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J. Phys. Chem. B 2007, 111, 6655-6666

6655

Reversible Interchange of Charge-Transfer versus Electron-Transfer States in Organic Electron Transfer via Cross-Exchanges between Diamagnetic (Donor/Acceptor) Dyads† Duoli Sun, Sergiy V. Rosokha, and Jay K. Kochi* Department of Chemistry, UniVersity of Houston, Houston, Texas 77204 ReceiVed: December 28, 2006; In Final Form: February 12, 2007

The choice of appropriate electron donors (D) and acceptors (A) allows for the first time the simultaneous observation of Mulliken charge-transfer states, [D,A], that can coexist in reversible equilibrium with electrontransfer states, {D+•,A-•}, for various diamagnetic organic redox dyads. The theoretical analysis based on the (two-state) Mulliken-Hush analysis of the intervalence optical transition, together with the spectral identification of the transient ion-radical pairs of D+• and A-•, leads to the construction of the unusual potential-energy surface consisting of a single minimum without any reorganizational barrier for electron-transfer crossexchanges with driving forces close to the isergonic limit. The mechanistic implications of this direct demonstration of the facile charge-transfer/electron-transfer interchange are discussed.

Introduction Mulliken1

Historically, conceived the diffusive interaction of organic and organometallic electron donors and electron acceptors to form labile 1:1 complexes showing distinctive chargetransfer absorptions at just about the same time that Taube2 independently formulated his groundbreaking dichotomy of electron-transfer mechanisms in terms of distinctive outer-sphere and inner-sphere pathways, all while they were both ensconced at the University of Chicago! Even more surprising and curious are that the subsequent evolutions of these related seminal ideas continued to follow two quite orthogonal courses thereafter for quite a long timesthe Mulliken charge transfer relating solely to spectroscopic (non-adiabatic) transitions3,4 and the Taube outer- and inner-sphere formalism taking on a dynamics (adiabatic) focus5,6suntil the Creutz/Taube electron-transfer conundrum7 was resolved some years later by the invocation of Mulliken charge transfer and Hush intervalence theories.3,8 Nonetheless, there is, as of this late date, no definitive study in which charge-transfer spectroscopy is directly interrelated to the various intermolecular electron-transfer phenomena that are extant in solution. The latter is perhaps somewhat understandable if we consider that the spectral observations of transient charge-transfer absorptions are commonly applicable to electron-donor/acceptor dyads in which the electron-transfer driving force is highly endergonic,9 that is, with ∆G°ET . 0, and thus the electron-transfer rates prohibitively slow. At the other extreme of highly exergonic electron transfers, the lifetimes of the charge-transfer state are expected to be too short to conveniently measure. If so, the obvious experimental solution to this impasse is to deliberately scrutinize various electron donors (D) and electron acceptors (A) that undergo reversible one-electron oxidation (E°ox) and reduction (E°red), respectively, at reasonable potentials and then carefully select only those donor/acceptor combinations in which the electron-transfer driving force is essentially isergonic, that is, with ∆G°ET ) F(E°ox - E°red) as close to nil as practicable. †

Part of the special issue “Norman Sutin Festschrift”.

After an extensive search, we identify in this study several pairs of diamagnetic donors and acceptors in which the distinctive charge-transfer state, [D,A],10 and its accompanying electron-transfer state, {D+•,A-•},11 can be independently observed and the reversible interchange, [D,A] a {D+•,A-•}, can be quantitatively established. Most important will be the experimental delineation of the precise molecular (X-ray) and electronic (UV-NIR) structures associated with such separate charge-transfer and electron-transfer states. In such an event, the diffusive charge-transfer association and attendant electronic transition,12 that is, KCT

hνCT

D + A {\} [D,A] {\} [D+•,A-•]

(1)

is to be reconciled with the electron-transfer kinetics for the diamagnetic cross-exchange (CE) process, that is, kCE

D + A {\} D+• + A-•

(2)

in a manner analogous to the corresponding self-exchange (SE) of the paramagnetic D/D+• and A-•/A dyads examined in the foregoing study,13 based on the two-state model developed by Sutin.14,15 Results I. Identification of Isergonic Donor/Acceptor Dyads. Critical to our quantitative study of the facile interchange between charge-transfer (CT) and electron-transfer (ET) states are the series of organic donor/acceptor dyads identified in Table 1, with each accompanied by an acronym to facilitate its structural identification. In order to analyze the relevant charge-transfer/electrontransfer interchanges, it was first necessary to establish the structural, spectral, and electrochemical properties of these electron donors and acceptors, as well as those of their cationradical and anion-radical product, respectively, as they related to eq 2. Some of the relevant data are available in the chemical literature,16-21 but Table 1 contains an important pair of organic electron donors, DO and TMDO,22 for which the experimental

10.1021/jp068994o CCC: $37.00 © 2007 American Chemical Society Published on Web 03/24/2007

6656 J. Phys. Chem. B, Vol. 111, No. 24, 2007

Sun et al.

TABLE 1: Reversible Redox Potentials of Electron Donors and Acceptors

a

In dichloromethane at 22 °C, as described in the Experimental Section.

SCHEME 1

Figure 1. ORTEP diagram of the neutral donor TMDO.

