Accurate Prediction of One-Electron Reduction Potentials in Aqueous

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Letter

Accurate Prediction of One-Electron Reduction Potentials in Aqueous Solution by Variable-Temperature H-atom Addition/Abstraction Methodology Daniel Bim, Lubomir Rusilek, and Martin Srnec J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.5b02452 • Publication Date (Web): 08 Dec 2015 Downloaded from http://pubs.acs.org on December 9, 2015

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The Journal of Physical Chemistry Letters

Accurate Prediction of One-Electron Reduction Potentials in Aqueous Solution by Variable-Temperature H-atom Addition/Abstraction Methodology Daniel Bím,‡ Lubomír Rulíšek,‡ Martin Srnec†* †

J. Heyrovský Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, Dolejškova 3, 182 20 Praha 8, Czech Republic; ‡Institute of Organic Chemistry and

Biochemistry, Academy of Sciences of the Czech Republic, Flemingovo náměstí 2, 166 10 Praha 6, Czech Republic

Corresponding Author *E-mail: [email protected] Tel: +420 266052077 Fax: +420 286582307

ACS Paragon Plus Environment

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Abstract A robust and efficient theoretical approach for calculation of the reduction potentials of charged species in aqueous solution is presented. Within this approach, the reduction potential of a charged complex (with a charge |n| ≥ 2) is probed by means of the reduction potential of its neutralized (protonated/deprotonated) cognate, employing one or several H-atom addition/abstraction thermodynamic cycles. This includes a separation of one-electron reduction from protonation/deprotonation through the temperature dependence. The accuracy of the method has been assessed for the set of fifteen transition-metal complexes that are considered as highly challenging systems for computational electrochemistry. Unlike the standard computational protocol(s), the presented approach yields results that are in excellent agreement with experimental electrochemical data. Last but not least, the applicability and limitations of the approach are thoroughly discussed.

TOC Graphic

Keywords computational

electrochemistry,

implicit

solvation

models,

reduction

potential,

transition-metal complexes


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Electron transfer between various (bio)chemical entities or units represents one of the most fundamental processes in chemistry and biology. It is involved in a broad spectrum of redox processes, from electrolysis of water on the laboratory bench to many vital and complex biochemical transformations in cells, such as mitochondrial respiration,1 photosynthesis,1 nitrogen fixation,2 and free-radical production and scavenging.3 For these electrochemical reactions, the key property is a tendency of reactants, oxidant and reductant, to acquire and lose an electron. This is quantitatively expressed in terms of a well-defined thermodynamic quantity, the reduction potential (E°), and tabulated with respect to a reference (e.g., the standard hydrogen electrode, SHE, in aqueous solution). In physico-chemical terms, the reduction potential is directly related to the thermodynamic driving force of a particular redox reaction (i.e., G[eV] = E°(Red1/Ox1) – E°(Red2/Ox2)). Throughout the last decade, theoretical chemistry has become an integral part of many electrochemical studies.4,5,6 The condition sine qua non for its usefulness in chemical applications is the accuracy of computed reduction potentials (it should be borne in mind that “a fairly small” error of 2.3 kcal mol-1 in calculated ∆G(ox/red) translates to 0.10 V in E°). Hence, enormous effort has been directed towards developing computational protocols for calculations of reduction potentials4 that are defined as a Gibbs free-energy difference between the oxidized and reduced states (Gox and Gred), with respect to the absolute potential o of a reference electrode, E abs (reference) :

o E o [V ] = G ox [ eV ] − G red [eV ] − E abs ( reference )[ eV ]

(1)

Different free-energy evaluation strategies have been developed for various levels of structural complexity.4 For models that explicitly include the solvent molecules, both the solute and the solvent can be described quantum mechanically, employing ab initio molecular dynamics (MD).7,8 This has been successfully applied to small-sized redox systems.9


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Alternatively, other methods treat the solute and the solvent at the quantum and molecular mechanical levels of theory, respectively (QM/MM models), while sampling the solvent conformational space using MD- or Monte Carlo based statistical techniques.10 Such a multiscale (QM/MM) partition is the only practical strategy that is applicable to large biological systems such as proteins, with QM description of the active site. Different QM/MM-based techniques have been employed to calculate the reduction potentials of various (metallo)enzymatic complexes.11,12,13,14,15,16 The conceptually and computationally simpler approach for free-energy calculations used in this study describes the solute explicitly, whereas the solvent environment is represented as a surrounding polarizable dielectric medium. Within this description, the Gibbs free energy (at a given temperature T) is evaluated as the sum of three energy terms: G (T ) = E el + [E ZPVE + RT − RT ln Q (T )] + Gsolv (T )

