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Computational Electrochemistry as a Reliable Probe of Experimentally Elusive Mononuclear Non-Heme Iron Species Daniel Bím, Lubomír Rulíšek, and Martin Srnec J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b02698 • Publication Date (Web): 01 May 2018 Downloaded from http://pubs.acs.org on May 4, 2018

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The Journal of Physical Chemistry

Computational Electrochemistry as a Reliable Probe of Experimentally Elusive Mononuclear Non-Heme Iron Species Daniel Bím,a,b Lubomír Rulíšekb and Martin Srneca,*

a

J. Heyrovský Institute of Physical Chemistry, The Czech Academy of Sciences, Dolejškova 3, Prague

8, 18223, Czech Republic. b

Institute of Organic Chemistry and Biochemistry, The Czech Academy of Sciences, Flemingovo nám.

2, Prague 6, 16000, Czech Republic.

Corresponding Author *E-mail: [email protected]

1 ACS Paragon Plus Environment

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ABSTRACT Despite the growing number of reported FeIVO complexes, an unambiguous experimental characterization of their redox properties, such as one-electron reduction potentials, remains a challenging task. To this aim, we describe an efficient and straightforward theoretical protocol for accurate calculations of redox potentials and calibrated the protocol on a set of diverse 37 mononuclear non-heme iron (NHFe) redox couples. It is shown that the methodology, further applied to a set of ten FeIVO species, not only serves for near-quantitative predictions of reduction potentials, but it is also an elegant tool for interpretation of the experimental electrochemical data. The general need for such a computational methodology is illustrated on the prototypical example of the (N4Py)FeIVO complex, whose electrochemistry has been studied for many years and still raises many questions.


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INTRODUCTION Iron, as the most abundant redox-active metal in biology, appears in diverse functional forms, such as Fe/S,1 S-adenosylmethionine radical,2 heme iron,3 and mononuclear and binuclear non-heme iron (NHFe and NHFe2)4 enzymes. Due to its versatility in Nature, much effort has been devoted to preparation of novel (bioinspired) iron-containing model complexes, including mononuclear NHFe biomimetics, which are in focus of this study. An important common theme for all of these species is that their chemistry is closely related to their redox properties, which are in turn determined by many factors: variability in oxidation, spin, and protonation states, molecular charges, types of ligands, coordination geometries (ligand fields), and solvent (protein) environments. Despite the growing body of computational, mostly density functional theory (DFT)based, studies of reaction mechanisms of biological and synthetic redox-active NHFe complexes,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20 formulation of a robust and reliable methodology for calculations of their redox properties (i.e., reduction potentials) is still in the ongoing effort of many groups. Such a protocol is envisaged as being a highly useful tool for: (i) the interpretation of electrochemical data, including the assignment of redox couples and characterization of their geometric/electronic properties, (ii) the description of redox and catalytic properties of otherwise experimentally elusive NHFe species, and (iii) correlations of their electron-transfer, proton-coupled electron-transfer, and H-atom-abstraction reactivities. Recently, several computational protocols or approaches that aim at the correct prediction of reduction

potentials

of

transition

metal

containing

complexes

were

reported.21,22,23,24,25,26,27,28,29,30,31,32,33 These efforts were motivated by relatively successful applications of computational electrochemistry

in

the

realm

of

small-sized,

rigid


compounds

in

less

polar


environments,34,35,36,37 where computations not only provided accurate numbers, but also assisted in interpretations of experimental data. For more charged solutes and/or more polar, protic solvents, a reliable prediction of redox potentials has been limited by the accuracy of description of solvation effects (in addition to accurate computation of electron affinities for reduction of the solute).38,39,40 For such cases, an improvement at the level of an implicitsolvation description has been only recently achieved by employing a new generation of modern solvation models such as COSMO-RS41,42 or SMD.43 Alternatively, an approach aiming at the improved description of solvation contributions to reduction potentials through a variable temperature hydrogen atom abstraction/addition (VT-HAA) scheme was developed in our laboratory.44 A strategy employing a parametrized pseudo-counterion correction was recently developed by Matsui et al.45 Herein, we report an efficient COSMO-RS based computational protocol for calculation of one-electron reduction potentials that benefits from its calibration on an unprecedentedly diverse set of nearly 40 mononuclear NHFe redox couples. To prove its accuracy and robustness, the methodology was further applied to redox properties of selected non-heme FeIVO complexes – systems whose electrochemical data pose great challenges for their correct interpretation. Demonstrating its strength in assisting with the identification of redox couples involved in various electrochemical processes that have been subject of controversies over many years, we believe that the methodology has a potential to elucidate key correlations between reactivities and redox properties of many NHFe complexes.


