DOI: 10.1002/chem.201406597

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& Reduction Potential

What Makes a Strong Organic Electron Donor (or Acceptor)? Benjamin Eberle, Olaf Hbner, Alexandra Ziesak, Elisabeth Kaifer, and Hans-Jçrg Himmel*[a] Dedicated to Professor Manfred Scheer on the occasion of his 60th birthday

but also decreases the solvent stabilization. Hence, intrinsic and extrinsic effects compete against each other; generally the extrinsic effects dominate. We suggest a simple relationship between the redox potential in solution and the gasphase ionization energy and the volume of an organic electron donor. We finally arrive at formulas that allow for an estimate of the (gas-phase) ionization energy of an electron donor or the (gas-phase) electron affinity of an electron acceptor from the measured redox potentials in solution. The formulas could be used for neutral organic molecules with no or only small static dipole moment and relatively uniform charge distribution after oxidation/reduction.

Abstract: Organic electron donors are of importance for a number of applications. However, the factors that are essential for a directed design of compounds with desired reduction power are not clear. Here, we analyze these factors in detail. The intrinsic reduction power, which neglects the environment, has to be separated from extrinsic (e.g., solvent) effects. This power could be quantified by the gasphase ionization energy. The experimentally obtained redox potentials in solution and the calculated ionization energies in a solvent (modeled with the conductor-like screening model (COSMO)) include both intrinsic and extrinsic factors. An increase in the conjugated p-system of organic electron donors leads to an increase in the intrinsic reduction power,

Introduction

usually employed to differentiate between the electron-donor strength of compounds. Consequently, extrinsic factors, for example, solvation energies, come into play. Intrinsic effects, which consider the compound in the gasphase and neglect the medium, have to be well separated from extrinsic effects (the interaction of the compound with the environment, for example, the solvent). Solvent stabilization is an effect that could be of much greater importance than creation of aromaticity. Hence, the gain from aromatic stabilization (e.g., benzene exhibits a resonance energy of ca. 1.3 eV) could be small in comparison with the solvent stabilization (5 eV and more for a dication in a polar solvent, see the discussion). The main goal of this work is to shed light on the factors that make a good electron donor and thereby provide a fundament that allows for a directed design of organic electron donors with a defined reduction power. The arguments are presented with the help of some representative examples (see Scheme 1), but we aim at a general understanding that (under some assumptions) is valid for most organic electron donors. At the end of this article, we will provide a formula that links the intrinsic reduction power (gas-phase ionization energy) with the redox potential measured in solution for organic electron donors. Moreover, a similar formula could be provided for electron acceptors that links the intrinsic oxidation power (gasphase electron affinity) with the redox potential measured in solution. A prominent (and archetypical) example for an electron donor is tetrakis(dimethylamino)ethylene (TDAE, 1), which was first synthesized in 1950.[3] The related compound 1,1’,3,3’-tet-

Research on organic electron donors continues to increase in intensity, because such species have a variety of attractive applications spanning synthesis[1] to materials. In contrast to inorganic reducing agents such as alkali metals, the electron-donor strength (reduction power) of organic reducing agents could, at least in principle, be tuned by directed synthetic variations. Such a directed approach requires a detailed knowledge of the factors that govern the electron-donor strength of an organic compound. However, as discussed in the seminal review article by Broggi, Terme and Vanelle,[1] these factors are not clear. Often, the argumentation relies on “intrinsic” factors, which do not depend on the environment (such as creation of aromaticity upon oxidation or an extended p-system).[2] These “intrinsic” factors determine the gas-phase electron-donor strength, and could be quantified by the (adiabatic) gas-phase ionization energy. On the other hand, organic electron donors are generally not used in the gas-phase, but in solution. Therefore, it is not the gas-phase ionization energies, but the redox potentials measured by cyclic voltammetry (CV) experiments (which are related to the adiabatic ionization energies in solution) that are [a] B. Eberle, Dr. O. Hbner, A. Ziesak, Dr. E. Kaifer, Prof. H.-J. Himmel Anorganisch-Chemisches Institut Ruprecht-Karls Universitt Heidelberg Im Neuenheimer Feld 270, 69120 Heidelberg (Germany) Fax: (+ 49) 6221-545707 E-mail: [email protected] Supporting information for this article is available on the WWW under http://dx.doi.org/10.1002/chem.201406597. Chem. Eur. J. 2015, 21, 1 – 14

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Full Paper ied their chemistry.[7] Murphy et al. explained the higher redox potential in solution of 4 compared with those of 1 and 3 by the loss of aromaticity upon oxidation.[9] We will show herein that this explanation is incorrect. We also include the GFA compound 5 in our analysis. For this compound, the 10p-aromatic system is removed upon oxidation, but a 6p-aromatic system is formed. Compound 5, as well as stable salts of the dication 52 + and even the tetracation 54 + (in this case the 6paromatic system that is created upon two-electron oxidation is removed), were already synthesized and structurally characterized.[10] This work alludes to another highly important issue. For applications of organic electron donors or acceptors in functional materials, the redox potential measured in solution is often used to estimate the HOMO or LUMO energy. Generally, simple formulas are employed for this purpose, which include the orbital energy of ferrocene (Fc) and the Fc/Fc + redox potential as the only additional parameters. However, the inobservance of the difference in solvation of the considered organic compound and Fc/Fc + could be a source of very large flaws.

Results and Discussion The results are presented and discussed in three sections. The first deals with the difference between intrinsic (or gas-phase) electron-donor strength and the experienced electron-donor strength in solution, which includes extrinsic (solvent) effects. The experimental results obtained from cyclic voltammetry measurements are compared with quantum chemical calculations. In the second section, we discuss the changes in the electron-donor strength for smaller modifications of a given electron donor. It will be shown that, for certain modifications, intrinsic arguments are sufficient to explain differences in the electron donor strength in solution. In the third, and key section, the results of the previous sections are used to establish a relationship that allows for an estimate of the redox potential in solution with just two molecular parameters.

Scheme 1. Five typical organic electron donors: tetrakis(dimethylamino)ethylene (TDAE, 1), 1,1’,3,3’-tetraphenyl-2,2’-biimidazolidinylidene (2), the special tetrakis(dialkylamino)ethylene 3, and the GFA compounds 1,2,4,5-tetrakis(tetramethylguanidino)benzene (4), and 1,4,5,8-tetrakis(tetramethylguandino)naphthalene (5).

raphenyl-2,2’-biimidazolidinylidene (2) followed ten years later.[4] Both compounds have been used extensively in redox reactions, and also for the formation of carbene complexes.[5] Further modifications led to compound 3 (Scheme 1),[6] which was termed a “super electron donor”. Upon oxidation of 3, aromaticity is created, and this aromatic stabilization of the monocationic and dicationic forms is responsible for the stronger reduction power of 3 compared with 1 or 2.[2] In 2008, our group reported the first member of a new class of strong electron donors, which we termed guanidino-functionalized aromatic compounds (GFAs),[7, 8] namely 1,2,4,5-tetrakis(tetramethylguanidino)benzene (4; Scheme 1). The neutral compound 4 as well as complexes of the radical monocation 4 + · and the dication 42 + were synthesized and structurally characterized. In the case of 4 and most other GFAs, aromaticity is present in the neutral form, but removed upon oxidation to the monocation or dication. The structure of 42 + is in line with the description of a pair of bisguanidino-allyl cations that are connected by two CC single bonds (see the Lewis structure in Scheme 1). The alternative description as a quinonediiminium dication does not correctly describe the electronic situation (see the examples provided below). In the following years, we synthesized a number of GFA compounds and stud&

