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Achieving Accurate Reduction Potential Predictions for Anthraquinones in Water and Aprotic Solvents: Effects of Inter- and Intra-Molecular H-Bonding and Ion Pairing Hyungjun Kim, Theodore Goodson III, and Paul M. Zimmerman J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b07558 • Publication Date (Web): 13 Sep 2016 Downloaded from http://pubs.acs.org on September 17, 2016

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The Journal of Physical Chemistry

Achieving Accurate Reduction Potential Predictions for Anthraquinones in Water and Aprotic Solvents: Effects of Inter- and Intra-molecular H-Bonding and Ion Pairing Hyungjun Kim, Theodore Goodson, III, and Paul M. Zimmerman∗ Department of Chemistry, Ann Arbor, Michigan 48109, United States E-mail: [email protected] Phone: 734) 615-0191

Abstract In this combined computational and experimental study, specific chemical interactions affecting prediction of 1-electron and 2-electron reduction potentials (V) for anthraquinone derivatives are investigated. For 19 redox reactions in acidic aqueous solution, where AQ is reduced to hydroanthraquinone, density functional theory (DFT) with polarizable continuum model (PCM) gives a mean absolute deviation (MAD) of 0.037 V for 16 species. DFT(PCM), however, highly overestimates three redox couples with a MAD of 0.194 V, which is almost five times that of the remaining 16. These three molecules have ether groups positioned for intramolecular hydrogen bonding, which are not balanced with the intermolecular H-bonding of the solvent. This imbalanced description is corrected by quantum mechanics/molecular mechanics (QM/MM) simulations, which include explicit water molecules. The best theoretical ∗

To whom correspondence should be addressed

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estimations result in a good correlation with experiments, V (Theory) = 0.903 × V (Expt.) + 0.007 with R2 of 0.835 and MAD of 0.033 V. In addition to the aqueous test set, 221 anthraquinone redox couples in aprotic solvent were studied. Five anthraquinone derivatives spanning a range of redox potentials were selected from this library and their reduction potentials were measured by cyclic voltammetry. DFT(PCM) calculations predict the first reduction potential with high accuracy giving the linear relation, V (Theory) = 0.960 × V (Expt.) − 0.049 with R2 = 0.937, and MAD of 0.051 V. This approach, however, significantly underestimates the second reduction potential, with a MAD of 0.329 V. It is shown herein that treatment of explicit ion-pair interactions between the anthraquinone derivatives and the cation of supporting electrolyte is required for the accurate prediction of the second reduction potential. After correction, V (Theory) = 1.045 × V (Expt.) − 0.088 and R2 = 0.910 with MAD reduced by more than half, to 0.145 V. Finally, molecular design principles are discussed that go beyond simple electron-donating and electron-withdrawing effects to lead to predictable and controllable reduction potentials.

Introduction Redox flow batteries (RFB) are considered to be highly promising for the storage of intermittent renewable electricity. In RFB the anode- and cathode-active materials are stored in separate tanks, allowing a highly scalable strategy for accumulation and release of the stored energy. While RFB have many advantages, including easy scale-up, flexible power tuning and safety, this type of battery has suffered from relatively low energy density (≤ 25 Wh/L). 1,2 Many attempts to overcome the low energy density have employed various transition metal complexes as the active material, for instance vanadium, iron, chromium and zinc redox couples have been investigated. 1–8 Alternatively, organic molecules have recently been highlighted as potential active materials due to their low cost of production and highly tunable electrochemical windows. 9 Quinones and their derivatives are considered as especially promising candidates for application in RFB because these are inexpensive, stable, highly soluble in organic solvent, and undergo rapid redox reactions.


