Electron Paramagnetic Resonance Spectroscopy of Bis(triarylamine


Jan 27, 2009 - The coalescence rate constants, |γeΔB|/√2, amount to 1.12 × 108 s−1 for pairs of lines separated by aN and to 2.24 × 108 s−1 ...
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J. Phys. Chem. C 2009, 113, 2983–2995

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Electron Paramagnetic Resonance Spectroscopy of Bis(triarylamine) Paracyclophanes as Model Compounds for the Intermolecular Charge-Transfer in Solid State Materials for Optoelectronic Applications Daniel R. Kattnig,† Boryana Mladenova,† Gu¨nter Grampp,*,† Conrad Kaiser,‡ Alexander Heckmann,‡ and Christoph Lambert*,‡ Institut fu¨r Physikalische and Theoretische Chemie, Technische UniVersita¨t Graz, Technikerstrasse 4/I, A-8010 Graz Austria, and Institut fu¨r Organische Chemie, Julius-Maximilians UniVersita¨t Wu¨rzburg, Am Hubland, D-97074 Wu¨rzburg, Germany ReceiVed: December 8, 2008

A set of seven bis(triarylamine) mixed-valence radical cations with different bridging moieties were investigated by temperature-dependent electron paramagnetic resonance (EPR) spectroscopy in methylene chloride and ortho-dichlorobenzene to evaluate the thermal electron transfer rate constants. The bridges used comprise [2,2]paracyclophane and [3,3]paracyclophane as well as fully conjugated phenylene spacers. The cyclophanes serve as model structures for studying the intermolecular electron transfer in solid state materials. The activation barriers derived by EPR measurements are compared with those estimated by the two-state Marcus-Hush analysis as well as by its extension to three states. Both methods gave good agreement with the EPR data, the three-state method being slightly better than the two-state method. On the basis of the choice of the different bridging groups, our study shows that the bridge can have a significant influence on the internal reorganization energy. [2,2]Paracyclophane and [3,3]paracyclophane bridge units show practically the same electronic coupling and thermal barrier. Conjugated bridges have thermal rates about 1 order of magnitude larger than the radical cations with broken conjugation. These two aspects show that in solid state materials triarylamines drawn close to their van der Waals radii may exhibit efficient coupling and rate constants by only 1 order of magnitude smaller than fully conjugated materials. Introduction Mixed-valence (MV) compounds, in which two or more structurally identical redox centers in different formal redox states are connected via saturated or unsaturated bridges, are well-known model compounds for fundamental electron transfer studies.1-4 The virtue of this class of compounds is that the intramolecular electron transfer (ET) can be induced optically as well as thermally. By means of Hush’s theory and its successors, the two most fundamental ET parameters, the reorganization energy, λ, and the electronic coupling matrix element, V, are accessible from the charge-transfer absorption bands associated with the optical ET. The thermal process can be discerned from temperature-dependent electron paramagnetic resonance (EPR) studies. Only rarely have both methods been employed concurrently.5-12 Organic MV systems with triarylamine redox centers are the focus of many studies13-32 because of their close relationship to the triarylamine systems that are widely used as hole conductive layers in (opto)electronic devices such as organic light-emitting diodes, field-effect transistors, or solar cells.33-40 In these devices, the dynamics of intermolecular hole transfer play a crucial role, and tuning this process is of the utmost importance for device optimization. While many studies of charge carrier mobility in triarylamine-based solid state materials are available,41 almost nothing is known about the rates of the elementary hole transfer step between two adjacent triarylamine * Corresponding authors. E-mail: [email protected]; uni-wuerzburg.de. † Technische Universita¨t Graz. ‡ Julius-Maximilians Universita¨t Wu¨rzburg.

[email protected]

groups. In the past ten years, we and others have focused on evaluating the electronic coupling in and reorganization energies of triarylamine-based MV radical cations by analyzing their optical spectra.13-22,26,28 For this purpose, the traditional twostateMarcus-Hush(MH)relationshiphasoftenbeenemployed.42-47 In this paper, we focus on the evaluation of thermal hole transfer rate constants in bis(triarylamine) MV radical cations by EPR spectroscopy in liquid solution. We thereby concentrate on MV compounds with paracyclophane spacers interconnecting the triarylamine centers and on some fully conjugated systems for comparison (see Chart 1). The optical spectra of these radical cation systems with the exception of IV+ were published recently.15,48,49 The paracyclophane bridges will serve as scaffolds mimicking the situation of intermolecular charge transfer in solid state arrangements. In particular, these units act to bring the two π-faces of the triarylamine moieties in close contact without establishing one fully conjugated π-system. The situation is, thus, intermediate between the intermolecular linkage in solid triarylamine semiconductors, in which the amine units are stacked instead of wholly conjugated, and the situation resulting for fully conjugated intramolecular linkage.50 For the [2,2]paracyclophane, the π-systems are forced to be as close as 3.1 Å,51,52 which is distinctly smaller than the van der Waals (vdW) radius of carbon (2 × 1.7 Å ) 3.4 Å). For [3,3]paracyclophane, a π,π-distance of 3.3 Å53 results, which is only slightly smaller than the vdW distance. Additionally, in [2,2]paracyclophanes, one can speculate about the contribution of the ethylene bridges (through bond interactions) to the π,π-interactions,51,54-57 a factor which is absent in [3,3]paracyclophanes. In particular, the latter is not expected to induce a coupling

10.1021/jp8107705 CCC: $40.75  2009 American Chemical Society Published on Web 01/27/2009

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CHART 1

beyond that realized by distinct molecules at the vdW contact distance. [4,4]Paracyclophane, on the other hand, gives rise to a π,π-distance of ca. 4 Å,58 which is much larger than the vdW distance. Thus, we decided to concentrate on bis(triarylamine) radical cations with [2,2]paracyclophane and [3,3]paracyclophane bridging moieties. Note that while the charge transfer along conjugated backbones is usually fast it often is the charge transfer between the conjugated entities that limits the overall ET rate. With respect to molecular structure, the compounds studied in this contribution share the following characteristics (cf. Chart 1): First, the triphenylamine groups carry methoxy substituents in para position, which give rise to a lower oxidation potential59 and rather stable radical cations that can be investigated in a variety of solvents over large temperature intervals. In fact, triphenylamine cation radicals that are not protected in para position dimerize readily yielding, after releasing two protons, benzidine derivatives.60 Second, the rigid spacers employed restrict the number of thermally accessible conformers essentially to rotamers about the center-center axis (not regarding reorientations of the diphenylamine moiety itself). In this way, nominal N-N distances up to 28.7 Å (VII+; based on AM1 calculations on the diamagnetic precursor), which correspond to 25 alternately unsaturated bonds, are realized. Three model compounds (I+-III+) are interlinked by bridges containing the [2,2]paracyclophane unit. The compounds are pseudopara connected and span a range of distances from 15.0 Å (16 bonds) to 25.0 Å (24 bonds). Finally, in compound IV+, a [3,3]paracyclophane bridge is employed, which serves primarily to physically connect the moieties. For comparison, we also studied several systems of intermediate length with direct π-conjugation mediated by the p-xylene

