Standard Redox Potentials of Fe(III) Aqua Complexes Included Into

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Standard Redox Potentials of Fe(III) Aqua Complexes Included Into the Cavities of Cucurbit[n]urils (n = 6-8): A DFT Forecast Alexey Nikolajevich Masliy, Tatiana Nickolaevna Grishaeva, and Andrey Mikhailocich Kuznetsov J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.9b04053 • Publication Date (Web): 05 Jun 2019 Downloaded from http://pubs.acs.org on June 5, 2019

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The Journal of Physical Chemistry

Standard Redox Potentials of Fe(III) Aqua Complexes Included Into the Cavities of Cucurbit[n]urils (n = 6-8): A DFT Forecast A.N. Masliy*, T.N. Grishaeva, A.M. Kuznetsov, Department of Inorganic Chemistry, Kazan National Research Technological University, 420015, Kazan, K. Marx Street 68, Russian Federation e-mail: [email protected]

ABSTRACT An approach for estimating at the DFT level of the standard redox potentials of the inclusion compounds based on Fe(III) and Fe(II) aqua complexes inside the cavities of cucurbit[n]urils (n=68) has been proposed. These inclusion compounds were established to have compositions which can be described by the formulas [Fe(H2O)6]3+/2+@CB[6] and [Fe(H2O)6·4H2O]3+/2+@CB[7,8]. Redox potentials E0 relative to the standard hydrogen electrode for the half-reaction Fe(III)/Fe(II) in the CB[n] cavities calculated at the PBE/TZVP level within the molecular-continuum solvation model are 1.607 V, 0.949 V and 0.847 V for n = 6, 7, and 8, respectively. The obtained values indicate a relative increase of the oxidative ability of Fe(III) aqua ions in the cavities of the examined CB[n], especially in CB[6], compared to the calculated value (E0=0.786 V) for the same half-reaction in the bulk of aqueous solution. Possible causes of the detected trend are discussed. The calculations also showed that the Fe(III) aqua complex inside the CB[6] changes its magnetic properties, transforming into a low-spin state with a total spin S=1/2, whereas for all other systems high-spin states in accord with the classical ligand field theory are realized.

INTRODUCTION Cucurbit[n]urils (С6nH6nN4nO2n, CB[n], n=5-10) is a family of macrocyclic cavitands with a fairly rigid, highly symmetric structure and a hydrophobic inner cavity, which is accessed through two hydrophilic portals formed by carbonyl groups. One of the significant features of CB[n] is their ability to form supramolecular inclusion compounds by the host-guest mechanism with the full or partial entry of the guest particle into the cavity of cavitand. The binding of the “guest” with the “host” CB[n] occurs mainly due to Van der Waals interactions with the “host” cavity and the formation of hydrogen bonds with carbonyl oxygen atoms of two CB[n] portals. This leads to the preferred binding of CB[n] with neutral and positively charged "guests". The results of works devoted to the synthesis, theoretical and experimental study of the structure and properties of CB 1 ACS Paragon Plus Environment

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[n] and their compounds, as well as the thermodynamic and kinetic aspects of the formation of guest-host complexes, are summarized in a number of reviews and articles1-16. CB[n] have low toxicity at doses many times higher than those required for use in pharmacology, as has been proven in a number of studies7,17,18. This suggests that in the near future they will be able to completely replace molecular containers, such as cyclodextrins, widely used for targeted drug delivery. To date, anticancer drugs containing compounds of the inclusion CB[7] and CB[8] on the basis of platinum, palladium and gold complexes19–22 have already been patented. There is evidence that the inclusion of metal complexes into the cavities of CB[n] can change their structural, spectral, magnetic, electrochemical and photochemical characteristics, as well as reactivity7,14,19,23. One of the important characteristics of a complex is its standard redox potential, which determines the behavior of the complex in various kinds of redox processes. Whereas the standard redox potentials of many metal complexes are well known, experimental measurement of the corresponding potentials for complexes embedded in CB[n] presents a certain problem. From our point of view, theoretical prediction based on quantum chemical calculations can be promising for these purposes. Quantum-chemical methods previously have been successfully used in many studies for calculating standard redox potentials involving a number of complexes in aqueous solutions as well as in proteins. In most cases, between the calculated and available experimental values of the electrode potentials was achieved good agreement24–35. Unfortunately, examples of the application of quantum chemistry methods for predicting the redox potentials of complexes embedded in CB[n] are not known to us. For this reason, in this work, we first attempted to calculate the standard redox potential of Fe(III)@CB [n]/Fe(II)@CB[n] (n = 6-8) in comparison with the experimental value for the half-reaction Fe(III)/Fe(II) in the bulk of aqueous solution. COMPUTATIONAL DETAILS E0 – standard electrode potentials of half-reactions, measured relative to the standard hydrogen electrode E(H), can be calculated from the following relationship: E0 = –ΔG0/nF – E(H)

