Role of intramolecular hydrogen bonds in promoting electron flow through amino acid and oligopeptide conjugates

The synthesis of the DBA complexes is outlined in Scheme 1. The design of these dyads is based on the following principles: 1) propensity of free-base corroles to form strong hydrogen bonds; 2) ability of short peptides to fold via intramolecular C=O^…HN hydrogen bonds; 3) the presence of C=O in PDI, which may contribute to the folding process via hydrogen bonds; 4) evidence from our earlier work that efficient ET occurs between corrole and PDI (30, 31).

The DBA complexes take advantage of a unique structural motif of amide-containing corroles that we recently discovered (32). Specifically, trans-A₂B-corroles, bearing –OCH₂CONHR substituents at the ortho positions of the meso-phenyl group, exhibit a pronounced propensity for hydrogen bonding between the amide carbonyl and corrole-NH (33). X-ray crystallography and NMR spectroscopy confirm this strong interaction between groups located at meso-10 position with the NH of the macrocyclic core in the solid state and in solution (32–34). This hydrogen bonding locks the amide group above the corrole cavity, resulting in pronounced upfield shifts of its proton NMR signals (Δδ ∼ −3 ppm). Since this intramolecular hydrogen bonding perturbs the macrocycle structure, we use Cor-Phe as a model for the electron donor (Fig. 1). Critically important are the two electron-withdrawing C₆F₅ groups at positions 5 and 15 that serve to stabilize the corrole core (35).

Our work on CT dyads of covalently linked Cor as an electron donor and PDI as an electron acceptor (30, 31) guided the choice for DBA scaffolds (Fig. 2). Selective excitation of Cor at its Soret band between 390 and 440 nm or at wavelengths longer than 570 nm triggers ET to the acceptor; and excitation of PDI in the 460- to 530-nm region where Cor absorbs ≤10% of the light induces HT to the donor (Fig. 3). Moreover, the large overlap of PDI fluorescence and Cor absorption create the potential for Förster resonance energy transfer (EnT) from the excited PDI to Cor (R₀ = 46 Å assuming random orientation) (36).

The tetrapeptide bridge in the Cor-(Ala)₄-PDI DBA conjugate provides two important features. 1) Adding 12 covalent bonds to an electronic-coupling pathway along the peptide backbone should decrease the CT rate constant (k_CT) by more than five orders of magnitude (37), ensuring that any alternative short pathway, composed of hydrogen bonds or van der Waals contacts, would dominate the CT kinetics. 2) Alanine oligomers usually fold into helical loops that tend to have 3₁₀-helix hydrogen-bonded configurations for short sequences (38–40). We would like to know whether intramolecular hydrogen bonding with the donor and the acceptor alters the propensity for formation of such 3₁₀-helix patterns.

Shortening the (Ala)₄ bridge to a single residue (Ala, Phe) should increase the rates of through-bond CT. Therefore, the Cor-Ala-PDI conjugate (Fig. 1) serves as a control to test for contributions from through-bond coupling pathways to the CT kinetics. The side chains can play a role in protein CT by providing electronic-coupling pathways (41–43) and steric hindrance that preferentially tightens some of the conformational folds. The phenyl group in the bridge of the Cor-Phe-PDI DBA conjugate provides a means to test for such effects.

Our recent studies of self-organization in trans-A₂B-corroles bearing –OCH₂CONHR groups at the ortho position of the meso-phenyl substituent revealed the propensity for intramolecular hydrogen bond formation between pyrrole NH groups and the oxygen of the amide carbonyl (26–28). Cor-Phe has 4 hydrogen-bond donors and 4 hydrogen-bond acceptors; Cor-Ala-PDI and Cor-Phe-PDI, 5 hydrogen-bond donors and 7 acceptors (2 of the 7 are on the distal end of PDI, however); and Cor-(Ala)₄-PDI, 8 hydrogen-bond donors and 10 acceptors (Fig. 1). The high density of H-bonding groups, along with the flexibility of the bridges, make these conjugates highly prone to intramolecular hydrogen bonding, especially in nonpolar media. Amides possess large electric dipole moments (44) that can be stabilized by burial inside folded molecular structures in nonpolar media.