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Electron donor strength: intrinsic and extrinsic factors Intrinsic electron donor strength The gas-phase adiabatic ionization energy is certainly the best parameter for indicating the intrinsic electron donor strength (or reduction power) of a compound because it is experimentally accessible, at least in principle. In experiments, both the adiabatic and the vertical ionization energy, which does not consider structural relaxation of the compound upon oxidation (according to the Franck–Condon principle), could be determined. These values are measured, under the premise that the compound is volatile, for example, by photoelectron spectroscopy. In the case of 1 (and 2), such measurements are available.[11] The vertical ionization energy was estimated to be 5.95 eV for 1 on the basis of He(I) photoelectron spectra. Another work puts the vertical ionization energy of 1 at 6.11  0.02 eV, and the adiabatic ionization energy at  5.36  0.02 eV.[12] Finally, based on electron ionization and photoionization experiments, adiabatic ionization energies of 5.3  0.2 2

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Full Paper and 5.20  0.05 eV were measured for 1.[13] In general, the experiments overestimate the correct value for the adiabatic ionization energy slightly, and therefore one could state that the measurements predict the adiabatic ionization energy to be approximately 5.2 eV. With modern quantum-chemical methods, the ionization energies of relatively simple organic compounds could be calculated accurately. Such studies have already been carried out for compound 1. Hence, by using B3LYP with two different basis sets, vertical ionization energies of 5.28 (4-21G) and 5.62 eV (cc-pVDZ), and adiabatic ionization energies of 4.65 (4-21G) and 4.95 eV (cc-pVDZ), were obtained.[14] In another study, also using the B3LYP functional, vertical and adiabatic ionization energies of 5.83 and 5.15 eV, respectively, were obtained with 6-311 + + G(d,p), and 5.72 and 5.16 eV, respectively with 6-311 + G(d,p).[13] These results indicate that the B3LYP functional, in combination with a basis set that is not too small, gives adiabatic ionization energies that are in satisfactory agreement with the experimental values (see Table 1). On the basis of these previous studies, we decided to

Table 2. Results of quantum chemical calculations (B3LYP/TZVP) on the oxidation of the electron donors 1, 3, 4, and 5 in the gas phase.[a]

1 3 4 5 Na K Mg Ca Ba

I1

Ref.

exptl exptl exptl B3LYP/4-21G B3LYP/cc-pVDZ B3LYP/6-311 + G(d,p) B3LYP/6-311 + + G(d,p) B3LYP/TZVP

 5.36  0.02 5.3  0.2 5.20  0.05 4.65 4.95 5.16 5.15 5.03

[12] [13] [13] [14] [14] [13] [13] this work

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2nd oxidation I2 [eV] V2 + [3]

296 254 707 787 27 49 17 32 43

5.03 4.43 4.66 4.63 5.14 4.34 7.65 6.11 5.21

9.08 8.52 7.31 7.32 47.28 31.63 15.04 11.87 10.00

295 255 701 757 7 15

285 257 702 740

3 6 14

because the first ionization energy of Na atoms is significantly higher (5.14 eV). In fact, all four organic electron donors have an I1 value smaller than that of Na. The I1 value of 3 is even similar to that of K atoms. Moreover, the sum of first and second ionization energies (I1+I2) is much lower than for all stable alkaline earth metals (of which only Mg, Ca, and Ba are listed in Table 2) in the gas-phase. We see from a comparison between the I1 values of 4 (4.66 eV) and benzene (9.24 eV), that functionalization with four guanidino groups lowers the ionization energy by as much as 4.58 eV. This value is much larger than the resonance energy of benzene (1.3 eV), which clearly shows that the loss of aromatic stabilization upon oxidation of 4 is overcompensated for by the gain in delocalization of the positive charge. According to the calculations, the first ionization energy increases in the order 3 < 5  4 < 1. The intrinsic one-electron donor strength of compounds 4 and 5 is therefore larger than that of 1. This implies again that loss of aromatic stabilization upon oxidation of 4 is overcompensated for by charge delocalization into the guanidino groups (as evident by the large number of mesomeric structures that can be drawn for the radical monocation 4 + ·). However, the differences in the I1 values are relatively small for all compounds ( 0.60 eV). The second ionization energy (I2) is clearly lower for compounds 4 and 5 than for 1 and 3. In this case, the differences are already much larger ( 1.77 eV), and the order is 4  5 ! 3 < 1. Compounds 4 and 5 are better two-electron donors than 1 and 3 in the gas-phase. One could also formulate gas-phase redox equations to illustrate this point, as done in Table 3. In this table, the DH0 and DG0 values (at 298 K), which include thermal contributions, are also considered. A negative value means that the compound, which is in its neutral form on the left side of the equation, is the stronger electron donor, because it could reduce the oxidized form of the other electron donor. A further, extremely important parameter, namely the volume of the molecules/atoms, is included in Table 2. It is clear that the positive charge is stabilized by delocalization

use the B3LYP functional with the TZVP basis set for our analysis. With B3LYP/TZVP, we calculated an adiabatic first ionization energy (defined as the difference between the zero-point energy corrected total energies of the oxidized and the neutral molecule) of 5.03 eV for 1. The difference between B3LYP calculations with the SV(P) and the TZVP basis sets are relatively small, at least for the GFA electron donors. For 4 and 5, we calculated ionization energies of 4.57 and 4.57 eV with SV(P), and 4.66 and 4.63 eV with TZVP. The gas-phase ionization energies from B3LYP/TZVP calculations for compounds 1, 3, 4, and 5 are listed in Table 2. We included both the first (I1) and the second (I2) ionization energies. Calculations on the second ionization energy are certainly more unreliable than on the first. Moreover, the experimental gas-phase data for two-electron ionization measured for compound 1 are extremely difficult to interpret,[15] and therefore we cannot compare the theoretical values with experimental data. In the case of 1, the second ionization energy was previously calculated to be 9.12 eV (B3LYP/6-311 + G*).[15] This compares with a value of 9.08 eV calculated by us with B3LYP/ TZVP. In a review article, compound 3 was called “organic sodium”.[16] If one just considers the gas-phase ionization energies, this is even an underestimation of the reduction power, Chem. Eur. J. 2015, 21, 1 – 14

1st oxidation I1 [eV] V + [3]

[a] I1 and I2 are the adiabatic first and second ionization energies. V0, V + , and V2 + are the calculated volumes of the neutral, monocationic and dicationic compounds. In the case of the metals, exp. ionization energies are given, and the volume was calculated as 4/3pr3 using the covalent radii r for the atoms (coordination number = 8 for Na, K, and Ba) and the ionic radii for the ions (all with coordination number = 6).[17]

Table 1. Comparison between experimental and calculated adiabatic first ionization energy (I1, in eV) for compound 1. Method

V0 [3]

3

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Full Paper work. The previously reported E1/2 value of 4 in CH2Cl2 of 0.76 V[19] then shifts to 0.70 V. We measured CV curves for compounds 1 and 4 in four solvents of different polarity to study the effect of solvent stabilization. In all experiments, Bu4NPF6 was used as supporting electrolyte. The curves are shown in Figure 1 and Figure 2. The CV curves of 1 (TDAE) differ considerably in different solvents.

