Spectroscopic Studies of Bridge Contributions to Electronic Coupling in a Donor-Bridge-Acceptor Biradical System

Abstract

Variable temperature electronic absorption and resonance Raman spectroscopies are used to probe the excited state electronic structure of Tp^Cum,MeZn(SQ-Ph-NN) (1) – a donor-bridge-acceptor (D-B-A) biradical complex and a ground state analog of the charge-separated excited state formed in photoinduced electron transfer reactions. Strong ferromagnetic exchange coupling that is mediated by the para-phenylene bridge stabilizes the triplet ground state of this molecule. Detailed spectroscopic and bonding calculations elucidate key bridge distortions that are involved in the SQ(π)_SOMO→NN-Ph (π*)_LUMO D→A charge transfer (CT) transition. We show that the primary excited state distortion that accompanies this CT is along a vibrational coordinate best described as a symmetric Ph(8a)+SQ(in-plane) linear combination and underscores the dominant role of the phenylene bridge fragment acting as an electron acceptor in the D-B-A charge transfer state. Our results show the importance of the localized phenylene bridge LUMO wavefunction in promoting (1) electron transfer in D-Ph-A systems, and (2) electron transport in biased electrode devices that employ a 1,4-phenylene linkage. We have also developed a relationship between the spin density on the acceptor, as measured via the isotropic NN nitrogen hyperfine interaction, and the strength of the D→A interaction given by the magnitude of the electronic coupling matrix element, H_ab.

INTRODUCTION

Considerable effort has been expended in developing an understanding of how molecular bridge (B) fragments facilitate electron transfer over long distances. The fundamental mechanisms responsible for non-resonant electron transfer processes in molecular systems¹ include superexchange, which involves electron (e^-) or hole (h⁺) transfer via the bridge without discrete redox changes in the bridge, incoherent e^-/h⁺ tunneling, and thermally activated hopping. The latter mechanism involves discrete oxidation or reduction of the bridge fragment. A number of models have been developed to understand adiabatic and nonadiabatic electron transfer rates as a function of thermodynamic driving force and the geometry and nature of the bridge in photoinduced electron transfer (PET) reactions between donor (D) and acceptor (A) fragments in a D-B-A system.^2-17 In the PET process, photoexcitation of D yields a D*-B-A excited state which may undergo facile electron transfer to form a spin singlet biradical D⁺-B-A^- charge separated state. Photogenerated D⁺-B-A^- biradicals have been used to probe structural effects on electron transfer rates through correlating the magnetic exchange interaction, J, with the electronic coupling matrix element H_ab.^1,16,18-21 These data show that ET rates through phenyl bridges possess exponential distance dependence with β ~ 0.5, in excellent agreement with theory and direct electron transfer rate studies. Recently, we showed that covalently linked, nondisjoint heterospin triplet D-A biradicals (Fig. 1) may be thought of as ground state analogues of the charge separated states that derive from PET. In these studies, a valence bond configuration interaction (VBCI) model that utilizes spectroscopic and magnetic observables was used to understand the electronic origin of both H_ab and the strong ferromagnetic coupling in the semiquinone nitronylnitroxide (SQ-NN) D-A biradical series, Tp^Cum,MeM(SQ-NN).²²

Figure 1.

Donor-acceptor and donor-bridge-acceptor biradicals used in this study.

Electron transport mediated by single molecule bridges (wires) that span nanoscale electrodes (E_(+/-)) can be related to PET processes. In these E₍₊₎ – molecule - E₍₊₎ systems, an applied nanoelectrode bias can result in electron transport across the molecular wire.^23,24 Molecular electron transport systems have been devised to promote spin polarized electron transport by using magnetic electrodes and magnetic bridge fragments, and to allow for unidirectional electron transport (molecular rectification) by asymmetric attachment of the bridge to the electrodes or by using an asymmetric D-A type bridge fragment.^25-27 With respect to molecular rectification, Aviram and Ratner²⁸ originally suggested that a covalently linked D-B-A molecule could function as a molecular rectifier²⁶ and allow for unidirectional current flow via the formation of a D⁺-B-A^- electronic configuration at appropriate bias voltages. These rectifying D⁺-B-A^- bridges can be described as donor-acceptor biradicals that have been created by e^- or h⁺ injection into the A or D fragments from the electrode Fermi levels. Thus, it is the inherent electronic asymmetry in a D-B-A system that may allow unidirectional electron transport. Both the magnitude of the D-B-A coupling, H_ab, and the inherent electronic structure of the bridge fragment are likely to provide key contributions to a high rectification ratio and a properly functioning rectifying device.

