H$_2$O$_2$ coordinating to and reacting with Fe$^{2+}$

Transition metal catalyzed reactions are often assumed to start with coordination of a reactant to the transition metal ion by a ligand substitution reaction. If the substitution reaction is dissociative, a vacant coordination site is first created, which is frequently induced by thermal or photochemical means. The relative probability of a dissociative mechanism for the substitution of a H$_2$O ligand for H$_2$O$_2$ in the Fenton reaction is not known. However, rather than starting from the coordinated H$_2$O$_2$ as in section 5.3.2, we wish to investigate in the present section whether formation of an iron oxo species is also probable when we start from a vacant coordination site to which the hydrogen peroxide will coordinate in the first step of the reaction. The energetic requirements will be essentially different since the 23 kcal/mol bond energy of H$_2$O$_2$ to pentaaquairon(II) will become available in this first step. So in this section we present the results of the AIMD simulation of a reaction pathway for the reaction of hydrogen peroxide with an aqua iron(II) complex containing a vacant coordination site. Waiting for the spontaneous diffusion of H$_2$O$_2$ to the vacant iron site could take a very long time in an AIMD simulation, simply because the reactants are as likely to separate as to approach each other and secondly because the vacant iron site is more likely to be occupied by one of the solvent water molecules than by the single H$_2$O$_2$. To increase the probability of observing a reactive encounter we need a favorable set of momenta for the reactants and the solvating water molecules to start with. In the following we will describe the method we used to obtain such a set of momenta for a configuration of separated reactants in water followed by the simulation of the reactive pathway.

We started an AIMD simulation of the pentaaqua iron(II) hydrogen peroxide complex in water, similar to the approach in the previous section. As we now know, this complex is unstable against the iron(IV) dihydroxo complex, so we constrained the H$_2$O$_2$ oxygen-oxygen bond distance to $R_{\mathrm{OO}}=1.5$ Å to prevent the dissociation to occur. After an equilibration time of 5 ps, we perturbed the system to force the H$_2$O$_2$ ligand to leave the complex and diffuse into the solvent. There are several possibilities to make a ligand dissociate from the complex, such as adding a potential or changing the velocities of the iron complex and the H$_2$O$_2$ into opposite directions. We, however, chose to shorten the Fe-O bond distances for the five water ligands, which causes the complex to expel the hydrogen peroxide ligand. In figure 5.5, we show the evolution of the two Fe-O (of Fe $^{\mathrm{II}}$-H$_2$O$_2$) distances in the upper graph, starting with the last two ps of the equilibration phase. The lower graph shows the constrained O-O bond distance and the HO$^\beta$ distance, with $\beta$ denoting the hydrogen peroxide oxygen which is not bonded to iron (and $\alpha$ denoting the other oxygen). The shorter Fe-O$^\alpha$ distance fluctuates around 2.11 Å which is slightly shorter than the average water ligand Fe-O binding of 2.17 Å in this complex. We already expected similar bonding properties for the H$_2$O$_2$ and H$_2$O ligands from the first bond dissociation energies in the gas phase complexes (see table 5.2) being almost equal. The hydrogen peroxide ligand is well solvated by water molecules. Both hydrogens form hydrogen bonds to solvent water molecules and also the oxygen O$^\beta$ accepts on average 1 to 2 hydrogen bonds from solvent molecules.

Figure 5.5: Upper graph: The two Fe-O (H$_2$O$_2$ oxygens) distances as a function of time, starting from the last part of the equilibration phase (coordinated Fe-H$_2$O$_2$ complex). At t=5.1 ps H$_2$O$_2$ is pulled away from Fe $^{\mathrm{II}}$. At t=5.7 ps the velocities are reversed. Lower graph: The O-O distance is initially fixed until t=5.7 ps. At t=6.5 ps O-O bond cleavage takes place. The OH ligand bond is broken at t=6.85 ps, when the OH. radical grabs its hydrogen.

At $t=5.1$ ps, we constrained the Fe-O distances of the five water ligands at their actual value and shortened the bond length in the following 100 steps (ca. 19.4 fs) to $R=1.8$ Å. The result is that the H$_2$O$_2$ ligand is expelled from the iron(II) coordination shell and moved into the solvent, which is shown by the upper graph in figure 5.5. The dotted lines starting at $t=5.1$ ps show an unsuccessful attempt, where we shortened the five iron water ligands distances to only $R=2.0$ Å. The solid and dashed lines, however, show the successfully enforced dissociation, where especially $R_{\mathrm{Fe-O^\alpha}}$ increases rapidly, within 600 fs, to a distance of 5.4 Å. The other oxygen, O$^\beta$ is hydrogen bonded to 2 solvent water molecules and also the hydrogen bonded to O$^\beta$ forms a hydrogen bond to a solvent water, which makes this part of H$_2$O$_2$ more difficult to move and causes the H$_2$O$_2$ to rotate during the separation, bringing $O^\alpha$ furhter away from Fe than $O^\beta$. At $t=5.7$ ps, we now have a configuration of separated reactants in water, with a set of momenta that will lead to further separation. This configuration we take as the starting point for our reaction pathway and we reverse all atomic velocities to obtain a set of momenta that will lead to approaching reactants. Also, the velocities of the fictitious plane wave coefficient dynamics are reversed as well as the velocity of the Nosé thermostat variable. We remove the H$_2$O$_2$ oxygen-oxygen bond distance constraint to allow dissociation to occur and also the five iron water ligand bond distance constraints are removed. From this point we start the simulation of the reaction pathway.