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lishing a linear correlation between adiabatic electron affinity and reduction potential. Shamsipur et al. have presented computational and experimental examination of 33 redox couples involving 9,10-anthraquinone derivatives (AQs) in acetonitrile. 24 In that study, computational predictions made use of the semiempirical method, PM3, and B3LYP with 6-31G* to create quantitative structure-electrochemistry relationships. Similar relations were found for p-benzoquinone derivatives, 27 and various quinone family derivatives. 28,29 Other studies found that improved linear correlations can be obtained when the geometries are optimized in solution using conductor-like PCM (C-PCM). 27 Going beyond implicit solvation, a recent study by Bachman et al. investigated the dianion reaction and ion-pairing with lithium cations. 29 Namazian et al. have evaluated the reduction potential between two quinone derivatives (isodesmic reaction) to take advantage of error cancellation in their quantum chemical models. 30,31 The reduction in acidic aqueous solution, the twoelectron, two-proton redox behavior is also investigated by many researchers including Pakiari and Er. Pakiari et al. have studied the two-electron, two-proton reduction of eight benzoquinone and naphthoquinone derivatives in aqueous solution using a variety of quantum chemical methods. 25 They found that the results using MP3/6-31G** agreed best with experiment. In addition to these studies, research on substitution effects has been performed for benzoquinone, naphtoquinone, and anthraquinone in acidic aqueous solution for the cases of mono- and full-substitution with 18 functional groups. 26 In summary, there have been a variety of informative studies on quinone redox behavior, with little work exploring the role of specific environmental interactions on the redox process. In this paper, we seek to determine the role of explicit solute-solvent and solute-electrolyte interactions on redox behavior of anthraquinones. As a first test set, the reduction potentials of 19 AQs in acidic aqueous solution are computed and compared to existing experiments. While the theoretical results of the DFT(PCM) protocol using the ωB97X-D functional are comparable to previously reported values, explicit consideration of hydrogen-bonding interactions will be shown to be necessary to accurately predict aqueous redox potentials. Quantum mechanics/molecular mechanics (QM/MM) calculations will be shown to be effective at correcting errors in the implicit


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cal factor. Tetrabutylammonium hexafluorophosphate (TBAPF6 ) is used as supporting electrolyte. Hygroscopic TBAPF6 can easily absorb water molecules, therefore, TBAPF6 is recrystallized to remove water moieties and any impurity before measurements. The concentration of AQs (TBAPF6 ) is 1 mM (100 mM), respectively. The prepared samples are purged with pure nitrogen gas for 20 mins to remove remaining dissolved oxygen gas. A three-electrode system, a glassy carbon working electrode, a platinum coiled wire counter electrode, and a Ag/AgCl reference electrode, is used to measure reduction potential. CV was performed with a scan rate of 0.1 V/s.

Computational Details The reduction potential with respect to the reference electrode is calculated using the following equation: abs abs (V) − Eexpt,ref (V) = − Ecalc (V vs. ref) = Ecalc

∆Gsoln,calc abs − Eexpt,ref (V) nF

(1)

where n is the number of transferred electrons during the redox reaction, F is the Faraday constant abs of 23.06 kcal/mol. Ecalc (V) is the absolute reduction potential of the given redox reaction obtained abs by theoretical calculations. Eexpt,ref (V) is the experimentally measured absolute reduction potential

of the reference electrode. ∆Gsoln,calc is the calculated Gibbs free energy change in solution state. abs For the redox reactions in AN, the potential of Ag/AgCl reference electrode, Eexpt,ref , is referenced

to 4.305 V. 32,33 For the two-electron, two-proton reduction in water, the reduction potential is abs compared to the reported potential of SHE in water, Eexpt,ref , 4.44 V. 34 According to the equation

1, the change of Gibbs free energy in solution, ∆Gsoln,calc , is required to predict the reduction potential, and this can be evaluated by using the thermodynamic cycles in Figure 3. Q and H2 Q are the anthraquinone and hydroanthraquinone derivatives, respectively. For the redox couples in aprotic solvent, the value of n, 0 or 1, corresponds to the first or second reduction process. The chemical state of gas (solution) is marked as g (soln) in parentheses or subscript, respectively. ∆Gg (∆Gsoln ) represents the change of Gibbs free energy during the reduction in gas (solution). Gibbs free energy of a free electron is chosen to be 0.0 kcal/mol, and a detailed dis-


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domly in each of the x, y, and z directions. The first solvation box is constructed by CHARMM, 43 and 9 structures are generated from the first box. These 10 solvation boxes serves as a seed for the remaining 90 solvation configurations and all configurations are then optimized. The Boltzmann factor weighted average Gibbs free energy is then obtained for Q and H2 Q. The Boltzmann factor (wi ) is defined as e−(

Gi −Gmin ) RT

, where Gi is the free energy of i-th snapshot, Gmin is the minimum

Gibbs free energy among the 100 snapshots, R is gas constant, and T is room temperature of 298.15 ∗

∗

PN

w ×G

i i i . The K. The Boltzmann factor weighted average (G ) is calculated as follows, G = P N wi i rP ∗ N i wi ×(Gi −G ) PN , corresponding Boltzmann factor weighted standard deviation is defined as, σ ∗ = w i

i

and standard errors of Boltzmann factor weighted average are used to estimate the quality of random sampling is given as