Key questions in molecular electron transfer/transport focus on 1) determining the magnitude of the electronic coupling mediated by a given molecular bridge fragment, 2) relating the magnitude of the electronic coupling to the intimate electronic and geometric structure of the bridge, and 3) understanding the nature of molecular distortions in the bridge that are coupled to electron transfer/transport. Understanding bridge contributions to D-B-A electron transfer/transport is particularly important in light of recent work which has shown that a molecular junction formed by a single benzene molecule bridging two biased Pt electrodes results in electron transport with a conductance approaching the maximum allowed for single channel conductance, G₀.^29,30 Prior studies by our group on Tp^Cum,MeZn(SQ-bridge-NN) molecules focused on using EPR spectroscopy to understand the spin density distributions, bridge conformations, and the degree of D→A charge transfer in these biradicals.³¹ In this manuscript, we use a combination of variable temperature electronic absorption and resonance Raman spectroscopies to probe the nature of the bridge fragment in Tp^Cum,MeZn(SQ-Ph-NN) 1, which possesses a semiquinone radical (SQ) donor, a nitronylnitroxide radical (NN) acceptor, and a phenylene bridge that constitute a D-B-A array. The spectroscopic studies have been evaluated in the context of detailed bonding calculations and, through the use of a valence bond configuration interaction (VBCI) model, allow for deep insight into how the excited state electronic structure and the nature of the bridge fragment affect the magnitude of H_ab mediated by a phenylene. Coupled with our earlier work,³¹ this has also allowed us to develop a relationship between experimentally determined H_ab values and isotropic nitrogen hyperfine parameters on the NN acceptor fragment.

EXPERIMENTAL

General Considerations

All compounds were synthesized as previously described.^32,33

Electronic Absorption Spectroscopy

Electronic absorption spectra were collected on a Hitachi U-3501 UV-Vis-NIR spectrophotometer capable of scanning a wavelength region between 185 and 3200 nm using a double-beam configuration at 2.0 nm resolution. The instrument wavelength was calibrated with reference to the 656.10 nm deuterium line. Background spectra were collected to correct for residual absorption due to the solvent and automatically subtracted from the sample spectrum by the Hitachi Grams software. Low temperature (~10 K) spectra were collected using a Janis STVP-100 continuous flow cryostat mounted in a custom designed cradle assembly, and the sample temperature was monitored with a Lakeshore silicon-diode (PT-470) and regulated by a combination of helium flow and dual heater assemblies. Solution spectra were collected in 1.0 mm path length spectrosil quartz masked cells (Starna). Solution samples were prepared in dichloromethane or methylcyclohexane. Solid-solution spectra were collected on thin polystyrene (MW = 280,000) polymer films prepared by evaporation of the saturated polystyrene solutions dispersed on glass. Gaussian resolution of spectral bands and corrections for light scattering were accomplished with the Grams 386 software package.

Resonance Raman Spectroscopy

Coherent Innova 70-5 Ar⁺ ion (457.9̃528.7 nm) and Coherent Innova 300C Kr⁺ ion (406.7̃676.4 nm) lasers were used as the excitation sources. The scattered radiation was dispersed onto a liquid N₂ cooled 1” Spex Spectrum One CCD detector using a Spex 1877E triple grating monochromator equipped with 600, 1200, and 1800 gr/mm holographic gratings at the spectrographic stage. The laser power at the sample was kept between 40 and 100 mW to prevent thermal or photo degradation of the sample. Raman data were collected as dichloromethane solutions. The prepared sample was then sealed in an NMR tube with a rubber septum and Parafilm. Room temperature spectra were obtained with the sample tube placed in a modified NMR sample holder/spinner and collected using a 135° backscattering geometry.

