Excitation Energy Transfer and Exchange‐Mediated Quartet State Formation in Porphyrin‐Trityl Systems

Abstract Photogenerated multi‐spin systems hold great promise for a range of technological applications in various fields, including molecular spintronics and artificial photosynthesis. However, the further development of these applications, via targeted design of materials with specific magnetic properties, currently still suffers from a lack of understanding of the factors influencing the underlying excited state dynamics and mechanisms on a molecular level. In particular, systematic studies, making use of different techniques to obtain complementary information, are largely missing. This work investigates the photophysics and magnetic properties of a series of three covalently‐linked porphyrin‐trityl compounds, bridged by a phenyl spacer. By combining the results from femtosecond transient absorption and electron paramagnetic resonance spectroscopies, we determine the efficiencies of the competing excited state reaction pathways and characterise the magnetic properties of the individual spin states, formed by the interaction between the chromophore triplet and the stable radical. The differences observed for the three investigated compounds are rationalised in the context of available theoretical models and the implications of the results of this study for the design of a molecular system with an improved intersystem crossing efficiency are discussed.

Out of these four compounds, MgTPP-trityl was especially prone to oxidation during the purification process. The oxidation transforms the radical center into the corresponding diamagnetic triphenylmethanol moiety (H 2 TPP-trityl-OH). As shown in Figure S1, the H phenyl signals of the trityl core are broadened beyond visibility due to paramagnetic relaxation enhancement induced by the trityl radical (highlighted region). In contrast, these signals can be observed for the diamagnetic impurities, enabling the quantification of the radical content. Using this approach, H 2 TPP-trityl and ZnTPP-trityl show no clear indication of diamagnetic impurities, whereas MgTPP-trityl exhibits a porphyrin:radical ratio of 1:0.75, determined by integration of It should be noted that this method is likely not sensitive enough to detect an impurity content lower than a few percent, so small amounts of a diamagnetic impurity cannot be completely excluded even for H 2 TPP-trityl and ZnTPP-trityl. In addition, it needs to be added that neither MALDI(+) nor ESI(+) mass spectrometry allow a reliable quantification in the present case, since signals belonging to sulfoxide impurities (M+16) can hardly be distinguished from trityl alcohol (M+17) impurities. Moreover, the presence of free-base porphyrin could also be probed by 1 H-NMR through observation of the characteristic signal at approximately −2.8 ppm. As shown in Figure S1, neither the zinc nor the magnesium complex contained any significant amount of free-base porphyrin.

UV-vis absorption spectra
The UV-vis spectra of the three investigated porphyrin building blocks, ZnTPP, H 2 TPP and MgTPP, recorded in toluene solution at room temperature are shown in Figure S4. As it is typical for this class of chromophores, the most intense absorption peak in the visible range is observed around 420 nm (Soret band), while the absorption peaks of the much less intense Q-bands cover the region from about 500 to 660 nm. From the characterisation of the porphyrin-trityl compounds it is known that, in a few percent of the sample, the trityl is present in its alcohol rather than its radical form. From the UV-vis and fs-TA spectra of the compounds it can be estimated that this percentage of diamagnetic impurity amounts to roughly ∼0−3 % in the case of ZnTPP-trityl and H 2 TPP-trityl and to roughly 30 % in the case of MgTPP-trityl (for reasons detailed in the synthesis section above). In the transient EPR experiments, these molecules, where the trityl radical has been deactivated, will show up as a triplet 'impurity' and contribute to the background signal. Since the triplet signal from porphyrins is quite strong (triplet yields of >80 % [4,5] and strong spin polarisation), this background can be quite substantial compared to the intensity of the quartet signal.

Approximation of the Förster energy transfer rate
The molar absorption coefficient of the trityl radical was estimated from UV-vis data of ZnTPP and ZnTPPtrityl (cf. Figure S4), taking into account the known molar absorption coefficient of ZnTPP at the Soret band maximum of 5.7 · 10 5 M −1 cm −1 [3,6]. It was assumed that the molar absorption coefficient at the intensity maximum of the porphyrin Soret band is the same for ZnTPP and ZnTPP-trityl and that the spectrum of ZnTPP-trityl (at least at 460 nm) is equal to the sum of the spectra of ZnTPP and trityl radical with a molar ratio of 1:1. The value for the fluorescence quantum yield of ZnTPP was taken from reference [7] and the center-to-center distance r DA from a DFT model of the ZnTPP-trityl stucture. The Förster radius R 0 (obtained in nm) can be calculated according to [8] 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 and FRET efficiency are then given as and 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-S5 center distance (point dipole) between donor and acceptor. The results obtained for ZnTPP-trityl assuming different values for κ 2 are summarised in Table S1. The spectral overlap of the trityl absorption and ZnTPP fluorescence spectra is illustrated in Figure S5.