(V+) and the p-phenylene bridge (VI+). Compound VII+ is the largest purely organic mixed valence compound for which intervalence charge-transfer (IV-CT) phenomena have so far been observed.49 To disentangle the hyperfine patterns of these compounds, we have studied the two monomeric triarylamines VIII+ and IX+. Although powerful, the investigation of near-infrared IV-CT absorptions alone yields only limited insight into the microscopic details of the electron transfer in mixed-valence compounds. In particular, only energetic factors are revealed, while the dynamic aspects of the process are unavailable. Though the reorganization energy, λ, and, with some restrictions, the electronic coupling, V12, between the diabatic states are accessible from the analysis of the IV-CT bands, the actual rates of thermal ET remain entirely undisclosed. Furthermore, insights on the barrier heights of the thermal hole transfer processes remained at best semiquantitative. In addition, for organic mixed valence compounds, there is a great uncertainty associated with the diabatic electron transfer distances, r12,61-64 that renders the estimate of |V12| from the MH analysis vague for Robin-Day Class II species, in which the charge is strongly localized at one redox center (λ > 2|V12|). In the past, some of us have attempted to overcome this issue by detailed analysis of the IV-CT absorption bands within the generalized Mulliken-Hush (GMH) framework65-68 or by modeling the entire potential energy surface (PES).15,17,48 Since in the former case the analysis has been supplemented by calculated permanent dipole moments, the question of the exchange distances partly sustains. A critical evaluation of the validity of these approaches is still missing. For the above-mentioned reasons, we decided to undertake temperature-dependent EPR measurements on the IV-CT com-

Spectroscopy of Bis(triarylamine) Paracyclophanes

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Figure 1. Transition dipole moment representation (ε/ν)71 of the VIS/NIR spectra of (a) II+ and (b) IV+ in methylene chloride solution and their decomposition into three Gaussian functions.

pounds I+-VII+. Our goal is to compare the ET barrier parameters derived from the EPR measurements with those derived from analysis of optical spectra within a two-state or three-state model (vide infra). In particular, our investigations attempt to answer the question to what extent coupling matrix elements and reorganization energies extracted from the IVCT bands provide reliable estimates of the activation barrier of the thermal electron transfer process. In general, EPR studies on MV compounds are still scarce; only a few purely organic mixed valence compounds were subjected to a comprehensive study by both EPR and optical methods.5-12,46,69 In a recent study on vinylene-bridged bisdianisylamine compounds, i.e., compounds that are analogous to ours except for the kind of unsaturated bridges, Barlow et al.28 have obtained poorly resolved EPR spectra of the monocations, which were not found useful in unraveling the thermal ET process. Unlike this group, we have been able to disentangle the EPR spectra of the radical cations and extract the rate of thermal electron transfer from temperature-dependent alternating line width phenomena. Except for a study of a Si-bridged triarylamine by Hirao et al.,27 this is the only successful attempt of determining thermal electron transfer rates of bis(dianisylamine) IV-CT compounds so far. Results Electrochemical Characterization. The redox chemistry of the compounds I-IX is characterized by the reversible oxidation of the triarylamine centers, as expected. All compounds show a first oxidation wave between 200 and 300 mV vs ferrocene/ ferrocenium in CH2Cl2 (MC; for details see Supporting Information).15,48,49 Furthermore, the bis(triarylamines) exhibit a second reversible oxidation process due to the additional center, which however is not resolved. Digital simulation clearly distinguishes the cyclic voltammogram wave from a simultaneous two-electron process and yields a half-wave potential difference, ∆E, of ca. 50 mV for all compounds. This value is close to, however larger than, the static value of 35.6 mV for two noninteracting redox centers. This is a hint that the two centers interact weakly. Indeed, the monoradical cations have been found to be IV-CT species of Robin-Day Class II. We shall furthermore point out that the redox potentials of the mononuclear compound IX and that of its bis(triarylamine) analogues V (and also IV) match, indicating that for V (and IV) the electron is indeed confined to one redox center and possibly the bridge. In addition, it is remarkable that the first oxidation potentials increase with intercenter distance; e.g., for

the cyclophane bridged compounds, the potential increases from 200 to 240 and 290 mV when introducing the acetylene and butadiyne spacer, respectively. This indicates a stabilization of the HOMO and/or increased free energy of solvation due to delocalization over the increasingly large electrophore as the bridge is elongated. In solution, the monoradicals of bis(triarylamines), D+, are subject to the disproportionation reaction

D+ + D+ h D + D2+ The associated equilibrium constant Kdisp assumes a value of 1/4 for noninteracting radicals and a value of 0.14 assuming ∆E ) 50 mV at 298 K. Thus, in the EPR studies we have typically used a 10-fold excess of D to detect the monoradical for the most part free of disturbance from the biradical/triplet. Assuming ∆E ) 50 mV (35.6 mV), the ratio of the concentrations of the mono- and the biradical amounts to 65 (38) for a 10-fold excess of the diamagnetic precursor with respect to the oxidizing agent, cOx/c0 ) 10. Note that in addition the concentration of the diamagnetic precursor, c0, has to be constrained to less than approximately 5 × 10-3 M in order to not induce a significant broadening by the intermolecular degenerate electron transfer reaction. The quoted limit is set by the “natural” EPR line width of the radical cations and assuming a rate constant of degenerate, intermolecular ET of the typical order of magnitude 109 M-1s-1 (see Experimental Details).70 Optically Induced Charge Transfer. Figure 1 exemplarily illustrates the VIS/NIR absorption spectra of the radical cations of the [2,2]paracyclophane and [3,3]paracyclophane bridged intervalence compounds II+ and IV+ in dichloromethane (MC). The spectra of the other radical cations can be found in refs 15, 48, and 49. All spectra of all radical cation compounds exhibit a broad absorption band in the NIR region between ca. 6000 and 12 000 cm-1 (see Table 1), which is associated with the optically induced intramolecular hole transfer from the oxidized triarylamine moiety to the neutral one (IV-CT band). In two cases (IV+ and VII+), this band overlaps with a second very intense band at higher energy and is, thus, only visible as a broadening at the foot of this band. The origin of the low-energy bands can best be understood in terms of a three-state model. The potential energy diagram (Figure 2) comprises three diabatic (formally noninteracting) states: two (degenerate) states (Ψ1 and Ψ2), for which the hole is localized at either triarylamine moiety, and a third state (Ψ3), in which the hole is localized at the bridge.

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TABLE 1: Parameters Extracted from the Generalized Mulliken-Hush Analysis of the Intervalence Transitions in MCa +

I II+ III+ IV+ V+ VI+ VII+

ν˜ a

ν˜ b

V12b,d

V13b,d

V23b,d

Vtwo-levelc

lit.

6230 5870 7500 8500 7500 8060 11790

11870 10730 11100 10610 11590 12000 14100

970 580 220 110e 1220 1000

990 1850 1070 1530e 1590 560

1550 860 710 720e 510 1570

710 310 70 320 1030 770 190

48 48 48 this work 48 15 49

a ν˜ a and ν˜ b denote the position of the absorption maxima due to the degenerate charge shift and due to the charge transfer to the bridge state, respectively. The electronic couplings Vij are derived from the GMH analysis, while Vtwo-state is derived from the two-state Marcus-Hush treatment, which neglects the bridge state. Refer to the cited literature for details. All values are given in cm-1. b Obtained by the GMH three-state model. c Obtained by the GMH two-state model. d Odd number of positive coupling values. e Uncertain due to band overlap issues.

Figure 2. Projection of the potential energy surfaces onto the asymmetric ET coordinate.

