Studies of Potential Inversion in an Extended Tetrathiafulvalene

Langmuir 2006, 22, 10683-10688

10683

Studies of Potential Inversion in an Extended Tetrathiafulvalene† Nadine E. Gruhn, Norma A. Macı´as-Ruvalcaba, and Dennis H. Evans* Department of Chemistry, UniVersity of Arizona, Tucson, Arizona 85721 ReceiVed April 27, 2006. In Final Form: May 31, 2006 Electrochemical oxidation of the extended tetrathiafulvalene 9,10-bis(1,3-dithiole-2-ylidene)-9,10-dihydroanthracene (2) was studied in N,N-dimethylformamide. A single, two-electron oxidation peak occurs, and on the return sweep of a cyclic voltammogram, a two-electron reduction peak is seen. The oxidation of 2 to its cation radical and dication occurs with potential inversion (i.e., removal of the second electron occurs more easily than removal of the first). The extent of potential inversion was estimated by cyclic voltammetry to be 0.28 V by analysis of the process in terms of concerted structural change and electron transfer. Failure to detect the cation radical by EPR of an equimolar mixture of neutral 2 and the dication is consistent with this value. The inner reorganization energy of the cation radical was determined by gas-phase photoelectron spectroscopy (PES) to be 0.31-0.35 eV. Calculations, consistent with earlier experimental data, show rather large changes in structure associated with the oxidation processes. These large structural changes contrast with the relatively small inner reorganization energy found by PES. This observation prompted an analysis of voltammetry in terms of two-step processes, with structural change either preceding or following electron transfer. Agreement of simulations based on this mechanism with experimental voltammograms was equally as good as with the concerted mechanism. Notably, the two-step mechanism produced more realistic values of the transfer coefficient and electron-transfer rate constant for the first step of oxidation.

Introduction Tetrathiafulvalene (1) (TTF) and derivatives have long been studied because of their ability to form “organic metals” and more recently as building blocks for macromolecular structures as well as a number of other applications.1 The electrochemical oxidation of 1 proceeds in two steps, first forming the cation radical and then the dication.2 The potentials are ordered normally (i.e., the formal potential of the second step of oxidation is more positive than that of the first). By contrast 9,10-bis(1,3-dithiole2-ylidene)-9,10-dihydroanthracene (2) and certain of its derivatives show a single, two-electron oxidation peak2a suggesting the possibility that the potentials are inverted (i.e., the formal potential of the second step is actually somewhat less positive than that of the first).3

There have been several qualitative reports on the oxidation of 2, and all agree that the oxidation is an overall two-electron process and that the associated reduction peak, if present, is well separated from the oxidation peak.2a,4 In the present work, we have carried out a quantitative evaluation of the nature of the oxidation of 2 as well as the reduction of 22+ focusing upon the extent of potential inversion, identification of structural changes †

Part of the Electrochemistry special issue. * To whom correspondence should be [email protected].

addressed.

E-mail:

(1) (a) Segura, J. L.; Martı´n, N. Angew. Chem., Int. Ed. 2001, 40, 1372-1409. (b) Bryce, M. R. J. Mater. Chem. 2000, 10, 589-598. (c) Nielsen, M. B.; Lomholt, C.; Becher, J. Chem. Soc. ReV. 2000, 29, 153-164. (2) (a) Pe´rez, I.; Liu, S.-G.; Martı´n, N.; Echegoyen, L. J. Org. Chem. 2000, 65, 3796-3803. (b) Lichtenberger, D. L.; Johnston, R. L.; Hinkelmann, K.; Suzuki, T.; Wudl, F. J. Am. Chem. Soc. 1990, 112, 3302-3307. (3) For a recent example of potential inversion and extensive references, see Macı´as-Ruvalcaba, N. A.; Evans, D. H. J. Phys. Chem. B 2006, 110, 5155-5160.