(1)

where ΔG0 is the Gibbs free energy of the reaction, F is the Faraday constant, n is the number of electrons involving in the reaction, and the quantity E(H) (the Trasatti potential) is determined from the expression: (2) which contains the Gibbs free energy of the hydrogen molecule dissociation, of ionization of the hydrogen atom and the “chemical” energy of the proton hydration. In our calculations, the most probable value of the Trasatti potential equal to 4.30±0.02 V was used (see, for example, the discussion and references in ref.29). The Gibbs free energy ΔG0 in (1) is calculated as the difference between the total free energies of products and reactants: ΔG0 = G0(aq)(prod) – G0(aq)(react)

(3)

The total free energies G0(aq) of the aqua complexes were calculated quantum-chemically taking into account the influence of the dielectric environment (aqueous solution) within the framework of the molecular-continuum model. It is known that purely continuum solvent models 2 ACS Paragon Plus Environment

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give unsatisfactory results in calculations of the thermodynamic properties of ionic species that have highly concentrated charge densities together with strong local solute/solvent interactions. More adequate results can be obtained using a combined molecular-continuum model, when several solvent molecules (for example, water) are included in the nearest environment of a particle (complex), and the interaction of such a supermolecule with a dielectric medium is taken into account in the continuum model (e.g., polarized continuum model PCM). Calculations of the Gibbs free energy by (3) require optimization of the geometry of the complexes, taking into account the influence of the solvent, followed by conducting a thermochemical analysis to calculate the total Gibbs energy of the initial reactant and product. Performing such quantum chemical calculations for inclusion compounds is extremely difficult due to the significant requirements imposed on computing systems and considerable expenditure of computation time. For this reason, we used a more economical calculation methodology consisting in the following. The optimization of the geometrical parameters of the complexes and inclusion compounds as well as the calculation of thermal corrections to energy in calculating the Gibbs free energy were carried out for the gas phase using the Priroda program package36 in the framework of the PBE37 density functional method employing for all atoms the atomic basis set TZVP of Ahlrich et al.38. For the gas-phase optimized geometry, the solvent effects were taken into account in the framework of the PCM model39 using the Gaussian0940 program package at the same level of theory PBE/TZVP. The standard Gibbs free energy of a particle in aqueous solution was obtained by the formula: G298(aq) = E0(aq) + δG298,

(4)

where E0(aq) is the total energy of the system in aqueous solution at 0K, calculated using the Gaussian09 program, δG298 is the correction to the total energy to obtain the Gibbs free energy for the gas phase (at 298.15 K and pressure 1 atm), calculated using the Priroda program package. RESULTS AND DISCUSSION The standard electrode potential E0 of the Fe(III)/Fe(II) redox couple in aqueous solution corresponds to the half-reaction: Fe3+(aq)+ e = Fe2+(aq),

(5)

where Fe3+(aq) and Fe2+(aq) aqua ions are six-coordinated high-spin aqua complexes [Fe(H 2O)6]3+ and [Fe(H2O)6]2+, correspondingly. Therefore, the half-reaction (5) can be represented as follows: [Fe(H2O)6]3+(aq)+ e =[Fe(H2O)6]2+(aq)

(6)