(2)

namely the in vacuo energy of the solute ( Eel ); thermal enthalpic and entropic contributions to the solute energy [ EZPVE + RT − RT ln Q ] with EZPVE and Q being the zero-point vibrational energy and the product of the vibrational, rotational, and translational partition functions, respectively; and the free energy of solvation (Gsolv). Although the static approach, represented by eq 2, has been shown to yield good results for rigid and/or low-charged molecules,17,18,19,20,21 it significantly deteriorates for systems with a high molecular charge and/or in the presence of a polar (and protic) solvent.22 This is due to an incomplete description of electrostatics, hydrogen bonds, dispersion and other solvation effects by implicit-solvation models. Within the modern COSMO-RS23,24 and SMD25 solvation models, many such shortcomings have been remedied. However, inaccuracies in ∆Gsolv calculations still remain as a limiting factor for quantitatively correct predictions of reduction potentials of highly charged species, as documented in ref. [22] (e.g.,


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for the [Ru(CN)6]4–/3– couple in aqueous solution: E0expt= 0.86 V vs. E0“COSMO-RS” = 1.94 V vs. E0“SMD” = 0.12 V). In addition, it was demonstrated that the inclusion of some explicit water molecules in the structural model (without considering any sampling of their conformational space) significantly improves theoretical results, but the deviations from experimental data remain relatively large (cf., ∆E0[calcd vs. expt] = 1.08 V for [Ru(CN)6]4–/3– and 0.38 V for [Ru(CN)6]4–/3–·(H2O)18).22 Similarly, a thorough analysis of explicit first and second hydration shell effects on the calculated reduction potential of the [Ru(H2O)6]3+ complex was performed by Jaque and co-workers.26 Herein, we present the derivation of a simple but efficient approach and its application to the selected (highly charged) redox couples. Its advantages and limitations relative to the standard methodology (eqs 1 and 2) are presented.

Figure 1. Thermodynamic cycle connecting four structures of the general formula [ML] (M is a metal center, L is a ligand set, and k and n are positive integers; H+ denotes extra proton). It includes protonation/deprotonation (vertical arrows), reduction/oxidation (horizontal arrows) and H-atom addition/abstraction (diagonal arrows) half-reactions. The corresponding thermodynamic quantities – acidity constant (pKa), reduction and hydrogenation potentials (E° defined by eq 1 and EHo by eq 4) – are also shown. For the cycle involving cationic species, see the analogous Figure S1.


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Let us consider an anionic complex [Mk+ L]n– as in Figure 1, and its standard reduction potential ( E 2o in Figure 1) that we aim to calculate by means of the reduction potential of its protonated (i.e., less charged) counterpart [Mk+ L(H+)](n–1)–. The reduction potential of this “auxiliary” complex ( E1o in Figure 1) is calculated according to eq 1, i.e.:

[

 E1o [V ] = Gox  M k + L (H + ) 

]

( n −1) −

[

   − G red  M ( k −1)+ L (H + )  

]

n−

 o  − E abs (SHE ) 

(3)

where Gox and Gred are the free energies of the oxidized and reduced forms of the ML(H+) o solute, respectively, and Eabs (SHE ) is the absolute potential of SHE. It should be mentioned

that throughout this article, all energy terms are considered in eV (the universal gas constant R is then in eV K–1). Following the thermodynamic cycle in Figure 1, it is advantageous to define the “hydrogenation” potential, ∆EHo , of the [Mk+ L]n– system as: ° ∆EHo = ∆Gdiag + Gsolv (H + ) − Eabs (SHE )

(4)

with ∆Gdiag being the “diagonal” free-energy difference between [Mk+ L]n– and [M(k–1)+ L(H+)]n– :

[

 ∆Gdiag = G M k + L 

]

n−

[

   − G M ( k −1)+ L (H+ )  

]

n−

  

(5)

The H-atom addition pathway (diagonal in red in Figure 1) must be thermodynamically equivalent to: (i) protonation followed by 1e– reduction (green in Figure 1) and (ii) 1e– reduction followed by protonation (blue in Figure 1). Thus,

∆EHo = E1o − RT ln(10) × pK a ,1 = E2o − RT ln(10) × pK a , 2


(6)

