Modeling the Effect of the Electrolyte on Standard Reduction

Article Cite This: J. Phys. Chem. C XXXX, XXX, XXX−XXX

pubs.acs.org/JPCC

Modeling the Effect of the Electrolyte on Standard Reduction Potentials of Polyoxometalates Alena Kremleva† and Notker Rösch*,†,‡ †

Department Chemie and Catalysis Research Center, Technische Universität München, 85747 Garching, Germany Institute of High Performance Computing, Agency for Science, Technology and Research, 1 Fusionopolis Way, #16-16 Connexis, Singapore 138632, Singapore

‡

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S Supporting Information *

ABSTRACT: The electrochemistry of transition metal oxide systems is gaining much interest in the context of energy storage. Yet, predicting the redox behavior of such systems remains very challenging for computational chemistry. In this work, we examined instead a computational strategy for related nano-sized molecular transition metal polyoxoanions, as such polyoxometalates (POMs) can be treated at manageable computational costs. As an example, we addressed the effects of an aqueous electrolyte at the atomic scale for estimating the standard reduction potentials Mn(IV/III) and Mn(III/II) of the tri-Mn-substituted W-based Keggin ion. The electrolyte model involves explicitly solvated Li+ counterions and accounts for the fluctuating aqueous medium, described in firstprinciples molecular dynamics simulations. After equilibration, the systems showed different local structures of the electrolyte around the POM, depending on the oxidation state of the Mn centers. These varying local structures affect the Mn reduction potentials differently for the redox couples under study. Hybrid DFT calculations yield rather accurate absolute redox potentials for Mn, in good agreement with experiment, i.e., within 0.1 eV. This is in strong contrast to analogous results from an implicit solvation model, where redox potentials were notably underestimated, whereas models with counterions added, but without explicit solvation, notably overestimated the redox potentials, by up to 1 eV. Only by taking into account the full atomistic structure of the multicomponent system, solute, and surrounding electrolyte is one able to estimate the electrochemical properties of nanostructured transition metal oxide systems with acceptable accuracy.

1. INTRODUCTION Modeling the electrochemical behavior of transition metal oxide (TMO) materials in contact with electrolyte media is very timely. Energy-efficient water desalination relies on electrochemical storage of sodium ions from aqueous electrolytes in TMOs.1 Adding electrolyte as a gate insulator to thinfilm transistor with TMO as an active channel results in electrochemically switchable functional devices.2 Electrodes in storage devices with TMO overlayers (RuO2,3,4 MnO2,4,5 and Fe3O46,7) in general play a role for storage device, e.g., batteries of various types,8,9 pseudocapacitors, and supercapacitors.10,11 The properties of these devices, in particular their redox characteristics, depend notably on the electrode material and its interaction with the electrolyte.12 Modeling the structure and the redox behavior of (transition) metal oxide surfaces/films in the presence of an electrolyte is challenging due to the complexity of these systems, especially in view of the irregular surface/spatial structure and the inherent difficulties associated with describing the electronic structure of transition metal oxides.13−15 In contrast to these extended systems, nanosized molecular objects admit computational studies with quantum chemical approaches at manageable cost. Recently, © XXXX American Chemical Society

we presented calculations of redox potentials of tri-Mnsubstituted W-based Keggin ions.16 Keggin ions are polyoxometalates (POMs),17 a class of nano-sized compounds formed by linking early transition metal polyhedra via oxygen centers located at their vertices.18−20 POMs exhibit welldefined structures and may be viewed as models of nanostructured metal oxide materials. POMs are also considered for redox flow batteries,11,21 suitable as electrochemical energy storage system for renewable energy sources due to their safety and energy/power separation. POMs by themselves are of high interest in various research fields, e.g., electrocatalysis, biology, medicine, and materials science.19,22−24 In that context, an adequate computational modeling of redox potentials of POMs and a deeper understanding of their electrochemical behavior are of direct significance. Earlier computational studies25−27 of standard reduction potentials of various POMs did not involve pertinent counterions and were limited to representing the electrolyte Received: June 6, 2018 Revised: July 20, 2018

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DOI: 10.1021/acs.jpcc.8b05426 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C environment by a polarizable continuum model (PCM),28,29 e.g., the COSMO approach.30,31 In passing, we note that these types of solvation models are well-known for having severe issues with quantitatively describing solvent effects of highly charged anionic species. 28 In those earlier works on POMs, 25−27 the simplifications of the PCM/COSMO approach led to significant uncertainties in the absolute reduction potentials. In our preceding study,16 we included a sufficient number of Li+ counterions to achieve a neutral molecular model before applying a COSMO treatment of the surrounding aqueous environment. The counterions were adsorbed at the surface of the POM in an inner-sphere fashion.16 The strongest interaction was determined for Li+ ions at 4-hollow sites. With this model, trends of the Mnrelated redox potentials and their pH dependence were reproduced rather well, but the absolute values of the redox potentials were not satisfactory.16 This outcome was assigned in part to a poor representation of the electrolyte environment where the Li+ ions were distributed rather symmetrically around the POM in consequence of the COSMO description of the solvation field being far too homogeneous and isotropic.16 Calculating redox potentials of transition metals in aqueous solution is still challenging.32 To note, earlier studies on M(III/II) redox potentials for transition metal ions (M = Ti, V, Cr, Mn, etc.)33 in solution overestimated the U0red values by over 1.6 eV compared to experiment, when only first solvation shell was treated explicitly and long-range solvation effects were included at the PCM level.33 These large errors were attributed to the fact that the solvent representation did not account for the molecular structure of the second solvation shell.33 With a hierarchic QM/MM approach the errors were reduced to 0.3 eV on average.33 More such examples can be found in a recent review of the status of computational electrochemistry.32 There seems to be sufficient evidence that an improved representation of solvation effects is crucial for an adequate modeling reduction potentials. The present study presents a strategy for doing just that for redox potentials of POMs. We are going to show that the local structure of the electrolyte, generated in first-principles molecular dynamics (FPMD) simulations, plays a crucial role when modeling the electrochemical behavior of nanostructured transition metal oxide systems. Specifically, we explore the effect of explicitly solvated counterions and the fluctuating aqueous medium on calculated redox potentials on the example of a tri-Mn-substituted Wbased POM.