Electronic Structure Calculations

Spin unrestricted gas-phase geometry optimizations for compounds 1 and 2 were performed at the density functional level of theory using the Gaussian 03W software package.³⁴ All calculations employed the B3LYP hybrid functional, and a 6-31G(d’p’) basis set, a split valence basis set with polarizability functions, was used for all atoms. Input files were prepared using the molecule builder function in the Gaussview software package and the t-butyl substituent on the semiquinone was modeled/represented as a methyl group. Frontier molecular orbitals (MOs) were generated for the optimized ground states. Frequency calculations were performed on the geometry optimized SQ-Ph-NN and SQ-NN ligands. Time-dependent DFT calculations were performed on the optimized ground-state geometries, and the first 20 excited states were calculated. Electron density difference maps (EDDMs) were constructed from the output of the time-dependent calculations using the GaussSum suite of programs.³⁵

RESULTS AND DISCUSSION

Frontier Molecular Orbitals, Electronic Absorption Spectroscopy, and Band Assignments

We present a simplified molecular orbital diagram showing the relevant SQ, Ph, and NN frontier molecular orbitals (MOs) of 1 in Figure 2. This simplified MO diagram was derived from the results of DFT and Hückel bonding calculations, and is similar to the diagram we previously presented for 2, which lacks a phenylene bridge.²² Here we have included the doubly degenerate, in the D_6h symmetry of the localized bridge, lowest unoccupied molecular orbital (LUMO) set localized on the Ph bridge (Ph(e₁) and Ph(e₂)). The bonding calculations indicate strong orbital mixing between the NN(π*) and Ph(e₁) orbitals leading to an energetically stabilized NN-Ph(π*-e₁) bonding MO. The Ph(e₂) orbital does not possess the appropriate symmetry to interact with the SQ and NN frontier MOs and is essentially non-bonding in character. We have used the results of these bonding calculations, time-dependent density functional theory (TD-DFT) calculations, and previous spectral assignments for 2, Tp^Cum,MeCu(SQ-NN) (3), arylnitronylnitroxide (Ar-NN), and other SQ-based chromophores to assign the prominent spectral features in 1.²²

Figure 2.

Qualitative π-molecular orbital diagram for 1.

The room temperature solution electronic absorption spectrum of Tp^Cum,MeZn(SQ-Ph-NN) (1) is presented in Figure 3. Numerous electronic transitions are observed between ~11,000cm^-1 and ~20,000cm^-1 in Tp^Cum,MeM(SQ-NN) compounds,^22,36 all of which possess relatively weak intensity (ε ~ 400-1,100 M^-1cm^-1). The most intense of these transitions have been assigned as NN(π)→SQ(π)_SOMO, SQ(n)→SQ(π)_SOMO, and NN(n)→NN(π)_SOMO, where n represents in-plane MOs on NN and SQ. Prior spectral assignments have placed the SQ(n)→SQ(π)_SOMO transition in the 10,000–15,000 cm^-1 region, and the NN(n)→NN(π)_SOMO transition in the ~18,000 cm^-1 region.^22,36 We note that the low-energy transitions in 1 are noticeably broadened when compared to the corresponding bands in other Tp^Cum,MeM(SQ-NN) compounds.²² The intense transition at 22,870 cm^-1 (ε ~ 8,000 M^-1cm^-1) is not present in the constituent SQ and NN chromophores,²² and possesses an apparent high energy shoulder at 24,250 cm^-1. We therefore assign this band as the SQ(π)_SOMO→ NN-Ph(π*-e₁) intraligand transition that possesses considerable D→A charge transfer character in accordance with previous assignments for 2 and 3.²² The SQ(π)_SOMO→ NN-Ph(π*-e₁) charge transfer band in 1 is ~1,700 cm^-1 lower in energy than the corresponding SQ(π)_SOMO→ NN(π*) transition in 2, which lacks the phenylene bridge. The lower energy of this transition in 1 can be understood in the context of Figure 2, where the strong NN(π*) - Ph(e₁) orbital mixing effectively lowers the energy of the NN(π*) - Ph(e₁) bonding MO relative to the SQ(π)_SOMO. An electron density difference map (EDDM) associated with the SQ(π)_SOMO→ NN-Ph(π*-e₁) transition is shown in Figure 4. The EDDM depicts the change in the electron density of 1 that accompanies the SQ(π)_SOMO→ NN-Ph(π*-e₁) charge transfer excitation and clearly shows the dominant D→A nature of the intraligand SQ(π)→NN-Ph(π*-e₁) transition and the importance of the phenylene bridge as part of the acceptor fragment. Finally, we assign the high energy transition at 26,800 cm^-1 as a NN π→π* transition based upon the spectral assignments for 2 and 3 and the presence of a similar band in Ar-NN.²²

Figure 3.

