PDI–trityl dyads as photogenerated molecular spin qubit candidates

Owing to their potential applications in the field of quantum information science, photogenerated organic triplet–radical conjugates have attracted an increasing amount of attention recently. Typically, these compounds are composed of a chromophore appended to a stable radical. After initialisation of the system by photoexcitation, a highly spin-polarised quartet state may be generated, which serves as a molecular spin qubit candidate. Here, we investigate three perylene diimide (PDI)-based chromophore–radical systems with different phenylene linkers and radical counterparts by both optical spectroscopy and transient electron paramagnetic resonance (EPR) techniques. Femtosecond transient absorption measurements demonstrate chromophore triplet state formation on a picosecond time scale for PDI–trityl dyads, while excited state deactivation is found to be slowed down considerably in a PDI–nitroxide analogue. The subsequent investigation of the coherent spin properties by transient EPR confirms quartet state formation by triplet–doublet spin mixing for all investigated dyads and the suitability of the two studied PDI–trityl dyads as spin qubit candidates. In particular, we show that using tetrathiaryl trityl as the radical counterpart, an intense spin polarisation is observed even at room temperature and quartet state coherence times of 3.0 μs can be achieved at 80 K, which represents a considerable improvement compared to previously studied systems.

All reactions were performed under an argon atmosphere unless otherwise indicated.All reagents and solvents were purchased at the highest commercial quality and used without further purification unless otherwise noted.Thin layer chromatography was performed with TLC silica on aluminium foil (Silica gel/UV254, Aldrich).Irradiation using a Bioblock VL-4C UV-lamp (6 W, 254 nm and/or 365 nm) was used as well as suitable TLC stains for visualisation.Preparative thin layer chromatography (PTLC) was performed using commercial silica gels plates (Merck Z740216, 60 Å pore size). 1 H NMR spectra were recorded on a Bruker Avance III HD 400 MHz spectrometer equipped with a BBFO probe at 298 K.The spectra were internally referenced to the residual proton solvent signal.For 1 H NMR the chemical shifts are given in ppm.Coupling constants J are listed in Hz.Standard abbreviations indicating multiplicity were used as follows: s = singlet, d = doublet, dd = doublet of doublets, t = triplet, q = quartet, quintet, m = multiplet, br = broad signal.Ultra performance liquid chromatography coupled to mass spectrometry (UPLC-MS) was carried out on a Waters Acquity UPLC-SQD apparatus equipped with a PDA detector (190−500 nm, 80 Hz), using a reverse phase column (Waters, BEH C18 1.7 µm, 2.1 mm × 50 mm), and the MassLynx 4.1 -XP software with a gradient (water-acetonitrile + 0.1 % formic acid) as eluent.High-resolution mass spectra (HRMS) were recorded on a Thermo Fisher Scientific Exactive mass spectrometer with an orbitrap analyser using either atmospheric pressure chemical ionisation (APCI)   or electrospray ionisation (ESI).