accompanying the oxidation, attempts to distinguish between concerted and two-step electron-transfer and structural change, and estimation by photoelectron spectroscopy of the inner reorganization energy of the cation radical of 2. The electrochemical behavior of some compounds related to 2, vinylogous tetrathiafulvalenes, has been studied, and some are found to feature single two-electron oxidation waves.5 Experimental Section Chemicals and Reagents. The source and treatment of N,Ndimethylformamide (DMF) and the tetrabutylammonium hexafluorophosphate electrolyte were the same as previously reported.6 The preparation of 2 followed published procedures.7 The sample of 2 so obtained contained 22% electrochemically inactive impurities as determined by controlled potential coulometry. These impurities gave resonances in the methyl and methylene regions of the 1H NMR spectrum. The solution concentrations were corrected from their apparent values by multiplying by 0.78. Electrochemical Cells, Electrodes, and Instrumentation. Except as indicated below, these were the same as previously reported including the polishing of the glassy carbon electrode (0.0814 cm2) and the determination of the uncompensated resistance.6 A circulating water bath was used to maintain the jacketed cell temperature for experiments between 257 and 328 K. The potential of the silver reference electrode (Ag, 0.010 M AgNO3, 0.10 M Bu4NPF6 in acetonitrile) was periodically measured versus the potential of the ferrocenium/ferrocene couple in the solvent being studied, and all potentials are reported versus ferrocene. Controlled potential coulometry was conducted with a platinum gauze working electrode as described earlier.8 The potential for (4) (a) Bryce, M. R.; Moore, A. J. Synth. Met. 1988, 27, B557-B561. (b) Moore, A. J.; Bryce, M. R. J. Chem. Soc., Perkin Trans. 1 1991, 157-168. (c) Martı´n, N.; Pe´rez, I.; Sa´nchez, L.; Seoane, C. J. Org. Chem. 1997, 62, 870-877. (d) Liu, S.-G.; Pe´rez, I.; Martı´n, N.; Echegoyen, L. J. Org. Chem. 2000, 65, 9092-9102. (e) Dı´az, M.; Illescas, B. M.; Martı´n, N.; Stoddart, J. F.; Canales, M. A.; Jime´nez-Barbero, J.; Sarova, G.; Guldi, D. M. Tetrahedron 2006, 62, 1998-2002. (5) (a) Bellec, N.; Boubekeur, K.; Carlier, R.; Hapiot, P.; Lorcy, D.; Tallec, A. J. Phys. Chem. A 2000, 104, 9750-9759. (b) Carlier, R.; Hapiot, P.; Lorcy, D.; Robert, A.; Tallec, A. Electrochim. Acta 2001, 46, 3269-3277. (c) Guerro, M.; Carlier, R.; Boubekeur, K.; Lorcy, D.; Hapiot, P. J. Am. Chem. Soc. 2003, 125, 3159-3167. (6) Macı´as-Ruvalcaba, N. A.; Evans, D. H. J. Phys. Chem. B 2005, 109, 1464214647. (7) Moore, A. J.; Bryce, M. R. Synthesis 1991, 26-28.

10.1021/la0611460 CCC: $33.50 © 2006 American Chemical Society Published on Web 06/30/2006

