Bridge-mediated hopping or superexchange electron-transfer processes in bis(triarylamine) systems

Abstract

Hopping and superexchange are generally considered to be alternative electron-transfer mechanisms in molecular systems. In this work we used mixed-valence radical cations as model systems for the investigation of electron-transfer pathways. We show that substituents attached to a conjugated bridge connecting two triarylamine redox centres have a marked influence on the near-infrared absorption spectra of the corresponding cations. Spectral analysis, followed by evaluation of the electron-transfer parameters using the Generalized Mulliken–Hush theory and simulation of the potential energy surfaces, indicate that hopping and superexchange are not alternatives, but are both present in the radical cation with a dimethoxybenzene bridge. We found that the type of electron-transfer mechanism depends on the bridge-reorganization energy as well as on the bridge-state energy. Because superexchange and hopping follow different distance laws, our findings have implications for the design of new molecular and polymeric electron-transfer materials.

Main

It is an ongoing debate whether electron transfer (ET) in donor-bridge-acceptor triades proceeds by hopping or by superexchange. In the superexchange mechanism, the bridge solely serves to mediate donor and acceptor wavefunctions, but in the hopping mechanism the electron is located at the bridge for a short time during its journey from one redox centre to the other. What parameters govern these alternative pathways? This basic question concerns a large number of organic and inorganic ET systems^1,2,3,4,5,6, mixed-valence compounds⁷, molecular wires⁸, polymeric or low-molecular-weight electron- or hole-transport materials^9,10, as well as proteins^11,12 or DNA^13,14, and is therefore of general interest. One particular concern is the role that the bridge plays in the ET process, because the bridge-state energy is expected to have a marked influence on the ET mechanism.

In this article we investigate adiabatic ET processes within the mixed-valence radical cations of one-dimensional bis(triarylamine) molecules^15,16, in which two triarylamine redox centres are connected by an unsaturated 1,4-diethynylarene bridge (see Fig. 1). This type of bridge was chosen because the energy of local bridge states can be easily tuned by using different arene units: for example, the highest occupied molecular orbital–lowest unoccupied molecular orbital (HOMO–LUMO) gap decreases in the order benzene (1), naphthalene (2) and anthracene (3), whereas on going from benzene (1) to 1,4-dimethoxybenzene (4) only the HOMO energy increases. The benzo[15]crown-5 bridge in 5 was used to tune the ET by an external stimulus such as metal complexation. For comparison with 1 and 3, compounds 6 and 7, in which only one triarylamine moiety is linked to the bridge, were also investigated.

Figure 1

One-dimensional bis(triarylamine) system whose conjugated bridge is varied to tune the electron transfer (ET) process of the corresponding radical cation.

The ultraviolet/visible/near-infrared spectra of the radical cations of 1–5 are characterized by a broad and intense band in the near infrared, which we assign to an intervalence charge transfer (IV-CT) band. This IV-CT band is associated with an optically induced hole transfer from the triarylamine radical cation centre to the neutral triarylamine (see Fig. 2 and Supplementary Information)^15,16,17. In addition to this band, another very strong absorption is visible in the spectra of the radical cations and di-cations at about 13,000 cm⁻¹. This 'radical band' occurs owing to a localized π–π^* excitation within the triarylamine radical cation moieties^18,19,20. A closer inspection of the near-infrared spectra of 1⁺, 2⁺, 4⁺ and 5⁺ reveals an additional band between the triarylamine radical band and the IV-CT band. We assign this additional band (hereafter called the 'bridge band') to an optically induced hole transfer from a triarylamine radical cation to the bridge. The assignment of these bands is proved by the spectrum of 6⁺, which shows the radical band and the bridge band only. Also the ET parameters of 6⁺ (see below) are in good agreement with the analysis of 1⁺. Additional support comes from the fact that for 1⁺, 2⁺, 4⁺ and 5⁺, both the bridge band and the radical band increase in intensity when the radical cation is oxidized to the di-cation, whereas the IV-CT band disappears. Such bridge bands have previously been observed in organic and inorganic mixed-valence species in rare cases, for example in a bis(hydrazine)anthracene derivative^7,21,22.

Figure 2: The ultraviolet/visible/near-infrared spectrum of 4 ⁺ measured in CH ₂ Cl ₂ (solid line).

The spectrum was deconvoluted by gaussian functions (dotted lines). The sum of the dotted lines is the dashed line, which closely matches the measured spectrum. The numerical simulations of the spectrum are given as squares (IV-CT band) and circles (bridge band).

