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Redox-Inert Cations Enhancing Water Oxidation Activity: The Crucial Role of Flexibility Florian H. Hodel, and Sandra Luber ACS Catal., Just Accepted Manuscript • DOI: 10.1021/acscatal.6b01218 • Publication Date (Web): 30 Aug 2016 Downloaded from http://pubs.acs.org on September 2, 2016
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Redox-Inert Cations Enhancing Water Oxidation Activity: The Crucial Role of Flexibility Florian H. Hodel and Sandra Luber* Department of Chemistry, University of Zurich, Winterthurerstrasse 190, CH-‐8057 Zurich, Switzerland Abstract: The devastating effects of global climate change, which is in part caused by anthropogenic CO2 emissions from fossil fuels, force us to find clean fuels produced by environmentally friendly methods. Splitting water into oxygen and hydrogen using solar light is one possible solution, the successful implementation of which depends not least on the de-‐ velopment of efficient water oxidation catalysts (WOCs). With the water splitting reaction of photosystem II, specifically the oxygen evolving complex, which features a cubane structure with a redox-‐inert metal center, nature provides us with clues for the construction of such WOCs. Any approach more sophisticated than a simple trial-‐and-‐error method will rely on knowledge of mechanistic details of biomimetic catalysts. Recently, a step in that direction has been made with com-‐ putational investigations of the different possible catalytic pathways of a {Co(II)4O4} cubane-‐based WOC. The present study, which focuses on the {Co(II)3LnO4} (Ln=Er, Tm) cubane family, is complementary to the previous one and sheds light on the importance of redox inert Ln3+ cations for the mechanism of water oxidation. Using density functional theory and an explicit solvation shell, as well as a solvent continuum model, the WOCs are compared in terms of relative free energies of their catalytic states, as well as the reaction barriers of water attack and oxygen release. Furthermore, in-‐depth investigations into the electronic and molecular structures of the catalysts are carried out resulting in the discovery of a flexibility of the cubane-‐cage during the catalytic cycle. KEYWORDS: homogeneous water oxidation • artificial photosynthesis • cubane • density functional theory • minimum energy path
Introduction Fossil fuel combustion and cement production were respon-‐ sible for 91% of all anthropogenic CO2 emissions between 1 2004 and 2013. The development of clean, sustainable fuels and fuel production methods should therefore be not only one of the most important, but also one of the most urgent scientific goals of our time. Hydrogen is such a zero emission fuel, either by itself, or as an intermediate for liquid hydro-‐ 2 carbon fuels, but 90% is produced via steam reforming of 3 natural gas or light oil. An alternative to this environmental-‐ ly less than desirable production method is photocatalytic water splitting, converting 2 water into 2 hydrogen and one oxygen molecules. The efficiency bottleneck of this process is 4 the oxidation half reaction requiring the transfer of 4 elec-‐ trons and protons and the formation of an O-‐O bond, with an experimentally determined change in free energy ΔGexp: +
-‐
2H2O → O2 + 4H + 4e , (1) ΔGexp(pH=0, NHE)=113.46 kcal/mol. Nature holds an abundance of interesting concepts and mechanisms in store, many of which have led to important inventions and novel materials such as Gecko-‐inspired adhe-‐ 5 6 7 sives , Velcro® , or superhydrophobic, self-‐cleaning surfaces. It might therefore be highly rewarding to apply the same approach to the catalysis of water splitting. Artificial photo-‐ 8,9 synthesis, or, more precisely, mimicking nature’s oxygen
evolving complex (OEC) of photosystem II taking part in the light-‐dependent reaction of photosynthesis is a promising starting point to develop efficient water oxidation catalysts (WOCs). The OEC is a CaMn4O5 cluster, consisting of a CaMn3O4 cubane with coordinating amino acids and a dangling man-‐ 10-‐12 ganese connected to it via an oxygen atom. It oxidizes water by going through 5 catalytic states (S0-‐S4) constituting 13-‐15 the Kok cycle. Both the precise structure of the OEC, as well as the mechanism of O-‐O bond formation have however still not been completely elucidated and are subject of ongo-‐ 16-‐22 ing research. The ideal WOC to mimic the OEC would be built from abundant, cheap elements and exhibit not only a low overpotential, but also high turnover numbers (TON) and frequencies (TOF). In 2013 the first Co(II)-‐cubane based WOC was synthesized 23 and characterized by Evangelisti et al. The homogeneous II catalyst [Co 