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COMPUTATIONAL METHODS Theoretical background for calculation of reduction potentials The one-electron reduction potential (E° in V) is defined as a quantity reflecting Gibbs free energy change upon 1e− reduction of a solute, –∆Gred/ox (= – (Gred – Gox) = ∆Gox/red) : E°(H) = ∆Gox/red – E°abs[reference] (+ Gsolv,H+)

(1)

where ∆Gox/red (= Gox – Gred) is the free energy difference between the oxidized and the reduced state of a solute, E°abs[reference] is the absolute potential of a reference electrode, and Gsolv,H+ is the free energy of solvation of a proton (all terms on the right-hand-side of Eq. 1 are in eV). The term Gsolv,H+ is included only if one-electron reduction of a solute is coupled with its concomitant protonation (then, we refer to proton-coupled reduction potential, E°H). Note that three common reference electrodes with their absolute potentials in different solvent environments as well as Gsolv,H+ are listed in Table 1. The Gibbs free energy differences ∆Gox/red from Eq. 1 are evaluated using the equation: ∆G = ∆Eel + ∆Gsolv + ∆[EZPVE + pV – RT lnQ]

(2)

where ∆Eel (= Eel,ox – Eel,red) is the in vacuo energy difference between oxidized and reduced structures, ∆Gsolv (= ∆Gsolv,ox − ∆Gsolv,red) is the difference in their solvation energies, and ∆[EZPVE + pV – RT lnQ] is the difference in the thermal enthalpic and entropic contributions (ZPVE – zero-point vibrational energy; Q – molecular partition function).

Table 1. Absolute reduction potentials of three reference electrodes as well as the solvation free energies of a proton in various solvents.a Solvent: CH3CN H2O

DMSO

DMF

THF

Fc+/0 b

4.98e

5.04e

4.97f

5.17f

SCEc

4.60e

NHEd

4.68g 4.28h 5 ACS Paragon Plus Environment


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Gsolv(H+) −260.2i −265.9j −273.3i a Reduction potentials are reported in eV for 298 K (these are approximated in this work as temperature-independent b

constants)

and

solvation

free

energies

in

kcal/mol.

Ferrocene/ferrocenium. cSaturated calomel electrode. dNormal hydrogen electrode. eRef. 46.

f

Ref. 47. gRef. 48. hRef. 49. iRef. 50. jRef. 51.

Quantum-chemical calculations of reduction potentials If not stated otherwise, calculations were carried out with the Turbomole 6.6 program.52 All of the structures were optimized using the BP86 functional,53,54 the def-TZVP basis set,55 and the zero-damping dispersion correction56 (denoted as -D3), with the inclusion of the effect of solvation on geometry optimizations by employing the implicit conductor-like screening model (COSMO)57 with a dielectric constant specific for a given solvent. The calculations were expedited by expanding the Coulomb integrals in an auxiliary basis set, the resolutionof-identity (RI-J) approximation.58 The equilibrium geometries of reduced/oxidized forms were then used to calculate all of the terms contributing to ∆G (Eq. 2). (i) The ∆Eel term was calculated using the hybrid functionals (B3LYP,59 PBE060,61) and RI-J approximation, combined with the -D3 correction and the def2-TZVPD62 basis set. Alternatively, the BP86+x%HF/def2-TZVP level of theory, including Hartree–Fock exchange contributions of x = 10%, 20%, or 25%, was used, employing the Gaussian09 program.63 (ii) The temperaturedependent ∆[EZPVE + pV – RT lnQ] term was obtained from frequency calculations with the rigid rotor/harmonic oscillator approximation (for p = 1 bar), considering low-frequency vibration modes (≤100 cm−1) to contribute to Q as hindered rotors.64 (iii) ∆Gsolv was calculated using the conductor-like screening model for real solvents (COSMO-RS) with the radii-based

isosurface

cavity

and

the

COSMOtherm

parameter

set

BP_TZVPD_FINE_C30_1501.ctd as available in COSMOtherm15.65 The COSMO-RS calculations were carried out following the recommended protocol: RI-BP86-D3/def2-