For the anthracene derivative 3⁺, a single very intense and asymmetric band was observed at 4,640 cm⁻¹ in the near infrared. Our analysis is based on the assumption that this near-infrared band mainly consists of the bridge band. This assignment is supported by the band asymmetry, which resembles that of model compound 7⁺, and by the fact that the subsequent analysis yielded reasonable electronic couplings (see below). Owing to the asymmetry of the near-infrared band of 7⁺, we needed two gaussian functions for a fit. For 3⁺, a total of three gaussian functions were necessary for a good fit (see Supplementary Information). Two of these functions at lower energy were assigned to the asymmetric bridge band. We assume that the band asymmetry was because 3⁺ approaches the class II/III borderline, where the charge becomes delocalized over the whole system, which implies a rather low ET barrier¹⁶. The third function at higher energy (7,270 cm⁻¹) was assigned to the IV-CT band. Thus, a bridge band/IV-CT band 'inversion' occurs in 3⁺ (ref. 7).

The near-infrared band of all the other radical cations, 1⁺, 2⁺, 4⁺ and 5⁺, were analysed by fitting a single gaussian band to the IV-CT, and another one to the bridge band. Although the use of a gaussian function for the IV-CT band deconvolution in 1⁺, 2⁺, 4⁺ and 5⁺ is justified by Hush theory^16,23, which holds for relatively weak couplings and high ET barriers (see Table 2), that for the bridge band must be considered as a first-order approximation.

Table 2 ET parameters for 1 ⁺ – 7 ⁺ in CH ₂ Cl ₂ from the GMH analysis and PES fits.

The transition moments associated with the IV-CT and the bridge bands were used to calculate the electronic coupling energies V₁₂ and V₁₃ between the three diabatic (non-interacting) states (three-state model^24,25,26,27) by the Generalized Mulliken–Hush (GMH) theory. This gives two degenerate states in which the hole is localized either on the triarylamine on the left (state 1) or on the right (state 3), and a third state (2) in which the hole is localized on the bridge^28,29,30. See Fig. 3. These electronic coupling energies were used to calculate the potential energy surfaces (PES) starting from a two-dimensional three-level approach, equation (1). In these secular equations, x denotes the electron-transfer coordinate, which transforms state (1) into state (3) (asymmetric vibrational mode). The other ET coordinate depends on both x and y, and transforms state (1) or (3) into (2) (symmetric vibrational mode^24,25,26,27). λ₁ pertains to the Marcus reorganization energy associated with states (1) and (3), λ₂ is associated with the bridge state (2) and ΔG° is the relative free enthalpy of the diabatic bridge state (2) versus the degenerate triarylamine states (1 and 3) and E is the energy eigenvalue. Our analysis contrasts the approach of Nelsen et al.⁷, who analysed their spectra by employing a one-dimensional three-state model in which a single ET coordinate for the superexchange and the hopping pathway is used³¹. Our two-dimensional analysis with two different ET coordinates (one symmetric and one asymmetric mode) follows previous work^24,25,26,27 and is essential because the modes being associated with the ET coordinates belong to two different irreducible representations. We stress that applying Nelsen's one-dimensional analysis to our data gives quite different and inconsistent results.

Figure 3: The three diabatic states that are coupled in equation (1).

In two of these states, (1) and (3), the radical cation is centred at a triarylamine moiety, in the third (2) it is centred at the bridge.

In the secular equations (1) we assumed parabolic functions for the diabatic potentials, augmented by quartic functions³² for the triarylamine radical cation-centred states only. The parameters λ₁, λ₂ and ΔG°, as well as the asymmetry parameter C for quartic augmentation, were adjusted in a way such that, starting from the Boltzmann-weighted ground-state population, the IV-CT bands and the bridge bands calculated from the energy differences between the ground state and the two excited-state PES gave the best fit to the experimental spectra. The asymmetry parameter C makes the IV-CT band slightly asymmetric and broader with a tailing to the high-energy side, than the gaussian-shaped band at the high-temperature limit³². The experimental data of the near-infrared bands are given in Table 1, and the data of the GMH analysis as well as the PES parameters from the fit are collected in Table 2.

Table 1 Optical data for the IV-CT band and the bridge band of 1⁺ – 7⁺ in CH₂Cl₂.

Although the effective ET distance, as well as its conjugation path, is constant for all compounds 1⁺–5⁺, it is apparent from Table 2 that the electronic coupling V₁₃ between states in which the positive charge is localized at different triarylamine centres varies significantly from about 260 to 520 cm⁻¹ depending on the bridge type. This coupling refers to the superexchange between both triarylamine-located radical-cation states (1) and (3) (see Fig. 3). For 1⁺–5⁺ the V₁₃ coupling is much smaller than V₁₂, whereas in 5-Ca⁺ they are about equal. In a fairly good approximation, V₁₃ of 1⁺–5⁺ could also be calculated from a classical one-dimensional two-level model with quadratic diabatic potentials in which λ₁ = ṽ_opt, V₁₃ = μ _eg ṽ_opt/(e × r) where e is the elementary change and r is the effective diabatic electron transfer distance, and ΔG^* = λ ₁/4−V₁₃ + V₁₃²/ λ₁ (ref. 29).

