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6549f26248dad231203fd0e0 | 15 | ∆+PHS Staphylococcal nuclease (SNase) variant (PDB: 3BDC ) and protein deglycase DJ-1 (PDB: 1P5F ), were taken from the PDB database. A double system in a single box setup was used, with a 3 nm distance between the protein and peptide (ACE-AXA-NH 2 ); this ensured charge neutrality during the alchemical transition. To prevent consequential protein-peptide interactions, a single Cα in each molecule was positionally restrained. We used the CHARMM36m 52 (with CHARMM-modified TIP3P 53 ) force field. A salt concentration consistent with the experimental setup was used. If no salt concentration was reported only K + or Cl -counterions were added. For all systems, an initial minimization using the steepest descent algorithm was performed. A constant temperature corresponding to the reference experimental setup was maintained implicitly using the leap-frog stochastic dynamics integrator with an inverse friction constant of γ = 0.5 ps -1 . The pressure was maintained at 1 bar using the Parrinello-Rahman barostat with a coupling time constant of 5 ps. The integration time step was set to 2 fs. Long-range electrostatic interactions were calculated using the Particle-mesh Ewald method with a real-space cut-off of 1.2 nm and grid spacing of 0.12 nm. Lennard-Jones interactions were force-switched off between 1.0 and 1.2 nm. Bonds to hydrogen atoms were constrained using the Parallel LINear Constraint Solver. To improve sampling, systems were run for 50 ns in 4 independent replicas, and the first 10 ns of each simulation was discarded as equilibration. From the remaining 40 ns, 400 non-equilibrium transitions of 500 ps each were generated and work values from the forward and backward transitions were collected using thermodynamic integration. These values were then used to estimate the corresponding free energy difference with Bennett's acceptance ratio as a maximum likelihood estimator relying on the Crooks fluctuation theorem. Bootstrapping was used to estimate the uncertainties of the free energy estimates, and these were propagated when calculating ∆∆G values. |
6549f26248dad231203fd0e0 | 16 | Constant-pH (CpHMD) simulations were performed using a recent GROMACS 2021 implementation with a modified CHARMM36m force field. This approach is based on the λ-dynamics method developed by Brooks and co-corkers . The system setup was similar to that discussed in the above section; however, to agree with the recommended CpHMD setup, both the leapfrog integrator and velocity rescaling with a 0.5 ps coupling time, as well as a PME Fourier spacing of 0.14 nm were used. Because only aspartate and glutamate were considered, a single-site representation (i.e., the proton can be bound to only one heavy atom in the residue) was employed; here, the A and B states represent the protonated and deprotonated forms of the titratable residue. The mass of the λ particle was set at 5 AU, and its temperature was maintained at 300 K using velocity rescaling with a 2 ps coupling time. |
6549f26248dad231203fd0e0 | 17 | We considered three SNase dyads and one DJ-1 dyad, resulting in four sets of simulations. SNase simulations were performed at pH values from -1 to 7 with 0.25 pH increments and from 7 to 14 with 0.5 pH increments, while DJ-1 simulations were performed from 0 to 14 with 0.5 pH increments. Regarding SNase, both residues in the dyad (i.e., D21-D19, D21-D40, and D21-D83) were allowed to (de)protonate as a function of pH, which in two cases resulted in non-sigmoidal curves. In the case of DJ-1, we allowed only E18 to titrate, while holding C106 fixed to a protonated or deprotonated state; this resulted in sigmoidal curves. |
6549f26248dad231203fd0e0 | 18 | Block averaging was used to determine the protonation probabilities and standard deviations at each pH value. Fittings to both a single and double Henderson-Hasselbalch (HH) curve were performed via bootstrap; specifically, each protonation probability was normally expanded about its mean and a point was randomly selected from the distribution. The resultant set of points was fit to a single: |
6549f26248dad231203fd0e0 | 19 | Consider the system given in Figure . Note that the interaction energy between the states is zero, as evidenced by the equality of opposite paths; the protonation of A 1 has no effect on the free energy required to protonate B 2 and vice-versa. It follows that ∆G titr (pH) is zero for all pH and ∆G protein (pH) is constant, implying pK a = pK int (Figure ). Computing the pK a , we obtain values of approximately 3 and 2.6 for A 1 and B 2 , respectively, unchanged and decreased from their reference values according to Equation . |
6549f26248dad231203fd0e0 | 20 | Consider the system given in Figure . In this example, unlike in the first, the interaction energy is non-zero. The free energies suggest that the first deprotonation event results in a less favorable second deprotonation. This is to be expected for nearby coupled residues, where the electrostatic repulsion associated with the introduction of a second negative charge would result in a less favorable free energy change. Instead of reporting a linear dependence, the ∆G protein (pH) curves each have an inflection point and two asymptotic values, corresponding to the protonation free energy of one residue, while the other residues remain in the same protonation state (Figure as evidenced by the flattening in the ∆G curve and an increase in the apparent pK a of A 1 : the formation of B - 2 makes the formation of A - 1 less favorable. Because the reference pK • a values of A 1 and B 2 are similar, this flattening occurs almost simultaneously with that of B 2 . In this regime, the ∆G protein for both residues changes slower and, in this example, remains relatively close to zero. We can think of this as the pH range over which the groups buffer each other, altering the favourability of protonation. As the pH continues to increase, a linear dependence is restored. Construction of the titration curves computed from the microscopic pK a values reveals the coupling between residues (Figure , bottom). The non-sigmoidal form of the curves follows from the fact that the singly protonated microstates for both residues occur with a similar probability. |
6549f26248dad231203fd0e0 | 21 | Consider the system given in Figure . In this example, the ∆∆G values along the branches are the same as in Example 2; however, the reference pK • a values have changed. We now consider the coupling between a residue C that has a reference value 5 pK units higher than B. |
6549f26248dad231203fd0e0 | 22 | Although ∆G protein (pH) does report a non-linear ), which varies as a function of pH between its asymptotic values (dotted). The zero point of this curve (single dot) is used to resolve the corresponding pK a value. The middle plots (dashed) depict the pH-dependent pK a value (Equation ). Each residue has two limiting pK a values (dotted) which correspond to the cases when the other coupled residue is protonated or deprotonated. As the pH changes, the probability that the other residue is deprotonated shifts, resulting in a pH-dependent pK a . The lower plots depict several probabilities. The solid lines correspond to the protonation probabilities of the individual sites; these are a composite probability of the doubly protonated (i.e., ⟨A H B H ⟩) and singly protonated (i.e., ⟨A H B -⟩) microstates (see Equation ). |
6549f26248dad231203fd0e0 | 23 | Because we resolve the pK a at a single pH, these curves are sigmoidal. Observe that with no coupling (left column), the pK a values are constant; however, when coupling is introduced, this is no longer the case. Columns a-d correspond to four different coupling scenarios. dependence, the large difference in reference values means that the pH effects dominate; both inflection points of the free energy curves and the inflection point of the pH-dependent pK a values occur far from one another. As a result, the titration curves computed from the microscopic pK a values suggest that there is no coupling between residues. The singly protonated microstates for each residue occur with a dramatically different probability, that is, residue B 2 is never protonated while C 1 deprotonates. |
6549f26248dad231203fd0e0 | 24 | Consider the system given in Figure . Relative to As in Example 2, constructing the titration curves computed from the microscopic pK a values reveals the coupling between residues (Figure , bottom). Here, plateaus are evident for both residues over pH ∈ [6, 9], implying the existence of both singly protonated microstates. Moreover, the residue with the higher reference pK • a , perhaps counterintuitively, titrates first. |
6549f26248dad231203fd0e0 | 25 | We consider four potential dyads: three from the SNase variant (PDB: 3BDC ) and one from protein deglycase DJ-1 The three SNase pairs exhibited different levels of coupling: the D21-D83 dyad showed almost no coupling (Figure ), as evidenced by the absence of inflection points in the ∆G and pK a curves, the D21-D40 showed moderate coupling (Figure ), and the D21-D19 dyad showed significant coupling (Figure ). In this latter case, as in the second toy example, the residues clearly acted to buffer one another, resulting in a flattening of ∆G for both curves around pH ∈ [3, 5]. |
6549f26248dad231203fd0e0 | 26 | In the case of E18-C106, again a flattening in the ∆G buffer region and, evidently, non-sigmoidal individual site pK titration curves suggested a coupling between the residues (Figure ). Here, computing the adjusted pK a downshifts C106 from 12.18 ± 0.07 to 8.84 ± 0.04, bringing the estimate closer to the experimental value of 5.4 ± 0.2 (Figure ). However, this still leaves more than a 3 pK unit discrepancy between calculation and experiment. Previous work on homodimeric DJ-1 has revealed that two arginine residues (R48 and R28 from the other monomer) facilitate anion binding, which results in pK a elevation (Figure , right). In our simulations only positive counterions (i.e., no salt concentration) were present; however, through-space interactions as a result of a second arginine may also play a role in affecting the pK a . To this end, we probed the pK a of monomeric DJ-1. We found similar qualitative agreement in the curves between the dimeric and monomeric forms; however, rather than raising the pK a , the elimination of the second arginine shifted the pK a of C106 down to 6.78 ± 0.19 (Figure , left). |
6549f26248dad231203fd0e0 | 27 | We note that in both cases an exceptionally high pK a for E18 is predicted. While previous work on DJ-1 has suggested that E18 is protonated over the titration regime of C103 and glutamate residues have been reported with pK a values greater than 9, 62 it would seem improbable that the pK a is actually this high. Structurally, a second glutamate (E18) and a nearby histidine (H126) likely play roles within the lower pH regime (i.e., < 7). We preface the following section by noting that a high glutamate pK a value is also suggested by the CpHMD simulations and PropKa as described further. |
6549f26248dad231203fd0e0 | 28 | Regarding DJ-1, the large pK a value of E18 implied by free energy calculations is also suggested by the constant-pH simulations on monomeric DJ-1, where values of 9.48 ± 0.42 pK and 20.99 ± 0.05 pK were calculated in the cases of protonated C106 and deprotonated C106, respectively. Here, only a single fit to Equation 10 was performed and the Hill coefficient was not fixed to n = 1. C106 was not probed as cysteine residues are not yet supported by the current CpHMD implementation. We close this section by briefly comparing our results with the popular computational pK a predictor PropKa. Overall, for PropKa, we find good agreement for the SNase dyads, but a worse accuracy for C106 in DJ-1. Specifically, estimates from PropKa were: D19: 3.21, D21: 5.44, D40: 4.30, D83: 1.21, and C106: 14.19 (Figure ). |