To calculate for this half-reaction the free energy gain ΔG0 in the formula (1) from the relationship (3), the supermolecule-continuum (or cluster-continuum) solvation model can be employed. In this approach, the metal cation (Fe 3+ or Fe2+) together with six water molecules of its first hydrate sphere are considered to form a single species referred to as a supermolecule. Such supermolecule (or a cluster) is treated quantum-mechanically and its interaction with a dielectric surrounding in solution is taken into account using a continuum model (e.g., polarized continuum model PCM). The cluster-continuum solvation model has been successfully used in extensive prior studies (e.g., see ref.41 and ref. therein). For instance, results presented in that study demonstrate that the use of a supermolecule consisting of a Cu(II) ion with 18 water molecules forming two hydration shells around the central ion increases the accuracy of calculated Cu(II) hydration free energy up to 2 kcal/ mol. 3 ACS Paragon Plus Environment


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Taking into account these established facts, we decided to extend the composition of the Fe(III) and Fe(II) aqua complexes by supplementing them with water molecules of the second coordination sphere. The second coordination sphere of these aqua complexes in aqueous solution was modeled by adding twelve water molecules hydrogen-bonded with six water-molecular ligands of the first coordination sphere. Thus, instead of equations (5) and (6) we get: [Fe(H2O)6·12H2O]3+(aq) + e = [Fe(H2O)6·12H2O]2+(aq)

(7)

Figure 1A shows the starting structure used to optimize the geometry of aqua complexes [Fe(H2O)6·12H2O]3+/2+. In this structure, the central atom of the complex is symmetrically surrounded by six water molecules with the r(Fe-OH2) distance of about 2Å. Further in the examined structures, each water molecule of the first coordination sphere is connected by hydrogen bonds with two water molecules of the second coordination sphere, which, in turn, are connected by two hydrogen bonds with two other water molecules of the first coordination sphere. Thus, each water molecule of the first coordination sphere forms four hydrogen bonds, and each water molecule of the second coordination sphere forms two hydrogen bonds. The length of the hydrogen r(O…H-O) bonds was taken about 2.5 Å. Hydrogen atoms not participating in the formation of hydrogen bonds in the water molecules of the second coordination sphere were oriented so that the full symmetry of the entire system would be broken. As a result of the full optimization of the geometry without any symmetry constrains, the starting geometry was transformed to the structure of Fe(III) and Fe(II) aqua complexes shown in Figure 1B. As can be seen from this figure, a network of hydrogen bonds between the molecules of the first and second hydration sphere of the complexes is preserved. However, unlike the starting structure, the water molecules of the first hydration sphere have two or four hydrogen bonds with the molecules of the second sphere. Qualitatively, the structures of both complexes are the same, although there are some differences in geometrical parameters. These differences can be analyzed in detail from the atomic Cartesian coordinates for these complexes given in SI section(Table S4). The calculations according to the proposed technique of the standard electrode potentials E 0 for half-reactions (6) and (7) using relations (1) and (3) yielded the values of 2.284 V and 0.786 V, respectively. In comparison with the experimental value of E 0(Fe(III)/Fe(II)), equal to 0.771 V42, the calculated value for the half-reaction (6) differs significantly from the experimental one, while the model which takes into account 12 additional water molecules of the second coordination sphere, leads to a fairly good agreement of the theory and experiment. For comparison, Tables S1 and S2 in the SI section present the bond lengths r(M–OH 2) and standard electrode potentials M(III)/M(II) for some other six-coordinated octahedral metal complexes (M = Ti, V, Cr, Mn and Co), which were also calculated taking into account 18 water molecules in the first and second hydrate sphere. Without analyzing here the results of these calculations, we note that the obtained values of E 0(M(III)/M(II)) generally agree quite well with the experimental values, which largely confirms the adequacy of the model used. Thus, the obtained results suggest that the proposed computational methodology can be suitable for predicting the electrode potentials of complex chemical systems, in particular inclusion compounds based on dmetal complexes and macrocyclic cavitands CB[n]. At the next stage, based the proposed approach, the electrode potentials for the Fe(III)/Fe(II) half-reaction inside the cavities of CB[n] (n=6-8) were evaluated. It is quite obvious that the number of water molecules in the second coordination sphere of the Fe(III) and Fe(II) aqua-ions inside CB[n] depend on the size of the CB[n] cavity. Recently, our work43 showed that in the case of the incorporation of the Cu(II) aqua-ion into the CB[6] cavity its first coordination sphere contains six water molecules with a tetragonally distorted octahedral environment of the central atom (i.e. [Cu(H 2O)6]2+ aqua complex). These molecules form hydrogen 4 ACS Paragon Plus Environment