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TZVPD/COSMO(εr = ∞) ≡ ECOSMO,∞ and RI-BP86-D3/def2-TZVPD/in vacuo ≡ Ein single-point calculations were used to calculate Gsolv(T) = (ECOSMO,∞ – Ein RS(T),

vacuo)

vacuo

+ µCOSMO-

where µ(T) is the temperature-dependent COSMO-RS chemical potential as defined in

ref. 41. In the main article, the methodologies based on the RI-B3LYP-D3 and BP86+x%HF functionals for ∆Eel are denoted as the B3LYP-D3/COSMO-RS and BP86+x%HF/COSMORS levels of theory, respectively. If not stated otherwise, reduction potentials were calculated using the free energies of the lowest ground spin states. The complete active space self-consistent field (CASSCF) and multiconfiguration pair-density functional theory (MC-PDFT) calculations were carried out using the MOLCAS 8.2 program.66 For all atoms, the ANO-RCC basis set, contracted to [6s5p3d2f1g] for Fe, [5s4p2d1f] for the chelating P and Si atoms, [4s3p2d] for chelating N and C atoms, [3s2p] for other N, C and B atoms and [2s] for H atoms, was used. The second-order Douglas-KrollHess (DKH2) one-electron spinless Hamiltonian was applied for all the calculations in order to allow for spin-free relativistic effects.67,68 In all the CASSCF calculations, a level shift of 5 a.u. was used in order to improve convergence. To approximate the two-electron integrals, the Cholesky decomposition technique with a threshold of 10−6 was used.69 The MC-PDFT energies were obtained using the tBLYP functional on top of the DFT-optimized geometries with the active space including 6 electrons in 4 orbitals (4×3dFe), 7 electrons in 4 orbitals and 8 electrons in 4 orbitals for [FeII(SiPiPr3)(N2)]+, [FeI(SiPiPr3)(N2)] and [Fe0(SiPiPr3)(N2)]−, respectively.



RESULTS AND DISCUSSION Experimental and Calculated Reduction Potentials of Non-Heme Iron Complexes All of the NHFe complexes studied here are depicted in Figure 1. The systems possess different ligands (including redox non-innocent molecules such as nitric oxide), which translates into a multitude of coordinating atoms (C, N, O, F, S, Cl, Si, P) that give rise, together with different coordination geometries, to distinct ligand fields (octahedral, trigonalbipyramidal, tetrahedral). As such, the selected NHFe systems form a rich pool of structural frameworks comprising 37 experimentally defined reversible (= ‘Nernstian’) redox systems. Within this set, there are significant variations in total molecular charge (from +3 to −4), iron oxidation state (from V to 0), total spin state (from S = 5/2 to S = 0), solvent environment (from nonpolar tetrahydrofuran to polar water), temperature, and reference electrode (listed in Table 1). This variability in geometric/electronic structure, solvent, and temperature is reflected by a wide range of reduction potentials (see the experimental data − E°expt in Table 2).


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Figure 1: Geometric structures of synthetic non-heme iron complexes, specified in Table 2 and Table 3 (the label X denotes various ligands). 9 ACS Paragon Plus Environment


Page 10 of 27

Reduction potentials calculated at the B3LYP-D3/COSMO-RS level of theory are summarized in Table 2. The oxidized and reduced forms of solutes were assumed to be in their lowest spin states, as predicted by calculations. The energetics of three lowest spin states (that differ in spin multiplicity) for each form is available in Table S1. For systems with experimentally determined ground spin states of the oxidized and/or reduced forms (Sox/red;expt), we obtained 89 % of correct predictions (see the Sox and Sred values in Table 2 and Table S2). For remaining 11 %, the error in calculated splitting between two lowest spin states is estimated to be less than 4.0 kcal mol-1, as deduced from a rather small mean unsigned deviation of calculated reduction potentials from the experimental data (see below). Keeping in mind the fact that spin-state energetics remain very challenging for electronicstructure calculations such as DFT methods,70,71,72,73,74,75 as well as for its sensitivity with respect to structural and solvation perturbations,76 we consider the performance of the B3LYP-D3/COSMO-RS approach for such a broad and diverse set of the NHFe systems to be satisfactory.

