On the photoluminescence in triarylmethyl-centered mono-, di-, and multiradicals

Introduction

Gomberg-type, triarylmethyl-centered radicals represent a class of stable organic radicals that exhibit luminescence. Typically, organic radicals that are luminescent exhibit poor photostability, and many representatives of the triarylmethyl family degrade upon photoexcitation [1-4]. For example, the photoluminescence of solutions containing perchlorotriphenylmethyl (PTM) or tris(2,4,6-trichlorophenyl)methyl (TTM) radicals degrades to half of their intensity within just a few minutes, while for their corresponding di- and multiradicals no fluorescence data is reported at all (see Figure 1a for chemical structures) [5,6].

However, research on fluorescent radicals has seen new impetus during the last decade, stimulated by the development of highly efficient electroluminescent devices based on donor-functionalized TTM radicals [7-13]. Today, new derivatives of donor-functionalized triarylmethyl radicals are being synthesized with enhanced photoluminescence quantum yield (ϕ) combined with improved photostability.

The spin-allowed transition from the excited doublet state to the ground state [7-13], combined with the absence of competing triplet states – which is a major pathway of efficiency loss in closed-shell emitters – promises to overcome the spin-statistical problem that limits the performance of conventional organic electronics. Without the chance to populate any dark triplet or quartet states, light-emitting radicals possess a theoretical internal quantum efficiency of up to 100% in electroluminescent devices [5,7,8,14].

While first examples of radical emitters in light-emitting diodes (LEDs) only delivered around 12% internal quantum efficiency [7], representing no improvement compared to conventional emitters, optimization of the donor-functionalized TTM radical and of the device geometry quickly allowed demonstration of LEDs with 100% internal quantum efficiency [8,12]. Modern approaches also incorporate light-emitting TTM radical derivatives into LEDs based on thermally activated delayed fluorescence to moderate excited triplet, doublet, and singlet states in an attempt to improve the overall device and emission performance [15].

Other prospective applications utilize the manipulation of the spin-state of the unpaired electron and the potential for optical readout of the spin state for quantum technological information processing, communication, or chemical and biological sensing [16-18].

However, there is a lack of understanding of why the absorption and photoluminescence of D₃ symmetrical triphenylmethyl radicals are so weak in the visible spectrum. While it is understood that the functionalization with donor moieties breaks the D₃ symmetry, the ϕ varies greatly among different donors and also when two or three donors are attached to the triarylmethyl radical center. Current approaches to improve the luminescence performance are limited to trial-and-error approaches or systematic screening of donors, while the underlying fundamental reasons for high or poor performance remain unclear.

The strong emission in some of the donor-functionalized triarylmethyl radicals has been explained by improved orbital overlap between the ground D₀ and excited D₁ states, while often geometrical alignment with a certain angle between the donor and the triarylmethyl units is being discussed. (The reader may note: electronic states are denoted in upright letters, e.g., D₀, while symmetry descriptors are denoted in italics, e.g., D₃.) Moreover, symmetry arguments are being employed to explain why certain transitions may be forbidden. This concept holds true for TTM and PTM with their D₃ symmetries in comparison to triarylmethyl units that have been symmetry broken by the single substitution with a donor. However, simple symmetry arguments cannot explain why threefold-substituted triarylmethyl radicals have often comparable or higher ϕ than their monofunctionalized homologues. Also, the concept of intensity borrowing from higher excited states, due to orbital overlap, does not explain the improved performance sufficiently, especially when comparing the oscillator strengths that can be determined using density functional theory (DFT) studies [19-21]. Moreover, when looking at di- or multiradicals, there are no reports on substantial photoluminescence, nor are there concepts to increase the ϕ in such systems, despite the many examples of highly emissive donor-substituted PTM- and TTM-based mono-radicals.

In this overview, we will focus on reviewing the different hypotheses for the mechanisms governing the luminescence performance and we will provide examples and connections between reports, where the hypotheses have been tested and proven. We do not attempt to give a comprehensive overview of the entire research field of organic triarylmethyl-centered radicals, since there already exists a body of reviews covering the different molecular structures of mono-, di-, and multiradicals, synthetic approaches [22-25], state dynamics in luminescent radicals [26], and their application in light-emitting devices [27-29].

Instead, we aim to provide insight and understanding into the mechanisms and reasons behind the fluorescence color and the fluorescence quantum yield and derive structure–optical property relationships. We will provide the reader with an overview of the perspectives and challenges of open-shell light-emitting radicals and discuss what to do to solve the remaining problems in the future and prepare organic radicals for the challenges in emerging quantum technological applications.

Review

Triarylmethyl monoradicals

The importance of symmetry in triarylmethyl radicals

Gomberg’s radical is unstable at room temperature and dimerizes quickly to a closed-shell molecule. Only at temperatures as low as 90 K, the monoradical is stable, allowing recording of the absorption and emission spectra [30]. Symmetrical halogenation of the triphenylmethyl (or trityl) unit increases stability of the molecule, compared to the parent unsubstituted trityl radical first reported by Gomberg (see TTM and PTM in Figure 1a) [31]. Gomberg’s radical emits light in the green region of the visible spectrum, which is shifted bathochromically by substituting the ortho- and para-positions of the trityl phenyl rings with halogens. However, all symmetrical halo-trityl radicals exhibit low ϕ, usually below 3%. Such perhalo- or nonahalo trityl radicals exhibit a D₃ propeller symmetry, which allows assigning of individual orbital geometries (see Figure 1b). Furthermore, such radicals follow the alternant hydrocarbon rule of the Hückel theory [32,33], which dictates that the highest singly occupied molecular orbital (SOMO) is non-bonding and energetically located exactly between the highest doubly occupied molecular orbital (HDMO) and the lowest unoccupied molecular orbital (LUMO) (see Figure 1b) [19].