In the series 1⁺–3⁺ with increasing π-bridge system, the IV-CT bandwidth decreases. The IV-CT bandwidth is larger (positive C) for 1⁺ than that expected from a classical two-level approach²³ with quadratic diabatic potentials, but is distinctly smaller for 3⁺. From 1⁺ to 3⁺ the coupling V₁₂ increases and the reorganization energy λ₁ decreases. This is concomitant with the decreasing bridge-state energy ΔG°. The low bridge-state energy of 3⁺ is reflected in the easily oxidizable character of the anthracene bridge (see Supplementary Information for the electrochemical characterization) and, together with the low reorganization energy λ₂ of the bridge, causes the bridge band/IV-CT band 'inversion' (see above). Whereas the ET barrier ΔG^* of 1⁺ and 2⁺ are about equal (approximately 1,500 cm⁻¹), that of 3⁺ is much lower (940 cm⁻¹). Raising either λ₂ or ΔG° of 3⁺ by 10,000 cm⁻¹ gives ΔG^* = 1,470 cm⁻¹ in good agreement with 1⁺ and 2⁺. In contrast, the ET barriers ΔG^* of 1⁺, 2⁺, 4⁺ and 5⁺ do not vary much (only ±50 cm⁻¹) on raising ΔG° by 10,000 cm⁻¹ or on lowering λ₂ to 3,000 cm⁻¹, with all other parameters kept constant. Therefore, the low ΔG^* is a direct consequence of both low ΔG° and low λ₂. Although in the classical Marcus–Hush theory²³ λ and V are independent parameters, λ being mainly associated with the redox centres (and the solvent), and V being mainly associated with the bridge, it appears that they are coupled in 1⁺–3⁺ (ref. 33). The relatively high V₁₂ coupling and the relatively low V₁₃ coupling in 3⁺ compared to 1⁺ and 2⁺ might be due to intensity transfer from the IV-CT band to the bridge band, which should be stronger the smaller the energy difference³⁴. Actually, this difference is about 2,600 cm⁻¹ for 3⁺ but 4,000 cm⁻¹ for 1⁺ and 2⁺.

Owing to the low-lying bridge state in 3⁺, there is a shallow bay on the PES at the bridge site which is much less pronounced in either 1⁺ or 2⁺ (see Fig. 4a). Actually, this bay might be a very shallow minimum, because the PES at that point strongly depends on the parameters used for the fit for 3⁺.

Figure 4: Plot of the ground-state PES of : a, 1⁺ and b, 4⁺.

The minima around the (0,0) and (1,0) coordinates refer to triarylamine radical cation-centred states, and that around (0.5,0.87) refers to the bridge state. The yellow lines refer to the superexchange and hopping pathways. The figures given in yellow indicate the relative energies of the transition states and the bridge state versus the triarylamine-centred minima.

The attachment of methoxy groups to the bridge phenylene ring in 1⁺ lowers ΔG° by 6,800 cm⁻¹, and leads to somewhat larger couplings V₁₃ and V₁₂ in 4⁺ than in 1⁺. Owing to the higher reorganization energy λ₂ of the bis(methoxy)phenylene bridge (which is due to a quinoidal distortion^22,35) compared with the unsubstituted phenylene or to anthracene, the ET barrier ΔG^* of 4⁺ is about the same as that of 1⁺ and 2⁺. The very low bridge energy ΔG° in 4⁺ leads to a deep bridge-state minimum on the PES (see Fig. 4b), much deeper than the bay of 3⁺. For both compounds 3⁺ and 4⁺, ΔG° is lower than the crossing point of the diabatic states (1) and (3) for the ET along the x coordinate. In 4⁺ the bridge-state minimum vanishes for ΔG° ≥3,400 cm⁻¹, which is much higher than the crossing point (1,800 cm⁻¹). The ET barrier to the bridge-state minimum is actually somewhat lower (1,300 cm⁻¹) than that of the direct superexchange pathway (1,450 cm⁻¹). This bridge-state minimum serves as an intermediate in a hopping ET pathway. Thus, in 4⁺ rather than being alternatives, hopping and superexchange are both possible ET mechanisms.