The Verlet algorithm used for the integration of the equations of motion is time reversible so that the system initially tracks back onto the ``forward'' trajectory of the separating reactants, when the velocities are reversed. This can be seen from the symmetry of the $R_{\mathrm{Fe-O}}$ plots in the upper graph (figure 5.5) close to the mirror line at $t=5.703$ ps. However, due to the removal of the bond distance constraints, the reversed trajectory diverges rapidly from the forward path, as should be expected from the well-known Lyapunov instability of MD trajectories towards small differences in the initial conditions. In fact, the trajectory followed by the approaching reactants is so much different from the trajectory followed by the separating reactants that now the other H$_2$O$_2$ oxygen O$^\beta$ forms a bond with the iron(II) complex at $t=6.5$ ps, i.e. 0.8 ps after the velocities were reversed. Almost immediately after the Fe-O$^\beta$ bond is formed the H$_2$O$_2$ dissociates, which can be seen from the increasing $R_{\mathrm{Fe-O^\alpha}}$ and $R_{\mathrm{O-O}}$ after $t=6.5$ ps in figure 5.5. The first three pictures in figure 5.6 show snapshots of the system (with omission of all solvent water molecules, except one, for clarity) during this coordination process. Note that the incoming hydrogen peroxide, in the lower part of the unit cell in panel 1, to the right, enters the vacant coordination site of the pentaaqua Fe(II) complex in panel 2. Apparently, the incoming hydrogen peroxide does not equilibrate in the local minimum representing the iron hydrogen peroxide complex, but instead it dissociates as soon as the iron oxygen distance reaches the short value of 2.1 Å forming the (formally) Fe$^{3+}$-OH$^-$ complex and a hydroxyl radical. The much shorter average iron hydroxo ligand bond length of $R_{\mathrm{Fe-O^\beta}}=1.84$ Å and the higher frequency compared to the Fe-O bond of a H$_2$O$_2$ or H$_2$O ligand confirm that indeed the O$^\beta$H. brought the iron to the higher oxidation state of +3, increasing the bond strength by the extra electrostatic attraction. About 350 fs after the O$^\alpha$H. radical is formed, it is attracted by the hydrogen of the O$^\beta$H$^-$ hydroxo ligand, which is abstracted about 50 fs later to form a water molecule and the ferryl ion moiety. The average Fe$^{4+}$=O$^{2-}$ bond length of 1.72 Å is even shorter than the iron-oxygen bond in the Fe$^{3+}$-OH$^-$ complex (see again figure 5.5) and also the frequency increases with 100-200 cm$^{-1}$ to roughly 700 cm$^{-1}$ (the statistics do not allow for an accurate number for the frequency). Again, we have found the spontaneous formation of the ferryl ion.

Figure: Six snapshots of the reaction path, starting with the configuration where the velocities were reversed. In this reactive trajectory, the hydrogen peroxide coordinates at the vacant Fe $^{\mathrm{II}}$ site after 0.7 ps. The O-O bond dissociates and the OH. radical wanders off (frame 3 and 4). Then in a second step the OH. radical takes the hydroxo group hydrogen forming a water molecule and the ferryl complex. One solvent molecule that accepts a ligand proton is also shown, but for simplicity, the other solvent water molecules are left out. See also text.

One of the side effects of the increasing oxidation state of the iron complex, going from 2+ to 4+ during the reactive pathway, is that the acidity of the complex increases. We have already seen this phenomenon in the simulation described in the previous section. Again, as shown in the last three snapshots in figure 5.6, hydrolysis of one water ligand takes place at a time somewhere between the moment that the Fe $^{\mathrm{III}}$ complex was formed and the momemt that Fe $^{\mathrm{IV}}$ was formed. So also in this reactive pathway we end up with the [(H$_2$O)$_4$Fe(IV)(OH)(O)]$^{+}$ complex and an extra proton in the solvent.

Although the same iron(IV)oxo complex is formed as in the previous simulations starting from the equilibrated pentaaqua iron(II) hydrogen peroxide complex, there is a difference in the mechanism. In the previous sections, we have seen the formation of the dihydroxo iron(IV) complex as the initial step, as was also predicted by our gas phase study. The iron(IV)oxo complex (ferryl ion) can then be formed in a second step by hydrolysis of an hydroxo ligand (as demonstrated by our first simulation, section 5.3.2). Instead, in the present simulation starting from separated reactants, the ferryl ion is formed via a more direct mechanism. The OH. radical does not find a fast terminating route along an H-bond wire to a water ligand to form a dihydroxo complex, but stays in the neighborhood of the formed OH$^-$ ligand and then finds a quenching pathway by abstracting its hydrogen after roughly 0.3 ps. Apparently, in this case, a pathway to quench the radical in concertation with the O-O bond cleavage and make the process exothermic is not necessary. Indeed, in the present simulation, the energy balance is different. Starting from coordinated H$_2$O$_2$ (section 5.3.2) the energy needed for the OH. formation is equal to the energy needed to dissociate the oxygen-oxygen bond of H$_2$O$_2$ (A in table 5.2) minus the energy gain of replacing the Fe $^{\mathrm{II}}$-H$_2$O$_2$ bond with the much stronger Fe $^{\mathrm{III}}$-OH bond (C-D). Starting with a vacant coordination site and H$_2$O$_2$ in solvation (the present simulation) leaves us with an extra 23 kcal/mol (neglecting the solvent effects), which is enough to form the OH. radical without the need of a fast transfer to an exothermic termination.

The reactive pathways presented in this work illustrate possible microscopic routes via which the chemical reactions could take place. In a next study, will test how realistic the last pathway, illustrating coordination and reaction of H$_2$O$_2$ with iron(II), is, by initiating many new reactive trajectories from this last pathway using the method of transition path sampling.