Synthetic protocols
The synthetic procedure to prepare I-eTEMPO has been reported previously, [1] and the synthesis of precursor PDI−biph−Bpin will be reported in due time as part of a different publication that includes also the syntheses of PDI−ph−trityl and PDI−biph−trityl.Nevertheless, the corresponding 1 H NMR spectrum is reported in a double panel (Figure S25) showing the expected changes following the preparation of PDI−biph−eTEMPO.While a complete structural elucidation of radical compounds by NMR is not possible in chromophore-radical systems like those reported here, it is often possible to clearly identify the features distant from the radical unit.In a round-bottom flask (50 mL), PDI−biph−Bpin, (1 eq., 10 mg, 7 µmol), I-eTEMPO (1.5 eq., 3.0 mg, 10.6 µmol) and sodium carbonate (3.9 eq., 3.0 mg, 28 µmol) were dissolved in a mixture of water/THF/toluene (1:1:1 -18 mL).Pd(PPh 3 ) 4 (0.05 eq., 0.4 mg, 0.4 µmol) was added and the reaction S1 mixture was stirred at 80 • C for 3 h (monitoring by UPLC).After the reaction was completed, a saturated solution of Na 2 CO 3 (15 mL) was added and the mixture was extracted with dichloromethane (3×50 mL).
The combined organic extracts were dried over Na 2 SO 4 and filtered.The solvent was removed under reduced pressure and the residue was purified by PTLC (SiO 2 , DCM) to yield PDI−biph−eTEMPO (9 mg, 6.2 µmol, 88.4%) as a deep purple solid.R f (DCM 2%(v/v) acetone) ∼ 0.4.Steady-state absorption measurements of the samples in toluene were carried out on a Shimadzu UV-1601 UV-vis spectrometer.Figure S1 shows the normalised UV-vis spectra of the three investigated dyads.
400 500 600 700 800 900 Figure S1: UV-vis spectra of the three investigated PDI-based dyads.The spectra have been scaled to match the molar absorption coefficient of PDI of 3.1 • 10 4 M −1 cm −1 at 579 nm. [2]r the fluorescence measurements, the samples were diluted substantially, corresponding to absorbances < 0.1 at the excitation wavelength.Steady-state fluorescence spectra were recorded on a FluoroMax-4 fluorimeter from Horiba.The raw spectra were corrected for the spectral sensitivity of the instrument and fluctuations of the excitation light source.
Fluorescence quantum yields were determined using a C11347 absolute photoluminescence quantum yield spectrometer from Hamamatsu Photonics K.K., Japan.The same solutions as prepared for the fluorescence measurements were used.An excitation wavelength of 530 nm was chosen and the analysis was performed using the tools provided with the data acquisition software.decay function was fit to the experimental data using a least-squares fitting approach (minimisation of the residuals using a built-in trust-region-reflective algorithm).The data obtained for PDI−biph−eTEMPO are shown in Figure S2.

Calculation of the Förster resonance energy transfer rate constants
Since Förster-type excitation energy transfer (FRET) between PDI and trityl is very likely and has previously been observed, [3] we calculated the theoretically expected EET rate constants for the investigated dyads.
As can be seen from the formulae for the calculation of the FRET rate constants below, i.e.Equations (S1) to (S3), the efficiency of this process will depend primarily on (i) the spectral overlap of chromophore emission and radical absorption and, (ii) the relative orientation of the transition dipole moments of chromophore and radical (κ 2 ), in addition to the distance r DA between the donor and acceptor moieties.A visualisation of the spectral overlap is shown in Figure S3.While it is significant in the case of trityl, it can be seen that there is almost no spectral overlap between the PDI emission and the absorption of the eTEMPO radical.

eTEMPO absorption PDI emission
Figure S3: UV-vis absorption spectrum of the trityl radical (left) and eTEMPO radical (right) together with the fluorescence emission spectrum of PDI for an illustration of the spectral overlap.
The transition dipole moment (TDM) of the PDI chromophore lies along the long axis of the molecule, which corresponds to the chromophore−radical bonding axis.Since the TDM of trityl is also roughly alined with the bonding axis, [4] a κ 2 value of four can be assumed.As shown previously, [1] the TDM of S3 the eTEMPO radical is perpendicular to the bonding axis, so that κ 2 = 0. Considering also the poor spectral overlap, FRET can most likely be excluded for PDI−biph−eTEMPO.
For the calculation of the FRET rate constants k FRET for the PDI−trityl dyads, the molar absorption coefficient of the trityl radical was taken to amount to 3.8 • 10 4 M −1 cm −1 at its absorption maximum of 460 nm. [3]The fluorescence quantum yield and lifetime of the PDI chromophore were taken from reference 2, while the center-to-center distances, r DA , were taken from DFT models of the structures (vide infra) and amount to 1.59 nm for PDI−ph−trityl and 2.02 nm for PDI−biph−trityl, respectively.
An overview of the results and parameters is provided in Table S1.The Förster radius R 0 (obtained in nm) can be calculated from [5] (R 0 ) 6 = 8.785 with where Φ D F,0 and I D F are the fluorescence quantum yield and fluorescence intensity of the donor, ε A is the molar absorption coefficient (in M −1 cm −1 ) of the acceptor and n the refractive index of the medium.The orientation factor κ 2 accounts for the relative orientation of the two transition dipole moment vectors (emission of donor and absorption of acceptor) with respect to the axis connecting the FRET pair.
The energy transfer rate constant is then given as where τ D F,0 is the fluorescence lifetime of the donor in the absence of any quenchers and r DA is the center-to-center distance (point dipole) between donor and acceptor.

