doi.org/10.26434/chemrxiv.7755302.v1

Computational Screening of Roles of Defects and Metal Substitution onReactivity of Different Single- vs Double-Node Metal–OrganicFrameworks for Sarin DecompositionMohammadReza MomeniTaheri, Christopher J. Cramer

Submitted date: 22/02/2019 • Posted date: 22/02/2019Licence: CC BY-NC-ND 4.0Citation information: MomeniTaheri, MohammadReza; Cramer, Christopher J. (2019): ComputationalScreening of Roles of Defects and Metal Substitution on Reactivity of Different Single- vs Double-NodeMetal–Organic Frameworks for Sarin Decomposition. ChemRxiv. Preprint.

Understanding how different factors affect the electronic prop-erties of metal-organic frameworks (MOFs) iscritical to under-standing their potential for catalysis and to serve as catalyst supports. In this work, periodicdispersion corrected PBE cal-culations are performed to assess the catalytic activity of dif-ferent Zr6 vs Zr12metal-organic frameworks (MOFs) for the heterogeneous catalytic hydrolysis of the chemical warfare agent(CWA) sarin. Using a comprehensive series of extended periodic models capable of capturing long-rangesar-in/water/framework interactions in both Zr6 and Zr12 MOFs, the effect of numbers and morphologies ofdefective sites as well as ZrIV substitution with heavier CeIV are thoroughly in-vestigated. Our calculationsshow that hydrogen bonds in-volving both metal-oxide nodes and organic linkers can play important roles inthe catalysis. Insights derived from this work should inform the design and realization of more effec-tive androbust next-generation MOF-based heterogeneous catalysts.

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† Current address: Department of Chemistry and Biochemistry, University of California, San Diego, La Jolla, California 92093, United States

Computational Screening of Roles of Defects and Metal Substitution on Reactivity of Different Single- vs Double-Node Metal–Organic Frameworks for Sarin Decomposition Mohammad R. Momeni*† and Christopher J. Cramer

Department of Chemistry, Minnesota Supercomputing Institute, and Chemical Theory Center, University of Minnesota, Minneapolis, Minnesota 55455, USA

ABSTRACT: Understanding how different factors affect the electronic properties of metal-organic frameworks (MOFs) is critical to understanding their potential for catalysis and to serve as catalyst supports. In this work, periodic dispersion corrected PBE calculations are performed to assess the catalytic activity of different Zr6 vs Zr12 metal-organic frameworks (MOFs) for the heterogeneous catalytic hydrolysis of the chemical warfare agent (CWA) sarin. Using a comprehensive series of extended periodic models capable of capturing long-range sarin/water/framework interactions in both Zr6 and Zr12 MOFs, the effect of numbers and morphologies of defective sites as well as ZrIV substitution with heavier CeIV are thoroughly investigated. Our calculations show that hydrogen bonds involving both metal-oxide nodes and organ-ic linkers can play important roles in the catalysis. Insights de-rived from this work should inform the design and realization of more effective and robust next-generation MOF-based heteroge-neous catalysts.

KEYWORDS: Metal-Organic Framework (MOF), Zr6 vs Zr12 MOFs, Heterogeneous Catalysis, Chemical Warfare Agent Hy-drolysis, Sarin

Phosphorous-based chemical warfare agents (CWAs) are vola-tile chemicals known to inhibit the enzyme acetylcholine esterase (AChE) by phosphonylating its catalytic serine203-OH residue, thereby leading to accumulation of the neurotransmitter acetyl-choline in receptors, overstimulation, and ultimately death.1,2 First isolated from Pseudomonas diminuta, phosphotriesterase enzyme (PTE) with a positively charged bi-metallic ZnII complex in its active site is shown to selectively hydrolyze different phos-photriesters including organophosphate pesticides and CWAs (Scheme 1a).3-5 Owing to the well-known high sensitivity of en-zymes to environmental conditions and their fast deactivations, molecular engineering has been used to alter PTE in order to de-sign alternative more robust (heterogeneous) biomimetic catalysts with high substrate specificity for practical real-world applica-tions.6,7 The mechanistic details of PTE hydrolysis, for both wild-type and mutated enzymes, some including different transition

metals in the active site, have been the subject of numerous exper-imental as well as theoretical studies.3,5,30-37

