-IM2. Subsequently, a [1,3]-H shift takes place via a four-membered cyclic ¹a-6-TS2, generating a H₂O-containing molecular complex ¹a-6-IM3. Finally, ¹a-6-IM3 sets the H₂O molecule free, leaving behind quinone ¹a-2O. The reaction pathway P6-a possesses the EHHP of 219.4 kJ mol⁻¹ at ³a-6-TS1 and the HEB of 195.1 kJ mol⁻¹ at the reaction step of ³a-6-IM1 → ³a-6-TS1.

As shown in Fig. 6, for P6-z, from semiquinone to quinone oxidized by hydroxyl, the reaction pathway is similar to that for P5-z from hydroquinone to semiquinone oxidized by hydroxyl. The reaction pathway P6-z involves an EHHP of 26.2 kJ mol⁻¹ at ¹z-6-TS1 and a HEB of only 4.0 kJ mol⁻¹ at the reaction step of ³z-1-IM2 → ³z-6-TS1.

Compared to P6-a, P6-z is kinetically more favourable, because of its lower EHHP (26.2 vs. 219.4 kJ mol⁻¹) and HEB (4.0 vs. 195.1 kJ mol⁻¹). This indicates that the armchair semiquinone should be more easily oxidized to quinone than the zigzag semiquinone by consuming the hydroxyl radical.

It is evident that once the semiquinone is formed, it could react with hydroxyl radical or hydroxybenzene radical. Thus, these reactions are competitive. Herein, we list the EHHPs for the reactions of semiquinone or quinone with hydroxyl and/or hydroxybenzene radicals in Table 1.

Table 1 The energy heights of the highest point (EHHPs) (in kJ mol⁻¹) for the typical reaction pathways

EHHP	P3	P4	P6	P7
Armchair	92.3	181.4	219.4	72.4
Zigzag	97.9	130.4	26.2	162.2

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As shown in Table 1, for the armchair semiquinone, the EHHP of P3-a is the lowest among the three reaction pathways of semiquinone with hydroxyl or hydroxybenzene radical (P3-a, P4-a, and P6-a). This indicates that the armchair semiquinone would rather react with the hydroxybenzene radical and then regenerate the active defect of AC than react with hydroxyl radical and then be oxidized to quinone. The armchair configuration defect was successfully identified experimentally.⁶ Besides, we would discuss the reaction pathway P7, vide infra.

In addition, as shown in Table 1, for the zigzag semiquinone, the EHHP of P6-z is the lowest among the three reaction pathways of semiquinone with hydroxyl or hydroxybenzene radical (P3-z, P4-z, and P6-z). This indicates that the zigzag semiquinone prefers to react with the hydroxyl radical and then be oxidized to quinone. Once the zigzag semiquinone is formed, it could be also easily oxidized to quinone and then consume the hydroxyl radical.

3.3.3 Phenol formation from hydroxybenzene radical on quinone. The geometric structures and the schematic energy diagrams for the phenol formation from hydroxybenzene radical on the armchair and zigzag quinones of carbon in acetonitrile solution are shown in Fig. 7 and denoted as P7-a and P7-z, respectively.

Fig. 7 The geometric structures (a) and the schematic energy diagrams (b) with the relative Gibbs free energy (G_r, kJ mol⁻¹) relative to the phenol formation from hydroxybenzene radical on the armchair and zigzag quinones of carbon in acetonitrile solution. For clarity, hydrogen atoms on carbon are not shown. Bond lengths are reported in Å.

As shown in Fig. 7, for P7-a and P7-z, at the beginning, the Ph(H)OH radical attacks the oxygen atom of carbonyl in quinone ²a-2O or ²z-2O, respectively. Then, the C–H bond cleavage occurs via a linear three-membered ²a-7-TS1 or ²z-7-TS1, leading to a phenol-containing molecular complex ²a-7-IM2 or ²z-7-IM2, respectively. Subsequently, the molecular complex ²a-7- IM2 or ²z-7-IM2 liberates the free phenol molecule, leaving behind the armchair ²a-OH–O or zigzag ²z-OH–O, respectively. The reaction pathway P7-a or P7-z possesses an EHHP of 72.4 or 162.2 kJ mol⁻¹ at ²a-7-TS1 or ²z-7-TS1 with a HEB of 72.4 or 9.4 kJ mol⁻¹, respectively.