6549f26248dad231203fd0e0 | 29 | Here, our NEQ approach provided estimates of both D40 and C106 that were in closer agreement with the experimental values while exhibiting comparable performance on the other three residues. Considering the overall performance we found that the introduction of coupling dramatically improves agreement with experiment reducing our ), which varies as a function of pH between its asymptotic values (dotted). The zero point of this curve (single dot) is used to resolve the corresponding pK a value. The middle plots (dashed) depict the pH-dependent pK a value (Equations 9). Each residue has two limiting pK a values (dotted) which correspond to the cases when the other coupled residue is protonated or deprotonated. As the pH changes, the probability that the other residue is deprotonated shifts, resulting in a pH-dependent pK a . The lower plots depict several probabilities. Solid lines correspond to the protonation probabilities of the individual sites; these are a composite probability of the doubly protonated (i.e., ⟨A H B H ⟩) and singly protonated (i.e., ⟨A H B -⟩) microstates (see Equation ). |
6549f26248dad231203fd0e0 | 30 | Because we resolve the pK a at a single pH, these curves are sigmoidal. Observe that with no coupling (left column), the pK a values are constant; however, when coupling is introduced, this is no longer the case. Vertical spans in the lower row indicate experimental pK a values and uncertainties (note that D83 has a pK a < 2.2). Error bands were bootstrapped. a-c correspond to the SNase + ∆PHS system, while d corresponds to the DJ-1 system. |
6549f26248dad231203fd0e0 | 31 | with regard to the former, this performance was comparable to PropKa (0.63±0.22) (Figure ). We also found that CpHMD could accurately resolve the four aspartates within 0.5 pK. It is probable that both a limited training set and a less frequent dyad (i.e., a large difference in reference pK • a values) results in the markedly poorer estimate for C106 from PropKa. |
6549f26248dad231203fd0e0 | 32 | and compute the corresponding ∆∆G values in each case: ∆∆G 0 , ∆∆G 1 , and ∆∆G 2 . A fourth ∆∆G is implied by cycle closure; however, this can also be explicitly computed. Note that these are double free energy differences because of the simulation setup, where both the protein and peptide are present. |
6549f26248dad231203fd0e0 | 33 | where pK • a is the reference pK a of the residue under consideration. We can use this relationship to calculate ∆G 1 (pH) = ∆∆G 1 + RT log pK • a -pH and ∆G 2 (pH) = ∆∆G 2 + RT log pK • a -pH ; here, pK • a corresponds to the reference pK a of residue B. |
6549f26248dad231203fd0e0 | 34 | Note that ∆G 1 (pH) and ∆G 2 (pH) act on the "reactants" and "products" of the upper branch in Figure : a more favorable ∆G 1 (pH) will increase ∆∆G 0 while a more favorable ∆G 2 (pH) will decrease ∆∆G 0 , and vice-versa. here, pK • a corresponds to the reference pK a of residue A. |
6549f26248dad231203fd0e0 | 35 | The importance of accounting for residue coupling is multifaceted and particularly relevant in the context of enzymatic active sites that are often enriched in protonatable residues. The theoretical formalism to describe such couplings in polyprotic acids has been detailed by Ullman. Based on earlier work by Edsall and co-workers, Ullman defines equilibrium protonation constants for all microstates and derives partition functions that fully describe the thermodynamics of these systems. This approach was then applied in a protein context using continuum electrostatics calculations to resolve the free energies between microstates. Here, we demonstrate that such a framework can be readily extended to double free energy difference calculations based on molecular dynamics simulations and introduce a thermodynamic cycle approach that allows one to resolve the apparent pK a s of coupled residues. This demonstration and extension is particularly relevant in the context of alchemical free energy calculations, which give access only to such ∆∆G values. |
6549f26248dad231203fd0e0 | 36 | Our overall aim was simple: demonstrate that insights into residue coupling can be resolved by means of alchemical free energy calculations. While such insights can be directly resolved via constant-pH molecular dynamics simulations -an exceedingly powerful method -we demonstrate with both toy examples and real protein systems that similar insights can be extracted via a different approach. |
6549f26248dad231203fd0e0 | 37 | One such insight is the the buffering of a residue dyad which maintained the free energy of protonation near zero (e.g., DJ-1: C106-E18). In various protein contexts, tuning the local residue environment surrounding pairs or groups of titratable residues to create large buffer regions over which the ∆G of protonation is close to zero could make the binding of a substrate more than sufficient to significantly alter the (de)protonation of a residue and ultimately the enzymatic activity. |
6549f26248dad231203fd0e0 | 38 | Comparison with a recent GROMACS-based CpHMD implementation 37 also revealed a good pK a prediction accuracy for coupled residues. This result suggests that both CpHMD and alchemical free energy methods can resolve pK a values in both coupled and uncoupled contexts. We note that CpHMD has the distinct advantage that all residues can be simultaneously assessed for coupling, and deprotonation can dynamically occur over the course of a simulation due to structural changes in the protein or environment. This allows for the resolution of potentially more complex biophysical pheneomena that could rely on protein dynamics. On the other hand CpHMD simulations can be computationally expensive and here, we demonstrate, that sometimes similar insights can be extracted from "plain" molecular dynamics simulations paired with alchemical free energy methods. |
6549f26248dad231203fd0e0 | 39 | A second comparison with PropKa suggested that although accurate estimates could be made for SNase, the pK a of C106 in DJ-1 was significantly overestimated, possibly due to the limited cysteine data in the PropKa training set and the implicit assumption that E18 is deprotonated at the pH where C106 deprotonates. |
6549f26248dad231203fd0e0 | 40 | The role of MD simulations and free energy calculation methods such as those employed here may provide insight not readily accessible to conventional prediction methods. One particular insight, namely the pK a values of coupled residues, requires careful consideration of the role of nearby protonatable residues. Moreover, given that these residues are often found at the active site -frequently the target of engineered therapeutics -the relevance of this problem extends beyond basic research. |
6549f26248dad231203fd0e0 | 41 | We underscore that while here we have employed non-equilibrium free energy calculations, the approaches outlined can be employed alongside any alchemical-based free energy method (e.g., FEP); however, the cost associated with converging such calculations should be further investigated. The ability to seamlessly and consistently integrate pH-dependent calculations into existing alchemical free energy workflows may prove useful for accurately resolving binding affinities or enzyme activities and thermostabilities. |
6549f26248dad231203fd0e0 | 42 | To this end, we have elsewhere investigated the ability of alchemical free energy calculations to compute a large number of pK a values in a variety of protein contexts. As with the results here, our approach showed strong performance, further suggesting the potential for a consistent integration of pH-dependent calculations into a broader alchemical free energy framework. Appendix A |
6549f26248dad231203fd0e0 | 43 | Alchemical free energy calculations are particularly well suited for computing the free energies that underly pK a calculations (see section pK a values and free energies). One such approach combines fully atomistic molecular dynamics simulations and thermodynamic integration to compute the non-equilibrium, alchemical work distributions associated with transforming a structure in one state into a structure in another state. |
6549f26248dad231203fd0e0 | 44 | These are restrained to prevent consequential interactions, and then the work required to alchemically transform (i.e., A H p → A - p and A - s → A H s ) these residues into their complement (i.e., (de)protonated form) is computed. This construct ensures a neutral simulation box at all times during an alchemical transition. Given two equilibrium ensembles (e.g., A p and A s ), the distributions of work values generated by rapidly transforming residues from the first ensemble into residues from the second (and vice versa) allow one to estimate the free energy difference. Here, the transformation is alchemical, the transitions are on the order of 100 ps, and the free energy difference is estimated using Bennett's acceptance ratio (BAR) relying on the Crooks fluctuation theorem 60 (CFT). Previous work has demonstrated the ability of this NEQ approach to resolve folding free energies and binding affinities within experimental uncertainty. |
6549f26248dad231203fd0e0 | 45 | Since the early work of Tanford and Kirkwood, several methods have emerged that can tackle the problem of residue coupling. In recent years, constant-pH molecular dynamics simulations, based on λ-dynamics or Monte Carlo sampling, have become increasingly popular. Rather than keeping the protonation state fixed, titratable sites are allowed to dynamically follow the free energy gradient. Such sampling of (de)protonation events allows one to explicitly capture coupling. We make note of one particular CpHMD approach by Chen and Roux 41 that employs non-equilibrium transformations to generate potential protonation configurations that are accepted or rejected based on a Monte Carlo criterion; this method was assessed for consistency using the Crooks fluctuation theorem. We underscore that our approach, while employing similar transformations, is not a constant-pH method. Instead, we rely on double free energy differences calculated between fixed microstates. Nevertheless, CpHMD is an exceptionally powerful approach for studying pH-dependent phenomena and can readily capture coupling between tittratable sites. |
6549f26248dad231203fd0e0 | 46 | Two potential limitation of CpHMD simulations are the computational cost and ability to integrate such a method into existing alchemical free energy frameworks. An alchemical approach based entirely on free energy calculations avoids the need for many simulations across a pH spectrum, instead allowing one to resolve the individual coupled pK a s by computing only three ∆∆G values. As alluded to, a key motivation of relying on alchemical free energies is that a coupled pK a prediction scheme can be seamlessly integrated into existing workflows (e.g., pmx, FEP+, etc.). |
6549f26248dad231203fd0e0 | 47 | In summary, titration curves and pK a values may exhibit diverse pH-dependent behaviors due to the coupling of titratable sites. The pK a s of such coupled site residues may be difficult to resolve, and even if a curve is resolved, a singular pK a may overlook unique functionally relevant microstates. Probing these states and the microscopic pK a values between them using free energy calculations based on a rigorous formalism may be a worthwhile approach to provide additional insight into this key biophysical phenomenon. In this work, we derive a formalism to quantify individual site pK a s in coupled residues starting from double free energy differences. This is particularly convenient, as such ∆∆G values can be efficiently computed by means of alchemical free energy calculations. Moreover, we demonstrate how such ∆∆G values can be used to extract relevant coupling insights within an existing framework based on ligand binding partition functions. |
6549f26248dad231203fd0e0 | 48 | Note that the (de)protonation of the sidechain of an amino acid can be described using a standard equilibrium binding formalism. Specifically, the "binding" of protons can be fully described by the proton concentration (c) and the binding constant (K), from which it follows that the grand partition function is ξ = 1 + Kc and the fractional occupation of the side chain by a proton is |
6549f26248dad231203fd0e0 | 49 | Values in brackets indicate the microstate (e.g., [11] : doubly protonated, [10] : first residue protonated, etc.) and four corresponding dissociation constants. In the fully uncoupled case, K 1 = K 4 and K 2 = K 3 , and each (de)protonation event can be considered separately; this is not true when K 1 K 4 and K 2 K 3 . In this case, we have a more complex partition function given by ξ |
