The methane coordination mechanism

Figure 8.1: Geometries and energy profile (in kcal/mol) of the intermediate steps along the methane coordination mechanism of the methane-to-methanol oxidation by the tetraaqua iron(IV)oxo species. The energy of the separated reactants is set to zero.

Figure 8.1 shows the energy profile and the complex geometries along the reaction coordinate for the reaction between tetraaqua iron(IV) oxo and methane, following the methane coordination mechanism. The sum of the energies of the optimized methane molecule and the optimized tetraaqua iron(IV) oxo complex (i.e. the reactants), is taken as the off-set for the energy scale. The initial step is the coordination of methane at the vacant coordination site of the metal center, forming a weekly bound reactant complex. The interaction energy is less than 6 kcal/mol. For comparison, the interaction of a fifth H$_2$O ligand at the [Fe$^{\rm IV}$O(H$_2$O)$_4$]$^{2+}$ complex equals 29.2 kcal/mol, which indicates that, in aqueous solution, the required CH$_4$/H$_2$O ligand exchange process is endothermic, by more than 20 kcal/mol. The transformation of the reactant complex into the product-complex of methanol bound to tetraaqua iron(II) occurs in two steps. In the first step, a hydrogen is abstracted from the weakly bound methane by the oxo-ligand, forming a hydroxo ligand and a (formally) CH$_3^-$ ligand bound to iron(IV). This step is overall exothermic by 15.5 kcal/mol, but has a significant barrier of 22.8 kcal/mol, associated with a strained four-membered ring in the transition state. In the second step, the CH$_3$ group is transferred from the metal center to the oxygen of the hydroxo ligand, forming a bound methanol group. The oxidation state of iron is simultaneously lowered from Fe$^{\rm IV}$ to Fe$^{\rm II}$, as both ligands (i.e. OH$^-$ and CH$_3^-$) donate an electron to the metal $d$-manifold. The energy barrier for the, again exothermic, second step is not very high: 11.6 kcal/mol. The bonding of the methanol to Fe$^{\rm II}$(H$_2$O)$_4$ is found to be 31.4 kcal/mol strong. The final separation in aqueous solution can however be expected to be almost thermoneutral ( $\Delta E = 5.4$ kcal/mol, neglecting solvent effects) if it is accompanied by the coordination of a solvent water to the vacant coordination site of the five-fold coordinated product complex, i.e.:

$$\hspace{-10mm} {\rm Fe^{II}(H_2O)_4(CH_3OH)} + {\rm H_2O} \rightarrow {\rm Fe^{II}(H_2O)_5(CH_3OH)} \hspace{8mm} \Delta E = -20.3~{\rm kcal/mol}$$

$$\hspace{-10mm} {\rm Fe^{II}(H_2O)_5(CH_3OH)} \rightarrow {\rm Fe^{II}(H_2O)_5} + {\rm CH_3OH} \hspace{20mm} \Delta E = +25.7~{\rm kcal/mol}$$

(methanol is stronger bonded to tetraaquairon(II) than to pentaaquairon(II) by $31.4-25.7=5.7$ kcal/mol).

Table 8.2: Relevant bond lengths (in Å) and angles as well as Mulliken charges and spin populations, for the reaction intermediates in the methane coordination mechanism of the methane-to-methanol oxidation by the tetraaqua iron(IV)oxo species.

	Free	Reactant	Trans.	Inter-	Trans.	Product	Free
	Reactants	Complex	State 1	mediate	State 2	Complex	Products
$R$FeO	1.62	1.61	1.73	1.74	1.79	2.03
$R$OH		2.51	1.13	0.98	0.97	0.97	0.97
$R$FeC		3.02	2.20	2.06	2.46	3.18
$R$OC		3.62	2.34	2.70	2.18	1.48	1.43
$R$CH	1.10	1.12	1.30	2.90	2.40	2.02	1.96
$\angle$OFeC		98.	72.	90.	59.	21.
$q$Fe	1.22	1.24	1.43	1.40	1.32	1.25	1.28
$q$O	-0.16	-0.20	-0.25	-0.21	-0.30	-0.08	-0.09
$q$C	0.30	0.41	0.19	0.20	0.41	0.29	0.22
$q$H	-0.08	-0.11	0.03	0.08	0.08	0.06	0.07
$s$Fe	3.10	3.07	3.68	3.74	3.87	3.82	3.84
$s$O	0.73	0.72	0.28	0.37	0.26	0.04	0.00
$s$C	0.00	0.04	-0.19	-0.32	-0.31	0.00	0.00
$s$H	0.00	0.01	0.05	0.02	0.01	0.00	0.00