4(hmp)4(μ-‐OAc)2(μ2-‐OAc)2(H2O)2] (hmp=2-‐ (hydroxymethyl)pyridine) (1) (see Figure 1) closely resembles the OEC in its cubane structure and ligand environment. Recently, we shed light on the mechanistic details of its cata-‐ lytic activity and suggested possible design options by com-‐ putationally comparing different pathways in terms of ther-‐ modynamic free energy differences as well as barrier heights 24 and structural properties. In 2015 Evangelisti et al. succeeded in improving the perfor-‐ mance of their catalyst by slightly modifying the ligand envi-‐ ronment and, more importantly, substituting one Co(II) 25 center with a lanthanide cation. The cubane series II [Co 3Ln(hmp)4(OAc)5H2O]; (Ln = Ho – Yb) have not only
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been the first 3d-‐4f complexes to act as photochemical 3+ WOCs, but also, by virtue of the redox inert Ln cation mim-‐ 2+ icking Ca , have shown even closer OEC analogies than 1. Kohn-‐Sham density functional theory (DFT) based molecular dynamics (MD) simulations have revealed that the acetate ligands of the {Co3ErO4}-‐cubane are thermodynamically far 25 less stable than the ones of 1. They are preferably replaced with hydroxide, or, in the case of ligands bridging two metal centers, detached from one of them, and the newly created empty coordination site is filled by water.
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II
[Co 3Ln(hmp)4(OAc)5H2O] (Ln=Er, Tm) and replaced all non-‐bridging acetate ligands of the original molecule with hydroxide, which provided us with the catalytic ground state of our catalysts, hereafter referred to as 2-‐Er and 2-‐Tm, re-‐ spectively (see Figure 1 and SI, Ground State Structure for a more detailed discussion). While 2-‐Tm was reported to show the lowest catalytic activi-‐ ty of the series in terms of TONs and TOFs, 2-‐Er resided at 25 the upper end of the spectrum. Our findings complement 24 our previous study on the catalytic mechanisms of 1, and together they constitute another essential step forward to-‐ wards the mechanistic understanding of biomimetic WOCs.
Methods
Figure 1. Structure of 1 (top) and 2-‐Er/2-‐Tm (bottom) and labeling of the cobalt centers, two bridging oxygen at-‐ oms, and the “active” ligands “a” and “b”. The Co center oxidized during the catalytic cycle is Co1. Additional solvent molecules are omitted for the sake of clarity. In the present study, we set out to investigate the mechanism by which {Co3LnO4}-‐cubanes catalyze water oxidation using DFT calculations with explicit as well as implicit solvation to determine not only free energy differences between the states (S0-‐S4) of the catalytic cycle (which will be described in section Results, Mechanism, specifically in Scheme 1), but also minimum energy paths and barriers. To this end, we focused our attention on two catalysts of the series
The methods we used are to a large extent identical to the ones we had employed and described in our study of the catalytic pathways of 1, where we had also justified our 24 choices of procedures, set-‐ups, and parameters. We there-‐ fore give here only a brief overview, especially highlighting methodological differences from the earlier study. We used two different and somewhat complementary ap-‐ proaches to obtain structures, electronic energy differences and other properties of the catalytic states. Employing the 26 CP2K program package, we performed geometry optimiza-‐ tions and single point energy calculations of all states includ-‐ ing an explicit water shell of 68 molecules. Because the struc-‐ tural differences between the states are small and geometry optimizations starting from different water shell structures led to similar results, we reasoned that this method is accu-‐ rate enough for our purposes and molecular dynamics or 24 other sampling techniques were not necessary. Neverthe-‐ less, neglecting such atomistic-‐level fluctuations of the sol-‐ vent constitutes an approximation made in this approach. 27 Using the Turbomole 6.5 program package, we carried out calculations of the same systems, this time however with the 28 conductor-‐like screening model (COSMO). While an obvi-‐ ous shortcoming of this approach is the neglect of short-‐ range solute-‐solvent interactions, such as hydrogen bonding, it is computationally cheaper and provides “averaged” sol-‐ 29 vent effects. The calculations carried out with CP2K and explicit solvent consisted of geometry optimizations with the BP86 ex-‐ 30,31 change-‐correlation density functional, followed by single point energy calculations with the B3LYP hybrid density 32,34 functional. The initial configurations of the S0 states were extracted from a DFT-‐based MD run of 2-‐Er by deleting excess water molecules (see SI, Ground State Structures for details). The initial configurations of the geometry optimiza-‐ tions of the other states were obtained by removing a proton and an electron from the previous state (and forming an O-‐O bond with a solvent shell water molecule for S3). For the systems with implicit solvation, we additionally performed