Figure 1. (a) Initial structure of Li4[Mn(III)3(H2O)3] in a cubic unit cell filled in addition with 148 water molecules. (b) Structure snapshot of Li4[Mn(III)3(H2O)3]·8H2O from FPMD simulations at 22 ps. (c) Structure snapshot of Li4[Mn(IV)3(OH)3]·12H2O from FPMD simulations at 69 ps. Color coding: Mn = light green, O = red, H = white, W = blue, Si = gray, Li = purple, and water molecules = light blue sticks.

ligands together with the overall charge. Similarly, we label the corresponding POM with three Mn centers in oxidation state II as [Mn(II)3(H2O)3]7−. For brevity, we shorten the labels to Mn(VI), Mn(III), and Mn(II) when the systems under discussion are clear from the context. The oxidation of Mn(III) to Mn(IV) involves a proton-coupled electron transfer (PCET) mechanism where H2O ligands deprotonate as Mn(III) changes to Mn(IV). The label of the resulting POM structure with three Mn(IV) centers is [Mn(IV)3(OH)3]4−. In this study we consider only POMs in the presence of Li+ counterions. Earlier we introduced various arrangements of Li+ ions around the POM structure such that the overall system becomes neutral; for details, see Figure S1 of the Supporting Information.16 To explore the effect of explicit solvation, we started an FPMD simulation with the POM structure [Mn(III)3(H2O)3]4− and four Li+ counterions in configuration 1321 (Figure S1). In this structure, counterions are located in 4-fold coordinated positions, three of them close to the Mn

2. METHODS AND MODELS The original Keggin ion has the general formula [XM12O40]n−, with a heteroatom X at the center of an overall symmetrical (tetrahedral) arrangement of the metal atoms M; its structure is termed α-ion.17 We modeled an α-Keggin ion with X = Si and M = W (fully oxidized), where three neighboring M centers directly above the triangular face of the central SiO4 tetrahedron are substituted by M′ = Mn, the latter in oxidation states IV, III, or II (Figure 1a). Depending on the oxidation state, the terminal O centers of the substituted W centers convert to OH or H2O ligands (Figure 1). The full formula of the POM with all Mn in oxidation state III is [Mn(III)3(OH)3(H2O)3(A-α-SiW9O34)]4−. We refer to this nano-oxide structure by the label [Mn(III)3(H2O)3]4−, where we specify the oxidation state of the Mn centers and the corresponding B


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The Journal of Physical Chemistry C centers while the fourth ion is located in the other “lower” hemisphere of the metal oxide structure, opposite to the Mn triangle. This initial system was placed in a unit cell of 18 × 18 × 18 Å3, filled by water molecules, using the solvation module “gmx solvate” of the software GROMACS.34 That unit cell contained 148 H2O molecules, reproducing the density of bulk water, 1 g cm−3. FPMD simulations were carried out to equilibrate first the system (see below), before starting a production run of at least 10 ps. During this latter phase, we took 10 structure snapshots, separated by 1 ps, focusing on the POM itself, the Li+ counterions, and 8 water molecules in the first coordination shell of the Li ions, namely, only those molecules with Li−O distances up to 300 pm (Figure 1b). Before calculating the standard reduction potentials U0red for Mn(III/II) (see below for details), we optimized the structure of the POM itself, keeping the positions of the Li ions and the aqua ligands fixed, as obtained in the FPMD run, and applying the COSMO model for long-range solvation effect. The resulting reduction potentials exhibit standard deviations of at most 0.04 eV. As these values can be considered sufficiently small, we refrained from introducing more snapshots. The snapshots are quite similar with respect to the positions of the Li cations around the POM structure. Indeed, Si−Li distances exhibit RMSD values of 7−14 pm only, which is 2% of the distance. In contrast, Li−O distances to the POM and to aqua ligands are more flexible, as they exhibit RMSD values of up to 24 pm, which is up to 12% of the distances in question. Thus, the snapshots feature rather similar arrangements of the Li cations, but a fluctuating aqueous environment. In other words, the snapshots capture essential aspects of the electrolyte surrounding the POM structure. As next step, starting from the equilibrated solvated POM structure with all Mn in oxidation state III, we carried out a stepwise oxidization of the Mn(III) centers. In this process, we removed, one at a time, a hydrogen atom from the H2O ligand of each of the Mn(III) centers to create the corresponding Mn(IV) center with an OH ligand. Each hydrogen (proton + electron) removal was accompanied by an FPMD equilibration run of 4 ps. In this way, ultimately the model of a solvated POM structure [Mn(IV)3(OH)3]4− was created. This system also was equilibrated for ∼15 ps before entering a production run of more than 10 ps. In the same manner as for Mn(III/II), 10 structure snapshots (Figure 1c) were taken to be used for calculating the standard reduction potential of Mn(IV/III). For this system, we included 12 H2O molecules in the cluster model, in addition to the Li cations and the POM, i.e., all the aqua ligands of the first coordination shells of the Li ions. In addition, we carried out a computational experiment in which we probed the hypothesis35 of the PCET mechanism as well as the ability of our modeling procedure to describe such events. To this end, we simulated the oxidized system Mn(IV) for which we reduced the number of Li counterions to one, resulting in the neutral model Li[Mn(IV)3(H2O)3], where each Mn(IV) center carries an H2O ligand instead of OH. As initial state, we employed the POM in the structure with all Mn in oxidation state III. Before starting the equilibration simulation, we optimized the structure of the system at the PBE+U level to bring it to a local minimum with minimal forces. Already during this optimization, one of the three H2O ligands of the Mn(IV) centers deprotonated, and a H3O+ moiety was formed in the vicinity of the POM. The optimized system was equilibrated for 6 ps, during which the two remaining H2O ligands of the Mn(IV) centers of the POM

