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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 A. N. Masliy,* T. N. Grishaeva, and A. M. Kuznetsov Department of Inorganic Chemistry, Kazan National Research Technological University, K. Marx Street 68, 420015 Kazan, Russian Federation

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S Supporting Information *

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 = 6−8) 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 molecularcontinuum solvation model are 1.607, 0.949, 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 highspin states in accord with the classical ligand field theory are realized.

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INTRODUCTION

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 reactivity.7,14,19,23 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 wellknown, 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, good agreement was achieved between the calculated and available experimental values of the electrode potentials.24−35 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.

Cucurbit[n]urils (C6nH6nN4nO2n, CB[n], n = 5−10) are 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 and theoretical and experimental study of the structure and properties of CB[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 articles.1−16 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 studies.7,17,18 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. © 2019 American Chemical Society

Received: April 30, 2019 Revised: June 5, 2019 Published: June 5, 2019 5341

DOI: 10.1021/acs.jpca.9b04053 J. Phys. Chem. A 2019, 123, 5341−5346

Article

The Journal of Physical Chemistry A

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G298(aq) = E0(aq) + δG298

COMPUTATIONAL DETAILS E standard electrode potentials of half-reactions, measured relative to the standard hydrogen electrode E(H)can be calculated from the following relationship: 0

E 0 = −ΔG 0 /nF − E(H)

where E0(aq) is the total energy of the system in aqueous solution at 0 K, calculated using the Gaussian09 program, and 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.

(1)

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where ΔG0 is the Gibbs free energy of the reaction, F is the Faraday constant, n is the number of electrons involved in the reaction, and the quantity E(H) (the Trasatti potential) is determined from the following expression: ÅÄÅ 1 ÑÉÑ 0 0 (chem) E(H ) = −ÅÅÅÅ ΔGdis (H 2) + ΔGion (H) + ΔG hyd (H+)ÑÑÑÑ/F ÅÇ 2 ÑÖ

RESULTS AND DISCUSSION The standard electrode potential E0 of the Fe(III)/Fe(II) redox couple in aqueous solution corresponds to the halfreaction Fe3 +(aq) + e = Fe 2 +(aq)

(2)

3+

(5)

2+

where Fe (aq) and Fe (aq) aqua-ions are six-coordinated highspin aqua complexes [Fe(H2O)6]3+ and [Fe(H2O)6]2+, correspondingly. Therefore, the half-reaction 5 can be represented as follows:

which contains the Gibbs free energy of the hydrogen molecule dissociation and 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 eq 1 is calculated as the difference between the total free energies of products and reactants: ΔG 0 = G 0(aq)(prod) − G 0(aq)(react)

(4)

[Fe(H 2O)6 ]3 +(aq) + e = [Fe(H 2O)6 ]2 +(aq)

(6)

To calculate for this half-reaction the free energy gain ΔG0 in the formula 1 from the relationship 3, the supermoleculecontinuum (or cluster-continuum) solvation model can be employed. In this approach, the metal cation (Fe3+ 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 references 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 2 hydration shells around the central ion increases the accuracy of calculated Cu(II) hydration free energy up to 2 kcal/mol. 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 12 water molecules hydrogen-bonded with 6 watermolecular ligands of the first coordination sphere. Thus, instead of eqs 5 and 6 we get

(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 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 eq 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 of the following. The optimizations 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 in 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

[Fe(H 2O)6 ·12H 2O]3 +(aq) + e = [Fe(H 2O)6 ·12H 2O]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 2 Å. 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 5342

DOI: 10.1021/acs.jpca.9b04053 J. Phys. Chem. A 2019, 123, 5341−5346

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its first coordination sphere contains six water molecules with a tetragonally distorted octahedral environment of the central atom (i.e., [Cu(H2O)6]2+ aqua complex). These molecules form hydrogen 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

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 the Supporting Information section).

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 the Supporting Information section (Table S4). The calculations according to the proposed technique of the standard electrode potentials E0 for half-reactions 6 and 7 using relations 1 and 3 yielded the values of 2.284 and 0.786 V, respectively. In comparison with the experimental value of E0(Fe(III)/Fe(II)), equal to 0.771 V,42 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 Supporting Information section present the bond lengths r(M−OH2) and standard electrode potentials M(III)/M(II) for some other sixcoordinated 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 E0(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 d-metal complexes and macrocyclic cavitands CB[n]. At the next stage, based on 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) aquaions 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

Figure 2. Optimized structures of the inclusion compounds [Fe(H2O)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 the Supporting Information section).

Cartesian coordinates are given in Supporting Information section). In accord with the above, the Fe(III)/Fe(II) halfreaction in this case can be represented as follows: [Fe(H 2O)6 ]3 + @CB[6](aq) + e = [Fe(H 2O)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 (E0 = 0.786 V) in the bulk of solution (eq 7). As shown earlier in refs 12, 13, and 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 H2O molecules of the second coordination sphere of the 5343

DOI: 10.1021/acs.jpca.9b04053 J. Phys. Chem. A 2019, 123, 5341−5346

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The Journal of Physical Chemistry A 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(H2O)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:

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 12 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−OH2) to 1.95 Å (Table 2).

[Fe(H 2O)6 ·4H 2O]3 + @CB[n](aq) + e = [Fe(H 2O)6 ·4H 2O]2 + @CB[n](aq)

(n = 7, 8)

(9)

The redox potentials calculated for the Fe(III)/Fe(II) halfreactions proceeding in CB[6−8] are listed in Table 1. Table 1. Calculated Redox Potentials of Half-Reactions Involving Fe(III) and Fe(II) Aqua-Ions inside the Cavities of CB[n] (n = 6−8) and in the Bulk of Aqueous Solution E0, V

half-reaction 3+

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

2+

[Fe(H2O)6] @CB[6](aq) + e = [Fe(H2O)6] @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)

r(Fe−OH2), Å

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:

aqua complex

m=3

m=2

[Fe(H2O)6]m+@CB[6] [Fe(H2O)6·4H2O]m+@CB[7] [Fe(H2O)6·4H2O ]m+@CB[8] Fe(H2O)6·12H2O ]m+(aq) [Fe(H2O)6]m+(aq) (exptl44)

1.950 2.066 2.077 2.057 2.000

2.151 2.162 2.160 2.180 2.120

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 2.15 Å, close to those in CB[7], CB[8], and [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. 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 example, due to the O2 + 4H+ + 4e = 2H2O halfreaction with the standard redox potential E0 = 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 half-reaction [Fe(H2O)6]3+@CB[6](aq) + e = [Fe(H2O)6]2+@

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: 5344

DOI: 10.1021/acs.jpca.9b04053 J. Phys. Chem. A 2019, 123, 5341−5346

The Journal of Physical Chemistry A 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 half-reactions 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.

ACKNOWLEDGMENTS

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REFERENCES

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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 CB[7] and CB[8], these aqua-ions include four additional 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 hydrogenbridging 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, 0.949, 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 = 0.786 V), 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 low-spin state with a total spin S = 1/2. ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.9b04053.

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This work was supported by the Ministry of Education and Science of the Russian Federation (Project No. 4.5382.2017/ 8.9).

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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 (PDF)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

A. N. Masliy: 0000-0001-7494-8089 Notes

The authors declare no competing financial interest. 5345

DOI: 10.1021/acs.jpca.9b04053 J. Phys. Chem. A 2019, 123, 5341−5346

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DOI: 10.1021/acs.jpca.9b04053 J. Phys. Chem. A 2019, 123, 5341−5346