6549f26248dad231203fd0e0 | 50 | The form is similar to the partition function of the single-site case; however, here we include a new (un)cooperativity term which follows from the fact that: 1) the cycle is closed (i.e., K 1 + K 3 = K 2 + K 4 ), and 2) there is an "interaction free energy", w, associated with the second (de)protonation event given the first. When this interaction is zero, we have a standard two-site binding equilibrium: the proton can bind to either site, and this is governed only by the proton concentration and binding constants; however, when this interaction is positive or negative, the initial binding to one site will disfavor or favor the binding of a second proton to the other site. This interaction notation, as defined by T. L. Hill, |
6549f26248dad231203fd0e0 | 51 | When w (Equation ) is negative, e -β w is greater than one and the unbinding of the second proton is enhanced by the first. On the contrary, when w is positive, e -β w is less than one and the second unbinding is impaired given the first. The energy of interaction, w, depends on structural changes in the protein and through-space interactions between sites. |
6549f26248dad231203fd0e0 | 52 | Here, ∆∆G 0 corresponds to ∆∆G env : the free energy of deprotonating residue A while in the presence of protonated B. Similarly, ∆∆G 3 corresponds to the deprotonation of A in the presence of deprotonated B. In both cases, the remaining protonatable sites in the protein are fixed to their model states at pH 7.4 (i.e., Asp/Glu: deprotonated, Lys/Cys: protonated). We also have ∆∆G 1 and ∆∆G 2 , which will shift the populations of "reactants" and "products" with |
6549f26248dad231203fd0e0 | 53 | In this case, we focus on the overall ∆pK a for the deprotonation of residue A by explicitly considering all possible protonation states of residue B. When considering the free energy difference between protonation in a folded protein and protonation in a capped peptide, one can resolve ∆∆G 30 = ∆G 0 -∆G 3 (note that this is equal to ∆∆G 0 ); however, we can also resolve ∆G 1 and ∆G 2 from ∆∆G 41 and ∆∆G 52 , respectively. |
6549f26248dad231203fd0e0 | 54 | Recall that for an isolated protonatable group (e.g., capped peptide) with a known reference pK • a , the free energy of deprotonation is not fixed, but is linearly related to the pH via ∆G(pH) = RT log Equation 25 provides a family of solutions that depend on the pH value. To determine the pK a , we find the point where ∆G protein (pH) = 0. This pH corresponds to the pK a that would be observed in a titration experiment and follows from the Henderson-Hasselbalch equation (Equation , main text). |
6549f26248dad231203fd0e0 | 55 | Computationally, we also have access to the whole set of pK a solutions which are not necessarily limited by this Hesenderson-Haselbalch relation. We can combine Equations 3 (in the main text) and 25 and compute these pK a values at various pH: ). The singly protonated probabilities are indicated with dashed-dotted lines. Vertical spans indicate experimental pK a values and uncertainties (note that D83 has a pK a < 2.2). Error bands were bootstrapped. In the case of E18, CpHMD simulations were run with C106 protonated (C H ) or deprotonated (C -). |
630f1b79eadd9a9acd8865bb | 0 | The reversible addition of H2 to metal sites is a fundamental step in catalysis. The importance of the reversibility of this step is perhaps most clearly illustrated in hydrogen-for-deuterium (H/D) exchange reactions. In its simplest form, H/D-exchange involves the selective isotopic labelling of molecules through reaction with D2. Catalysts which promote this type of H/Dexchange must be capable of reversible activation of H2 (and its isotopomers). |
630f1b79eadd9a9acd8865bb | 1 | In recent years, there has been growing interest in the use of transition metal complexes bearing main group ligands for small molecule activation. Several systems incorporating B, Al-In, , Zn and Sn ligands have been reported for H2 activation. A number of potential mechanisms for H2 activation, some of which involve cooperative behaviour of the main group Scheme 1. Reversible reaction of 1 with H2 to form Pd-Mg and [2]2 ligand, have been discussed. Defined examples of reversible behaviour are more limited, the majority of these involve boron-based ligands. For example, Sabo-Etienne and co-workers reported the reversible addition of H2 to a ruthenium complex supported by a borylene ligand. Peters and co-workers documented reversible reactions of H2 to a nickel-borane, iron-borane, and cobaltborane complexes. More recently, Okuda and co-workers reported the reversible reaction of H2 with a Ga-Zn compound, mediated by changes in solvent polarity. Reversible dihydrogen activation by these systems offers a potential approach to catalytic H/D-exchange. |
630f1b79eadd9a9acd8865bb | 2 | However, reports of such reactivity are limited. Lu and co-workers have demonstrated isotopic scrambling of H2 + D2 mixtures to form HD using 1 st row transition metal complexes bearing Al, Ga or In based ligands. In this paper, we report a rare example of H2 activation using a transition metal complex supported by Mg-based ligands. We show that this reaction is reversible and leads to a palladium tetrahydride complex, featuring an unusual structural motif. Based on DFT calculations, a mechanism for H2 activation involving a ligand-assisted pathway is proposed. |
630f1b79eadd9a9acd8865bb | 3 | We recently reported the hexagonal planar palladium complex 1. Addition of 1 bar of H2 to a C6H6 solution of 1 at 25 °C resulted in clean formation of Pd-Mg and 0.5 equiv. of the molecular magnesium hydride In C6H6 solution, Pd-Mg demonstrated a characteristic hydride resonance at = -6.64 ppm integrating to four protons. The simplicity of the 1 H-NMR spectrum was suggestive of a highly symmetric structure. H2 activation to 1 was found to be reversible. Removal of H2 from mixtures of Pd-Mg + [2]2 by freeze-pump-thaw cycles results in the regeneration of 1. Due to its reversible formation, attempts to isolate Pd-Mg were unsuccessful; 1 crystallises preferentially from solution. As such, we undertook alternative synthetic approaches to verify the structure of Pd-Mg. |
630f1b79eadd9a9acd8865bb | 4 | The reaction of [Pt(Me)2( 2 -TMEDA)] with excess [2]2 in C6H6 at 25 °C for 4 days, yielded Pt-Mg•TMEDA as the major reaction product (Scheme 2). DOSY studies on Pt-Mg•TMEDA suggest that coordination of TMEDA to Mg is fast and reversible, with Pt-Mg being generated in C6H6 solution at 298 K. Consistent with this argument, the Pt NMR spectrum shows a characteristic quintet resonance at = -5851 ppm ( 1 J195Pt-1H = 836 Hz) due to the coupling of the Pt centre to four equivalent hydride ligands. The corresponding hydride resonance appears at = -7.24 ppm in the 1 H NMR spectrum. The presence of four hydride ligands rather than two in this complex likely arises from reaction of intermediate species with the solvent (C6H6). |
630f1b79eadd9a9acd8865bb | 5 | Similarly, reaction of [Pt(Me)2( 2 -TMEDA)] with excess of the molecular zinc hydride [{(ArNCMe)2CH}Zn(H)] (Ar = 2,6-di-iso-propylphenyl, 2) afforded colourless crystals of Pt-Zn in 63% yield (Scheme 2). A quintet resonance was observed in the Pt NMR spectrum at = -6079 ppm ( 1 J195Pt-1H = 772 Hz) and a diagnostic hydride resonance with Pt satellites in the H NMR spectrum at = -6.05 ppm. In this case, small amounts of [{(ArNCMe)2CH}ZnPh] (Ar = 2,6-di-iso-propylphenyl) were observed during the formation of Pt-Zn confirming the role of the solvent as a source of hydride ligands. T1 relaxation times of Pt-Mg•TMEDA and Pt-Zn are long (0.6-0.7 s) and exclude the possibility of significant H---H interactions or dihydrogen character. A closely related species Ni-Mg has very recently been reported by Xu and coworkers. |
630f1b79eadd9a9acd8865bb | 6 | Both Pt-Mg•TMEDA and Pt-Zn could be isolated as crystalline solids. X-ray diffraction studies confirmed that the coordination geometry at the transition metal is square planar. In the solid state, the four hydride ligands of Pt-Zn are organised in a near symmetric configuration around the transition metal and sit in the same plane as both the Pt and Zn atoms. The hydride atoms were located within the Fourier difference map and their positions confirmed by DFT calculations. The geometry at Zn is near tetrahedral and the -diketiminate chelate twisted and orthogonal to the plane created by the hydrides. The Pt---Zn distance in Pt-Zn is 2.4466(4) Å. Despite being close to the sum of the covalent radii (Pauling, 2.53Å; Pyykkö, 2.38 Å), computational analysis of the bonding suggests weak metal-metal interactions at best (vide infra), which supports assignment of the geometry at Pt as 4-coordinate square planar. The average H-Pt-H angle across all unique solid-state structures for Pt-Mg•TMEDA and Pt-Zn is 89.9(3) (74.2(3)-105.7(3)). This tetrahydride core is reminiscent of a Ru-Zn2 tetrahydride complex reported by Fischer and coworkers, in which the four hydride ligands are arranged in the equatorial plane, but two phosphine ligands make the central Ru octahedral. Pt-Mg•TMEDA appears as a dimer in the solid state due to the ability of TMEDA to act as a bridging ligand. As a result, there are some differences in the heterometallic core of Pt-Mg•TMEDA compared to Pt-Zn. Increasing the coordination at one magnesium site results in a distortion of the position of the -diketiminate ligand and induces an asymmetry in the Pt---Mg distances. These take values of 2.5605(15) and 2.7124(15) Å to the 4-and 5-coordinate magnesium centres respectively, with the longer distance consistent with the higher coordination number at Mg. Ternary hydrides of s-block and group 10 metals have been reported and characterised by neutron diffraction, and one homometallic complex featuring a [Ni3H4] 2-core has been reported. The bonding in a series of heterometallic tetrahydride complexes (M 1 = Ni-Pt; M 2 = Mg or Zn) was investigated by computational methods. Superficially this structural type resembles that of 1, in that it contains six co-planar atoms closely arranged around a palladium centre. |
630f1b79eadd9a9acd8865bb | 7 | However, the electronic structure of these species is different. The analysis supports only a very small component to the metal---metal bonding in these tetrahydride complexes relative to the metal-hydride interactions. In general, while weak the significance of the metal-metal interaction marginally increases for Pt > Pd > Ni and Zn > Mg. |
630f1b79eadd9a9acd8865bb | 8 | NBO calculations are consistent with a large ionic contribution to the bonding based on the large amount of charge separation with positive charges on the main group atoms (>1.5) and negative charges on the hydrides (< -0.3). To a first approximation these species can be formalised as containing [NiH4] To gain further insight into the mechanism of H2 activation by 1 a series of pathways were calculated by DFT. Both associative and dissociative mechanisms were considered. The HOMO of 1 is mainly composed of the Pd dz2 orbital, lying perpendicular to the tetrahydride plane. Although this has the appropriate orientation and symmetry to interact with H2 in an associative step, calculations did not lead to identification of any clear minima for the hydrogen adduct of 1 (1-H2) on the potential energy surface. In contrast, a dissociative mechanism for H2 splitting was calculated to be a facile and reversible process. Hence, dissociation of an equiv. of 2 from 1 is calculated to form Int-1 with a small energy cost (Gº298K = 10.3 kcal mol - 1 ). This process occurs with a shift in the bonding of 1 along the continuum from hexagonal planar toward trigonal planar, strengthening the Mg---H interactions in the equatorial plane, and pre-organising the complex for dissociation of an equivalent of 2. Similarly coordinatively unsaturated intermediates were recently described in related systems for the zincation of C-H bonds. Association of H2 generates the dihydrogen complex Int-2 with subsequent H2 activation occurring by a ligand-assisted oxidative addition through TS-1 (G ‡ 298K = 13.6 kcal The calculated mechanism bears some resemblance to a s-complex assisted metathesis pathway. H2 addition to a Ni complex related to 1 has been calculated to occur by a sbond metathesis pathway. Despite these precedents, NBO analysis of key