5.3 Results and Discussion
5.3.1 Validation of the Computational Methodology: Geometry
a Mn3Ca complex. It is the first example where the Ca atom has been incorporated with Mn into a cubane that resembles the OEC (Figure 5.2). They were also able to synthesize an all Mn cubane Mn4. This opens the possibility of studying the role of the Ca in the oxidation states of the Mn.
Thus in this work we validate a methodology to reproduce and predict the reduction potential of the biomimetic model for the OEC using the rigid ligand 1,3,5-triarylbenzene spacer which incor- porates six pyridine and three alcohol groups (TAB-H3) shown in Figure 5.2. We then can use this method to design new compounds that structurally and electronically resemble to a high degree the most oxidized state of the OEC.
calculate the RMS on the core and the first coordination shell of this cluster; 20 atoms. The comparison of positions between experimental and the calculated geometry give us an RMS of 0.114
˚A. This can be broken down to RMS of 0.007 ˚A for the comparison of bonds and RMS of 0.384◦ in the estimation of bond angles. This gives us confidence that our QM methodology can reproduce the geometry of the CaMn3O4-Full ligand compound.
Next, we use our QM methodology to calculate the optimized structure of the Mn4O4-Full ligand as it is shown in Figure 5.3b. We found that when comparing the position of the 134 atoms between the experimental and the QM structure, the RMS is 0.530 ˚A. The main difference between these structures is again between the unbound pyridines. When comparing only the Mn4O4 cluster and the first coordination shell between the experimental and QM structure it is found an RMS of 0.086
˚A. This is composed from the estimation of bonds with an RMS of 0.012 ˚A and RMS of 0.060◦ for the estimation of bond angles. In general, the estimation of the general structure for the Mn4
is slightly worse than for the CaMn3 case, however when estimating the core cluster the reverse happens.
Full system RMS = 0.417 A
Cubane structure RMS = 0.086
RMS (bond) = 0.012 A RMS (angle) = 0.060o
a) b)
Cubane structure RMS = 0.114 A RMS (bond) = 0.007 A RMS (angle) = 0.384o
Full system RMS = 0.530 A
Figure 5.3: Comparison of geometries obtained from experiment (colored: Ca; magenta, Mn; light blue, O; red, C; grey, H; white) and theory (black) using the full ligand. We show the root mean square (RMS) to compare all the atoms in the structure (top) and the cubane (bottom).
a) b)
Full system
RMS = 0.348 A Full system
RMS = 0.292 A
Simplified Ligand RMS = 0.125 A RMS (bond) = 0.007 A RMS (angle) = 0.397o
Simplified Ligand RMS = 0.093 A RMS (bond) = 0.012 A RMS (angle) = 0.074o
Figure 5.4: Comparison of geometries obtained from experiment (colored: Ca; magenta, Mn; light blue, O; red, C; grey, H; white) and theory (black) using the simplified ligand. We show the root mean square (RMS) to compare all the atoms in the structure (top) and the cubane (bottom). The structures with this simplified ligand are almost identical to the ones obtained with the full ligand (Figure 5.3).
However, we need to calculate many properties of these compounds such as the vibrational modes and having to do this for 147 or 134 atoms is too expensive computationally. We postulate that the TAB ligand, although serving to support the metallic cluster, should not participate in the important electrochemical reactions. Thus we simplified our compound by removing the four benzene rings at the bottom and the three unbound pyridines. In addition we fix the carbon that bridges the oxo and bound pyridine in order to mimic the presence of the stiffness of the full TAB ligand. The results are shown in Figure 5.4. The first simplification was done on the CaMn3O4 containing compound as it is shown in Figure 5.4a. By comparing the position of atoms between the geometry obtained from experiments with the one obtained from the simplified ligand, we obtained a RMS of 0.348 ˚A.
This is a smaller number than the one obtained from QM with the full ligand because there are less atoms. In the case of the simplified ligand we have 84 atoms while with the full ligand we treated
147 atoms. Since we are most interested in the estimation of the metallic core, we compared the geometry between this core including the first coordination shell, and the RMS obtained is 0.125 ˚A.
In a more detailed fashion, this is a RMS of 0.007 ˚A for the estimation of bonds and RMS of 0.397◦ for the estimation of angles. This is basically the same accuracy as with the full ligand model.
We performed a similar simplification for the Mn4O4containing compound as it is shown in Figure 5.4b. When comparing the structure from experiment and the one obtained with this simplified ligand, we found a RMS for the position of the atoms of 0.292 ˚A. This is smaller than with the full ligand due to the smaller number of atoms being compared. With the full ligand we treat 134 atoms while with this simplification on the ligand we only need to handle 71 atoms. In this case, we are also interested in how accurate we can predict the geometry of the Mn4O4 cluster and the first coordination shell, since we believe most of the electrochemical processes occur there. By comparing the experimental and the computational geometry of the cluster obtained with the simplified ligand we obtained an RMS of 0.093 ˚A for the estimation of the geometry. The RMS is 0.012 ˚A for estimation of bonds and the RMS is 0.074 ◦ for the estimation of angles. This is practically the same as with the full ligand. With the simplified ligand we obtain a better estimation of the geometry for the Mn4case than for the CaMn3structure, including when only taking into account the cluster and its first coordination shell.
Thus, the models with the simplified ligand gives an accurate description of the geometry observed in experiments and speeds up our calculation by reducing the number of atoms to be treated to almost a half.