As mentioned earlier, once the hydroxybenzene radical is formed, it could react with the semiquinone or quinone. Furthermore, the two reactions are competitive. As shown in Table 1, the EHHPs and HEB for the armchair and zigzag quinones on carbon, which reacted with hydroxybenzene (P7), are markedly lower than those for the armchair and zigzag semiquinones (P3 and P4), respectively. This indicates that the hydroxybenzene radical should consume quinone more easily than semiquinone. Therefore, once the quinone is formed, it could easily react with the hydroxybenzene radical and then be reduced to semiquinone, yielding phenol.

3.4 Comparison of four main reaction pathways over carbon

Based on the above results, on the defect armchair ³a-O, there are two catalytic cycles for the entire reaction of benzene + H₂O₂ → phenol + H₂O. One is composed of P1-a, P2-HB, and P3-a, and another is composed of P1-a, P2-HB, and P4-a and denoted as CA-1 and CA-2, respectively. Through TOF analysis using the energetic span model, for CA-1, the TDI and TDTS are ¹a-3-IM3 and ³a-1-TS1 for the hydroxyl radical formation, respectively. Furthermore, for CA-2, the TDI and TDTS are ¹a-2OH and ³a-4-TS2 for the regeneration of defect active sites, respectively. Herein, the rate constant k_CA-1 of ³a-O + ¹H₂O₂ → ³a-1-TS1 and the rate constant k_CA-2 of ¹a-2OH → ³a-4-TS2 are representative of the total reaction constant. Over the 313–353 K temperature range, the rate constants k_CA-1 (in s⁻¹ mol⁻¹ dm³) and k_CA-2 (in s⁻¹) can be fitted by the following expressions:

k_CA-1 = 6.528 × 10⁵  exp(−35 994/RT) (iii)

k_CA-2 = 6.927 × 10¹³  exp(−410 362/RT) (iv)

It is evident that the activation Gibbs free energies in k_CA-2 are about 10 times higher than that in k_CA-1, over the 313–353 K temperature range. It emphasizes that the catalytic cycle CA-1 is kinetically more favourable than CA-2. In other words, once the armchair hydroquinone is formed, it would not be beneficial for further reaction for the recovery of active defects.

In addition, on the zigzag defect ³z-O, there are two catalytic cycles. One comprises P1-z, P2-HB, and P3-z, and another comprises P1-z, P2-HB, and P4-z and denoted as CZ-1 and CZ-2, respectively. By TOF analysis using an energetic span model, for CZ-1, the TDI and TDTS are ¹z-3-IM2 and ³z-1-TS1 for the hydroxyl radical formation, respectively. Moreover, for CZ-2, the TDI and TDTS are ¹z-2OH and ³z-4-TS2 for the regeneration of defect active site, respectively. Therefore, the rate constant k_CZ-1 of ³z-O + ¹H₂O₂ → ³z-1-TS1 and the rate constant k_CZ-2 of ¹z-2OH → ³z-4-TS2 are characteristic of the total reaction constant. Over the 313–353 K temperature range, the rate constants k_CZ-1 (in s⁻¹ mol⁻¹ dm³) and k_CZ-2 (in s⁻¹) can be adapted by the following expressions:

k_CZ-1 = 1.603 × 10⁵  exp(−23 984/RT) (v)

k_CZ-2 = 2.594 × 10¹³  exp(−367 420/RT) (vi)

It could be noted that the activation Gibbs free energies in k_CZ-2 is about 14 times higher than that in k_CZ-1, over the 313–353 K temperature range. It echoes that the catalytic cycle CZ-1 is kinetically more preferable than CZ-2. In other words, once the zigzag hydroquinone is generated, it would be not advantageous for further reaction for the recovery of active defect.