Table 3. Reaction energies including ZPE contributions (DEZPE), enthalpies (DH0) and Gibbs free energies (DG0) at 298 K for gas-phase redox reactions between some organic electron donors shown in Scheme 1 (all values in eV). Redox equation

DEZPE

DH0

DG0

1 + 4 + ·!1 + · + 4 3 + 4 + ·!3 + · + 4 5 + 4 + ·!5 + · + 4 1 + 42 + !12 + + 4 3 + 42 + !32 + + 4 5 + 42 + !52 + + 4

0.36 0.23 0.03 2.14 0.97 0.02

0.36 0.24 0.02 2.11 0.95 0.01

0.37 0.24 0.05 2.23 1.02 0.02

over a large volume. This is especially important in the case of dications, for which one has to assume electrostatic repulsion between the two positive charges. In the organic electron donors, the positive charge is distributed over a large percentage of the molecular volume, ideally over the complete volume. Under this simplifying assumption, a large molecular volume is advantageous. Compounds 1 and 3 have quite similar volumes (296 and 254 3), which are much smaller than for compounds 4 and 5 (707 and 787 3). It could also be seen from Table 2 that the volume decreases only slightly upon ionization. Therefore, the reason for the low I1 and I2 values of 4 and 5 is their relatively large volume. It also is clear that for all organic electron donors the volume is much larger than for the alkali metal and alkaline earth metal atoms and ions, for which oxidation even leads to a significant volume reduction. This could be the reason for their relatively high ionization energies in comparison to the organic electron donors. On the other hand, small species could be better stabilized by a solvent. This means that charge delocalization over a large volume lowers the ionization energy, but also lowers the stabilization by the solvent. Hence, we expect a competition between the effects of charge delocalization and solvent stabilization once the solvent comes into play. The solvent stabilization is an extrinsic effect, and will be discussed in the following.

Figure 1. Comparison between the CV curves of tetrakis(dimethylamino)ethylene (1) in four solvents with different polarity (SCE potentials given relative to Fc/Fc + , Bu4NPF6 as supporting electrolyte, 100 mV s1 scan speed).

Electron donor strength in solution Experiments: Cyclic voltammetry (CV) measurements are commonly used to access the electron donor strength in solution. The potentials in this work are given vs. the ferrocene/ferrocenium (Fc/Fc + ) redox couple.[18] Ideally, the ferrocene is added (as an internal reference) to the solution of the electron donor. However, this is only possible if the Fc/Fc + redox couple does not interact with the organic electron donor in all relevant oxidation states. We previously reported values using ferrocene as an internal reference, because we observed no change in the redox wave of 4 upon addition of ferrocene directly during the CV measurement (see the curves in Figure S1 of the Supporting Information).[19] However, we also measured ferrocene before and after addition of the electron donor (reverse experiment), and detected a small but significant shift in the ferrocene redox potential upon addition of 4 (see Figure S1). Therefore, we used Fc/Fc + as an external reference throughout this &

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Figure 2. Comparison between the CV curves of 1,2,4,5-tetrakis(tetramethylguanidino)benzene (4) in four solvents with different polarity (the numbers in parentheses are the dielectric constants of the solvents, SCE potentials given relative to Fc/Fc + , Bu4NPF6 as supporting electrolyte, 100 mV s1 scan speed).

As seen from Figure 1, they show two reversible one-electron waves in CH3CN (with E1/2 values of 1.13 and 0.97 V), a reversible one-electron wave (with E1/2 = 1.14 V) and a second nonreversible one-electron wave in CH2Cl2, a two-electron reversible wave in N,N-dimethylformamide (DMF) (with E1/2 = 1.07 V), and a two-electron nonreversible wave in tetrahydrofuran (THF). It was already reported that the CV curve of 1 in CH3CN shows two reversible one-electron waves,[20, 21] whereas 4

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Full Paper in DMF one reversible two-electron wave is observed.[21, 22] In CH3CN, E1/2 values for the two one-electron oxidation steps of 0.78 and 0.61 V vs. SCE were reported, which could be converted into 1.18 and 1.01 V vs. the Fc/Fc + redox couple. In DMF, the E1/2 value for the two-electron oxidation step was 0.62 V vs. SCE, or 1.02 V vs. Fc/Fc + . Hence, our values deviate slightly (by 0.05 V) from the previously obtained results. The difference between the first and second gas-phase ionization energies for 1 was calculated to be 4.05 eV (see previous section of this work), but nevertheless the E1/2 values for the first and second oxidation step differ only by 0.16 V in CH3CN and they are virtually identical in DMF. This already underlines the importance of solvent effects. The changes from CH3CN to DMF were explained as follows: “The superposition of the two one-electron steps points out that considerable conformational changes take place upon oxidation, and this effect is enhanced in DMF.”[21] This explanation certainly is not fully satisfactory. One could, on the other hand, comprehend that the E1/2 value for the two-electron oxidation in DMF is close to the average between the two one-electron redox potentials in CH3CN, (E1/2(1) + E1/2(2))/2. More specifically, the comproportionation equilibrium constant Kcomp can be expressed by Equation (1), in which DE0 is the difference between the second and first formal one-electron redox potentials (E20E10), which constitute the two-electron transfer process. In the case of a positive DE0 (normal potential ordering), Kcomp is larger than unity, but it is less than unity if DE0 is negative (“potential inversion”).[23] The solvent influence on Kcomp for various redox-active compounds was demonstrated in several studies.[24]  Kcomp ¼ exp

F DE 0 RT

Table 4. CV measurements of 1, 4, and 5 in different solvents.[a]

1

THF CH2Cl2 DMF CH3CN THF CH2Cl2 DMF CH3CN CH2Cl2

0.86 1.06 1.03 1.09 0.57 0.62 0.65 0.69 0.55

E1/2

2nd Eox

E1/2

1.14 1.07 1.13 0.71 0.70 0.68 0.73 0.65

0.86 0.84 1.03 0.93 0.57 0.62 0.65 0.69 0.55

1.07 0.97 0.71 0.70 0.68 0.73 0.65

[a] All potentials in V vs. Fc/Fc + , Bu4NPF6 as supporting electrolyte. Eox is the potential (in V vs. Fc/Fc + ) at the maximum of the oxidation wave.