Table 2. Calculated reduction potentials (E°calc) for a diverse set of mononuclear NHFe redox couples. The experimental data taken from the literature are provided for comparison (E°expt). Information on the calculated and experimental ground spin states of the oxidized and reduced forms as well as the experimental conditions (reference electrode, solvent, temperature) is also included. Redox couple [FeV/IV(PhB(tBuIm)3)(N)]+/0 [Fe

IV/III

(TMG3tren)(CN)]

3+/2+

[FeIV/III(Me3cyclam-acetate)F]2+/+ [Fe

IV/III

2+/+

[Fe

IV/III

2+/+

(Me3cyclam-acetate)Cl]

Soxb

td

1/2 (1/2)

h

h

tbp

0 (0)

oct

1 (1)

oct

Sredc

5/2 (5/2) h

Reference electrodeg

h

5/2 (5/2)

1

E°exptf [mV]

Solvent

T [°C]

−918

−530

Fc+/0

THF

22

h

1188

1400

Fc+/0

CD3CN

−40

h

1259

1230

Fc+/0

CH3CN

25

h

1430

1380

Fc+/0

CH3CN

25

+/0

0 (0)

5/2 (5/2)

h

E°calcd,e [mV]

h

oct

1 (1)

5/2 (5/2)

1347

1150

Fc

CH3CN

25

[FeIII/II(OH)(H3Buea)]-/2-

tbp

5/2

2

−1846

−1850

Fc+/0

DMF

25

[FeIII/II(OH)(H3Buea)]-/2-

tbp

5/2

2

−1809

−1790

Fc+/0

DMSO

25

+/0

[Fe

(Me3cyclam-acetate)N3]

Ligand Fielda

III/II

(TMG3tren)(CN)]

2+/+

tbp

5/2 (5/2)

[FeIII/II(cyclam-acetate)Cl]+/0

oct

1/2 (1/2)

[FeIII/II(cyclam-acetate)(N3)]+/0

oct

1/2 (1/2)

h h h

h

−354

−270

Fc

CD3CN

−40

h

−477 (−931)

−640

Fc+/0

CH3CN

−

h

-614 (−1014)

−750

Fc+/0

CH3CN

−

2 (2) 2 (0) 2 (0)


j j

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[FeIII/II(Me3cyclam-acetate)F]+/0

oct

+/0

oct

[FeIII/II(Me3cyclam-acetate)N3]+/0

oct

[Fe

[Fe

III/II

(Me3cyclam-acetate)Cl]

III/II

Ph

(SiP 3)(CH3)]

+/0

[FeIII/II(SiPiPr3)Cl]+/0 [FeIII/II(SiPPh3)Cl]+/0 [Fe

III/II

[Fe

III/II

(N3PySO2)(NCS)] Me2

N4(tren))(N3)]

+/0

5/2 (5/2) 5/2 (5/2)

[Fe

(CN)6]

[FeIII/II(edta)]-/2[Fe

III/II

3+/2+

(bipy)3]

[FeIII/II(phen)3]3+/2+ [Fe

III/II

3-/4-

[Fe(N3PyS)(NO)]

2+/+

[Fe(N3PyS)(NO)]

+/0

[Fe(SMe2N4(tren))(NO)]2+/+

25

+/0

−570

Fc

THF

25

−670

Fc+/0

THF

−

h

−975

−400

Fc+/0

j

THF

−

+/0

CH3CN

25

−1

2

−603

−410

SCE

CH3CN

25

i

2

−623

−335

SCE

CH3CN

25

2

−545

−805

SCE

CH3CN

25

h

754

810

SCE

CH3CN

20

h

1104

771

NHE

H2O

25

h

135

370

NHE

H2O

25

h

593

−120

NHE

H2O

25

h

911

1110

NHE

H2O

25

h

932

1130

NHE

H2O

25

1/2 (1/2)

oct

1/2 (1/2)

oct

5/2 (5/2)

oct

1/2 (1/2)

oct

5/2 (5/2)

oct

1/2 (1/2)

oct

1/2 (1/2)

h h h h h h h

h

1 (1) 1

2 (2) 2 (2) 0 (0) 2 (2) 0 (0) 0 (0)

h

29

5

NHE

H2O

25

2 (0)

h

−257 (−517)

−226

Fc+/0

CH3CN

25

1/2

−3196

−2300

Fc+/0

THF

25

−1767

−1000

Fc

+/0

THF

−

−3037

−2100

Fc+/0

THF

−

−3099

−2200

Fc+/0

2 (2)