TABLE 2: Geometries of TMDO and DO Moieties in the Donor, in the Cation Radical, and in the Complexes with DDQa

TMDO TMDO+•SbCl6[TMDO,DDQ] [2TMDO,DDQ](TMDO) DO DO+•SbCl6[2DO,DDQ]d

a, Å

b, Å

c, Å

d, Å

1.380 1.421 1.397 1.401b 1.356c 1.383 1.421 1.385 1.370

1.387 1.375 1.379 1.383b 1.388c 1.383 1.376 1.382 1.376

1.379 1.336 1.356 1.355b 1.390c 1.381 1.332 1.366 1.388

1.455 1.457 1.461 1.470b 1.457c 1.431 1.423 1.431 1.434

R, deg β, deg 2.9 0.7 3.3 1.1b 2.9c 3.9 0.7 2.3 3.2

13 1.2 22.5 21.6b 22.3c 17 1.7 14 7

a Average bond length (Å); see Supporting Information Table S2 for geometry details. b TMDO moiety within a complex with DDQ. c Separate TMDO moiety. d Two independent moieties.

results have to be separately detailed. As such, we will mainly focus hereinafter on TMDO (and DO) as the prototypical aromatic donor in its interaction with the prototypical organic acceptor, DDQ.18 A. Molecular Structures. The X-ray analysis of the colorless single crystals of TMDO and DO revealed the quasi-chair conformation with two pairs of oxygens of each donor deviating slightly to opposite sides of the aromatic plane with a dihedral angle of ∼3° and the two oxole carbons bent in the reverse directions (with dihedral angles of ∼15° relative to the benzenoid plane), as illustrated in Figure 1 (see also Supporting Information Figure S1). The details of the geometric characteristics of TMDO and DO are elaborated in Table 2. B. Electrochemical Studies. Electrochemical studies in dichloromethane revealed the reversible one-electron oxidation waves with E°ox ) 0.74 V versus the saturated calomel electrode (SCE) for TMDO and 0.94 V versus SCE for DO (see Supporting Information Figure S2). Thus, the corresponding cation radicals

can be easily produced by either electrochemical oxidation at a controlled potential or direct treatment with one-electron oxidants.23 Indeed, the oxidation of the neutral donors with NO+SbCl6- allowed us to isolate dark yellow crystals of TMDO+•SbCl6- and DO+•SbCl6- suitable for the X-ray crystallography (see the Experimental Section). Structure analysis (see Supporting Information Figure S3) established that the oneelectron oxidation was accompanied by significant elongation of bond “a” and contraction of bond “c” (see the graphics above Table 2).24 Notably, both cation-radical moieties are nearly planar, with the R and β dihedral angles being close to zero (compare Scheme 124). C. Persistent Ion-Radical Structures in Solution. Direct dissolution of the crystalline salt TMDO+•SbCl6 in dichloromethane (under an argon atmosphere) led to a stable yellow solution exhibiting an intense absorption band at 483 nm ( ) 14 700 cm-1 M-1) and a weaker band at 449 nm ( ) 6700 cm-1 M-1), as illustrated in Supporting Information Figure S4. Likewise, DO+•SbCl6 showed essentially the same spectrum with absorption maxima at 486 and 452 nm. Indeed, such a clear spectral delineation accompanying the one-electron oxidation of the electron donor to its stable cation radical, together with the relatively small potential difference of E°ox - E°red ) 0.22 V, identified the TMDO/DDQ dyad as the donor/acceptor pair of choice for further study of the chargetransfer association and the electron-transfer equilibrium, as follows. II. Spectral Identification and X-ray Structures of the Charge-Transfer State. A. DiffusiVe Electron-Donor/Acceptor Interactions. Diffusive electron-donor/acceptor interactions were immediately apparent upon the addition of the neutral TMDO donor to the dichloromethane solution of the neutral DDQ acceptor by the new appearance of a broad (unresolved) band at λmax ) 940 nm (fwhm ) 5.0 × 103 cm-1) in the UV-NIR spectral region otherwise transparent for either the donor (TMDO), the acceptor (DDQ), or their ion radicals (TMDO+• and DDQ-•).25 The absorption of the new Gaussian band (Supporting Information Figure S5) rose progressively as the TMDO concentration increased, as shown in Figure 2, and the Benesi-Hildebrand analysis (inset, Figure 2A) together with

Reversible Interchange of CT vs ET States

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Figure 2. (A) Spectral changes upon the incremental addition of TMDO to the 2.5 M solution of DDQ in dichloromethane showing the rise of the 930 nm band of the [DDQ,TMDO] complex with the Benesi-Hildebrand plot as the inset. (B) Temperature dependence of the spectrum of a dichloromethane solution containing equimolar concentrations of DDQ and TMDO (2.5 mM each) showing the increase of the 930-nm band upon lowering the temperature, with ln KCT vs 1/T as the inset.

Figure 4. ORTEP diagram of the π-separation in the TMDO/DDQ complex.

Figure 3. Mulliken plot for TMDO complexes with various acceptors, as indicated.

the Job plot confirmed the 1:1 stoichiometry for formation of the donor/acceptor complex according to eq 3: KCT

TMDO + DDQ {\} [TMDO,DDQ]

(3)

Quantitative analysis of the concentration dependence led to a formation constant of KCT ) 5.0 M-1 at 15 °C and an extinction coefficient of CT ) 4900 cm-1 M-1 at 940 nm (see the Experimental Section for details). Furthermore, lowering the temperature of the equimolar solution of DDQ and TMDO in dichloromethane resulted in a significant increase of the NIRband intensity to indicate the equilibrium shift in eq 1 to the right. The linear dependence of ln KCT with inverse temperature afforded the thermodynamic parameters ∆HCT ) -31 kJ M-1 and ∆SCT ) -102 J M-1 K-1. Most importantly, analogous new absorption bands were observed when TMDO was exposed to various other electron acceptors, and the charge-transfer character of the electronic transitions was established by the Mulliken correlation of their reduction potentials in Figure 3. Likewise, the DDQ acceptor with various other electron donors (including TMDO) showed the same Mulliken correlation of their E°ox values.26 Finally, the UV-NIR spectrum of the DDQ acceptor complexed with the DO donor afforded a similar broad NIR band with the maximum at λCT ) 910 nm, and the quantitative treatment of the concentration and temperature dependence confirmed the 1:1 complex formation analogous to eq 1. These linear relationships afforded the thermo-