Overall, both the zigzag and armchair defect sites show good catalytic performance. Besides, the ratio of k_CZ-1/k_CA-1 is calculated to be about 25–15, over the 313–353 K temperature range. This indicates that the zigzag defect ³z-O exhibits better catalytic performance than the armchair defect ³a-O.

3.5 Origin of catalytic activity difference between armchair and zigzag carbon

3.5.1 Activation strain analysis of the HO–OH bond activation in –H₂O₂ moiety catalyzed by ³a-O and ³z-O. To shed some light on the origin of the catalytic activity difference between the defect armchair ³a-O and the zigzag defect ³z-O, we discuss the catalytic performance of active species (³a-O and ³z-O) by analysing the activation strain of the HO–OH bond cleavage of H₂O₂. The trends in reactivity were analysed using the activation strain model of chemical reactivity.^47,48 In this model, the activation energies ΔE^≠ of the TS are divided into the activation strain ΔE^≠_strain and the stabilizing TS interaction ΔE^≠_int, i.e., ΔE^≠ = ΔE^≠_strain + ΔE^≠_int. The activation strain ΔE^≠_strain is the strain energy associated with deforming the reactants from their equilibrium geometry to the geometry they adopt in the TS. The stabilizing TS interaction ΔE^≠_int is the actual interaction energy between the deformed reactants in the TS.^47,48

The results of the activation strain analysis are listed in Table 2. As shown in Table 2, the activation energy, ΔE^≠, decreases from 33.9 kJ mol⁻¹ (³a-O) to 22.9 kJ mol⁻¹ (³z-O). The activation strain, ΔE^≠_strain, increases from 23.6 kJ mol⁻¹ (³a-O) to 24.8 kJ mol⁻¹ (³z-O). The substrate H₂O₂ activation-strain term, ΔE^≠_strain [H₂O₂], increases from 22.8 kJ mol⁻¹ (³a-O) to 24.4 kJ mol⁻¹ (³z-O), whereas the ΔE^≠_strain [Cat] value is so low that it could be neglected both for ³a-O and ³z-O. It is apparent that the activation strain is related to the percent extent of HO–OH bond stretching in the TS. Furthermore, the H₂O₂ activation strain, ΔE^≠_strain [H₂O₂], correlates nearly with the activation strain, ΔE^≠_strain, which increases in the same order. Moreover, the activation strain ΔE^≠_strain is in the reverse order as the activation energy ΔE^≠. Furthermore, the stabilizing TS interaction ΔE^≠_int decreases from 10.4 kJ mol⁻¹ (³a-O) to −2.0 kJ mol⁻¹ (³z-O).

Table 2 Activation strain analysis of transition state (in kJ mol⁻¹) and typical lengths (in Å) for the HO–OH bond cleavage of H₂O₂ catalyzed by armchair and zigzag carbon

Catalyst	TS	Length in H2O2	Length in TS	Stretching in TS	Stretching in TS (%)	ΔE^≠strain [H2O2]	ΔE^≠strain [catalyst]	ΔE^≠strain	ΔE^≠int	ΔE^≠
Armchair	^3a-1-TS1	1.421	1.574	0.153	10.8	22.8	0.7	23.6	10.4	33.9
Zigzag	^3z-1-TS1	1.421	1.578	0.157	11.0	24.4	0.4	24.8	−2.0	22.9

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Overall, the lower activation energy stems primarily from the strengthening of the stabilizing TS interaction by 12.4 kJ mol⁻¹, whereas the activation strain changes by only 1.2 kJ mol⁻¹. Therefore, the stabilizing TS interaction ΔE^≠_int almost correlates with the activation energy ΔE^≠. This could be ascribed to the fact that there is one H-bonding in ³z-TS1 and not in ³a-TS1.