For each diabatic state, we assume a quartically augmented3,15,17,48,72 harmonic potential with reorganization energy λ1 for state 1 and 2 and λ2 for state 3. While in Figure 2 a two-dimensional projection onto the asymmetric ET coordinate, x, is represented, a third dimension along a symmetrical ET mode, y, is necessary for an accurate description3,15,17,48,72 which is omitted here for the qualitative discussion. The symmetric mode, however, was included for the evaluation of the data in Table 1. The three diabatic states are mixed by the electronic coupling matrix

elements Vij to yield three adiabatic states. By diagonalizing the diabatic Hamiltonian matrix

Hdiab )

(

)

H11(x, y) V12 V13 V12 H22(x, y) V23 with V12 ) V13 V23 H33(x, y) ˆ |Ψ2 〉 etc. (1) 〈Ψ1|V

here a double minimum potential results for the ground state, Ψg. Furthermore, two excited states, Ψa and Ψb, are obtained. Optical excitation from the ground-state minimum to the first excited state gives rise to an IV-CT band whose energy, hcν˜ a, approximately corresponds to the reorganization energy, λ1, for Robin-Day Class II compounds. In a two-state model (neglecting the bridge state and assuming harmonic potentials), hcν˜ a exactly equals the reorganization energy. The IV-CT band is absent in the diamagnetic parent molecule as well as the biradical. Model compounds that contain a single amine center lack the transition too, as no intramolecular charge transfer may occur. It is remarkable that the band is subject to a distinct hypsochromic shift when assayed in acetonitrile (AN) instead of the less polar MC. For I+, the absorption is, e.g., shifted from 6230 cm-1 in MC to approximately 7500 cm-1 in AN. This solvatochromism can be explained in terms of an increase of solvent reorganization energy in AN due to its larger Pekar factor (γ ) 1/n2 - 1/εs), γ(AN) ) 0.529 as compared to γ(MC) ) 0.380 for CH2Cl2 (295 K). From this shift, the inner sphere reorganization energy can be estimated to be 3000 cm-1. The extinction coefficient and, thus, the transition dipole moment decrease with increasing N-N distance. This is in line with a decreasing |V12| and/or increasing outer-sphere (solvent) contributions to λ as the distance increases. In all spectra, another IV-CT absorption band appears in the range ν˜ b ) 10 610-14 100 cm-1. This band has been assigned to the hole transfer from the oxidized triarylamine moiety to the bridge (see Figure 2). The band is also found for the monotriarylamine radicals and likewise shows a strong hypsochromic shift in AN. In addition to the IV-CT bands, all compounds exhibit a band between 13 000 and 13 500 cm-1, which lacks any pronounced solvatochromism. It corresponds to a localized π,π*-transition that is characteristic for triarylamine radical cations containing the dianisylamine chromophore.73 The absorption bands of I+-VII+ were fitted by several Gaussians to decompose the CT transition energies and the associated transition moments. For IV+, this decomposition proved difficult because of strong band overlap between the

Figure 3. EPR spectra of the radical cation III+ (a) and V+ (b) in methylene chloride at 270 and 310 K, respectively. The dotted, gray lines illustrate the simulation in terms of one (a) and two (b) equivalent nitrogens with a hyperfine coupling constant of 0.869 and 0.400 mT, respectively. A constant line width has been assumed. The solid, red lines reproduce the simulation taking the degenerate electron exchange between the two triarylamine moieties into account. The dominant features of the proton hyperfine coupling have been included in terms of the two sets of orthoprotons. Confer to the main text for details. The rate constants amount to 1.1 × 107 s-1 (a) and 1.55 × 109 s-1 (b), respectively.

Spectroscopy of Bis(triarylamine) Paracyclophanes

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IV-CT band and the bridge band. In fact, in this case, a separated IV-CT band is not visible but can be estimated to peak around 8000-10 000 cm-1 based on the broad tail of the higher-energy band. We approximated the position of the IV-CT band by subtracting the spectrum with half-intensity of IV2+ from that of IV+. This yields an IV-CT band at around 9000 cm-1. This energy was used as a starting value in the fit of the reduced absorption spectrum by three Gaussian functions, which yields 8500 cm-1 as a lower bound of the IV-CT band energy. The fact that the IV-CT band in IV+ is at a much higher transition energy than in II+ is supported by AM1-CISD calculations, which include the solvent shifts by the COSMO method (see Supporting Information). To determine the electronic couplings between the diabatic states, the individual CT band energies and extracted transition moments thus obtained were subject to a generalized MullikenHush (GMH) analysis as detailed in refs 15 and 48. This analysis rests on the unitary transformation of the adiabatic dipole matrix and the adiabatic energy matrix using a common transformation matrix. This similarity transformation yields the diabatic dipole and energy matrices, the latter of which contains the electronic couplings Vij between the diabatic states. The experimental (adiabatic) energy and dipole data were supplemented by the AM1-CI computed permanent dipole moment of and transition dipole moments between excited states, because these data are not easily experimentally accessible. When applied to two states only, the GMH procedure is equivalent to the traditional Hush approach. Here, the electronic coupling between the two diabatic states can be determined by the simple, analytical eq 2, where µga is the transition moment of the IV-CT band (evaluated by eq 3 neglecting the refractive index corrections of the solvent), ν˜ a is the IV-CT band maximum; and ∆µ12 is the diabatic dipole moment difference between the two states. The latter quantity is usually not directly accessible by experiment but is evaluated using eq 4 from the adiabatic dipole moment difference µaa - µgg and the transition moment µga. The former is determined by AM1-CI computations with the COSMO solvent model. Both the three-state and the two-state GMH treatment yield a set of coupling elements, which are summarized in Table 1. The details of this procedure can be found in refs 15 and 48 (see also the Supporting Information for the data of II+ and IV+).

Vtwo-level ) µ2ga )

µgaν˜ a ∆µ12

3hcε0 ln 10 2000π2N

∫ νε˜ dν˜

∆µ12 ) µ22 - µ11 ) √(µaa - µgg)2 + 4µ2ga

(2) (3) (4)

Using the electronic couplings from the three-state GMH analysis, the entire, two-dimensional potential energy surface can be constructed with a model similar to that illustrated in Figure 2, however, expanded in three dimensions (free energy as a function of one averaged asymmetrical and one averaged symmetrical mode). In the high temperature limit, the absorption spectrum can then be reproduced easily by adjusting chosen parameters (reorganization energies λ1 and λ2 for the triarylamine centered states and the bridge state, respectively, the bridge energy ∆GB, and Nelson’s quartic parameter, C6). In this limit, a time-dependent formalism yields practically identical results.74 For the coupling matrix elements to the bridge, the validity of the Condon approximation was furthermore assumed; i.e., the

coupling to the bridge was accounted for by the coordinateindependent estimate Vbr ) (V13 + V23)/2. From this model, which we will call the three-state GMH-PES model, one can easily obtain the barrier height ∆G* for thermal hole transfer in the ground state by numerical evaluation of the potential energy of the transition state and the ground state. Note that the ground-state PESs of all compounds studied exhibit a double minimum with only a weak indentation at the position of the diabatic bridge state minimum. Depending on ∆GB, the notch is more or less profound; however, no additional minimum forms. These findings preclude a hopping mechanism for the thermal ET and allow for the important conclusion that the electron transfer occurs solely by a superexchange mechanism. Within the two-state model the ET barrier can easily be obtained by eq 5 if harmonic potentials are assumed.