Room temperature solution electronic absorption spectrum of 1, and resonance Raman excitation profile of the 1591cm^-1 band showing large resonance enhancement of this mode when exciting into the SQ(π)_SOMO→ NN-Ph(π*-e₁) CT band (see text).

Figure 4.

Calculated electron density difference map (EDDM) for the SQ(π)_SOMO→ NN-Ph(π*-e₁) D→A charge transfer band in 1 depicted at an isodensity value of 0.002 a.u. Red regions indicate a loss of electron density in the transition to the excited state and blue regions indicate a gain of electron density in a transition to the excited state.

Nature of the Bridge in the D→A Charge Transfer Excited State

Figures 2 and 4 indicate the importance of the phenylene bridge fragment in the SQ(π)_SOMO→NN-Ph(π*-e₁) charge transfer transition. The importance of the phenylene bridge in mediating strong exchange coupling between the SQ and NN radical spins in 1 is also apparent in the magnitude of the ferromagnetic exchange interaction (2J = +200 cm^-1) determined from magnetic susceptibility experiments.³² Here we use a combination of resonance Raman spectroscopy, Raman excitation profiles, and hot band spectroscopy to gain greater insight into how the phenylene bridge contributes to the strong D-B-A interaction and how the bridge distorts in the SQ(π)_SOMO→ NN-Ph(π*-e₁) charge transfer excited state. These spectroscopic studies are important for developing a greater understanding of bridge distortions that accompany molecular electron transfer/transport phenomena and contribute to the suppression of ballistic electron transport.

The solution resonance Raman spectra of 1 and 3 are shown in Figure 5 for comparative purposes.

Figure 5.

Room temperature resonance Raman spectra of Tp^Cum,MeCu(SQ-NN) 3 (blue) and Tp^Cum,MeZn(SQ-Ph-NN) 1 (red) at 413.7nm. The solvent is CH₂Cl₂.

The data were collected using 413.7nm excitation, which is in resonance with the SQ(π)_SOMO→ NN-Ph(π*-e₁) and SQ(π)_SOMO→ NN(π*) charge transfer bands of 1 and 3, respectively. Vibrational bands in the 1,200-1,600 cm^-1 region have previously been assigned as in-plane stretching vibrations associated with the SQ-NN ligand and were used to support the assignment of the SQ(π)_SOMO→NN(π*) charge transfer band in 2 and 3. The presence of highly coupled, in-plane SQ-NN modes for 1 is supported by the strong spectral similarity between 1 and 3 in the 1,200-1,600 cm^-1 region of the spectrum. Compound 1 displays additional vibrations in the 1,100-1,250 cm^-1 region of the spectrum, and an intense Raman band at 1,591 cm^-1. The additional vibrational modes observed in 1 are anticipated to involve phenylene character due to their absence in the Raman spectra of 2 and 3. The frequency of the 1,591 cm^-1 vibration is very similar to the benzene e_2g vibration which occurs at ~1,600 cm^-1 (Figure 6, top).

Figure 6.

Top: Representations of the e_2g vibrational modes of benzene. Bottom: Representations of the two SQ-Ph-NN vibrational modes that possess contributions from the 8a (e_2g) benzene vibrational mode.

Vibrational frequency calculations performed on the SQ-Ph-NN ligand show modes at 1,664- and 1,618 cm^-1, both of which possess large displacements localized on the phenylene bridge that very closely resemble the 8a component of the doubly degenerate benzene e_2g vibration that is split in the low-symmetry environment of 1. The 1,664 cm^-1 mode can be described as an antisymmetric linear combination of the localized benzene 8a mode and an in-plane SQ mode (Ph(8a)-SQ) while the 1,618 cm^-1 mode represents the symmetric, Ph(8a)+SQ combination (Figure 6, bottom).