In other words, in such D₃ symmetrical alternant hydrocarbons the HDMO–SOMO and the SOMO–LUMO energy gaps are identical and their respective transitions exhibit identical transition dipole moments [19,32,33]. For the |D₁⟩ transition these two degenerate transitions mix in an out-of-phase fashion leading to the observed weak absorption at 544 nm (see Figure 1b and c). When looking at the Mulliken symmetry labels, one realizes that the |D₁⟩ transition is in fact symmetry forbidden. By contrast, in-phase mixing of the transitions for the |D₂⟩ transition leads to strong absorption at 374 nm, a transition that is symmetry allowed (see Figure 1b and c).

In TTM, the ϕ is independent of the excitation wavelength (see Figure 1c). Excitation at 374 nm or 544 nm both lead to fluorescence with an identical fluorescence decay profile and identical ϕ of ≈2% (see Figure 1c). This behavior hints at the fact that the relaxed excited state, from which the emission occurs, is the same for excitation at 374 nm and 544 nm. Therefore, the higher energy for excitation to the D₂ state must quickly be lost during relaxation to the relaxed D₁ state, rendering the emission indistinguishable from the higher energy excitation.

While for TTM and PTM there is no transient absorption data to further elucidate the excited state dynamics, there is evidence for this fast relaxation in donor-functionalized TTM radicals [26].

Moreover, transient absorption has been employed to elucidate the formation of a non-luminescent side-product in trityl radicals. During photodegradation, two halogens are lost and two phenyl rings planarize to fuse to a fluorenyl unit, rendering the radical non-emissive [35,36].

According to “valence shell electron pair repulsion” (VSEPR) theory, one would expect a geometrical change of the TTM molecules from D₃ to a pyramidal C₃ symmetry upon excitation. However, for steric reasons the molecule remains mostly planar in the excited state [37]. As a result, we observe weak emission in the yellow to red spectrum, because the respective transition remains symmetry forbidden.

Circularly polarized photoluminescence

PTM has been developed prior to TTM, as the first stable triphenylmethyl radical [38,39]. In contrast to the Gomberg radical, the perchlorination prevents dimerization through the para-position. Moreover, the chlorine substituents in the ortho-positions twist the phenyl rings into a propeller conformation and out of the sp²-hybridization plane of the central methine radical unit. Now, the chlorine substituents screen the hemispheres above and below this plane, protecting the unpaired electron in the p-orbital from oxidation or other detrimental degradation. The weak emission of PTM with ϕ of 0.7% peaks at 609 nm (in tetrachloromethane (CCl₄)) [40]. The racemic mixture of right- and left-handed propellers can be resolved by chiral high pressure liquid chromatography (HPLC) into the P- and M-enantiomers, respectively [40,41]. However, due to the low racemization barrier of only about 22 kcal mol⁻¹, the enantiomers racemize within minutes at room temperature. TTM is synthesized with slightly improved ϕ of 2% and a blue-shifted emission compared to PTM with a maximum photoluminescence wavelength λ_em = 569 nm (in CCl₄) [40,42]. The racemization barrier remains almost identical at 21.1 kcal mol⁻¹. Both PTM and TTM exhibit circularly polarized emission (CPL) for the time that they remain in their enantiopure state. The g_lum as a measure for the strength of CPL is of order 8 × 10⁻⁴ for PTM and 5 × 10⁻⁴ for TTM.

Mixed halide triarylmethyl radicals

Substitution of all para-positions in PTM with iodine atoms yields the 3I-PTM radical with a red-shifted emission compared to PTM, peaking at 625 nm in tetrahydrofuran (THF) (see Figure 1a). Unfortunately, the photostability of para-iodinated radicals is too low to record ϕ in solution [43]. However, when the 3I-PTM radical is incorporated into a crystalline matrix of the closed-shell 3I-PTM-H compound, the radical is stabilized and a remarkably high ϕ of 91% can be recorded. This high value is explained by a reduction of the non-radiative pathways by inclusion of the 3I-PTM into the rigid 3I-PTM-H crystal, and a charge transfer (CT) from the high bandgap 3I-PTM-H matrix to the 3I-PTM radical, which is further supported by the heavy atom effect of iodine, that also allows intersystem crossing (ISC) between triplet states in the matrix and the emissive doublet states of 3I-PTM. Interestingly, functionalization of all three para-positions in TTM with chalcogens in the form of aryloxy- and aryl thioethers leads to improved photostability (see Figure 1a). While the triaryl oxyether-TTM does not enhance the ϕ, triaryl thioether-TTM exhibits a ϕ of up to 37.5% (in cyclohexane). Due to the stronger electron donating effect of the chalcogens compared to halogens, the emission is shifted to lower energies with λ_em = 625 nm for the triaryl oxyether-TTM and λ_em = 655 nm for the triaryl thioether-TTM (in dichloromethane (DCM)) [44]. The stronger bathochromic shift and the loss of vibrational features in the photoluminescence spectrum point towards a CT excited state in the triaryl thioether-TTM, which could explain the strong increase in ϕ; however, no further information is given to support this claim.

While substitution of all para-positions with hetero-halogens or chalcogens does not induce a different symmetry in the ground state of the molecule, substitution of only one of the para-chlorines of PTM with bromine or iodine should break the symmetry; however, no effect on the absorption spectra and especially on the lower energy |D₁⟩ transition has been reported [45]. Interestingly, substitution of one of the para-chlorines in TTM by iodine (I-TTM) has been reported to enable Pd-catalyzed cross-coupling, allowing functionalization with a much broader variety of donors (and even acceptors) than is possible through a radical-mediated nucleophilic aromatic substitution (S_RN1, see also below) [3,46,47]. The I-TTM has a maximum emission at λ_em = 578 nm and a ϕ of 3% (in cyclohexane), indicating that the symmetry does not seem to be altered sufficiently to evoke a noticeable improvement of the ϕ [48]. This also holds true for mono-para-substitution with boronic acid derivatives, yielding λ_em = 580 nm and ϕ of 1–3% (in dichloromethane) [49]. Substituting one or two of the 2,4,6-trichlorinated rings in TTM with 2,4,6-tribromophenyl units shifts the photoluminescence systematically towards the red (see Figure 2a–c) [50]. The ϕ also decreases systematically, demonstrating that also more pronounced mixed halogenation does not significantly change the symmetry of the locally excited (LE) state. The tris(2,4,6-tribromophenyl)methyl (TTBrM) radical exhibits λ_em = 593 nm and ϕ of 0.8% (in dichloromethane-solution, at room temperature) [50,51].