Non-enzymatic approaches to nerve agent hydrolysis are also of considerable interest. Metal-organic frameworks (MOFs) are promising porous organic/inorganic hybrid materials which due to their robust chemical nature have found many applications in sorption, separation and catalysis.8-12 Of particular interest for this work, missing linker defective zirconium-based MOFs12-14 with adjacent open metal sites resembling those found in the active site of PTE have been shown to be highly active for the hydrolysis of CWAs in buffered aqueous media.7,15-29 Recently, we reported a detailed investigation of the the hydrolysis mechanism of sarin, a CWA belonging to the G series of nerve agents that has been extensively studied experimentally, catalyzed by different Zr-based MOFs.38,39

Scheme 1. (a) Active Site of PTE40 and (b) Mechanistic

Scheme for Hydrolysis of Sarin on ZrIV-MOFs.

With respect to those details, we found that for all studied Zr6-MOFs except MOF-808, the rate-determining step (RDS) for hydrolysis is the displacement of terminal Zr-OH2 groups by sar-in, which explains why the experimentally observed hydrolysis rates increase upon a decrease in pH15 and/or dehydration16 of the Zr–SBUs (see Scheme 1b for a more complete mechanistic

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scheme).38 In another very recent study, we showed that a new [Zr6(µ3-O)4(µ3-OH)4(µ2-OH)6]2 double-node MOF has superior reactivity than various Zr6 single-node analogs.39 The importance of adopting a reasonable computational model for studying the catalytic activity of these systems was also emphasized in our prior work and we showed how reactivity trends for different MOFs change when different truncated clusters are employed as models.38,39

From a mechanistic point of view, the existence of open metal sites, which often but not always originate from missing linker defects, is crucial for most bond-breaking and bond-forming reac-tions catalyzed by MOFs. Given the relative ease with which the extended framework may be structurally altered, either inadvert-ently or by design, under different experimental conditions such as temperature, pressure, solvent, and co-solvent or guest load-ings, it is clearly important to take into account the presence of defects when designing realistic materials for catalytic and/or other applications. The ubiquitous presence of defects in porous materials, especially MOFs, is fully embraced by the community, and indeed engineering them has recently become a topic of great interest to both theoretical and experimental groups, with the ma-jority of studies focused on UiO-6641 as the archetype of stable Zr6O8 MOFs. Many interesting correlations between de-fects/structural disorder and observed chemical properties and activities have been reported.42-62 With respect to catalysis, which is the focus of the current study, understanding the intrinsic nature of individual defect sites can shed light on their propensity to be responsible for observed experimental activities. For example, Harvey et al. computed binding energies of different CWAs, in-cluding sarin, to Zr6-UiO-66 and Y6-UiO-66 MOFs focusing on the impact of different missing linker defect sites on computed energetics.63 While adsorption of CWA is known to not to be the RDS for the hydrolysis reaction,38,39 this contribution is the first study of its kind to shed light on the systematic nature and chemi-cal properties of defect sites in robust MOFs as they interact with CWAs. Focusing on the complete hydrolysis reaction coordinate, in addition to identifying the correct proton topology of a newly synthesized Zr12 double-node MOF,64 we recently predicted high-er reactivities for hydrolysis of sarin by its bi-defective framework than for any of its single-node analogs (Figure 2).38,39

Considering other variations in MOF composition, Farha et al.23 have shown that replacing ZrIV in UiO-66 with f-block CeIV transition metals in CeIV-BDC can lead to enhanced reactivities for the hydrolysis of the CWA soman as well as the nerve agent simulant dimethyl 4-nitrophenyl phosphate (DMNP). Theoretical mechanistic studies have not yet been reported for the effects of metal substitution on the catalytic activity of this MOF or others.