σ∗ √ . N

In the QM/MM simulations, AQs are completely described by QM, and all the water molecules are included in the MM region. For the geometry optimization, the solute molecule in the QM region is treated at the ωB97X-D/6-31G* level of theory. The water molecules in the MM region are modeled by the CHARMM version of the TIP3P force field, 44 which places Lennard-Jones potentials on hydrogen atoms, which are absent in the original TIP3P. The number of explicit water molecules in the QM/MM calculations is determined by the size of a solvation box which encapsu˚ The interaction between the QM and MM lates the solute in a rectangular box with sides of 7.5 A. regions is treated with the electronic embedding scheme. This approach yields the total energy as the sum of energy in the QM, E(QM), and in the MM regions, E(MM). 45 E(MM) therefore includes van der Waals interactions between QM and MM atoms, and the Coulomb interactions between the QM and MM region are included in E(QM). This approach therefore the polarizes the electron density in the QM region by the fixed charges in the MM region. Frequency corrections are applied using the optimized geometries QM/MM geometries for the QM atoms only. Single point energy calculations using the ωB97X-D/G3Large for the QM region and the same force field used in the geometry optimization for the MM region. All simulations were performed using Q-Chem 4.0. 46


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Results and Discussion Reduction potential in acidic aqueous solution As a first test set to evaluate the applicability of quantum chemical simulation approaches to redox potentials, we collected 19 reported two-electron, two-proton reduction potential of AQs in acidic aqueous solution. 9,11,18,47,48 This set is denoted as quinone in water (QW). In order to minimize the effect of varying experimental conditions, these redox couples were chosen because they have the same reference electrode and measurements were performed under similar experimental conditions, such as temperature and supporting electrolyte. The individual structure is identified with the position of functional groups in Table 1 and graphical description is available in Figure S1 of Supporting Information. DFT with PCM (ωB97X-D/G3Large/PCM(Bondi)//ωB97X-D/6-31G*) yields somewhat scattered results for the two-electron, two-proton reduction potential with a mean absolute deviation (MAD) of 0.062 V (DFT(PCM) and Outlier:DFT(PCM) in Figure 4). See the Supporting Information for all reported redox quantities (DFT(PCM) column in Table S1). The linear regression gives the low R2 correlation value of 0.533, suggesting serious deficiencies in the DFT(PCM) model. These problems with standard PCM are also seen when using the SM8 model, which is a PCM variant that treats non-bulk electrostatic effects differently than PCM. 49 As shown in the Supporting Information (DFT(SM8) column in S1), SM8 provides an MAD of 0.098 V, and an R2 of 0.367, suggesting that specific solvation effects are responsible for these errors. When the individual deviations are examined, it is observed that three specific redox couples show severe overestimation in redox potentials. (Outlier:DFT(PCM) in Figure 4) The MAD of these outliers is 0.194 V, and this is five times as large as the MAD of the rest 16 redox couples, 0.037 V. The three outliers in the PCM results are similar in that they contain ether groups immediately adjacent to the central carbonyl groups (Figure 5). When these AQs are reduced to hydroanthraquinones, intramolecular hydrogen-bond interactions form between the H atom of the hydroxyl groups and the O atom of the ether (Opaque ball and stick model in Figure 6B). While this interaction is expected, water molecules would form intermolecular hydrogen-bond-like interaction with 9 ACS Paragon Plus Environment



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0.5 Outlier:DFT(PCM) Outlier:QM/MM DFT(PCM)

0.4

Reduction potential (Theory) [V]

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0.3 0.2 0.1 0.0 MAD = 0.033 V V(Theory) = 0.903×V(Expt.) + 0.007 2 R = 0.835

-0.1 -0.2 -0.2

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

Reduction potential (Expt.) [V]

Figure 4: Two-electron, two-proton reduction potential of AQs in QW set. Black triangle (N) represents the three outliers of the DFT(PCM) calculation. Open blue circle (◦) represents the QM/MM results of the outliers in the DFT(PCM) calculations. The DFT(PCM) calculations (•) are detailed in the main text. Blue line is the linear regression of the best theoretical results, which consist of the DFT(PCM) results for the 16 redox couples and the QM/MM results of three outliers. Black line represents the perfect matches between experiments and calculations.




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˚ between explicit water molecules and the oxygen atoms Table 2: The shortest bond distance (in A) of the ether groups in quinone form (Q) and hydroquinone form H2 Q.