Calculation of the driving forces for electron transfer
The calculations of the driving forces −∆G 0 for charge separation (CS) and charge recombination (CR) were performed assuming the validity of the following equations: [6] −∆G 0, CS = −∆G 0, IP + E 00 (S4) where the subscript IP stands for ion pair, E 00 is the energy of the first excited singlet state and E ox (D) and E red (A) are the oxidation potentials of the electron donor and reduction potentials of the electron acceptor, respectively.The terms C and S represent the coulomb and solvent correction terms, defined as where r ee , ε r , ε 0 , ε r, ref and r i are the edge-to-edge distance between the reaction partners, the relative solvent permittivity, the vacuum permittivity, the relative permittivity of the solvent used to determine the redox potentials and the Van-der-Waals radii, respectively.
The standard electrode potential of the trityl radical (E trityl + /trityl ) is 0.61 V vs. SCE (in H 2 O), [7] while the standard electrode potential of the PDI acceptor (E PDI/PDI − vs. SCE) amounts to −0.67 V (in CH 2 Cl 2 , ε r = 9). [8]The solvent toluene, used for the spectroscopic measurements, has a relative dielectric constant of ε r = 2.4 at room temperature. [9] 00 for PDI (corresponding to E S1 ) is calculated from the crossing point of the absorption and fluorescence spectra and amounts to 2.11 eV (588 nm).The energy of the PDI triplet state was estimated from quantum chemical calculations (vide infra) and amounts to E T1 = 1.30eV.The energy of the charge transfer state generated by electron transfer from trityl to PDI, E CT , corresponds to −∆G 0, CR and was calculated using the parameters given above.It amounts to roughly 1.34 eV for PDI−ph−trityl, and 1.57 eV for PDI−biph−trityl, which corresponds to values for −∆G 0, CS of 0.77 eV and 0.54 eV, respectively.Finally, the excited state energy of the trityl radical, E R* , can be estimated from its UV-vis absorption spectrum and amounts to roughly 900 nm, i.e. 1.38 eV.
According to these calculations, electron transfer could thus be feasible in toluene.The absence of any ion signatures in fsTA experiments might be explained by inverted kinetics as suggested also earlier for a PDI-TEMPO dyad. [2]From a purely energetic point of view, recombination to the PDI triplet state should be possible from both the charge separated state and the excited doublet state of the radical, as they lie energetically above the excited triplet state of the PDI chromophore.

Femtosecond TA data acquisition
[12][13] In brief, a Ti:Sapphire amplified laser system (Coherent Libra) with a repetition rate of 1 kHz, a pulse duration of 100 fs, and a wavelength of 800 nm was used as the pulse source.Part of its output was used to pump a TOPAS-White non-collinear optical parametric amplifier tuned to deliver pulses peaking at 530 nm.The pump power at the sample position amounted to 1 mW (i.e., 1 µJ/pulse).For probing (330−740 nm), a supercontinuum was generated in a CaF 2 plate.The pump beam diameter at the sample was 160 µm (FWHM), while the diameter of the probe beam was 100 µm.The relative polarisation of pump and probe beams was set to the magic angle and the instrument response time was ∼180 fs (FWHM).