Compared to the methane-to-methanol oxidation by bare metal-oxo species, for which the methane coordination mechanism was found to be the most likely mechanism, there are a number of differences. In the reactant complexes of methane coordinated to bare FeO, FeO$^+$ and FeO$^{2+}$, the binding of methane is $\eta^2$ or $\eta^3$-type, with Fe-C distances as short as 2.32, 2.36 and 2.07 Å respectively[170]. The interaction energy between CH$_4$ and FeO$^{2+}$ was found to be extremely high, namely 70.3 kcal/mol, compared to 22.8 and 5.7 kcal/mol, for the high-spin methane FeO$^+$ and FeO complexes, respectively. The interaction energy with the MnO$^+$ ion (which is isoelectronic with FeO$^{2+}$) is only 16.2 kcal/mol[191]. Instead, we find for our aqua ligated complexes only a weak interaction between methane and the iron(IV) complex (5.8 kcal/mol), with methane bonded to the metal via a single hydrogen; the Fe-H bond distance being 2.17 Å, and a Fe-C distance of 3.02 Å. The relevant geometrical parameters, as well as Mulliken charges $q$ and spin populations $s$ are compiled in table 8.2, for the structures shown in figure 8.1. The Mulliken charge on iron of $q$Fe=1.22 is relatively high compared to e.g. the five-fold coordinated [Fe$^{\rm IV}$(OH)$_4$(H$_2$O)]$\cdot$H$_2$O complex ($q$Fe=0.85[163]), due to the total +2 charge of our systems, and hardly changes after forming the reactant complex with methane. Also, the different basis sets used in our work and in that in the literature can give rise to differences in the Mulliken charges, so that these comparisons are to be regarded with reservation. The spin-density on iron(IV) of $s$Fe=3.10, on the other hand, agrees very well that of other iron(IV) complexes, such as the tetrahydroxo complex ($s$Fe=3.10[163]) and in MMO models ($s$Fe=3.11-3.55[185,164,186]). The rest of the spin-density (the total spin-density is 4) is mainly located on the oxo ligand. The geometries of transition state no.1 (TS1) and the hydroxo intermediate agree qualitatively with the ones found for this first step for the bare [FeO-HCH$_3$]$^{2+}$[170]. Quantitatively, the bond lengths differ in the order of 0.1 Å, with notably shorter Fe-O bond lengths of 1.614 Å and 1.675 Å for the TS1 and intermediate, respectively (where we find 1.73 Å and 1.74 Å), and a larger O-H bond distance of 1.443 Å for the transition state (we find 1.13 Å), in the case of the bare [FeO-HCH$_3$]$^{2+}$ chemistry. The energetics are again very different. For the bare [FeO-HCH$_3$]$^{2+}$ first step, the barrier is only 4.9 kcal/mol (here, 22.8 kcal/mol), whereas the overall transformation energy equals -52.0 kcal/mol (we find -15.5 kcal/mol). The [MnO-CH$_3$]$^{+}$ profile shows only slightly better comparison, with a barrier of 9.4 kcal/mol and -36.1 kcal/mol overall. The CH$_3$ ligand interacts much more strongly with the metal center than CH$_4$, giving a bonding energy of -31.2 kcal/mol in the hydroxo intermediate. The positive Mulliken charge on the carbon in the hydroxo intermediate has decreased by 0.2 electron with respect to the reactant complex, and gained a spin density of 0.36. The spin density on iron of $s$Fe=3.74 is in between the spins usually found for Fe(IV) and Fe(III). The second step, the formation of the methanol, which we found to be exothermic by 34.1 kcal/mol with a moderate barrier of 11.6 kcal/mol, was found to be energetically unfavorable for the bare [FeOH-CH$_3$]$^{2+}$ case, and was not further discussed[170]. Also with manganese (i.e. bare [MnOH-CH$_3$]$^{2+}$), this step is not exothermic (by 0.2 kcal/mol), and has a very high barrier, equal to 35.9 kcal/mol[191].

We conclude that the oxidation of methane to methanol by the tetraaqua iron(IV) oxo species is exothermic in vacuo following the methane coordination pathway, with a highest barrier for the hydroxylation step of 22.8 kcal/mol. If one were to start from pentaaqua iron(IV)oxo (as in aqueous solution), the first step is the water-methane ligand exchange reaction, which in vacuo is endothermic by 23.4 kcal/mol. The reaction energy profile shows large differences with that of methane oxidation by a bare FeO$^{2+}$ ion, which casts doubt on the use of bare transition metal-oxo species as models for ligated transition metal oxo moieties, such as in enzymes and in solution.