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where E1o and ∆EHo are defined by eqs 1 and 2, pK a ,1 is the acidity constant of the [Mk+ L(H+)](n–1)– complex, E 2o is the reduction potential of the [Mk+ L]n– species, and pK a , 2 is the acidity constant of [M(k–1)+ L(H+)]n–. The combination of eqs 4 and 6 gives:

° ∆Gdiag + Gsolv (H + ) − Eabs (SHE ) =

(

(

)

1 o 1 E1 + E2o − RT ln(10) × pK a ,1 + pK a , 2 2 2

)

(7)

which, after considering

° Eeff =

(

(

)

1 o 1 E1 + E2o and pK a ,eff = pK a ,1 + pK a , 2 2 2

)

(8, 9)

can be rewritten as

∆Gdiag (T ) T

=

ε T

− R ln(10) × pK a ,eff

(10)

( )

o o (SHE ) − Gsolv H + with ε = Eeff + Eabs

(11)

From eq 10, ∆Gdiag (T ) is temperature dependent, whereas ε defined by eq 11 and pK a ,eff are supposed to be temperature independent (an assumption that is essentially valid for small temperature differences; then the ∆Gdiag (T ) / T term is linearly dependent on 1 / T ). This allows us to separate ε from the − R ln(10) × pK a ,eff term by differentiating eq 10 with respect to T:



d (∆Gdiag (T ) )

 

dT

ε =  ∆Gdiag (T0 ) − T0

   T =T0 

(12)

This equation, combined with eqs 8 and 11, can be finally transformed into:

  d (∆Gdiag (T ) )  + 2G H + − 2 E o (SHE ) − E o E2o = 2 ∆Gdiag (T0 ) − T0 solv abs 1   dT T =T0  

( )


(13)

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Thus, we obtained the reduction potential of an anionic complex [Mk+ L]n− ( E 2o ) as a function of the reduction potential of its protonated cognate ( E1o ), and ∆Gdiag and its temperature

( )

o derivative. The 2Gsolv H + − 2 Eabs (SHE ) term is taken in this study as a constant of –31.6 eV

( )

o (for the aqueous environment at 25 °C Eabs (SHE ) = 4.34 eV27 and Gsolv H + = –11.46 eV4).28

In practice, E 2o from eq 13 can be determined as illustrated in Figure 2. While eq 13 was derived for anionic species, it is also valid for cationic redox couples, but with

[

 ∆Gdiag = G M ( k +1)+ L (-H+ ) 

]

n+

[

 k+   − G M L  

]

n+

  

(14)

and E1o for the auxiliary redox couple [M(k+1)+ L(–H+)]n+ / [Mk+ L(–H+)](n–1)+ that lacks one proton as compared to the target system (Figure S1). The above presented protocol is referred to in the following text as the variable-temperature H-atom addition/abstraction (VT-HAA) methodology for the calculation of reduction potentials.

Figure 2. Computational protocol for prediction of the reduction potential of a negatively (or positively) charged complex (E2°) by means of the reduction potential of its protonated (or deprotonated) counterpart (E1°). As an example, the reduction-potential calculation for


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[MnO4]− is schematically depicted. Note that the constant of –31.6 eV corresponds to

( )

o 2Gsolv H + − 2 Eabs (SHE ) from eq 13.

In comparison to the standard approach (eq 1), the VT-HAA methodology (eq 13 and Figure 2) exhibits two important features: (i) the reduction potential of an ionic complex with charge n (A|n|±) is calculated on the basis of the reduction potential of its protonated/deprotonated cognate (A(|n|-1)±). This approach seems advantageous considering that solvation (electrostatic) interactions of A(|n|-1)± are expected to be described more accurately than the corresponding interactions of the more highly charged A|n|±. (ii) the diagonal term ε from Figure 2 is determined by the free-energy difference (∆Gdiag) between two molecular cognates that possess the same molecular charge. Gsolv values of these equivalently charged systems are expected to be of the same order of magnitude, implying small errors in prediction of their solvation energy difference (∆Gsolv). In the context of (i) and (ii), it is noteworthy that a computational scheme that employs a parameterized pseudo-counterion correction was recently developed for the calculation of reduction potentials of highly charged species.29


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Figure 3. The multiple-cycle extension of the computational protocol from Figure 2 is exemplified by two redox couples [Ru(CN)6]3−/4− (A) and [Ru(H2O)6]2+/3+ (B). The reduction potentials associated with these two systems (E4° in A and E3° in B) are calculated on the basis of the reduction potential of the neutralized cognate (E1°) and VT-HAA-derived terms εi according to eq 15 (see note in ref. [30]). It should be noted that structures on the diagonal within each cycle differ by one H atom and hence possess the same charge.