were deprotonated. The protons were released into the solvent region, also forming H3O+ moieties (see Figure S2). This deprotonated configuration of the POM, [Mn(IV)3(OH)3]4−, with 1 Li+ adsorbed on the POM surface and 3 H3O+ moieties in the solvent region of the unit cell, remained unchanged during the following 5 ps of the simulation. Thus, this computational experiment confirmed that H2O ligands initially assigned to the POM with Mn in oxidation state IV are not stable. Rather, these ligands of the Mn(IV) centers prefer to be deprotonated, yielding H3O+ ions in solution. This computational experiment also confirmed the proton-coupled electron transfer for the Mn(III/IV) oxidation, as already noted in the experimental study.35 The first-principles molecular dynamics calculations (FPMD simulations) were carried out with the plane-wave based Vienna ab initio simulation package, VASP, version 5.4.36−39 We used the PBE variant of the generalized gradient approximation (GGA) as exchange-correlation potential in the unrestricted Kohn−Sham (UKS) electronic structure calculations.40,41 The overall spin density was fixed at 12 unpaired electrons for the system Li4[Mn(III)3(H2O)3] and at 9 unpaired electrons for Li4[Mn(IV)3(OH)3]. The effect of the core electrons was represented by the full-potential projectoraugmented wave (PAW) method as implemented in VASP.42,43 Scalar relativistic effects were incorporated in the PAW potential via mass-velocity and Darwin corrections.44 To achieve a proper localization of d electrons of Mn and W, we applied a DFT+U variant45 where rotationally invariant Hubbard-like correction terms are introduced into the d blocks of the Kohn−Sham Hamiltonian as well as a corresponding term in the total energy.45 We chose the values U(3d Mn) = U(5d W) = 3.0 eV.46,47 Integrations over the Brillouin zone were carried out using the Γ-point only. To facilitate the FPMD runs, we used D atoms instead of H atoms, which allowed us to increase the time step to 0.5 fs. The temperature was set to 350 K using a Nosé−Hoover thermostat. The plane-wave energy cutoff was set to 300 eV. For calculating the standard reduction potentials, we used the software TURBOMOLE 6.6.48−50 In the UKS calculations, we employed the GGA functional PBE40,41 as well as the hybrid DFT approach B3LYP.51,52 To accelerate the DFT calculations, we applied the resolution-of-identity (RI-J) approximation for evaluating the Coulomb part of the electron−electron interaction, together with a suitable auxiliary basis set.53 We represented the Kohn−Sham orbitals using standard triple-ζ basis sets (def2-TZVP)54 together with effective core pseudopotentials for Mn (ecp-10-mwb)55 and W (def2-ecp),56 with 12 and 68 core electrons, respectively. In the UKS iterative process the total energy was converged to 10−6 au. For the structure optimizations, the energy gradient on each atomic center was required to be less than 10−3 au. In addition, we calculated charges and spin densities using a natural population analysis.57 The free energy of solvation ΔGsolv was estimated using the polarized continuum solvation model COSMO as implemented in TURBOMOLE.30 For more computational details, see refs 16 and 30. Standard reduction potentials U0red were estimated from the formal equation POM + 3e− → POM3 −

(1)

0 Ured = −ΔE1/3F − 4.28 (eV)

(2)

as

C


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The Journal of Physical Chemistry C where ΔE1 is the reaction energy of eq 1 and 4.28 eV is the reference for the normal hydrogen electrode.58 Previously, we showed that thermodynamic corrections to U0red, calculated using eq 2, are only about 0.02 eV.16 Therefore, they were neglected in this study.