10684 Langmuir, Vol. 22, No. 25, 2006 oxidative coulometry of 2 was 0.04 V, and for reduction of the dication, it was -0.58 V. Each electrolysis required approximately 50 min to reach completion. Electron Paramagnetic Resonance. Attempts to detect cation radicals in equilibrium with equimolar concentrations of the neutral and the dication were carried out using electron paramagnetic resonance (EPR) spectroscopy. The experiments were performed at room temperature on a Bruker EPR spectrometer, model ESP-300. The solutions were prepared by controlled potential electrolysis with the passage of sufficient charge to convert half of the neutral 2 to the dication. For each measurement, a thin (0.8 mm i.d.) capillary was filled with sample solution to a length exceeding the height of the resonator and was inserted in such a way that both ends protruded from the resonator. The spectra were recorded at a microwave (mw) frequency of 9.653 GHz, mw power of 200 µW, modulation amplitude of 1 G, and a sufficient range to encompass radicals with g values from 1.950 to 2.065. No cation radicals could be detected. An upper limit for the concentration of the cation radicals was estimated by comparison with the doubly integrated spectrum of a 0.40 mM solution of the standard, DPPH (1,1-diphenyl-2-picrylhydrazyl radical). That upper limit was approximately 10 µM cation radical in equilibrium with 1.04 mM neutral and dication. Photoelectron Spectroscopy. Gas-phase He I photoelectron spectra were recorded using an instrument that features a 36-cm hemispherical analyzer9a and a custom-designed photon source, sample cells, and detection and control electronics.9b The ionization energy scale was calibrated using the 2P3/2 ionization of argon (15.759 eV) and the 2E1/2 ionization of methyl iodide (9.538 eV). The argon 2P 3/2 ionization also was used as an internal calibration lock of the absolute ionization energy to control spectrometer drift throughout data collection. During data collection, the instrument resolution, measured using the full width at half-maximum of the argon 2P3/2 ionization, was 0.024 eV or better. The sample of 2 sublimed cleanly over a wide temperature range with no sign of decomposition or ionizable contaminants in the gas phase. Data were collected over a sublimation temperature range of 200-280 °C with data collection (at 10-4 Torr). Temperatures were monitored using a K-type thermocouple passed through a vacuum feedthrough and attached directly to the ionization cell. The vertical length of each data mark in the spectra represents the experimental variance of that point. The reorganization energy was estimated to be the low-energy half-width of the lowest-energy band.12 A published2b spectrum of 1 was analyzed in the same manner. Calculations. Digital simulations were conducted using DigiElch, version 2.0, a free software package for the Digital simulation of common Electrochemical experiments (http://www.digielch.de).10 (8) Macı´as-Ruvalcaba, N. A.; Evans, D. H. J. Electroanal. Chem. 2005, 585, 150-155. (9) (a) Siegbahn, K.; Nordling, C.; Fahlman, A.; Nordberg, R.; Hamrin. ESCA: Atomic, Molecular and Solid State Structure Studied by Means of Electron Spectroscopy; Almqvist & Wiksells: Uppsala, Sweden, 1967. (b) Lichtenberger, D. L.; Kellogg, G. E.; Kristofzski, J. G.; Page, D.; Turner, S.; Klinger, G.; Lorenzen. J. ReV. Sci. Instrum. 1986, 57, 2366. (10) (a) Rudolph, M. J. Electroanal. Chem. 2003, 543, 23-29. (b) Rudolph, M. J. Electroanal. Chem. 2004, 571, 289-307. (c) Rudolph, M. J. Electroanal. Chem. 2003, 558, 171-176. (d) Rudolph, M. J. Comput. Chem. 2005, 26, 619632. (e) Rudolph, M. J. Comput. Chem. 2005, 26, 633-641. (f) Rudolph, M. J. Comput. Chem. 2005, 26, 1193-1204. (11) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A., Jr.; Vreven, T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A. Gaussian 03, revision C.02; Gaussian, Inc.: Wallingford, CT, 2004. (12) Gruhn, N. E.; Macı´as-Ruvalcaba, N. A.; Evans, D. H. J. Phys. Chem. A 2006, 110, 5650-5655.

Gruhn et al.

Figure 1. Voltammograms of nominally 0.79 mM 2 before (-) and after (- -) electrolysis in DMF containing 0.10 M tetrabutylammonium hexafluorophosphate. Glassy carbon working electrode. Scan rate: 2.0 V/s at room temperature.

Figure 2. Charge-time curves for the controlled potential oxidation of 0.61 mM 2 (- -) and for the controlled potential reduction (-) of the dication formed in the first electrolysis. Other conditions are the same as in Figure 1. Complete geometry optimization and frequency calculations were performed according to the density functional theory (DFT) using the B3LYP/6-31G(d,p) level with the Gaussian 03 program.11 For the cation radical, the corresponding unrestricted (UB3LYP) method was used. Structural optimization was followed by frequency calculations to be certain that there were no imaginary frequencies.