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geometry optimizations with B3LYP. In all calculations, we 35 employed Grimme’s D3 dispersion correction. The set-‐up of the CP2K calculations, which used the 36 QUICKSTEP program, consisted of mixed Gaussian and plane wave basis sets in combination with (relativistic) 25,37,38 Goedecker-‐Teter-‐Hutter (GTH) pseudopotentials, 39 DZVP-‐MOLOPT-‐GTH basis sets (DZVP-‐MOLOPT-‐SR-‐GTH for Co, and a double-‐zeta valence basis set for Er and 25,38 Tm ), and a plane wave cutoff of 400 Ry. The systems were 3 contained in a 30 Å3 box. 40,41 The Turbomole calculations used def2-‐TZVP basis sets, a scalar relativistic effective core potential (ECP-‐28) for Er and Tm, and the resolution-‐of-‐the-‐identity density-‐fitting tech-‐ 42 43 nique with corresponding auxiliary basis sets. In all catalytic states, the Co and Er/Tm centers were as-‐ sumed to couple ferromagnetically with each other and, except for Co1 (for the numbering of the metal centers see 24,25,44 Figure 1), to be in a high-‐spin state. While for S0, we took Co1 to be in a quartet state, for S1-‐S4, we determined the local minimum energy configuration and the associated electronic energy for three different total multiplicities corre-‐ sponding to three possible spin states of Co1. The actual spin configurations on the metal centers and the “active” oxygen ligands were monitored with Mulliken spin populations, which however depend on the basis set and in general do not 45 converge to a basis set limit. Nevertheless, Mulliken spin population analysis is routinely applied. Following the ap-‐ 46-‐49 proach by Nørskov et al., we then calculated free energy differences ∆G!!! between a state i and the catalytic ground state as
∆G!!! = E! + E!"#,! + 0.5iE!! + 0.5iE!"#,!! − E! − E!"#,! + i ∆H − T∆S , i = 1, … ,4. (2) Ei denotes the electronic energy of the state Si, EH2 the elec-‐ tronic energy of a hydrogen molecule, E0 the electronic ener-‐ gy of S0 and EZPE the corresponding zero point energies, which we obtained from normal mode analyses (see SI, Table S3) employing the setup described above. ΔS=0.016 kcal/(K*mol) is half the entropy of H2 at standard conditions 50 taken from thermodynamic tables. Similarly, the enthalpy can be calculated as ΔH=1.153 kcal/mol. For the systems with implicit solvent, where the attacking water molecule does not originate from the solvation shell, the free energy of a single water molecule needs to be included in equation (2) 24 for states S3 and S4. We approximated the overpotential η using the largest free energy difference between two consecutive states of the !"# catalytic cycle ΔG!!(!!!) and the computational value of the reaction free energy of equation (1), ΔG!"#$ (H2O), (see sec-‐ 46,51 tion Free Energy Differences) according to
!"# η=ΔG!!(!!!) −
Δ!!"#$ (H2O) 4
(3)
For the calculation of minimum electronic energy reaction paths and the barriers associated with them, we used the nudged elastic band (NEB) method as implemented in CP2K. The calculations of electronic energies and forces were done exactly the same way as for the geometry optimizations de-‐ scribed above. Due to high computational cost of hybrid functionals, only the BP86 functional was employed, which, however, tends to describes electron distribution in too delo-‐ 52,53 calized way compared to B3LYP. Except where noted otherwise, all NEB calculations consisted of 8 replicas or 54 frames and were optimized by a climbing image NEB every th 55 5 step and the improved tangent method for all others. The initial guesses for the intermediate frames were obtained by linear interpolation of the atom positions. We assumed every replica to have the same total number of unpaired electrons as the first one. For those first frames, we chose the BP86 minimum electronic energy spin multiplicities, which can differ from the B3LYP minimum electronic energy multi-‐ plicities used for the calculations of free energy differences (see SI, Tables S1 and S2). To compare the reaction paths of the two cubanes only considering differences stemming directly from the (electronic) structure of the catalysts them-‐ selves, disentangled from contributions of solvent interac-‐ tions, we performed the NEB calculations of the O2 release from 2-‐Er and 2-‐Tm in vacuo. For the visualization of the molecular structures we used 56 VMD 1.9.1.