Functionalization of TTM in the para-position has also been achieved with a pseudo-halide, namely a nitrile group. While the absorption and emission spectra are slightly bathochromically shifted for mono- and bis-para-nitrile TTM radicals, successive nitrilation increases the ϕ to 4.6% and 7.4% (in cyclohexane) [53]. This improvement is most likely induced by symmetry breaking, resulting in excited states with some charge-transfer character. Moreover, the photostability of such nitrile-bearing TTM equivalents is greatly enhanced.

Interestingly, much like TTM, TTBrM exists also as enantiomeric propellers; however, in TTBrM radicals the resolved enantiomers are stable at room temperature, making these molecules interesting as chiral emitters with g_lum of 7 × 10⁻⁴, despite their low ϕ (see Figure 2a) [50,51].

Perfluorinated triphenylmethyl radicals have been reported as well; however, neither UV–vis nor photoluminescence data are available [54]. Mixed perhalogenated triphenylmethyl radicals with fluorine, chlorine, and bromine substituents have been synthesized in an attempt to break the symmetry. Here, the molecule consists of a pentalchloro phenyl and two tribromophenyl units (PCl-TBr₂M) [55], or with two p-bromotetrafluorophenyl rings (PCl-TFBr₂M) (see Figure 2d–f) [52]. DFT calculations for these mixed per- and trihalophenylmethyl radicals and their orbitals show a change from the D₃ symmetry as observed in TTM to a C₂ symmetry in the orbital distribution in the ground state. In spite of this break in symmetry to C₂ – where all relevant transitions will be allowed – an enhancement of the respective absorption bands or an improvement in the ϕ has not been observed. However, one can observe a loss of the vibronic features in the fluorescence signal, indicating that the emission occurs from a CT state, in agreement with the DFT orbital distribution in the ground state geometry (see Figure 2e for different orbital location in HDMO and SOMO). Interestingly, successive bromine substitution decreases the spin–lattice relaxation time T₁ of the radical electron. This is due to increased spin–orbit coupling in the brominated species. By contrast, the phase memory time T_m becomes longer for successively brominated radicals, visible from the concurrent spectral broadening in electron paramagnetic resonance (EPR). This enables improved homogeneity in quantum phase evolution and superior T_m, rendering brominated trityl radicals interesting for quantum memory applications [55].

Symmetry in N-heteroaryl-functionalized diphenylmethyl radicals

Another approach to affect the symmetry in triarylmethyl radicals is by touching the triphenylmethyl scaffold itself, rather than only its substitution pattern. A variety of studies have been concerned with the pyridine-diphenylmethyl (PyBTM) motif, which has one of the para-carbons replaced by a nitrogen (see Figure 3) [56]. Surprisingly, these molecules display greatly enhanced photostability compared to PTM and TTM. The ortho-positions on the pyridyl ring have been substituted with fluorine, chlorine, and bromine moieties, and it was found that the change in substitution affects the emission color from yellow in case of fluorine, to orange for chlorine, and to red for bromine [6,57]. This shift can be explained by the decreasing electronegativity of the halide substituents. The more electronegative fluorine will reduce the HDMO energy more strongly than the bromine, while the SOMO remains energetically almost unaffected, explaining the higher energy gap with increasing electronegativity.

Moreover, the photostability increases from fluorine to bromine-substituted PyBTMs. Higher photostability has only been observed in a bispyridyl-phenylmethyl radical (Py₂MTM) [58]. While PyBTM is 70 times more stable than TTM, the photostability in Py₂MTM is increased 3000-fold. The nuclear spin of the nitrogen in PyBTM and Py₂MTM can couple with the radical electron spin, leading to EPR spectra with hyperfine structure [58].

Effectively, the substitution in ortho-position has strong electronic as well as steric effects, allowing to tune the emission properties of such X₂PyBTM molecules [6]. The ϕ is highest for the F₂PyBTM with 6%, Cl₂PyBTM has 3% and Br₂PyBTM 2% [6,57]. The increase in ϕ for the most electronegative substituent might be explained by a somewhat more pronounced CT excited state, due to the stronger electron-withdrawing character of the fluorine substituent. When gold atoms are coordinated to the pyridine nitrogen, a ϕ as high as 8% has been observed [57]. The reason for this increase in ϕ to 8% for Au-Cl₂PyBTM and 20% for Au-F₂PyBTM is unknown, but the increase in the presence of a heavy atom might point at an improved ISC, opening up more pathways for radiative relaxation.

When one couples mesityl units as weak donors to the para-positions of the two chlorophenyl rings of a F₂PyBTM, the ϕ is improved to 69% (in Mes₂F₂PyBTM) (see Figure 4) [59]. The DFT studies suggest that there is a clear CT excited state, where the hole will reside on the mesityl and phenyl units (HDMO) and the electron resides on the PyBTM core (SOMO) (see Figure 4b).