A resonance Raman excitation profile has been constructed for the 1,591 cm^-1 band in Figure 3, and the data show strong resonance enhancement of this vibration with excitation into the SQ(π)_SOMO→ NN-Ph(π*-e₁) charge transfer band. The strong resonance enhancement of the 1,591 cm^-1 band directly results from a large excited state distortion along this vibrational coordinate. The origin of the strong resonance enhancement along an asymmetric Ph(8a)-SQ(in-plane) coordinate can be understood in terms of the Kohn-Sham orbitals (Figure 7) that are associated with the dominant SQ(π)_SOMO→ NN-Ph(π*) one-electron promotion and the associated EDDM of Figure 4.

Figure 7.

Top: Principle Kohn-Sham orbitals of 1 that are involved in the SQ(π)_SOMO→ NN-Ph(π*) charge transfer (orbitals depicted at an isovalue of 0.05). Bottom: Symmetrized excited state distortion coordinate derived from EDDM and Kohn-Sham orbitals associated with the SQ(π)_SOMO→ NN-Ph(π*-e₁) charge transfer transition in 1.

The transfer of SQ(π)_SOMO electron density to the NN-Ph(π*) fragment in the charge transfer excited state results in a phenylene bridge distortion along a mode that closely resembles the benzene 8a vibration. This bridge mode is enhanced via the Albrecht A-term mechanism³⁷ since this bridge mode transforms as a₁ in the localized D_2h phenylene symmetry present in the SQ-Ph-NN ligand. The phase of the SQ in-plane distortion relative to the phenylene 8a-type mode is more difficult to ascertain, however. Inspection of orbital bonding and antibonding interactions in Figure 7 indicates that a depletion of SQ(π)_SOMO electron density in the charge transfer excited state, coupled with population of the localized NN-Ph(π*) fragment, should result in a SQ-Ph-NN excited state distortion along the symmetrized coordinate given in Figure 7 (bottom). In fact, the anticipated excited state distortion closely resembles the atom displacements present in the 1,618cm^-1 ground state vibrational mode. Thus, the primary excited state distortion that accompanies SQ(π)_SOMO→ NN-Ph(π*-e₁) charge transfer is along a vibrational coordinate best described as a symmetric Ph(8a)+SQ(in-plane) linear combination and this underscores the dominant role of the phenylene bridge fragment acting as an electron acceptor in the D-B-A charge transfer excited state.

Additional evidence supporting an excited state distortion along the Ph(8a)+SQ(in-plane) symmetry coordinate derives from the variable temperature electronic absorption spectra of 1 given in Figure 8.

Figure 8.

Variable temperature absorption spectra for 1 collected as a thin polymer film. Data collected at 5K, 75K, 150K, 200K, and 250K. Inset: Normalized absorption intensity measured at 22,870 cm^-1 (red circles) and at 28,200 cm^-1 (blue circles). Red and blue lines are the Boltzmann populations of the ³GC and ¹GC, respectively, determined by magnetic susceptibility measurements.

The ground state of 1 is a spin triplet (S=1) with an exchange coupled singlet (S=0) excited state residing 200 cm^-1 higher in energy (J = +100 cm^-1).³² The inset of Figure 8 displays the same temperature dependence that is predicted from the Boltzmann population of the spin triplet (³GC) and spin singlet (¹GC) ground configurations determined from variable temperature magnetic susceptibility measurements.³² Therefore, both the 22,870 cm^-1 SQ(π)_SOMO→ NN-Ph(π*-e₁) charge transfer band and its 24,250 cm^-1 shoulder derive from the ³GC ground configuration. Thus, we suggest that the 24,250 cm^-1 band is the 0→1’ vibronic transition built upon the 0→0’ origin at 22,870 cm^-1, resulting in an excited state vibrational frequency of 1,380 cm^-1. This excited state frequency represents an ~13% reduction when compared with the ground state Ph(8a)+SQ(in-plane) mode at 1,591 cm^-1 that is strongly resonance enhanced in the Raman spectra of 1. The observed frequency reduction of the Ph(8a)+SQ(in-plane) mode in the excited state is consistent with our spectral assignment and results from population of the NN-Ph(π*-e₁) orbital which possesses considerable antibonding character. In summary, the results of bonding calculations, resonance Raman excitation profiles, and variable temperature electronic absorption spectroscopy point to a dominant excited state distortion along a Ph(8a)+SQ(in-plane) symmetry coordinate. Furthermore, the results underscore the importance of the Ph(e₁) phenylene bridge orbital in facilitating D→A charge transfer in 1, and electron transport mediated by a 1,4-phenylene molecular wire placed between biased electrodes in a nanoscale device.