1/2 (1/2) h

tbp

1 (1)

tbp

1/2 (1/2) 1 (1)

tbp

3/2 (3/2)

h

3/2 (1/2)

oct

0

0 3/2 (3/2)

h

0

oct

h

1/2

h

tbp

oct

h

h

h

1 (1)

3/2 (1/2) h

Fc

j

−99 (−168)

tbp

[Fe(TMG3tren)(NO)]2+/+

25

CH3CN

2 (0)

tbp

[Fe(TMG3tren)(NO)]

CH3CN

Fc+/0

i

[FeII/I(SiPPh3)(CH3)]0/-

3+/2+

Fc

−360

5/2

5/2

[FeI/0(SiPiPr3)(N2)]0/-

−290

−375

oct

5/2 (5/2)

[FeII/I(SiPPh3)Cl]0/-

−231

−732

h

oct

(SiPiPr3)(N2)]+/0

25

−1286

1 (1)

oct

II/I

CH3CN

+/0

h

3/2

[FeIII/II(N3PyS)(NCCH3)]2+/+

[Fe

(ox)3]

Fc+/0

h

tbp

oct

3-/4-

2 (2)

1 (1)

[FeIII/II(SMe2N4(tren))(CN)]+/0

III/II

h

−614

−532

2 (2)

1 (1)

5/2

(TPEN)]

h

3/2

5/2

[FeIII/II(H2O)6]3+/2+

h

h

2 (2)

3/2

oct

3+/2+

h

tbp

oct

III/II

h

tbp

[FeIII/II(SMe2N4(tren))(OAc)]+/0

[Fe

(S

+/0

5/2 (5/2)

h

1 3/2 (3/2)

547

670

−1459

−1340

278 (−4)

13

−1471 (−1189)

−1180

302

450

h

j j j

THF

−

+/0

CH3CN

−

Fc+/0

CH3CN

−

Fc

+/0

CH3CN

25

Fc

+/0

CH3CN

25

SCE

CH3CN

−

Fc

j j

j

a

Ligand field geometries are characterized by abbreviated symbols: td (four-coordinate tetrahedron), tbp (five-coordinate trigonal-bipyramid), or oct (six-coordinate octahedron). bCalculated ground spin state of the oxidized form of a solute. cCalculated ground spin state of the reduced form of a solute. d B3LYP-D3/COSMO-RS level of theory (for PBE0 functional and BP86+x%HF/COSMO-RS, see Table S3 and Figure S1). All reduction potentials are based on the lowest-lying ground spin states, as determined by calculated free energies (reduction potentials calculated according to the experimentally determined spin states are shown in parentheses). eInclusion of scalar relativistic contributions has a negligible effect on the calculated E° (for details, see Figure S2). fReferences, along with details on experimental electrochemical potentials, are shown in Table S3. gThe list of reference electrodes and their absolute reduction potentials in different solvents are provided in Table 1. hThe experimental ground spin state value (in parentheses) taken from the literature. iFrom ref. 77, S = 1/2 is dominantly populated at T < 130 K, while S = 5/2 becomes accessible at ambient temperature. jWhere the experimental temperature is not available, T was assumed to be 25 °C in the calculation).

It can be seen that reduction potentials calculated at the B3LYP-D3/COSMO-RS level are also in very good agreement with the experimental data (Table 2). The only exceptions are for Si/P-ligated complexes Fe(SiPPh3)(X) and Fe(SiPiPr3)(X), see Figure 1, for which E°calc is significantly more negative than E°expt (Figure S3). This failure of the DFT-based 11 ACS Paragon Plus Environment