Instead of pyridine also carbazole (Cz) units have been coupled to produce N-carbazolyl-bis(2,4,6-trichlorophenyl)methyl radicals (CzBTM) (see Figure 5a). ϕ is highest at λ_em = 697 nm with 2% (in cyclohexane) [10]. DFT calculations display that the Cz unit acts as an electron-donor moiety, facilitating a CT excited state with a clear C₂ symmetry (see Figure 5b). Similarly, a biscarbazolylanthracenylmethyl radical has been reported; however, the ϕ has been too low to be determined [60]. Apparently, in these symmetry-broken triarylmethyl radicals there are other non-radiative relaxation pathways at play, reducing the ϕ.

Summary: triarylmethyl monoradicals

In conclusion to this section, one has to accept that some of the transitions in D₃-symmetric molecules are forbidden. While the transition to the |D₁⟩ state is forbidden due to out-of-phase mixing of the degenerate HDMO–SOMO and SOMO–LUMO transitions (as explained by the alternant hydrocarbon rule), the in-phase transition to the |D₂⟩ state is allowed, as seen in the respective UV–vis absorption spectra of these compounds.

Breaking of the symmetry for the |D₁⟩ transition by incorporating a donor moiety, leads to enhanced intensity as reflected by growing absorption coefficients ε with increasing donor strength (see Table 1). Replacing one of the phenyl rings for carbazole in triarylmethyl radical leads to much-increased transition dipole moments M_|D1⟩ from ≈1.2 D to 3.0 D, accounting for the much-increased CT character of the |D₁⟩ state (cf. TTM and Cz-BTM in Table 1).

However, for the emission of all triarylmethyl radicals, the symmetry plays less of a role. While the excited state geometry changes to the C₂ symmetry, where all relevant transitions are allowed, the ϕ varies between <1% and 69%.

Therefore, the poor emission performance in triarylmethyl radicals seems to be primarily governed by the CT strength of the excited state. For radicals with more LE contribution to the |D₁⟩ state, dark quartet states might play a more prominent role in the non-radiative relaxation than currently acknowledged in the literature. The quartet state in triarylmethyl radicals – which is analogous to the dark triplet relaxation pathway in closed-shell emitters – might contribute to non-radiative excited-state relaxation (because of spin selection rules forbidding the direct transition from the quartet to the doublet state). While for TTM and PTM substituted with weak donors such energetically low-lying quartet (Q₁) states have been observed in TD-DFT calculations [20,62] and EPR spectroscopy [63], there are no such investigations reported for the pure TTM and PTM systems. Also, the widespread assumption that the Q₁ in triarylmethyl radicals is typically higher in energy than the D₁ state, might not always hold true, as the polarity of the environment, for example solvents or matrices, might shift the respective energy levels. In the future, the tuning and energetic positioning of the quartet states should receive more attention to improve the photoluminescence performance of triarylmethyl radicals. Alternatively, there might be strong vibronic interactions, which could also contribute to non-radiative decay of the excited state in trityl radicals. Depending on the pattern of functionalization, the frequency of such vibrational modes might be shifted, or the vibrations might be suppressed altogether. These non-radiative decay pathways could explain the variable performance of trityl radicals and should be further investigated in the future.

In view of future applications in quantum technology, further effort should be directed at ways to increase coherence time, as was done in the study of increasing bromination of trityl radicals [55]. Moreover, such systems would also benefit from strategies to increase their fluorescence, as this would potentially allow to read out their spin state optically.

Donor-functionalized triarylmethyl monoradicals

Mono-functionalized triarylmethyl radicals

Functionalization of the triphenylmethyl radical with electron-donating Cz, has been reported long before the above discussed Cz-BTM (see Figure 6). In fact, TTM-Cz is the first donor-functionalized triarylmethyl radical that has been reported and immediately showed very high ϕ between 88–91%, with λ_em = 628 nm (in cyclohexane, the original report only claimed 53%, which was determined using a relative method [61,64]) [65,66]. Like in the heteroaryl-BTM radicals, the donor moiety produces a CT excited state, where the hole (h⁺) resides on the Cz unit and the electron (e⁻) resides on the TTM unit. The previously discussed low energy absorption becomes somewhat more pronounced in TTM-Cz, which is sensible as TTM-Cz exhibits a C₂ geometry in the ground state, where all relevant transitions will be allowed. However, CT transitions typically exhibit a low oscillator strength and therefore it is not surprising that the corresponding absorption is not strongly enhanced by attachment of the Cz unit [19,61].

The same appears to be true for donor functionalization of Cz-BTM. Attachment of an acridine-derived donor to the para-position of one of the phenyl units in the BTM subunit, boosts the ϕ to 55% (in toluene) [67]. Quantum chemical calculations corroborate that the CT excited state is much more pronounced in acridine functionalized Cz-BTM than in pristine Cz-BTM, with a charge separation distance in the excited state of 0.68 nm versus 0.21 nm, respectively.

Quantum chemical investigations have also been employed to understand the strong emission observed experimentally in TTM-Cz. One explanation is based on intensity borrowing from higher excited states. While first hypotheses suggested a vibronic coupling between the D₁ and D₂ states on the TTM moiety [19], recent calculations propose vibronic intensity borrowing from higher excited states as high as D₇, which represent LE states with high oscillator strengths that are typically in resonance with the LE D₂ state [68]. However, elsewhere it was found that the oscillator strength of such resonant higher lying states may be insufficient for substantial intensity borrowing that could explain the high ϕ [21].

The role of Q₁ states as a dark deactivating pathway has been investigated by DFT analysis. The position of the spin-quartet is in part dictated by the triplet state of the donor moiety. For example, strong donors like benzocarbazole exhibit low lying triplet states, which in combination with the TTM unit lead to the Q₁ state being reduced in energy below the D₂ states [20,69]. Here, the Q₁ state remains energetically above the D₁ state so that it does not seem to affect the ϕ, but one might consider other donor geometries and substitution patterns, where the Q₁ energy is reduced even further, so that it interferes with the excited-state relaxation.