Analysis of ¹H NMR spectra, along with COSY, HSQC, and HMBC, revealed several key structural features. The ¹H and ¹³C NMR spectra reveal that some linker resonances in Cor-Ala-PDI, Cor-Phe-PDI, and Cor-(Ala)₄-PDI are shifted upfield by as much as −2.9 ppm from typical δ values. Upfield shifts indicate protons in proximity of the magnetic dipole axis created by the corrole macrocyclic ring current induced by the external magnetic field. On the basis of the hydrogen-bonding propensity of the pyrroles with linker carbonyls, we attribute the upfield-shifted resonances to protons located at similar distances from the corrole ring in the three DBA complexes (Figs. 1 and 2). Furthermore, ROESY spectra of Cor-(Ala)₄-PDI exhibit through-space NOE correlations that indicate conformers in which some corrole-ring β-protons are in proximity to the methyl and the N-terminal amide of the third alanine (Fig. 2C).

The tendency of corroles to deprotonate in weakly basic polar media [e.g., nitriles, DMF (45)] dictated the choice of toluene as the solvent for ET investigations. The absorption spectra of the DBA conjugates in toluene are unchanged over a 1 to 100 μM concentration range (Fig. 3), indicating that the Cor and PDI derivatives do not aggregate in toluene at micromolar concentrations. Incorporation of Cor and PDI into the DBA conjugates causes minor perturbations in their absorption spectra, predominantly in the bands of the Cor moiety (Fig. 3A). These small differences between the absorption spectra of Cor and the DBA conjugates are most pronounced for Cor-(Ala)₄-PDI (Fig. 3). We ascribe these subtle variations in the spectra to intramolecular interactions, such as hydrogen bonding, because of the lack of concentration dependence of the optical spectra (Fig. 3 B–D). The absence of significant broadening and CT absorption precludes π-stacking between the donor and the acceptor. Furthermore, the lack of apparent CT absorption bands in the DBA spectra indicates weak donor–acceptor electronic coupling.

Attaching even a single amino acid residue with a stereogenic carbon center to the corrole moiety (e.g., Cor-Phe) introduces pronounced optical activity in the Soret region of the spectrum (Fig. 4). Adding PDI to the structures amplifies circular dichroism (CD) signals; and changing the Ala bridge to Phe further enhances the optical activity of the DBA conjugates (Fig. 4 A and B). These findings suggest that the additional aromatic and PDI moieties tighten structures in conformers with preferred chirality.

The Soret CD spectra of Cor-Phe, Cor-Ala-PDI, and Cor-Phe-PDI exhibit negative Cotton effects originating from splitting of the Soret band: 1) at about 426 nm, dominating the CD signal; and 2) at the absorption maximum at about 413 nm, responsible for the hypsochromic CD shoulder (Fig. 4 A and B). The sharp features in the Cor-(Ala)₄-PDI Soret CD spectrum indicate a tighter structure with the tetrapeptide bridge.

The NMR findings, and prior X-ray diffraction data (32–34), guide construction of computational models of the DBA conjugates. Geometry optimization at the DFT/B3LYP/6-31G(d,p) level of theory with implementation of a PCM solvent model (46) yields structures that are consistent with the experimental findings (Figs. 1 and 2). For the structures containing single-residue linkers (Cor-Ala-PDI, Cor-Phe-PDI), the amino acid and first methylene group from the aliphatic linker lie above the corrole ring (Fig. 2 A and B), consistent with upfield shifts of ¹H NMR resonances for these groups (Fig. 1). Intramolecular hydrogen bonding between a pyrrole nitrogen proton and the C-terminal carbonyl of the amino acid, along with favorable interactions of the amide NH (from N terminus) with two oxygen atoms (one ethereal and the other carbonyl from the C terminus), stabilize a folded motif, leaving one carbonyl oxygen (an H-bond acceptor) and one amide hydrogen (an H-bond donor) available for further interactions. The calculations show that an additional engagement between the NH of the C-terminal amide of the amino acid and one of the PDI carbonyl oxygen atoms produces a conformer with an eight-bond ring that is energetically favorable in low-polarity media. In toluene, for example, hydrogen bonding and folding stabilize the DBA conjugate by 164 meV (6.5k_BT at T = 20 °C). The folded structure brings the corrole and PDI to a center-to-center separation of 13.3 Å and creates an electronic-coupling pathway comprising two covalent and two hydrogen bonds [(Cor)NH^…O=C–NH^…O=C(PDI)] (Fig. 2 A and B).