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bonds directly with the oxygen atoms of the CB[6] portals and firmly fix the position of the aqua complex in the cavity of cavitand. We assumed that Fe(III) and Fe(II) ions in CB[6] will have a hydrate environment similar to that of Cu(II), and corresponding inclusion compounds can be described as [Fe(H2O)6]3+/2+@CB[6].Thus, in this case, the role of the second coordination sphere in the [Fe(H2O)6]3+/2+ aqua complexes is played by the inner wall of CB[6], and not by water molecules, as in the case for these complexes in the bulk of aqueous solution. The optimized geometric structure of the [Fe(H2O)6]3+/2+@CB[6] inclusion compounds is shown in Figure 2A (atomic Cartesian coordinates are given in SI section). In accord with the above, the Fe(III)/Fe(II) half-reaction in this case can be represented as follows: [Fe(H2O)6]3+@CB[6](aq) + e = [Fe(H2O)6]2+@CB[6](aq)

(8)

The calculated redox potential of this half-reaction is 1.607 V. As can be seen, this value is almost two times larger than what we obtained earlier for the Fe(III)/Fe(II) half-reaction (E 0=0.786 V) in the bulk of solution (Eqn. 7). As shown earlier in ref.12,13,43, the fixation of metal complexes in CB[n] with volumes larger than CB[6], for example, CB[7] or CB[8], is supported by additional water molecules that form bridge hydrogen bonds with ligands of the inner coordination sphere and oxygen atoms of the CB [n] portals. In ref.43, when simulating the incorporation of Cu(II) aqua-ions into the CB[8] cavity, it was established that four H 2O molecules of the second coordination sphere of the Cu(II) aqua complex perform this function. In other words, the inclusion compounds in this case have the composition [Cu(H2O)6·4H2O]2+@CB[8]. We assumed that these qualitative results can be transferred to the Fe(III) and Fe(II) aqua-ions inside CB[7] and CB[8], and the corresponding inclusion compounds can be represented by the formula [Fe(H 2O)6·4H2O]3+/2+@CB[n] (n=7,8). Optimized structures of these compounds are shown in Figure 2B and 2C. Taking into account the arguments presented above, the half-reaction for the Fe(III)/Fe(II) redox couple in the CB[7] and CB[8] cavities can be represented by the following equation: [Fe(H2O)6·4H2O]3+@CB[n](aq) + e = [Fe(H2O)6·4H2O]2+@CB[n](aq) (n=7,8)

(9)

The redox potentials calculated for the Fe(III)/Fe(II) half-reactions proceeding in CB[6–8] are listed in Table 1. Table 1 Calculated redox potentials of half-reactions involving Fe(III) the cavities of CB[n] (n=6-8) and in the bulk of aqueous solution Half-reaction 3+ [Fe(H2O)6] @CB[6](aq) + e = [Fe(H2O)6]2+@CB[6](aq) {[Fe(H2O)6·4H2O]3+}@CB[7](aq) + e = {[Fe(H2O)6·4H2O]2+}@CB[7](aq) {[Fe(H2O)6·4H2O]3+}@CB[8](aq) + e = {[Fe(H2O)6·4H2O]2+}@CB[8](aq) [Fe(H2O)6·12H2O]3+(aq) + e = [Fe(H2O)6·12H2O]2+(aq)