∆G*two-state ) λ ⁄ 4Vtwo-state + Vtwo-state2 ⁄ λ

(5)

In addition, we shall utilize eq 5 in combination with V12 as determined from the three-level GMH analysis. In this approximate approach of evaluating the barrier height, the influence of the bridge state is neglected and the diabatic potentials are assumed to be harmonic. This approach is justified for bridge states that are energetically well separated from the ground state. We refer to both models as the two- and three-state GMH approaches, respectively. Electron Paramagnetic Resonance. Generally, all mixedvalence species studied exhibit a characteristic temperature dependence of the EPR line-shape, which substantiates a double minimum ground state: At low temperature, unresolved three line spectra are observed, confirming the N-centered charge localization. Exemplarily, the spectrum of III+ in MC is reproduced in Figure 3a. The EPR line shape can tentatively be simulated in terms of a single nitrogen (I ) 1) and a hyperfine coupling constant of aN ) 0.87 mT. The lines are, however, inhomogeneously broadened and, thus, not Lorentzian. For this reason, a bad agreement of the experimental and simulated spectrum results at the wings of the outer lines when utilizing this simplistic approach. Note furthermore that for the compounds studied the line widths are in general not identical for each nitrogen hyperfine component, a phenomenon that is wellknown from nitroxide spin labels.75,76 In particular, the central line is narrower than the outer lines, which show comparable width. In the framework of Redfield theory,77,78 this indicates that cross-relaxation processes involving the anisotropic part of the g- and the hyperfine interaction are insignificant for these compounds. On the other hand, dipole-dipole terms, which give rise to the mN2 contributions of the line width, are important. Upon warming, the spectra undergo line broadening and exhibit alternating line width effects. Eventually, a spectrum with five major lines ensues. Figure 3b reproduces the high temperature situation for the comparably short aminium cation V+. The spectrum can be rationalized in terms of two equivalent nitrogens with approximately half the coupling constant from above (2 × aN ) 0.40 mT). This hyperfine coupling constant is somewhat below that in the N,N,N’,N’-tetraanisylphenylenediamine radical cation, a clearly charge deloclalized system.79,80 The expected intensity pattern, 1:2:3:2:1, is not clearly observed due to the large line width, which furthermore depends on the hyperfine component. In any way, this is indicative of the complete delocalization of the hole over the two redox centers on the EPR time scale. Note that a weak decrease of the nitrogen hyperfine coupling constant with temperature is observed. The actual kinetic information manifests itself in between the described slow and fast exchange limit.

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Figure 4. EPR (a) and ENDOR (b) spectrum of the radical cation VII+ in trifluoroacetic acid. For the ENDOR spectrum, 125 accumulations were collected within 6 h. νn denotes the free proton Larmor precession frequency. For (a), the simulation (red) based on the hyperfine coupling constants given in Table 2 is overlaid to the experimental spectrum.

In general, the chemical rate process leads to a random, though well-defined, exchange of the nuclear environment sensed by the electron spin. This process can be accounted for by augmenting the Liouville-von Neumann equation81 of the spin density operator by an exchange term, which accommodates the permutation of the nuclear spin basis brought about by exchange events. The details of the modeling process have been given by Binsch82,83 and Heinzer.84 In fact, the program devised by the latter is still in widespread use to analyze the line-shapes of EPR spectra subject to intramolecular exchange. To simulate the spectra here, we have designed a novel program, which supersedes Heinzer’s implementation by allowing for the dependence of the line width on the nitrogen spin state and correcting for Zeeman modulation effects. Note that in the setting of two exchanging nitrogens with the hyperfine interaction to the second nitrogen being negligible, the three line pattern in the slow exchange limit will evolve in a five line pattern as described above. In this process, one instance of the initial triplet and the spectral width will remain unaltered. The coalescence rate constants, |γe∆B|/2, amount to 1.12 × 108 s-1 for pairs of lines separated by aN and to 2.24 × 108 s-1 for those separated by 2aN before and after the ET event (assuming aN ) 0.9 mT). Indeed, the EPR spectra of the MV compounds I+-VII+ can be simulated in terms of two interchanging nitrogen nuclei. The agreement of simulated and experimental spectra attainable in this way is, however, scarce. The discrepancy is primarily due to not accounting for the hyperfine interaction of the protons surrounding the center (vide supra). Although the odd electron is nitrogen centered, significant spin density extends into the attached aryl groups.85 Since all MV compounds yielded unresolved spectra with no hyperfine interaction to protons being apparent, the necessary hyperfine interactions can only be estimated from nonexchanging, single-centered model compounds or molecular structure calculations. Hirao et al.27 have employed density functional calculations in their study on spiroSi bridged triarylamines. Note, however, that the self-interaction error inherent to common functionals leads to the delocalization of the odd charge being overestimated.86 As a consequence, symmetric, charge delocalized structures are usually found by DFT calculations of bis(triarylamines),25 and the technique cannot be applied directly for modeling the charge localized species. Instead, simpler, single-centered model compounds have to be studied as well. UB3LYP/EPR-II87 calculations of the hyperfine coupling constants of the radical cation VIII+ (using the UB3LYP/6-31G(d,p) optimized structure) yielded the (unrealistically small) estimate for the nitrogen coupling constant of 0.65 mT.88 In fact, this value compares unfavorably to the experimental result of 0.92 mT (cf. below). We thus decided to refrain from model calculations and rather to study the mono-

TABLE 2: Hyperfine Coupling Constants Determined for the Radical Cation VIII+ from the ESR Spectrum at 295 K and the ENDOR Spectrum at 265 K in Trifluoroacetic Acid designation

no. of nuclei

ai (ESR)/mT

ai (ENDOR)/mT

Hortho Hortho Hmeta Hmeta HCH3 Hpara N

4 2 2 4 3 1 1

0.203 0.160 0.094 0.055 0.084 0.21 0.921

0.202 0.157 0.093 0.052 0.084 0.202 -

nuclear model compounds VIII+ and IX+ experimentally by means of EPR and ENDOR spectroscopy. The dianisylphenyl aminium radical cation VIII+ is, despite its apparent simplicity, neither commercially available nor is its EPR spectrum described in the literature. Its structure led us to expect that it shares the unpleasant property with other, in para-position unprotected, phenylamine radical cations to dimerize easily yielding benzidine derivatives. For exactly this reason, no EPR spectrum of N,N-dimethylaniline seems to be known in the literature.89 It has been suggested that in the final step of this bimolecular reaction two protons are released. Thus, a longer radical lifetime can be expected in acidic media. Indeed, in trifluoroacetic acid the stability was found to be sufficient to observe the EPR and even the ENDOR spectrum, both of which are shown in Figure 4. Phenyliodine(III)-bis(trifluoroacetate) (PIFA) was used as the oxidizing agent here. The hyperfine coupling constants extracted at 265 K from the ENDOR spectrum can be utilized to reproduce the well resolved, lownoise EPR spectrum at 295 K. Indeed, an excellent congruency is obtained for the coupling constants given in Table 2. At 265 K, the hyperfine coupling constants of four protons and that of the isolated proton in para-position coincide. In agreement with the radical cations of tris(anisyl)amine (aH(ortho) ) 0.185 mT, aH(meta) ) 0.059 mT) and similar compounds, we assign the larger coupling constants referring to four and two protons, respectively, to the ortho-positions and the smaller set to the meta-positions. This assignment is also fostered by EPR-III/ B3LYP density functional calculations, which reproduce the same qualitative trend but quantitatively disagree. Not surprisingly in view of the reactivity of VIII+, the para-proton exhibits the large coupling of aH(para) ) 0.21 mT (295 K). Eventually, the question to what extent the spin density delocalizes into the bridge has to be tackled. To elucidate this issue, the monotriarylamine radical cation IX+ was investigated in some detail. Note that this subunit reappears in the p-xylylene and the intermediately sized cyclophanylene bridged mixed valence compounds. The EPR spectrum in DCB does not exhibit any resolved hyperfine interactions except for that due to the

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TABLE 3: Hyperfine Coupling Constants of the Radical Cation IX+a ENDOR designation

AN

DCB

TABLE 4: Activation Parameters of the Thermal Electron Transfer in Compounds I+-VII+ in ortho- Dichlorobenzene (DCB) and Methylene Chloride (MC)a

EPR AN

DCB

no.