The Cor-(Ala)₄-PDI DBA complex has considerably more conformational freedom. Owing to the upfield shifted resonances in the NMR spectrum, we constrained structural models for Cor-(Ala)₄-PDI to have two alanine residues within the aromatic-ring current of the corrole. The remaining two Ala residues admit a broad distribution of energetically accessible conformations. Our calculations suggest that in toluene two folded structures and one extended structure have energies within 5k_BT of one another, spanning center-to-center distances of 12.7 to 19.8 Å (Fig. 2, also see SI Appendix). Among these structures, the shortest electronic coupling pathway has 2 covalent and 2 hydrogen bonds; the longest pathway is composed of 15 covalent bonds.

With the modeled structures in hand, we calculated CD spectra using time-dependent density-functional theory (TD-DFT). We initially treated the two chromophores separately with fragments of the amino acid bridge. Calculations for the PDI fragment indicate that hydrogen bonding with the amino acid induces CD with the same sign and shape as the band in the experimental spectrum (Fig. 4D). The calculations reproduce well the energies of the bands for the Cor fragment and demonstrate that the signs of CD signals are sensitive to fine structural details. Armed with findings on the separate fragments, we proceeded to calculate CD spectra for the optimized geometries of Cor-Ala-PDI and Cor-(Ala)₄-PDI (Fig. 4 E and F). The signs of the bands in the experimental and calculated spectra are in reasonable agreement, supporting the modeled folded structures containing the (Cor)NH^…O=C–NH^…O=C(PDI) motif in the three DBA conjugates.

The reduction potentials associated with Cor oxidation and PDI reduction [$E_{Co{r}^{•+}|Cor}^{\left(1/2\right)}$ and $E_{PDI|PD{I}^{•-}}^{\left(1/2\right)}$, respectively], along with their zero-to-zero excitation energies (${\mathcal{E}}_{00}$), allow estimation of the driving forces for photoinduced charge transfer (PCT) in media with different dielectric constants, ε (47, 48):For ΔG_ET⁽⁰⁾, ${\mathcal{E}}_{00}$ = ${\mathcal{E}}_{00}^{\left(\mathrm{Cor}\right)}$; and for ΔG_HT⁽⁰⁾, ${\mathcal{E}}_{00}$ = ${\mathcal{E}}_{00}^{\left(\mathrm{PDI}\right)}$. While toluene is the medium of choice for these photoinduced CT studies, relatively polar media, with dielectric constants ε_D and ε_A, are essential for electrochemical determination of $E_{Co{r}^{•+}|Cor}^{\left(1/2\right)}$ and $E_{PDI|PD{I}^{•-}}^{\left(1/2\right)}$, respectively. The Coulombic work term, W, accounts for the interaction between Cor^•+ and PDI^•-. For n-ET between a donor with an initial charge x and an acceptor with an initial charge y, the Born solvation term, ΔG_S, corrects for the differences between medium polarities for CT studies and electrochemical measurements (Eq. 2) (48, 49):where q_e is the electron charge, and r_D and r_A are effective radii of the donor and acceptor, respectively.