Our objective in this work is twofold: first, through performing systematic, dispersion-corrected quantum mechanical calculations on periodic models of different single- vs double-node ZrIV-MOFs (Figures 1 and 2), we aim to understand the impact of the number and morphology of defect sites on the reactivity of different MOFs in sarin hydrolysis as a test case. Having atomistic details for the effects of defect sites on reactivity in different MOFs may inform defect engineering opportunities to achieve higher reactivi-ties or selectivities. Second, we aim to assess the effects of replac-ing ZrIV with CeIV f-block transition metals in catalytic hydrolysis of sarin in both UiO-66 and MOF-808. Results presented in this work can then serve as a benchmark for future theoretical studies as well as guide experimental design and synthesis of more reac-tive MOF-based heterogeneous catalysts for specific applications. Number and morphology of missing linker defects in single- vs double-node ZrIV-MOFs and their impact on the reactivity for sarin hydrolysis: Our previous work identified three elemen-tary steps for the catalytic hydrolysis of sarin, namely, (i) water displacement by sarin (ii) nucleophilic attack of water on the P=O

bond and (iii) HF elimination. Step (i) was computed to be the RDS for all of the single- and double-node ZrIV-MOFs we exam-ined except for MOF-808 (Scheme 1).38,39 However, we observed significant variations in computed energetics as a function of the size of capping groups in truncated cluster models, with increas-ing size showing improved fidelity with fully periodic calcula-tions, suggesting that the latter model is to be preferred when computationally tractable, and results discussed here are all from periodic calculations.

Figure 1. Optimized structures for (a) MOF-808, (b) NU-1000 c pore, (c) benzene dicarboxylate linker, (d) benzene tricarboxylate linker, (e) pyrene tetracarboxylate linker, (f) benzene triphenyl dicarboxylate linker, (g) pristine UiO-66-12, (h) mono-defective UiO-66-11, (i) bi-defective UiO-66-10-I, (j) bi-defective UiO-66-10-II, and (k) bi-defective UiO-66-10-III. Generated empty pores after BDC linker removal are highlighted for different UiO-66-10 isomers. Legend: Gray, red, white, and cyan represent C, O, H, and Zr atoms, respectively. See SI, Table S1 for relative energies of the different bi-defective UiO-66 isomers as well as optimized lattice constants of all studied MOFs.

Figure 2. Optimized crystal structures of (a) pristine Zr12, (b) mono-defective Zr12, (c) bi-defective Zr12, (d) tetra-defective Zr12-I, (e) tetra-defective Zr12-II, (f) tetra-defective Zr12-III double-node Zr12 MOFs. Generated empty pores after TPBDC linker removal are highlighted. Legend: Gray, red, white, and cyan rep-resent C, O, H, and Zr atoms, respectively. See SI, Table S1 for

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relative energies of the different tetra-defective Zr12 isomers as well as optimized lattice constants of all studied MOFs.

Another important technical point is to note that, owing to the chirality of sarin and the different faces of the single- and double-node ZrIV metal-oxide nodes, many alternative local minima must be surveyed for every minimum-energy and transition-state (TS) structure (crystallography information files (CIFs) for all optimized structures are included as part of the Supporting Information (SI)). In the case of NU–1000, we consider coordination only to “c pore” active sites since as shown in our previous study,38 the c pores are more active than the large pores in this MOF presumably due to the existence of rather strong dispersion like interactions in the narrower c pores than the large ones. This also agrees with recent studies reporting larger heats of adsorption for small substrates65 as well as selective precursor deposition in atomic layer deposi-tion66,67 in the c pores of this MOF. We further consider mono- and bi-defective UiO-66 as well as mono-, bi- and tetra-defective Zr12 MOFs. Also, to examine the effects of changes in morphology of defect sites on reactivity, three different isomers were considered for both bi-defective UiO-66-10 and tetra-defective Zr12 MOFs, with the isomers I–III spanning in relative electronic energies 5.7 kcal/mol for the former (Figure 1) and 3.7 kcal/mol for the latter (Figure 2). The Computation-al Methods section below provides additional methodological details.

Figure 3. Periodic PBE-D3/DZVP-MOLOPT computed lowest energy paths for catalytic hydrolysis of sarin on different single-node ZrIV-MOFs relative to their separated reactants. Key bond distances (in Å) are given for MOF-808 optimized displacement (TSDisplace) and addi-tion (TSAddition) transition states; all optimized structures are given in SI Figure S1.