dynamic parameters ∆HCT ) -24 kJ M-1 and ∆SCT ) -72 J M-1 K-1 and an extinction coefficient of CT ) 5000 M-1 cm-1 at 910 nm. B. X-ray Structures of Electron-Donor/Acceptor Complexes. The donor/acceptor combinations afforded three crystalline modifications, the preparations of which were dependent on the use of either TMDO or DO and the specific experimental conditions. 1. Discrete 1:1 Complex. The slow cooling of a dichloromethane solution of TMDO and excess of DDQ to -65 °C resulted in the formation of dark brown crystals, the X-ray analysis of which revealed the triclinic unit cell and the 1:1:1 stoichiometry TMDO/DDQ/CH2Cl2 in which the donor and acceptor pair are arranged cofacially (Figure 4) at a short interplanar distance of 3.0 Å. The donor moiety exists in [TMDO,DDQ] as the quasi-boat conformation, with the central ring bent toward the acceptor (see Figure 4). Note that this structure contrasts with the chairlike geometry of the separate donor (see Figure 1) and the nearly planar but still chairlike cation radical (see Supporting Information Figure S3). Most remarkably, the C-C bond lengths of the TMDO moiety in [TMDO,DDQ] are intermediate between the corresponding values in the separate donor and in the cation radical (see Table 2) to indicate the partial oxidation of the complexed donor. The quantitative analysis (similar to that comparatively applied earlier to other systems with partial charge transfer27) of the corresponding bond-length differences among the cation radical, the complexed TMDO, and the isolated neutral donor led to the estimate of the partial charge on the TMPD moiety as qD ) +0.5 ( 0.1 (see the Supporting Information for details). In a similar vein, the C-C bond lengths in the acceptor moiety within the [TMDO,DDQ] complex are also intermediate between the corresponding values characteristic of the neutral

6658 J. Phys. Chem. B, Vol. 111, No. 24, 2007

Figure 5. ORTEP diagram of the 2:1 TMDO/DDQ complex.

Figure 6. ORTEP diagram of the 2:1 DO/DDQ complex.

acceptor and its anion radical (see Supporting Information Table S3). As such, the quantitative bond-length analysis led to a partial charge of qA ) -0.5 on the DDQ acceptor, in harmony with the estimate of the partial charge transfer based on the geometry of the TMDO moiety. 2. Discrete 2:1 Complex. Under slightly different experimental conditions, the equimolar mixture of TMDO and DDQ dissolved in n-butyronitrile afforded the crystalline complex with 3:1 stoichiometry upon slow evaporation at room temperature. X-ray analysis showed the unit cell of the dark brown single crystal to consist of a mixture of the 2:1 donor/acceptor complex [2TMDO,DDQ] and a third, unassociated TMDO donor which existed separately without any close intermolecular contacts. The donor/acceptor complex has a “sandwich” structure in which the TMDO donors are arranged cofacially on both DDQ faces at close separations of rπ ≈ 3.1 Å (Figure 5). Importantly, the geometries of both complexed TMDO moieties are intermediate between those of the neutral donor and its cation radical so that the partial charge transfer of qD ) +0.5 ( 0.1 is the same as that found in the 1:1 complex (Figure 4). The structure of the third isolated TMDO is essentially unchanged from that found in the parent donor (Table 2). 3. Infinite 2:1 Stack. The third donor/acceptor structure was obtained upon the slow diffusion of hexane into the dichloromethane solution containing equivalent amounts of DO and DDQ at -60 °C to afford brown crystals with 2:1 stoichiometry, 2DO/DDQ, in which X-ray analysis revealed the presence of infinite ...DDADDA... stacks. Importantly, the close D/A interplanar separations of rπ ≈ 3.1 Å between DDQ and the adjacent DO donors indicated the 2:1 interaction shown in Figure 6 which is similar to that with TMDO described above. However, the geometry of the DO moiety in this complex is close to that of the neutral DO donor (Table 2), to indicate the rather limited degree of charge transfer with qCT ≈ 0. III. Reversible Interchange between the Charge-Transfer State versus the Electron-Transfer State. A. Spectral Iden-

Sun et al.

Figure 7. Electronic spectra (black line) of the equimolar acetonitrile solution of TMDO and DDQ (20 mM) and its simulation (red dashed line) as the spectral superposition of TMDO+• and DDQ-• individually (shown in the insets), indicating the presence of a charge-transfer absorption band analogous to that in Figure 2.

tification and SolVent Dependence of the Electron-Transfer States. Electron transfer between the diamagnetic donor and acceptor dyads was readily observed when the solvent was simply changed from dichloromethane to the more polar acetonitrile or propylene carbonate.28 Thus, the series of UVNIR spectra in Figure 7 obtained in acetonitrile is to be directly compared with those in Figure 2 obtained in dichloromethane under otherwise the same experimental conditions. Most prominent in Figure 7 is the principal component consisting of multiple transitions in the high-energy UV region between 400 and 600 nm, the digital deconvolution of which established its composite nature as TMPD+• plus DDQ-• (see insets)29 to indicate the facile transformation of the donor/acceptor dyad to its electron-transfer state, that is, KET

TMDO + DDQ {\} TMDO+• + DDQ-•

(4)

Indeed, quantitative analysis confirmed that the overall (400600) envelope consisted of the simple spectral superposition of TMDO+• and DDQ-•, as shown by the red dashed curve in Figure 7. The further scrutiny of Figure 7 identified the additional (weak) NIR absorption characteristic of the chargetransfer transition previously identified in Figure 2. In other words, such spectral studies qualitatively indicated that the extent of electron transfer in eq 4 was highly dependent on solvents of such significantly different polarity as the weakly polar dichloromethane to generate the charge-transfer complex, and in the strongly polar acetonitrile to generate the contact ion pair (CIP) or the separated ion pair (SIP). Proceeding further with increasing solvent polarity, we found the charge-transfer absorption in the most polar solvent propylene carbonate28 to be much weaker that that observed in acetonitrile. We thus deduced that the TMDO+•/DDQ-• ensemble existed largely or solely as the separated ion pairs in this highly polar medium.29 B. Temperature Dependence of the Charge-Transfer and Electron-Transfer States. Lowering the temperature of the donor/ acceptor mixtures uniformly led to the dramatic increases in the charge-transfer absorption of [TMDO,DDQ] irrespective of solvent. The absorption increases in Figure 8 of the low-energy band at λmax ) 930 nm were linear with temperature in accordance with the formation of the 1:1 donor/acceptor complex in eq 3, which allowed us to evaluate the formation constants as KCT ) 0.5 M-1 in propylene carbonate at 23 °C. Its temperature dependence (Figure 8, inset) afforded the thermodynamic parameters ∆HCT ) -15 kJ M-1 and ∆SCT ) -55 J M-1 K-1.