Results Mechanism. Our investigations of the catalytic cycle of 1 had focused on two catalytic pathways, a single-‐site and an oxo-‐oxo coupling 24 mechanism involving two Co centers. Assuming that all ligands in the structure of 2 (see Figure 1) are stable, it is obvious that a pathway with two participating metal centers is impossible for this catalyst due to the absence of water or hydroxide ligands or free coordination sites on Co2 and Co3. The only possible coupling partner for an oxo ligand on Co1 is a hydroxide ligand attached to the same Co1 or the lantha-‐ nide atom. While geminal coupling of two non-‐bridging 57 ligands on the active Co would warrant further research 3+ beyond this study, Ln is thought to behave as a redox-‐inert 2+ 25 analog to Ca in the OEC. We therefore did not consider any reactions requiring the direct participation of Er or Tm and refer the reader to our study of the mechanism of 1 where we have discussed (and ruled out) a number of other 24 possible mechanisms. Thus, we are left with a single-‐site pathway (see Scheme 1) with Co1 as the active metal center. We assume 4 consecutive proton-‐coupled electron transfer (PCET) steps between the 5 states (S0-‐S4) of the catalyst and that the O-‐O bond formation takes place as a water molecule from the solvent shell attacks the oxyl ligand of S2 prior to
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the PCET. Due to the lower acidity of the hydroxide ligand, the initial step of the single-‐site mechanism is the deprotona-‐ tion of the water ligand and the concurrent oxidation of Co(II) to Co(III) resulting in a dihydroxo species (S1). The proton of the second PCET could originate from either OH-‐ ligand, resulting in the bifurcation of the pathway (denoted a and b in Scheme 1).
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the thermodynamic limit of water oxidation (upper graph of Figure 2 and SI, Figures S1 and S2, Table S4). Secondly, based 60 on the Sabatier principle and the idea that a thermodynam-‐ ically ideal catalyst would exhibit equal free energy differ-‐ ences between its states, we compared the various systems with such an ideal catalyst (lower graph of Figure 2 and SI, 61,62 ope S2). Finally, we calculated overpotentials by approxi-‐ mating them using the largest free energy difference between two consecutive states of the catalytic cycle (SI, Table S5), an 46,51 approach introduced by Nørskov et al.