intermediates is consistent with the assignment as a ligand-assisted oxidative addition. Throughout the pathway the NPA charge on Pd becomes more positive (Int-1 = -0.37; Int-2 = -0.17; TS-1 = -0.16; Int-3 = -0.07; TS-2 = -0.05) suggestive of an increase in formal oxidation state of the transition metal on addition of H2. The Wiberg Bond Index (WBI) of the breaking H 1 ---H 2 bond is 0.82 in Int-2 and 0.45 in TS-1. The involvement of both the Pd and a Mg centre in this transition state is supported by NBO calculations which show a charge asymmetry across the dihydrogen unit (H 1 = -0.21; H 2 = 0.12) along with a small but significant H 1 ---Mg interaction characterised by a WBI of 0.09. Ligand-assisted oxidative addition is increasingly recognised as a mechanism of importance for heterometallic complexes. Previous calculations have suggested this mechanism may be in operation for addition of C-F to Pd---Mg complexes and H2 addition to Ru-Zn complexes. The proposed mechanism of H2 activation by 1 involves both breakage and formation of H-H and Mg-H bonds in the equatorial plane and strongly suggests that the activation of both these types of bonds is possible at the same transition metal centre. This idea was further exploited through the development of a catalytic protocol for H/D-exchange. In summary, we report a rare example of reversible H2 activation at a palladium complex bearing Mg-based metalloligands. The product of H2 addition is an unusual tetrahydride complex of palladium containing a PdH 4 Mg 2 core, and analogous PtH 4 Mg 2 and PtH 4 Zn 2 containing species were isolated by independent synthesis. DFT calculations support a dissociative mechanism in which, following generation of a coordinatively unsaturated intermediate, H2 splitting occurs by ligand-assisted oxidative addition. These findings were used to develop a simple approach to catalytic H/D-exchange into main group hydrides using D2; a reaction that may have wide synthetic applications giving the utility of these reagents and scarcity of suitable methods (and deuterium sources) for preparation of isotopically labelled analogues. |
64e76bc53fdae147fabbf1bb | 0 | Lanthanides (Lns) have numerous applications due to their unique physicochemical properties. The textbook description of the electronic structure of Ln ions in the dominant 3+ oxidation state is that due to poor shielding the valence 4f orbitals are "core-like," and as a result chemical bonding involving Ln ions is predominantly ionic. In contrast to Ln, the early actinides (An) exhibit variable oxidation states and participation in metal-ligand multiple bonding, which indicates greater involvement of the 5f (and 6d) valence orbitals in bonding regimes. This is important because the extent of covalency in chemical bonding has direct impacts on electronic properties and chemical behavior of Ln and An, and such differences are exploited in, for example, separations technologies. The use of relatively soft donor ligands, such as substituted cyclopentadienyls (Cp R ), can introduce interesting bonding regimes, and [Ln/An(Cp)3] type complexes have long been used as a computational test-bed to investigate trends in the nature of f-element bonding. Since the majority of Ln and An 3+ ions are paramagnetic, electron paramagnetic resonance (EPR) spectroscopy should carry important information on metal-ligand bonding, particularly if resolution of ligand nuclear hyperfine interactions can be resolved. However, this is rarely the case in continuous wave (CW) EPR because of the intrinsically broad linewidths. This can in principle be addressed by pulsed EPR hyperfine methods. However, there are surprisingly few pulsed EPR studies on molecular Ln complexes, with the notable exception of those of the 8 S7/2 Gd 3+ ion, and even fewer for An complexes. Most Ln 3+ pulsed EPR studies have been performed on doped minerals or glasses, and have tended to focus on relaxation behaviour. In 2011 Denning and co-workers reported pulsed EPR measurements on [Yb(Cp)3], enabling quantification of the significant spin density at the C atoms of the Cp rings, which was discussed in terms of mixing of the 2 F7/2 ground term with low-lying charge-transfer states. More recently, some of us reported pulsed EPR studies of two An complexes, [An(Cp tt )3] (1-An; An = Th, U; Cp tt = C5H3 t Bu2-1,3), again showing significant spin density on the Cp tt ligands for both the U 3+ and Th 3+ analogues. Here we report pulsed EPR studies on a family of early Ln 3+ complexes [Ln(Cp tt )3] (1-Ln, Ln = La, Ce, Nd, Sm). This allows: (i) investigation of any trends across the series, from the "parent" diamagnetic, f 0 complex through the paramagnetic f 1,3,5 analogues. The latter are chosen because they are all Kramers ions and hence are expected to be EPR-active; (ii) comparison with the late Ln 3+ complex [Yb(Cp)3]; (iii) comparision of 1-Ln with the early An 3+ homologues 1-An. The latter includes direct comparison of the valence isoelectronic Nd 3+ (4f 3 ) and U 3+ (5f ) pair, which is the only comparison available between 4f and 5f M 3+ ions that does not require designated radiochemical laboratories (although Ce 3+ and Th 3+ have the same number of valence electrons, the Th 3+ ion favours the 6d 1 rather than 5f 1 configuration). Complexes 1-Ln are readily prepared by reacting LnCl3 with three equivalents of KCp tt ; 1-Ce and 1-Sm have been prepared previously by alternative synthetic routes, whilst 1-La and 1-Nd are structurally characterised here for the first time. We report the CW and pulsed EPR data for 1-Ce, 1-Nd and 1-Sm, along with the NMR data of diamagnetic 1-La. We quantify the hyperfine interaction in paramagnetic 1-Ln with ligand nuclei, originating from interaction with the Ln 3+ centres, and show that we can model these data using a simple point-dipole model. This is in agreement with fully-ab initio complete active space self-consistent field spin-orbit (CASSCF-SO) calculations that directly report hyperfine coupling parameters, as well as spin densities. We find, using either the simple or ab initio methods, that there is negligible spin density on the Cp tt ligands in 1-Ln, in contrast to unequivocal spin delocalisation in U 3+ and Th 3+ analogues [An(Cp tt )3], clearly highlighting the differences between early 4f and early 5f bonding in tris-Cp complexes. 9-13 Since the ability to perform such studies are limited by electron spin relaxation times, we also report relaxation data for 1-Ln by pulsed EPR methods. We find that 4f 1-Ln relax orders of magnitude faster than their 5f An analogues, despite preconceptions that relaxation rates increase for heavier elements due to increased spin-orbit coupling. |
64e76bc53fdae147fabbf1bb | 1 | Complexes 1-Ln (Ln = La, Ce, Nd, Sm) were prepared from the parent LnCl3 and three equivalents of KCp tt (Scheme 1) by modification of the reported syntheses of 1-Sm using SmI3 and KCp tt , and 1-Ce from Ce(OTf)3 and LiCp tt . The crystalline yields for 1-La, 1-Ce, 1-Nd and 1-Sm were 41%, 54%, 34% and 52%, respectively. NMR spectroscopy was used to analyse C6D6 solutions of 1-Ln (Supporting Information Figures ). 1 H NMR spectra were fully assigned for all 1-Ln; in each case three signals were observed in a ratio of 54:6:3 that correspond to the t Bu groups and the two unique environments of the Cp tt ring protons, respectively. The paramagnetism of 1-Ce, 1-Nd and 1-Sm precluded assignment of their C{ 1 H} NMR spectra, however, for diamagnetic 1-La this could be interpreted, with the two t Bu group resonances seen at 32.77 and 33.75 ppm and the three Cp tt ring carbon environments found at 110.57 (CH-Cp), 110.69 (CH-Cp) and 143.45 (C-Cp) ppm. Although NMR spectroscopy showed few protic impurities, elemental analysis results for 1-Ln consistently gave low carbon values; this was previously seen for [An(Cp tt )3], and is ascribed to carbide formation leading to partial combustion, a common issue with these experiments. In the case of 1-Sm elemental analysis results were not in accord with expected values, but ATR-IR spectra of all complexes were essentially superimposable, giving confidence to their bulk purities (Supporting Information Figures ). |
64e76bc53fdae147fabbf1bb | 2 | The solid-state structures of 1-Ln were determined by single crystal XRD (1-Nd is depicted in Figure , see Supporting Information Figures ). The structural data of 1-La and 1-Nd are reported here for the first time, whilst 1-Ce and 1-Sm have been structurally authenticated previously. As expected, the structures of 1-Ln are trigonal planar with respect to the η 5 -Cp tt centroids, with the three C2 atoms (Figure ) in the plane defined by the Ln 3+ ion and the three Cp tt centroids. The three Cp tt ligands adopt the same orientation to form a "picket-fence" motif with three t Bu groups above and three below the trigonal plane. Complexes 1-Ln do not show high symmetry in the solid state, consistent with the solid-state structures of [M(Cp tt )3] (M = Th, U, which has an analogous electronic configuration (Nd 3+ : [Xe]4f 3 ; U 3+ : [Rn]5f 3 ). Conversely, in 1-Ce, the mean M … Cpcentroid distances are longer than those seen in [Th(Cp tt )3] [2.566 Å], which has a different valence electronic configuration (Ce 3+ : [Xe]4f 1 ; Th 3+ : [Rn]6d 1 ) due to the near-degeneracy of the 5f and 6d orbitals for Th 2 and the stabilization of the 6dz2 orbital in trigonal ligand environments. |
64e76bc53fdae147fabbf1bb | 3 | The measured χT values of 1.45 and 0.75 cm 3 mol -1 K at 300 K for 1-Nd and 1-Ce, respectively (Figure ), are close to the expected values of 1.63 and 0.80 cm 3 mol - 1 K for Nd 3+ ( 4 I9/2) and Ce 3+ ( 2 F5/2). The χT product decreases gradually upon cooling until below 50 or 60 K, where it drops to reach 0.44 and 0.30 cm 3 mol -1 K at 1.8 K, respectively. For 1-Sm, χT is 0.20 cm 3 mol -1 K at 300 K, which is larger than expected for an isolated free-ion 6 H5/2 term of 0.09 cm 3 mol -1 K, owing to thermal population of the low-lying 6 H7/2 term. The decrease of χT in all cases is due to the depopulation of the crystal field states. Isothermal magnetisation measurements of all compounds deviate from values expected for pure Ising-like mJ states (Supplementary Information Figures ), indicating significant mixing of mJ states. To corroborate these results, we performed CASSCF-SO calculations using a minimal n-electrons in 7 orbital active space (where n = 1 for Ce 3+ , n = 3 for Nd 3+ and n = 5 for Sm 3+ ; see Supplementary Information for details) and the solidstate XRD geometries (Tables ). These give excellent reproductions of the magnetic data (Figures and) and confirm substantially mixed mJ states (Tables ); the ground Kramers doublet for 1-Ce is dominated by |mJ| = ½, with the first excited state at 105-135 cm -1 , while for 1-Nd the ground Kramers doublet is dominated by mJ = ±5/2 mixed with ∓7/2, with a first excited state at 26 cm -1 . For 1-Sm the ground Kramers doublet is dominated by mJ = ±3/2, with a first excited state at 400 cm -1 . |
64e76bc53fdae147fabbf1bb | 4 | CW EPR spectra of 1-Nd, 1-Ce and 1-Sm are observed at temperatures below ~30 K (Figures 4 and Supporting Information Figures ). Much sharper spectra are observed from powders (such that it is difficult to remove polycrystalline effects) than from frozen solutions (toluene/hexane 9:1 v/v), indicating some relaxation and strain of the structures in the latter medium. The spectra are dominated in each case by the rhombic or axial effective g-values arising from transitions within a thermally isolated ground Kramers doublet of the ground Russell-Saunders state, which can be treated as an effective spin-1/2. In this approximation, the frozen solution EPR spectrum for 1-Nd (Figure ) can be modeled with the spin Hamiltonian Eqn 1. |
64e76bc53fdae147fabbf1bb | 5 | This gives gx,y,z = 3.33, 1.22, 0.56, and hyperfine coupling constants of Ax = 1280 MHz (Ay and Az unresolved; we have assumed 𝑔̿ and 𝐴 ̿ are collinear) to the I = 7/2 nuclear spin of Nd (natural abundance: 12.2% 143 Nd and 8.3% 145 Nd). Similarly, frozen solution spectra of 1-Ce and 1-Sm can be simulated with gx,y,z = 3.15, 1.88, 0.64 for 1-Ce (Figure ; note there are no isotopes of Ce with I 0), and gx = gy = 0.92 for 1-Sm (Figure ). The gz component of 1-Sm is not well resolved in cw spectra but is more clearly defined in pulsed spectra giving gz = 0.45 (Figure ; see below). CW spectra of the related [Nd(Cp′′)3] (Cp′′ = C5H3-(SiMe3)2-1,3) have been reported, and although the precise g-values differ the pattern is similar. . |
