Elementary Fenton and Fenton-like reactions in vacuo

Table 6.1: Comparison of DFT-BP reaction energies (kcal/mol) starting with either an iron(II) complex ($n$=2) or an iron(III) complex ($n$=3). The last column shows the reaction energy starting with iron(III) ($n$=3), but with one water ligand replaced by an hydroxo ligand, so that the complex has the same total charge as the iron(II) complex.

Gas phase reaction		Fe(II)	Fe(III)	Fe(III)OH$^-$
A	Fe$^{n+}$(H$_2$O)$_6$ $\rightarrow$ Fe$^{n+}$(H$_2$O)$_5$ + H$_2$O	22.1	45.7	24.7
B	Fe$^{n+}$(H$_2$O)$_5$(H$_2$O$_2$) $\rightarrow$ Fe$^{n+}$(H$_2$O)$_5$ + H$_2$O$_2$	22.8	46.4	25.4
C	Fe$^{n+}$(H$_2$O)$_5$(H$_2$O$_2$) $\rightarrow$
	Fe$^{(n+1)+}$(H$_2$O)$_5$(OH$^-$) + HO.	20.7	60.8	38.5
D	Fe$^{n+}$(H$_2$O)$_5$(H$_2$O$_2$) $\rightarrow$
	Fe$^{(n+2)+}$(H$_2$O)$_5$(O$^{2-}$) + H$_2$O	-8.0	56.9	9.6
E	Fe$^{3+}$(H$_2$O)$_5$(H$_2$O$_2$) + H$_2$O $\rightarrow$
	Fe$^{3+}$(H$_2$O)$_5$(OOH$^-$) + H$_3$O$^+$		-156
F	Fe$^{3+}$(H$_2$O)$_5$(H$_2$O$_2$) + H$_2$O $\rightarrow$
	Fe$^{3+}$(H$_2$O)$_4$(OH$^-$)(H$_2$O$_2$) + H$_3$O$^+$		-145
G	Fe$^{3+}$(H$_2$O)$_5$(OOH$^-$) $\rightarrow$ Fe$^{2+}$(H$_2$O)$_5$ + HOO.		36.8	40.6
H	Fe$^{3+}$(H$_2$O)$_5$(OOH$^-$) $\rightarrow$ Fe$^{3+}$(H$_2$O)$_5$ + HOO$^-$		417	281.
I	Fe$^{3+}$(H$_2$O)$_5$(OOH$^-$) $\rightarrow$
	Fe$^{4+}$(H$_2$O)$_5$(O$^{2-}$) + HO.		42.6	26.1
J	Fe$^{3+}$(H$_2$O)$_5$(OOH$^-$) $\rightarrow$
	Fe$^{5+}$(H$_2$O)$_5$(O$^{2-}$) + HO$^-$		444.	281.

We have computed the reaction energies of the elementary Fenton and Fenton-like reactions of the hydrated iron complexes in vacuo, among which the ones mentioned in the introduction (equations 6.1-6.6), and compiled the results in table 6.1. The first two columns of numbers on the left-hand-side show the reaction energies in kcal/mol with an iron(II) complex and an iron(III) complex as the reactant, respectively. Hydrated metal ions can be acidic, the acidity increasing with increasing oxidation state of the metal ion. For example, the acidity constant of [Fe$^{\rm {III}}$(H$_2$O)$_6$]$^{3+}$ equals p$Ka=2.2$[154], so that in aqueous solution hydrolysis easily takes place to form the iron(III)hydroxo complex [Fe$^{\rm {III}}$(H$_2$O)$_5$(OH)]$^{2+}$ and a free hydronium ion. As we shall see, the lowering of the total charge on the metal complex from 3+ to 2+ has a significant effect on the reactivity. The reaction energies of the present elementary reactions starting from such an iron(III)hydroxo complex are given in the last column of table 6.1. Deprotonation of an iron(II) complex is less likely. The acidity constant of hexaaquairon(II) is p$Ka=9.5$[143], so that the [Fe$^{\rm {II}}$(H$_2$O)$_5$(OH)]$^{+}$ complex forms an improbable starting species.

Starting from hexaaquairon complexes, we see after comparing reactions A and B, that the ligand exchange of a water ligand by hydrogen peroxide is almost thermoneutral, but that the water (and H$_2$O$_2$) ligands are much stronger bonded to the 3+ charged iron(III) complexes than to the 2+ charged iron(II) and iron(III)hydroxo complexes (by more than 20 kcal/mol). The production of a free hydroxyl radical, starting from hydrogen peroxide coordinated to iron(II) (as in the Haber and Weiss mechanism, reaction 6.1) costs 20.7 kcal/mol (reaction C in the table), a reduction of 39.2 kcal/mol with respect to the dissociation of free hydrogen peroxide into two hydroxyl radicals ($\Delta E=59.9$ kcal/mol at the same level of theory and 54 kcal/mol including the zero point energy, in reasonable agreement with the experimental value at 25$^\circ$C of 51.2 kcal/mol). For hydrogen peroxide coordinated to pentaaquairon(III) on the other hand, does the O-O dissociation and free OH. radical formation not lead to a reduction compared to free H$_2$O$_2$ dissociation, but is even slightly more endothermic (by 1 kcal/mol). The OH. radical produced in reaction C can also abstract the hydrogen from the produced hydroxo ligand to form the ferryl ion ([Fe$^{\rm {IV}}$(H$_2$O)$_5$O]$^{2+}$) and a water molecule, following the Bray and Gorin mechanism (reaction 6.2) when starting from [Fe$^{\rm {II}}$(H$_2$O)$_5$(H$_2$O$_2$)]$^{2+}$ or the [Fe$^{\rm {V}}$(H$_2$O)$_5$O]$^{3+}$ species and H$_2$O when starting from [Fe$^{\rm {III}}$(H$_2$O)$_5$(H$_2$O$_2$)]$^{3+}$ (reaction D in the table). In the first case, the overall reaction is exothermic by 8 kcal/mol, but starting with iron(III), the formation of the oxo species is again energetically very unfavorable ($\Delta E=56.9$ kcal/mol). These numbers clearly show, in the first place, that the highly reactive OH. radical and high-valent iron oxo species are much more easily formed from Fenton's reagent (Fe$^{2+}$/H$_2$O$_2$) than from the Fenton-like reagent (Fe$^{3+}$/H$_2$O$_2$), confirming the experimentally observed difference in oxidative reactivity between the two reagents. In the second place, reactions C and D indicate that the ferryl ion is a much more likely candidate for the active species in Fenton chemistry than the free OH. radical. In refs franco1,bernd3,bernd4,bernd5, we have discussed the Fenton reagent more extensively, and we have shown that in the two-step process that leads to formation of the ferryl ion, the highest of the two transition states is only 6 kcal/mol. We have also investigated the reactivity of the ferryl ion towards organic substrates by simulating the oxidation of methane to methanol by the ferryl ion[198]. We will now continue to focus solely on the Fenton-like reagent.