3.5.2 HOMO and LUMO molecular orbitals for the defect ³a-O and ³z-O. As mentioned earlier, for the HO–OH bond cleavage of H₂O₂, the reactivity difference of ³a-O and ³z-O arises primarily from the corresponding difference of the stabilizing interaction ΔE^≠_int. Herein, we investigate the origin of the stabilizing interaction difference of ³a-O and ³z-O toward H₂O₂ by analyzing the HOMO and LUMO molecular orbitals. The HOMO and LUMO molecular orbitals for the defects ³a-O and ³z-O are depicted in Fig. 8. As shown in Fig. 8, the HOMO–LUMO gaps are 5.73 and 5.27 eV for the defect ³a-O and ³z-O, respectively. It is apparent that the HOMO-LUMO gap for ³a-O is larger than that for ³z-O. This indicates that there exist different HOMO–LUMO orbital interactions in ³a-O and in ³z-O, which make them perform differently in the reaction. Therefore, ³a-O possesses lower reactivity than ³z-O.

Fig. 8 Highest occupied molecular orbital (HOMO), lowest unoccupied molecular orbital (LUMO) and the HOMO–LUMO energy gap for the defect ³a-O and ³z-O.

In summary, from the MERPs for the oxidation reaction of benzene to phenol, the catalytically active site of both ³a-O and ³z-O is referred to the defect, which can play a central role of the HO–OH bond cleavage of H₂O₂. Furthermore, the defect ³z-O exhibits better catalytic performance than the defect ³a-O, which stems from a narrower HOMO–LUMO gap in ³z-O than in ³a-O.

4. Conclusions

The catalytic performance of the defect site on carbon for the hydroxylation of benzene to phenol in acetonitrile solution has been theoretically investigated. The following conclusions can be drawn from the present calculation.

Two model catalysts of armchair and zigzag edges have been optimized to mimic carbon materials with the defect site. For both the armchair and zigzag carbons, neither hydroquinone nor semiquinone exhibits any catalytic performance toward the decomposition of H₂O₂. The active defect plays an essential role in the hydroxyl radical formation from H₂O₂, which is the rate-determining step for the benzene hydroxylation to phenol in the presence of H₂O₂.

Both the zigzag and armchair defect sites should show excellent catalytic performance. Furthermore, the zigzag defect on carbon exhibits better catalytic performance than the armchair defect. Through activation strain analysis, there is a stronger stabilizing TS interaction in the zigzag defect carbon than that in the armchair defect carbon, which arises from a narrower HOMO–LUMO gap in ³z-O than in ³a-O. We are actively studying the larger system of carbon materials to simulate the real reaction environment, to gain deeper insight into the catalytic nature for the hydroxylation of benzene to phenol.

Author contributions

The manuscript was written through contributions of all authors. Y.-J. Lyu is responsible for the main computation, T. Qi for part of the computation, H.-Q. Yang for part of the computation, analysis, and writing, and C.-W. Hu for design and revision. All authors have given approval to the final version of the manuscript.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

The authors are grateful for financial support by the National Natural Science Foundation of China (No: 21372167) and the 111 Project (B17030).

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Footnote

† Electronic supplementary information (ESI) available: Sum of electronic and thermal free energies (G_c, hartree), and relative energies (G_r, kJ mol⁻¹) various species with respect to the ground reactants calculated at M06-2x/6-311++G(d, p) level in acetonitrile solution under atmospheric pressure and experimental temperature (1.0 atm and 343 K). The standard orientations of various species calculated at M06-2x/6-311++G(d, p) level for the catalytic hydroxylation of benzene to phenol over the carbons with armchair and zigzag defects. Arrhenius plots of calculated rate constants for the crucial reaction step for the catalytic hydroxylation of benzene to phenol over the carbons with armchair and zigzag defects. See DOI: 10.1039/c7cy01648d

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