Initially, in the overall configuration 1321 (Figure S1), each of the four Li cations is 4-coordinated to the POM [Mn(III)3(H2O)3]4−. During first 10 ps of the FPMD simulation, 3 Li cations leave their 4-hollow sites, of which two adjust to a monodentate coordination to the POM; the third Li ion returns to its 4-hollow site. After ∼18 ps, the coordination modes of all Li cations to the POM stabilized (Figure 2). We consider this situation as sufficiently equilibrated. In total, 32 ps of FPMD was carried out. We used the last 10 ps of the production run, between 22 and 32 ps, for collecting 10 structure snapshots. In the right-hand part of Figure 2, from 40 to 78 ps, we show the FPMD results of the fully oxidized POM Li4[Mn(IV)3(OH)3], af ter stepwise removal of three hydrogens from the system (see section 2). The data with Mn centers in mixed oxidation states, including the equilibration runs of 4 ps each, are shown in the middle part of Figure 2, between 32 and 40 ps. Interestingly, during the (formal) oxidation process, none of the Li cations underwent a significant change in position relative to the POM, although one Li+ (green line in Figure 2) changed its coordination from monodentate to outer sphere for a short time. The full oxidation to Li4[Mn(IV)3(OH)3], as just described, results in a separation of the Li cations from the POM structure, already at the beginning of the equilibration phase, at 42 ps (Figure 2). At the end of the equilibration, after simulating the system with Mn(IV) for ∼23 ps, at 63 ps total time in Figure 2, two Li cations no longer have any direct contact to the POM structure, CN = 0 (red and blue lines in Figure 2), one Li+ ion is monocoordinated to the POM, CN = 1 (green line in Figure 2), and another Li+ is bicoordinated, CN = 2 (pink line in Figure 2). Subsequently, we carried out a production run of 15 ps, and we took the structure snapshots during the final 10 ps. While the POM itself exhibits C3 symmetry, the distribution of the counterions in the surrounding electrolyte is not symmetric at all, independent of the oxidation state of the Mn centers. In this context, recall a similar computational result from an FPMD study of the tricarbonato complex of uranyl with two Ca2+ counterions in aqueous solution.60 This complex exhibits Cs symmetry, which is broken by the solvated Ca2+ cations which were calculated to bind to the complex at different strengths. Furthermore, although both POM systems, [Mn(III)3(H2O)3]4− and [Mn(IV)3(OH)3]4−, exhibit the same charge, −4e, one obtains two rather different distributions of Li cations around these POMs. Overall, 4 Li+ ions exhibit 10 Li−OPOM bonds when all Mn centers are in oxidation state III but only 3 Li−OPOM bonds for the system with three Mn(IV) centers. Leroy et al.61 studied various (nonsubstituted) Keggin ions in aqueous solution with Li+, Na+, and K+ cations by force-field MD simulations.61 In that study, the central atom of the Keggin structure was altered to change the overall charge of the POM from −3e to −5e.61 The authors suggested that POMs of a higher charge have a stronger propensity for forming ion pairs than POMs of a lower charge (see Table 1 of ref 61). Ion pairing is the result of two competing effects electrostatic attraction of oppositely charged ions and the solvation of these ions. If the gain in full solvation of the ions is larger than their interaction energy, then these ions will not undergo pairing, but rather stay separately solvated. The POM structures differ in the protonation state of the Mn ligands, H2O vs OH, and the oxidation state of the three

3. RESULTS AND DISCUSSION First we will discuss the equilibration of the systems studied and Li rearrangement around the POM in the presence of an explicit aqueous solvent (section 3.1). Then we examine the charges of the POMs and the spin densities of the corresponding Mn centers, obtained for the partially optimized snapshot structures, treated at the PBE and B3LYP levels of theory (section 3.2). The structure parameters obtained by the two methods are given in Tables S1 and S2. The main structural changes of these POMs upon reduction were already examined in our earlier work;16 as those same trends also hold for the present extended models, we refrained from discussing them here. Finally, we calculate the standard reduction potentials and analyze these results (section 3.3). 3.1. Generating Equilibrated Structures of Li4[Mn(III)3(H2O)3] and Li4[Mn(IV)3(OH)3]. In equilibrated systems, one expects that the positions of Li cations are relatively stable in the vicinity of the POM. During the equilibration and the FPMD production runs, we tracked the coordination number of each Li cation to the nearest O centers of the POM. We measured the Li−O distances to the O centers of the POM and determined the coordination number (CN Li−OPOM) of Li to the POM as the number of Li−OPOM bonds shorter than 300 pm (Figure 2). In water, typical Li−O bond lengths are

Figure 2. Moving average of coordination numbers CN of each Li cation to the O centers of the POM from FPMD simulations; averages calculated over 1 ps at steps of 0.5 ps. The first 32 ps of the simulation was carried out for the system Li4[Mn(III)3(H2O)3]; the next two intervals of 4 ps each represent in turn the systems Li4[Mn(III)2Mn(IV)(H2O)2(OH)] and Li4[Mn(III)Mn(IV)2(H2O)(OH)2]. The remainder of the simulation, from 40 ps, shows the results for the system Li4[Mn(IV)3(OH)3]. The data for the four Li+ cations are represented in different colors.

estimated at ∼200 pm for CN = 4.59 In this study we noticed that Li cations may exhibit coordination numbers up to 5. Therefore, we extended the upper limit for the “accepted” bonds to be counted for the CN Li−OPOM from 200 to 300 pm. Figure 2 shows the results for the systems studied. For easier perception we present moving average values of the corresponding CNs; averages are calculated over 1 ps at steps of 0.5 ps. D


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Table 1. Calculated Results for Mn Centers of the POMs Li4[Mn(IV)3(OH)3] and Li4[Mn(III)3(H2O)3] as Well as Their Reduced Forms: Average Atomic Charges q, Spin Densities ζ, and Standard Reduction Potentialsa ⟨U0red⟩ from Cluster Modelsb (CM) at the PBE and B3LYP Levels of Theory ζ, e

q, e Mn(X), Mn(X/X − 1)

IV

III

II

IV

III

2.83 2.84

3.75 3.76

⟨U0red⟩, eV II

IV/III

III/II

PBE Li4[Mn(IV/III)3(OH)3]0/3− CM, no H2O + solv CM, H2O + solv expc Li4[Mn(III/II)3(H2O)3]0/3− CM, no H2O + solv CM, H2O + solv expc