QW-11 QW-12 QW-13

O index O1 O2 O1 O2 O1 O2

Q 1.700 ± 0.008, 1.831 ± 0.019 1.664 ± 0.003, 1.763 ± 0.005 1.661 ± 0.003, 1.857 ± 0.014 1.700 ± 0.004, 1.736 ± 0.006 1.681 ± 0.012, 1.800 ± 0.019 1.693 ± 0.006, 1.736 ± 0.006

H2 Q 1.659 ± 0.012 1.676 ± 0.007 1.619 ± 0.012 1.778 ± 0.062 1.659 ± 0.010 1.757 ± 0.025

*The index of oxygen atom in ether groups can be found in Figure 5. ˚ or the both *In a hydroquinone form, the second shortest bond length is larger than 2.5 A hydrogen atoms belong to one water molecule.

bound water molecule(s) in the QM/MM simulation is one (two) for each functional group in hydroquinone (quinone) form. This difference reduces the energy gap between a quinone and a hydroquinone form, which will reduce the overestimation of the reduction potentials. The QM/MM simulations are consistent with reports on the H-bonds near ether groups from prior experiment 50 and computations. 51 The bulk water structure, however, is certainly not rigid and more than one solvent configuration is needed to systematically quantify the solvent effect. To do so, 100 random solvent configurations were sampled to obtain statistically converged data. For the quinone form, this approach generates the local minima having average energy of 0.024, 0.018, and 0.020 eV higher than global minimum with standard errors of 2×10−4 , 1×10−4 , and 1×10−4 eV for QW-11, QW12, and QW-13, respectively. For the hydroquinone form, the energies are higher than the global minimum by 0.028, 0.018, 0.037 eV on average for QW-11, QW-12, and QW-13, respectively, with corresponding standard errors of 1×10−4 , 1×10−4 , and 1×10−4 eV. These values are all consistent with the thermal average available energy, kT∼0.026 eV. These statistics suggest that the random sampling has generated a set of realistic solvent configurations for quantifying the redox potential. The QM/MM representation including explicit water molecules and thermal sampling substan-



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tially corrected the outliers from the DFT(PCM) approach. The reduction potential (standard error) were calculated to be 0.164 (2×10−4 ), 0.164 (1×10−4 ), and 0.150 (1×10−4 ) V for QW-11, QW12, and QW-13, respectively, where the DFT(PCM) protocol gave values of 0.318, 0.395, and 0.321 V. The small error bars, ∼10−4 , suggest that statistical convergence is reached. The linear regression based on the DFT(PCM) values for the 16 redox couples and the QM/MM results for the three outliers shows much improved correlation, V (Theory) = 0.903 × V (Expt.) + 0.007 with R2 = 0.835. The MAD of these three couples is reduced from 0.194 V to 0.008 V, and MAD for the whole set is reduced to 0.033 V from 0.062 V. Considering that the predicted reduction potential range spans a range of 0.4 V (from −0.1 V to 0.3 V), the MAD of 0.033 V is only 10% of the range, making this approach cover a wide area of AQs reduction potential with predictive accuracy. Reduction potential in aprotic solvent For our second test set, the first and second reduction potential of 221 AQs in AN were computed using ωB97X-D/G3Large/PCM(Bondi)//ωB97X-D/6-31G*. All the AQs are commercially available or their synthetic routes are reported, 52 making this a good choice of moieties despite the lack of prior experimental redox characterization. The second AQ test sets contains various functional groups including alkoxy and amine groups as electron donating groups (EDGs), and cyanide, nitro and sulfonic acid groups as electron withdrawing groups (EWG). There are 67 unique functional groups, and the number of total substitutions is 565, covering a great variety of AQs. Unique functional groups are categorized into eight sites of AQs and listed in Table 3. The chemical structures and reduction potential values of each redox couple can be found in Supporting Information. (Table S2) The distribution of computed reduction potentials is histogrammed in Figure 7, which shows the number of AQs whose reduction potential belonging to certain reduction potential range with step size of 0.1 V. The graph resembles a normal distribution at the center of AQ reduction potential. Generally, the first reduction spans higher region than the second reduction. There is, however, a long tail toward positive-direction in the second reduction potential. Most of these cases are the


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Table 3: Functional groups present in the second AQ test set.