and Fe(II) aqua-ions inside E0, V 1.607 0.949 0.873 0.786

As can be seen from these data, the calculated redox potentials significantly depend on the size of the CB[n] cavity, with the largest E0 value equal to 1.607 V observed for the smallest CB[6] cavitand. In the case of the largest CB[8] cavitand, the redox potential (0.873 V) is close to the potential calculated for the Fe(III)/Fe(II) redox couple in the bulk of aqueous solution (0.786 V). The results obtained indicate that with a decrease in the size of the cavitand, the oxidative activity of the Fe(III) aqua-ion included in the cavity of CB[n] increases and, correspondingly, the reductive activity of the Fe(II) aqua-ion decreases. It is known that in aqueous solution, the [Fe(H2O)6]2+ aqua complex with the electron configuration t2g4eg2 due to the loss of one electron is easily oxidized, for example, by molecular oxygen, to [Fe(H2O)6]3+ and acquires the energetically more stable electron configuration t2g3eg2:

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In this case, the [Fe(H2O)6]2+ and [Fe(H2O)6]3+ complexes are high-spin ones with a total spin S=2 and S=5/2, respectively. Our calculations showed that similar patterns are also observed for the all considered complexes inside CB[n] with the exception of the [Fe(H2O)6]3+@CB[6]. In this complex, the doublet state with one unpaired electron (S=1/2) is energetically most favorable. Accordingly, the oxidation of [Fe(H2O)6]2+ @CB[6] can be represented by the following scheme:

Thus, for [Fe(H2O)6]3+@CB[6], the electron configuration t2g5eg0 is energetically most stable. In the ligand field theory, such a configuration is usually characteristic for octahedral complexes in the case of the strong ligand field (large values of the splitting parameter Δ). When the Fe(III) aqua-ion is encapsulated into the CB[6] cavity, its nearest hydrate environment is substantially rearranged: instead of twelve water molecules of the second coordination sphere, the inner wall of the cavitand plays the role of the second coordination sphere. Due to its rigid structure, this wall facilitates some shortening of the distance between the six water molecules of the first coordination sphere with the central ion, which manifests itself in a decrease in the distance r(Fe-OH 2) to 1.95Å (Table 2). For the Fe(II) aqua-ion, due to its smaller total charge, such changes are less pronounced, and therefore the distance r(Fe-OH2) in [Fe(H2O)6]2+@CB[6] is equal to 2.15Å, close to those in CB[7], CB[8] and in [Fe(H2O)6·12H2O]2+(aq) (Table 2). Thus, it can be formally concluded that in the [Fe(H2O)6]3+@CB[6] inclusion compound, the H2O molecules manifest a stronger ligand field compared to that in free aqua complexes, where the H2O ligands are considered as ligands of the weak field. This is the reason for the appearance in [Fe(H2O)6]3+@CB[6] of the electron configuration t2g5eg0, which is usual for the strong field ligands. Table 2 Calculated average r(Fe-OH2) bond lengths in Fe(III) and Fe(II) aqua complexes inside the cavities of CB[n] (n=6-8) and in the bulk of aqueous solution Aqua complex r(Fe-OH2), Å m=3

m=2

[Fe(H2O)6]m+@CB[6]

1.950

2.151

[Fe(H2O)6·4H2O]m+@CB[7]

2.066

2.162

m+

2.077

2.160

m+ (aq)

2.057

2.180

2.000

2.120

[Fe(H2O)6·4H2O ] @CB[8] Fe(H2O)6·12H2O ]

[Fe(H2O)6]m+(aq) (exp.44)

Thus, the obtained results demonstrate an increase in the redox potential E0 of the Fe(III)/Fe(II) half-reactions with the inclusion of Fe(III) and Fe(II) aqua-ions into the CB[n] cavity (n=6-8), with the highest value for the CB[6] cavitand with the smallest size of the internal cavity. An increase of the redox potential indicates an increase in the oxidative ability of Fe(III) aqua-ions inside CB[n] and, accordingly, a decrease in the reductive ability of Fe(II) aqua ions. It is known that in aqueous solution the [Fe(H2O)6]2+ aqua complexes can easily be oxidized to form [Fe(H2O)6]3+. As noted above, this can occur under the influence of molecular oxygen, for 6 ACS Paragon Plus Environment