hand, the difference in the measured redox potentials is approximately 0.4 V in all solvents. Hence, the discrepancy between DI1 (gas phase) and e·DE1/2 (solution) is approximately 0.77 eV. This result highlights the importance of including solvent effects in any discussion of the reduction power. In other cases, the differences between DI1 (gas phase) and e·DE1/2 (solution) of two organic electron donors is much smaller. Hence, for the pair of compounds 1 and 3, DI1 = 0.60 eV, and DE1/2 = 0.53 V in DMF (with E1/2 = 1.60 V vs. Fc/Fc + for 3 in DMF).[1, 2] In this case, the difference in the intrinsic electron donor strength (e.g., creation of aromaticity upon oxidation in 3 but not 1) explains the differences in the redox potential in solution. The question arises: Why could intrinsic arguments (gasphase ionization energies) be used if 1 is compared with 3, but not if 1 is compared with 4? This question will be answered below. The CV curves for 4 and 5 in CH2Cl2 are compared in Figure 3. It can be seen that the E1/2 value (for two-electron oxidation) is higher for 5 than for 4 (0.65 vs. 0.70 V), indicating that 5 is a weaker electron donor than 4. If the loss/ change of aromaticity upon oxidation is the dominating factor (as suggested by Murphy et al.),[2, 3, 9, 25] then one would expect

The CV curves recorded for 4 are much less sensitive to solvent changes. In all applied solvents, reversible two-electron waves were measured, but the difference between the oxidation and reduction wave varied from only 0.06 V in DMF to 0.28 V in THF. The half-width of the waves also altered. The large half-width in THF might be interpreted as a sign of two overlapping one-electron waves with slightly different potentials. Nevertheless, the removal of two electrons at similar potential in all solvents is again a remarkable experimental finding, bearing in mind the significant calculated energy difference (2.65 eV) between the first and second ionization energy in the gas phase. The four solvents differ in their dielectric constants (THF 7.58, CH2Cl2 8.93, DMF 37.0 and CH3CN 37.5). One should expect a charged species to be stabilized best by a polar solvent with a high value of the dielectric constant. Only in the case of 4, do the Eox values follow this trend. In all cases, one sees that the measured potentials vary only very slightly when the solvent is changed. When the potentials measured for 1 and 4 are compared (see Table 4), it could be stated that, in all solvents, compound 1 is a stronger electron donor than 4, although the latter is the stronger electron donor in the gas phase. The gas-phase I1 values of 1 and 4 differ by + 0.37 eV, and the difference in the gas-phase I1 + I2 values is even larger (+ 2.1 eV). On the other

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1st Eox

5

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Solvent

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Figure 3. CV curves recorded for the GFA compounds 4 and 5 (CH2Cl2 solutions, SCE potentials given relative to Fc/Fc + , Bu4NPF6 as supporting electrolyte, 100 mV s1 scan speed).

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Full Paper Table 5. Influence of the supporting electrolyte on the redox potentials (in V vs. Fc/Fc + ) of 4 dissolved in CH2Cl2. Supporting electrolyte

Eox

E1/2

Bu4NBr Bu4NClO4 Hex4NBF4 Bu4NPF6 Bu4NBPh4

0.69 0.63 0.65 0.62 0.55

0.76 0.74 0.75 0.70 0.68

5 to be a stronger electron donor. This again shows that the loss of aromaticity in 4 is overcompensated for by other factors. Finally, we studied the effect of ion pairing by measuring the CV curves of 4 in CH2Cl2 with different supporting electrolytes. From the data collected in Table 5 (see Figure S2 of the Supporting Information for the CV curves), it can be seen that the effect on the redox potential is comparable to the effect of solvent changes (in the order of 0.1 V). As expected, small anions, which could establish larger electrostatic interactions with the cationic organic electron donors, lead to slightly more negative redox potentials. The E1/2 value reaches a minimum of 0.76 V with Bu4NBr as supporting electrolyte and a maximum of 0.68 V with Bu4NBPh4 as supporting electrolyte. Overall, the effect of ion pairing on the redox potential is relatively small.

Figure 4. COSMO calculations (B3LYP/TZVP) on the solvation energy of the radical monocation 1 + ·. (er, DEsolv) number pairs: (1,0), (2, 0.740), (4, 1.234), (10, 1.588), (20, 1.718), (40, 1.785), (80, 1.819), (1, 1.8539).

CH3CN). A similar plot for anions was already discussed by Krossing and Raabe in the context of weakly coordinating anions.[27] The solvent stabilization energies (the difference between the total energy in the gas phase and in solution) of 1, 3, and 4 and their mono- and dications for er values of 2 and 38 are summarized in Table 6. As expected, solvent stabilization in-

Calculations: We used the conductor-like screening model (COSMO) to estimate the solvent effects. Although this model is limited, for example it does not consider chemical bonding interactions (orbital overlap) between the organic electron donor and the solvent molecules, it should help us to understand the differences in extrinsic and intrinsic electron donor strength. Moreover, the COSMO model was shown previously to be useful for modeling redox reactions in solution.[26] By using COSMO, we neglect the effect of ion-pairing, which was shown to be relatively small for 4. The CV experiments in Figures 1 and 2 show that the redox potentials vary only slightly when the solvent is changed. This is in line with other studies on larger molecules.[18] Consequently, the formal potentials for most couples are not quoted in dependence of the solvent. However, the observation that the changes upon solvent exchange are small does not imply that there is no large solvent effect. To illustrate this point, we plotted in Figure 4 the solvation energy (difference between the total energies calculated with solvent and in the gas phase) for the radical monocation 1 + · versus the dielectric constant er . An er value of 1 means gas-phase conditions. One could see that the energy changes are large for er values smaller than approximately 10 and quickly approach the er = 1 energy value for larger er values. At er = 10, one reaches already 86 % of the DEsolv value at er = 1 (1.85 eV), leaving only 14 % change from er = 10 to er = 1. Most organic redox couples are, however, not soluble in unpolar solvents with er values smaller than approximately 8. Therefore, one measures only small effects upon changing the solvent, although the er value changes greatly (e.g., er = 7.58 for THF and er = 37.5 for &

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Table 6. Results of quantum chemical calculations (B3LYP/TZVP) on the solvation energies of the electron donors 1, 3, and 4, and their radical monocations and dications in solvents of different dielectric constants (COSMO). DEsolv. [eV]

E(g) [Hartree] 1 3 4 1+ 3+ 4+ 12 + 32 + 42 +

614.263601 685.655184 1677.356742 614.081877 685.495654 1677.188004 613.752359 685.185932 1676.922754

er = 2

er = 38

0.02 0.12 0.22 0.74 0.78 0.65 2.81 2.88 2.03

0.05 0.33 0.62 1.78 1.88 1.60 6.77 6.95 4.91

creases with charge. The largest DEsolv value for a dication was calculated for 32 + (6.95 eV at er = 38), and for a radical monocation for 3 + · (1.88 eV at er = 38). Although these values are large and underline the importance of solvent effects, they are much smaller than the energy changes upon solvation of alkali cations or alkaline earth dications. Hence, solvation of Na + and Mg2 + ions in water is associated with DEsolv values of 4.21 and 19.91 eV, respectively. This is the reason why, in solution, the alkali and alkaline earth metals are stronger reducing agents than the organic electron donors. Clearly the solvation energy depends heavily on the size of the species. The calculations could not explain sufficiently the coincidence of the first and second electron oxidation waves as observed by CV measurements in some solvents for all organic 6