R1 R2

R3 R4 R5 R6 R7 R8

Functional groups b, c, d, e, f, g, h, j, k, l, Allyloxy, Br, Cl, F, Me, NEt2 , NH2 , NHC6 H11 s , NHCOφm , NHi Pr, NHMe, NMe2 , NO2 , Oφm , OCH2 OMe, OH, OMe, SBr, SO3 H t Bu, a, ab, ac, ad, n, Acetyl, Allyl, Br, CCl3 , CH=Nφm , CH2 Br, CH2 Cl, CH2 OH, CH2 φm , CHO, Cl, CN, CO2 Et, CO2 H, COCl, Et, F, Me, NH2 , NHBu, NHCOφm , NHMe, NO2 , Oφm , O(CH2 )2 OH, OH, OMe, Pentyl, S(CH2 )2 OH, Sφ, SH, SO3 H n, ab, Br, CF3 , CH2 Br, CH2 OH, CHBr2 , Cl, CN, CO2 H, F, Me, NH2 , NO2 , Oφm , OCH2 OMe, OH, OMe, SO3 H b, l, o, q, r, u, w, x, y, z, aa, Br, Cl, CO2 H, F, Me, NEt2 , NH2 , NHi Pr, NHφm , NHC6 H11 s , NHCOφm , NHMe, NMe2 , NO2 , OH b, c, d, e, r, Cl, F, NH2 , NHi Pr, NHφm , NHCOφm , NO2 , OCH2 OMe, OH, OMe, Oφm , SO3 H, Sφm t Bu, F, Me, NH2 , OCH2 OMe, OH, OMe, SO3 H OCH2 OMe, OMe, SO3 H b, r, Br, Cl, F, NH2 , NHφm , NHCOφm , NO2 , Oφm , OCH2 OMe, OH, OMe, SO3 H Total number of substituted functional groups: 565 Total number of unique functional groups: 67 Numbering of substitution on anthraquinone can be found in Table 1.

a) Piperidin-1-yl, b) p-Toluidino-2’-sulfonic acid, c) 2-Nitrophenylamino, d) 2,4-Dinitrophenoxy, e) Phenylethylamino, f ) N=N-C6 H4 NMe2 , g) 3-Methoxyphenoxy, h) NH(CH2 )3 OMe, i) Prefix, iso, j) 1,3-Dioxolan-2-yl, k) Hexa-2,5-dienyloxy, l) 2-(4-Hydroxyphenyl)ethylamino, m) φ: phenyl ring, n) Ethoxyphenoxy, o) 4-Methylphenylsulfonicamido, p) Prefix, para, q) NH(CH2 )NMe2 , r) p-Toluidino, s) Cyclohexyl, t) Prefix, tert, u) p-Methylaminomethylanilino, w) 2,4-Eiethyl-6-methylphenylamino, x) 4-Acetylaminoanilino, y) NH(CH2 )2 OH, z) NH(CH2 )4 NMe2 , aa) p-Methoxybenzoylamino, ab) p-Methoxyphenyl, ac) CH2 CH=CHCH2 CH3 , ad) CH=CH-(CH2 )2 -CH3



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result of proton transfer from the sulfuric acids to central C=O group. Some AQs are predicted to undergo chemical reactions during reduction such as reductive dehalogenation or intramolecular protonation by sulfonic acid groups or hydroxyl groups. For example with the 1st reduction, the bromide can be dissociated from bromothiol group. There are six AQs whose reduced carbonyl group is protonated by adjacent functional groups, such as NH2 or SO3 H. Furthermore, in some cases AQs undergo chemical reactions in the 2nd reduced state due to the increased negative charge. For instance, when Br atoms are bonded to methyl group, they easily dissociate from the dianion, which is not observed in the 1st reduction. In contrast to anion case, carbonyl groups in dianion AQs are protonated by adjacent hydroxyl groups since sufficient negative charge is accumulated on the carbonyls. In total, 13 cases undergo protonation by adjacent OH groups in the dianion state, and 5 cases by NH2 or NH groups next to C=O group. The strong acid group, SO3 H, does so whenever it is present at the 1-, 4-, 5-, or 8-position. Carbonyl-adjacent OH, NH, NH2 , or SO3 H therefore can behave as proton sources and cause increases in reduction potentials, with stronger acids resulting in higher reduction potentials. In some exceptional cases, even remote sulfuric acids group can donate a proton to reduced carbonyls. This is observed with the combination of OH and SO3 H functionalization, where OH groups are present between the SO3 H group and carbonyl group. In 8 redox couples, there exist chain proton transfer (H+ transfer from SO3 H to OH, then H+ from OH to C=O), with the net result of protonation of C=O group by sulfuric acids. All of these protononation events have significant effects on the redox potentials beyond the electron donating or withdrawing effects of the substitutions themselves. The five AQs in Figure 2 were selected for experimental study to validate the theoretical approach. These are expected to cover the potential range of 0.8 V (−1.140 V to −0.339 V) for the first reduction, and 0.7 V (−1.783 V to −1.110 V) for the second reduction potential. The CV scan results of the selected five AQs are shown in Figure 8. The two reversible peaks are the result of two sequential one-electron reductions (see Table S3 in Supporting Information for relevant quantities) that are assigned to parent AQ derivative reductions. The small peak at 0.67 V of 4 is attributed to irreversible cleavage of a C-Cl bond, as previously noted. 53,54 For dihydroxy AQ (2),