Room temperature setup and spectra
For the room temperature femtosecond TA experiments the samples were prepared in either toluene or 2-methyl-THF solutions. 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. Care was taken that the absorbance in the Soret-band region did not exceed a value of about 1.5, to avoid optical saturation of the ground state bleach (GSB) and thus ensure accurate intensity readings in this region. As a consequence, the absorbances at the excitation wavelengths of either 400 nm or 550 nm were fairly low (0.02−0.1).
The setup used for the room temperature measurements was described in detail elsewhere [9][10][11][12]. 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 550 nm. 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 amounted to 100 µm. The relative polarisation of pump and probe beams was set to the magic angle and the IRF was about 180 fs. accounted for in the processing of the TA spectra. 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 [13].
The TA data were analysed using home-written MATLAB routines. After subtraction of the solvent background, the data were chirp-corrected by interpolation in the time domain using a function of the form x 4 with parameters p n determined by analysis of the corresponding OKE experiment (i.e. fit of f (x) to the OKE data as a function of wavelength).
The femtosecond TA experiments at room temperature were also carried out at an excitation wavelength of 400 nm and using a solvent with a significantly higher dielectric constant (2-methyltetrahydrofuran vs toluene). No significant differences in either the spectral signatures or kinetics were observed in these two cases as shown below.  Several scans needed to be averaged until an acceptable signal-to-noise ratio could be obtained. Between individual scans, the cryostat was laterally displaced, whenever necessary, to minimise the effects of sample degradation on the acquired spectra. All TA spectra were acquired using an excitation energy of ∼1 µJ.
In order to obtain an appreciable signal, a relatively high sample OD of about 0.3−0.6 at the excitation wavelength was required, resulting in optical saturation in certain regions of the spectrum around the intensity maxima of the UV-vis spectra. In addition, artifacts from pump light scatter at the excitation wavelength S8 could not be avoided when using the cryostat. The wavelength ranges dominated by artefacts from either excitation light scattering or optical saturation were cut out from the spectra. The data were analysed in a similar way as described above for the room temperature experiments.

Global kinetic analysis
To get a better estimate of the time constants of the excited state reaction processes, a model-free global kinetic analysis of the recorded fs-TA data was carried out [14]. In the case of the porphyrin chromophores and porphyrin-trityl compounds it was found that three and four time constants, respectively, were required in order to accurately reproduce the data recorded at room temperature, while only two time constants were needed for a satisfactory simulation of the trityl radical spectra.
The decay associated spectra (DAS) obtained for ZnTPP and H 2 TPP are shown in Figure S9. The fs-TA spectra of the porphyrin chromophores, ZnTPP and H 2 TPP, are well known and have been extensively analysed in the literature [15][16][17]. In general, after photoexcitation of the porphyrin, the first excited singlet state decays with a time constant of about 13 ns or 2.6 ns for H 2 TPP and ZnTPP, respectively, to form the porphyrin triplet state in high yield [4,5,7]. The latter then lives for about 1 µs in solution at room temperature [7]. The signatures of the porphyrin excited singlet and triplet states are very similar in both cases and may therefore be hard to distinguish.
The first time constants in Figure S9 can be attributed to vibrational relaxation processes occurring in the first excited singlet state of the chromophores, while the second and third time constants represent the decay of the porphyrin singlet and triplet states, respectively. Figure S10 shows the kinetic analysis of the room temperature fs-TA spectra of the trityl radical. The experimental data could be reproduced with only two time constants, attributed to (i) relaxation within S 1 and (ii) the excited state decay of the trityl radical.
The kinetic analysis of the fs-TA spectra of ZnTPP-trityl and H 2 TPP-trityl is shown in Figure S11.  were necessary to satisfactorily reproduce the data. It can be seen that the overall kinetics are somewhat slower in frozen solution, but the general trends and spectral features observed at room temperature are conserved: The trityl radical excited state lifetime is increased from about 120 ps to 650 ps. However, the deactivation of the excited porphyrin species in the presence of the stable radical is still almost equally fast (∼10 ps). Thus, even at 85 K, energy transfer from the porphyrin to the trityl radical seems to dominate the excited state dynamics.
Also for this set of data, the analysis of the fs-TA spectra of ZnTPP-trityl and H 2 TPP-trityl was performed twice, either with the third time constant fixed to the determined decay time of the trityl radical species (i.e. 650 ps) or leaving the third time constant to vary freely. As before, almost identical decay associated spectra were obtained in both cases. The variations in the decay times were very minor for ZnTPP-trityl (τ -values of (i) 1.6 ps, (ii) 10 ps, (iii) 560 ps); identical time constants were obtained for H 2 TPP-trityl.