Quantum chemical investigations have also brought forth that the dihedral angle between the TTM radical plane and the carbazole donor increases when exciting the molecule from the D₀ ground state to the excited D₁ state. In the D₁ state the Cz is aligned almost perpendicular to the TTM plane, which will stabilize the charge transfer state [37]. This substantial conformational change between the ground and excited states could also be responsible for the comparably long fluorescence lifetimes τ, which are in the range of 30–50 ns, which is long even for CT excited states [68]. The steric demand as well as electronic effects will cause the Cz-unit to twist out of conjugation almost completely with the TTM radical core plane, leading to marginal orbital overlap between the D₀ and D₁ states. The reason for this increase in fluorescence lifetime τ is not completely understood; however, if the emission involves a CT state and the orbital overlap between D₁ and D₀ is small, then this could lead to stable D₁ and long τ [69-71].

Interestingly, the Cz-functionalized tris(2,3,5,6-tetrachlorophenyl)methyl radical (DTM-Cz) has been synthesized, in which the chlorines in the meta-positions of the phenyl ring sterically arrest the Cz unit in a position perpendicular to the DTM plane (see Figure 6) [47]. This geometry resembles the excited state in TTM-Cz, while a change in the dihedral angle between donor and radical plane is almost impossible – meaning that the dihedral angle is almost identical in the ground and excited state geometries. Surprisingly, this leads to a decrease in the ϕ to 2%, while the emission wavelength is at 700 nm (in cyclohexane). Moreover, DFT calculations display that the Cz-donor moiety is not involved in the frontier orbitals and the excited state resembles an LE state, which is almost exclusively located on the triphenylmethyl fragment, which might explain the similar ϕ to PTM (0.7%) and TTM (2%). This suggests that sufficient overlap between the D₀ and D₁ charge transfer states is required to achieve strong ϕ. Interestingly, when 3PCz is connected to PTM (PTM-3PCz) the ϕ is enhanced to 57%, as opposed to TTM-3PCz with a ϕ of 27% (see Table 2) [72,73]. Here, the slight restriction in rotation around the bond between the radical plane and donor seems to improve the radiative relaxation yield. The same is observed in triphenylamine (TPA) and phenylcarbazol (PhCz) where the ϕ is improved when connected to PTM rather than the TTM radical moiety. These results point at the involvement of the orbital overlap integral between the D₀ ground state and the D₁ excited state playing a role in determining the ϕ of donor-functionalized triarylmethyl radicals.

To provide evidence that this effect is not due to the changed electron accepting strength, TTM radicals with additional chlorination only at the phenyl ring, to which the donor moiety is connected have been synthesized. Also here, a strong increase of the ϕ compared to the donor-functionalized TTM radicals has been observed (see Table 2). Analysis of the Huang-Rhys factors delivered that the meta-chlorinated phenyl units do indeed restrict the rotation of the donor. Moreover, the reduction of the LE character of the D₁-excited state and a reduction of coupled vibrational modes in the regime from 1000–2000 cm⁻¹ seem to decrease the non-radiative pathways, while the rates for emission remain almost unchanged between the donor-functionalized TBTM and TTM series [73].

This effect has also been investigated by excited state vibrational spectroscopy, where (among other compounds) TTM-TPA and TTM-3PCz have been investigated [74]. The donor-functionalized trityl molecules exhibit only few vibrational modes in the above mentioned spectral range, leading to relatively high ϕ at long wavelengths (≈800 nm). These molecules seem to overcome the typical restriction of the energy gap rule, where the ϕ of conventional fluorophores deteriorates in the near-infrared region.

Moreover, the donor strength plays an important role for the ϕ. A slight adjustment of the donor strength of TPA has been investigated in PTM-TPA by introducing electron-donating and electron-withdrawing units on the para-position of the free phenyl rings in TPA (see Figure 7). For chlorine substituents an optimized ϕ of 38% with λ_em = 763 nm could be achieved (in cyclohexane) [71]. Units that are more electron-donating increase the donor strength of TPA, while electron-withdrawing units will reduce the donor strength of TPA, both effects lead to decreasing ϕ. This observation has been explained by the potential of the TPA unit to stabilize the positive charge that would reside here after excitation and formation of the CT state [71]. In a similar fashion also electron-donating and withdrawing units on Cz-donors in TTM-Cz have been screened; however, the ϕ could not be improved beyond that of TTM-Cz (see Figure 7) [21,64,65,75].

An expanded meta-analysis of unprecedented and reported TTM-based radicals functionalized with Cz-derivatives and other N-coupled donors has provided further insight into the effect of the donor strength on the emission wavelength maximum λ_em and the ϕ (see Figure 8) [63].

In the meta-analysis the donor strength is approximated by the ionization energy (IE), which has been determined using DFT calculations. Plotting of the maximum emission wavelength and the ϕ versus the calculated IEs produces a systematic increase for λ_em and a bell-shaped distribution for ϕ. The bathochromic shift in λ_em has previously been described to result from the better stabilization of the CT excited state for stronger donors, and therefore a stabilization of the highest occupied molecular orbital (HOMO) when only considering the acceptor moiety (see also reduction in energy from weak to strong CT in Figure 9) [62,71]. The bell shape of the ϕ dependency on the donor strength could be explained by employing a three-state model, in which one assumes that the excitation of the donor-functionalized TTM radical occurs adiabatically into an LE state, followed by relaxation into the CT D₁ state, from where emission back to the D₀ ground state may occur.