Results and Discussion Study of the Electron Stoichiometry of the Oxidation of 2. Figure 1 shows voltammograms for nominally 0.79 mM 2 before (solid curve) and after (dashed curve) controlled potential coulometry carried out at 0.04 V. Before electrolysis, a single oxidation peak occurs at -0.04 V, and it is accompanied by a single reduction peak at -0.38 V. After electrolysis, the oxidation peak has disappeared and is replaced by the reduction peak encountered on an initial scan in the negative direction. The corresponding charge-time curve is shown in Figure 2 (lower trace) where it can be seen that the electrolysis is essentially complete after about 50 min where the charge no longer changes with time. During electrolysis, the solution became orange, the color of the dication. At the end of the electrolysis, the solution of the dication of 2 was subjected to a second controlled-potential electrolysis at -0.58 V so as to reduce the dication back to 2. Notably, the charge recovered was within 5% of that required for the initial oxidative electrolysis, attesting to the excellent stability of the dication (Figure 2, upper trace). However, the amount of charge required for both oxidation and reduction is, through application of Faraday’s law, only 78% of that predicted for two-electron reaction of the amount

Potential InVersion in Extended TetrathiafulValene

Langmuir, Vol. 22, No. 25, 2006 10685

Table 1. Experimental Conditions and Simulation Parametersa conc/mM

temp/°C

E°1/V

E°2/V

E°ov/Vb

E°1- E°2/V

ks,1/cm s-1

ks,2/cm s-1

R1

R2

D × 106/cm2 s-1

rangec

0.77 0.61 0.46

25 roomd 25

-0.029 -0.044 -0.030

-0.318 -0.316 -0.320

-0.174 -0.180 -0.175

0.289 0.272 0.290

0.022 0.037 0.027

0.0050 0.0059 0.0052

0.27 0.30 0.25

0.62 0.62 0.60

5.01 5.57 5.81

0.10-30.0 0.10-10.0 0.10-10.0

0.77e

-16 -8 2 10 18 25f 35 45 55

-0.021 -0.017 -0.018 -0.009 -0.015 -0.029 -0.028 -0.032 -0.034

-0.396 -0.389 -0.375 -0.370 -0.344 -0.318 -0.303 -0.289 -0.272

-0.208 -0.203 -0.196 -0.190 -0.180 -0.174 -0.166 -0.160 -0.153

0.375 0.372 0.357 0.361 0.329 0.289 0.275 0.257 0.238

0.0015 0.0030 0.0045 0.010 0.015 0.022 0.023 0.025 0.029

0.00018 0.00042 0.00080 0.0020 0.0030 0.0050 0.0063 0.0097 0.013

0.30 0.28 0.30 0.26 0.28 0.27 0.29 0.29 0.25

0.50 0.50 0.52 0.55 0.58 0.62 0.63 0.63 0.63

2.47 3.06 3.62 4.09 4.65 5.01 5.64 6.51 7.33

0.10-1.0 0.10-2.0 0.10-2.0 0.10-10.0 0.10-10.0 0.10-30.0 0.20-30.0 0.20-30.0 0.30-30.0

0.61g

roomd

-0.042

-0.317

-0.180

0.275

0.037

0.0042

0.17

0.59

5.00

0.10-10.0

a

The same values were used to fit all scan rates included in range (final column). Potentials are with respect to the ferrocene couple measured in DMF at 298 K. Resistance compensation. Format: temperature (°C)/total resistance (Ω)/resistance electronically compensated (Ω): -16/520/420; -8/470/420; 2/380/330; 10/340/300; 18/320/270; 25/290/250; 35/260/210; 45/235/200; 55/247/185. The residual uncompensated resistance was included in the simulations. b Overall standard potential for DC2+ + 2e- h N. E°ov ) (E°1 + E°2)/2. c Voltammograms were simulated over this range of scan rates (V/s). d These experiments were conducted in an electrolysis cell that was not fitted for temperature control. e Solution prepared at 25 °C. Concentrations at other temperatures have not been corrected for thermal expansion/contraction. f Repeat of the first-row entry g Solution of the dication (22+) prepared by controlled potential electrolysis.