The VT-HAA methodology from Figures 1 and 2 is extended by setting a relationship between the reduction potential of the target (highly charged) system and its neutral counterpart through several thermodynamic cycles, as exemplified by [Ru(CN)6]3−/4− and [Ru(H2O)6]3+/2+ in Figure 3. This multiple-cycle VT-HAA approach is represented by the following recursive formula:

n

E no +1 = 2∑ (− 1) i =1

n −i

δ = 0 if n is even ε i + (− 1)n E1o − 31.6 × δ    δ = 1 if n is odd 


(15)

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where ε i is calculated according to eq 12, n (≥1) is the number of cycles (also corresponding to the charge n from Figure 1), and i = 1, 2,…, n. Thus, within this scheme, the only reduction potential that has to be explicitly calculated (according to eq 1) is that associated with the low-charged systems (e.g., the [ox]0/[red]1− or [ox]1+/[red]0 redox couple). This, in combination with the diagonal terms ε i (each of these terms is calculated for systems with the same

charge),

allows

prediction

of

the

target

reduction

potential

(e.g.,

E4° = 2ε3 −2ε2 +2ε1−E1°−31.6 for [Ru(CN)6]3−/4−; E3° = −2ε2 +2ε1+E1° for [Ru(H2O)6]3+/2+). In Figure 4, the VT-HAA reduction potentials (along with the results obtained using the standard theoretical protocol) of seven anionic and six cationic transition-metal complexes (labeled as 1–13) are plotted against the experimental data. For all of these systems, the VT-HAA protocol provides more accurate results than the corresponding standard approach. From Figure 4A (results for the COSMO-RS solvation model), the mean unsigned error ( MUE ≡ 1 n ∑i E °calcd,i − E ° expt ,i ) of the VT-HAA E° series is ~0.15 V (with the largest n

deviation of 0.33 V for the RuO42–/1– couple). The standard protocol exhibits MUE of ~0.42 V and the largest deviation from the experimental data of 0.80 V (again for RuO42–/1–). This relatively large MUE is mostly caused by a systematic shift with respect to the experimental data. Such a shift is not observed for the VT-HAA approach (linear regression parameters shown in the inset in Figure 4A). Surprisingly, a very good correlation between the VT-HAA results and experimental data is also evident for the considerably less sophisticated COSMO31 solvation model (Figure 4B; note that this solvation model is temperature-independent; see also

the

discussion

in

Supporting

Information

(SI)

concerning

various

temperature-dependence approximations and their effects on the accuracy of results that are provided in Tables S2 and S3). In this case, the MUE is reasonably small (~0.24 V), whereas the maximum reaches 0.48 V (the MnO42–/1– couple). In contrast, the COSMO-based standard theoretical procedure yields completely unreliable results (MUE of ~1.1 V with the largest


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deviation of 1.75 V for RuO42–/1–). According to Figure 4B (and the linear regression parameters therein), all of the COSMO-based VT-HAA results stay close to their experimental counterparts (i.e., E°calcd = 1.072 E°expt – 0.218 V with R2 = 0.96). The opposite is true for the COSMO-based standard protocol calculations, which in fact show extremely large scatter of the values between different types of species. More specifically, for the [M(H2O)6]2+/3+ series (8–13 in green in Figure 4B), the regression line is essentially parallel to the diagonal E°expt = E°calcd and shifted by ~1.0 V to higher values, whereas for the [M(CN)6]3–/4– series (1–4 in green in Figure 4B), a similar slope for the regression line is observed, but with a shift of ~1.1 V to lower values (as a result, the correlation factor of the regression for the whole set of molecules is wholly unsatisfactory, i.e. R2 = 0.44). It is also remarkable that the COSMO-based VT-HAA results are in better agreement with the experimental values than the results calculated by the standard protocol that is combined with the more advanced COSMO-RS solvation model (cf., data in green and red in Figures 4A and 4B).


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Figure 4. Calculated reduction potentials versus experimental electrochemical data. The theoretical results (green and red circles) were calculated using the standard and VT-HAA protocols (eqs 1 and 15), respectively, and employing two different solvation models: COSMO-RS (graph A) and COSMO (graph B). Labels 1–13 refer to the coordination complexes from Table 1. Slopes and intercepts of the regression lines along with the R2 correlation factors are also given. All of the theoretical results are presented for the levels of theory that are referred to in Table 1 as “VT-A/B” (VT-HAA) and “Std-A/B” (standard methodology).