Determination of Intrinsic VBCI Parameters and Electronic Coupling Matrix Elements

Having developed a molecular orbital and vibronic description of how the phenylene bridge facilitates D-A coupling, we wish to further evaluate the nature of the D-A coupling by quantifying the magnitude of the electronic coupling matrix element (H_ab) in 1. In order to accomplish this, we will use a valence bond configuration interaction (VBCI) approach. The VBCI model differs from the MO picture by virtue of the fact that it provides a state rather than an orbital description of the system. This is particularly relevant for spectroscopic studies since electronic transitions occur between states. In the VBCI model, D-A and D-B-A bond covalency results from configuration interaction between the ground configuration and excited configurations with H_ab being the off-diagonal matrix element that connects ground and excited state configurations of the same spin multiplicity. We previously used the ground state magnetic exchange coupling (J), the mean D-A charge transfer energy, U (U=(E_3EC+E_1EC)/2), and an exchange integral (K₀) describing the ³EC-¹EC splitting within a perturbative VBCI model to determine H_ab for 2 and 3 (Figure 9).²² Here, the ^1,3GCs are given by $a_2^1{\overline{b}}_2^1$ and $a_2^1{b}_2^1$, and the ^1,3ECs by $b_2^1{\overline{b}}_2^1$ and $b_2^1{b}_2^1$. Due to the large magnitude of H_ab in these D-A biradicals, we use here a full-matrix diagonalization approach to determine the electronic coupling matrix element, H_ab⁰ in non-bridged 3. A combination of magnetic susceptibility and variable-temperature electronic absorption spectroscopy allowed us to determine the final state energies of ³GC, ¹GC, ³EC, and ¹EC for 3. These energies are simply the eigenvalues of the 4×4 VBCI Hamiltonian matrix given below.

	1GC	1EC	3GC	3EC
1GC	0-E	Hab	0	0
1EC	Hab	(U+K0)-E	0	0
3GC	0	0	0-E	Hab
3EC	0	0	Hab	(U-K0)-E

Figure 9.

The VBCI model. Top: Simplified orbital diagram for 2 and 3 using SQ(π)_SOMO (b₂), NN(π)_SOMO (a₂), and NN-Ph(π*-e₁) (b₂) basis functions (left), and a state diagram (right) deriving from, $a_2^1{\overline{b}}_2^1$ (¹GC), $a_2^1{b}_2^1$ (³GC), $b_2^1{\overline{b}}_2^1$ (¹EC), and $b_2^1{b}_2^1$ (³EC) configurations. Primes indicate perturbed configurations. Note that a₂ and b₂ are local orbital symmetry labels, and the singlets are multi-determinantal wavefunctions. Bottom: The VBCI wavefunctions derived from the 4×4 VBCI secular determinant (see text).

The simple VBCI matrix block diagonalizes into two 2×2 sub-matrices that yield four linear equations, allowing one to easily solve for H_ab, U, and K₀ analytically. The calculation yields U= 19,885 cm^-1, K₀ = 2,275 cm^-1, and H_ab= 8,517 cm^-1, where the analytical value of H_ab for 3 compares with a value of 13,460 cm^-1 using the perturbative approach.²² The VBCI wavefunctions are given in Figure 9 (bottom). Using the expression,

$$\frac{J_{\mathit{SQ}-\mathit{Ph}-\mathit{NN}}}{J_{\mathit{SQ}-\mathit{NN}}}=\frac{H_{\mathit{SQ}-\mathit{Ph}-\mathit{NN}}^2}{H_{\mathit{SQ}-\mathit{NN}}^2}$$ Eqn. 1

with J_SQ-NN = 550 cm^-1 for 2, and J_SQ-Ph-NN = 100 cm^-1 and H_SQ-NN = 8,517 cm^-1 for 2, we obtain H_SQ-Ph-NN = 3,632 cm^-1 for 1.^22,32 This represents a 57% decrease in H_ab when a phenylene bridges the SQ donor and NN acceptor. The large H_ab values that we have determined for these SQ-NN and SQ-Ph-NN biradicals result from their near coplanar structure and the strong π conjugation across the entire molecule.^22,32