Scheme 1. Catalytic cycle of 2-‐Er and 2-‐Tm. Only Co1 and the ligands actively participating in the reactions are shown. For both S2 states, two resonance structures exist (only drawn for S2a in Scheme 1): Co(IV) with an oxo ligand and Co(III) and an oxyl radical, which has been shown for other 59 systems to facilitate O-‐O bond formation and had also 24 computationally been found to be favored by 1. Next, a nucleophilic attack by a water molecule takes place and is followed by the third PCET to form S3a or S3b. Finally, the fourth proton and electron are lost leading to the S4a or S4b state. As for S2, resonance structures with radical character on the ligand can be envisioned. We had shown that 1 prefers a configuration which is best described by resonance struc-‐ 24 tures similar to the middle and right one in Scheme 1. The same holds true for 2-‐Er and 2-‐Tm. The final step restoring the catalyst to its ground state is the release of O2 and the uptake of a water molecule. The structure of each catalytic state can be found in the SI (Figures S4-‐S6). Overall, as re-‐ + quired by equation (1), O2, 4H and 4 electrons have been produced from 2 water molecules. Free Energy Differences. We calculated free energy differences according to equation (2) (for now considering only the spin multiplicities of each state with the lowest electronic energy) and compared the two different lanthanide-‐containing cubanes and the two 24 cubane-‐types (2 and 1 ) (for results obtained with varying computational methods, see SI, Relative (Free) Energies). To this end, we processed and analyzed the free energies in three ways: Firstly, we plotted free energy profiles including
Figure 2. Free energy differences between the states i and state 0 of the catalytic cycle. (B3LYP; explicit solva-‐ tion; for results obtained with other set-‐ups, see SI, Figures S1 and S2 and Table S4). The dotted lines and bars correspond to the “b-‐states”. Upper graph: Relative free energies and the computed thermodynamic limit. Lower graph: Free energies
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compared to an “ideal” catalyst [scaled by ΔGexp(H2O) / ΔGcomp(H2O)]. We plotted ΔGi-‐0, the free energy difference between state i and the catalytic ground state, calculated with CP2K, B3LYP and explicit solvation, in the upper graph of Figure 2 (for results obtained using COSMO, see SI, Figure S2) The ther-‐ modynamic limit in this graph is not the experimental reac-‐ tion free energy ΔGexp(H2O) of equation (1), but the computa-‐ tional one (ΔGcomp(H2O)=102.6 kcal/mol) obtained with the 61 same set-‐up as the states of the catalytic cycle. Graphs comparing free energy profiles obtained with implicit solva-‐ tion and other exchange-‐correlation functionals can be found in Figure S1 in the SI. From the upper graph of Figure 2, we can see that pathway b lies lower than pathway a, and 2-‐Er is below 2-‐Tm with respect to free energy differences. The only exception is S2 where 2-‐Tm-‐S2b is slightly below 2-‐Er-‐S2a, and 2-‐Er-‐S2b lies higher than any other system in the S2 state. This stands in connection with a structural change of the catalysts, best described as “opening” of the cubane cage, which will be further discussed in section Electronic Struc-‐ ture and Molecular Geometry. Except for cycle b of 2-‐Er, all pathways exceed the thermodynamic limit already with their S3 state. While the single-‐site pathway of 1 is thermodynami-‐ cally most favorable for S1 and S2 (together with 2-‐Tm-‐ 24 S2b), for S3 and S4, 2-‐Er shows the lowest free energy dif-‐ ferences, irrespective of the pathway. The lower graph of Figure 2 was obtained by multiplying the relative free energies by 1.1, the ratio of ΔGexp(H2O) to ΔGcomp(H2O), to provide the experimental reaction free ener-‐ gy of water oxidation and account for errors inherent to our 61 approach. While in their S1 state, all systems are close to the ideal catalyst, they diverge more and more for S2 and S3 and appear too destabilized. For 2-‐Tm, it would be most beneficial to stabilize S3, whereas the catalytic cycle of 2-‐Er could be brought closer to the ideal case by lowering S2 and S3 in free energy. As mentioned above, 2-‐Er is the only sys-‐ tem for which the last PCET step and the evolution of oxygen is endothermic (only in cycle b). With implicit solvation (SI, Figure S2) all systems reproduce