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First Second

The number of derivatives

30

20

10

0 -2.5

-2.0

-1.5

-1.0

-0.5

0.0

0.5


Figure 7: Distribution of theoretical reduction potential of AQs in the library. the anodic peak has disappeared, likely due to reaction with trace O2 . 55 A similar effect is seen for 1,4-, 1,5-, and 1,8-dihydroxyanthraquinone, which all contain two OH substitutions. Also, the self-protonation and subsequent chemical reactions may explain this irreversibility. 14,56 Since the purpose of current work is to establish correlation between theory and experiment, however, these details of the reduction mechanism are not considered further. For the first reduction of 2, the theoretical value is compared to the forward sweep peak, corresponding to the initial reduction. With these results in hand, Figure 9 provides a graphical comparison of the reduction potentials predicted by theory to the CV measurement. 1 4

150

2 5

3

100

Current [A]

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50 0 -50

-100 -2.2

-2.0

-1.8

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-1.4

-1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

Voltage [V]

Figure 8: Cyclic voltammogram for 1mM of the selected five AQs at scan rate of 0.1 V/s. Current amplitude of 2 and 5 is doubled for better resolution.



The first reduction potential

0.0

Solute-only model -0.2

MAD = 0.051 V V(Theory) = 0.960×V(Expt.) - 0.049 2 R = 0.937

-0.4

-0.6

-0.8


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-1.0

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-1.0

-0.8

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-0.4

-0.2

0.0

The second reduction potential -0.8

IP-corrected model Solute-only model -1.0

MAD = 0.145 V V(Theory) = 1.045×V(Expt.) - 0.088 2 R = 0.910

-1.2

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-1.8

-2.0 -2.0

-1.8

-1.6

-1.4

-1.2

-1.0

-0.8

Reduction potential (Expt.) [V]

Figure 9: Correlation of reduction potential between the theory and the experiment. MAD and the result of linear regression are shown. (Top:The first reduction potential. Bottom:The second reduction potential. Black solid line represents the perfect correlation. Solute-only model means the DFT(PCM) calculation for the only solute molecule, and IP-corrected model is the DFT(PCM) calculation with the IP correction.)


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DFT(PCM) predictions using the solute molecule alone will be named as Solute-only model to distinguish it from IP-corrected model which will be discussed later. The predictions from Solute-only model match well with the experimental observations for the first reduction potential (blue line in top graph of Figure 9): the linear regression gives the slope close to the unity, and the y intercept is small. The overall MAD is 0.051 V and maximum deviation is −0.100 V for 1. For the first reduction process, DFT(PCM) approach can achieve similar accuracy to that of QM/MM-corrected results in the aqueous cases due to the lack of strong AN-solute interactions. Unfortunately, the quality of predictions employing Solute-only model becomes worse for the second reduction potential, where the anion accepts one extra electron to be reduced to dianion (Purple line with circles in bottom graph of Figure 9). The theory underestimates the reduction potential in all cases, with a large MAD of 0.329 V. Considering that the computations for the first reduction potential are highly accurate, the errors in the second reduction potential likely arise from the treatment of the dianion state specifically. In redox experiments, there exist many charged species in solution such as AQ anions or dianions, TBA+ and PF− 6 of supporting electrolyte which all may interact. Specifically, the attractive interaction between AQs− (AQs2− ) and TBA+ emerges and may significantly influence the formation of the dianion AQs. Therefore the possibility of IP formation between the dianion AQs and TBA+ must be taken into account. 57 Two types of interaction, solvation free energy of each free ion, and Coulomb attraction between these ions, determine the stability of the IP, ∆GIP . The former quantity, solvation free energy, would be decreased when the IP is formed since the accumulated charge would be partly neutralized. If the Coulomb attraction is strong enough to compensate the loss of solvation free energy due to the IP formation, the IP will be stable. In the opposite case where the solvation free energy of individual free ion is too large compared to the coulomb interaction, free ions are preferred. Since the IP may stabilize the dianion AQs ∆GIP , this could raise the second reduction potential. When these effects are considered, we denote this model as IP-corrected model. Previous research has observed IP formation between the solute ion and supporting electrolyte 58–64 or in ionic liquids, 65 and the measurements show that the reduction potential is in-