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Full Paper electron donors.[28] Nevertheless, due to the massive increase of solvent stabilization with charge, the difference between first and second ionization energy decreases from 2.7–4.0 eV in the gas phase to less than 1 eV in a polar solvent with er = 38. It is clear that calculations come to their limit for dications. Calculations on the second ionization energy in the gas phase are much less reliable than on the first ionization energy. In solution, the dications could interact more strongly with polar solvent molecules, leading to the failure of the simple COSMO model. As to the experiments, image charge effects involving the electrode could affect the kinetics of electron transfer between the molecule in solution and the electrode. Therefore, the quantitative analysis presented below is restricted to the first ionization step. Nevertheless, the computed results for the second ionization energy show a qualitative agreement. The ionization energies for the organic electron donors 1, 3, 4, and 5 in solutions of er = 2 and 38 are compared in Table 7. The ionization energy of 3 is now clearly lower than for all

Table 8. Reaction energies including ZPE contributions (DEZPE), enthalpy (DH0 at 298 K) and Gibbs free energy (DG0 at 298 K) changes (all in eV) for some redox-reactions between the organic electron donors in solvents of different polarity (er = 2 and 38, COSMO model, B3LYP/TZVP). Redox equation er = 2 1 + 4 + ·!1 + · + 4 3 + 4 + ·!3 + · + 4 5 + 4 + ·!5 + · + 4 1 + 42 + !12 + + 4 3 + 42 + !32 + + 4 5 + 42 + !52 + + 4

1 3 4 5

er = 38

er = 2

er = 38

4.31 3.77 4.24 4.21

3.30 2.87 3.68 3.65

7.01 6.41 5.93 5.95

4.09 3.45 4.00 4.04

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0.09 0.47 0.08 1.13 0.00 0.01

0.38 0.81 0.02 0.32 1.38 0.02

er = 2

DG0 er = 38

0.08 0.48 0.05 1.25 0.07 0.00

0.37 0.82 0.05 0.20 1.31 0.01

We have seen in the last section that intrinsic arguments could be used to explain the differences in the redox potential between compounds 1 and 3. Compound 3 is a special modification of 1, and therefore the question arises if one could generally use intrinsic arguments for modifications of a given system. We will answer this question by inspecting variations of GFA 4 (see Scheme 2). The great advantage of GFAs is that different kinds of modifications could easily be made. We consider here the effects of aromatic substitution, complexation, and protonation. The results are summarized in Table 9.

other compounds. The GFA compounds 4 and 5 are still stronger one-electron donors than 1 in a solvent of er = 2, but for er = 38 compound 1 exhibits a lower I1 value. In DMF (er = 37.0), the CV measurements show reversible two-electron oxidation waves for both 1 and 3. With E1/2 values of 1.60 V vs. Fc/Fc + (1.20 V vs. SCE) for 3 and 1.07 V vs. Fc/Fc + for 1, the difference DE1/2 amounts to 0.53 V. This is between the calculated difference of 0.43 eV for DI1 (er = 38) and of 0.64 eV for DI2 (er = 38). For the pair of compounds 1 and 4, the calculated differences are DI1 (er = 38) = 0.38 eV and DI2 (er = 38) = + 0.09 eV. Hence, the calculations predict 1 to be a stronger two-electron donor compared with 4, but a weaker one compared with 3. Indeed, the experimental difference between the reversible (two-electron) oxidation waves in DMF of 0.39 V is in excellent agreement with the calculated energy difference DI1 of 0.38 eV. In summary, one could state that the experimental results are in reasonable agreement with the predictions from the COSMO model. Reaction energies, standard enthalpies and Gibbs free energy changes (at 298 K) for some model reactions in solution are presented in Table 8. The DG0 values in solution are very different to the DG0 values calculated for the same reactions in the gas phase (see Table 3). For example, the redox reaction between 1 and 4 + · is endergonic in the gas phase, but exergonic in solution (er = 38). The difference is 0.74 eV! As expectChem. Eur. J. 2015, 21, 1 – 14

0.38 0.81 0.03 0.29 1.36 0.01

DH0 er = 38

Effect of modifications within one compound class on the redox potential

I2

I1

0.07 0.47 0.03 1.16 0.02 0.00

er = 2

ed, the differences are even larger when dications are involved.

Table 7. First (I1) and second (I2) ionization energies (in eV) of compounds 1, 3, 4, and 5 in solvents of different dielectric constants (B3LYP/TZVP, COSMO).

er = 2

DEZPE er = 38

Scheme 2. Modifications of GFA 4 studied in this work.

Aromatic substitution We synthesized two new compounds, namely 4-Cl2 (see Scheme 2) and the corresponding bromo-substituted compound 4-Br2. The dications [4-Cl2]2 + and [4-Br2]2 + were also ob7

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Full Paper on(III/II) redox couple a comparable influence of 0.1 eV is observed for substitution of Cl on the bipyridinyl ligand. However, we note that in that case the redox active site is the iron atom and not the organic ligand.

Table 9. Measured Eox,1 and Eox,2 values and the corresponding E1/2 values (all in V, in CH2Cl2 solution), the calculated molecular volume V (in 3) as well as the first (I1) and second (I2) gas-phase ionization energies (in eV). Compound

Eox,1 (E1/2)

Eox,2 (E1/2)

4 4 H+ [4(ZnCl2)2] [4(CoCl2)2] [4{Cu(OAc)2}2] 4-Cl2 4-Br2

0.62 0.39 0.02 0.12 0.33 0.44 0.43

0.62 0.02 0.02 0.05 0.14 0.44 0.43

(0.70)

(0.39) (0.52) (0.52)

(0.70)

V 707 692 [a] [a]

(0.20) (0.52) (0.52)

1007 733 [a]

I1

I2

4.66 7.40

7.31 10.18

[a]

Coordination

[a]

[a]

[a]

5.32 4.95

7.94 7.51

[a]

[a]

Another possibility to increase the redox potential (reduce the electron-donor strength) is the coordination of transition metals to the electron donor. GFAs are excellent ligands, and exhibit a rich coordination chemistry.[7] The CV curves of 4, [4{Cu(OAc)2}2],[30] [4(CoCl2)2],[10a] and [4(ZnCl2)2] are compared in Figure 6.[31] The redox potential increases with increasing Lewis

[a] Not calculated.

tained. All compounds were structurally characterized (singlecrystal X-ray diffraction, see Figure S3 and S4 of the Supporting Information). The structures show the usual changes upon oxidation, indicating loss of aromaticity and formation of two bisguanidino-allyl cations connected by two CC single bonds in the dication. The CV curves are compared in Figure 5. The