Figure 3. Cyclic voltammogram of 0.61 mM 2 at 2.0 V/s. Other conditions are the same as in Figure 1. Full curve: experimental background-corrected voltammogram. Symbols: simulation using parameters in Table 1.

of 2 taken. The oxidative electrolysis was repeated, and a total of four experiments indicated that the percent of 2 in the preparation was 77.7 ( 1.4%. Thus, on the basis of coulometric analysis, we conclude that 22% of 2 consisted of electrochemically inert impurities. For the remainder of the experiments, the apparent concentration of 2 was corrected to give actual concentrations that are 22% lower. Analysis of Cyclic Voltammograms of 2. Figure 3 compares a simulation with an experimental voltammogram for 0.61 mM 2 at 2.00 V/s and 25 °C. The simulation is based on two electrontransfer reactions with their associated equilibrium and kinetic parameters (eqs 1 and 2; E°: formal potential; ks: standard heterogeneous electron-transfer rate constant; R: electron-transfer coefficient). Disproportionation reaction 3 was not included because it was found to have only minor effects when introduced into the simulation.

CR•+ + e- h N

E°1, ks,1, R1

(1)

DC2+ + e- h CR•+

E°2, ks,2, R2

(2)

2CR•+ h N + DC2+

Kdisp, kf, kb

(3)

Here, N is the neutral, CR•+ the cation radical, and DC2+ is the dication. Simulations of voltammograms for scan rates from 0.10 to 30.0 V/s were carried out, and the parameters that provided the best fit for all scan rates are given in Table 1. Comparisons

Figure 4. Cyclic voltammogram of 0.61 mM dication 2 at 2.0 V/s. Other conditions are the same as in Figure 3.

of simulations with experimental voltammograms for other scan rates are given in the Supporting Information. A total of three data sets (two at 25 °C and one at room temperature) were analyzed, and the results are also shown in Table 1. Potential inversion is consistently indicated for all data sets, giving an average value of E°1 - E°2 of 0.284 ( 0.010 V. Though the precision is good, it is difficult to assess the error, particularly when such a large inversion is found.3b,6,12-14 Nevertheless, it is clear that the potentials are strongly inverted. The results of controlled potential electrolysis (Figures 1 and 2) indicate that the dication is quite stable. Therefore, simulations were performed for voltammograms obtained with a solution of dications prepared by electrolysis. An example of a fit of simulation to experiment is shown in Figure 4, and the simulation parameters are included in Table 1 (last entry). The parameters so obtained are in good agreement with those from experiments with solutions of neutral 2. Experiments with neutral 2 were conducted over a range of temperatures from -16 to 55 °C with the hope of detecting intermediate species following electron transfer (low temperatures) or intermediate species formed before electron transfer (high temperatures). No new peaks appeared in the voltammograms, and in fact, the data could be accounted for adequately using the same mechanism as employed at 25 °C, namely, reactions 1 and 2. The simulation parameters are also included in Table 1, where it may be seen that the potential inversion (13) Kraiya, C.; Evans, D. H. J. Electroanal. Chem. 2004, 565, 29-35. (14) Lehmann, M. W.; Singh, P.; Evans, D. H. J. Electroanal. Chem. 2003, 549, 137-143.

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Gruhn et al.

exists at all temperatures. The extent of inversion is smallest at the highest temperature, which is consistent with an exothermic disproportionation reaction. The overall standard potential for the DC2+ + 2 e- h N couple varies only 55 mV over the entire temperature range. Both rate constants show the expected decrease with decreasing temperature, and the diffusion coefficient increases about 1.4%/ °C with increasing temperature. Clearly, this simple mechanism accommodates the data quite well and with reasonable values of the equilibrium (potentials) and rate (ks, D) parameters. The single exception is the value of R1, which falls in the range of 0.25-0.30, rather far removed from the normal value near 1/2. Electron Paramagnetic Resonance (EPR) Spectroscopy Used to Estimate a Lower Limit to the Equilibrium Constant for Disproportionation. The equilibrium constant for reaction 3 is related to the standard potentials for reactions 1 and 2 by eq 4:

Figure 5. Two lowest-energy bands in the photoelectron spectrum of 2. Line: baseline. Full curves: fits with asymmetric Gaussian functions. 6.61 eV band: low-energy half-width ) 0.35 eV, high energy half-width ) 0.54 eV. 7.15 eV band: low energy half-width ) 0.19 eV, high energy half-width ) 0.42 eV.