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example, due to the O2 + 4H+ + 4e = 2H2O half-reaction with the standard redox potential E 0=1.23 V, which is less than the standard redox potential of the half-reaction Fe3+(aq) + e = Fe2+(aq) (E0=0.771 V). Our results demonstrate that the Fe(II) aqua-ion, embedded in the cavity CB[6], cannot be oxidized by oxygen from the thermodynamic point of view, since the redox potential of the halfreaction [Fe(H2O)6]3+@CB[6](aq) + e = [Fe(H2O)6]2+@CB[6](aq), according to our estimates, is about 1.6 V, which is larger than E0=1.23 V for the above half-reaction with O2. Based on these considerations, it can be assumed that the macrocyclic CB[6] cavitand can serve as a kind of container for “storage” of Fe(II) aqua-ions in order to prevent them from possible oxidation. The theoretical results we obtained are more likely to be predictive, and therefore the practical application of our finding requires experimental examination. We believe that the proposed methodology of evaluating the redox potentials of halfreactions involving the Fe(III) and Fe(II) aqua-ions in the CB[n] cavities (n=6-8) can be easily applied for the study of redox properties of other metal complexes that are relevant from the viewpoint of their practical application in modern supramolecular chemistry. CONCLUSIONS Structures of inclusion compounds of Fe(III) and Fe(II) aqua complexes with CB[n] (n=6-8) have been established based on quantum-chemical modeling. In CB[6], which has a relatively small internal cavity, the inclusion compounds of Fe(III) and Fe(II) aqua-ions can be represented by the formula [Fe(H2O)6]3+/2+@CB[6]. Inside the larger cavitands СB[7] and СB[8], these aqua-ions include additional four H2O molecules in the second hydration sphere. These molecules are involved in the structural fixation of the aqua complexes in the macrocycles cavities due to hydrogen-bridging bonds with the portal oxygen atoms. In this case, the corresponding inclusion compounds can be represented by the formula [Fe(H2O)6·4H2O]3+/2+@CB[7,8]. Using the molecular-continuum solvation model, we calculated the redox potentials E0 relative to the standard hydrogen electrode for the half-reactions of Fe(III)/Fe(II) in the cavities CB[n]: 1.607 V, 0.949 V and 0.847 V for n = 6, 7, and 8, respectively. In comparison with the calculated potential of the same reaction in the bulk of aqueous solution (E0=0.786V), the obtained values indicate a relative increase in the oxidative ability of Fe(III) aqua ions in the cavities of examined CB[n], especially in CB[6]. The calculations performed in this work showed that, in accordance with the ligand field theory, the Fe(III) and Fe(II) aqua complexes both in the bulk of the aqueous solution and inside CB[n] cavity are high-spin, with the exception of the [Fe(H2O)6]3+ aqua complex, which in CB[6] changes its magnetic properties, transforming into a lowspin state with a total spin S=1/2. Acknowledgment This work was supported by the Ministry of Education and Science of the Russian Federation (Project No. 4.5382.2017/8.9). Supporting Information Supplementary data associated with this article (tables presenting Cartesian coordinates of Fe(III) and Fe(II) aqua complexes in the bulk of aqueous solution as well as in the cavities of CB[6-8] modeled in this study) can be found in the online version of this paper.



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A

B

Figure 1 − Start (A) and optimized (B) structures of [Fe(H2O)6·12H2O]3+/2+ aqua complexes (atomic Cartesian coordinates for these complexes are given in SI section)



A

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B

C Figure 2 − Optimized structures of the inclusion compounds [Fe(H 2O)6]3+/2+@CB[6] – A, [Fe(H2O)6·4H2O]3+/2+@CB[7] – B and [Fe(H2O)6 ·4H2O]3+/2+@CB[8] – C (atomic Cartesian coordinates for these structures are given in SI section)


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TOC Graphic

Standard Fe(III)/Fe(II) redox potential In aqueous solution E0calc= 0.786 V

In the cavity of CB[6] E0calc = 1.607 V


Standard Redox Potentials of Fe(III) Aqua Complexes Included Into

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