Weak donors will exhibit a high energy transition state to crossover from the excited LE to the CT state (large ΔG_CT^‡, point 1 in Figure 9). In absence of any excess energy, the LE will relax non-radiatively to the ground state without crossing over to the CT state. The fact that excited LE states relax non-radiatively has been discussed above for TTM, PTM, as well as for DTM-Cz, all of them featuring low ϕs. Interestingly, for the very weak benzotriazole unit a quartet state could be identified after excitation, hinting at the type of non-radiative decay pathways in these molecules [63]. For medium strong donors the Gibbs energy of activation ΔG_CT^‡ for crossing over into the CT state is low, and emission can occur from here with high ϕ (see point 2 in Figure 9). For strong donors, ΔG_CT^‡ is close to 0 allowing almost barrier-free transition into the CT state. However, here a conical intersection with the ground state can occur, which enables non-radiative relaxation to the ground state and therefore low ϕ (see point 3 in Figure 9).

This simple three-state model can explain a large variety of different donor–acceptor radical systems; however, it breaks down for very large donor systems. In a dendronized carbazole donor, where the Cz units are coupled to the para-positions with respect to the N-position (first generation: TTM-Cz, second generation: TTM-tercarbazole (G2TTM), third generation: hepta-carbazole-functionalized TTM (G3TTM), fourth generation: pentadeca-carbazole-functionalized TTM (G4TTM)) (see Figure 10) [76]. Typically, one would expect the donor strength to increase with extended electron donation throughout the dendronized carbazole donor; however, this is only true for G2TTM, which is further red-shifted and reduced in ϕ compared to TTM-Cz (cf. compounds 31 and 33 in Figure 8a and b). Higher generations (G3TTM, G4TTM) exhibit hypsochromically shifted emission maxima compared to the G2TTM and increased ϕ (52% and 63% respectively (in cyclohexane)) (see Figure 10). This effect can be explained by recognizing that the donor dendron is large and its inertia prevents fast conformational changes between the D₀ and D₁ states. This inertia is also reflected in the increasing fluorescence lifetimes, which increase from τ = 17.3 ns for G2TTM, to τ = 48.8 ns for T3TTM and τ = 120.0 ns for G4TTM. Moreover, the counterintuitive effect of an increasing D₀ to D₁ energy gap and ϕ with growing donor strength (from G2TTM to G4TTM) has been explained by a reduction of non-radiative relaxation processes, due to the decrease of the electron–electron repulsion in the occupied dendron orbitals.

In a similar fashion, a simple extension of the Cz donor structure to benzocarbazole (BCz) and dibenzocarbazole (DbCz) follows the trend of the above described three-state model (see Figure 11). However, further extension to aza[7]helicenes also leads to contradiction with the model (cf. compounds 35 and 36 in Figure 8a and b). The ϕs of TTM-BCz and TTM-DbCz decrease in accordance with the increasing strength of the respective donors to 61% and 3%, respectively (in cyclohexane) [77]. By contrast, further extension to TTM-DNC and TTM-DPC leads to increased ϕs despite bathochromic shifting of the emission wavelength. Here, the strain in the donor molecule might lead to reduced electron–electron repulsion in the extended systems improving the emission characteristics [66].

Circularly polarized photoluminescence

The TTM-DNC and TTM-DPC with their helical donors are chiral and can be separated for the axial chirality of the helicene donor unit (see Figure 11). Chiral chromatography provides access to all four stereoisomers, as both, the helicene and the TTM unit, are chiral (as discussed above). However, the TTM propellers racemize quickly so that effectively one receives the diastereomers with the respective helicene chirality, and a racemic mixture of TTM propellers. Surprisingly, only the TTM-DNC showed acceptable CPL with g_lum = 5 ×10⁻⁴, whereas the TTM-DPC, despite its respectable ϕ, did not exhibit appreciable CPL. While the g_lum is not higher than for the enantiomerically resolved TTM propellers, the TTM-DNC diastereomers are stable and in contrast to the TTM propellers, they do not racemize further. Moreover, the good ϕ leads to a respectable CPL brightness B_CPL = 0.25 M⁻¹cm⁻¹, compared to 0.0007 M⁻¹cm⁻¹ for TTM [66].

Other examples of introducing fixed chiral units beyond the racemizing TTM propeller yielded g_lum as high as 1.51 × 10⁻³, for chiral emitters at 5 wt % dispersed in a matrix of polymethylmethacrylate (PMMA). Unfortunately, these pillarene-bridged TTM radicals with a TPA donor did not exhibit CPL in solution [78]. This report signifies that CPL is more easily achieved in the solid phase, where even racemic mixtures of the interconverting PTM-PhCz, TTM-3PCz, and TTM-Cz propellers can exhibit CPL, when doped into a PMMA together with a chiral gelator or when in presence of a chiral (liquid crystalline) mesogen. In these cases, g_lum in the range of 10⁻³ and 4 × 10⁻² was obtained respectively [79]. In the latter case, alternation of an electric field would realign the mesogen allowing for reversible switching between CPL and depolarized emission.