S5
Femtosecond transient UV-vis absorption (fsTA) spectra were recorded at 139 different time delays, where 50 linear time steps between −1 and 1 ps were followed by linear steps on a logarithmic scale up to roughly 4 ns.A total of 2000 spectra were acquired per time point and averaged over four successive scans.The chopper in the probe beam path was set to a frequency of 500 Hz, while that in the pump path was set to 250 Hz.For every time point, four different sets of data were collected: (i) only the white light (probe) reaches the sample, (ii) pump and probe both blocked, (iii) pump and probe both reach the sample, (iv) only the pump reaches the sample.Signals (i) and (iii) are used for the calculation of ∆A, while signals (ii) and (iv) are needed to account for dark signals and pump light scattering.The chirp of the white light was measured in a separate (optical Kerr effect, OKE) experiment and accounted for in the processing of the TA data.In addition, solvent spectra were recorded separately under identical conditions as the samples and subtracted from the sample data following the procedure detailed in reference 14.
The TA data were analysed using lab-written MATLAB routines.After subtraction of the suitably scaled solvent background, the data were chirp-corrected by interpolation in the time domain using a , where f (t D ) is the instrumental delay time and the parameters p n are obtained by fitting the temporal peaks of the OKE response as a function of wavelength.
For the room temperature femtosecond TA experiments the samples were prepared in toluene solutions with an absorbance between 0.3 and 0.4 at the excitation wavelength of 530 nm in a 1 mm cuvette.During the experiments, the sample solutions (∼ 2 mL) were flown continuously.In addition, UV-vis spectra were taken before and after the measurements to verify the sample absorbances and confirm the absence of sample degradation during the measurement.

Additional fsTA data and global kinetic analysis
The contour plots of the fsTA data recorded for PDI−biph−trityl and PDI−biph−eTEMPO are shown in Figures S4 and S5.Compared to the data for PDI−ph−trityl discussed in the main part, it can be seen that the photophysical behaviour of PDI−biph−trityl is qualitatively similar, only that the excitation energy transfer is somewhat slower.In contrast, neither excitation energy or electron transfer seem to occur in PDI−biph−eTEMPO, resulting in a comparatively slow deactivation of the excited singlet state of PDI (5.2 ns, see Figure S2), as might be expected for the rather large distance between chromophore and radical of about 1.9 nm. [1]f the fsTA data was carried out for all compounds.In a first step, the number of time constants required to reproduce the experimental data satisfactorily was determined by computation of the decay associated spectra (DAS). [15]Here, a multi-exponential function convoluted with the instrument response function In a second step, species associated spectra (SAS) were computed assuming a branched model of the form: for the two PDI-trityl compounds and a sequential model (A' Table S2 gives a summary of all time constants obtained from the kinetic analysis.The triplet yield of the dyads can either be estimated from (i) measurements of the singlet oxygen quantum yield or by (ii) careful analysis of the time-dependence of the ground state bleach amplitude in fsTA experiments (cf.reference 2).
For the singlet oxygen quantum yield measurements, all samples were prepared in toluene solutions with matched absorbances of 0.1 (pathlength 10 mm) at the excitation wavelength of 510 nm.A Continuum Horizon OPO pumped by the third harmonic of a Continuum Surelite laser operated at 10 Hz was used for photoexcitation, whereby the laser intensity was adjusted to amount to 0.5 mJ at the sample using a combination of a half-waveplate and a Glan-Taylor polariser (spot size ∼5 mm, pulse length ∼5 ns).The samples (∼ 2.5 mL) were contained in quartz cuvettes with a pathlength of 10 mm inside a 3D-printed sample holder that can accommodate a cuvette-sized magnetic stirrer.During the measurements, the air saturated solutions were continuously stirred at a speed of 400 RPM to replenish the solution with oxygen.