Reversible Interchange of CT vs ET States

J. Phys. Chem. B, Vol. 111, No. 24, 2007 6659

Figure 8. Temperature-dependent spectral changes of the equimolar solution of TMDO and DDQ (10 mM) in propylene carbonate upon lowering the temperature from 74 °C to 41, -4, -24, -32, -46, -51, -59, and -74 °C, indicating the increase of the CT band at 930 nm and the concomitant decreases of the TMDO+• band (490 nm) and the DDQ-• band (500-600 nm). Insets: linear dependence of ln(K) vs 1/T for KET (left) and KCT (right) calculated on the basis of the intensity of the low-energy and the 400-600 nm absorption bands, respectively.

Inspection of Figure 8 also revealed the absorption change of the high-energy band of the electron-transfer state which decreased uniformly with the temperature rise according to eq 4, the equilibrium constant for which was evaluated as KET ) 2.2 × 10-3 M-1 together with the thermodynamic parameters ∆HET ) 11 kJ M-1 and ∆SET ) -32 J M-1 K-1 at 23 °C. Furthermore, the reversibility of all spectral changes established the thermal equilibration between these states,11,30 that is, KCT/ET

[TMDO,DDQ] {\} {TMDO+•,DDQ-•}

(5)

which allowed us to calculate the interchange constant KCT/ET ) 5.6 × 10-4 M-1 and the accompanying thermodynamic parameters ∆HCT/ET ) 24 kJ M-1 and ∆SCT/ET ) 19 J M-1 K-1 (see Table 3). Most importantly, the thermodynamic parameters for the equilibrium between charge-transfer and electron-transfer states calculated directly from the concentrations of the donor/acceptor complex and the cation-radical/anion-radical pair agreed well with that calculated from the separate values of KCT and KET, to indicate the consistency of the two sets of measurements. Furthermore, we found the microscopic reverse process to pertain by mixing equimolar amounts of the pure TMDO+• and DDQ-• salts in dichloromethane at low temperatures (-95 °C).31 This resulted in the immediate bleaching of the yellow color of the cation radical and the dark red color of the anion radical, leaving the residual (broad) NIR absorption with λmax ) 940 nm characteristic of the charge-transfer band. Finally, raising the temperature of the mixture to 23 °C led to the (reversible) diminution of the CT band, identical to that obtained by mixing of the TMDO donor and DDQ acceptor. Similar effects were also obtained when these cation and anion radicals were mixed in acetonitrile and propylene carbonate.32 Such spectral measurements thus clearly demonstrated the occurrence of reversible

Figure 9. Mulliken dependence of νCT on E°ox for donor/acceptor complexes of TCNE (A) and DDQ (B) with various donors (see ref 33 for the donor identification).

equilibration among neutral donor/acceptor dyads, their chargetransfer complex, and the electron-transfer products according to eq 6: KCT

KCT/ET

TMDO + DDQ {\} [TMDO,DDQ] {\} TMDO+• + DDQ-• (6) In contrast to the behavior of TMDO, no cation radicals were observed in dichloromethane solutions containing the unmethylated analogue DO, as well as in either acetonitrile or propylene carbonate. Moreover, the geometries of both the donor and the acceptor moieties in the solid-state DO/DDQ associates were quite close to those of their separate parents, indicating the existence of little or limited degree of charge transfer (Table 2). Such distinctions are directly related to the oxidation potential of DO that is ∆E°ox ) 0.2 V higher than that of TMDO. Therefore, in order to establish further the effects of such minor differences of the donor/acceptor redox potentials, let us now turn to the characterization of several other donor/acceptor dyads. C. Near-Isergonic Electron Transfer with the Other Donor/ Acceptor Dyads. Near-isergonic electron transfer with the other donor/acceptor dyads included in Table 1 consistently revealed the ubiquitous existence of charge-transfer absorption bands that resulted from a span of electron-transfer driving forces: ∆GET ) F(E°ox - E°red) as listed in Table 1. For example, the diffusive encounter of the TMDO donor in dichloromethane solution with tetracyanoethylene (TCNE), p-chloranil, and o-chloranil (CA) with ∆GET ) 55, 57, and 73 kJ M-1 resulted in the appearance of new NIR bands at λCT ) 807, 765, and 810 nm, respectively. Analysis of the dependence of the band intensities on reactant concentrations indicated that they all resulted from 1:1 complexes, and the Mulliken correlation verified their charge-transfer character (see Figure 9 and Supporting Information Figure S6). Similar CT complexes without any sign of ion radicals were observed when TMDO was added to the same acceptors in other solvents, in contrast to the distinctive behavior of the DDQ/ TMDO pair (vide supra). Therefore, in order to observe the CT/

TABLE 3: Thermodynamics of the Charge-Transfer and Electron-Transfer Equilibria for the TMDO/DDQ Dyad in Various Solvents charge-transfer state solvent

KCT,a M-1

∆HCT, kJ M-1

∆SCT, J M-1 K-1

KETa

PC MeCN DCM

0.5 ( 0.1 0.5 ( 0.1 5.0 ( 1

-15 ( 2 -22 ( 2 -31 ( 5

-55 ( 4 -80 ( 8 -102 ( 5

(2.2 ( 0.3) × (3.4 ( 0.4) × 10-5

a

CT/ET interchangeb

electron-transfer state 10-4

∆HET, kJ M-1

∆SET, J M-1 K-1

∆H, kJ M-1

∆S, J M-1K-1

11 ( 2 4(1

-32 ( 4 -87 ( 8

24 ( 2 (26) 25 ( 3(26)

19 ( 1(23) 5 ( 1(-7)

At 15 °C. b Values in parentheses computed from individual values of KCT and KET.