−3.78 −3.93

−6.71 −6.88

−3.75 −3.81

−6.68 −6.76

3.75 3.75

0.77 (0.03) 0.01 (0.02) 0.85d 4.66 4.65

0.35 (0.07) −0.08 (0.04) 0.65

B3LYP Li4[Mn(IV/III)3(OH)3]0/3− CM, no H2O + solv CM, H2O + solv expc Li4[Mn(III/II)3(H2O)3]0/3− CM, no H2O + solv CM, H2O + solv expc

−3.79 −3.92

−6.72 −6.88

−3.75 −3.80

2.93 2.92

−6.68 −6.76

3.84 3.85

3.84 3.84

1.63 (0.04) 0.77 (0.03) 0.85d 4.73 4.72

1.05 (0.07) 0.55 (0.04) 0.65

a Standard deviations over the set of snapshots given in parentheses. bPOM structure optimized in a fixed matrix of counterions, without and with explicit water molecules (H2O), surrounded by a polarizable continuum (solv); see text for details. cReference 35. dpH 6.

Mn centers, III vs IV. In consequence, the sizes of the POM structures are also different. Upon Mn(IV/III) reduction, the effective overall radius of the POM structures increases from 667 to 697 pm. From Tables S1 and S2 one can observe that typical Mn−O bonds elongate, when Mn(IV) reduces to Mn(III). The size change does affect the solvation energies. Indeed, for the bare POMs, [Mn(IV)3(OH)3]4− and [Mn(III)3(H2O)3]4−, we calculated solvation energies of −1891 and −1864 kJ mol−1, respectively, at the PBE level, with the COSMO solvation model. The stronger solvation effect suggests an easier dissociation of Li+ ions from the surface of the POM with Mn(IV). The solvation energies for the systems Li4[Mn(IV)3(OH)3] and Li4[Mn(III)3(H2O)3] with all Li adsorbed on the 4-hollow sites on the surfaces of the POMs (configurations 1321, Figure S1) were calculated at −282 and −398 kJ mol−1, respectively, using the same computational approach. Therefore, solvation stabilizes the POM structure with Mn(III) and Li cations on its surface more than the corresponding complex with Mn(IV). In summary, one expects a lower propensity for the formation of ion-pair structure motifs between Li cations and [Mn(IV)3(OH)3]4−. Thus, the formation of ion pair motifs is not just a consequence of the overall charge of a POM but also the oxidation state of the metal centers in question; the overall size of the POM structure also plays a role. 3.2. Charge Distribution and Spin Densities of the POMs. The structure snapshots used for further geometry optimization and subsequent examination contain the POM structures themselves, the neutralizing 4 Li cations, and 8 aqua ligands for Mn(III) and 12 aqua ligands for Mn(IV). Figures 1b and 1c show typical configurations. Table 1 contains average charges of the POMs and spin densities of the Mn centers obtained from the partially optimized snapshot structures calculated at the PBE and B3LYP levels. The charges calculated with the two exchange-correlation approximations are very similar (Table 1). A similar observation also

holds for the structure parameters from these two method variants (Tables S1 and S2). Corresponding bond lengths differ on average by 2 pm, but at most by 6 pm. This similarity of the structure results does not carry over to the results for the spin densities, which differ significantly between the hybrid DFT approach and the pure GGA exchange-correlation functional (Table 1). The B3LYP calculations yield more a localized spin distribution and therefore are expected to predict the redox potentials at a better accuracy. Thus, we will discuss in the following mainly the B3LYP results. First of all, we note that the spin densities (B3LYP level) about 2.92 e for Mn(IV), 3.84 e for Mn(III), and 4.72 e for Mn(II)do not depend on the arrangement and the explicit solvation of the Li cations (Table 1). For the test purposes, we also calculated the spin densities for the bare POMs (no counterions); the corresponding spin densities are identical to the results shown in Table 1. Therefore, as expected, the spin density is not affected by the presence of the counterion or other aspects of the solvation model. However, the spin density strongly depends on the exchange-correlation functional used (see Table 1). The effective charges of the POMs were derived from a natural population analysis, calculated as total charge of the system minus the sum of charges of all counterions and the corresponding aqua ligands present. Li is the most electronegative alkali metal; therefore, it does not keep its positive charge unless shielded by aqua ligands. For the systems with four Li+ counterions occupying 4-hollow sites and without explicit water, the effective charges of the POMs are calculated to be less negative compared to the models with rearranged Li cations and explicit aqua ligands (Table 1). Partially solvated Li cations maintain a larger positive charge. The effect is stronger for the POM with Mn(IV) centers and its reduced congener. In this case, the Li cations were more solvated; two out of four cations are in an outer-sphere coordination relative to the POM. More explicit water molecules present imply a E