Considering one-electron oxidation and reduction of noncharged donors and acceptors, i.e., n = 1 and x = y = 0, for identical electrochemical solvents, i.e., ε_D = ε_A = ε_E, simplifies the expression for the PCT driving force as well as the dependence of the potential differences, $\mathrm{\Delta }{E}_0^{\left(1/2\right)}\left(\epsilon \right)=E_{Co{r}^{•+}|Cor}^{\left(1/2\right)}\left(\epsilon \right)-E_{PDI|PD{I}^{•-}}^{\left(1/2\right)}\left(\epsilon \right)$, on the medium polarity as implemented by the Born solvation energy:where S_1/r is the sum of the inverse radii of the donor and acceptor: S_1/r = r_D⁻¹ + r_A⁻¹.

The acidity of pyrrole protons in oxidized free-base corroles affects their electrochemical behavior (50, 51). The first one-electron oxidation leads to triprotonated radical cations, Cor[H₃]^•+, that have increased acidity and readily protonate basic solvents, B, or other corroles within voltammetry timescales (milliseconds to seconds): Cor[H₃]^•+ + Cor[H₃] → Cor[H₂]^• + Cor[H₄]⁺; Cor[H₃]^•+ + B → Cor[H₂]^• + BH⁺. Positive-sweep cyclic voltammograms of free-base corroles, therefore, show anodic waves corresponding to the oxidations of Cor[H₄]⁺ and Cor[H₂]^• that closely follow the initial one-electron oxidation wave (51).

For a low-polarity solvent such as CH₂Cl₂, positive-sweep cyclic voltammograms of Cor-Phe show a well-defined anodic wave corresponding to the initial oxidation, with a peak potential at about 1 V vs. SCE (Fig. 5A). While occasionally a small cathodic peak around 0.85 V vs. SCE becomes detectable at low concentrations of supporting electrolyte, C_el, the oxidation of Cor-Phe tends to exhibit irreversibility at scan rates on the order of 100 mV⋅s⁻¹ (Fig. 5A). For irreversible oxidation, the inflection point of the first anodic wave provides an estimate for $E_{Co{r}^{•+}|Cor}^{\left(1/2\right)}$ (52). Increasing solvent polarity not only causes negative shifts of the oxidation features in the voltammograms, but also broadens the first anodic wave and merges it with the waves that follow. An increase in electrolyte concentration also induces slight negative shifts in the reduction potentials of Cor^•+-Phe (Fig. 5A). For each solvent, extrapolation to zero electrolyte concentration, i.e., C_el = 0, allows estimation of the potentials for neat solvent, $E_0^{\left(1/2\right)}$ (Fig. 5B) (53–55).

The cyclic voltammograms of PDI show two reversible reduction waves (Fig. 5A), consistent with previously reported electrochemical behavior for this chromophore (56). The mean of the first cathodic and anodic peak potentials provides estimates for $E_{PDI|PD{I}^{•-}}^{\left(1/2\right)}$. Combining the results for PDI and Cor-Phe for three different solvents allows an estimation of the potential difference $\mathrm{\Delta }{E}_0^{\left(1/2\right)}$ for toluene from the linear fit of $\mathrm{\Delta }{E}_0^{\left(1/2\right)}\left(\epsilon \right)\mathrm{vs}\mathrm{.}{\epsilon }^{-1}$: S_1/r = 0.36 ± 0.07 Å⁻¹, and $\mathrm{\Delta }{E}_0^{\left(1/2\right)}\left({\epsilon }_{toluene}\right)=2.3\pm 0.1\mathrm{eV}$ (Fig. 5C and Eq. 3b). The uncertainty indicated by the shading around the curves for ΔG_CT⁽⁰⁾ (Fig. 5C) originates from the uncertainty in estimating $\mathrm{\Delta }{E}_0^{\left(1/2\right)}$ in toluene.