compound +

aN a1 a2 a3 a4 a5 a6 a7 a8

0.19

0.18 0.16

0.077 0.053 0.102

0.078 0.047 0.097 a4

0.022

0.026 a5

0.868 0.188 0.159 0.078 0.053 0.101 0.053 0.012 0.092

0.862 0.175 0.159 0.078 0.047 0.101 0.052 0.022 0.101

1 4 2 2 4 6 1 1 3

a The hyperfine coupling constants have been determined by ENDOR spectroscopy in acetonitrile (AN, 210 K) and orthodichlorobenzene (DCB, 260 K). The EPR coupling constants apply to 320 and 330 K in AN and DCB, respectively. All coupling constants are given in mT (1 mT ) 28.02 MHz).

nitrogen. However, in AN at high temperatures and, thus, sufficiently low rotational correlation times, a partly resolved spectrum was obtained. This alone does not allow for an assignment of all possibly contributing protons. The ENDOR spectra recorded at low temperatures in DCB as well as AN, however, revealed up to six distinct proton coupling constants. We are hence confronted with the challenge of assigning this set of hyperfine coupling constants, augmented by the value 0 mT, in an optimal manner to the 10 groups of equivalent protons of IX+ such that the resolved EPR spectrum in AN at 330 K is reproduced. In assigning the 7 distinct values to 10 groups, we are restricted to combinations that comprise every hfc constant at least once. The value of 0 mT has been included since a priori we could not preclude that the spin density (at the nucleus) does not vanish for some groups of equivalent nuclei. Though straightforward at first view, this is a daunting problem. In fact there are 1 592 880 unique combinations. This number already takes into account that on permuting two different hfc’s among groups comprising the same number of nuclei no new assignment results. From density functional simulations (B3LYP/EPRII//B3LYP//6-31G(d,p)), we infer that one of the methyl groups and one isolated proton at the terminal xylyl group (the ones in meta-position with respect to the charge bearing amino group) contribute comparably little to the hfc pattern (aH ) 0.046 mT, aMe ) -0.032 mT). Excluding these two groups gives rise to the manageable problem of assigning seven distinct hfc’s to eight groups of nuclei. This results in 49 410 combinations to be tried. Since many assignments yield EPR spectra with a total width grossly deviating from the experimental spectrum, the number of combinations may be reduced further to 9270. Since the coupling constants do show some temperature dependence, Levenberg-Macquard optimizations with the ENDOR hfc’s taken as initial values were carried out for every possible assignment. Despite our exhaustive search, it turned out that several possible sets of parameters yield a similar goodness of fit. We eventually settled for the one which resembles that of the smaller model compound VIII+. Table 3 summarizes the hfc’s of compound IX+. On the basis of this appraisal, we may conclude that although some spin density is indeed transferred to the bridge the charge carrying unit still resembles that of the simpler monotriarylamine. The proton coupling constants obtained above certainly pertain to the particular model compounds. With respect to the protons in immediate adjacency to the nitrogen center, the generalization to the bis(triarylamines) is still expected to be reliable. This is apparent from the fact that the (resolved)

I

II+ III+ IV+ V+ VI+ VII+

solvent MC DCB MC DCB MC DCB MC DCB MC MC DCB MC DCB

∆T/K 255-310 255-315 250-310 255-305 290-313 280-350 250-310 265-300 245-310 260-305 275-325 265-310 260-325

∆S+/J K-1 mol-1

∆H+/cm-1

-57.7 ( 1.5 -68.5 ( 1.2 -49 ( 4 -50.5 ( 2.4 -48 ( 12 -59.1 ( 2.5 -36.1 ( 2.4 -42 ( 4 -34.5 ( 1.8 -22 ( 7 -37 ( 4 ≈ -22 ≈ -26

780 ( 30 490 ( 30 1150 ( 90 1000 ( 60 1500 ( 300 1080 ( 60 1415 ( 60 1200 ( 100 900 ( 40 1160 ( 150 900 ( 100 ≈ 2000 ≈ 1800

a ∆T gives the temperature range that has been considered in the analysis. The enthalpy of activation, ∆H+, and the entropy of activation, ∆S+, have been determined from linearizing the Eyring-Polanyi equation, i.e., assuming the validity of transition state theory.

TABLE 5: Hyperfine Coupling Constants of the Nitrogen, aN, and Rate Constant of Degenerate Exchange, kex, in Methylene Chloride (MC) and ortho-Dichlorobenzene (DCB) at 300 K kex/108 s-1

aN/mT compound

MC

DCB

MC

DCB

I+ II+ III+ IV+ V+ VI+ VII+

0.88 0.844 0.877 0.825 0.824 0.839 0.832

0.876 0.838 0.873 0.839 0.857 0.833

1.4 0.69 0.2 0.90 13 16 0.3

1.5 1.2 0.3 1.2 10 0.5

nitrogen hfc’s of all exchanging compounds are of comparable magnitude as for the single-centered model compounds, indicating a similar spin distribution at the N-center (compare Table 5).90 On the other hand, our preliminary density functional calculations do not appear to be well suited for supplementing hfc’s of the bridge protons. Taking over all coupling constants extracted for compound IX+ as representative for the IV-CT compounds appears equally speculative. Fortunately, due to the unresolved structure of the exchanging compounds, it turns out that the inclusion of merely those two groups of four and two equivalent protons that contribute most is sufficient. Since these are the ortho-protons of the anisyl and phenylene substituent of the amine, they are present with the same local environment in each MV compound. Hence, their consideration is clearly justified. In fact, even if we do not account explicitly for the hyperfine interaction of the protons at all, we obtain very similar energies of activation compared to those obtained when the two groups are included. The line shape however is significantly better reproduced with the two additional couplings. Thus, the exchange spectra were simulated taking into account the two ortho-couplings with 4 × aH,1 ) 0.188 mT and 2 × aH,2 ) 0.159 mT. No hyperfine interactions to the bridge and the reduced triphenylamine moiety have been included. Furthermore, as indicated above, the temperature dependence of the nitrogen hyperfine coupling and the dependence of the line width on the nitrogen hyperfine component have fully been accounted for. Figure 3 gives the simulation for V+ at high temperatures and III+ at low temperatures. The full range of temperature dependence of the spectral shape for II+ is

2990 J. Phys. Chem. C, Vol. 113, No. 7, 2009

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Figure 5. EPR and ENDOR spectra of radical cation IX+. (a) and (b) illustrate the EPR spectra in acetonitrile (AN) at 320 K and in orthodichlorobenzene (DCB) at 330 K. The red lines correspond to the simulations employing the coupling constants compiled in Table 3. (c) and (d) give the ENDOR spectra in AN at 240 K and DCB at 260 K. Note that in DCB the two largest hyperfine coupling constant are degenerate within the spectral resolution of the method. In AN, however, the presence of two distinct groups of nuclei is apparent (although the transitions are not resolved).

illustrated in Figure 6. Note that in general the relative changes of the rate constant can be determined with high accuracy within a temperature series. Due to the dependence of the simulation on the (less accessible) natural line width and the hyperfine coupling constants of the surrounding, significantly larger errors pertain to the absolute rate constants. Table 4 summarizes the activation parameters obtained for the radical cations of compounds I+-VII+ in MC and DCB. Eyring’s equation

kex )

(

)