Multi-donor-functionalized triarylmethyl radicals

Before iodinated TTM derivatives became available – enabling mild reaction conditions for precise C–C and C–N cross-coupling reactions only at the site of the iodine – donors were attached to TTM by radical-mediated nucleophilic aromatic substitution S_RN1. The leaving group is the para-chlorine atom, of which a TTM molecule has three. It is therefore less than surprising that during this S_RN1 the desired mono-substituted donor-functionalized TTM is obtained next to substantial amounts of the bi- and tri-functionalized units. In case of S_RN1 with Cz as a donor, the TTM-Cz, TTM-Cz₂, and TTM-Cz₃ are obtained. TTM-Cz₃ exhibits D₃ symmetry, for which we have previously discussed that certain transitions are forbidden. However, this does not reflect in the ϕs, which for the TTM-Cz₃ has been determined to be 52% whereas TTM-Cz₂ has delivered 54% and TTM-Cz has been determined to be 53% (while more recent studies have produced ϕs between 88–91%) [3]. By contrast, the maximum emission wavelength λ_em is not constant and shifts bathochromically from λ_em = 628 nm, 651 nm, to 654 nm for increasing donor functionalization (all reported in cyclohexane). Similar results have been obtained for a series of TTM-3PCz₂ and TTM-3PCz₃ [80]. These data suggest that the ground state symmetry does not play a dominant role here and in fact natural transition orbital (NTO) calculations of a related tris(2,7-dinitrilecarbazole)-TTM (TTM-CzCN₃) in its excited state geometry show that the excited state reduces to a D₂ symmetry, where all relevant transitions are symmetry allowed [21]. The nitrile units are electron withdrawing, therefore reducing the donor strength of the Cz unit and the ϕ is augmented to 76%, compared to TTM-Cz₃. TTM-CzCN₃ shows a clear CT state in the D₁ geometry, with quite some orbital overlap between the hole (residing on two of the dinitrile-Cz units) and the electron (residing on the TTM moiety) across the central methyl unit. Such clearly symmetry broken CT states have also been discussed for tri(phenylethynyl)-substituted PTM radicals [81] and trimesityl-functionalized TTM (TTM-Mes₃) radicals [82,83]. The TTM-Mes₃ is of high interest as the mesityl unit is an extremely weak donor (and TTM-Mes₁ has only a ϕ of 1% in toluene) and will not by itself induce a strong charge transfer as potent donors like Cz do. In DTM-Cz, the rotationally restricted Cz produces such a CT state even in its ground state, in solvents of high polarity [47]. However, upon excitation of TTM-Mes₃ one of the mesityl groups twists further out of the plane of the TTM, while the other two units acquire a more planarized structure with the central TTM unit. These DFT results show that also TTM-Mes₃ performs symmetry breaking upon excitation, which leads to a substantial ϕ of 23% (in toluene) [82].

Summary: donor-functionalized triarylmethyl monoradicals

Donor functionalization of trityl radicals induces a CT excited state, which lifts any symmetrical constraints on the emission pathway. However, depending on the strength of the donor, the energies of the states (especially SOMO and LUMO) will be shifted, which can lead to detrimental relaxation pathways through dark quartet states or non-radiative rotational and vibronic relaxation. Typically, the exited-state geometry of donor-functionalized trityl is different from the ground state with the donor unit being twisted into a more or less perpendicular arrangement to the trityl plane. This structural change between excited and ground state entails relatively long fluorescence lifetimes. Future research should be directed towards the challenge of reaching high ϕ, while reducing τ. To date, there is no organic laser reported that employs organic radicals as a gain medium – the reason for this might lie in this discrepancy. For an organic laser one would require high ϕ but short τ.

Diradicals based on the triarylmethyl motif

Molecules that have two unpaired electrons are coined diradicals [84] and in some more specific cases biradicals [85], in which the two electrons act nearly independent of each other. Diradicals that do exhibit some degree of delocalization and combination of the radical electrons can also be called diradicaloids. Since we discuss a variety of different molecules with two unpaired electrons, we will use the more general nomenclature of diradicals here – accepting that some of the described molecules would fall under the more specific and accurate terms biradical or diradicaloid. Diradical is the most widely preferred termination in the community, when the general concept and class of molecules with two unpaired electrons is discussed.

Combination of two trityl motifs to produce diradicals, is a synthetic challenge that is almost as old as the realization of the triarylmethyl radical. Like the triarylmethyl radical or Gomberg’s radical [31], the resulting diradicals typically carry the name of their discoverers. Coupling of two trityl radicals through their para-positions results in the Chichibabin hydrocarbon (e.g., TTM-TTM, PTM-PTM) [86]. If an additional phenyl ring is incorporated between the trityl units, we obtain Müller’s hydrocarbon (TTM-PhTTM) [87]. When two of the trityl radicals overlap in one ring and the radical electrons can delocalize in a quinodal structure because of the para-linkage, these molecules are termed Thiele’s hydrocarbons (e.g., TTH, PTH) (see Figure 12) [88]. These molecules, in which the electrons can be formally delocalized are termed Kekulé diradicals (diradicaloids). By contrast, if the methylene radicals are connected through the meta-positions of the central phenyl ring, Schlenk-Brauns (m-PTH) diradicals are obtained where no Kekulé-conjugation between the radical centers is possible (see Figure 13) [89]. While the para-coupled Thiele, Chichibabin, and Müller radicals can acquire a closed-shell quinodal electronic structure, diradicals with broken Kekulé-conjugation exhibit much stronger diradical character. In accordance with the above-described nomenclature, these diradicals are termed non-Kekulé diradicals.

This tendency of diradicals to form a closed-shell electronic configuration can be described using the diradical index y₀, which corresponds to a closed-shell system for y₀ = 0 and a purely open-shell diradical for y₀ = 1. In the open-shell electron configuration, the diradicals can acquire a singlet state with open-shell but antiparallel spins (total electronic spin, S = 0) or a triplet ground state with parallel spins and S = 1 for the diradical molecule. Whether a molecule has a singlet or triplet ground state can be expressed by the energy difference between the first singlet and first triplet states ΔE_ST. When the energy difference is negative, ΔE_ST < 0, the diradical exists in a singlet ground state. When the energy difference is positive ΔE_ST > 0, the diradical has in a triplet ground state. Often the energy difference is very small, so that thermal effects come into play and higher lying electronic states can be populated at room temperature.

In the following, we will discuss such diradicals and we group the molecules in accordance with their type of conjugation.