The estimated $\mathrm{\Delta }{E}_0^{\left(1/2\right)}$ in toluene simplifies the calculations of CT driving forces pertinent to this study (Eq. 3a). The dependence of the Coulombic term, W (Eqs. 1 and 3a), on the center-to-center donor–acceptor distance, R_DA, which is especially pronounced for nonpolar media (57), can induce variations in ΔG_CT⁽⁰⁾ that amount to half an eV (Fig. 5D). An increase in R_DA causes negative shifts in ΔG_ET⁽⁰⁾ and ΔG_HT⁽⁰⁾, and a positive shift in ΔG_CR⁽⁰⁾ (Fig. 5D). For a center-to-center distance between PDI and Cor exceeding about 20 Å, ΔG_ET⁽⁰⁾ assumes positive values such that ET is unfavorable. Conversely, ΔG_HT⁽⁰⁾ and ΔG_CR⁽⁰⁾ are negative over the entire R_DA range (Fig. 5D).

Electrochemical and photophysical analyses of Cor-Phe and PDI reveal favorable thermodynamics for the formation of a CT state, Cor^•+–PDI^•−, via multiple pathways (Scheme 2). Whether CT reactions can compete with deactivation of locally excited (LE) states (¹Cor*, ¹PDI*), however, depends on the strengths of electronic couplings within the amino acid linkers.

Cor and PDI fluorescence quantum yields (ϕ_f) indicate accelerated excited-state decay when incorporated in DBA conjugates. Selective Cor (λ_ex = 620 nm) or PDI excitation (λ_ex = 465 nm) in DBAs reveals quenched fluorescence (Table 1), consistent with efficient ET, HT, and EnT, even in the conjugate with a tetrapeptide bridge. That ϕ_f in Cor-(Ala)₄-PDI is just three to seven times greater than that of Cor-Ala-PDI or Cor-Phe-PDI indicates that the tetrapeptide bridge does not substantially retard ET and HT reactions in these conjugates (37, 58). The quantum yields indicate that deactivation of ¹PDI* via EnT and HT is more efficient than ET from ¹Cor* in the three DBA conjugates. The estimated Förster distance for ¹PDI*→Cor EnT (46 Å) exceeds R_DA even for fully extended DBA conformations, consistent with efficient EnT. For HT to contribute to ¹PDI* decay, the HT rates must be comparable to those of EnT.

The exponential fluorescence decay times of ¹Cor*-Phe and ¹PDI* (4.5 and 4.7 ns, respectively; Table 1) correspond to radiative (k_f) and nonradiative (k_nr) decay rate constants k_f = 3.3 × 10⁸/k_nr = 1.9 × 10⁹ s⁻¹ for ¹Cor*-Phe, and k_f = 1.8 × 10⁹/k_nr = 3.2 × 10⁸ s⁻¹ for ¹PDI*. The three DBA conjugates exhibit multiexponential fluorescence decays, consistent with CT quenching by multiple DBA conformers (SI Appendix). The ϕ_f values for Cor-Ala-PDI and Cor-Phe-PDI suggest that HT and ET rate constants (k_HT and k_ET) exceed 10¹⁰ s⁻¹, but the time resolution of the fluorescence decay measurements (∼50 ps) prevented observation of the fastest excited-state decay components. Consequently, we turned to femtosecond transient absorption (TA) spectroscopy to explore the earliest DBA excited-state events (Scheme 2).

TA spectroscopy reveals that Cor photoexcitation in DBA derivatives is followed by a picosecond rise of PDI^•− and Cor^•+ 650/850 nm transients (30), and there is concurrent bleaching of PDI ground-state absorptions (Figs. 6 and 7 A–D). As with fluorescence decay measurements, we observed heterogeneous TA kinetics for the DBA conjugates with decay components of 3–5, 40–60, and 160 ps (Table 1 and Fig. 8 A–C). In addition, a 1.4-ns decay was observed in Cor-(Ala)₄-PDI. Importantly, these results suggest comparable donor–acceptor coupling pathways in all three DBA conjugates.

