Introduction

Oxidation of organic compounds catalyzed by transition metal complexes is of great importance in industrial and biological processes. The most efficient oxidation catalysts are enzymes found in nature--examples are the chromophore P450, the anti-tumor drug bleomycin and methane monooxygenase (MMO). MMOs are a group of enzymes with two active iron centers, which are even capable of directly converting methane to methanol, whereas nowadays methanol is commercially produced in a two-step process via synthesis gas, which is thermodynamically less efficient. In order to improve industrially applied catalysts, study of these enzymes can be very helpful. Oxidations by Fenton's reagent[128,155] (i.e. a mixture of Fe$^{2+}$ and H$_2$O$_2$) are particularly interesting because it not only shows several mechanistic similarities with biochemical enzymes but it has also found industrial applications in for instance paper bleaching and polluted soil cleaning. However, the reaction mechanisms within Fenton chemistry, i.e. oxidation reactions initiated by Fenton's reagent, are still not fully understood, despite the intensive research for more than 60 years.

It is generally believed that the active species in Fenton chemistry is the free OH. radical, which is produced by the iron catalyzed dissociation of hydrogen peroxide, as already proposed in 1932 by Haber and Weiss[156] (reaction equation 8.1).

$$\rm {Fe}^{2+} + \rm {H}_2\rm {O}_2 \rightarrow \rm {Fe}^{3+} + \rm {OH}^- + \rm {OH}\mbox{\.{}}$$ (78)

$$\rm {Fe}^{2+} + \rm {H}_2\rm {O}_2 \rightarrow \rm {FeO}^{2+} + \rm {H}_2\rm {O}$$ (79)

According to the most popular alternative, the active intermediate is a high-valent iron oxo species, the ferryl ion, which was actually already suggested in 1930, by Bray and Gorin[157](reaction equation 8.2). Due to the extremely short lifetimes of the proposed active intermediates, which makes direct detection experimentally very difficult, the controversy remains. The elucidation of the mechanism is further complicated by its complex dependence on the reaction conditions, such as the ligation of the metal, the solvent, the pH and the organic substrate.

We have recently performed static density functional theory (DFT) calculations on aquairon hydrogen peroxide complexes in vacuo as well as ab initio (DFT) molecular dynamics (AIMD) simulations on Fenton's reagent in aqueous solution, without an organic substrate.[145,171,146,197] Our studies show that the ferryl ion is easily formed from hydrogen peroxide coordinated to pentaaqua iron(II), and from the energetic point of view much more likely than the formation of free OH. radicals, thus favoring Bray and Gorin's proposal (reaction equation 8.2). However, to definitively accept the ferryl ion as the active species in aqueous Fenton chemistry, we need to investigate whether the ferryl ion is indeed capable of oxidizing organic substrates. This is the main goal of the present study.

For the organic substrate, we have chosen methane as our model system, which commends itself for a number of reasons. In the first place is the conversion of methane to methanol commercially very interesting, as mentioned before. Secondly, methane is a simple and small system which should limit the chemical complexity and also the computational requirements. In the third place, since the C-H dissociation energies of alkanes range from 103 kcal/mol (calculated at the DFT-BP+ZPE level of theory) for methane to about 90 kcal/mol for tertiary positions, oxidation of other alkanes by the ferryl ion should, at least thermodynamically, be no problem if the ferryl ion is shown to be capable of oxidizing methane. And in the last place, C-H bond activation of methane by transition metal complexes has already been investigated extensively, which makes it possible to compare the reactivity of the aqua iron oxo species to other iron-oxo moieties, such as the earlier mentioned enzymes. In practice, methane is not a Fenton's reagent substrate in aqueous solution, due to its very low solubility in water.

The bare FeO$^+$ ion has been shown to oxidize methane to methanol in the gas phase, under ion-cyclotron resonance conditions[217,218], which has led to a number of theoretical investigations of oxidation reactions by FeO$^+$ and other bare metal oxo species[170,191,192,193,194,195,168]. Bare iron-oxo species were also believed to model the enzyme oxidations by cytochrome P450[195] and MMO[191,170,192]. For the methane-to-methanol oxidation by FeO$^{n+}$, $n$=0,1,2 , Yoshizawa et al. found that a concerted reaction mechanism, via a four-centered transition state (with methane coordinated to iron) is energetically more favorable than a direct H-abstraction by the oxo ligand. Secondly, FeO$^{2+}$ is much more effective for C-H bond cleavage in this methane coordination mechanism than FeO$^{+}$ and FeO.[170] Also, MnO$^+$, which is isoelectronic to FeO$^{2+}$, is most effective in C-H bond activation, compared to FeO$^+$ and CoO$^+$[219,191]. Shaik et al. have proposed low-energy reaction paths, via a double crossing of the high-spin and low-spin energy surfaces--the so-called two-state reactivity[195,220,168].

The active states of the bioorganic molecules MMO[221,222,223] and cytochrome P450[224,225], capable of hydroxylating and oxidizing organic substrates, also involve an Fe$^{\rm IV}$O intermediate. The latest theoretical (DFT) studies on methane-to-methanol oxidation by MMO[163,185,164,186] and P450[190,160] confirm the consensus oxygen-rebound mechanism for these systems. The rate limiting step is the methane H-abstraction, via a linear (Fe)O$\cdots$H$\cdots$C complex, forming a .CH$_3$ radical, which can rearrange to form the alcohol in the rebound step. The oxygen-rebound mechanism is supported by the high measured[226,227,228] and calculated[190,162] kinetic isotope effects. Ultrafast radical clock experiments, timing the rate of the rebound step, have however measured extremely short intermediate lifetimes, casting doubt on the presence of free radicals, which occur in a rebound mechanism[229,230]. Ogliaro et al explained the fast radical clock results for the P450 system with the aforementioned two-state reactivity[160]. For MMO, the radical clock experiments were explained by Siegbahn by an electron transfer of the substrate to the metal complex, forming a cation instead of a free radical[185].

We have calculated the reaction energy profiles for the oxidation of methane into methanol by the aqua iron(IV)oxo species in vacuo following the two mechanisms proposed in the literature. (A third mechanism, the so-called oxene-insertion, is now generally believed to be unlikely as it is characterized by very high energy barriers.[168]) First, the results for the methane coordination mechanism are presented in section 8.3.1, and next we discuss the results for the oxygen-rebound (radical) mechanism in section 8.3.2. To investigate the solvent effects on oxidation chemistry by the ferryl ion, we have also computed the free energy profile for the methane hydroxylation by the ferryl ion (according to the oxygen-rebound mechanism) in aqueous solution, using constrained ab initio molecular dynamics (section 8.4). We will first summarize the computational details, before presenting our results.