The formation of the iron(III)hydroperoxo species from iron(III)hydrogen-peroxide in aqueous solution (reaction 6.3), which is believed to be the initial step in Fenton-like chemistry (reaction E in table 6.1), is poorly modeled in vacuo. The absolute reaction energies of such charge separation reactions are typically highly overestimated, due to the omission of the screening of the solvent and the energies of solvation. The hydrolysis of hexaaquairon(III) for instance, forming pentaaqua hydroxo iron(III) by donating a proton to a water molecule in vacuo, results in an energy gain of 145 kcal/mol, whereas the experimental acidity constant of p$Ka=2.2$ indicates an (free) energy loss of 3 kcal/mol. However, we can nevertheless compare the reaction energies of charge separation processes for which the solvent effects are expected to be similar. Hydrolysis of coordinated H$_2$O in pentaaquairon(III)hydrogen-peroxide (reaction F in table 6.1), for example, is not expected to be much different from the hydrolysis of hexaaquairon(III), and the reaction energies in vacuo are indeed in both cases found to be -145 kcal/mol. Now, we can compare reaction E and F, assuming no large differences in energies of solvation for the products, and conclude that the formation of the iron(III)hydroperoxo species in aqueous solution indeed is a likely initial step in Fenton-like chemistry, and that the hydrolysis of the H$_2$O$_2$ ligand is probably even favored over the hydrolysis of a H$_2$O ligand. Nevertheless, we want to stress that the proper inclusion of the solvent effects is required to accurately model this first step in Fenton-like chemistry.

Reactions G till J in the table are possible reactions of a second step, in which the iron(III)hydroperoxo species forms very reactive particles such as radicals and high-valent iron oxo species. We see that the unscreened charge separation processes of Fe-O bond or O-O bond heterolysis (reactions H and J, respectively) again results in very high values for the reaction energies in vacuo (this time uphill), which makes it impossible to compare these reactions with the homolysis equivalents (reactions G and I, respectively), although we doubt that inclusion of the solvent screening and solvation energies will bring the reaction energies of reaction H and J in aqueous solution below 50 kcal/mol. The energies for the homolysis of the Fe-O or O-O bond of 36.8 kcal/mol and 42.6 kcal/mol are also rather high. An important difference between the two reactions is that, although they both produce highly reactive radicals, in the Fe-O homolysis (G) the formal oxidation state of iron is lowered, whereas in the O-O homolysis (I) the formal oxidation state of iron increases. As the acidity of hydrated metal ions increases with the oxidation state of the metal (see before), hydrolysis of the metal complex works in opposite directions for the two homolysis reactions. Taking the hydrolysis effect into account results in O-O homolysis forming the most probable second step in Fenton-like chemistry, with a reaction energy of 26.1 kcal/mol in vacuo, comparable to the initial ligand expulsion step, reaction A (see the third column of table 6.1 for the reaction energies when first hydrolysis of an H$_2$O ligand has occurred). As in this reaction both OH. radicals and ferryl ions are formed, it is particularly interesting to study this O-O homolysis in more detail with inclusion of the water environment. In section 6.3.3, we will compute the free energy barrier for the O-O homolysis reaction in aqueous solution, and will then consider the role of (simultaneous) hydrolysis of a H$_2$O ligand in more detail.

Summarizing, the static DFT calculations show that for iron(III)hydrogen-peroxide the direct formation of the OH. radical (C) or the high-valent iron oxo species(D) is energetically much less favorable than for iron(II)hydrogen-peroxide. Secondly, the acidity of iron(III) complexes is expected to play an important role as the hydrolysis of a water ligand lowers the reaction energies dramatically, particularly in the case of the iron(V)oxo complex formation (D). In the third place, hydrolysis of the H$_2$O$_2$ ligand of [Fe$^{\rm {III}}$(H$_2$O)$_5$(H$_2$O$_2$)]$^{3+}$, producing the iron(III)hydroperoxo species (E) is energetically favored over hydrolysis of a water ligand (F). In the next section, we will show that in aqueous solution indeed the hydrolysis of the H$_2$O$_2$ ligand (E) forms the initial step in the Fenton-like chemistry, so that for the next step the transformation of the iron(III)hydroperoxo species becomes important. Fourth, possible second-step transformations are the homolysis of the Fe-O bond (G) and the O-O bond (I) of which the latter becomes particularly interesting when a second hydrolysis (of a water ligand) takes place. We will investigate the O-O bond homolysis and the simultaneous second hydrolysis in aqueous solution in section 6.3.3.