PDI photoexcitation is followed by a ground-state bleach, stimulated emission (SE), and a broad TA signal in the 650- to 850-nm region attributable to a singlet excited state (Fig. 6B). Within 1 to 2 ps in the DBA conjugates, the PDI stimulated emission disappears and the broad 650- to 850-nm ¹PDI* TA evolves into bands corresponding to PDI^•− and Cor^•+ transients (Fig. 7 E–G). The dynamics are consistent with 1) photoinduced HT to Cor and 2) EnT to Cor, followed by ET (Scheme 2). After these ultrafast changes in TA spectra, a further increase in the radical-ion TA accompanies growth of the PDI ground-state bleach (Fig. 7 E–G), consistent with the ET from ¹Cor* to PDI observed upon direct photoexcitation of the donor (Fig. 7 A–C). The observation of 30- to 70-ps ET upon photoexcitation of the acceptor indicates that ¹PDI* to Cor EnT accompanies the initial HT.

Global fitting can help distinguish HT from EnT–ET processes. In the case of HT, for example, the PDI ground-state bleach does not change during ¹PDI TA decay. In the case of EnT, on the other hand, the PDI bleach recovers during ¹PDI* TA decay. The ET that follows EnT restores the PDI bleach but not SE or ¹PDI* TA.

Picosecond HT accompanies EnT that can be in the subpicosecond time domain (Table 1). The heterogeneity of the kinetics reflects the diversity of conformational populations of DBA conjugates. For Cor-Ala-PDI and Cor-Phe-PDI, HT does not contribute substantially to ¹PDI* deactivation (Table 1), consistent with the large R₀ and favorable orientation of transition dipole moments of the donor and acceptor. For Cor-(Ala)₄-PDI, however, HT is a key deactivation channel for ¹PDI* (Table 1). Unlike Cor-Ala-PDI and Cor-Phe-PDI, the picosecond decay of ¹PDI* in Cor-(Ala)₄-PDI appears to accompany TA growth of radical ions (Figs. 7H and 8 D–F), consistent with HT (Scheme 2). As CD shows, Cor-(Ala)₄-PDI forms structures more tightly folded than those of Cor-Ala-PDI and Cor-Phe-PDI (Fig. 4 A–C).

The changes in TA spectra of the DBA conjugates when exciting the acceptor do not provide sufficient resolution for global fitting to determine the rates of competing HT and EnT processes. Nevertheless, comparison of exponential amplitudes [α_i(λ)] for sequential ET and charge recombination (CR) reveals that roughly 60% of Cor-Ala-PDI and Cor-Phe-PDI CT states originate from ET from ¹Cor* to PDI. For Cor-(Ala)₄-PDI, on the other hand, 90% of the CT state is generated by direct HT from ¹PDI* to Cor. These findings indicate that Cor-(Ala)₄-PDI EnT is much less efficient than that of either of the other two DBA conjugates.

While the calculated R₀ value of 46 Å assumes random D and A transition-dipole-moment orientations, i.e., κ = 2/3, this assumption may not be justified for these DBA conjugates, particularly Cor-(Ala)₄-PDI. The CD results (Fig. 4C) and lower EnT efficiency suggest that Cor-(Ala)₄-PDI adopts tight conformations in toluene where the PDI emission transition dipole moment is roughly orthogonal to that for Cor S₀→S₁ absorption.

The DBA CR reactions (CR, Scheme 2) display multiexponential kinetics with time constants in the 0.4- to 2.6-ns time range. That the CR reactions are substantially slower than the excited-state charge separation processes (Table 1, Figs. 7 D and 8 A–C) even though there is 1.0- to 1.4-eV greater free-energy release (Fig. 5D) is a clear indication of inverted driving-force behavior.