64e76bc53fdae147fabbf1bb | 6 | For 1-Ce and 1-Nd, CASSCF-SO calculations (Tables S10-S13; note there are two non-equivalent molecules in the XRD structure of 1-Ce) give effective g-values for the lowest Kramers doublets as gx,y,z = 2.1, 3.0, 0.7 and 2.2, 2.4, 1.1, respectively, with the numerically smallest value (gz) corresponding to the orientation of the pseudo-C3 axis (Figure ); the anisotropy patterns agree with the experiments. For 1-Sm, CASSCF-SO calculations give gx,y,z = 0.4, 0.4, 0.6 for the lowest Kramers doublet. This has the opposite sense of anisotropy (gx,y < gz) to the experimental data (gx,y > gz), but given the numerically similar and very low (all < 1) effective g-values, such a switch in anisotropy will be very sensitive to subtle state mixing effects. Nevertheless, given the axially symmetric form of the EPR spectrum, gz must be associated with the pseudo-C3 axis. |
64e76bc53fdae147fabbf1bb | 7 | Echo-detected field-swept spectra (EDFS) of 1-Nd, 1-Ce and 1-Sm (in toluene-hexane) are observed up to 10 K (see Supplementary Information for all pulsed EPR spectra). These were recorded by integration of the Hahn echo generated with the standard pulse sequence π/2 -τ -π -echo, where π/2 and π are microwave pulses and τ is the inter-pulse delay. The EDFS spectra at 5 K for 1-Nd, 1-Ce and 1-Sm (Figures and) are consistent with the CW spectra, Qband EDFS are consistent with the rhombic g-values of 1-Nd and 1-Ce (Figure ). Measurements of the spin-lattice (T1) and phasememory (Tm) relaxation times were performed at Xband on 10 mM frozen solution samples of 1-Nd, 1-Ce and 1-Sm at 5 K. T1 data were recorded with an inversion recovery pulse sequence, and the data fitted with a bi-exponential function (see Supporting Information Eqn 3; Figures and), where the fastest process is assigned to the spectral diffusion and the slow process is attributed to the spin-lattice relaxation. The T1 value for 1-Nd is field-dependent and reaches a maximum value of 12 μs at the highest field g-value (12360 G, Table ). Measured at the maxiumum of the EDFS (6040 G), T1 is 5 μs. Much longer maximum T1 times of 89 and 150 μs were obtained for 1-Ce (at the high-field g-value, 11228 G) and 1-Sm (at the low-field g-value, 6936 G), respectively (Tables and). For comparison, T1 measured at the EDFS maxima are 78 and 118 μs for 1-Ce and 1-Sm, respectively. |
64e76bc53fdae147fabbf1bb | 8 | Tm was determined by fitting Hahn echo decays to a stretched exponential function (see Supporting Information Eqn 1; Figures ). The maximum Tm relaxation times observed are 0.7, 1.0 and 1.7 μs for 1-Nd, 1-Ce and 1-Sm, respectively (Tables ), in each case measured at the highest field g-value. Tm measured at the EDFS maxima are 0.5, 0.6 and 1.6 μs, respectively. |
64e76bc53fdae147fabbf1bb | 9 | An interesting comparison can be made between 1-Nd and its valence isoelectronic An 3+ analog 1-U. Complex 1-U has T1 and Tm times of 860 and 0.8 μs, measured at the EDFS maximum under similar conditions, compared to 5 and 0.5 μs for 1-Nd. Hence, T1 for the Ln 3+ 4f 3 complex is more than two orders of magnitude shorter than for its An 3+ 5f 3 analogue. In general, electron spin-lattice relaxation times are expected to decrease going down the Periodic Table, as modulation of the electronic structure by vibrational modes (which is a dominant factor for T1 relaxation in immobilised samples ) impacts the orbital angular momentum. This is connected to the spin via spin-orbit coupling (SOC), and SOC increases with atomic number; the values for for Nd 3+ and U 3+ are 900 and ca. 1700 cm -1 , respectively. It seems reasonable to assume that the slower T1 relaxation of 1-U is due to the partial quenching of the orbital angular momentum by the larger crystal field interaction for U 3+ cf. Nd 3+ . This is promising for future pulsed EPR studies of Ancontaining materials. The 4f 1 complex 1-Ce also has a much shorter T1 than its An 3+ analogue 1-Th (T1 ca. 21 ms under similar conditions): this is due to the orbital singlet 6d 1 configuration of 1-Th, compared to 5f 1 for 1-Ce. |
64e76bc53fdae147fabbf1bb | 10 | Comparing the relaxation data for the 1-Ln series, it could be inferred that 1-Nd has the shortest T1 because it has the largest ground state orbital angular momentum (L = 6) and indeed the largest total angular momentum (J = 9/2). However, comparison with T1 data for these Ln 3+ ions at similar concentrations and temperatures in water/ethanol glasses gives a different trend, with Nd 3+ having the longest T1. This emphasises the importance of the crystal field on the relaxation behaviour of Ln 3+ ions. In our case, of the three complexes studied, 1-Nd has, by some margin, the lowest energy excited state and indeed the smallest energy spread of mJ states desite having the largest multiplicity (Tables ). More densely-packed electronic states renders the states more sensitive to perturbations (following textbook perturbation theory arguments), and so we can speculate that this exposes 1-Nd to more influences from spin-vibration coupling, and thus causes a shorter T1. |
64e76bc53fdae147fabbf1bb | 11 | The Tm values for 1-Ln complexes studied are all similar, around the 1 μs mark. These are ample to allow further investigation of the complexes by multipulse microwave sequences. In order to quantify the weak hyperfine interactions between the electron spin(s) and surrounding 1 H and C nuclei, we employed two-dimensional hyperfine sub-level correlation (HYSCORE) spectroscopy, which uses a four-pulse spin echo envelope modulation sequence; π/2 -τ -π/2 -t1 -π -t2 -π/2 -echo, with t1 and t2 independently varied. In the HYSCORE experiment the first two π/2 pulses generate nuclear coherences, which are then transferred between electron spin states by the π pulse. In the 2D frequency domain spectrum, cross-peaks appear for weakly-coupled nuclei (2|νn| > |A|) in the (+, +) quadrant straddling the nuclear Larmor frequencies (νn). Ridges in the spectra are due to the anisotropic hyperfine couplings. X-band HYSCORE spectra measured at static magnetic fields corresponding to orientations in the molecular xy plane for 1-Nd and 1-Ce (B0 = 353.0 and 348.2 mT, respectively) reveal signals from C and 1 H nuclei (Figure ). HYSCORE signals for 1-Sm were too weak to detect when measured under similar conditions; this does not appear to be relaxation limited given the similar Tm (see above), and may be a function of the very low effective g-values. The 13 C features for 1-Nd and 1-Ce are similar, consisting of a ridge extending beyond the C Larmor frequency by ca. ± 1 MHz. The 1 H features are also similar, with a ridge extending νn ± 2.5 MHz. |
64e76bc53fdae147fabbf1bb | 12 | In a first attempt to model the HYSCORE data of 1-Ce and 1-Nd, we used a simple point dipolar approach assuming the electron spin density to be located at the Ln 3+ ion, calculated (Supplementary Information Eqn 4) using the experimental g-values and the atomic coordinates from XRD (thus neglecting structural relaxation in solution). The calculated point dipolar hyperfine values for the Cp-ring hydrogen and carbon atoms (Tables and) were then used with EasySpin to calculate HYSCORE spectra. The calculated spectra show excellent agreement with the experimental data. (Figure ). |
64e76bc53fdae147fabbf1bb | 13 | Comparing the HYSCORE data of 4f 1-Ce and 1-Nd to their 5f analogues 1-An, C HYSCORE spectra measured for 1-Th under equivalent conditions have ridges that spread νn ± 2.4 MHz, substantially larger than for 1-Ce. We did not have sufficient signal to measure the full C hyperfine pattern for 1-U, but we did measure well-resolved 1 H ridges in the gx,y region: these spanned νn ± 2.5 MHz, which is much larger than for 1-Nd. The spectra for 1-Th and 1-U could not be modelled on a simple point dipole basis, requiring significant additional contributions to the hyperfine interactions. |
64e76bc53fdae147fabbf1bb | 14 | We futher confirmed these results using CASSCF-SO calculations (see Supporting Information). To compare with the HYSCORE experiment, we approximate solution phase structures by optimising the molecular geometry of each complex in the gasphase using density-functional theory (DFT) methods (see Supporting Information for details), and then use the optimised geometries to perform another set of minimal CASSCF-SO calculations. We then use the Hyperion package to calculate the relativistic hyperfine coupling tensors directly for the nuclei of interest (Tables and); note that the Hyperion method implicitly includes all through space dipolar and Fermi contact terms, as well as relativistic paramagnetic spin-orbit terms. Inspection of the computed hyperfine values show the C(Cp) and H(Cp) atoms couple more strongly than any other Cp tt ligand atoms. Hence, we simulate C and 1 H HYSCORE spectra using five C and three H nuclei from one Cp tt ligand, again using EasySpin; these calculations provide excellent reproductions of the experimental data (Figure ). The calculated Mulliken spin populations (Table ), show that only ~0.1% of the total spin density is transferred to the C1-C5 atoms of the three Cp tt ligands. However, we note that the density does increase slightly with increasing Ln 3+ atomic number (1-Ce < 1-Nd < 1-Sm). |
64e76bc53fdae147fabbf1bb | 15 | We have synthesised a family of Ln 3+ complexes [Ln(Cp tt )3] (1-Ln; Ln = La, Ce, Nd, Sm) using a salt metathesis route. The solid-state structures of 1-Ln reveal that the distances between the Ln 3+ centres and the Cp tt centroids decrease regularly from La 3+ to Sm 3+ due to the ionic radii of Ln 3+ ions decreasing across the series. Complexes 1-La and 1-Nd exhibit pseudotrigonal planar geometries, which is consistent with the previously reported structures of 1-Ce, 1-Sm and 1-Yb. Continuous wave and pulsed EPR studies were performed on 1-Nd, 1-Ce, and 1-Sm. The CW spectra show rhombic systems with anisotropic gvalues for both frozen solution and powder samples for 1-Nd and 1-Ce. HYSCORE spectroscopy shows resonances for C and 1 H regions for both 1-Nd and 1-Ce, and point-dipole simulations provide excellent agreement with experimental data. CASSCF-SO calculations effectively reproduce magnetic data, and fully-ab initio simulations of the HYSCORE spectra are also in excellent agreement with experiment, confirming minimal spin density at ligand nuclei. The larger ligand hyperfine interactions observed for 1-Th cf. 1-Ce are consistent with the 6d 1 vs. 4f 1 configurations of Th 3+ and Ce 3+ , respectively, and the significant radial extent of the 6d orbital(s). Comparing the results for 1-Nd with 1-U shows larger ligand hyperfines observed for the latter, highlighting the difference between 4f and 5f valence orbitals. |
64e76bc53fdae147fabbf1bb | 16 | The results show that the interactions between Ln 3+ ions and the ligands in the early Ln complexes 1-Ln can be considered as being mostly ionic. The results are consistent with early CW EPR studies of U 3+ and Nd 3+ doped fluorite (and later studies on other inorganic lattices), where superhyperfine coupling to F was observed for the former but not the latter. These are mineral lattices with hard ligands, and we have now shown related effects in molecular species with very soft ligand sets. The results on 1-Ln also contrast with HYSCORE studies of a closely related complex of Yb 3+ , 20 a late Ln complex (4f ), which showed far more significant metal-ligand interactions. This highlights the importance of ligand substituents and Ln ion charge density in controlling the magnitude of 4f metal-ligand interactions, and shows that pulsed EPR spectroscopy is a sensitive probe to study these effects. |