S9
Singlet oxygen is generated by reaction of molecular triplet states with triplet oxygen dissolved in the solution.The IR light emitted by 1 O 2 was collected at 90 • using a collimating lens and a back mirror both with a focal length of 50 mm.It passes an interference filter from Spectrogon adapted to the wavelength of 1270 nm before the signal is detected by an IR photomultiplier (Hamamatsu H10330-45) and recorded using a transient digitiser.A total of 256 averages were collected for each sample.The quenching of singlet oxygen is followed by monitoring the transient signal of 1 O 2 and the intensity maximum of the signal after laser excitation allows the determination of the singlet oxygen quantum yield by comparison to the behaviour of a known system measured under identical conditions.Under the applied experimental conditions, it is assumed that triplet quenching by oxygen is complete, meaning that every quenching event generates singlet oxygen.
The data were referenced against PDI 4sg −TEMPO investigated in reference 2 with a known triplet state formation quantum yield of 50 %.
Figure S10 shows the transient singlet oxygen signal obtained for the three PDI-based dyads and the reference compound PDI 4sg −TEMPO [2] after photoexcitation at 550 nm.A narrow spike, originating from scattered excitation light, was observed at time zero.To avoid any effects of this spike on the intensity readings used for the determination of the singlet oxygen quantum yields, only the decay beyond 0.5 µs was analysed.To calculate the yields given in the main part the relative intensities at 1.0 µs were used.entering the detection circuitry.Typically, for every magnetic field value, a time trace with 4096 points was recorded using a time base of 4 ns.After data acquisition, the 2D spectra were baseline-corrected in both dimensions using a lab-written MATLAB routine.
The spectra shown in the figures have been averaged over a time window from 0.2 µs to 1 µs after laser excitation unless otherwise stated.All EPR spectra were frequency-corrected to either 9.75 GHz (X-band) or 34.0 GHz (Q-band) and field-corrected using a carbon fibre standard with g = 2.002644. [16]ansient pulse EPR.Echo-detected field-swept EPR spectra at the Q-band were recorded using the

EPR characterisation of the radical and triplet precursors
The room temperature continuous wave (cw) EPR spectra of all three dyads, dissolved in toluene, are overlaid in Figure S11.As expected, the dark state spectra of the two PDI−trityl dyads are almost identical.It can be seen that the trityl radical is characterised by a very narrow EPR line with a peak-to-peak linewidth ∆B pp of 0.056 mT, due to the absence of any magnetic nuclei in the vicinity of the unpaired electron spin.To the left and right of the central line, low-intensity satellite-peaks are observed that arise from hyperfine coupling to 13 C with natural abundance. [17]6 347 348 349 The cw EPR spectrum of PDI−biph−eTEMPO exhibits the characteristics of a typical nitroxide spectrum.Three lines with a peak separation of ∼1.5 mT are observed, resulting from the coupling of the unpaired electron spin to the 14 N nucleus (I = 1) of the nitroxide group.
To determine the trityl g and A tensors, as needed for the simulation of the trEPR spectra of the S13 coupled dyads, cw EPR and pulse Q-band EPR data of PDI−ph−trityl were recorded and later fitted simultaneously.The data and fits are shown in Figure S12.
The triplet state parameters of the PDI chromophore were already determined elsewhere [18] and amount to g T = 2.00403, D T = 970 MHz, E T = −185 MHz with initial relative zero-field populations of P = [0.62 0.38 0] (from low to high energy).