methodology may result from a possible delocalization error, which overstabilizes the oxidized form of a solute and which we attribute to an artificially large delocalization of dFe electron density over Si/P ligating atoms as tested at various level of theory, including delocalization-error free MC-PDFT theory78,79,80 (cf. Figure S4). Excluding the SiPPh3 and SiPiPr3-ligated complexes, E°calc correlates with the experimental data with an R2 of 0.94 (interpolation line: E°calc [mV] = 0.988 E°expt [mV] − 25.1). The mean unsigned error (MUE) of the computed potentials is 0.17 V (the region lying within the MUE is marked by gray diagonal strips in Figure 2).81 If we take into account (i) limitations of the theoretical protocol (as discussed above), (ii) inaccuracies of considered absolute potentials of the reference electrodes, as well as (iii) possibly non-negligible variations in measured E° due to seemingly unimportant changes in experimental conditions, such as for example a choice of the supporting electrolyte (see Ref. 82 for how much this can influence ferrocene, a prototypical ‘Nernstian’ redox potential), the MUE of 0.17 V computed for such a large and diverse set of NHFe species that we gathered from various experimental works reported in literature is, in our opinion, very encouraging. It can be mentioned that Roy et al.21 reported the mean deviation of ~0.16 V for calculated reduction potentials of ferrocene and small low-charged first-, second-, and third-row transition-metal compounds. However, they also observed a significant deterioration of their computed results in going to more charged (anionic and cationic) species. For a similar set of compounds, Liang et al.26 showed a mean absolute deviation of 0.23 V using the B3LYP functional combined with the IEFPCM solvation model. We also note that Hughes et al.23 calculated E° for 95 first-row transition-metal complexes with the mean deviation of only 0.12 V. However, despite the large number of complexes in their database, only the octahedral structures with metal oxidation states altering mostly between II and III are included (in addition to this, authors introduced an empirical correction scheme for 12 ACS Paragon Plus Environment

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B3LYP). From this perspective, we consider our approach to be of a more general applicability in NHFe redox chemistry.

Figure 2. Plots of calculated vs. experimental electrochemical potentials associated with the complexes from Figure 1. Interpolation is indicated by a dashed red line, while the region lying within the mean unsigned error is indicated by a gray diagonal strip. Panels A–F: redox couples classified according to the total charge (A), different solvent environments (B), reference electrodes (C), ligand field of ox/red forms (D; octahedral; trigonal-bipyramidal;



tetrahedral), iron oxidation state (E), and total spin states (HS – high spin, LS – low spin, IS – intermediate spin) (F). The MUE values for each of groupings in all of the panels are given in Table S4.

Importantly, the B3LYP-D3/COSMO-RS methodology performs very well over a wide range of reduction potentials for NHFe complexes, irrespective of their molecular properties (highlighted in Figures 2A-F). Specifically, in Figure 2A, the reduction potentials are divided into groups according to the overall molecular charges of the oxidized/reduced forms. The accuracy of the computed values is independent of these charges, indicating a well-balanced description of solvation effects by the COSMO-RS approach. Overall, a reliability of COSMO-RS is also documented in Figure 2B and 2C, in which reduction potentials are color coded according to the solvent and reference electrodes used. Similarly, the particular ligand field geometry does not appear to have any significant effect on the predicted accuracy (cf. octahedral vs. trigonal-bipyramidal structures in Figure 2D). In Figure 2E, the reduction potentials are sorted according to metal oxidation states of the redox couples. This shows that E°calc values of the most numerous FeIII/FeII couples are predicted with comparable accuracy to the others. Systems including the motifs {FeNO}6/7 and {FeNO}7/8 with redox-non-innocent NO and spanning a range of 2 V are also satisfactorily predicted. The only FeV/FeIV couple present in the set is offset by ca. 0.39 V from the experimental value. Finally, in Figure 2F, redox couples are classified according to the total spin states. Herein, we recognize couples such as LSox/HSred or ISox/LSred, where LSox or ISox is an oxidized form in its low or intermediate spin state, while HSred would correspond to the reduced form in its high spin state (note for example that the LS, IS and HS states of an FeIV complex would correspond to S = 0, 1 and 2, respectively). From Figure 2F, six spinox/spinred combinations are uniformly scattered along the ‘E°expt = E°calc’ diagonal, mostly falling into the MUE region of ≤ 0.17 V. A notable exception are the E°calc values for all four


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low-spin/low-spin (LSox/LSred) couples that are ca. −0.30 V systematically shifted from the diagonal, which is consistent with the tendency of B3LYP to overstabilize species with unpaired electrons. This is mostly attributed to the HF exchange contributions as justified at the BP86+x%HF/COSMO-RS level of theory which gives the shifts of −0.23 V, −0.20 V and −0.12 V for x = 25%, 20% and 10%, respectively. No systematic shift of E°calc relative to