Figure 6. Comparison between the CV curves of 4, [4{Cu(OAc)2}2], [4(CoCl2)2], and [4(ZnCl2)2] (CH2Cl2 solutions, SCE potentials given relative to Fc/Fc + , Bu4NPF6 as supporting electrolyte, 100 mV s1 scan speed).

acidity of the coordinated metal ion, indicating that intrinsic effects dominate. However, reversible oxidation was only observed in the case of [4{Cu(OAc)2}2]. Indeed, [4{Cu(OAc)2}2],[30] [4{Cu(OAc)2}2] + ·, and [4{Cu(OAc)2}2]2 + were synthesized and structurally characterized. Moreover, in solution, [4{Cu(OAc)2}2] and [4{Cu(OAc)2}2]2 + were shown to comproportionate to [4{Cu(OAc)2}2] + ·. For [4{Cu(OAc)2}2], a gas-phase I1 value of 5.32 eV was calculated. Hence, upon coordination of 4 (I1 = 4.66), the gas-phase I1 value changes by + 0.66 eV. The E1/2 value for oxidation changes by + 0.31 V. The discrepancy is relatively small, but already larger than for the considered substitution. The volume changes upon coordination (from 707 3 for free 4 to 1007 3 for [4{Cu(OAc)2}2]) are already quite large.

Figure 5. Comparison between the CV curves of 4, 4-Cl2, and 4-Br2 (CH2Cl2 solutions, SCE potentials given relative to Fc/Fc + , Bu4NPF6 as supporting electrolyte, 100 mV s1 scan speed).

redox potentials are very similar for 4-Cl2 and 4-Br2. The E1/2 value at 0.70 for 4 shifts to 0.52 V for 4-Cl2 and 4-Br2. We also calculated the gas-phase first ionization energy (I1) for 4Cl2 (4.95 eV). The difference between the E1/2 values for 4 and 4-Cl2 of 0.18 V compares with a difference in the first ionization energies (in the gas phase) of 0.29 eV. Hence, we could state that, within the usual error margins, the difference in the intrinsic donor strength could be used to estimate the measured potential difference, and solvent effects could be neglected. Compounds 4 and 4-Cl2 have similar volumes (707 and 733 3), and this will be shown to be the key parameter to explain the similarity of the extrinsic contributions (the solvation energies) of these compounds (see below). A related study, concerned with the impact of different substitutions on the reduction potential of 2,2’-bipyridinyl iron complexes, recently appeared (employing a similar computational approach to that described in this work).[29] For the tris(2,2’-bipyridinyl)ir&

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Protonation Guanidines are strong Brønsted bases. The uptake of protons should shift the redox potential massively towards higher values. The changes in the CV curve upon addition of up to 2.0 equivalents of HCl are shown in Figure 7. The reversible oxidation wave at E1/2 = 0.70 V gradually decreases, and two irreversible oxidation waves at 0.39 and 0.02 V grow in. We also carried out quantum chemical calculations to compare the 8

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Full Paper formly over the molecule. Under these assumptions, there should be a relatively simple relationship between the solvation energy and the size (and/or shape) of the molecule. The extrinsic (solvation) effects on the first ionization energy (oxidation potential multiplied by the elemental charge) could be expressed as the difference between the first ionization energy in the gas phase and in solution. It was shown above that the ionization energies in solution are very similar in all solvents of er > 8 (see the CV curves in Figure 1 and Figure 2, and the plot in Figure 5). Solvents with er > 8 have to be applied in redox reactions for practical reasons, because they dissolve both neutral and oxidized species. This means that the extrinsic effects generally do not strongly depend on er. To establish a relationship between the difference DI1 = I1 (gas phase)I1 (solvent) and the size of the molecule, we considered a conjugated carbon chain in all-trans-conformation of different length. The assumptions of a relatively uniformly distributed charge and no static dipole moment are fulfilled in this case. The calculated gas-phase and solution (er = 38) first ionization energies and the volume V of the neutral carbon chain compound in all-trans-conformation by B3LYP/TZVP calculations are listed in Table 10. A detailed summary of these

Figure 7. Changes in the CV curve of 4 upon addition of up to 2.0 equivalents of HCl (CH2Cl2 solutions, SCE potentials given relative to Fc/Fc + , Bu4NPF6 as supporting electrolyte, 100 mV s1 scan speed).

gas-phase ionization energies of 4 with 4H + . The calculations predicted an increase in the ionization energy of as much as 2.74 eV upon protonation. This large increase could be explained by the formation of a dication 4H2 + upon oxidation. Although the volume difference between 4 and 4H + is small, the effect of protonation on the redox potential could certainly not be explained by the increase of the gas-phase ionization energy upon protonation. The solvation energy is very different for neutral and charged species. In summary, we could state that for modifications that do not change the charge and the static dipole moment of the molecule, intrinsic factors could be used to explain the differences in the redox potentials in solution, if the volume changes are not large.

Table 10. Parameters for the organic electron donors which were used to establish a correlation. The conjugated carbon chains (all in all-trans-conformation) with an uneven number of carbon atoms are radicals (I1 values in eV). Compd ·

CH3 C2H4 C3H5· C4H6 C5H7· C6H8 C7H9· C8H10 C9H11· C10H12 1 3 4 5 6 7 8 9

Estimation of the oxidation potential with two molecular parameters (gas-phase ionization energy and volume) Clearly, solvent effects are stronger for small ions than for large ions.[18] In the case of spherical ions (with a symmetric charge distribution), the solvation energy could be estimated through the Born equation [Eq. (2)],[27] in which z is the charge of the cation, e0 and er are the dielectric constants in vacuum and in the solvent, and r is the ionic radius. DGsolv ¼

  z 2 eNa 1 1 8pe0 r er

ð2Þ

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I1 (e = 38)

DI1

V [3]

V1/3 [1]

9.85 10.18 8.03 8.63 7.24 7.76 6.75 7.20 6.42 6.80 5.03 4.43 4.66 4.63 5.44 5.61 5.83 5.82

6.51 7.27 5.40 6.23 5.00 5.68 4.78 5.34 4.64 5.11 3.30 2.87 3.68 3.65 3.45 4.06 4.19 4.46

3.34 2.91 2.63 2.40 2.24 2.08 1.97 1.86 1.78 1.69 1.73 1.56 0.98 0.98 1.99 1.55 1.64 1.36

37 54 73 91 110 128 147 166 185 203 296 254 707 787 113 313 223 316

0.300 0.265 0.239 0.222 0.209 0.198 0.189 0.182 0.175 0.170 0.150 0.158 0.112 0.108 0.207 0.147 0.165 0.147

calculations is provided in the Supporting Information (the changes in volume upon oxidation could be neglected). Furthermore, we included compounds 1, 3, 4, and 5, the Lewis structures of which are shown in Scheme 1. Finally, to increase the diversity of electron donors, we added the following compounds (see the Lewis structures in Scheme 3): tetraaminoethylene (6), tetramethylurea azine (7), p-bis(dimethylamino)ethylene (8), and N,N,N’,N’-tetramethylbenzidine (9). The data for the conjugated carbon chains are included in Figure 8 as rectangles, the data for 3–5 and 7–9 as circles, and the data for compounds 1 and 6 as triangles.