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Figure 10. Solvent-dependent electronic spectra of solutions containing p-CA/TTF dyads showing the decrease in the intensity of the chargetransfer (NIR) band and the increase in the intensity of the TTF+• cationradical band (at 580 nm) when dichloromethane (dashed black line) is replaced by acetonitrile (solid gray line) and propylene carbonate (solid black line). (In order to exhibit the 580 nm band in propylene carbonate, the absorption was divided by 5 in the 450-700 nm range.)

ET equilibria with these somewhat weaker acceptors, we turned to the stronger tetrathiafulvalene (TTF) and tetramethyl-pphenylenediamine (TMPD) donors. 1. Tetrathiafulvalene (TTF). TTF is a somewhat better electron donor than TMDO by virtue of its reversible oxidation potential which is 0.37 V (or 8.7 kcal mol-1) less positive. Indeed, the diffusive interaction of TTF with the quinone acceptors resembled that of the TMDO/DDQ pair. Thus, the study of the TTF/p-CA dyad in dichloromethane revealed the predominance of the charge-transfer complex with the NIR band at λCT ) 1190 nm, whereas mixtures of the CT complex and the ion-radical pair were observed in the more polar acetonitrile and propylene carbonate (Figure 10). The temperature dependence of the charge-transfer and ion-radical bands led to the thermodynamic parameters for the charge-transfer and electrontransfer states analogous to eqs 3 and 4 (Supporting Information Table S4). Somewhat similar behavior was also observed for the TTF/o-CA dyad in these solutions, as well as in the solidstate complexes, both with the significant degree of charge transfer described earlier.34 2. Tetramethyl-p-phenylenediamine (TMPD). TMPD was the best electron donor examined in this study, with a value of E°ox ) 0.12 V placing the donor/acceptor dyad with tetracyanoethylene at the isergonic limit. Accordingly, the diffusive interaction of TMPD and TCNE in dichloromethane resulted in the formation of two groups of absorption bands: (a) the predominant (high-energy) intense absorption in the 400-600 nm range characteristic of the TMPD+•/TCNE-• ion-radical pair and (b) the minor low-energy (broad) absorption band of the chargetransfer state centered at λmax ) 1000 nm (Supporting Information Figure S7). In the polar acetonitrile and propylene carbonate media, only the electron-transfer state was apparent and ionpair formation was thus essentially quantitative, with eq 4 being shifted completely to the right. X-ray analysis established the 1:1 donor/acceptor stoichiometry in single crystals consistently obtained from low-temperature crystallizations of various TMPD/TCNE solutions, but the geometries of the TCNE and TMPD moieties indicated that they always consisted of equimolar mixtures of cation and anion radicals. Moreover, these ionradical mixtures contained the distinctive dimers [TMPD2]2+ and [TCNE2]2- (see Supporting Information Figure S8), and the very close intradimer separations of rπ ) 3.1 and 2.9 Å, respectively, were similar to those found in other π-dimers of these ion radicals.35,36 Crystallographic data thus indicated that

Sun et al. complete electron transfer predominated for the TMPD/TCNE dyad. Moreover, the charge-transfer state of the TMPD/TCNE dyad only predominated in solvents of the lowest polarity. Although the high-energy band of the TMPD+•/TCNE-• pair could be observed in dichloromethane, its presence was undetectable when diethyl ether was used as the solvent of lowest polarity, with only the broad charge-transfer absorption at λCT ) 1000 nm being apparent. The concentration dependence of the intensity of the NIR bands pointed to the 1:1 complex, and its analysis allowed the formation constant and extinction coefficient to be evaluated as KCT ) 1 × 103 M-1 and CT ) 7 × 103 M-1 cm-1. The absorption band of this isergonic [TCNE,TMPD] dyad deviated slightly but notably (i.e., it had higher energy) from the Mulliken correlation observed for other complexes of donors with higher oxidation potentials (see Figure 9A). Importantly, such a deviation was quite common,9 as these complexes approached the isergonic region and beyond, to the exergonic electron-transfer range. Indeed, the scrutiny of the Mulliken dependence of the CT absorption also revealed such a divergence of the o-CA complex with TTF (see Supporting Information Figure S6). Notably, the most pronounced deviation from the Mulliken dependence was observed with the DDQ/ TMPD dyad (Figure 9B and Supporting Information Figure S9) which could be observed in nonpolar solvents only at very low temperatures owing to the highly favorable electron-transfer thermodynamics, as followed from the redox potentials listed in Table 1. Discussion I. Mulliken and Hush Theories for the Precursor Complex. Generalized Potential-Energy Surfaces for Intermolecular Electron Transfer. The diffusive encounter of electron donors (D) and acceptors (A) leading to intermolecular electron transfer can be mechanistically presented in the most general (and simplest) context as kdiff

kET

D + A {\} [D,A] {\} {D+•,A-•} a D+• + A-•

(7)

where the first set of brackets identifies the precursor or encounter complex which is transformed to the successor complex in the rate-limiting activation process. If so, the precursor complex is to be identified spectroscopically by its diagnostic charge-transfer transition according to Mulliken theory.1,3 Within the Marcus-Hush (two-state) paradigm,8,37-40 the potential-energy surface for the precursor complex can be presented in terms of the three limiting mechanisms illustrated in Figure 11. These are based on the relative magnitudes of the electronic coupling element (Hab) and the Marcus reorganization energy (λ), namely, type S with Hab , λ/2, type M with Hab e λ/2, and type L with Hab g λ/241 for an isergonic electrontransfer process. A continuum of outer-sphere and inner-sphere electrontransfer mechanisms as implied by Figure 11 was proposed in our earlier study13 of the most basic electron-transfer process involving the self-exchange of electron donors (D) with their paramagnetic cation radical (D+•) as well as electron acceptors (A) with their paramagnetic anion radicals (A-•), that is, kSE