Characterisation of the coupled systems by trEPR
Figure S13 shows the trEPR spectra of PDI−ph−trityl in toluene solution at different time delays.It can be seen that the shape of the signal varies significantly as a function of time.As expected, the quartet multiplet polarisation decays more rapidly than the net polarisation of the quartet state.In addition to the rather broad quartet state features centred at g(Q) = 2.0035, two sharp peaks are observed in the centre of the trEPR spectra at early times after photoexcitation (up to ∼1.5 µs).These additional features could potentially be assigned to the polarised trityl radical ground state (D 0 , g(D 0 ) = 2.0025) and the excited doublet state (D 1 , g(D 1 ) = 2.0045), based on the expected differences in their isotropic g values. [19]A similar observation is made for PDI−biph−trityl as shown in Figure S14.At the X-band, a g value difference of 0.001 only corresponds to a magnetic field shift of about 0.175 mT, while the same g value difference corresponds to a ∆B 0 of 0.6 mT at the Q-band.To clarify the presence of these different species further, room temperature solution trEPR measurements should be performed at higher microwave frequencies.quartet feature is found to vary depending on the measurement condition.In all cases, the multiplet spin polarisation is found to have decayed after ∼10 µs.However, the signal does not decay to baseline level.Instead, an absorptive signal with an intensity of about 5 % of the initial signal intensity remains, attributed to the quartet net polarisation (| + 1 2 ↔ | − 1 2 transition) based on its spectral position and width (see also Figure S16, left).

Simulation of the trEPR spectra
The room temperature trEPR spectra of PDI−ph−trityl and PDI−biph−trityl, shown in the main part, were simulated using the current developer version of EasySpin (v6.0.0-dev.50). [20,21]The function 'pepper' was used for the simulation of the powder spectra of the coupled spin systems and the simulation was carried out in the eigenbasis of the high-field states.During the fitting procedure, the magnetic parameters of the radical and chromophore precursor molecules (g g g R , g g g T , D T ) were held fixed, so that only the coupling parameters (D TR , J TR ), linewidths, and the populations of the quartet spin states needed to be adapted.The results are summarised in Table S3.
The exchange interaction J TR was assumed to be negative (corresponding to ferromagnetic coupling in EasySpin), in agreement with the exchange coupling calculations shown below (Subsection 4.4).Note that our exchange coupling calculations and the EasySpin software rely on a different definition of the exchange coupling Hamiltonian: in our quantum chemical calculations, a positive value of J TR indicates ferromagnetic coupling (i.e.E Q < E D1 ).All quantum chemical calculations were carried out using ORCA 5.0.3. [22]1 Optimisation of the structures The structures shown in Figure S21 and Figure S22 were optimised at the BP86/def2-SVP level of theory. [23]The calculations were accelerated with the RIJCOSX approximation using the def2/J auxiliary basis set. [24]gure S21: Structures of the PDI−trityl dyads calculated at the BP86/def2-SVP level of theory.

Triplet state energy of PDI
The adiabatic triplet state energy of PDI was calculated by considering the optimised structures of the singlet and triplet states which are shown in Figure S23.The optimisations were carried out at the M06/def2-TZVP level of theory. [23,25]The final energy of the triplet state was then calculated by a TDDFT calculation (M06/def2-TZVP level of theory) using the triplet state optimised geometry but starting from the restricted Kohn-Sham (RKS) singlet state.A value of ∆E = 1.30eV was obtained.state is too low.The protocol used in this calculation represents a compromise between the abovementioned procedures and was benchmarked on a bare perylene structure where the experimental triplet state energy is known.Using this method, an excellent agreement between experiment and calculation could be obtained (∆E = 1.57eV, in both cases).