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The Journal of Physical Chemistry C stronger screening of the Li cations, giving rise to a larger positive charge. In the case of the POM with Mn(III) centers, the Li counterions are stronger bound to the POM; no outersphere coordination is observed (see section 3.1). Therefore, the charge is less screened in this case. In summary, the local Li arrangement does not exert a notable effect on the spin densities of the Mn centers, while the geometry parameters are only slightly affected, mainly for the POM with Mn(II) centers (see Tables S1 and S2). The effective charges of the POMs are lower and therefore closer to the ideal charges of −4e (oxidized form) and −7e (reduced form), when the Li counterions are rearranged, occupying nonsymmetric positions around the POM. This effect is larger when Li ions exhibit outer-sphere coordination to the POM due to a better shielding by the explicit H2O molecules. 3.3. Standard Reduction Potentials. With eqs 1 and 2, we calculated standard reduction potentials U0red for each optimized snapshot structure (section 2). In Table 1, we show 0 the resulting average values ⟨Ured ⟩ and their standard deviations for the two exchange-correlation functionals PBE and B3LYP. As mentioned earlier, we expect B3LYP calculations to be more accurate due to a more localized spin density at the Mn centers. Therefore, we focus the following discussion on these latter results. In this study, we mainly compare two models, differing in the representation of the electrostatic field of the short-range electrolyte environment. In the original model, with four bare Li+ adsorbed at 4-hollow sites of the POMs,62 this electrostatic effect of the electrolyte field can be assumed to be overestimated, whereas from the model introduced here, reoptimized FPMD snapshots with explicit water molecules, a more adequate representation can be expected. To note, in the former model the whole system is optimized at the same level of theory. In contrast, in the present hierarchical model, only POM structure is optimized while keeping the positions of the Li cations and their aqua ligands fixed as obtained in the FPMD simulation. The total energies of the snapshot-derived partially optimized structures differ by up to 1.2 eV. However, the resulting U0red values vary by at most 0.1 eV(!). Thus, although different (rather distant) configurations on the potential energy surface have been considered, the resulting reduction potentials turn out to be rather similar. This is related to the fact that for all snapshots of the same system the Li coordination to the POM remains quite similar during the underlying trajectory of 10 ps (Figure 2), giving rise to a similar electrostatic effect of the electrolyte field on U0red. However, this may hint at a potential weakness of our procedure, as our simulation time is rather short because of the size of the system studied. This particular aspect could be tested in a future study of alternative counterions, using a classical force-field approach. The resulting ⟨U0red⟩ values decrease considerably when one uses the present extended model with explicit solvation, from 1.63 ± 0.04 to 0.77 ± 0.03 eV for Mn(IV/III) and from 1.05 ± 0.07 to 0.55 ± 0.04 eV for Mn(III/II) (Table 1, B3LYP section). Interestingly, the ⟨U0red⟩ values change by different amounts, depending on the reduction step of Mn: by 0.86 eV for Mn(IV/III) and by only 0.50 eV for Mn(III/II). This may be rationalized by the different local electrolyte structure (see section 3.1). However, there is the common trend for both reduction potentials: the further the Li+ cations are from the surface of the POM, and the lower is the calculated ⟨U0red⟩. The model with bare POMs and implicit solvation, without Li+

cations, represents a situation where the counterions may be considered as being far away compared to explicitly modeled Li cations. In that case, we calculated the U0red values at 0.52 eV for Mn(IV/III) and −0.01 eV for Mn(III/II). These latter results are in line with the trend just discussed. Higher U0red values imply easier reduction (addition of electrons) (see eq 2). A positioning of Li+ cations close to the POM creates a stronger positive electrostatic attraction for electrons. Therefore, electron transfer is easiest when Li+ cations all adsorbed at 4-hollow sites on the surface of the POM; the corresponding ⟨U0red⟩ values are the highest (Table 1). When Li+ cations are further away from the POM and shielded by water molecules, the positive field is weaker, and therefore the reduction is energetically less feasible; the ⟨U0red⟩ values are lower (Table 1). The least favorable reduction, with the lowest U0red values, are calculated for the bare POMs in combination with an implicit solvation model. The observed trend is in accordance with the energies of the LUMO, LUMO +1, and LUMO+2 levels of the neutral systems, before reduction (Table S3). Three lowest unoccupied molecular orbitals are destabilized when Li+ counterions are distant from the POM. For the Li4[Mn(IV)3(OH)3] system, the LUMO, LUMO+1, and LUMO+2 were destabilized by 0.7 eV on average compared to system with shielding water molecules. For Li4[Mn(III)3(H2O)3] the corresponding average destabilization is ∼0.5 eV (Table S3). The ⟨U0red⟩ values calculated in this study at the B3LYP level compare very well with experiment (Table 1).35 This comparison has to be done with care for the Mn(IV/III) reduction because the latter is a proton-coupled electron transfer. Therefore, the measured redox potential depends on the pH value used in the experiment.35 We estimate the U0red value without taking into account the protonation of the reduced POM. This roughly corresponds to a situation at high pH where protonation is prohibited. Therefore, we compare to the experimental value at the highest pH, 6, experimentally examined;35 the corresponding redox potential is measured at 0.85 eV. Our calculated value, 0.77 ± 0.03 eV, is very close indeed. For the Mn(III/II) reduction, the redox potential is measured at 0.65 eV,35 while the calculated value, 0.55 ± 0.04 eV, is similarly close (Table 1). Thus, with the extended model for the local electrolyte structure around POM presented in this study, we are able to reproduce the experimental redox potentials within 0.1 eV, i.e., at reasonable accuracy. Only a few computational studies on redox potentials of POMs have thus far been reported.25−27 The reduction energies of various Keggin and Dawson ions (bare, solvation treated by the COSMO method) were calculated with the functionals PBE and B3LYP. The absolute values underestimate experiment by up to 1 eV.25−27 However, relative values were reproduced rather well, in particular with the B3LYP approach.25,26 Our results for bare POMs without counterions, but with implicit solvation, show a similar accuracy: B3LYP values [0.52 eV for Mn(IV/III) and −0.01 eV for Mn(III/II)] underestimate the experimental redox potentials by up to 0.7 eV. Similar deviations from experiment are encountered for the calculations on redox potentials of transition metal ions in aqueous solution, when only the first solvation shell was explicitly accounted for.32 To reach an accuracy of ∼0.3 eV for transition metal ions in solution, two solvation shells had to be explicitly included in the quantum chemical model, in addition to invoking a polarizable continuum model;63 alternatively, a QM/MM embedding F