( ) (

kBT kBT ∆G+ ∆S+ ∆H+ ) exp exp exp h kBT h kB kBT

) (6)

has been used to characterize the electron transfer rates. The equation is based on transition state theory. For the electron transfer phenomena investigated here, the pre-exponential factor as well as ∆H+ depend on solvent parameters and thus temperature. The detailed dependence on T is not universal and is different for different ET domains, which are distinguished by the degree of adiabaticity and solvent friction.91,92 In general, however, this dependence is small and usually neglected. For example, a pre-exponential factor depending inversely on τL, the longitudinal solvent relaxation time, which itself is an activated quantity, could incur a contribution of no more than 60 cm-1 to the activation barrier for MC. This value is at worst of the same order of magnitude as the experimental error. The Pekar factor is often found to depend only linearly on temperature.93 We do not want to imply that transition state theory yields an adequate description of the ET processes studied here. Rather, we view eq 6 as a way to summarize and report our data. By comparing eq 6 with a variety of more elaborate ET models, ∆H+ can be identified with the Marcus free energy of activation, ∆G*, at an intermediate, characteristic temperature.91,92 ∆S+ collects the linear temperature dependence of the reorganization energies as well as the deviation of the pre-exponential factor from the vibronic frequency factor assumed in eq 6. Having

not yet identified a more elaborate electron transfer model that allows accommodating the entire temperature range studied, we here use eq 6 with ∆H+ directly identified with the thermal ET barrier and any implicit temperature dependences neglected. In fact, for intervalence compounds, the analysis of temperaturedependent rate constants in terms of plots of ln(kex/T) vs T-1 is well established throughout the literature.5,27,94,95 Arrhenius plots equally yield linear relations and give activations energies, Ea, that are larger by approximately 200 cm-1, as is expected from the algebraic identity ∆H+ ) Ea + kBT. Figure 7 gives the Eyring plots for the IV-CT compounds in MC and DCB. Within the analyzed temperature range, an approximately linear dependence of ln(kex/T) on T-1 is indeed found. The temperature range that has been considered is recorded in Table 4. This temperature interval is bound at low temperatures since either the electron transfer is getting too slow to induce significant changes in the line shape or slow tumbling phenomena set in that are not accommodated in our theoretical framework. The upper temperature limit is either imposed by the solvent boiling point (MC: 312.8 K) or radical decay. In DCB we have in addition observed deviations from the linear relation of ln(kex/T) on T-1 at high temperatures, which can probably be attributed to the failure of the Eyring model or to ion pairing. In any case, the slope of the Eyring representation was linear in a sufficiently large range surrounding room temperature to allow for the determination of the (room temperature) ET barriers. The very elongated molecules III+ and, in particular, VII+ mark the limit of applicability of the cw-EPR line broadening method (with inhomogeneously broadened lines). For these species, the temperature-dependent lineshapes deviate too little from the three line pattern (Figure 3a) to allow for an accurate determination of kex. Indeed, effects of the intrinsic line width and those due to the electron transfer are difficult to differentiate then, and the two parameters are becoming increasingly correlated. Clearly, this issue is particularly pronounced in solvents like MC that exhibit low boiling points. For III+, we do not take into account the intrinsic temperature dependence of the line width. The rates extracted

Spectroscopy of Bis(triarylamine) Paracyclophanes

Figure 6. Temperature dependence of the EPR line shape (black lines) of radical cation II+ in ortho-dichlorobenzene. The rates extracted by the simulation (red lines) amount to 4.49 × 107, 5.02 × 107, 5.65 × 107, 6.38 × 107, 7.12 × 107, 7.94 × 107, 8.77 × 107, 9.68 × 107, 1.14 × 108, 1.22 × 108, and 1.32 × 108 s-1.

in this way have to be viewed as upper limits. For VII+ with R ) -H, this approach did not yield a satisfactory agreement of the simulated and experimental lineshapes. When varying the natural line width, a pronounced correlation of the parameters used to account for the line width and the exchange rate is found for this compound. In terms of the simulation, this is obvious from a strong dependence of the fit parameters on the initial parameters. For compound VII+ with R ) -CN, the rate of thermal electron transfer is found to be smaller than that of VII+ with R ) -H. Quantification beyond this qualitative statement, however, does not appear reasonable. Discussion Provided that the rate of electron transfer exceeds 5 × 107 s , the barrier of thermal electron transfer can be accurately determined from the temperature dependence of the EPR line shape even though inhomogeneous broadening is significant. The ∆H+’s are of the same order of magnitude as that found for the spiro-fused triarylamine derivative (∆H+ ) 14 kJ mol-1, -1

J. Phys. Chem. C, Vol. 113, No. 7, 2009 2991 ∆S+ ) -13 J K-1 mol-1) reported by Hirao.27 Due to the larger ET distances and, thus, slower tunneling, the activation entropies of I+-VII+ are markedly smaller. For a diabatic, ET can be taken as A ) V2(π/(p2λkBT))1/2. Substituting V in this expression by the values given in Table 1 yields factors in the order of 1013-1014 s-1 (beyond applicability of the perturbation theoretical model though), which is too large and, therefore, incommensurate with a diabatic electron transfer reaction. Instead, the electron transfer is adiabatic, with the (vibrational) motion along the reaction coordinate being rate limiting. Kramer’s expression91,93 for the pre-exponential factor depends inversely on the solvent longitudinal relaxation time and reproduces the correct order of magnitude of the rate constants. This indicates a significant solvent dynamic effect. Several aspects emerge from a closer inspection of the activation barriers and rates: In the homologous series of the radical cations I+, II+, and III+, the energy of activation increases with the geometrical distance of the redox moieties. In MC, the increase in ∆H+ from 780 to 1500 cm-1 is paralleled by the decrease of the rate constant by 1 order of magnitude (cf. Tables 4 and 5). The increase of the ET barrier results from the increase in solvent reorganization energy, λo, and the concomitant decrease of the electronic coupling matrix element with distance. The trend in reorganization energy can directly be read off the position of the IV-CT absorptions (see Table 1). In DCB, the ET barriers are always smaller than that in DC due to the lower Pekar factor, γ, and, thus, smaller solvent reorganization energy (γ(DCB) ) 0.316, γ (MC) ) 0.378 at 298 K). In both solvents, the barrier height changes by approximately the same amount on going from I+ to II+. With experimental error, this can be taken to indicate similar geometrical changes, which determine λo. The fact that within the series I+-III+ the rate constants at 300 K do not change in DCB as pronounced as in MC indicates that the pre-exponential factors are more variable in DCB than in MC (cf. Table 5). Apart from the additional methylene group that widens the cyclophane spacer, compounds II+ and IV+ are identical. At first sight, it is reasonable to assume that the two compounds give rise to identical reorganization energies since the difference in center-center distance is negligible. Furthermore, the reorganization of the nitrogen center, which is identical for both radicals, is expected to determine primarily the inner sphere reorganization energy with the contribution of the bridge being small. However, much in contrast, the optical spectra of IV+ show an IV-CT band which is strongly shifted to higher energy compared to II+. Because the IV-CT band overlaps with the bridge band, we are unable to determine the band energy accurately; however, a lower limit of 8500 cm-1 was extracted (see above) by band subtraction. Within a two-state model, this energy equals the reorganization energy which, consequently, is significantly larger for IV+ than for II+, a fact which demonstrates that the bridge moiety has a strong influence on the internal reorganization energy. A similar conclusion has recently been drawn by the analysis of absorption bands of triarylamine-perchlorotriphenylmethyl radicals in the context of Bixon-Jortner theory.96 Within the two-state model, eq 5 yields ∆G* ) 1730 cm-1 for IV+. Thereby a much larger barrier for IV+ than for II+ is obtained. This contradicts the EPR results, which suggest an enthalpy of activation of 1410 cm-1. This value is only moderately larger than that found for II+ (1250 cm-1). Furthermore, the rates of thermal electron transfer at 300 K basically coincide for both solvents used (see Table 5). Unfortunately, the three-state model, which also takes into

2992 J. Phys. Chem. C, Vol. 113, No. 7, 2009

Kattnig et al.

Figure 7. Eyring plots for the degenerate electron exchange in the radical cations I+-VII+ in (a) methylene chloride and (b) ortho-dichlorobenzene.