Semiclassical theory (Eq. 4) provides a platform for analysis of CT processes (Table 1) (59).In Eq. 4, λ is the reorganization energy, comprising the inner (λ_ν) and medium (λ_m) contributions (λ = λ_ν + λ_m). The solvent reorganization energy depends on the distance between donor and acceptor (Eq. 5) (59); the low dielectric constant of toluene constrains λ_m to 25–55 meV over a 9- to 25-Å span of R_DA (Fig. 5D). The uncertainty in S_1/r, obtained from the slope of the linear fit of $\mathrm{\Delta }{E}_0^{\left(1/2\right)}$ vs. ε⁻¹ (Eq. 3b and Fig. 5C), has a relatively modest contribution to the uncertainty in λ:For reactions far into the inverted driving-force region [i.e., −ΔG_CT⁽⁰⁾ >> λ], semiclassical theory underestimates nuclear tunneling contributions. The Marcus–Levich–Jortner model is more appropriate for this regime, as it takes specific account of nuclear tunneling (60) (Eq. 6):In Eq. 6, ν_C represents a single high-frequency vibrational mode (or an average of frequencies). Values of inner-sphere reorganization energies for large polycyclic aromatic compounds tend to be less than 0.2 eV (61, 62). We can estimate λ_ν contributions to Cor and PDI CT on the basis of their fluorescence spectra. In a simple one-electron approximation, the fluorescent excited states of Cor and PDI arise from the promotion of one electron from the bonding highest-energy occupied molecular orbital (HOMO) to the antibonding lowest-energy unoccupied molecular orbital (LUMO). The inner sphere reorganization energy associated with this process will be an upper limit to that involved in removal of one HOMO electron (oxidation) or delivery of one LUMO electron (reduction). Two-mode (one classical, one quantum) Franck–Condon analyses of the ¹Cor and ¹PDI fluorescence spectra (see SI Appendix) indicate that the upper limit to the inner-sphere reorganization energy for Cor-PDI CT is about 0.26 eV (0.18 eV quantum; 0.08 eV classical). The lower limit is likely to be no less than half of this value, suggesting that the range for λ_ν is 0.13–0.26 eV (shaded region of the curve for λ in Fig. 5D).

The remaining unknown quantity in Eq. 6 is the electronic coupling strength, H_DA. The coupling along the (Cor)N–H⋯O=C–N–H⋯O(PDI) route can be estimated using the Beratan–Onuchic pathway model (37). This approach decomposes a pathway into a sequence of covalent bonds, hydrogen bonds, and through-space contacts, representing the overall coupling as repeated products of the coupling decays [ε^(C), ε^(H), ε^(S)] for each step (Eq. 7):The (Cor)N–H⋯O=C–N–H⋯O(PDI) pathway is composed of two covalent bonds [ε^(C) = 0.6] and two H bonds. Coupling decays across the latter scale exponentially with distance (^(H) = 0.36 exp[–1.7(r_i^(H) – 2.8)]). The computed structure (Fig. 2C), optimized for toluene as a solvating medium, predicts that r_(Cor)N-H⋯O^(H) = 2.98 Å and r_N-H⋯O(PDI)^(H) = 3.02 Å. The predicted coupling along the (Cor)N–H⋯O=C–N–H⋯O(PDI) pathway is H_DA = 0.024 H_DA⁽⁰⁾, where H_DA⁽⁰⁾ represents the electronic coupling when the donor and acceptor are in contact.

The electrochemical and optical properties of Cor and PDI (Fig. 5), the calculated structures (Fig. 2), and the solvent characteristics permit estimates of all parameters for the semiclassical analysis (Eq. 6) except H_DA⁽⁰⁾. The ET and HT rate constants (Table 1) are consistent with nonadiabatic reactions (H_DA = 3.1 meV, Fig. 9), corresponding to the pathway-model prediction of 130 meV for the coupling at contact. The CR rate constants, however, are much greater than predicted for this coupling strength. The electrostatic attraction between Cor⁺ and PDI⁻ in toluene is likely to drive a conformational change that brings the ions into contact or possibly separated by a single solvent molecule. If we assume that H_DA = 0.13 eV, the rate constant calculated using Eq. 6 is much closer to the experimental value (Fig. 9), although it is possible that conformational dynamics contribute to the observed recombination rate constants. Moreover, polarization of the wavefunctions in the radical ion pair could enhance electronic coupling for CR. Prior evaluations of electronic coupling across a single toluene molecule suggest a value of ∼2.5 meV (63). Investigations of CR in radical ion pairs indicate coupling strengths of ∼1.2 meV for solvent-separated ion pairs, and ∼0.12 eV for contact ion pairs (64).