the ideal catalyst better than with explicit solvation. Furthermore, the solvent continuum calculations predict cycle b of 2-‐Tm to come closest to the ideal case. Cycle a of 2-‐Er has an overpotential (vs. NHE, pH=0) of η=1.0 V associated, whereas the one of 2-‐Tm amounts to η=0.8 V. For both catalysts, the highest free energy difference of cycle a is between S2a and S3a. The overpotentials of cycle b of the two cubanes is higher, η=1.2 V (S1→S2b) for 2-‐Er and η=1.3 V (S2b→S3b) for 2-‐Tm. Calculations with implicit solvation consistently give lower free energy differences (see SI, Figure S1 and Table S4) and therefore also lower overpo-‐ tentials (SI, Table S5). A more detailed analysis of the influ-‐ ence of different functionals and solvation methods on the
relative free energies can be found in the SI, Relative (Free) Energies. Total Spin Multiplicities. In order to investigate the impact of different spin configura-‐ tions on the “active” Co1 center, we preformed all geometry optimizations of S1-‐S4 separately for the 3 total spin multi-‐ plicities corresponding to an initial guess of high-‐spin on Co2, Co3 and Ln and 3 different numbers of unpaired elec-‐ trons on Co1. In S1 and S3 of 2-‐Er, these numbers were 0,2 and 4 amounting to total spin multiplicities of M=10,12,14. In S2 and S4 of 2-‐Er, the number of unpaired electrons on Co1 was 1,3, and 5 corresponding to total spin multiplicities of M=11,13,15. For 2-‐Tm all total multiplicities are lower by 1 since Tm possesses one electron more than Er. It has to be kept in mind that predictions of low-‐spin-‐high-‐spin energy splittings are not a strong point of DFT. In particular, pure DFT functionals tend to predict low-‐spin states to have a lower electronic energy than higher spin states, whereas hybrid functionals, such as B3LYP, usually favor high-‐spin 63 states. This depends however strongly on the percentage of 64 exact exchange admixed. It can be seen from Tables S1-‐S2 and S22-‐S23 in the SI that, with explicit solvent and B3LYP, S1 favors the intermediate spin multiplicity, whereas the lowest electronic energy mul-‐ tiplicities of S2-‐S4 (of 2-‐Er and 2-‐Tm) are high-‐spin (except for S2a of 2-‐Er which is predicted to prefer the intermediate spin multiplicity). BP86 on the other hand predicts only S2b of both catalysts to clearly prefer a high-‐spin configuration (S4a of 2-‐Er also favors high-‐spin, but the low-‐spin configu-‐ ration is only 2.5 kcal/mol higher in electronic energy). These results point in the direction of the trend mentioned above. However, in our study of 1, we had found (using the exact same methods) that low spin multiplicities were predicted by B3LYP for all states of a catalytic cycle (except for one, which differed by only a few kcal/mol from the low-‐spin configura-‐ 24 tion). Furthermore, in that study, we had repeated all single point calculations with B3LYP* and had found no difference in the energetic ordering of the spin states and virtually no change in electronic energy differences. Finally, calculations with implicit solvation predicted only a few states to be high-‐ spin, irrespective of the functional employed (see SI, Tables S1-‐S2 and S22-‐S23). While the lowest electronic energy multiplicities depend on the computational set-‐up, they differ only slightly between the two catalysts investigated. With explicit solvent and B3LYP, only S2a shows a difference (intermediate multiplici-‐ ty for 2-‐Er and high-‐spin for 2-‐Tm). With the other methods, the picture is similar and most states show the same lowest electronic energy multiplicity for 2-‐Er and 2-‐Tm. According to calculations using explicit solvent and B3LYP, both cycles of both catalysts contain 2 spin crossing events. However, it should be kept in mind that no spin-‐orbit cou-‐