D + D+• {\} D+• + D kSE

A-• + A {\} A + A-•

(8a) (8b)

However, if such a mechanistic picture is to have any generality, it must also be more widely applicable to the related electron

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J. Phys. Chem. B, Vol. 111, No. 24, 2007 6661

Figure 11. Representative potential-energy surfaces for electron transfer for the precursor complex (see text) from ref 13.

transfers between diamagnetic donors and acceptors such as those examined in Table 1 for eq 2. Accordingly, let us examine how the unprecedented and simultaneous observation of chargetransfer and electron-transfer states as described in the Results section (Figures 2 and 7, Table 3) can be quantitatively treated with the aid of two-state Mulliken-Hush theory.15,39,40 Before proceeding, however, it is important to re-emphasize that the electron-donor/acceptor dyads we chose in Table 1 are special in that (1) their values of E°ox and E°red are such that the ET driving forces are uniformly close to the isergonic limit, (2) the precursor complexes show unusually high degrees of charge transfer with qCT ∼ 0.5, and (3) the separate (spectral) observations of the charge-transfer and electron-transfer states are strongly modulated by solvent polarity. II. Evaluation of the Electronic Coupling Element (Hab) and Reorganization Energy (λ) for Diamagnetic Donor/ Acceptor (Charge-Transfer) Dyads. According to the twostate model,14,15 the ground- and excited-state wave functions consist of linear combinations of the initial (D/A) and final (D+/ A-) states expressed as ψa and ψb, respectively:

ΨGS ) aψa + bψb

(9a)

ΨES ) a′ψa + b′ψb

(9b)

The solution of the secular determinant leads to the groundstate and excited-state energies as

EGS ) (Haa + Hbb)/2 - ((Hbb - Haa)2 + 4Hab2)1/2/2 (10a) EES ) (Haa + Hbb)/2 + ((Hbb - Haa)2 + 4Hab2)1/2/2 (10b) where Haa ) ∫ψaHψa and Hbb ) ∫ψbHψb represent the energies of the initial and final diabatic states and Hab ) ∫ψaHψb is the electronic coupling element.43 A. Electronic Coupling Energy. Experimentally, the electronic coupling element is evaluated from the intensity integral of the intervalence absorption via the Hush expression:8,40,44

Hab ) 0.0206(νCT∆ν1/2CΤ)1/2/rDA

(11)

where νCT and ∆ν1/2 are the spectral maximum and full width at half-maximum (cm-1), respectively, of the charge-transfer absorption band, CT is the extinction coefficient (M-1 cm-1), and rDA (Å) is the separation parameter.45 The electronic coupling elements based on eq 11 and the spectral and structural characteristics of the donor/acceptor complexes under study are listed in Table 4 and Table S5. B. Reorganization Energies. The intramolecular component (λi) of the reorganization energy for electron transfer within the

TABLE 4: Electronic Coupling Elements and Reorganization Energies for Electron Transfer within the Donor/Acceptor CT Complex complex

Hab,a 103 cm-1

λi,b 103 cm-1

λo,c 103 cm-1

λ,d 103 cm-1

[DDQ,TMDO] [DDQ,DO] [o-CA,TTF] [p-CA,TTF] [TCNE,TMPD]

3.6 3.2 3.6 1.8 3.8

4.2 4.3 3.1 3.2 3.8

3.5 1.8 1.7 3.8 4.0

7.7 7.1 4.8 7.0 7.8

a Calculated via eq 11 (see Supporting Information Table S5 for details). b Inner-sphere reorganization energy (see Supporting Information Table S6 for details). c Solvent reorganization energy. d λ ) λi + λo.

donor/acceptor complex is calculated as the difference between (a) the energy of the initial diabatic state (in which the electron is located on the donor and the reactants are in their relaxed nuclear geometries) and (b) the energy of the final diabatic state (in the same nuclear geometry as the relaxed initial state but with the electron transferred from the donor to the acceptor).46 Accordingly, we compute the inner-sphere reorganization energies (λi) for the electron donors and acceptors as described earlier,13,47 and the values for the dyads listed in column 3 of Table 4 are calculated as λi ) (λiA + λiD)/2 (see the Experimental Section for details). The solvent component (λo) of the reorganization energy is calculated using the Kirkwood solvation model48 with the charge-transfer complex considered as a cavity with an internal dielectric constant of in ) 2 immersed in dichloromethane with static and optical dielectric constants of s ) 8.93 and o ) 2.03, respectively.28 The application of this procedure results in the solvent reorganization components listed in column 4 of Table 4 (see the Experimental Section for details). Finally, the sum of the inner-sphere (vibration) and outer-sphere (solvent) components produces the total reorganization energies for various dyads listed in the last column of Table 4. III. Potential-Energy Surfaces for Cross-Exchange between Diamagnetic Donor/Acceptor Dyads. The potentialenergy surface for electron transfer is evaluated according to Sutin et al.14,15 via the amalgamation of the Mulliken formalism3 with the Marcus representation of the initial and final diabatic states37,38 at each point (X) along the reaction coordinate via the reorganization energy (λ) and the free-energy change (∆GET) given as Haa ) λX2 and Hbb ) ∆GET + λ(X - 1).2 The energy difference between initial and final diabatic states, that is, ∆GET between the non-interacting donor and acceptor and their ion radicals, is represented by the difference of the reversible redox potentials of the donor and the acceptor: ∆GET ) F(E°ox E°red). Thus, the interaction of the initial and final diabatic states

6662 J. Phys. Chem. B, Vol. 111, No. 24, 2007

Sun et al.

Figure 12. Two-state energy diagram for the electron transfer in the (A) [DDQ,TMDO] and (B) [TCNE,TMPD] dyads with the diabatic states (in gray) and with the single-minimum ground and excited states (in black).