Thus, the extensive potential inversion suspected in the present case should correspond to very large values of Kdisp. EPR can be used to determine the concentration of the cation radical in the presence of known amounts of the neutral and dication, leading to Kdisp and to E°1 - E°2 via eq 4. This approach was successfully employed with some analogues of tetracyanoquinodimethane.3 As described in the Experimental Section, measurements with a solution containing 1.04 mM neutral and 1.04 mM dication indicated that the concentration of the cation radical was less than about 10 µM, which corresponds to a lower limit for Kdisp of 104. This means that E°1 - E°2 > 0.237 V, which is consistent with the extent of inversion inferred from the voltammetry. That the cation radical should undergo disproportionation to form the neutral and dication is also supported by prior kinetic studies of the reaction of the radicals formed by time-resolved pulse radiolysis of 2 in dichloromethane.15 Inner Reorganization Energy of the Cation Radical as Determined by Photoelectron Spectroscopy (PES). The electron-transfer rate constants found by simulation (ks,1 ) 0.022 and ks,2 ) 0.0050 cm/s at 25 °C) are somewhat small when compared with those of other aromatic systems.16 As will be clear later in the discussion, it is likely that significant structural changes accompany one or both of the electron-transfer reactions. A possible explanation for small rate constants is that there is a significant inner reorganization energy associated with the reactions. We have recently used PES to demonstrate that the inner reorganization energy for the cation radicals of 9,10-bis(dimethylamino)anthracene and 3,6-bis(dimethylamino)durene are quite small, although their electron-transfer rate constants are abnormally small when evaluated in the manner employed in the present article.12 The gas-phase valence photoelectron spectrum of 2 is shown in the Supporting Information, and Figure 5 shows the two lowenergy bands that appear below 8 eV. The leading half-width of the lowest-energy band, which corresponds to ionization from the HOMO, is 0.35 eV, and this is a reasonable estimate of the inner reorganization energy. A detailed analysis of the shape of the lowest-energy band, as described earlier,12 yielded 0.31 eV, nearly the same as the leading half-width. From the leading

half-width of a published PES spectrum of 1,2b the inner reorganization energy of its cation radical was found to be 0.31 eV. The inner reorganization energy of 2 is about the same as that of 1, a compound that shows normal ordering of potentials with both reactions being quite reversible.2a Thus, the rather small values of the electron-transfer rate constants found for 2 cannot be attributed to a very large inner reorganization energy. As discussed in the case of some bis(dimethylamino)arenes,12 the reactions of 2 may actually be two-step processes consisting of structural change as a discrete chemical step either preceding or following electron transfer. Structural Changes Accompanying the Oxidation of 2. Structures of the neutral, cation radical, and dication, obtained through DFT calculations, are shown in Figure 6. The neutral and the dication have been the subjects of earlier theoretical calculations,17 and X-ray crystal structures of these forms of the derivative with methyl groups attached to the 4 and 5 positions of the dithiole rings have been published.18 A comparison of our calculated bond lengths and angles with the published data showed excellent agreement, which serves to validate our calculations and support the correctness of our calculated structure of the cation radical, which has not been considered previously. The “butterfly” shape of the neutral results from strong interactions between the sulfur atoms and hydrogen atoms on the central anthracene system. The result is that the two 1,3dithiol-2-ylidene moieties are pointed upward and the anthracene sytem is folded downward. The structure of the dication differs drastically from that of the neutral (Figure 6). The 1,3-dithiol2-ylidene groups are now turned out of the plane of the anthracene system (ca. 90°), and the latter has returned to an almost planar configuration. In our calculations for the cation radical, we were able to identify a structure (Figure 6) that resembles the structure of the neutral but with less folding of the anthracene system and a lower bowsprit angle for the dithiole groups. One other form of the cation radical was found in which the anthracene moiety was somewhat planar and the two dithiole units were directed to opposite sides, imparting a slight chairlike character to the central ring. The energy of this structure was 12 kcal/mol greater than that shown in Figure 6. The 0.31-0.35 eV reorganization energy of the cation radical found by PES corresponds to the difference in energy of the cation in the structure of the neutral and the