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Interestingly, for the series of transition-metal complexes (1–13) in Figure 4 and Table 1, the VT-HAA computational scheme, combined with both the COSMO-RS and COSMO solvation models, gives more accurate results than those calculated with the sophisticated polarizable QM/MM explicit solvation model from ref. [10] (root-mean-square deviation of 0.04/0.27 V [VT-HAA COSMO-RS/COSMO] vs. 0.36 V [QM/MM]). Nevertheless, it must be conceded that for several cationic complexes, such as [RuIII/II(en)3]3+/2+

and

[RuIII/II(NH3)6]3+/2+,

the

procedure

in

Figure

3B

(i.e.,

deprotonation/H-atom abstraction from the solute) fails. This likely arises from the fact that a deprotonated (or H-atom abstracted) ligand becomes redox non-innocent and therefore significantly affects the redox state of a metal center (this is documented for 14 and 15 in Table S5). For such cases, we propose a modification of the procedure from Figure 3B by introducing chloride counterions to neutralize a complex and then calculating the reduction potential of the target redox couple through thermodynamic cycles that also include successive protonation steps of the Cl– anions, with final substitution of HCl diatomics by solvent (water) molecules (as illustrated in Figure S2). By this chloride-based procedure, the E° results are significantly improved in comparison with the values from VT-HAA calculations from Figure 3B (cf., results for the systems 14 and 15 in Table 1 and Table S5). However, their accuracy remains relatively modest (deviations of 0.2–0.4 V; Table 1).

Table 1. Formal oxidation and spin states of the oxidized and reduced forms of the selected transition-metal complexes, along with the associated experimental and calculated aqueous standard reduction potentials (E°expt and E°calcd). In the case of the presented VT-HAA methodology, E° values for complexes 1–13 and 14–18 were calculated as depicted in Figure 3 and Figure S2, respectively (computational details are provided in SI).


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E°calcd /V VT-Ab Std-Ac VT-Bd f (∆calcd/expt) (∆calcd/expt) (∆calcd/expt)

Std-Be (∆calcd/expt)

0.56 (0.29)

0.06 (–0.31)

0.22 (–0.15)

–0.69 (–1.06)

0.86

0.9630 (0.10)

0.48 (–0.38)

0.69 (–0.17)

–0.19 (–1.05)

{1/2, 0}

0.63

0.62g (–0.01)

0.15g (–0.48)

0.47 (–0.16)

–0.50 (–1.13)

MnIII/MnII

{1, 1/2}

–0.24

–0.04 (0.20)

–0.65 (–0.41)

–0.43 (–0.19)

–1.42 (–1.18)

RuIII/RuII

{1/2, 1}

0.59

0.26 (–0.33)

–0.21 (–0.80)

0.12 (–0.47)

–1.16 (–1.75)

MnIII/MnII

{0, 1/2}

0.56

0.48 (–0.08)

–0.18 (–0.74)

0.08 (–0.48)

–1.10 (–1.66)

FeIII/FeII

{5/2, 2}

–0.12

–0.26 (–0.14)

0.04 (0.16)

–0.52 (–0.40)

–0.80 (–0.68)

[Fe(H2O)6]3+/2+ (8)

FeIII/FeII

{5/2, 2}

0.77

0.76 (–0.01)

0.67 (–0.10)

0.99 (0.22)

1.79 (1.02)

[Co(H2O)6]3+/2+ (9)

CoIII/CoII

{0, 3/2}

1.82

1.59 (–0.23)

1.14 (–0.68)

1.68 (–0.14)

2.52 (0.70)

[Ru(H2O)6]3+/2+ (10)

RuIII/RuII

{1/2, 0}

0.25

0.08 (–0.17)

–0.18 (–0.43)

–0.08 (–0.33)

1.28 (1.03)

[Ti(H2O)6]3+/2+ (11)

TiIII/TiII

{1/2, 1}

–1.29

–1.56 (–0.27)

–1.65 (–0.36)

–1.42 (–0.13)

–0.32 (0.97)

[V(H2O)6]3+/2+ (12)

VIII/VII

{1, 3/2}

–0.26

–0.31 (–0.05)

–0.62 (–0.36)

–0.37 (–0.11)

0.74 (1.00)

[Cu(H2O)6]3+/2+ (13)

CuIII/CuII

{1/2, 1}

2.40

2.27 (–0.13)

2.11 (–0.29)

2.53 (0.13)

3.45 (1.05)

[Ru(en)3]3+/2+ •2H2O (14)

RuIII/RuII

{1/2, 0}

0.21

–0.18 (–0.39)