In concordance with our previous theoretical studies,38,39 we find here that H2O displacement by sarin is the RDS for all studied single- and double-node ZrIV–MOFs. We note that in our previous mechanistic study of MOF-808 using formate-

and benzoate-capped cluster models, we found otherwise, and predicted water nucleophilic attack to be rate-determining.38 We attribute this discrepancy to the deficiencies associated with using truncated cluster models which neglect long-range framework-substrate interactions present in extended materials such as MOFs. Considering entirely the periodic results pre-

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sented here, the computed energies of activation for mono-defective UiO66-11, bi-defective UiO66-10-I, bi-defective UiO66-10-II, bi-defective UiO66-10-III, NU–1000 c pore, and MOF–808 are 26.8, 28.1, 21.7, 27.1, 26.1, and 21.9 kcal/mol, respectively (Figure 3 and SI Table S1). These data agree with experiment that finds MOF-808 is the most active of these catalysts for sarin hydrolysis, followed by NU-1000 and UiO-66 considering both mono-defective UiO-66-11 and bi-defective UiO-66-10-I.6 Meanwhile, the computed energies of activation associated with water displacement for mono-, bi-, and tetra-defective-Zr12 isomers I, II, and III are 20.0, 25.0, 35.0, 18.1, and 28.8 kcal/mol, respectively (Figure 4 and SI Table S1). The substantially greater variation in activation energy as a function of defect morphology in the Zr12 MOF compared to UiO-66 is interesting, as is the prediction that tetra-defective-Zr12-II should be more active than any Zr6 MOF given its low predicted activation energy of 18.1 kcal/mol. To date, this MOF has not been tested for sarin hy-drolysis.

Figure 4. Periodic PBE-D3/DZVP-MOLOPT computed lowest energy paths for catalytic hydrolysis of sarin on different double-node ZrIV-MOFs relative to their separated reactants. Key bond distances (in Å) are given for mono-defective Zr12 optimized dis-placement (TSDisplace) and addition (TSAddition) transition states; all optimized structures are given in SI Figure S1.

In the optimized displacement TS structures (SI Figure S1), the forming Zr−O(P) bond is the longest for MOF-808 and mono-defective Zr12, i.e., most reactant-like, and shortest in bi-defective UiO-66-10-III and tetra-defective Zr12-I. This is con-sistent with the Bell−Evans−Polanyi principle68,69 that a faster reaction is associated with a TS structure that is more reactant like. For most of the studied MOFs, two different, alternative first-order saddle points were located for the water displace-ment step in our climbing image nudged elastic band (CI-NEB) calculations, a lower energy TS which is structurally similar to the reactant, hereafter referred to as the early TS, and a second higher energy TS resembling the product, which we call the late TS (following Hammond’s postulate;70 see Figure 5 below for NU-1000 c pore TSs, and SI Figure S1 for

all optimized TS structures). Interestingly, we located two alternative TSs for each water addition step as well; a low energy TS in which the attacking water molecule is located above the µ3-OH group of the metal-oxide node and accepts a hydrogen bond (HB) from it and a second TS in which the attacking nucleophile is above the µ3-O group on the “other side” of the same node face, and has no specific interaction with it (Figure 5). Relative energies of these isomeric TSs were found to be 4.8 and 12.4 kcal/mol in favor of the hydro-gen-bonded TS structures for NU-1000 c pore and MOF-808, respectively. The substantial stabilizing influence of the HB is noteworthy as it would be expected to decrease the “absolute” nucleophilicity of the oxygen atom, but evidently that effect is outweighed in the confined space of the reaction environment.

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Hydrogen bonding also discriminates the TS structures for water displacement in the NU-1000 c pore (Figure 5). In the early TS, the departing water forms two HBs with a terminal OH and a pyrene carboxylate linker whereas in the late TS the water forms only one HB with a terminal hydroxyl group. This leads to a 7.6 kcal/mol difference in energies for these two TS structures.

Figure 5. CI-NEB optimized TS structures for water displacement (TSDisplace, top) and nucleophilic addition (TSAddition, bottom) in the NU-1000 c pore. Key geometric data as well as their electronic energies (in kcal/mol) relative to the HB isomer are given. See SI Figure S1 for the analogues structures of other MOFs.

Returning to the question of how the number and morphol-ogies of the missing linker defect sites may alter the reactivity of these materials, we note the existence of an important trend in Figures 3 and 4. In both UiO-66 and the double-node Zr12 MOF, the most active species is one characterized by multiple defects. Thus, for UiO-66, bi-defective isomer II is maximally active, and it is isomer II of tetra-defective Zr12-MOF that is also maximally active. However, the other isomers of these MOFs are predicted to be substantially less active than less heavily defected nodes, i.e., the mono-defective nodes in each case.