Clearly, the largest magnitude of H_ab in any SQ-NN based donor-acceptor biradical occurs in non-bridged SQ-NN, where the SQ and NN fragments are hard wired directly to allow for maximal exchange between the SQ and NN fragments. The smallest H_ab value for these D-B-A systems is anticipated to occur when the D-A distance is infinitely long or when the SQ, bridge, and NN π systems are orthogonal to one another. However, it would be convenient if relationships could be developed that allow for an explicit correlation between H_ab and geometric structure without having to perform a detailed spectroscopic analysis. Recently, we showed that the magnitude of the isotropic N hyperfine interaction on the NN acceptor is a linear function of the NN nitrogen spin populations, and that the isotropic N hyperfine is very sensitive to the nature and orientation of the bridge in SQ-bridge-NN donor-acceptor biradicals.³¹ We can therefore anticipate that an increase in D→A charge transfer for these donor-acceptor biradicals should result in a corresponding increase in spin density on the acceptor fragment, and this can be conveniently monitored via the increase in magnitude of the NN nitrogen isotropic hyperfine coupling constant. In Figure 10 we correlate the experimentally determined H_ab for 1 and 2 with their respective experimentally determined NN nitrogen isotropic hyperfine coupling constants. The calculated isotropic N hyperfine coupling for a modified structure of 2, where the SQ, phenyl, and NN rings are all mutually orthogonal, is presented in Figure 10 and serves as an analogue for a structure with H_ab ~ 0. An exponential rise function can be fit to these three data points to construct a calibration curve for the determination of H_ab for any SQ-bridge-NN system. An exponential rise function describing the magnitude of the D-A interaction is anticipated from simple orbital overlap considerations involving the exponential tail regions of the D and A wavefunctions. Furthermore, the beginning of the plateau region for an exponential rise function will be well-defined by the H_ab value for Tp^Cum,MeZn(SQ-NN), since H_ab for any D-B-A biradical should never exceed that of Tp^{Cum, Me}Zn(SQ-NN). The blue line in Figure 10 is the best fit of the exponential rise function to the N hyperfine vs. H_ab data for Tp^Cum,MeZn(SQ-bridge-NN) complexes using the biradical ligands SQ-NN and SQ-Ph-NN. However, we note that although the functional form for the A_iso vs. H_ab data is well-described by an exponential rise function, there are intrinsic uncertainties that arise from the exponential fit to three data points. Nevertheless, all that is required to estimate H_ab for a given SQ-bridge-NN system is a determination of the NN nitrogen isotropic hyperfine parameter obtained from a simple analysis of the fluid solution EPR spectrum. We have determined the isotropic N hyperfine parameters for Tp^Cum,MeZn(SQ-p-xylene-NN) and Tp^Cum,MeZn(SQ-thiophene-NN)³¹ and these are also included in Figure 10 for comparative purposes. The H_ab value is significantly reduced (~45%) for nonplanar Tp^Cum,MeZn(SQ-p-xylene-NN) from the corresponding value for Tp^Cum,MeZn(SQ-Ph-NN) due to the loss of conjugation between the xylene, NN, and SQ π-systems.³¹ The loss of conjugation is due to the presence of the p-xylene methyl groups which cause unfavorable steric interactions between the bridge and SQ and between the bridge and NN π systems and result in SQ-p-xylyl-NN torsional distortions.³¹ Additionally, we find that H_ab for Tp^Cum,MeZn(SQ-hiophene-NN) is ~40% greater than that for Tp^Cum,MeZn(SQ-Ph-NN). In summary, the results for Tp^Cum,MeZn(SQ-thiophene-NN) and Tp^Cum,MeZn(SQ-Ph-NN) are of interest for understanding long range electronic coupling in polyphenylene and polythiophene intrinsically conducting polymers.

Figure 10.

Plot of the experimentally determined isotropic N hyperfine on the NN acceptor fragment as a function of the electronic coupling matrix element for a series of SQ-bridge-NN systems. Blue line is the exponential rise function 6.04+1.65(1-exp(-0.33H_ab)) (R² = 0.999).