–0.09 (–0.30)

−

−

RuIII/RuII

{1/2, 0}

0.10

–0.13 (–0.23)

0.42 (0.32)

−

−

TiIII/TiII

{1/2, 1}

–1.29

–1.52 (–0.23)

–1.76 (–0.47)

−

−

Complex (label used in Figure 4)

Redox state ox/red

Spin (S) {ox, red}

E°expt /Va

[Fe(CN)6]3–/4– (1)

FeIII/FeII

{1/2, 0}

0.37

[Ru(CN)6]3–/4– (2)

RuIII/RuII

{1/2, 0}

[Os(CN)6]3–/4– (3)

OsIII/OsII

–/4–

[Mn(CN)6]3 (4)

[RuO4]1–/2– (5) –/2–

[MnO4]1 (6)

[Fe(EDTA)]1–/2– (7)

[Ru(NH3)6]3+/2+ •2H2O (15) [Ti(H2O)6 ]3+/2+ •2H2O (16)


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[Co(H2O)6]3+/2+ •2H2O (17)

CoIII/CoII

{0, 3/2}

1.82

1.62 (–0.20)

0.91 (–0.91)

−

−

[V(H2O)6 ]3+/2+ •2H2O (18)

VIII/VII

{1, 3/2}

–0.26

–0.17 (0.09)

–1.00 (–0.74)

−

−

a

References to the experimental data are provided in Table S2. bThe VT-HAA protocol at the 2c-PBE+D3/dhf-TZVP-2c//BP86/def2-TZVPD/COSMO-RS (“VT-A TZ”) level of theory (details in SI). Results obtained from an analogous protocol with the higher basis set dhf-QZVP-2c (approach denoted as “VT-A QZ”) are shown in Table S4. cThe standard protocol applied at the same level of theory as in a. dThe VT-HAA protocol at the 2c-PBE+D3/dhf-TZVP-2c//BP86/def2-TZVPD/COSMO (“VT-B TZ”) level of theory. eThe standard protocol applied at the same level of approximation as in c. f∆calcd/expt = E°calcd – E°expt. gThe corresponding non-relativistic “VT-A TZ” and “Std-A TZ” (i.e., PBE+D3/def2-TZVP//BP86/def2-TZVPD/COSMO-RS) values are ~0.87 V and ~0.33 V, respectively. The difference of ~0.2 V between the relativistic and non-relativistic calculations is due to a spin-orbit coupling effect, as previously described for complexes of this type in ref. [32].

To summarize, we have presented a theoretical implicit solvation-based approach for calculating the reduction potential of a charged complex (with charge |n| ≥ 2) based on the reduction potential of its neutralized cognate, taking advantage of one or several thermodynamic cycles that involve H-atom addition or H-atom abstraction to/from an anionic or cationic species, respectively. This includes a separation of one-electron reduction from protonation/deprotonation reactions through the temperature dependence. The accuracy of the VT-HAA method has been assessed for a set of fifteen transition-metal complexes in water. Unlike those from the standard computational protocol, the VT-HAA results were found to be in very good agreement with experimental electrochemical data (regardless of the solvation model used, i.e., COSMO-RS or COSMO). In spite of these findings, it appears that the VT-HAA methodology may not be useful for systems in which protonation/deprotonation (yielding the low-charged species) significantly alters the geometric/electronic structures of the redox-active centers. In this study, this was observed for a few cationic species, for which we propose the use of a modified VT-HAA protocol that employs Cl– counterions.


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METHODS All calculations were performed using the Turbomole 6.633 and COSMOtherm34 programs for electronic-structure/frequency and solvation-energy calculations. Computational details are provided in SI.

ASSOCIATED CONTENT The Supporting Information is available free of charge on the ACS Publications website at DOI: Full account of computational details, the general thermodynamic cycle for cationic species, the VT-HAA methodology employing Cl– counterions, a reliability of VT-HAA results with respect to molecular positions of added/abstracted protons, three different levels of approximation for temperature dependence of ε used in the VT-HAA protocol, effects of a basis set on predicted reduction potentials, analyses of the VT-HAA failures, coordinates of all calculated structures, and the illustrative workflow (in .xls document) of the VT-HAA application to the prototypical [Ru(CN)6]3-/4- redox couple (including values of all intermediate quantities).

AUTHOR INFORMATION Corresponding Author *E-mail: [email protected] Tel: +420 266052077 Fax: +420 286582307

Notes The authors declare no competing financial interests.