64e76bc53fdae147fabbf1bb | 17 | Synthesis. All manipulations were carried out using standard Schlenk line and glove box techniques under dry argon. Solvents were passed through columns containing alumina or were dried by refluxing over K, and were stored over K mirrors or 4 Å molecular sieves (THF) and degassed before use. For NMR spectroscopy C6D6 was dried by refluxing over K, degassed by three freeze-pump-thaw cycles, and vacuum-transferred before use. Anhydrous LnCl3 were purchased from Alfa Aesar and were used as received. KCp tt was synthesised by literature methods, whilst 1-Ln were prepared by modification of literature procedures. General synthetic procedures for 1-Ln are given below; full details can be found in the Supporting Information. 1 H (400 and 500 MHz) and C{ 1 H} (100 and 125 MHz) NMR spectra were obtained on Avance III 400 or 500 MHz spectrometers at 298 K. 1 H NMR spectra were measured from 0 to +10 ppm for diamagnetic 1-La and from -200 to +200 ppm for paramagnetic 1-Ce, 1-Nd and 1-Sm. ATR-IR spectra were recorded as microcrystalline powders using a Bruker Tensor 27 spectrometer. Elemental analyses were performed by Mrs Anne Davies and Mr Martin Jennings at The University of Manchester School of Chemistry Microanalysis Service, Manchester, UK. UV/vis/NIR spectroscopy was performed on samples in Youngs tap-appended 10 mm path length quartz cuvettes on an Agilent Technologies Cary Series UV/vis/NIR spectrophotometer at 175-3300 nm. CW EPR measurements were carried out on a Bruker EMX300 spectrometer; pulsed EPR X-band studies were performed on a Bruker ElexSys E580 spectrometer. The primary Hahn-echo sequence (/2----echo) was used for the two-pulse electron spin echo measurements, with initial /2 and pulse of 16 and 32 ns, respectively. For the relaxation time measurements, Tm studies were made by incrementing the time in the Hahn-echo sequence (longer pulses were used to suppress the 1 H modularion), T1 was measured by the inversion recovery sequence (-t-/2----echo) /2 and pulse of 16 and 32 ns, respectively, with a fixed = 300 ns. HYSCORE measurements were performed using the four-pulse sequence (/2--/2-t1--t2-/2-echo), /2 and pulse of 16 and 32 ns, respectively, initial times t1,2 = 0.1 s and values of 136 and 200 ns. |
6563b9805bc9fcb5c97135fa | 0 | Nanogenerators (NGs) can directly harness local energy sources, such as from motion or mechanical stress, to power portable and wearable devices. They are therefore attractive alternatives to batteries. Applications of NGs include sensors, actuators and electromechanical convertors. NGs use a dielectric layer for charge accumulation, which is typically a piezoelectric material. For NGs to be used in wearable electronics, flexibility is a key design parameter; however, existing piezoelectric-based NGsthat produce current ranging from nanoamperes to microamperesare often made up of bulk ceramics like lead zirconate titanate (PZT) with limited flexibility. For such applications, NGs that take advantage of the flexoelectric effect are especially attractive. Flexoelectricity is a basic property of any dielectric material wherein it exhibits a spontaneous electrical polarization induced by a strain gradient, rather than the coupling between polarization and homogeneous strain that exists in piezoelectric materials. Furthermore, as the magnitude of the strain gradient is inversely proportional to the relaxation length, flexoelectric effects are expected to increase in lower dimensional materials, making them a natural choice for flexible nanogenerators. In this aspect, two-dimensional (2D) materials provide enlarged strain gradients without compromising the flexibility of the device. However, the flexoelectric coefficients of available 2D materials are modest, with the highest reported value being 10 pC m -1 for MoS2 monolayers. In contrast to 2D materials, flexoelectric coefficients as high as μ1111 = 17.33 µC m -1 have been observed in bulk ceramics such as barium titanate that have limited flexibility. Hence, the performance of flexoelectric generators have been low. |
6563b9805bc9fcb5c97135fa | 1 | In this Article, we present a flexible nanogenerator (FNG) that incorporates enhanced flexoelectricity in few atomic layers-thick membranes of an inexpensive mineral, Hausmannite (Mn3O4), to produce up to 7.99 mW m -2 power density (active surface area ~2.5 cm 2 ). We exfoliated membranes with an average thickness of 2 -6 nm using a liquid exfoliation technique and characterized their structure and electronic properties. We fabricated flexible NGs with one of the electrodes being Mn3O4 membranes and observed a ~700% increment (at the highest load) in the voltage output of devices as compared to those having bulk Mn3O4 polycrystals as the electrode. Using first-principles calculations, we attribute the enhanced power output to flexoelectric effects. We show that flexoelectricity in bulk Mn3O4 is subdued due to a destructive interference between the bending and shearing modes; whereas in monolayer and bilayer Mn3O4, the contribution of the shearing mode diminishes, leading to flexoelectric coefficients that are two orders of magnitude larger than other 2D materials such as MoS2. We demonstrate generation of voltages up to 6.24 V (peak to peak) using these exfoliated Mn3O4-membrane-based FNGs from mechanical perturbations. These results open up a large family of centrosymmetric layered oxides as potential candidates for portable nanogenerators due to enhanced flexoelectricity. |
6563b9805bc9fcb5c97135fa | 2 | Mn3O4 was synthesized by a co-precipitation method. 0.22 M of manganese chloride tetrahydrate (MnCl2.4H2O) along with 1.37 mM hexadecyl trimethyl-ammonium bromide (CTAB) was stirred constantly. 0.44 M sodium hydroxide (NaOH) solution was prepared separately and added dropwise to the first solution and was kept under constant stirring for 24 hours. The final precipitate was filtered and washed with DI water and then ethanol for several times. The material was dried in the oven at 80°C overnight. |
6563b9805bc9fcb5c97135fa | 3 | Membranes of Mn3O4 were obtained using the liquid phase exfoliation technique by probe sonication method. Exfoliation techniques have ease of scalability in obtaining desired amounts of material. We used iso-propyl alcohol (IPA) solution as a solvent for the exfoliation of the Mn3O4 samples obtained by co-precipitation. The sample to solvent ratio was of the order 1:500 mg/ml. The probe sonicator frequency was at 30 kHz and exfoliation was done in pulses of 10 s each, for 4 hours at room temperature. The probe sonicator temperature was maintained well within the range of 30 ± 2 ⁰C. The suspension was then sonicated and dried to obtain a powdered form. |
6563b9805bc9fcb5c97135fa | 4 | The substrate used was copy paper. The surface area of the FNG cell was ~2.5 cm 2 . Cyanoacrylate glue was used for the device fabrication. The Mn3O4 membranes were mixed with cyanoacrylate (glue) in very low concentration, the homogeneous slurry was prepared with 1 mg: 1 ml ratio of sample to adhesive solution under constant stirring and was coated on to the paper substrate (first dielectric layer (d1)). Kapton tape was used as the second dielectric layer (d2). Aluminum and copper were used to form contacts at either ends (Schematic in Figure ). The entire arrangement was enclosed using a single layer of transparent polythene sheet to secure the device. Two separate nanogenerator devices were fabricated using either bulk Mn3O4 or Mn3O4 membranes for comparative testing. The thickness of the dielectric layer was ~ 80 µm, which is the sum of the substrate (50 µm), Mn3O4 membrane sample (2 -6 nm) and the adhesive (30 µm). 𝜀 𝑟 is the relative permittivity of the dielectric layer (3.780), 𝜀 𝑜 is the relative permittivity of air (8.854 x 10 -12 F m - 1 ) and Z is the gap between the electrodes; in this case, we use the height of the substrate to Kapton of 125 ± 10 µm. The above details were used for device calculations accordingly. |
6563b9805bc9fcb5c97135fa | 5 | Density functional theory (DFT) calculations were carried out with the Vienna Ab-initio Simulation Package (VASP) using the Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional. The generation of k-points meshes were done using the Monkhorst-Pack method. The number of k-point divisions along direction i, Ni, was chosen such that Ni × ai ≈ 25 Å for geometric optimizations, ~75 Å for static calculations, with ai being the length of the supercell. |
6563b9805bc9fcb5c97135fa | 6 | Geometric optimization was performed with a convergence criterion of 10 -2 eV/Å for the force on atoms. A kinetic energy cutoff of 700 eV was used for Born effective charge calculations and 500 eV for all other calculations. All calculations containing Mn were done with DFT+U method with a U parameter of 3.9 eV applied to Mn. All Mn3O4 calculations were initialized in a ferrimagnetic state; slab calculations tended to relax to different magnetic states due to changes in coordination. All crystal structures can be found at . |
6563b9805bc9fcb5c97135fa | 7 | The peaks were indexed using JCPDS card no 00-024-0734. The morphology of the samples was observed using JEOL (JED 2300) scanning electron microscope under high vacuum with an accelerating voltage of 20 kV and a current of 7.475 nA. Transmission electron microscopy (TEMFEI -TECHNAI G220S-Twin operated at 200 kV) was utilized to obtain high resolution micrographs. Atomic Force Microscopy (AFM) was done using Agilent Technologies Model No 5500. Drop deposition technique was used for sample deposition on monocrystalline silicon substrate. Particle size measurements were performed using a DLS based Horiba Scientific Nano Particle Analyzer SZ-100. The size distribution is determined by photon correlation spectroscopy (PCS) comparing the scattered light intensity at some reference and delay time. UV-vis absorption spectroscopy was carried out on the dispersion in transmittance mode. The voltage output was measured using a Textronix TBS1072B digital oscilloscope (70 MHz, 1GS/s) and Sigma 3A digital multimeter unit. To investigate oxidation states and surface composition of the materials, XPS ThermoFisher Scientific Nexsa was used, with Al-Kα radiation (λ=1486.71 eV) as source. |
6563b9805bc9fcb5c97135fa | 8 | Oxide membranes are starting to garner attention for energy applications. Manganese oxides are ubiquitous in nature. Due to it multivalent nature, Mn forms over 30 oxides with different structure and stoichiometry. Amongst them, hausmannite, Mn3O4 with the spinel structure has a wide bandgap and a high dielectric constant of 9.2, making it attractive for flexoelectricity. This is because flexoelectric tensor components are proportional to the dielectric susceptibility. Mn3O4 also has a quasi-layered structure along the [101] direction with long covalent bonds that are stronger than the van der Waals forces holding traditional layered materials but are weak enough to be cleaved. Previous studies have shown that Mn3O4 flakes can be cleaved along different crystallographic orientations by various chemical methods with relative ease. We used liquid-phase exfoliation with iso-propyl alcohol for the synthesis of ultrathin Mn3O4 membranes from Hausmannite, which we refer to as bulk Mn3O4. We obtained a uniform dispersion of the ultrathin membranes, as shown in the inset of Figure . |
6563b9805bc9fcb5c97135fa | 9 | The phase analysis was performed by X-ray diffraction (XRD) measurements in the 2θ range of 10º -60°. We observe prominent changes in the diffraction pattern of the exfoliated membranes compared to bulk Mn3O4, as shown in Figure and Figure (SI Section 1), respectively. The XRD profile of bulk Mn3O4 is indicative of a single phase, polycrystalline nature (Figure ). Upon exfoliation, peak positions changed with reference to that of the bulk structure. |
6563b9805bc9fcb5c97135fa | 10 | For the exfoliated membranes, the peak corresponding to the (101) basal plane was the most intense, indicating that the cleavage predominantly occurred perpendicular to these planes. Lattice compression during exfoliation resulted in a shift of the (101) peak (Figure ) to higher 2θ positions in the membranes, which corresponds to a decrease in the lattice spacing between (101) planes to 4.18 Å from 4.91 Å in bulk. |