TABLE 5: Structural and Energetics Criteria for Validation of the Two-State ModelsComparison of the Calculated and Experimental Results complex

Xmin

qCT

νCTcalcd,a 103 cm-1

νCTexptl, 103 cm-1

[DDQ,TMDO] [DDQ,DO] [o-CA,TTF]c [p-CA,TTF] [TCNE,TMPD]

0.15 0.08 0.25 0.04 0.8

0.5 0.0b 0.6 0.4d 1.0e

10.1 11.3 8.7 10.0 9.6

10.6 11.0 9.1 8.3 10.0

a Calculated as the ground- and excited-state energy difference at a ground-state minimum. b From the 1:2 complex. c From ref 34. d Neutral state, ionic state is characterized by q 27b e From CT ) 0.8. (TMPD)22+(TCNE)22-.

(shown as the gray curves in Figure 12) results in the formation of the adiabatic ground state and the excited state described by the wave functions in eq 9, with the energies presented by eq 10. Accordingly, the computations of EGS and EES are carried out using eq 10 with Haa ) λX2, Hbb ) ∆GET + λ(X - 1)2, and a constant value of Hab (determined via the Mulliken-Hush formalism) at each point along the reaction coordinate from X ) 0 (corresponding to the neutral donor/acceptor dyad) to X ) 1 (corresponding to the ion-radical pair). This leads to the adiabatic-state energies illustrated in Figure 12 for the DDQ/ TMDO and TCNE/TMPD dyads representing a pair of donor/ acceptor systems with slightly endergonic and exergonic driving forces, respectively (see Table 1). The potential-energy diagrams in Figure 12 (see also Supporting Information Figure S10) identify the existence of broad single-minimum ground states, with the minima significantly shifted from the initial diabatic state with X ) 0. As such, they derive from the predominant strong donor/acceptor electronic coupling, as reflected by the large value of Hab ∼ (2-4) × 103 cm-1 in Table 4, that essentially eliminates the barrier for electron transfer within the precursor complex (compare potentialenergy surface type L in Figure 11). However, before any further discussion of the mechanistic implications of this conclusion, let us consider how these diagrams (obtained via the combination of experimental data with semiempirical and ab initio computations) agree with the available spectral and structural data. First, the calculated positions of the ground-state minima (Xmin) in column 2 of Table 5 show a good correlation with the experimental degree of charge transfer (qCT) in column 3 obtained from the X-ray structural data.49,50 Next, the UVNIR measurements provide additional (reliable) information for the direct comparison of the experimental and calculated chargetransfer transition energies. Thus, the experimental data (Table 5) confirm the validity of the calculated energies based on the

combination of (a) the Mulliken-Hush coupling element, (b) the ab initio reorganization energies, and (c) the donor/acceptor redox potentials, as shown by the comparison of the computed values in column 4 with the experimental energies in column 5. In other words, the separate structural and energetics criteria together provide critical validation of the two-state model for these organic donor/acceptor complexes. Importantly, the application of the two-state model allows us to explain the deviation of the charge-transfer transition energies from the linear Mulliken correlation for donor/acceptor complexes at or near the isergonic/exergonic border, as presented in Figure 9. Thus, in the context of the two-state model, the difference of the diabatic-state energies (which includes the difference of the redox potentials) is represented as a quadratic term in eq 10. As such, any increase in the redox-potential difference between the donor and the acceptor would symmetrically increase the energy of the charge-transfer transition, with the result that the ground-state minimum for exergonic driving force will be shifted toward the product state (Figure 12B).51 Indeed, this prediction is borne out in Figure 9 for both the [TCNE,TMPD] and [DDQ,TMPD] systems. On the basis of such a consistency of the structural and spectral descriptions of the donor/acceptor complexes with the experimental data via the application of two-state model, let us now describe some interesting mechanistic facets about electron transfer in such systems. IV. Adiabatic Electron Transfer via Precursor Complexes with High Degrees of Charge Transfer. The intermolecular donor/acceptor interaction according to Mulliken results in their spontaneous association with no or little activation energy, as also observed by the immediate appearance of the diagnostic charge-transfer absorption bands. Most notably, the strong donor/acceptor coupling eliminates the activation barrier for the thermal electron-transfer step within the [D,A] complex as required for class III (delocalized) systems in the terms of the Robin-Day classification.42,52,53 As such, the separate precursor and successor complexes in the generalized mechanistic scheme (eq 7) must be replaced by the single intermediate, that is, (ii)

D + A {\ } [Dq+,Aq-] {\} D+ + A(i)

(12)

in which the precursor complex (enclosed in square brackets) is characterized by a significant degree of charge transfer with the charge q g 0.5. Thus, the overall electron-transfer process is best described as a simple two-step process: (i) the diffusive encounter of the donor/acceptor dyad to initially form a tightly