TABLE 6: Barrier Height in Methylene Chloride As Obtained from Equation 5 for ∆G*two-state and from Numerical Evaluation of the Potential Energy Surfaces As Obtained from the GMH Theory Together with the Three-State Two Mode Construction of PES (∆G*3state-GMH-PES)a +

I II+ III+ IV+ V+ VI+ VII+

∆G*3state-GMH-PES

∆G*3state-GMH

∆G*two-state

∆G*EPR

1090 1060 1580 2000 900 1050 -

750 1150 1650

930 1170 1810 1730 990 1320 2760b

780 1150 1500 1420 900 1160 2000c

850 1150 -

a ∆G*3state-GMH uses V12 from Table 1 together with eq 5. ∆G*EPR is the barrier obtained from the temperature-dependent EPR spectra. All values are given in cm-1. b R ) -CN. c R ) -H.

account the bridge state, is not applicable for a more detailed description of the potential energy surfaces because the energy of the IV-CT band is close to the one of the bridge transition. In this regime, the three electronic couplings within a threestate model are strongly dependent on the transition energies.48 Therefore, because of the very inaccurate IV-CT band energy, the application of the GMH theory within a three-state model will only result in extremely inaccurate couplings. Thus, we refrain from using this model and stay with the traditional MH two-state theory. The two-state model also suggests an equally efficient electronic coupling in IV+ as in the more tightly bound II+. This is a reassuring result in view of the application of noncovalently linked triarylamines in hole-conducting materials. Compounds V+ and VI+ are only distinguished by the presence of the additional methyl groups at the bridge for V+. The additional, electron-donating substituents increase the electron density at the bridge and, thus, give rise to a more efficient coupling. This is indeed reflected in the smaller ET barrier found for V+ than for VI+. The difference is, however, not found for the rate constants at 300 K in MC. Apparently, V+ shows a smaller well frequency than VI+. Interestingly too, although the activation barrier is smaller in DCB than in MC, the rate of electron transfer is faster in MC for VI+. Apparently, it is the diffusive motion along the reaction coordinate that controls the overall rate here. It is interesting to note that the analysis of the IV-CT transitions conveys the picture that V+ and VI+ are not as similar as one would expect from the chemical structure alone: Indeed, a difference of the reorganization energies of 500 cm-1 has been found. Since the compounds exhibit the

same center-to-center distance, similar λo’s are to be expected, and this difference would have to be attributed solely to the internal part, λi. Again, as in the case of II+ and IV+, this shows that superficially small modifications to the bridge may lead to significant changes of λi. Note that the direct π-conjugation in compounds V+ and VI+ gives rise to a rate of thermal electron transfer that exceeds that of the nonconjugated compounds of similar size, compounds II+ and IV+, by 1 order of magnitude. This even holds true for the significantly shorter compound I+. On the other hand, in the much longer compound VII+, the rate of electron transfer drops dramatically. This drop cannot be explained by the increased distance only but seems to indicate a twisted conformation that is not able to mediate efficiently the electron transfer. A similar drop has been observed for the exchange coupling of analogous (with respect to the bridge) nitroxide biradicals.97 We shall finally address the question to what extent ET parameters extracted from the analysis of IV-CT transitions are useful in predicting the barrier of thermal electron transfer. From the literature, the pessimistic picture emerges that the simplistic, two-state Marcus-Hush model is not well suited for purely organic mixed valence compounds, in particular, when diabatic dipole moment differences are estimated based on the geometrical center-center distance. The more sophisticated threestate model with an averaged asymmetric and symmetric mode, which has been introduced above, has not been evaluated in this respect so far. From the optical data summarized in Table 1, the activation energy was predicted in three ways and compared to the EPR barrier in Figure 8. It is reassuring that all three models reproduce the experimental trend. However, the activation barriers extracted on the basis of the two-state model systematically exceed those determined from EPR spectroscopy. In fact, a linear correlation yields a slope of 1.5. The reader should however be aware of the fact that this model does make use of Newton and Cave’s65-68 dissection of the diabatic dipole moment difference in terms of (in principle) measurable quantities. By utilizing computed adiabatic dipole moments, this approach already goes beyond the simplistic approach that is based on the redox center-to-redox center distances to estimate the effective charge transfer dipole moment. Using the latter, even larger barriers were predicted. Although depreciated, this approach continues to be in widespread use. On the other hand, for most compounds an exceptionally good agreement is found for the predictions of the PES approach seeded by the GMH three-state mode. Note that this model

Spectroscopy of Bis(triarylamine) Paracyclophanes

J. Phys. Chem. C, Vol. 113, No. 7, 2009 2993 The latter two aspects are of particular importance as it shows that triarylamines that come as close together in solid state materials as the vdW radius permits can show efficient coupling and rate constants only smaller by about 1 order of magnitude than fully conjugated materials. Of course, orientational effects will also play a role, which is in focus of forthcoming studies. We are also working on the identification of a comprehensive and consistent ET model that accounts for all rate constants at all temperatures. Our preliminary attempts indicate that solvent friction effects are significant. In particular, when augmented by λi (taking the Holstein correction into account), the model of Calef and Wolynes and that of Kramers91 can rationalize the experimental findings. Experimental Details

Figure 8. Comparison of the theoretical ∆G*two-state, ∆G*three-state-GMH and ∆G*three-state-GMH-PES derived from optical spectra with the experimental ∆G*EPR in methylene chloride. The line indicates a correlation with slope unity. (a) Three-state-GMH-PES value unreliable, see text. (b) EPR value for R ) -H and two-state value for R ) -CN.

utilizes Nelsen’s quartic parameter, C. Larger deviations only appear for the radical cation I+. However, the evaluation of the optical spectra in ref 48 involved major errors for the intensity of the IV-CT band which has direct influence on the electronic coupling and, thus, on the barrier. Note that a similarly good agreement is attainable by using eq 5 in combination with the coupling matrix element, V12 (see Table 1), extracted from the three-level GMH analysis. This approximation is viable since the bridge state has a minor effect on the shape of the ground-state potential energy surface only. In particular, the location of the transition state and that of the minima only deviate marginally from their two-state positions at the symmetric coordinate y ) 0. On the other hand, a significant increase of the estimate of V12 (by approximately 200 cm-1) results when considering the bridge state. Conclusions In summary, we conclude that all three methods that rest on the evaluation of optical data to elucidate the thermal ET barrier yield an exemplary agreement with the barriers extracted from the EPR data. Both three-state analyses as well as the two-state analysis yield correct trends of thermal ET barriers especially when augmented by computed adiabatic dipole moments. The three-state models are, however, in significantly better quantitative agreement. Both methods provide a framework that allows for the evaluation of ET parameters from optical properties that are actually transferable to the thermal counterpart. Furthermore, based on the choice of bis(triarylamines) with different bridge moieties, our study shows that: (a) the bridge has a significant influence on the internal reorganization energy. This conclusion is far-reaching inasmuch as many studies rest on the assumption that the redox center alone governs the internal part of λ. (b) [2,2]Paracyclophane and [3,3]paracyclophane as bridge units show practically the same electronic coupling and thermal barrier. This is surprising given the fact that the distance of π-faces in [2,2]paracyclophanes falls significantly below the sum of the vdW radii while it is only slightly below in [3,3]paracyclophanes. Furthermore, it emphasizes that the ethylene bridge orbitals in [2,2]paracyclophanes do not significantly add to the electronic coupling. (c) Radical cations with conjugated bridges have thermal rates about 1 order of magnitude larger than those with broken conjugation.