Article

The Journal of Physical Chemistry C approach was used with the first solvation shell in the QM partition.33 An excellent accuracy of 0.05 eV was reached for the Ru(III/II) reduction potential by employing a Boltzmann averaging over multiple molecular conformations for models with explicit treatment of the two solvation shells.64 Another noteworthy example for rather accurate calculations of Fe(III/ II), Os(III/II), and Ru(III/II) reduction potentials of solvated ions was obtained by applying the COSMO-RS solvation model.65 This latter studies succeeded without an explicit treatment of the second solvation shell. Thus, an adequate representation of solvation effects is essential for calculating the redox potentials of solvated transition metal ions. For calculating redox potentials of POMs, the present work demonstrates that beyond the aqueous environment, one has to account also for the atomistic structure of the electrolyte environment near the surface of the POMs; i.e., also the positions of the counterions play a crucial role for predicting reduction potentials. Thus, an adequate representation of the electrolyte field in the vicinity of the nanostructure POM solute is necessary. In our modeling, we observe rather strong effects of the electrolyte. Adding four Li+ cations to the bare POM and using only COSMO as solvation model affects the standard reduction potentials by ∼1 eV. Specifically, for the Mn(IV/ III) reduction potential, we calculated U0red = 0.52 eV for the bare POM (B3LYP+COSMO), but U0red = 1.63 ± 0.04 eV for POM + 4Li+ at the same level of theory. Some studies assumed that the cations of the electrolyte do not affect the redox potentials in a major way.35 Toth and Anson66 examined experimentally how the Fe(III/II) redox potentials of ironsubstituted Keggin ions with a central GeO4 tetrahedron (total charge of POM is −5e) changes for different cations in the electrolyte. They observed positive shifts of the order of tens of meV, with the size of the shift increasing in the order Rb+ > K+ > Na+ > Li+ (see Table 2A of ref 66). Interestingly, Friedl et al.35 did not observe any change upon replacing Li+ by K+ in the electrolyte when they measured Mn(IV/III) and Mn(III/ II) reduction potentials of tri-Mn-substituted POMs.35 It would be interesting to compare computationally the effect of various counterions on the electrochemical behavior of POMs. However, for the FPMD approach chosen here this will be rather costly as shown by our test calculations with K+ counterions. For a comparable quality, a substantially larger unit cell will have to be chosen as the K+ counterions are notably larger and interact weaker with the POM surface than Li+ ions. Careful calibration of a force-field approach will be required to ensure comparability with the present FPMD description of the dynamical behavior of counterions and POMs in aqueous solution.

this study where the counterions are treated together with solvation shells. In the model calculations, we compared POMs with the three Mn centers in the oxidation states IV and III together with four Li+ counterions to achieve a neutral system. These models were treated in ab initio molecular dynamics (FPMD) simulations and periodic boundary conditions together with 148 explicit water molecules in the unit cell. Both systems were equilibrated, followed by production runs of more than 10 ps. The equilibrated systems exhibit different local structures of the electrolyte: Li+ forms more ion-pair structural motifs with the POM with three Mn(III) centers compared to the POM with three Mn(IV) centers. Finally, from each production run, we took 10 snapshots with the POM, the four Li+ counterions, and the aqua ligands from their first solvation shells to calculate the standard reduction potentials using a hybrid DFT approach. This explicit (atomistic) modeling strategy of the aqueous electrolyte solution yields redox potentials in excellent agreement with experiment.35 In summary, the suggested approach, relying on FPMDderived structures, admits a reasonable description of the effect of solvated counterions and the fluctuating aqueous medium, while keeping the computational costs manageable. With this study, we convincingly showed how important the local atomistic structure of the electrolyte is for a reliable prediction of electrochemical properties of nanosized and nanostructured systems containing transition metals oxides. The good agreement achieved between measured redox potentials and calculated values is unprecedented for such complex molecular charge carriers. In view of our results, any computational modeling of the electrochemical behavior of TMO overlayers and surfaces has to include explicitly the electrolyte in the model. Symmetry-breaking effects of the ions in solution in the vicinity of TMO films/surfaces may affect the accuracy of the absolute values of the calculated redox potentials. The local structure of the TMO part of the system is important as well.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.8b05426. Schematic representation of various Li arrangements around the POM; structure parameters of the POMs studied and their reduced congeners, calculated at the PBE and B3LYP levels of theory; electronic structure data of the POMs [Mn(IV)3(OH)3]4− and [Mn(III)3(H2O)3]4− with and without Li+ counterions as well as with and without explicit aqua ligands; equilibrated unit cell with Li[Mn(IV)3(OH)3]3− and three H3O+ in an aqueous environment (PDF) xyz files of the optimized snapshots used for calculating the reduction potentials Mn(IV/III) and Mn(III/II) (ZIP)

4. SUMMARY AND CONCLUSIONS We demonstrated on the example of a tri-Mn-substituted Wbased Keggin ion in an electrolyte environment that one has to take into account the full atomistic structure of this multicomponent system when aiming at an adequate accuracy of calculated reduction potentials of such nanosized and nanostructured systems. Accordingly, the reduction potentials are notably affected by the local structure of the electrolyte. Models of bare POMs and an implicit solvation treatment underestimate the standard reduction potentials. Models of POMs and counterions adsorbed at their surface (as well as an implicit solvation treatment) overestimate standard reduction potentials. Therefore, we employed a hierarchical approach in