E°expt is observed for any other molecular property and solvent environment, cf. Figure 2. Among the mononuclear NHFe species, the high-valent iron-oxo complexes, i.e. complexes with the FeIVO core have attracted a lot of attention. This core is responsible for reactivity of many NHFe enzymes and biomimetic complexes towards H-atom abstraction (HAA) from unreactive C−H bonds. It has been shown that HAA reactivity of such species is closely related to their redox and acidobasic properties.83 From this perspective, the accurate calculation of their (proton-coupled) one-electron reduction potentials is also essential for a correct description of their HAA reactivity. In Table 3, a series of ten species with the FeO core is selected. For eight of them, the experimental electrochemical potentials correspond to the cathodic peak potentials (E°pc) as determined from cyclic voltammograms (CV). These

E°pc values may differ significantly from the standard E° or the half-wave (E1/2) potential for slow electron transfer between the electrode and the complex, which may mask a pure thermodynamic propensity of a species to acquire an electron in solution.84 Despite this fact, we have observed a very good correlation between E°pc and the calculated standard potentials. Other experimental potentials, used in Table 2 and Figure 2 as references for our calculations, have been reported in the literature as either the standard E° or E1/2 potentials. Since these are also well reproduced by the B3LYP-D3/COSMO-RS methodology, we believe that our calculations are actually capable of validating experimental E°pc data for FeIVO/FeIIIO couples that may serve as good probes of otherwise experimentally elusive standard E° potentials. Although the calculated ground spin states of several FeIVO/FeIIIO 15 ACS Paragon Plus Environment


Page 16 of 27

couples differ from their experimentally-derived counterparts (cf. Table 3), we note that the comparison of reduction potentials determined for experimental vs. calculated ground spin states reveals only minor deviations, indicating a rather small free-energy difference (< 4.0 kcal mol-1) between ground and excited spin states for these species. An exception is found for the [FeIVO(TMCS)]+ complex with the error in the free-energy separation to be larger than 5.6 kcal mol-1.

Table 3. Calculated reduction potentials (E°calc) for ferryl redox couples. The experimental data taken from the literature are provided for comparison (E°expt). Information on the calculated and experimental ground spin states of the oxidized and reduced forms as well as the experimental conditions (reference electrode, solvent, temperature) is also included. Ligand Fielda

Redox couple [Fe

IV/III

(O)(H3Buea)]

-/2-

tbp

Soxb h

2 (2)

h

5/2 (5/2)

[FeIV/III(O)L1(NCCH3)]2+/+

oct

2 (1)

[FeIV/III(O)(TMC)(NCCH3)]2+/+

oct

1 (1)

5/2 (3/2)

[FeIV/III(O)(Bn-TPEN)]2+/+

oct

1

5/2

[Fe

IV/III

(O)(TMC)(OOCCF3)]

[FeIV/III(O)(TMC)(N3)]+/0 [Fe

IV/III

2 +/0

(O)L ]

[FeIV/III(O)L2H]2+/+ [Fe

IV/III

(O)(TMCS)]

+/0

[FeIII/II(OH/H2O)(N4Py)]2+/2+

+/0

h

E°calcd,e [mV]

Sredc

5/2 (3/2)

h

−1244

h

412 (460)

h

E°exptf [mV]

Solvent

T [°C]

−900

Fc

+/0

DMSO

25

730

SCE

CH3CN

−35

−194 (−367)

−320

Fc+/0

CH3CN

25

257

490

SCE

CH3CN

25

+/0

h

5/2

−414 (−394)

−500

Fc

CH3CN

25

h

5/2

−565 (−461)

−600

Fc+/0

CH3CN

25

+/0

CH3CN

25

CH3CN

25

CH3CN/CH3OH 1:1

−30

H2O

25

oct

2 (1)

oct

2 (1)

h

3/2

−970

−1160

Fc

h

5/2

−487

−630

Fc+/0

oct

1 (1)

oct

1 (1)

h

oct

2 (1)

3/2

−843 (−599)

−1000

oct

5/2

2

641

518

a-h

Reference electrodeg

i

Fc

+/0

SCE

i

III

II

See specific details below Table 2. The experimental value for the Fe –OH/Fe –OH2 couple in aqueous solution is derived from the thermodynamic cycle from Scheme 2 in ref. 85.

The only redox system investigated in this work that was found to be associated with a proton-coupled electron transfer is a prototypical N4Py-supported FeIVO complex (N4Py =

N,N-bis(2-pyridylmethyl)-bis(2-pyridyl)methylamine). Here, it is singled out for ambiguities associated with the interpretation of its electrochemical data, which includes the assignment of reductive and oxidative processes in experiments and their quasi-reversibility or irreversibility

at

different

conditions.