All organic electron donors have extended p-systems. They all have only a very small or no (for a centrosymmetric structure) static dipole moment, leading to a generally small solvation energy of the neutral molecules (see Table 6). In the cation, we expect the charge to be distributed relatively uniChem. Eur. J. 2015, 21, 1 – 14

I1 (gas phase)

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Full Paper region of interest for this work, C2 could be assumed to be independent of the volume. The difference in the first ionization energies in solution of two organic electron donors A and B should be equal to the difference in their first oxidation potentials DE1/2 multiplied by the elemental charge e, resulting in Equation (4). DE1=2 ðcalcdÞ  e ¼ DI1 ðsolutionÞ ¼   1 1 ffiffiffiffiffi ffiffiffiffi ffi p p  DI1 ðgasphaseÞ  C1  3 VA 3 VB Scheme 3. Lewis structures for 6–9 included in the correlation.

ð4Þ

This formula allows for an estimate of the oxidation potential in solution without explicitly calculating solvent effects. The calculated DE1/2 values are compared with the observed values in Table 11. For compounds 7, 8, and 9, E1/2 values (vs.

Table 11. Comparison between DE1/2 values calculated with the formula established in this article, DE1/2(calcd), and the observed DE1/2 values from CV measurements.

Figure 8. Linear regression of DI1 of 1, 3, 4, and 5 and some all-trans-conjugated carbon chains plotted versus V1/3 to show the relationship between solvation energy and the molecular volume. The data for the conjugated carbon chains are included as rectangles, the data for 3–5 and 7–9 as circles, and the data for compounds 1 and 6 as triangles.

ð3Þ

A linear regression (see Figure 8) yields C1 = 12.29 eV  and C2 = 0.36 eV. The correlation coefficient R is 0.989 and the mean absolute deviation of datapoints from the linear regression is 0.053 eV. Hence, the general level of agreement is extremely pleasing. Compounds 1 and 6 (triangles in Figure 8) deviate most from the linear correlation. The reason for the deviation of 1 is discussed below. The 0.19 eV deviation of compound 6 from the value expected from Equation (3) might be a reasonable estimate for the (maximal) deviation one has to expect for different classes of redox-active compounds. It should be noted that Equation (3) will only be valid for molecules with a finite volume (at least up to 1000 3). For an infinite volume, the solvent effect should be similar for the neutral and the cationic species, and therefore I1(solution) should approach I1(gas phase). This means that C2 should approach zero for very large volumes. On the other hand, in the &

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B

DI1(gas phase) [eV]

DE1/2(calcd) [V]

DE1/2(obs) [V]

3 3 3 3 3 3

1 4 5 7 8 9

0.60 0.23 0.20 1.18 1.40 1.39

0.70 0.79 0.82 1.31 1.31 1.53

0.53 0.90 0.95 1.31 1.32 1.51

Fc/Fc + ) of 0.29,[32] 0.28,[33] and 0.09 V[34] were published. The calculated values (DE1/2(calcd)) still deviate from the experimental values (DE1/2(obs)), but generally much less than the gas phase DI1 values. Compound 8 and 9 exhibit similar ionization energies I1 in the gas phase, but the smaller size makes 8 a better electron donor in solution. One could also see that the extrinsic effects dominate over the intrinsic effects (e.g., creation of aromaticity, charge delocalization etc., which are all expressed by DI1) in the case of the pair of compounds 3/4 and 3/5. Although the DE1/2(obs) and DE1/2(calcd) values presented in Table 11 are in excellent agreement, it should be stressed that the calculations on the ionization potentials could be a major source of error. B3LYP is known to underestimate the ionization potential, for example, of oligoacenes.[35] On the other hand, the experiments tend to overestimate the real value for the adiabatic ionization energy slightly. In the case of compounds 8 and 9, experimental adiabatic ionization energy (I1) values of 6.1[36] and 6.4 eV[37] were reported, which are, as expected, larger than the values calculated herein (5.83 and 5.78 eV). The almost perfect agreement found in Table 11 certainly is fortunate. The most important point is that the volume correction term operates in the right direction. The only exception, for which the volume term does not operate in the right direction, is compound 1. This is an important exception, and the reason for the failure of Equation (4) could easily be understood. The eight methyl groups of 1 affect the ionization potential through their inductive effect,

Considering the Born equation, we plotted DI1 versus V1/3 and indeed obtained an approximately linear relationship (see Figure 8). This leads to Equation (3) for the first ionization energy in solution. C1 ffiffiffi þ C2 I1 ðsolutionÞ ¼ I1 ðgasphaseÞ  p 3 V

A

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Full Paper but are not involved in the delocalized system (that comprises only six atoms). A comparison between the volumes of 1 (tetraaminoethylene with methyl groups, 296 3) and 6 (without methyl groups, 113 3) shows that the “redox-active part” in 1 constitutes only approximately 40 % of the volume. This means that the effective volume that should be used in the equation is considerably smaller than the total volume. For all other compounds, the increase in the volume by the methyl groups has no significant consequences because the redoxactive part is considerably larger. In general, this result means that Equation (4) could not be applied if the molecule exhibits large “redox-inactive” groups. In such cases, one should instead use an “effective volume”. However, a deeper analysis is required for such cases, which is beyond the scope of the present work.

the considered organic molecule and the reference system (e.g., ferrocene) could still be a source of large flaws. Solvation of ferrocene and the ferrocenium cation in CH3CN were calculated by using the COSMO-RS method to be 0.32 and 2.31 eV, respectively.[45] These values, which are close to experimental estimates,[46] are generally different to the solvation energies of organic electron donors (see Table 6). In particular, if the size of the organic electron donors changes, if the molecule exhibits a static dipole moment, if the charge is not uniformly distributed over the molecule, or if two-electron oxidation processes are compared with one-electron processes, the solvation energy changes massively and such simple equations could not be applied.

Comment on relationships between HOMO (or LUMO) energy and redox potential measured in solution.

Conclusion We have analyzed in detail the factors that are responsible for the electron donor strength of an organic electron donor. The gas-phase ionization energy determines the intrinsic electron donor strength. The experimentally obtained oxidation potentials in solution were compared with the calculated ionization energies in solution. The (extrinsic) effect of solvation was analyzed. To increase the intrinsic reduction power, it is advisable to increase the size of the conjugated system of the electron donor. However, the resulting volume increase leads to a smaller solvent stabilization. Hence, intrinsic and extrinsic effects compete with each other, and often the extrinsic effects dominate. We established a simple relationship that should allow for an estimate of the oxidation potential in solution for an organic electron donor. The only parameters in this relationship are the gas-phase (adiabatic) ionization energy (which could be measured or calculated relatively accurately by quantum chemical methods) and the volume of the neutral molecule. We think that the relationship could be used for all molecular compounds with no or small static dipole moment and a relatively uniform charge distribution in the oxidized species. Given that the DE1/2 value could be relatively easily experimentally derived from CV measurements, the established equation could also provide an estimate for the (adiabatic) first ionization energies in the gas phase. At the end of this article, we could even go one step further. Considering that the extrinsic (solvation) effects of a species (if chemical bond interactions between solvent molecules and the species could be neglected) should not depend on the sign of the charge (positive or negative), a corresponding formula can be established for organic electron acceptors. Therefore, in summary, we have two formulas: Equation (5) for two organic electron donors A and B with molecular volumes VA and VB (zero or small static dipole moment, relatively uniform charge distribution in the oxidized species); DI1 = I1(A)I1(B) is the difference in the adiabatic gasphase first ionization energies, DE1/2 is the difference in the redox potential in solution (e.g., measured by CV measurements, and C1 = 12.29 eV ).