Relationship to Electron Transport using Molecular Wires

With respect to the large electronic coupling in 1 and 2, it is of interest to note that very recently a molecular junction formed by a single benzene molecule bridging two biased Pt electrodes was shown to possess excellent electron transport properties with a conductance approaching the maximum allowed for conductance via a single channel, the quantum of conductance, G₀.³⁰ In contrast to the 1,4-bridging geometry of benzene in 1, where the charge transfer direction is along the C₂ axis of the bridge, the benzene molecular junction in the nanoelectrode system is suggested to bridge Pt contacts in a cofacial manner whereby the C₆ axis of benzene is collinear with the charge transport direction. This leads to six channels for electron conductance using the 6 benzene p_z orbitals compared to a single channel available for π-type electron transfer/transport using a 1,4-phenylene linked system. Recently, van Ruitenbeek and coworkers used a combination of conductance measurements, isotope perturbations, and inelastic electron tunneling spectroscopy to probe the benzene distortion coordinate that is effectively coupled to charge transport.³⁰ They determined that that the distortion coordinate is described by a non totally symmetric ~400 cm^-1 rotational mode about the C₆ axis of the benzene molecular junction.³⁰ In contrast, the distortion coordinate in 1 is along the totally symmetric 1,4-phenylene stretch, describing an effective electron transport/transfer channel as possessing quinoidal phenylene e₁-π character. Our H_SQ-Ph-NN value of 3,632 cm^-1 for 1 strongly suggests high transmission coefficients are also possible in molecular junctions that utilize a 1,4-phenylene linkage with appropriate donor, bridge, an acceptor energy matching.

CONCLUSIONS

We have performed a detailed spectroscopic analysis on Tp^Cum,MeZn(SQ-Ph-NN) 1, which possesses a a 1,4-phenylene linkage that bridges the SQ donor and NN acceptor, in order develop greater insight into key bridge distortions that accompany electron transfer and electron transport in molecular and molecule-based systems. The intense charge transfer transition in 1 observed at 22,870 cm^-1 has been assigned as a SQ(π)_SOMO→ NN-Ph(π*-e₁) intraligand transition that originates from the S=1 ground state and possesses considerable D→A charge transfer character. A high energy shoulder is present at 24,250 cm^-1 and is assigned as the 0→1’ vibronic transition that is built upon the 0→0’ origin at 22,870 cm^-1, yielding an excited state vibrational frequency of 1,380 cm^-1. We have assigned the 1,591 cm^-1 Ph(8a)+SQ(in-plane) vibration as the 8a quinoidal type stretch in benzene, and the strong resonance enhancement of this vibration when exciting into the SQ(π)_SOMO→ NN-Ph(π*-e₁) D→A charge transfer band indicates there is a large excited state distortion along this vibrational coordinate. The excited state frequency is ~13% less than that observed for the 1,591 cm^-1 Ph(8a)+SQ(in-plane) ground state mode that is strongly resonance enhanced in the Raman spectrum of 1, consistent with our band assignment and the net antibonding character in the NN-Ph(π*-e₁) orbital. These data are consistent with the results of our bonding calculations that indicate a single phenylene bridge orbital (e₁) interacts very strongly with the NN acceptor fragment, but only weakly with the SQ donor fragment, and it is this strong NN(π*)-Ph(e₁) orbital interaction that effectively stabilizes the acceptor MO and lowers the intraligand CT transition in 1 relative to 2. We have used a non-perturbative VBCI model to obtain spectroscopically derived electronic coupling matrix elements for 1 and 2. The analysis yields H_SQ-NN = 8,517 cm^-1 for 2 and H_SQ-Ph-NN = 3,632 cm^-1 for 1, indicating hard wiring a 1,4-phenylene linkage between the SQ donor and NN acceptor results in a 57% decrease in H_ab compared to the non-bridged SQ-NN dyad. Finally, we have developed a relationship between experimentally determined H_ab values and NN acceptor isotropic nitrogen hyperfine parameters so that the analysis of a simple isotropic EPR spectrum is all that is required to determine the magnitude of H_ab for any Tp^Cum,MeZn(SQ-bridge-NN) D-B-A biradical system.