More

specifically,

for

CH3CN-solvated

[FeIVO(N4Py)]2+, Sastri et al.86 measured the CV cathodic (reduction) peak at E°pc = –0.44 V 16 ACS Paragon Plus Environment

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vs. Fc+/0, while Collins et al.87 determined its reduction potential to be +0.90 V (vs. Fc+/0 in CH3CN with 0.1 M H2O) and Lee et al.88 provided the value of +0.11 V (vs. Fc+/0 in CH3CN). It is also noteworthy that Wang et al.89 reported a first observation of a reversible CV wave for (N4Py)FeIVO in aqueous solution with E1/2 of +0.41 V vs. SCE, which was interpreted as the proton-coupled reduction of (N4Py)FeIVO to (N4Py)FeIIIOH. In an attempt to provide additional insight into the complexity of FeIVO(N4Py) redox chemistry, we probed its electrochemical behavior employing the presented B3LYPD3/COSMO-RS protocol. The proton-coupled reduction potential of the S = 1 FeIVO(N4Py) complex in water was calculated to be +1.35 V vs. SCE (Table S5), i.e. the potential that is more than +0.9 V higher than the potential assigned for this couple by Wang et al.89 Since we did not observe such a large discrepancy in the calculated reduction potentials for any of the other FeIVO complexes, or for any of the complexes in Table 2, we believe that the assignment made by Wang was incorrect. In fact, we suggest that a proton-coupled reduction of (N4Py)FeIIIOH to (N4Py)FeIIH2O was measured instead. For this H+/e− reduction, we calculated a value of +0.64 V (vs. SCE), which falls within the range of the expected error (Table S5). In addition, it is also in agreement with an experimentally derived value of +0.52 V, reported by Draksharapu et al.85

CONCLUSIONS We showed that a conceptually simple, but computationally efficient B3LYP-D3/COSMO-RS methodology, calibrated on a broad set of mononuclear NHFe complexes and solvent environments, represents a robust computational protocol for evaluating the energetics of redox reactions with these systems. Its reliability was further validated on a set of very challenging mononuclear FeIVO species that provide direct connection of our study to a



relevant field of biomimetic NHFe catalysis. With this computational tool at hand we propose an appealing possibility of computer-aided design of new catalysts by tuning the electrochemical properties in silico. The protocol is also suggested to be highly useful for the interpretation of electrochemical data of otherwise experimentally elusive NHFe species. Such a strategy was exemplified in the case study of (N4Py)FeIVO, for which the presented results indicate a potential of the methodology to correctly predict E°H’s that are associated with coupled H+/e− transfer processes. As the E°H potentials are crucial measures of the halfreaction thermodynamic driving forces for H-atom abstraction/transfer, we expect our methodology to be appropriate for description of a thermodynamic propensity for H-atom abstraction reactivity of NHFeIVO complexes.

ASSOCIATED CONTENT The Supporting Information is available free of charge on the ACS Publications website. Coordinates of all calculated structures. (TXT)

Figures showing (S1) the dependence of calculated reduction potentials on the amount of Hartree-Fock exchange, (S2) scalar relativistic vs. non-relativistic reduction potentials, (S3) correlation between calculated and experimental electrochemical data, (S4) reduction potentials of different forms of the Fe(SiPiPr3)(N2) complex calculated at various levels of theory. Tables showing (S1) total Gibbs free energies of the oxidized and reduced forms of non-heme iron complexes, (S2) calculated vs. experimental spin states, (S3) reduction potentials calculated at different levels of DFT theory, (S4) Average MUEs associated with the groupings in panels in Figure 2 (S5) proton-coupled reduction potentials of different forms of the Fe(N4Py) complex. (PDF)


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AUTHOR INFORMATION The authors declare no competing financial interests.

ACKNOWLEDGMENTS The project was supported by the Czech Science Foundation (Grant numbers: 15-10279Y and 18-13093S).



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64 Grimme, S. Supramolecular Binding Thermodynamics by Dispersion-Corrected Density Functional Theory. Chem. Eur. J. 2012, 18, 9955-9964. 65 COSMOtherm, C3.0, http://www.cosmologic.de

release

1501,

COSMOlogic

GmbH

&

Co

KG,

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