ACKNOWLEDGMENTS The project was supported by the Grant Agency of the Czech Republic (Grant No. 15-10279Y and 14-31419S). MS is also grateful to the Academy of Sciences of the Czech Republic for the Purkyně Fellowship.


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REFERENCES

(1) Karp, G. Cell and Molecular Biology, 5th Ed., Wiley, 2008. (2) Hoffman, B. M.; Lukoyanov, D.; Dean, D. R.; Seefeldt, L. C. Nitrogenase: a Draft Mechanism. Acc. Chem. Res. 2013, 46, 587-595. (3) Kirkinezos, I. G.; Moraes, C. T. Reactive Oxygen Species and Mitochondrial Diseases. Cell & Developmental Biology 2001, 12, 449-457. (4) Marenich, A. V.; Ho, J.; Coote, M. L.; Cramer, C. J.; Truhlar, D. G. Computational Electrochemistry: Prediction of Liquid-Phase Reduction Potentials. Phys. Chem. Chem. Phys. 2014, 16, 15068-15106. (5) Viswanathan, V.; Hansen, H. A.; Rossmeil, J.; Nørskov, J. K. Unifying the 2e– and 4e– Reduction of Oxygen on Metal Surfaces. J. Phys. Chem. Lett. 2012, 3, 2948-2951. (6) Ertem, M. Z.; Konezny, S. J.; Araujo, C. M.; Batista, V. S. Functional Role of Pyridinium during Aqueous Electrochemical Reduction of CO2 on Pt(111). J. Phys. Chem. Lett. 2013, 4, 745-748. (7) Cheng, J.; Liu, X.; VandeVondele, J.; Sulpizi, M.; Sprik, M. Redox Potentials and Acidity Constants from Density Functional Theory Based Molecular Dynamics. Acc. Chem. Res. 2014, 47, 3522-3539. (8) Blumberger, J.; Tavernelli, I.; Klein, M. L.; Sprik, M. Diabatic Free Energy Curves and Coordination Fluctuations For the Aqueous Ag+/Ag2+ Redox Couple: A Biased BornOppenheimer Molecular Dynamics Investigation. J. Chem. Phys. 2006, 124, 064507. (9) Ayala, R.; Sprik, M. Ligand Field Effects On the Aqueous Ru(III)/Ru(II) Redox Couple From an All-Atom Density Functional Theory. J. Chem. Theory Comput. 2006, 2, 1403-1415. (10) 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. (11) Heimdal, J.; Kaukonen, M.; Srnec, M.; Rulíšek, L.; Ryde, U. Reduction Potentials and Acidity Constants of Mn Superoxide Dismutase Calculated by QM/MM Free-energy Methods. ChemPhysChem 2011, 12, 3337-3347. (12) Li, J.-L.; Farrokhnia, M.; Rulíšek, L.; Ryde, U. Catalytic Cycle of Multicopper Oxidases Studied by Combined Quantum- and Molecular-Mechanical Free-Energy Perturbation Methods. J. Phys. Chem. B 2015, 119, 8268-8284. (13) Olsson, M. H. M.; Hong, G.; Warshel, A. Frozen Density Functional Free Energy Simulations of Redox Proteins: Computational Studies of the Reduction Potential of Plastocyanin and Rusticyanin. J. Am. Chem. Soc. 2003, 125, 5025-5039.