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creased by this effect. 60–63 For example, the association free energy of the IP between TBA+ and 9,9-dihexyl-9H-fluorene-2-carbonitrile (F1CN) is measured to be −0.29 eV in THF. 63 Theoretical investigations of the IP by Fry 66–70 examined the structures and thermodynamics of the various IP. For polycyclic aromatic hydrocarbon molecules, DFT and CBS-Q3 theories have shown significant effects of ion pairing on the 1st and 2nd reduction potentials. 66,67 To develop an accurate model for IP effects, the binding energy of F1CN with TBA+ in THF was considered at the same level of theory (ωB97X-D/G3Large/PCM//ωB97X-D/6-31G*) applied to the AQ test set. For the solvation energy calculation, the performance of two widely used atomic radii models, Bondi and UFF, are compared. The result shows that the binding energy is highly underestimated with Bondi radii, giving 0.05 eV compared to the experimental value of 0.29 eV. 63 The binding energy predicted using UFF cavity model is improved to 0.19 eV, which provides reasonable agreement with experiment. For the calculation of ∆GIP , UFF atomic radii are therefore selected to create the solute cavity. Gas phase geometries for the IP may show structures with an overestimated degree of Coulomb binding. To determine the significance of this issue, geometries were optimized using ωB97XD/6-31G* with treatment of solvent by PCM(UFF). The 3D structure of the IP for 3 in the solvent phase is described and key intermolecular distances listed in Figure 10. These three intermolecular distances represent the Coulomb attraction between the positively charged H atom of a TBA cation and the negatively charged O atom of 3. All three distances are significantly elongated by solventphase optimization, as expected by the dielectric effect. The ∆GIP values calculated using the solution state geometry, ωB97X-D/G3Large/PCM(UFF)//ωB97X-D/6-31G*/PCM(UFF), are denoted ∆GIP,sol , and their value can be found in the last column of Table 4. The compound 2 and 5 have unfavorable IP energies, suggesting they remain separated in DMSO. Molecules in high dielectric solvent prefer to be present as charged free species, since the ion stabilization energy is proportional to the dielectric constant. The results of the second reduction potential prediction with the correction of ∆GIP,sol , IPcorrected model are shown on the green line with filled triangle in Figure 9. The addition of


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|∆GIP,sol | to the second reduction potential obtained using DFT(PCM) with Solute-only model (Purple line with filled circles) has alleviated the serious underestimation of the latter protocol. Compared to DFT(PCM) with Solute-only model, an improved linear correlation results, V (Theory) = 1.045 × V (Expt.) − 0.088 (Green line in Figure 9) with R2 of 0.910, and the MAD drops to 0.145 V. To determine the importance of solution-phase optimization on computed energies, we have analyzed the IP interaction evaluated at the gas phase geometry, ωB97X-D/G3Large/PCM(UFF)//ωB97X-D/6-31G*, and called this quantity as ∆GIP,gas (see the second column of Table 4). Two derivatives, 2 and 5, do not form a stable IP based on the gas phase geometry. The remaining 3 molecules, however, are still predicted to have a stabilizing IP interaction of a few hundredths of eV. The inclusion of ∆GIP,gas slightly improves the prediction accuracy with the reduced MAD of 0.289 V compared to Solute-only model. The linear regression yields V (Theory) = 1.093 × V (Expt.) − 0.170 with R2 of 0.904, suggesting systematic errors are present. To better decompose the factors influencing the IP effect on the 2nd reduction potential, the individual energy contributions are analyzed further. First, the changes in gas phase energy from the solution-phase geometry relaxation (∆Eg ) are listed in the third column of Table 4. Next, the difference in solvation free energy upon the geometry relaxation (∆∆Gsolv ) are shown in the fourth column. As the IP geometries relax in solution, the Coulomb interaction becomes weaker, and the gas phase energy goes up by 0.087 eV in average. This relaxation, however, allows the IP to interact with solvent more strongly, and leads to the increase in solvation energy by the mean value of −0.241 eV. The resulting numerical values of ∆GIP,sol can be found in the last column of Table 4. This table suggests that the solvent geometry optimization of the IP, and ∆GIP value is influenced by more than 0.1 eV overall by solvent effects on the geometry. Given that the original MAD in reduction potentials without IP was 0.329 eV, it appears that solvent optimization of the IP is required to reach reasonable accuracy in second reduction potential prediction. The performance of SM8 model has been compared to PCM combined with the Solute-only model or IP-corrected model, and the results and discussion can be found in Table S3 of Supporting Information.