Samples of the monoradical cations were prepared in deaerated methylene chloride (MC, Roth, Rotipuran g99.8%, p.a.), ortho-dichlorobenzene (DCB, Aldrich, CHROMASOLV, g99%), and acetonitrile (AN, Roth, Rotidry, g99.9%) by mixing a 10fold excess of the diamagnetic precursor with tris(bromophenyl)ammoniumyl hexachloroantimonate(V) (Fluka, purum, g97.0%) or nitrosyl perchlorate (in AN). A radical concentration of 3.0 × 10-4 M was typically aimed for. The concentration of the diamagnetic precursor never exceeded 3.0 × 10-3 M. The solvents were dried beforehand by elution from a column of suitable molecular sieve followed by distillation under an argon atmosphere (vacuum for DCB). Prior to use, a stream of dried and purified argon was bubbled through the solvents for 15 min to dynamically remove oxygen. When utilizing tris(bromophenyl)aminium hexachloroantimonate(V) as the oxidizing agent, the samples were allowed to react for 20 min at 277 K. Aliquots of the oxidized samples were transferred by standard Schlenk techniques to EPR sample tubes of 1.5 mm inner diameter. The samples were sealed off after three freeze-pump-thaw cycles and directly subjected to the EPR measurements. To this end, the sample tubes were mounted by Teflon fittings inside 4 mm NMR tubes. No significant degradation was observed within several days, when storing the samples at 253 K. EPR measurements were performed on a Bruker ELEXSYS E-500 X-band EPR-spectrometer equipped with a digital temperature control unit. A cylindrical TM110 cavity was used at a Zeeman modulation frequency of 100 kHz. If necessary, spectra were accumulated with the field and frequency locked. For the exchanging IV compounds, a modulation amplitude of 0.05 mT was typically utilized, and the microwave power was chosen not to cause any saturation broadening. The temperature was measured directly below the sample tube. For thermal equilibration, the samples were kept at least 10 min at the desired temperature prior to measurement. The 10-fold excess of the donor employed guarantees that the monoradical cation is detected free of disturbances from the biradical/triplet. Note that due to the large distances and the rigid structure the biradical spectrum has been assumed to resemble that of the monoradical in fluid solution. We have preliminarily studied the diradical II2+ in 2-methyltetrahydrofuran. At room temperature, no marked EPR signal (except for that due to the excess of the oxidizing agent tris(bromophenyl)aminium hexachloroantimonate(V)) was observed. At 130 K, in the glassy state, a broad signal at 297 mT was detected (peakto-peak width: 30 mT, 9.408 GHz). Furthermore, at 158 mT, a weak half-field transition was found. These features are interpreted as to originate from the triplet state with a significant zero-field splitting. Further research activities in this direction employing better suited glassy solvents at lower temperature are being projected.

2994 J. Phys. Chem. C, Vol. 113, No. 7, 2009 At any rate, no interference from the triplet/biradical is expected under the conditions of the EPR experiments employed here. In addition, intermolecular degenerate electron exchange is not significant at the total concentration of c0 ≈ 5 × 10-3 M used; i.e., assuming kex ∼ 109 M-1s-1 (a large estimate),70 the self-exchange process contributes to the peak-to-peak line width no more than 0.02 mT. This is by far insignificant compared to the line width alternations brought about by the intramolecular process. Note that the solvent DCB appeared to be particularly well suited for this study due to its low Pekar factor, which determines besides geometrical factors the value of the Marcus solvent reorganization energy, and its concomitant applicability over a wide temperature range. This even allowed observing the thermal electron transfer of the radical cation VII+. The comparably large solvent longitudinal relaxation time of 6 ps is expected to limit the rate of thermal electron transfer though. Acknowledgment. The group in Wu¨rzburg kindly acknowledges the support by the Graduate College GRK 1221 of the Deutsche Forschungsgemeinschaft. Supporting Information Available: Details of electrochemical, semiempirical, and optical characterization. This material is available free of charge via the Internet at http:// pubs.acs.org. References and Notes (1) Demadis, K. D.; Hartshorn, C. M.; Meyer, T. J. Chem. ReV. 2001, 101, 2655–2685. (2) Launay, J.-P. Chem. Soc. ReV. 2001, 30, 386–397. (3) Brunschwig, B. S.; Creutz, C.; Sutin, N. Chem. Soc. ReV. 2002, 31, 168–184. (4) Bre´das, J.-L.; Beljonne, D.; Coropceanu, V.; Cornil, J. Chem. ReV. 2004, 104, 4971–5003. (5) Bonvoisin, J.; Launay, J.-P.; Rovira, C.; Veciana, J. Angew. Chem., Int. Ed. 1994, 33, 2106–2109. (6) Nelsen, S. F.; Ismagilov, R. F.; Powell, D. R. J. Am. Chem. Soc. 1997, 119, 10213–10222. (7) Nelsen, S. F.; Ramm, M. T.; Wolff, J. J.; Powell, D. R. J. Am. Chem. Soc. 1997, 119, 6863–6872. (8) Nelsen, S. F.; Trieber, D. A.; Wolff, J. J.; Powell, D. R.; RogersCrowley, S. J. Am. Chem. Soc. 1997, 119, 6873–6882. (9) Rovira, C.; Ruiz-Molina, D.; Elsner, O.; Vidal-Gancedo, J.; Bonvoisin, J.; Launay, J.-P.; Veciana, J. Chem.-Eur. J. 2001, 7, 240–250. (10) Sun, D.-L.; Rosokha, S. V.; Lindeman, S. V.; Kochi, J. K. J. Am. Chem. Soc. 2003, 125, 15950–15963. (11) Rosokha, S. V.; Sun, D. L.; Kochi, J. K. J. Phys. Chem. A 2002, 106, 2283–2292. (12) Sun, D.; Rosokha, S. V.; Kochi, J. K. J. Am. Chem. Soc. 2004, 126, 1388–1401. (13) Bonvoisin, J.; Launay, J.-P.; Verbouwe, W.; Van der Auweraer, M.; De Schryver, F. C. J. Phys. Chem. 1996, 100, 17079–17082. (14) Bonvoisin, J.; Launay, J.-P.; Van der Auweraer, M.; De Schryver, F. C. J. Phys. Chem. 1994, 98, 5052–5057; see also correction 1996, 100, 18006. (15) Lambert, C.; Amthor, S.; Schelter, J. J. Phys. Chem. A 2004, 108, 6474–6486. (16) Lambert, C.; No¨ll, G. Synth. Met. 2003, 139, 57–62. (17) Lambert, C.; No¨ll, G.; Schelter, J. Nat. Mater. 2002, 1, 69–73. (18) Lambert, C.; No¨ll, G. J. Am. Chem. Soc. 1999, 121, 8434–8442. (19) Lambert, C.; No¨ll, G. Chem.-Eur. J. 2002, 8, 3467–3477. (20) Lambert, C.; No¨ll, G. J. Chem. Soc., Perkin Trans. 2 2002, 2039– 2043. (21) Lambert, C.; Schma¨lzlin, E.; Meerholz, K.; Bra¨uchle, C. Chem.Eur. J. 1998, 4, 512–521. (22) Lambert, C.; No¨ll, G. Angew. Chem., Int. Ed. 1998, 37, 2107– 2110. (23) Coropceanu, V.; Malagoli, M.; Andre, J. M.; Bredas, J. L. J. Chem. Phys. 2001, 115, 10409–10416. (24) Coropceanu, V.; Lambert, C.; No¨ll, G.; Bre´das, J.-L. Chem. Phys. Lett. 2003, 373, 153–160. (25) Coropceanu, V.; Malagoli, M.; Andre´, J. M.; Bre´das, J. L. J. Am. Chem. Soc. 2002, 124, 10519–10530.

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