(15) Guldi, D. M.; Sa´nchez, L.; Martı´n, N. J. Phys. Chem. B 2001, 105, 71397144. (16) (a) Kojima, H.; Bard, A. J. J. Am. Chem. Soc. 1975, 97, 6317-6324. (b) Petersen, R. A.; Evans, D. H. J. Electroanal. Chem. 1987, 222, 129-150.

(17) Martı´n, N.; Sa´nchez, L.; Seoane, C.; Orti, E.; Viruela, P. M.; Viruela, R. J. Org. Chem. 1998, 63, 1268-1279. (18) Dı´az, M. D.; Illescas, B. M.; Martı´n, N.; Viruela, R.; Viruela, P. M.; Orti, E.; Brede, O.; Zilbermann, I.; Guldi, D. M. Chem.sEur. J. 2004, 10, 2067-2077.

F Kdisp ) exp (Eo1 - Eo2) RT

[

]

(4)

Potential InVersion in Extended TetrathiafulValene

Langmuir, Vol. 22, No. 25, 2006 10687 Scheme 1

Table 2. Parameters Used in Simulations According to Scheme 1a parameter

Figure 6. Optimized structures of neutral 2, the cation radical, and the dication.

cation in its optimized structure. The calculations give 0.14 eV for this energy difference. Whether by calculation or experiment, the inner reorganization for the oxidation of 2 to its cation radical is quite small. These calculations confirm that a major structural change occurs upon proceeding from the neutral to the dication. It is not clear whether the greater part of the structural change is associated with the first or with the second electron transfer or whether one of these structural changes is sufficiently small that it is reasonable to assume that it is concerted with electron transfer. Nevertheless, it is reasonable to assume that at least one of the reactions occurs as a two-step process with structural change occurring as a distinct chemical change (isomerization, conformational change, etc.) either preceding or following the electron transfer. Analysis of the Voltammograms According to Two-Step Processes. In this section, we will determine whether two-step processes can be the basis of a mechanism that will account for the data as effectively as the concerted processes used above. The mechanism is given as Scheme 1 in which the species labeled “DC” have structures similar to the structure of the dication, “CR” species have structures similar to that of the cation radical, and “N” species have structures similar to that of the neutral compound. This mechanism includes two-step processes for both electron transfers with structural change occurring both before and after electron transfer. One data set obtained at 25 °C was analyzed according to Scheme 1, and the best-fit parameters are given in Table 2. The agreement between simulation and data for scan rates from 0.10 to 30.0 V/s was of equal quality to that obtained in the simulations reported in Table 1 wherein the electron transfers and structural changes are considered to be concerted. Comparisons of data

KCR/N kNfCR kCRfN KCR+/N+ kN+fCR+ kCR+fN+ KDC+/CR+ kCR+fDC+ kDC+fCR+ KDC2+/CR2+ kCR2+ fDC2+ kDC2+fCR2+ o EDC 2+/DC+ ks, DC2+/DC+ o ECR 2+/CR+ ks, CR2+/CR+ o ECR +/CR ks,CR+/CR ENo +/N ks,N+/N o b EDC 2+/CR+ o b ECR +/N o Eoverall

5.5 × 10-6 0.9 s-1 1.6 × 105 s-1 1.8 × 103 5.1 × 109 s-1 2.9 × 106 s-1 2.2 × 10-3 1.1 × 104 s-1 4.8 × 106 s-1 4.7 90 s-1 19 s-1 -0.495 0.36 cm/s -0.299 V 0.030 cm/s -0.328 V 0.36 cm/s 0.175 V 2.6 cm/s -0.338 V -0.017 V -0.178 V

a Potentials are referred to the formal potential of the ferrocenium/ ferrocene couple. Measurement conditions: 0.77 mM 2, 25 °C; scan rates simulated: 0.10-30.0 V/s. Values of R for all four electron-transfer reactions were set at 0.50. Diffusion coefficient for all species: 5.3 × 10-6 cm2/s. b Values calculated from formal potentials and equilibrium constants from analysis according to Scheme 1.