6563b9805bc9fcb5c97135fa | 11 | The morphology of the membranes was analyzed using atomic force microscope (AFM) imaging scanned over a broad region, as shown in Figure . A histogram of the height profile of the membranes indicates that they vary in thickness from 2 -6 nm (Figure (ii)) corresponding to 3 -7 layers (c-axis lattice constant of Hausmannite is 0.947 nm). High-angle annular dark-field images (HAADF) of the membranes acquired using a scanning transmission electron microscope (STEM) are shown in Figures and. We observed that the exfoliated membranes were of cuboidal shape with lateral dimensions ranging from 25 -30 nm (Figure ). The interplanar spacing was found to be 0.49 nm (Figure ) corresponding to the spacing between (101) planes. This is in close agreement with results from DFT calculations that show a layer periodicity of 0.50 nm. In comparison, the results from TEM micrographs of bulk Mn3O4 (Figure ) showed that the sample lateral dimension was 100 -200 nm. We carried out dynamic light scattering (DLS) experiments to further measure the particle-size distribution by dispersing the samples in an ethanol solvent. The histogram plots (Figure ) indicate that the lateral size of the membranes was within a range of 75 -300 nm, which is smaller than the bulk Mn3O4 precipitates that span 250 -600 nm. |
6563b9805bc9fcb5c97135fa | 12 | X-ray photoelectron spectroscopy (XPS) measurements were done to analyze the contribution of surface oxygen sites for charge accumulation in the layer. Exfoliation of Mn3O4 membranes in the solvent resulted in Mn with both +2 and +3 oxidation states (Figure ). The surface of the exfoliated Mn3O4 membranes has more Mn (+3) at 64.87 at%, while the bulk has more of Mn (+2) at 69.13 at%. The three main deconvoluted peaks in the O 1s XPS spectra correspond to metal-oxygen bonds at 529 eV, loosely adsorbed oxygen species, which come from the creation of oxygen vacancies, at 531 eV, and surface adsorbed hydroxide intermediates at 532.7 |
6563b9805bc9fcb5c97135fa | 13 | With the (101) basal plane termination of the Mn3O4 membranes confirmed from XRD and HAADF-STEM (Figures and), we used DFT calculations to investigate the energetics of different surface terminations. Figure shows a visualization of the atomic model of Mn3O4 with colored polyhedra viewed along the [010] direction with the [101] direction pointing up. Here, MnO6 octahedra and MnO4 tetrahedra are shaded dark blue and light teal, respectively. There are two possible oxygen-terminated surfaces of Mn3O4 perpendicular to the [101] direction. One termination involves octahedrally coordinated Mn atoms, and the other involves a combination of tetrahedrally and octahedrally coordinated Mn atoms with the tetrahedrally coordinated atoms closest to the surface. We refer to these surface terminations as the octahedral and tetrahedral surfaces, respectively (see Figure ). We have additionally considered Mn-terminated surfaces. |
6563b9805bc9fcb5c97135fa | 14 | ). To determine which of these terminations is more likely to result from exfoliation, we calculated their surface energies (for details, see Theoretical Calculations in SI Section 2). Surface energies have been shown to correlate well with the work of adhesion, which is the energy per unit area required to cleave a crystal at a particular surface. This quantity is important for determining whether a non-van der Waals crystal, such as Mn3O4, can be mechanically exfoliated into few-layer structures. The surface energies of the two (101) terminations are shown in Figure for monolayer, bilayer, and bulk geometries of Mn3O4. The surface energy of two commonly used crystal substrates, (0001) ZnO and AlN, are included as references to show the feasibility for cleavage of Mn3O4. The octahedral surface termination has a lower energy for all thicknesses tested here with the bilayer having the lowest energy, which is about the same as (0001) ZnO by 1 meV/Å 2 . The lower surface energy of bilayer than the monolayer is because of a surface reconstruction that moves some of the Mn atoms in the interior to the surface (SI section 2, Figure S7). From these results, we conclude that the octahedral (101) surface termination is the basal plane termination in the exfoliated Mn3O4 membranes. |
6563b9805bc9fcb5c97135fa | 15 | For Mn3O4 membranes to be useful as a FNG, they must be able to produce charge separation without screening from free electrons. Mn3O4 nanoparticles have an experimental band gap in the range of ~3.2 to 3.8 eV, which varies with size. Figures and show the electronic density of states (DOS) plotted relative to the Fermi energy for monolayer and bulk geometries of Mn3O4, respectively. They show similar band gap of 0.9 eV for the monolayer and 1 eV for the bulk. While the predicted band gaps are expected to be underestimated due to the use of semi-local generalized-gradient approximation exchange-correlation functional, our calculations indicate minimal changes in the band gap upon exfoliation. This is confirmed by experiments wherein bulk Mn3O4 and the corresponding exfoliated membranes show a band gap of 3.8 and 4.0 eV, respectively (Figure ). |
6563b9805bc9fcb5c97135fa | 16 | We next describe the performance of the FNG devices having either bulk Mn3O4 or Mn3O4 membranes as the active layer. These devices were operated in vertical contact separation mode, which avoids direct friction between the layers and the resulting energy losses. The potential difference created by the small separation (Z) formed at the interface of the dielectric medium with the oppositely polarized electrode is responsible for the flow of electrons through the external load. |
6563b9805bc9fcb5c97135fa | 17 | shown in Figure . The cell was then laminated with a transparent tape leaving space for making connections to the electrodes. The replacement of a polymer binder by an ordinary glue is known to enhance the conductivity by reducing contact losses, and enables intimate contact between the material and the substrate. Cyanoacrylate present in glue provides an effective electron-hole conduction pathway for the surface charges. Without the addition of Mn3O4 membranes in the cellulose paper (substrate), we observe 1 µV voltage at 10 N force (Figure ) from the FNG device. This voltage is due to the difference in the dielectric constant (ε) of the paper (3.7) and Kapton (2.78). This measurement is considered as blank for reference in further device measurements. |
6563b9805bc9fcb5c97135fa | 18 | shows increased output voltage (Voc) from 2 V to 6.24 V (peak to peak) as the external force (Fz) increased from 10 N to 125 N, respectively. The application of higher magnitudes of Fz, up to 125 N, resulted in linear voltage increments in the device. In the Figure , we present a single pulse, where the positive part corresponds to external force/bend and negative part corresponds to the relaxation (back to original position) of the device. The response time of operation shows a sensitivity of 5 ms (Figure ) for the device. The internal resistance (RI) of the cell was also calculated (inset Figure ). A maximum voltage of ~2.9 V across the externalload resistance of 1 MΩ was obtained. The sensitivity of the NG device experienced due to external force was used to characterize the device response. A maximum sensitivity of 108 mV kPa -1 (< 10 N) was recorded for the device with Mn3O4 membranes (Figure ). This is higher than the sensitivity of 90 mV kPa -1 recorded till date for a lower-dimensional ZnO NG, which is a widely used as a triboelectric nanogenerator material. With increasing external load, the sensitivity of our device decreases to a minimum of 20 mV kPa -1 . This high sensitivity makes our device sensitive to detect small mechanical perturbations. The power density and current density was mapped for the force based measurements. Power density of 7.99 mW m -2 and current density of 3.4 mA m -2 were obtained for a minimum force of 10 N as seen in Figure . Our results compare favorably to other Mn-based NGs reported recently (see Table in Supporting Information for a comparison). |
6563b9805bc9fcb5c97135fa | 19 | As reported previously, several paper-based NGs have shown impressive power output up to ~130 -150 µW (polymer-based NGs). To measure the voltage output changes pertaining to the curvature of the substrate (strain based), bending experiments were performed on the Mn3O4membrane-based device. The variation in output voltage was observed to be linear as bending angle changes without application of external pressure. A maximum output voltage (Voc) of 1.3 and 1.8 V (peak to peak voltage) was obtained for 30° and 50° bend, respectively (Figure ). |
6563b9805bc9fcb5c97135fa | 20 | There was an almost 700% increment in Voc with Mn3O4 membranes as compared to its bulk counterpart (SI sections 3 and 5, and Table ). A linear increase in Voc was observed as the bend angle increased from 0° -50° with a step change of 10°, as shown in Figure . The inset in Figure shows a schematic representation of the bend angle of the device with a digital photograph of the cell at 30° bend. The charge storage capability of the device was additionally confirmed by charging an external capacitor (4.7 µF) connected through a full-wave bridge rectifier circuit (Figure ). A 4.7 µF capacitor was used, as it operates between the tested frequency range of 1 kHz or less in standard electronic circuits. The corresponding charge discharge characteristics of the external capacitor (4.7 μF) was recorded on application of periodical pressure of 10 N with frequency of ~5.72 Hz which is as shown in Figure . Discharge cycles were recorded of by disconnecting the FNG from the RC circuit. The FNG device was capable of charging the capacitor up to ~ 0.84 V with charging time of ~246 s (Figure ) and discharge time of ~195 s. Asymmetric charge-discharge cycles were observed. Therefore, the FNG device can be used to power small electronic devices. Figure shows a comparison of Voc of some of the recent NG devices based on dimensionally-reduced materials like oxides and chalcogenides. In comparison to the recent ZnO nanosheet-based NG device (900 mV), the maximum Voc of our cell was ~2 V (@ 10 N). Additionally, desired higher voltages can be obtained with a series connection of NGs. Here, increased voltage of ~2.4 V and ~3.6 V (positive cycle only) for 2 and 3 cells, respectively, was observed when cells were connected in a series combination (Figure ). We further used the NG as a proof of concept for sensing low pressure breathable sensors. The device showed excellent sensitivity and Voc was measured during normal breathing (walking) and exertion (running). The maximum Voc during walking was noted, persistently, to be ~1.6 V, (Figure ) whereas ~2.4 V was acquired during running (Figure ). |
6563b9805bc9fcb5c97135fa | 21 | To map the thickness-dependent surface potential or work function of the electrode material, we used Kelvin Probe Force Microscopy (KPFM). The instrument operates in amplitude modulation mode (tapping-non-contact mode), a type of dynamic force mode where a cantilever with a thin electrically conductive coating is driven at its resonance frequency. Using the local contact potential difference value between a conducting atomic force microscopy (AFM) tip and the sample, the surface potential was mapped. Figure shows Mn3O4 membrane topography mapped with homogeneous coating of the sample. The line profile indicates a membrane thickness of ~ 2 and 6 nm (Figure ), which is in range with the AFM studies done on exfoliated flakes (Figure and). An average surface potential of -213 mV was measured, as shown in Figure . As compared to silicon substrate potential, which was +306 mV (Figure ), a potential difference of 519 mV was observed. Figure shows a homogeneous phase angle depicting distribution for the flakes within the range of 44.5° to 48.5°. Through the contact potential map (Figure ), electrical properties of Mn3O4 thin membranes was mapped. for ZnO, Ref. for MoS 2 , Ref. for SnSe and Ref. for WSe2. |
6563b9805bc9fcb5c97135fa | 22 | The electrical output performance of the Mn3O4 membrane-based FNG device was further studied via electrical conductance, resistance, capacitance and quality factor at room temperature operation with varied frequencies. The frequency was varied from 1 kHz to 1 MHz on the FNG device for real time application studies. In Figure we see the resistance and conductance (1.58 nS) plots with variation of frequency with the values saturating from 100 Hz till 1 MHz. The capacitance (Cp) at zero bias voltage plays a major role for charge accumulation layer of the device and with it dielectric constant of the device was also plotted in Figure . The resonant frequency range of the fabricated FNG device shows that the capacitance dropped from 3.95 nF to 2.83 nF till 50 kHz and remained constant thereafter (∼2.7 nF). The drop in resonant frequency influences the conductance of the device to decrease upto a certain level (1.58 nS) as the resistance is higher at increased frequencies (skin effect) as seen in Figure . The dissipation factor (Q) influenced under Cp and self-heating under resonant frequency conditions changed from 142 to 96.8 in the 1 kHz to 1 MHz frequency range, respectively. The lower dissipation factor of the FNG system makes it a more efficient device for electrical applications. |