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pling is included in our calculations, which might facilitate spin-‐state crossing, in particular in the presence of the lan-‐ thanide metal centers. Electronic Structure and Molecular Geometry. Both exchange-‐correlation functionals, solvation methods, catalysts, and all total multiplicities have in common that they show large spin populations on the O-‐ and OO-‐ligands of the S2 and S4 states, respectively. HO-‐ and HOO-‐ligands have consistently smaller spin densities associated (see SI, Tables S7-‐S20). This agrees with our findings on the Co4-‐ 24 cubane catalyst and many other studies on different sys-‐ tems, which found the oxyl radical to play an important role in catalysis by enhancing the reactivity of the respective 59,65-‐67 intermediate. Throughout the catalytic cycle, spin density was not only found on the metal atoms, but also on all oxygen atoms bridging them. Furthermore, all calcula-‐ tions agreed that the spin density on the lanthanides stayed the same in every state, thus underscoring the role of Er and 2+ Tm as redox inert Ca -‐analogs. Next, we turned to the differences in molecular geometries between the two catalysts (see SI, Figure S8). Our investiga-‐ tions of the structure of the solvation shell and the position of the ligands are described in great detail in the SI (Struc-‐ tural Analysis). Here we focus on another effect: the confor-‐ mation of the cubane-‐cage itself. As already hinted at in our discussion of free energy differences, for some states the cubane is “opened”, i.e. the distances between Co1 and the two oxygen atoms (O1 and O2) that bridge Co1 to Co2 (see Figure 1) are increased. While for 2-‐Er, the Co1-‐O1 and Co1-‐ O2 distances are smaller in S1 and S2a than in S0, they are larger for 2-‐Tm (see Table 1). In S2b, the cubane cage of both 2-‐Er and 2-‐Tm is significantly “opened”; the effect is however more pronounced for 2-‐Tm. After the water attack, there are some fluctuations in the molecular geometry of the catalysts. However, when looking at the sum of the Co1-‐O1 and Co1-‐O2 distances in S3 and S4, it becomes apparent that firstly, the molecular geometry is similar for 2-‐Er and 2-‐Tm, and sec-‐ ondly, it is larger for the “a-‐states” than for the “b-‐states” (Figure 3). Hence, there is no significant difference in the sum of the two bond lengths, describing the “opening” of the cubane cage, between 2-‐Er and 2-‐Tm in states S0 and S3-‐S4. The pronounced differences observed for states S1, S2a and S2b, on the other hand, go along with a difference in frontier orbitals between the two cubanes (see below).
Figure 3. Sums of the Co1-‐O1 and Co1-‐O2 distances for both catalysts.
Table 1. Distances (in Å) between Co1 and the two bridging oxygen atoms O1 and O2 .
2-‐Er
2-‐Tm
Co1-‐O1
Co1-‐O2
Co1-‐O1
Co1-‐O2
S0
2.20
2.10
2.18
2.10
S1
2.01
1.99
2.25
2.20
S2a
2.06
2.05
2.22
2.41
2.49
2.22
2.67
2.21
2.1-‐2.3
2.1-‐2.2
2.1-‐2.3
2.1-‐2.2
S2b a
S3-‐S4 a
The sum of the two bond lengths in S3a, S3b ,S4a, and S4b are similar for 2–Er and 2-‐Tm. Molecular geometries obtained with Turbomole and COSMO are in most cases not significantly influenced by the choice of the functional (BP86 or B3LYP) employed for the geome-‐ try optimizations (see SI, Relative (Free) Energies for more details). The main difference in molecular geometries between calcu-‐ lations with CP2K including explicit solvation and Turbomo-‐ le in combination with COSMO is that with the former, ligands often interact and hydrogen bond with water mole-‐ cules of the solvation shell while with the latter, they often interact with other ligands. For all states, this influences the positions and orientations of the bridging acetates and the OH ligands on Ln, which appear to be less tightly bound and therefore more susceptible to solvation effects than the hy-‐ droxide ligands on Co1 (bond lengths of Ln-‐OH: 2.1-‐2.2 Å, Co-‐OH: 1.8-‐1.9 Å for both explicit and implicit solvation). A
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ACS Catalysis
more detailed analysis of the molecular geometries resulting from different treatments of the solvent can be found in the SI (Structural Analysis). From these investigations, it is ap-‐ parent that short range effects, hydrogen bonding and the inclusion of explicit solvation is most important for the fol-‐ lowing cases: Weakly bound ligands (Ln-‐OH), ligands being close enough to other ligands to preferentially interact with them instead of the continuum (Co1-‐OH and Ln-‐OH in the “a-‐states”) and larger ligands with more conformational degrees of freedom and more potential sites for solute-‐ solvent interactions (Co1-‐OOH) protruding far into the con-‐ tinuum or the solvation shell (bridging acetate). It can be concluded that firstly, the “opening” of the cubane is due to short-‐range solvation effects since the calculations with implicit solvation show no such distortions and only very small (