Continuous wave EPR
To characterise the g -value of the trityl radical, a continuous wave EPR spectrum of H 2 TPP-trityl in toluene was recorded in the dark at room temperature. The measurement was carried out at the X-band (9.75 GHz) using a modulation amplitude of 0.1 G and a microwave power of ∼ 0.13 mW. The recorded, backgroundcorrected spectrum was frequency-corrected to 9.75 GHz and field-corrected using a carbon fibre standard [18]. A g -value of 2.0028 was obtained for the trityl radical by simulation of the spectrum using EasySpin S11 [19] as shown below. For the transient cw EPR measurements at Q-band frequencies (34.0 GHz) a Bruker EN 5107D2 resonator was used and the samples were prepared in quartz tubes with an outer diameter of 1.6 mm (inner diameter S12 of ∼1 mm). The samples were again excited through the top of the sample holder using an excitation energy of only ∼0.5 mJ. All other experimental parameters were kept the same.

Triplet state spectra and simulations
Transient cw EPR spectra of the triplet states of H 2 TPP, ZnTPP and MgTPP recorded in frozen toluene at 80 K are shown in Figure S14. The shape of the spectra of these compounds was found not to change significantly over the course of the triplet state lifetime. The spectra shown in the figure were averaged over a time window from 0.2 µs to 1 µs after laser excitation. It can be seen that, due to different intersystem crossing mechanisms, the triplet states of H 2 TPP and ZnTPP show an opposite spin polarisation [20]. While the spin polarisation pattern in H 2 TPP (from low to high field) is eeeaaa, an aaaeee polarisation pattern is obtained for ZnTPP. The triplet state D-value of both compounds is known to be positive [21], therefore the observed spin polarisation corresponds to an overpopulation of the in-plane triplet sublevels (X , Y ) in S13 Apart from differences in the spin polarisation pattern, it is noted that the triplet state D-value, reflected in the width of the triplet state spectrum, is significantly smaller in ZnTPP as compared to H 2 TPP, potentially pointing either towards an increased delocalisation of the triplet state wavefunction in ZnTPP or a different excited state geometry (due to the fact that the porphyrin core is no longer planar in H 2 TPP).
In theory, spin-orbit coupling contributions to the ZFS parameter D could be expected in ZnTPP, but previous experiments on Zn-porphyrin triplet states suggest that this is not the case [22]. In addition, in a series of linear Zn-porphyrin oligomers, all experimental observations and trends in D could be consistently explained and reproduced by quantum chemical calculations, taking only the spin-spin contribution to the ZFS into account [20,23]. Also the fact that the experimental D-value (i.e. spectral width) is almost identical for MgTPP and ZnTPP suggests that only spin-spin contributions to D need to be taken into account.
An overview of the magnetic parameters obtained as a result from the spectral simulations of the triplet and quartet state spectra (cf. also main text) is given in Table S2.  Compound  To obtain the pure quartet state spectra as shown in the main text, experimental spectra of ZnTPP and H 2 TPP were recorded under the same conditions and multiplied by an appropriate scaling factor before subtraction from the corresponding porphyrin-trityl data. Exemplary spectra for ZnTPP-trityl and H 2 TPPtrityl before and after subtraction of the triplet signal are shown in Figure S15. 6.4 Temperature dependence of the transient EPR spectra Figure S16 shows transient cw EPR spectra of H 2 TPP-trityl and ZnTPP-trityl recorded at different temperatures. It is noted that the spectral shape of the quartet state does not seem to be significantly affected by temperature in the range between 50 and 140 K.   Figure S16: Intensity normalised transient cw EPR spectra of H 2 TPP-trityl (left) and ZnTPP-trityl (right) recorded at different temperatures (as indicated). S15 6.5 Additional quartet spectra and simulations Figure S17 shows a schematic energy diagram indicating the allowed EPR transitions of a quartet state. For every orientation of the magnetic field (with respect to the D-tensor axes), three transitions are possible, i.e. | ± 1 2 ↔ | ± 3 2 and | + 1 2 ↔ | − 1 2 . The maximum spectral separation arises from molecules with their Z -axis parallel to the magnetic field direction and corresponds to 4 D Q . Figure S17: Schematic representation of the energy levels of the quartet state and their Zeeman splitting at different orientations of the external magnetic field with respect to the zero-field-splitting tensor axes. The allowed EPR transitions are indicated by blue arrows.
A comparison of the Q-band transient cw EPR spectra of H 2 TPP-trityl and ZnTPP-trityl is shown in Figure S18.