Reversible Interchange of CT vs ET States bound π-complex that requires concomitant (major) redistribution of the electron pair originally located on the donor highest occupied molecular orbital (HOMO) to the molecular (CT) orbital with a significant contribution of the acceptor lowest unoccupied molecular orbital (LUMO), and (ii) the homolytic dissociation of such a precursor complex that leads directly to the adiabatic or thermally equilibrated ion-radical pair in eq 12ii and, on the other hand, its heterolytic dissociation in eq 12i results in the restoration of the starting donor/ acceptor dyad. Several examples of such equilibria are described in the Results section above. We further note that the electron-transfer process between the organic donor/acceptor dyads as presented herein is reminiscent of inorganic (inner-sphere) electron transfers in which the metal redox centers are covalently bonded via bridging ligands,54,55 as well as in the organic electron transfers involved in the addition/elimination reactions of paramagnetic radicals.56 However, the two most basic distinctions that characterize organic donor/acceptor π-complexes needs to be stressed. First, such a complex formation involves the redistribution of a pair of electrons from the donor HOMO to the acceptor LUMO,50 and this is tantamount to the formation of a discrete dative bond. As such, the overall single-electron transfer involves an electronpair redistribution as well as the single-electron movement, or in other words, a combined polar and single-electron-transfer pathway. Second, owing to the delocalized nature of the strong π-bonding within the precursor complex, the equilibrium donor/ acceptor separation (rDA) will be only moderately (0.3-0.5 Å) shorter than the sum of corresponding van der Waals radii.57 As a result, the orbital overlap is unlikely to hinder the application of the two-state model, because it provides a reasonable description of intermediate complex for the electron transfer with organic donor/acceptor dyads. Most importantly, the strong donor/acceptor interactions characteristic of organic dyads can overcome the reorganization penalty and otherwise eliminate the classical barrier for electron transfer.37,38 Summary and Conclusions The electron donors and acceptors in Table 1 allow the simultaneous observation of the Mulliken charge-transfer state, [D,A], that can coexist in reversible equilibrium with the electron-transfer state, {D+•,A-•}, for pairs of diamagnetic (organic) redox dyads, D and A. The quantitative application of the two-state methodology14,15 provides the theoretical basis for the construction of the potential-energy surface (Figure 12) for cross-exchange of redox systems with electron-transfer driving forces that lie at the limit of the endergonic/exergonic border. As such, these electron-donor/acceptor systems represent the extreme of the delocalized inner-sphere mechanism (type L in Figure 11c),41 in which there is essentially no activation barrier for electron transfer. Such an unusual electron-transfer process is thus barrierless and driven directly to the adiabatic ion pair {D+•/A-•} by the overall free-energy changes with ∆G ) F(E°ox - E°red), as qualitatively depicted in Chart 1.58 According to this mechanistic formulation, the highly polarized precursor complex is the predominant (thermodynamics) species lying in a deep chemical “black hole” (Table 3), and thus emergent to the non-adiabatic ion pair [D+•,A-•] only upon direct photoexcitation (hνCT) of the charge-transfer complex.34 If such a mechanistic picture is valid for donor/acceptor dyads at or near the isergonic limit, the question then arises as to whether the charge-transfer state can coexist in reversible equilibrium with the electron-transfer state in the more general situation in which the ET driving force is substantially different

J. Phys. Chem. B, Vol. 111, No. 24, 2007 6663 CHART 1

from nil.59 In addition, we hope to direct our search to newer donor/acceptor systems that will identify other charge-transfer/ electron-transfer interchanges that quantitatively describe the predicted localized inner-sphere mechanism (type M) with the double-minimum ground state predicted by Figure 11b. Experimental Section Materials. N,N,N,N-Tetramethyl-p-phenylenediamine (TMPD), tetrathiafulvalene (TTF), dichlorodicyanobenzoquinone (DDQ), tetracyanoethylene (TCNE), p-chloranil (p-CA), and o-chloranil (o-CA) from commercial sources were purified by sublimation in vacuo and/or by recrystallization. 2,2,6,6-Tetramethylbenzo[1,2-d;4,5-d]bis[1,3]dioxole (TMDO) and benzo[1,2-d;4,5-d]bis[1,3]dioxole (DO) were prepared according to the literature procedures.22 Solvents were prepared and handled as described earlier.16 Cation-radical salts TMDO+•SbCl6- and DO+•SbCl6were produced in dichloromethane by oxidation of donor with stoichiometric (1:1) amounts of nitrosonium salt NO+SbCl6-,23 and precipitated with hexane. The purity of both salts was >97% as determined by spectral titration with p-chloranil anion radical. Colorless single crystals of TMDO and DO were prepared by the slow evaporation of their solutions in dichloromethane at room temperature. Single crystals of their cation radicals were prepared by the slow diffusion of hexane into solutions of TMDO+•SbCl6- and DO+•SbCl6 salts in dichloromethane at -60 °C. Single crystals of the 1:1 [DDQ,TMDO] complex were prepared by slow diffusion of hexane into the dichloromethane solutions containing the TMDO donor and a large excess of DDQ acceptor at -60 °C. Single crystals of the 1:2 complex [DDQ,2TMDO] were prepared by slow evaporation of equimolar solutions of these donors in either dichloromethane or n-butyronitrile. Single crystals of the 1:2 complex [DDQ,2DO] were prepared by the slow cooling of the equimolar solution of this donor/acceptor dyad in dichloromethane from 0 to -60 °C. To prepare single crystals of [TCNE,TMPD], the separate dichloromethane solutions of the donor and acceptor were mixed at 0 °C and carefully layered with hexane and the mixture was cooled slowly to -30 °C. X-ray Crystallography. The intensity data for the X-ray studies were collected at -100 °C with a Bruker SMART Apex diffractometer equipped with a CCD detector using Mo KR radiation (λ ) 0.710 73 Å). The structures were solved by direct methods and refined by the full matrix least-squares procedure as described earlier.60 The crystallographic data are presented in Supporting Information Table S1. Electrochemistry. Cyclic voltammetry (CV) and Osteryoung square-wave voltammetry (OSWV) measurements were carried out on a BAS 100A electrochemical analyzer in dichloromethane solutions containing 1 mM electroactive compound and 0.1 M tetra-n-butylammonium hexafluorophosphate as the supporting electrolyte under an argon atmosphere. The cell was of an airtight design with high-vacuum Teflon valves and Viton O-ring

6664 J. Phys. Chem. B, Vol. 111, No. 24, 2007 seals to allow the inert atmosphere to be maintained without contamination by grease. All of the cyclic voltammograms were measured at the same sweep rate of 0.2 V s-1 (with iR compensation). The working electrode consisted of an adjustable platinum disk embedded in a glass seal to allow periodic polishing without significantly changing the surface area (∼1 mm2). The counter electrode consisted of a platinum gauze that was separated from the working electrode by ∼3 mm. The saturated calomel electrode (SCE) and its salt bridge were separated from the cathode by a sintered glass frit. The potentials were referenced to SCE, which was calibrated with added ferrocene (1 × 10-4 M). Controlled-potential coulometry was also conducted with a BAS100A electrochemical analyzer. The number of electrons transferred was calculated from the relation n ) Q/Fm, where F is the Faraday constant, m is the moles of the electroactive material, and Q is the coulombs passed at the time the current dropped to