Complexation of Ca²⁺ by the crown-ether derivative 5⁺ yields 5-Ca⁺, whose near-infrared spectra (ṽ_opt(IV-CT) = 8,830 cm⁻¹) significantly deviates from the empty crown-ether compound 5⁺ (ṽ_opt(IV CT) = 7,830 cm⁻¹). Nevertheless, apart from a dramatic change of V₁₂ from 950 cm⁻¹ to 480 cm⁻¹ on complexation, all other ET parameters remain essentially unchanged. However, because the bridge band in 5-Ca⁺ is only a slight shoulder, the spectral deconvolution, and consequently the ET parameters of 5-Ca⁺, is quite uncertain. If a classical two-level model with quadratic potentials is used, the ET barrier ΔG^* deviates significantly for the two species by about 400 cm⁻¹. Thus, it seems more likely that Ca²⁺ complexation has a marked influence on the relative ET rate constants. Whether this effect is due to a field (inductive) effect of the Ca²⁺ ion, or is induced by conformational changes of the crown ether—and, consequently, by modified oxygen lone-pair overlap with the phenylene ring—is unclear at present.

In this study we analysed the near-infrared spectra of a series of linear mixed-valence radical cations with two triarylamine redox centres, which essentially differ in the electronic structure of the bridge. In these systems both the coupling between the triarylamine-centred states and the coupling between these states and the bridge state are of comparable magnitude. This unique feature allows the determination of both coupling constants. From the spectral analysis we constructed the ground-state PES. The case of 3⁺ with the anthracene bridge shows that both a low-lying bridge state and a low bridge-state reorganization energy are necessary for lowering the superexchange ET barrier ΔG^* significantly. Furthermore, our study indicates that hopping and superexchange do not exclude each other but may both be present within one system if the bridge state is sufficiently low in energy, and its reorganization energy is high such as in 4⁺. These conclusions will be useful for the design of novel electron-transfer materials in which molecular-wire behaviour (hopping mechanism) is desired. So far, our analysis is solely on the basis of the optical properties and their simulation based on a PES construction. Therefore, the absolute values of all parameters should be taken with some caution. Further kinetic studies of the thermal ET barriers, as well as direct spectroscopic probes of the bridge state are necessary to gain more quantitative insight into the PES.

Methods

Analysis of spectra

The near-infrared spectra of all radical cations were initially deconvoluted by gaussian functions, which yields the energy of the IV-CT and bridge state and their associated transition moments. The electronic couplings V were evaluated by the GMH theory^28,29,30 from the following adiabatic (measurable) quantities: (1) the transition moments μ_gb (bridge band) and μ_gi (IV-CT band), which were derived from the integrated absorption bands; (2) the dipole moment differences Δμ_ii = μ_ii − μ_gg between the two triarylamine centred states and Δ μ_bg = μ_bb − μ_gg = 1/2 Δ μ_ig between the bridge state and one triarylamine state, Δμ_ig = e × _r = 92.6 D was derived from the N–N distance r = 19.3 Å (for a discussion about effective ET distances, see refs. 16,36); (3) the transition energies ṽ_max(IV-CT) and ṽ_max(bridge).

The first step of the GMH theory is to find the matrix C that diagonalizes the adiabatic matrix μ_adiab according to μ_diab = C^tμ_adiab Cwith:

The second step is to apply the same unitary transformation to the adiabatic energy matrix H_diab = CH_adiabC^t with:

which then gives the diabatic energy matrix from which the electronic couplings V₁₂, V₁₃ and V₂₃ can be directly obtained. In this way, the electronic couplings solely depend on the transition moments and the band energies, and thus on the initial spectra deconvolution by gaussian functions. Although V₁₂ and V₂₃ are different, they must be equal in the ET transition-state between the two triarylamine-centred states. For the construction of the PES we therefore omitted V₂₃ and only used V₁₂ and V₁₃. This inconsistency, which is already present in the two-level Mulliken–Hush approach, is due to the (neglected) dependence of V on the ET coordinate.

Using the fixed couplings V₁₂ and V₁₃, we constructed the PES by adjusting the parameters λ₁, λ₂, ΔG° (these parameters strongly dependent on each other) and C in equation (1) in such a way that the absorption spectra (calculated from the energy differences of the PES and a Boltzmann-weighting for the transition probability) gave the best fit to the experimentally observed spectra. Thus, the above quantities solely depend on the fit to spectra. The ET barriers were then obtained directly from the PES. It was found that C, as well as the electronic couplings V₁₂ and V₁₃ (the couplings only weakly dependent on each other), have only a modest influence on the PES, and consequently on the band energies and bandwidths. The error margins given in Tables 1 and 2 reflect the accuracy of the spectra measurement and the variation of the parameters for which a reasonable fit was obtained. Although the agreement between simulated and deconvoluted spectra is quite good, much larger systematic errors of all quantities are possible owing to the fact that the initial spectra deconvolution is to some extent uncertain, as well as to the fact that the accuracy for estimating Δμ_ig = e × r is unknown.