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (N.R.). ORCID

Alena Kremleva: 0000-0003-3330-0862 Notker Rösch: 0000-0002-4769-4332 Notes

The authors declare no competing financial interest. G


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The Journal of Physical Chemistry C

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(23) Pope, M. T.; Müller, A. Polyoxometalate Chemistry: An Old Field with New Dimensions in Several Disciplines. Angew. Chem., Int. Ed. Engl. 1991, 30, 34−48. (24) Freire, C.; Fernandes, D. M.; Nunes, M.; Abdelkader, V. K. POM & MOF-based Electrocatalysts for Energy-related Reactions. ChemCatChem 2018, 10, 1703−1730. (25) Aparicio, P. A.; Poblet, J. M.; López, X. Tungsten Redox Waves in XMW11O40(n-) (X = P, Si, Al and M = W, Mo, V, Nb, Ti) Keggin Compounds - Effect of Localised/Delocalised Charges. Eur. J. Inorg. Chem. 2013, 2013, 1910−1916. (26) Parent, L.; Aparicio, P. A.; de Oliveira, P.; Teillout, A. L.; Poblet, J. M.; López, X.; Mbomekalle, I. M. Effect of Electron (de)Localization and Pairing in the Electrochemistry of Polyoxometalates: Study of Wells-Dawson Molybdotungstophosphate Derivatives. Inorg. Chem. 2014, 53, 5941−5949. (27) Aparicio, P. A.; López, X.; Poblet, J. M. Ability of DFT Calculations to Correctly Describe Redox Potentials and Electron (de)Localization in Polyoxometalates. J. Mol. Eng. Mater. 2014, 2, 1440004. (28) Cramer, C. J.; Truhlar, D. G. Implicit Solvation Models: Equilibria, Structure, Spectra, and Dynamics. Chem. Rev. 1999, 99, 2161−2200. (29) Tomasi, J. Thirty Years of Continuum Solvation Chemistry: A Review, and Prospects for the Near Future. Theor. Chem. Acc. 2004, 112, 184−203. (30) Klamt, A.; Schüürmann, G. COSMO: A New Approach to Dielectric Screening in Solvents with Explicit Expressions for the Screening Energy and its Gradient. J. Chem. Soc., Perkin Trans. 2 1993, 5, 799−805. (31) Klamt, A. Conductor-like Screening Model for Real Solvents: A New Approach to the Quantitative Calculation of Solvation Phenomena. J. Phys. Chem. 1995, 99, 2224−2235. (32) Marenich, A. V.; Ho, J. M.; Coote, M. L.; Cramer, C. J.; Truhlar, D. G. Computational Electrochemistry: Prediction of LiquidPhase Reduction Potentials. Phys. Chem. Chem. Phys. 2014, 16, 15068−15106. (33) Wang, L.-P.; Van Voorhis, T. A Polarizable QM/MM Explicit Solvent Model for Computational Electrochemistry in Water. J. Chem. Theory Comput. 2012, 8, 610−617. (34) Pronk, S.; Páll, S.; Schulz, R.; Larsson, P.; Bjelkmar, P.; Apostolov, R.; Shirts, M. R.; Smith, J. C.; Kasson, P. M.; van der Spoel, D.; et al. GROMACS 4.5: A High-throughput and Highly Parallel Open Source Molecular Simulation Toolkit. Bioinformatics 2013, 29, 845−854. (35) Friedl, J.; Al-Oweini, R.; Herpich, M.; Keita, B.; Kortz, U.; Stimming, U. Electrochemical Studies of Tri-manganese Substituted Keggin Polyoxoanions. Electrochim. Acta 2014, 141, 357−366. (36) Kresse, G.; Hafner, J. Ab Initio Molecular Dynamics for Liquid Metals. Phys. Rev. B: Condens. Matter Mater. Phys. 1993, 47, 558−561. (37) Kresse, G.; Hafner, J. Ab Initio Molecular Dynamics Simulation of the Liquid-Metal-Amorphous-Semiconductor Transition in Germanium. Phys. Rev. B: Condens. Matter Mater. Phys. 1994, 49, 14251− 14269. (38) Kresse, G.; Furthmüller, J. Efficient Iterative Schemes for Ab Initio Total Energy Calculations using a Plane-Wave Basis Set. Phys. Rev. B: Condens. Matter Mater. Phys. 1996, 54, 11169−11186. (39) Kresse, G.; Furthmüller, J. Efficiency of Ab-initio Total Energy Calculations for Metals and Semiconductors using a Plane-Wave Basis Set. Comput. Mater. Sci. 1996, 6, 15−50. (40) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865−3868. (41) Perdew, J. P.; Burke, K.; Ernzerhof, M. Erratum: Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1997, 78, 1396−1396. (42) Blöchl, P. E. Projector Augmented-Wave Method. Phys. Rev. B: Condens. Matter Mater. Phys. 1994, 50, 17953−17979. (43) Kresse, G.; Joubert, D. From Ultrasoft Pseudopotentials to the Projector Augmented-Wave Method. Phys. Rev. B: Condens. Matter Mater. Phys. 1999, 59, 1758−1775.

ACKNOWLEDGMENTS The authors thank Sven Krüger for helpful discussions. The authors gratefully acknowledge funding (Project pr94je) by the Gauss Centre for Supercomputing e.V. by providing computing time on the GCS Supercomputer SuperMUC at Leibniz Supercomputing Centre.

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Modeling the Effect of the Electrolyte on Standard Reduction

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