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Table 4: Energy change upon the geometry relaxation in solution state and ∆GIP at the gas (solution) state geometry. (in eV)

1 2 3 4 5

∆GIP,gas a −0.089 no IP −0.029 −0.078 no IP

∆Eg b 0.068 0.099 0.102 0.066 0.098

∆∆Gsolv c −0.195 −0.265 −0.261 −0.212 −0.273

∆GIP,sol d −0.216 −0.166 −0.188 −0.223 −0.123

a) ∆GIP,gas is the ∆GIP obtained at the gas phase geometry. b) ∆Eg = Eg (solution state geometry)−Eg (gas phase geometry) c) ∆∆Gsolv = ∆Gsolv (solution state geometry)−∆Gsolv (gas phase geometry) d) ∆GIP,sol is the ∆GIP obtained at the solution state geometry.

The effect of intramolecular hydrogen bond on reduction potential Having screened a large number of anthraquinones for their reduction potentials, these derivatives can be grouped according to to their functional group substitution patterns. Three functional groups, an amine group and a hydroxyl group as an EDG, and a nitro group as an EWG, were selected for further analysis. Limiting the described cases to doubly substituted anthraquinones, the range of the first reduction potential of the AQs with the selected functional groups is displayed in Figure 11.

-1.2

-1.0

-0.8 -0.6 -0.4 Reduction potential (Theory) [V]

NH2

OH2

NO2

NO2+OH

-0.2

0.0

Figure 11: Range of reduction potential with the selected substitutional groups. OH: hydroxyl group, NO2 : nitro group, and NH2 : amine group. Anthraquinone without any substitutions is marked as AQ. Amine and nitro groups are EDGs and EWGs, respectively, and make the reduction potential decrease or increase accordingly compared to unsubstituted AQ. Some unexpected observations, however, can be found in the OH substitution block. First, while a hydroxyl group is considered as an EDG, OH groups raise the reduction potential in the certain derivatives. The reduction potential 23 ACS Paragon Plus Environment



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ory and experiment is found to be V (Theory) = 0.903 × V (Expt.) + 0.007 with R2 of 0.835 for the best theoretical model. In aprotic solvent, we have measured using cyclic voltammetry the reduction potential of the five selected AQs which spanned a range of one- and two-electron redox potentials. The protocol, ωB97X-D/G3Large/PCM(Bondi)//ωB97X-D/6-31G* for Solute-only model, gives excellent agreement for the first reduction potential, V (Theory) = 0.960 × V (Expt.) − 0.049, R2 = 0.937, and MAD = 0.051 V. This approach, however, shows relatively poor accuracy for the second reduction potential as a result of missing IP interaction between the AQs dianion and the electrolyte tetrabutylammonium cation. Geometry relaxation in solvent is required to describe the IP interaction accurately, and this interaction is calculated to shift reduction potential upward by 0.183 V on average compared to Solute-only model. The predictions of the second reduction potential with IP-corrected model is significantly improved, yielding the regression, V (Theory) = 1.045 × V (Expt.) − 0.088, R2 = 0.910, and MAD = 0.145 V. In aprotic solvent, we found that hydroxyl groups at positions 1, 4, 5, or 8 are expected to increase the reduction potential due to intramolecular H-bond. The intramolecular H-bond interaction becomes stronger as AQs are reduced to anion and dianion, outweighing the electron donating effect of the OH. This effect scales with the number of intramolecular H-bonds, showing that the combination of the OH groups and EWGs can be used to raise redox potentials in a synthetically accessible manner. This work demonstrates the capability of an efficient theoretical approach to evaluate the reduction potential of anthraquinones in aqueous and aprotic solvent with high accuracy, even when specific chemical interactions are present. The comparison with experimental results validated the theoretical approach, and additionally demonstrates that careful considerations of environment are required for predictive accuracy. Further cooperation between theory and experiment is expected to allow more complete control over redox behavior of AQs and other redox-active organic derivatives.


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Supporting Information Available The xyz coordinates of all compounds and numerical value of reduction potential are provided. This material is available free of charge via the Internet at http://pubs.acs.org/.

Acknowledgement The authors would like to thank the University of Michigan Energy Institute for funding.

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