Excited state exchange couplings
The excited state exchange couplings were calculated at the QD-NEVPT2/def2-SVP level of theory.
[28] Furthermore, the calculations were accelerated with the RIJCOSX approximation using the def2/J auxiliary basis set.The reference wavefunctions were obtained by a state-averaged CASSCF (3,3)   calculation, whereby the quartet state and the trip-doublet state were equally weighted by 50 %.The active orbitals were selected either from a previous TDDFT calculation or a MP2 calculation.The molecules and their active orbitals are shown in Figure S24.
The values for J TR , which are listed in Table S4, were calculated by using the QD-NEVPT2 energies of the quartet state and the trip-doublet state: The individual exchange interactions J 12 and J 23 , between the radical SOMO orbital (spin 2) and the chromophore HOMO and LUMO orbitals (spins 1 and 3), contributing to J TR according to [29] J TR = J 12 + J 23 2 (S9) were calculated by making use of the effective Hamiltonian theory.Here, the energies and wavefunctions of the quartet state, the trip-doublet state and the sing-doublet state are used to generate an effective Hamiltonian, whose eigenvalues are the energies of the three mentioned states.The three states are projected onto the subspace of neutral determinants, which allows for a one-to-one correspondence with the Heisenberg-Dirac-Van-Vleck Hamiltonian.The exact procedure is described in reference 29.The individual exchange interactions are given in Figure S24.
It should be noted here, that, for the two systems using trityl as the radical, the orbitals of the phenyl bridge may play an important role due to the highly delocalised nature of the radical.As a consequence, it is likely that the CAS(3,3) zeroth-order wavefunction is less well described in these two cases as compared to the other systems.One thus needs to be careful when comparing the results obtained for systems bearing different radicals.However, the results obtained for the two trityl-based systems should be comparable to each other.

Fluorescence lifetime measurements wereFigure S2 :
Figure S2: Fluorescence decay of PDI−biph−eTEMPO measured by single photon timing and best fit to the experimental data.

Figure S4 :
Figure S4: Contour plot of the fsTA data for PDI−biph−trityl recorded in toluene solution at room temperature after photoexcitation at 535 nm.

(
Figure S6: Decay associated spectra and time constants obtained from a global kinetic analysis of the fsTA data of PDI−ph−trityl (left) and PDI−biph−trityl (right) in toluene.

k 1 −
→) for PDI−biph−eTEMPO.The species A', A, B, and C are assigned to the vibrationally hot excited singlet state of PDI, the excited singlet state of PDI, the excited trityl radical, and the PDI triplet state, respectively.The branching ratio was adapted based on the experimentally determined triplet yields of 10 % for PDI−ph−trityl and 12 % for PDI−biph−trityl.The SAS obtained by plotting the contributions (i.e.amplitudes) of the individual time constants as a function of wavelength and assuming the validity of the chosen models are shown in Figures S7 to S9.

Figure S7 :
Figure S7: Species associated spectra obtained from a global kinetic analysis of the fsTA data of PDI−ph−trityl in toluene (left) and corresponding kinetics (right).

Figure S8 :Figure S9 :
Figure S8: Species associated spectra obtained from a global kinetic analysis of the fsTA data of PDI−biph−trityl in toluene (left) and corresponding kinetics (right).The time constants obtained for the formation and decay of the different species (elementary time constants) assuming a branched kinetic model are slightly different as compared to the lifetimes from the model-free analysis above.In addition, when incorporating the known triplet yield as an additional constraint, the time constant of triplet state formation can be calculated.

Figure S10 :
Figure S10: Measurement of the singlet oxygen signal as a function of time for the three investigated dyads and the PDI 4sg −TEMPO reference compound (cf.reference 2) with a known triplet yield of 50 %.The grey vertical line indicates the position where the intensities were read off for the determination of the singlet oxygen quantum yields.