Several reports (e.g., ref. [29]) have described a relationship between the oxidation potential and the HOMO energy (or between the reduction potential and the LUMO energy). Generally, such relationships neglect solvation effects. We want to briefly address this point in the following. According to Koopmans’ theorem, the HOMO energy determined by quantum chemical calculations could be regarded as the vertical ionization energy.[38] However, this theorem is not fulfilled for an electron transfer from the molecule in solution to the electrode (electron transfer reactions usually take place on the millisecond timescale). Large structural relaxation effects are, for example, responsible for the phenomenon of potential inversion (two-electron oxidation wave), which could be observed for all organic electron donors 1, 3, 4, and 5 studied in this article in certain solvents. Therefore, the redox potentials derived from CV measurements are related to the adiabatic ionization energies. Consequently, a simple relationship with calculated HOMO energies is, in principle, only sensible if the relaxation energy of the cationic species could be neglected. In the case of compound 1, the difference between vertical and adiabatic ionization energy is (according to the experiments) approximately 0.8 eV.[11–13] Even for benzene, which is a relatively rigid compound, the difference between adiabatic and vertical ionization energy is already 0.22 eV.[39] Other relationships were established between the ionization energy of thin films of the organic redox-active compounds (which is then often referred to as the HOMO energy) and the redox potential (the onset of the oxidation wave in the CV curve). The potentials given relative to Fc/Fc + are then added to the work function of ferrocene, resulting in formal potentials in the Fermi scale.[40–42] Furthermore, relationships were established between the “effective” optical HOMO energies and the redox potentials in solution.[43, 44] All these correlations should generally be used with caution because they neglect both the size of the molecular compounds and solvent effects. When compounds with similar volumes are compared, such a correlation is less critical. However, the disregard of the difference in solvation energies between Chem. Eur. J. 2015, 21, 1 – 14

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Full Paper   1 1 p ffiffiffiffiffi ffiffiffiffiffi DI1 ¼ e  DE1=2 þ C1 p  3 VA 3 VB

Equation (6) for two organic electron acceptors A and B with molecular volumes VA and VB (zero or small static dipole moment, relatively uniform charge distribution in the reduced species); DEA = EA(A)EA(B) is the difference in the adiabatic gas-phase electron affinities, DE1/2 is the difference in the reduction potential in solution (e.g., measured by CV measurements, and C1 = 12.29 eV ).

[4{Cu(OAc)2}2](0/ + /2 +) systems, the structures were also obtained with the def2-TZVP basis set; for [4{Cu(OAc)2}2](0/ + /2 +) they were obtained with the smaller def2-SV(P) basis set. The thermal contributions (frequency calculations) were obtained for 1, 3, 4, and 6–9, and for the polyenes with the def2-TZVP basis set and for the other systems with the smaller def2-SV(P) basis set. The volumes presented here and used for the relationship between the oxidation potentials and the gas-phase ionization energies are taken from the conductor-like screening model; they are the volumes that are enclosed within the surface generated by the conductorlike screening model.

  1 1 p ffiffiffiffiffi ffiffiffiffi ffi DEA ¼ e  DE1=2 þ C1 p  3 VA 3 VB

Acknowledgements

ð5Þ

ð6Þ

We considered in our analysis several different electrondonor compounds, namely tetraaminoethylene derivatives (1, 3, and 6), GFAs (4 and 5), a urea azine derivative (7), p-bis(dimethylamino)phenylene (8), N,N,N’,N’-tetramethyl-benzidine (9), and also conjugated carbon chains. The formulas should also be applicable to other molecules with zero or small static dipole moment and relatively uniform charge distribution in the oxidized species. Given that the calculations indicated that the ionization energy in solution is almost invariant to changes in the dielectric constant for solvents with er values exceeding 8 (see Figure 4), the er value is not included in the formula. In the presence of redox-inactive substituents, the formulas could only be used if the redox-active percentage of the molecular volume dominates. We hope that these two formulas will be verified by other groups and for other classes of compounds in the future.

The authors gratefully acknowledge financial support by the Deutsche Forschungsgemeinschaft (DFG). Keywords: electron transfer · ionization potentials · redox chemistry · reduction · solvent effects

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Experimental and Computational Details CV measurements: For the CV measurements an EG&G Princeton 273 apparatus with an SCE as reference electrode was used. The curves were recorded at room temperature at a scan rate of 100 mV s1. CH2Cl2 was used as solvent for the individual compounds (c = 103 mol L1), whereas Bu4NPF6 (electrochemical grade ( 99.0 %), Fluka) was employed as supporting electrolyte (c = 0.1 mol L1), if not stated otherwise. Materials: All solvents were dried with an MBraun Solvent Purification System, degassed by three freeze-pump-thaw cycles and stored over molecular sieves prior to their use. Tetrakis(dimethylamino)ethylene (1) was purchased from Sigma-Aldrich and used as delivered. 1,2,4,5-Tetrakis(tetramethylguanidino)benzene[7] (4) and 1,4,5,8-tetrakis(tetramethylguanidino)naphthalene[10] (5) were synthesized as described previously. The complexes [4{Cu(OAc)2}2],[30] [4(CoCl2)2],[10a] and [4(ZnCl2)2][31] were also synthesized according to the reported procedures. Synthetic and analytical details of the compounds 4-Cl2, 4-Br2, [4-Cl2]Cl2, and [4-Br2]Br2 are provided in the Supporting Information. Details of the quantum chemical calculations: The density functional calculations were carried out with the program package TURBOMOLE[47] employing the B3LYP functional[48] and the def2SV(P) and def2-TZVP basis sets[49] and relying on the conductor-like screening model for the inclusion of the influence of the environment. The different basis sets were used according to the size of the system. For all molecules and ions, the energies were obtained with the def2-TZVP basis set. For all molecules and ions except the

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FULL PAPER & Reduction Potential

Size matters: A relationship between the gas-phase ionization energy and the experienced redox potential in solution is derived. The results highlight the importance of molecular volume in determining the reduction potential in solution (see figure).

B. Eberle, O. Hbner, A. Ziesak, E. Kaifer, H.-J. Himmel* && – && What Makes a Strong Organic Electron Donor (or Acceptor)?

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What Makes a Strong Organic Electron Donor (or Acceptor)?

Organic electron donors are of importance for a number of applications. However, the factors that are essential for a directed design of compounds wit...
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