Considering the UiO-66 and double-node Zr12 cases in more depth, it is apparent that the relative orientations of the two defect sites plays a decisive role on activity. When the defect sites are on opposite faces of a single Zr6 component node (isomers III, in each case), high activation energies appear to be associated by a particularly stable H-bonded pre-complex (cf. Figures 3 and 4) that increases the activation energy for water displacement with particularly short HBs between water and terminal OH groups ranging from 1.442 Å in UiO-66-10-III to 1.415 Å in tetra-defective Zr12-III (see SI Table S2). When the two sites share a single Zr atom around one meridi-

an of a Zr6 core (isomers I, in each case), that too leads to very high water displacement activation energies, now primarily associated with rather weak HBs between the O(P) of sarin and µ3-OH group of the metal-oxide node in the TS structures themselves; this HB varies from 3.108 Å in isomer I to 2.158 Å in II and 2.619 Å in III in the case of the tetra-defective Zr12 systems agreeing perfectly with their computed order of acti-vation energies (cf. Figures 3 and 4 and SI Table S2 again). However, when the two defects do not share a common Zr atom, as is true in both isomers II, there is a favorable destabi-lization of the initial HB complex and a stabilization of the TS structure that leads to an especially low energy for water dis-placement. The correlation between HB strength and reactivity observed in this work resonates well with a very recent study on a variety of structurally modified UiO-66 MOFs in which the existence of a good correlation between the measured µ3-OH infrared frequencies of the modified UiO-66 nodes and electronic properties and reactivities in this MOF were report-ed.71 To further investigate the effects of stabilizing HB inter-actions on the observed electronic structure and reactivity of different single- and double-node MOFs we herein discuss our computed Restrained Electrostatic Potential (RESP) charges on both pre-complex and water displacement TS structures

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(see SI Table S3). In line with the observed HB distances dis-cussed above magnitude of the computed RESP charges on O(µ3-OH), H(µ3-OH) and terminal OH groups isomers I-III of both UiO-66-10 and tetra-defective Zr12 increase from isomers I to II and then decrease again in isomer III all pointing toward the existence of stronger HB interactions in isomers II of both the single-node UiO-66-10 and the double-node Zr12 MOFs which agrees perfectly with their computed activation energies (cf. SI Tables S2 and S3).

The take-away from this analysis is that, while the construc-tion of a material characterized by only mono defects might be expected to deliver a “good” catalyst, increasing the defecting level can give a better catalyst, but only if the “right” higher-order defects can be preferentially introduced, which certainly poses interesting synthetic challenges that we hope the exper-imental community will take up.

Reactivity of CeIV vs ZrIV Single-Node MOFs in Sarin Hy-drolysis

Owing to their high thermal, chemical, and mechanical ro-bustness, CeIV analogs of Zr6-MOFs have begun to attract in-terest for a variety of applications.23,72,73 While some interest has derived from the potential to exploit the CeIII/CeIV couple for electro- or photochemical purposes, even in the absence of redox processes one may expect the different Lewis acidity of CeIV compared to ZrIV together with different local structures to influence reactions catalyzed at the metal site. Indeed, Farha et al.23 have reported the catalytic activity of CeIV-BDC MOFs for the hydrolysis of CWAs and DMNP simulant. Here, we report the reactivity of the bi-defective Ce-UiO-66-10-I and Ce-MOF-808 compared to their Zr analogues following the usual mechanism. Both Ce-substituted MOFs showed superior activities for hydrolysis of sarin compared to their Zr ana-logues (Figure 6). Specifically, upon Ce substitution, comput-ed DE‡ values decreased from 28.1 to 14.3 kcal/mol for bi-defective UiO-66-10-I and from 21.9 to 11.0 kcal/mol for MOF-808. Interestingly, most of the acceleration is associated with the facility with which water is displaced in the Ce case compared to Zr, reflecting the weaker bonding of water to the Ce node that has been documented experimentally.74 Overall, our calculations show CeIV-MOF-808 to be the fastest of all studied MOFs for the hydrolysis of sarin. We note that func-tionalization of the linkers of CeIV-MOFs with, for example, -NH2 functional groups (that have been shown to enhance reac-tivity for their ZrIV analogues7,22,24,26,28) and recently iodine groups75 could offer additional opportunity to further enhance the reactivity of these systems. Such predictions await experi-mental verification.