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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(14) Cascella, M.; Magistrato, A.; Tavernelli, I.; Carloni, P.; Rothlisberger, U. Role of Protein Frame and Solvent for the Redox Properties of Azurin From Pseudomonas Aeruginosa. Proc. Natl. Acad. Sci. U.S.A. 2006, 103, 19641-19646. (15) Hong, G.; Ivnitski, D. M.; Johnson, G. R.; Atanassov, P.; Pachter, R. Design Parameters for Tuning the Type 1 Cu Multicopper Oxidase Redox Potential: Insight from a Combination of First Principles and Empirical Molecular Dynamics Simulations. J. Am. Chem. Soc. 2011, 133, 4802-4809. (16) Li, G.; Zhang, X.; Cui, Q. Free Energy Perturbation Calculations with Combined QM/MM Potentials: Complications, Simplifications, Applications to Redox Potential Calculations. J. Phys. Chem. B 2003, 107, 8643-8653. (17) Baik, M. H.; Friesner, R. A. Computing Redox Potentials in Solution: Density Functional Theory as a Tool for Rational Design of Redox Agents. J. Phys. Chem. A 2002, 106, 74077412. (18) Fu, Y.; Liu, L.; Yu, H. Z.; Wang, Y. M.; Guo, Q. X. Quantum-Chemical Predictions of Absolute Standard Redox Potentials of Diverse Organic Molecules and Free Radicals in acetonitrile. J. Am. Chem. Soc. 2005, 127, 7227-7234. (19) Keith, J. A.; Carter, E. A. Theoretical Insights into Electrochemical CO2 Reduction Mechanisms Catalyzed by Surface-Bound Nitrogen Heterocycles. J. Phys. Chem. Lett. 2013, 4, 4058-4063. (20) Keith, J. A.; Carter, E. A. Theoretical Insights into Pyridinium-Based Photoelectrocatalytic Reduction of CO2. J. Am. Chem. Soc. 2012, 134, 7580-7583. (21) Thapa, B.; Schlegel, H. B. Calculations of pKa’s and Redox Potential s of Nucleobases with Explicit Waters and Polarizable Continuum Solvation. J. Phys. Chem. A 2014, 119, 5134-5144. (22) Rulíšek, L. On the Accuracy of Calculated Reduction Potentials of Selected Group 8 (Fe, Ru, and Os) Octahedral Complexes. J. Phys. Chem. C 2013, 117, 16871-16877. (23) Eckert, F.; Klamt, A. Fast Solvent Screening via Quantum Chemistry: COSMO-RS Approach. AIChE Journal 2002, 48, 369-385. (24) Klamt, A.; Eckert, F. COSMO-RS: a Novel and Efficient Method for the A Priori Prediction of Thermophysical Data of Liquids. Fluid Phase Equilibria 2000, 172, 43-72. (25) Marenich, A. V.; Cramer, C. J.; Truhlar, D. G. Universal Solvation Model Based on Solute Electron Density and On a Continuum Model of the Solvent Defined by the Bulk Dielectric Constant and Atomic Surface Tensions. J. Phys. Chem. B 2009, 113, 6378-6386. (26) Jaque, P.; Marenich, A. V.; Cramer, C. J.; Truhlar, D. G. Computational Electrochemistry: The Aqueous Ru3+|Ru2+ Reduction Potential. J. Phys. Chem. C 2007, 111, 5783-5799.


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(27) Llano, J.; Eriksson, L. A. Oxidation Pathways of Adenine and Guanine in Aqueous Solution from First Principles Electrochemistry. Phys. Chem. Chem. Phys. 2004, 6, 47074713.

( )

o (SHE ) is equal to the sum Gsolv H + + IPH• →H+ − 12 G2H• →H2 , where (28) The quantity Eabs Gsolv H + is the solvation energy of the proton in the aqueous solution, IPH• →H + is the gas-

( )

phase ionization potential of the hydrogen atom, and G2H• →H is the gas-phase dissociation 2

( ) − 2E (SHE ) term from eq 13 is

energy of the hydrogen molecule. As a result, the 2Gsolv H

+

o abs

equivalent to − 2 × IPH• →H + + G2H• →H and it is thus independent of the solvent environment. 2

(29) Matsui, T.; Kitagawa, Y.; Shigeta, Y.; Okumura, M. A Density Functional Theory Protocol to Compute the Redox Potential of Transition Metal Complex with the Correction of Pseudo-Counterion: General Theory and Applications. J. Chem. Theory Comput. 2013, 9, 2974-2980. (30) The robustness of the presented VT-HAA protocol with respect to various locations of the added (or extracted) H-atoms/protons was tested for the [Ru(CN)6]3-/4- complex. As shown in Table S1, it has a small effect on the prediction of the target reduction potential. (31) Klamt, A.; Schuurmann, 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, 799−805. (32) Srnec, M.; Chalupský, J.; Fojta, M.; Zendlová, L.; Havran, L.; Hocek, M.; Kývala, M.; Rulíšek, L. Effect of Spin-Orbit Coupling on Reduction Potentials of Octahedral Ruthenium(II/III) and Osmium(II/III) Complexes. J. Am. Chem. Soc. 2008, 130, 1094710954. (33) TURBOMOLE V6.6 2014, a development of University of Karlsruhe and Forschungszentrum Karlsruhe GmbH, 1989-2007, TURBOMOLE GmbH, since 2007; DOI:10.1016/0009-2614(89)85118-8 (34) Eckert, F.; Klamt A., COSMOtherm , Version C3.0 , Release 15.01; COSMOlogic GmbH & Co. KG, Leverkusen, Germany, 2014.


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Accurate Prediction of One-Electron Reduction Potentials in Aqueous

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