with simulations for both mechanisms for this data set are shown in the Supporting Information. That equally good fits could be obtained using reactions 1 and 2 compared to Scheme 1 is not surprising in view of the additional array of parameters available in Scheme 1. What is more important is that, where comparisons can be made, there is reasonable agreement between parameters found for both mechanisms. These o include ECR +/N ) -0.017 V (Scheme 1, Table 2) and E° 1 ) o -0.029 V (reaction 1, Table 1), EDC 2+/CR+ ) -0.338 V (Scheme 1, Table 2) and E°2 ) -0.318 V (reaction 2; Table 1), E°ov ) -0.178 (Scheme 1; Table 2) and -0.174 (Table 1), and finally, E°1 - E°2) 0.321 V (Scheme 1) and 0.289 V (Table 1). The greatest improvement of Scheme 1 over reactions 1 and 2 (in which the structural changes and electron transfer are considered to be concerted) is that all R values were 0.50 for Scheme 1 whereas an abnormally low value of 0.25-0.30 was required for R1 when fitting with reactions 1 and 2. Similar healing of deviant R values was obtained when Scheme 1 was applied to the oxidation of two bis(dimethylamino)arenes.12 Also, according to Scheme 1 the rate constant for the first electrontransfer reaction (N f N•+ + e-) is large, ca. 2-3 cm/s, which is much more consistent with a reaction having the small inner

10688 Langmuir, Vol. 22, No. 25, 2006

reorganization energy found by PES and theoretical calculations than the much smaller value (0.022 cm/s) found when concerted electron transfer and structural change are assumed (reaction 1). By examining the dimensionless kinetic parameters19 for structural change preceding or following electron transfer and using the data in Table 2, it is possible to conclude that the first step of the oxidation proceeds virtually entirely along the path N f N•+ f CR•+ and the reduction process follows the reverse of this sequence. That is, the postulated neutral compound with a structure resembling the cation radical is of no importance in fitting the voltammograms. The second stage of oxidation is not as clear, with both pathways apparently contributing.

Conclusions The oxidation of 2 occurs with potential inversion, and the extent of inversion has been estimated from voltammograms obtained over a range of temperatures from -16 to 55 °C. The failure to detect by EPR any cation radical (2•+) in an equimolar mixture of dication 22+ and neutral 2 is consistent with the degree (19) (a) Nicholson, R. S.; Shain, I. Anal. Chem. 1964, 36, 706-723. (b) Bard, A. J.; Faulkner, L. R. Electrochemical Methods: Fundamentals and Applications, 2nd ed.; Wiley: New York, 2001; Chapter 12.

Gruhn et al.

of inversion found by voltammetry. PES shows that the inner reorganization energy of 2•+ is small, 0.31-0.35 eV. Calculations show that significant structural change accompanies the oxidation of 2 to the dication. This fact and the small inner reorganization energy found by PES suggest that the electron transfer and structural change probably occur in separate steps. Simulation of the voltammograms using these two-step reactions provides fits with agreement equally as good as that of simulations that consider electron transfer and structural change to be concerted. In addition, the two-step processes provide an R value of 1/2, a considerable improvement over 0.25-0.30 for R1 in the concerted mechanism. Acknowledgment. Support by the National Science Foundation, grant CHE 0347471, is gratefully acknowledged. We thank Dr. Andrei Astashkin, Electron Paramagnetic Resonance Facility, University of Arizona, for the EPR measurements. Supporting Information Available: PES spectrum of 2. Comparison of simulations of voltammograms of 2 using the concerted mechanism (reactions 1 and 2) and the two-step mechanism (Scheme 1) for 25 °C. This material is available free of charge via the Internet at http://pubs.acs.org. LA0611460