Computational Methods

All periodic calculations were performed at the PBE76 level with damped D3 dispersion correction77 with a cutoff radius of 15 Å using the hybrid Gaussian and plane wave formalism as implemented in the CP2K/Quickstep package.78 The molecu-larly optimized double–zeta valence with polarization DZVP-MOLOPT basis sets and core-electron pseudopotentials ac-cording to the Geodecker-Teter-Hutter formulation79 were used in these calculations. The H (1s), C (2s, 2p), O (2s, 2p), F (2s, 2p), P (3s, 3p), and Zr (4s, 5s, 4p, 4d) electrons were treated as valence. For all CeIV-MOFs, spin-polarized calcula-tions were performed with using a modified pseudopotential

and basis set in combination with DFT+U method with the U value set to 7.0 eV to properly account for the localized 4f electrons of the CeIV atoms.80 The plane-wave cutoff of the finest grid and REL_CUTOFF were set to 360 RY and 60 RY. The default value of 10-5 RY was used for all SCF conver-gences. Both atomic positions and cell parameters were re-laxed for all pristine and defective single- and double-node MOFs but lattice parameters were kept fixed when locating intermediates and first-order saddle points; a valid assumption since the crystal structures of all studied MOFs are not ex-pected to change much after loading the sarin substrate. All first-order saddle points along the reaction path of interest were located using the climbing-image nudged elastic band (CI-NEB) method.81 All CI-NEB calculations consisted of ten replicas for all studied single- and double-node MOFs. Chang-es in the electronic structure of all systems were examined by analyzing Restrained Electrostatic Potential (RESP) charges calculated at the PBE-D3/DZVP-MOLOPT level using the Repeating Electrostatic Potential Extracted ATomic (REPEAT) method,82 especially benchmarked for porous crys-talline solids such as MOFs. Partial numerical frequency cal-culations were performed using a neutral fragment comprised of the metal-oxide node (without the linkers) and the organo-phosphorus nerve agent at the G point to ensure a local mini-mum or a proper first-order saddle point along the reaction path of interest is located (CIFs of all optimized crystal struc-tures are included as part of the SI).

Conclusions

In summary, using fully periodic models and PBE functional with D3 dispersion correction we investigated in detail reactiv-ity of different single- and double-node MOFs in hydrolysis of the sarin nerve agent as a test case. Through careful investiga-tion of different factors including number and morphology of the missing linker defect sites we found that more defects can lead to lower or higher activity, depending on how they are arranged relative to one another. This poses an interesting synthetic challenge to the experimental community for making highly active MOF-based heterogeneous catalysts by engineer-ing defects in them. ZrIV substitution with CeIV was found to reduce the computed activation energies for bi-defective UiO-66-10-I and MOF-808 by half which agrees qualitatively with available experimental data on CeIV-BDC. Hydrogen bond formations with both the metal-oxide nodes and organic link-ers were shown to play an important role in decomposition of the sarin CWA. This study showcases the strength and im-portance of considering both defect engineering and metal substitution as means for tuning the reactivity of MOF-based porous materials and presents opportunities for applications that make use of defect engineering.

ASSOCIATED CONTENT

Supporting Information Details of the computations as well as CIF files of all optimized crys-tal structures reported in this work. The Supporting Information is available free of charge on the ACS Publications website.

AUTHOR INFORMATION

Corresponding Author

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mmomenit@umn.edu Notes The authors declare no competing financial interests.

ACKNOWLEDGMENT The Authors gratefully acknowledge the Defense Threat Reduction Agency (HDTRA1-18-1-0003) for the financial support. The authors also acknowledge the Minnesota Supercomputing Institute (MSI) for providing resources that contributed to the research results reported within this paper. MRM is grateful for helpful discussions with Omar Farha, Timur Islamoglu, Farnaz Shakib and Manuel Ortuño.

Figure 6. Periodic PBE-D3/DZVP-MOLOPT computed lowest energy paths for catalytic hydrolysis of sarin (in kcal/mol) on dif-ferent single-node ZrIV- vs CeIV bi-defective UiO-66-10-I and MOF-808 relative to their corresponding separated reactants. Key bond distances (in Å) are given for CeIV-MOF-808 optimized displacement (TSDisplace) and addition (TSAddition) transition states; all optimized structures are given in SI Figure S1.

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