6563b9805bc9fcb5c97135fa | 23 | To establish the reason for the large voltages generated by ultrathin Mn3O4 under stress, and their superior performance over bulk Mn3O4, we used DFT to calculate the coupling of electric polarization to strain and strain gradients in Mn3O4. Typically, piezoelectric materials develop voltages upon application of stress. A necessary condition for piezoelectric materials is the lack of inversion symmetry; however, we find that both bulk Mn3O4 and the two low surface energy (101) slabs with octahedral and tetrahedral termination are centrosymmetric. Centrosymmetric materials can develop voltages due to the coupling between electric polarization and strain gradientsthat break the inversion symmetry; this linear coupling is termed as flexoelectricity. More recently, it has been proposed that flexoelectric charges arising from strain gradients on nanoscale features leading to triboelectric charge separation. Therefore, we calculated the flexoelectric coupling constants in monolayer and bilayer Mn3O4 and compared them with bulk Mn3O4. The flexoelectric tensor is a rank-4 tensor that relates strain gradient to polarization via Equation 1: |
6563b9805bc9fcb5c97135fa | 24 | Here, Pi is the polarization along direction i, 𝜀 𝑘𝑙 is the strain tensor, 𝑥 𝑗 is a coordinate along the direction 𝑗, and 𝜇 𝑖𝑗𝑘𝑙 is the flexoelectric tensor. Given the flat, flexible nature of the Mn3O4 in FNGs, certain types of strain gradients are expected to be more relevant. Furthermore, we are former is an inhomogeneous shear strain along an in-plane direction while the latter is an in-plane uniaxial strain that varies along the out-of-plane direction. These inhomogeneous strains are chosen because they are common in a distorted sheet, such as the FNG cell during operation. While there are density functional perturbation methods for calculating flexoelectric coefficients, we elected for a simpler strategy involving calculations on a supercell with a manual, periodic strain imposed (see details in SI section 2, Theoretical calculations). We refer to the periodic strain modes corresponding to the calculation of 𝜇 3𝑘𝑘3 and 𝜇 33𝑘𝑘 as the shear and bending modes, respectively. Figures and show abstractions of the shear and bending modes, respectively (also Figure ). These abstractions are expressed more concretely in Figure shows the four flexoelectric coefficients calculated for three geometries of Mn3O4: monolayer, bilayer, and bulk. The magnitudes of several of these coefficients exceed 100 pC/m; this value is significantly larger than common 2D semiconducting materials, such as transition metal dichalcogenides, which only reach up to 10 pC/m in MoS2. Furthermore, we find an additional contribution to the flexoelectric coefficient of about 100 pC/m from finite surface effects for the bending modes. Details can be found in SI Sections 2 and 7. In monolayer and bilayer Mn3O4, the shear modes contribute negligibly to the flexoelectric response due to cancelations of positive and negative responses caused by anomalous positive Born effective charges in undercoordinated surface O atoms (see Figure ). For the bending mode in the monolayer structure, the anomalous Born effective charges do not lead to a cancellation and instead cause a sign reversal compared to the bulk structure. In contrast, both modes contribute significantly to flexoelectricity in bulk Mn3O4. |
6563b9805bc9fcb5c97135fa | 25 | To explain how strain gradients are transferred from the macroscopic device to the microscopic oxide particulates, we developed a model based on Euler-Bernoulli beam theory. The model treats the oxide particles as stiff plates/beams with an external parabolic force exerted by the surrounding medium through macroscopic bending. For visualizations, see Section 8 in the SI and for model details, see SI section 2. Our model shows that the magnitude of deflection is proportional to the in-plane particle length squared and inversely proportional to the cube of the particle thickness (Figure ). The magnitude of the bending mode strain gradient also shares the same proportionality relationship (see Figure ). In contrast, the shearing force is predicted to be independent of thickness (see Figure ). Furthermore, under the assumptions of the model, there are positive and negative shear gradients that exactly cancel out. This indicates that beyond the differences in the flexoelectric properties of the exfoliated and powdered Mn3O4 as determined by first-principles calculations, the enhanced effective flexoelectric response in our exfoliated oxide nanogenerators is also a result of dimensional reduction allowing for improved microscopic response to macroscopic strain gradients. To put it more concretely, we can predict the flexoelectric response of the exfoliated and powder Mn3O4 using this model and representative length scales from our experiments. Assuming a length and thickness of 25 nm and 6 nm for the exfoliated samples and a cube of size 300 nm, our model predicts an increase in response between the bulk and exfoliated oxides of almost three orders of magnitude. Such a dramatic increase is not observed, partially because the model is not well suited for cuboid particles, but the general trend with size is valid. |
6563b9805bc9fcb5c97135fa | 26 | In conclusion, we have demonstrated that Mn3O4 membranes showing enhanced flexoelectricity which has promising potential as a flexible energy harvester. Flexoelectric effects in 2D materials are known to enhance other electromechanical effects of the material like piezoelectric, electrostriction and triboelectric behavior. The improved FNG performance was shown to result from improved microscopic sensitivity to macroscopic strains in accordance with dimensionality reduction. This made ultrathin Mn3O4 FNG exceed voltage output by ~700 % greater when compared to its bulk counterpart with pressure sensitiveness as high as 108 mV/kPa (< 10 N). Measurement of flexoelectric constants has always been a tedious process as it involves specific boundary conditions and precise characterization techniques. Enhanced flexoelectricity is often observed in other dimensionally reduced layered structures such as perovskites, ferroelectrics, TMDCs and metal oxides. The effects of strain gradients contribute to the sensitivity of the device making it accurate for applications in sensors and structural health monitoring devices. These results represent a promising direction for centrosymmetric metal oxides for future energy applications. |
631a10083940c20533f81566 | 0 | The molecular mechanics force field (FF) is vital to the success of atomistic modelling of organic and biological systems. The FF typically encodes a library of transferable parameters that describe inter-and intramolecular interactions via physically-motivated models defined by an atomic environment . These models offer users the ability to rapidly parametrize vast regions of small-molecule drug-like chemical space, and simulate the dynamics of complex, heterogeneous systems with low computational cost. |
631a10083940c20533f81566 | 1 | For FF-based molecular modelling to be worthwhile, the FF must be accurate. That is, it should accurately describe the potential energy surface of the target molecule, and adequately describe the vital non-bonded interactions between the molecule and its (often condensed phase) environment. In an attempt to achieve this accuracy, most transferable FFs are parametrized following a similar philosophy. Specifically, a representative subset of small molecules is selected that contains key functional groups, such as those that appear frequently in drug-like molecules . For these molecules, parameters are then fit to a combination of experimental and quantum mechanical (QM) data, and transferability between similar chemical environments is assumed. |
631a10083940c20533f81566 | 2 | Parameter type MMFF OPLS3 OPLS3e Sage (OpenFF 2.0.0) Bond Such an approach to transferable FF design is often successful as evidenced by numerous retrospective and prospective studies, which show good agreement between experiment and simulation. Critical applications of FFs include alchemical free energy calculations, which have become a widespread, relatively low-cost computational tool to aid the identification and development of high binding affinity small molecules in the early stages of drug discovery campaigns . However, due to the vast size of chemical space, and the local limitation of atom types used to describe these environments, the number of parameters required for broad, accurate coverage has tended to increase dramatically during FF development. For example, the most recent OPLS3e FF library contains ∼150 K torsional parameters (Table ) . has replaced atom-typed parameter encodings with a technique termed direct chemical perception . |
631a10083940c20533f81566 | 3 | The chemical perception framework assigns parameters via standard chemical substructure queries implemented in the SMARTS language. This removes many redundancies, for example in equivalent parameters that would otherwise be applied to different combinations of atom types, and allows the OpenFF line of FFs (Parsley , Sage , ...) to be very compact without sacrificing accuracy (Table ). Given the hierarchical nature of these FFs, their extension becomes trivial. More specific substructure queries can be introduced for problematic areas of chemistry without affecting the more general, transferable parameters. |
631a10083940c20533f81566 | 4 | Even with significantly fewer parameters, the OpenFF family of FFs has been shown to offer competitive accuracy when benchmarked against QM geometric and energetic properties . However, torsion parameters, in particular, are known to be particularly sensitive to the local environment within the target molecule and may be expected to be less transferable than the other valence parameters. Torsional parameters must effectively account for many stereoelectronic and steric effects . In addition, resonance effects between aromatic rings, for example, can mean that even non-local substitutions, which may not be captured via chemical perception, can affect torsional profiles . Figure compares example potential energy surfaces of two molecular fragments calculated with contemporary general force fields OpenFF 2.0.0 (Sage) and GAFF 2.11, with a QM reference (see Methods). While the default, transferable torsional parameters show good performance in some cases (top panel), more complex chemical environments can lead to an inaccurate reproduction of the QM potential energy surface (lower panel), resulting from poor transferability. Thus, due to the complexity encoded in torsional parameters, and the resulting poor or partial transferability, they are often the target for reparametrization. To this end, several automated methods exist to derive torsion parameters that are specific to the target molecule under study. For example, an automated torsion parametrization package, named FFBuilder supplements the already extensive set of base library parameters in the proprietary OPLS3 FF . This allows users to fit new torsion parameters for novel chemistry that is poorly represented by the general FF using a consistent parametrization method. Several other tools also aid the fitting of bespoke torsion parameters to QM potential energy surfaces; these include QUBEKit , paramol , parmfit , qforce , JOYCE , DFFR , Rotational Profiler , or the algebraic method of Kania , to name a few. Although bespoke torsion parameters have the potential to improve the accuracy of molecular simulations, fitting these parameters to multiple QM torsion scans can significantly slow down the parameter assignment stage for users. However, there is now the opportunity to make use of recent advances in machine learning (e.g. ANI ) and semi-empirical (e.g. xTB ) |
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