Discussion of the low signal intensity in transient EPR
Unfortunately it is very difficult to make any predictions about the (expected) strength of spin polarised signals, since the mechanism of spin polarisation cannot be predicted easily. Weak spin polarised EPR signals might either arise from an intrinsically weak spin polarisation (i.e. only small population differences), fast spin relaxation, or the fact that the (potentially strongly) spin polarised species is produced only with a low yield.
Regarding the investigated porphyrin-trityl compounds, it is likely that the weak quartet signal observed by transient cw EPR is due to a low quartet formation yield, since no quartet signal could at all be detected in pulse mode (not even at temperatures as low as 5 K). This interpretation is also in agreement with the optical experiments, suggesting rapid and very efficient deactivation of the chromophore's excited state by energy transfer. In addition, no significant changes in the intensity of the radical signal could be observed S16 in pulse mode upon photoexcitation at 80 K (cf. Figure S19), also implying a rather low quartet formation yield (assuming that the excitation efficiency is high).  Figure S19: Comparison of the FID-detected field-swept EPR spectra of H 2 TPP-trityl recorded with and without photoexcitation in frozen toluene at 80 K.

DFT calculations
All DFT calculations were performed using the ORCA program package (version 4.0). For the calculation of the spin density, the structures were first optimised in their (singlet or doublet) ground states using different functionals (CAM-B3LYP, B3LYP, BP86) in combination with the def2-TZVP basis set, RI approximation, and dispersion correction to the energies (D3). Magnetic property calculations (spin densities and hyperfine coupling tensors) in the triplet or quartet states used either the B3LYP or BP86 functionals, in combination with the EPR-II basis set.
For the calculation of the rotational barrier using different functionals (CAM-B3LYP, B3LYP, BP86) in combination with the def2-TZVP basis set, a transition state search and optimisation was first carried out. Frequency calculations confirmed the presence of exactly one imaginary frequency. Starting from the transition state, a series of constraint geometry optimisation steps was performed, scanning the dihedral angle between the porphyrin plane and the plane of the phenyl substituent. Finally, for different thermally accessible dihedral angles, the triplet state spin density was calculated as described above.
A visual representation of some of these results is shown in Figure S20. The different functionals used here predict the energetic minimum for slightly different dihedral angles.
However, it can be stated that the energetically preferred dihedral angle is roughly equal to 70 • . At room temperature, all dihedral angles between 50 and 130 • can be assumed to be significantly populated.

S17
In low temperature measurements, the range of accessible conformations will be governed by the respective situation at the freezing point of the solvent. The freezing point of toluene amounts to roughly 180 K, while that of 2-methyl-THF is ∼ 110 K. The exchange interaction between triplet and radical, J TR , will necessarily be different for different molecular conformations since the orbital overlap is affected by rotation of the linker. It is therefore expected that the distribution of exchange interactions is significantly narrower in frozen solution, as compared to room temperature, and shifted towards lower values. The reduced conformational space in frozen solution (restricting the phenyl group rotation to less favourable conformations in terms of orbital overlap) should lead to an overall decrease in J TR , while in fluid solution also conformations with greater π − π overlap can be accessed.
From the visualisation of the porphyrin triplet state spin density for different dihedral angles of the phenyl linker in Figure S20, it can be seen that already at a dihedral angle of 50 • a significant amount of the spin density is spread out onto the phenyl linker.
From the optimised structure of ZnTPP-trityl, a center-to-center distance of 1.3 nm (as used in the calculations of the Förster energy transfer rate) was obtained. However, the effective coupling distance between the two spin centres is predicted to be considerably shorter than the center-to-center distance, due to a significant delocalisation of both the radical and triplet spin densities.