hν
sequence hν − DAF − π/2 − τ − π − τ − echo with DAF = 9 µs at 80 K (DAF ≡ delay after flash), τ = 180 ns, and a π-pulse length of 32 ns.Unless otherwise stated, a two-step phase cycle was applied in all pulse EPR experiments.The same pulse lengths were also used for the determination of T m .To record T m of the quartet state, a pre-saturation pulse was applied to avoid any contributions of the radical signal to the spin relaxation decay of the quartet state.For measurements of the polarisation lifetime, a Hahn echo detection sequence was used and the position of the laser pulse with respect to the echo detection sequence was varied by a gradual variation of the DAF.The pulse sequences used are shown below.Transient nutation measurements used the sequence hν − DAF − ξ − τ − π − τ − echo where the flip angle ξ was gradually increased by increasing the corresponding microwave pulse length in steps of 2 ns, starting at 16 ns (π/2).At specific magnetic field positions within the region of the quartet spectrum, the integrated echo intensity was then recorded as a function of this pulse length.The data were background corrected using a polynomial background function.The (cross-term averaged) Fourier transform was then calculated after dead-time reconstruction, windowing using a Hamming window, and zero filling to 2048 data points.The frequency spectra were normalised by division of the frequency axis by the reference frequency obtained for the same sample in the dark (doublet multiplicity).Whenever the dark state contribution to the transient signal at the chosen field position was still significant, a pre-saturation pulse was applied to limit any such contributions.This also applies to the transient Rabi oscillation experiments described hereafter.Transient Rabi oscillation measurements used the sequence hν − DAF − t p − T − π/2 − τ − π − τ − echo where the pulse length t p was gradually increased in steps of 2 ns, starting at 0 ns.At the chosen magnetic field position within the region of the quartet spectrum, the integrated echo intensity was then recorded as a function of this pulse length.The inter-pulse delay T needs to be considerably longer than T m and was set to a value of 5.4 µs for the measurements at 80 K.All other parameters were the same as listed above for a field-swept echo-detected experiment.

Figure S11 :
Figure S11: Comparison of the room temperature cw EPR data (field-modulated derivative shape) of all three investigated dyads.

Figure S12 :
Figure S12: Determination of the g and A tensors of the trityl radical by simultaneous fitting of the X-band room temperature cw EPR spectrum of PDI−ph−trityl (left, field-modulated derivative shape) and the corresponding pulse Q-band spectrum recorded in frozen toluene solution at 80 K (right, direct detection).

Figure S13 :
Figure S13: Room temperature trEPR spectra of PDI−ph−trityl in toluene solution at different time delays (as indicated) after laser excitation at 535 nm.The right panel shows a zoom into the data where the spectral positions corresponding to the isotropic g values of the quartet (Q) state, the polarised radical ground state (D 0 ), and the excited doublet state (D 1 ) are marked.

Figure S14 :Figure S15 :Figure S16 :Figure S17 :
Figure S14: Room temperature trEPR spectra of PDI−biph−trityl in toluene solution at different time delays (as indicated) after laser excitation at 535 nm.The right panel shows a zoom into the data where the spectral positions corresponding to the isotropic g values of the quartet (Q) state, the polarised radical ground state (D 0 ), and the excited doublet state (D 1 ) are marked.

Figure S18 :B 0 Figure S20 :4
Figure S18: Comparison of the pulse EPR spectra of the PDI−trityl compounds recorded at the Q-band at 80 K in the dark (left) and after photoexcitation at 535 nm (right).The dark state background was subtracted from the light-induced spectra.

Figure S23 :
Figure S23: Structures of the S 0 and T 1 states of the PDI chromophore calculated at the M06/def2-TZVP level of theory.A single TDDFT calculation using only the S 0 optimised structure usually leads to an overestimation of the triplet state energy, whereas the restricted open-shell Kohn-Sham (ROKS) energy of the triplet

Table S2 :
Time constants and triplet yields obtained from a global kinetic analysis (SAS) of the fsTA data of PDI−ph−trityl, PDI−biph−trityl, and PDI−biph−eTEMPO in toluene solution at room temperature.A red, green and blue colour coding is used for the time constants representing (i) the S 1 state deactivation of PDI, (ii) the decay of the excited state absorption of the trityl radical, and (iii) PDI triplet state formation, respectively.compound τ 1 / ps τ 2 / ps τ 3 / ps τ 4 / ps τ 5 / ps

Table S3 :
Simulation parameters for the coupled PDI-trityl systems.

Table S4 :
Calculated values of J TR for different PDI-based chromophore−radical systems.