Kekulé-conjugated diradicals

Trityl radicals and trityl-derived diradicals have been reported to be instable especially under light irradiation and in the presence of oxygen. As for the monoradicals, also chlorination appears to be a favorable route to render the different diradicals stable. For the non-chlorinated and the perchlorinated (PTH) Thiele radicals, the ground states have been confirmed to be singlet states, with little to no diradical character (y₀ = 0) [90,91], while more recent investigations have produced y₀ = 0.3 for the non-chlorinated Thiele diradical [92]. Interestingly, the Thiele hydrocarbon without chlorination in the meta-positions of the four peripheral phenyl-rings (TTH), exhibits higher y₀ of up to 0.4, indicating the mesomeric equilibrium to be further on the open-shell side (see Figure 12a) [92]. Also the perfluorinated version of the Thiele hydrocarbon (TFC) has comparable diradical character of y₀ = 0.35 [93]. This increased diradical character has been attributed to increased structural flexibility in TTH and TFC. Their C–C bonds are longer than in the non-chlorinated Thiele radical, and TTH, and TFC are not as sterically congested as PTH. In TTH, the photoluminescence shifts with increasing solvent polarity while the ϕ increases from 69% in cyclohexane (λ_em = 691 nm) to 83% in chloroform (CHCl₃) and 84% in toluene (λ_em = 716 nm) (see Figure 14a). This shift in the emission wavelength points towards a CT excited state. Apparently upon excitation, symmetry breaking charge separation [94] occurs leading to a (zwitterionic) CT excited state with a diarylmethylene unit acting as a donor and a trityl unit acting as an acceptor [92]. This symmetry breaking charge separation seems to be supported in solvents of higher polarity. By contrast, when the polarity of the solvent is increased beyond that of toluene, the ϕ drops to about 10% in THF (λ_em = 785 nm), which is typical for CT excited states that are stabilized by polar solvents (see Figure 14a) [92].

Similar observations can be made for the Chichibabin congeners PTM-PTM and TTM-TTM (see Figure 12a). The perchlorinated PTM-PTM exhibits a strongly twisted diphenyl bridge and therefore almost no conjugation between the two radical centers (y₀ = 0.998) (see Table 3) [90,95]. The negative ΔE_ST indicates a singlet ground state; however, singlet states should not produce EPR signals (see Figure 12b). The yet obtained EPR signal indicates that the triplet state is thermally accessible, which is reasonable considering the small ΔE_ST of <0.1 kcal mol⁻¹ (as determined by us on the UB3LYP/def2-SVP level of theory as part of this review, see Table 3). Cooling leads to a reduction of the intensity of the central EPR signal, fine structure, and significant diradical anisotropy, indicating that the triplet state becomes less and less populated (see Figure 12b) [95].

By contrast, the TTM-TTM analogue without chlorine substitution in the meta-positions of the phenyl rings has a perfectly flat biphenyl bridge and therefore a much-reduced diradical index (y₀ = 0.58) [97]. The increased conjugation of the flat diphenyl bridge in TTM-TTM is responsible for the reduced diradical character and leads to a shift of the emission into the near-IR (λ_em = 780 nm, ϕ = 0.8% in toluene). While the ϕ of TTM-TTM is low, no photoluminescence has been reported for PTM-PTM. ΔE_ST of TTM-TTM is at −1.22 kcal mol⁻¹ indicating a singlet ground state as well; however, the value is larger than for PTM-PTM, requiring heating to observe increased population of the triplet state and strengthening of respective EPR signals [97].

Further extension of the hexadeca-chlorinated diradicals (TTH, TTM-TTM) yields Müller’s TTM-PhTTM diradical (see Figure 12a) [96]. The additional phenylene ring disturbs the conjugation between the radical centers sufficiently to increase the diradical character to y₀ = 0.9. DFT corroborates that the three bridge phenylenes are twisted against each other by about 35°. ΔE_ST has been determined from EPR measurements to be −1.51 kcal mol⁻¹, whereas DFT gave −0.11 kcal mol⁻¹. This ΔE_ST interval indicates that the triplet state is thermally accessible, represented by the improving EPR signal with increasing temperature (see Figure 12c) [96].

Increasing the distance between the radical centers even further by extending the bridge as in the case of bPTM, yields a diradical with full diradical character y₀ ≈ 1 and minute ΔE_ST of order 10⁻⁷ kcal mol⁻¹ (see Figure 12a) [98]. No photoluminescence has been reported for bPTM; however, this diradical shows extremely long coherence times of order T₁ = 1 s (thermalization, spin lattice relaxation) and T_M ≈ 67 µs (phase memory time), both determined in carbon disulfide as a solvent and at low temperatures of 7 K and 15 K, respectively. These staggeringly long coherence times showcase the potential of precisely designed diradicals for molecular quantum applications [98].

Non-Kekulé diradicals with broken conjugation

The non-Kekulé equivalent to the Thiele diradical is represented by the Schlenk–Brauns diradical. The more stable perchlorinated version of this molecule (m-PTH) has been reported in a set of publications [99-101]; however, while this body of work reports the most extensive characterization of these molecules, it has hardly been picked up thereafter (see Figure 13). A “m-TTH” version of the diradical without chlorine substitution in the meta-positions, at least in the peripheral rings has not been reported to date. m-PTH exhibits a triplet ground state, represented by a positive ΔE_ST = 1.6 kcal mol⁻¹ and a diradical character of y₀ = 0.78 (as determined by us on the UB3LYP/def2-SVP level of theory as part of this review). While no photoluminescence data has been reported for m-PTH in the original publications, we here report a ϕ of 1.4% (in cyclohexane).

The meta-coupled equivalent to the Chichibabin radical has only been explored theoretically. Here, the radical centers are also connected by a biphenyl linker; however, not through the para-positions like in the Chichibabin diradical but through the respective meta-positions of the phenyl rings (with regard to the phenyl–phenyl connection) (cf. TTM-TTM in Figure 12) [102]. The resulting non-Kekulé diradical belongs to the group of alternant hydrocarbons and is supposed to exhibit a triplet ground state like m-PTH but with relatively high ϕ, offering the opportunity for optically detectable magnetic resonance (ODMR).

The next heavier homologue – the meta-coupled isomer of the Müller diradical (TTM-PhTTM) – has been synthesized as TTM-mPh-TTM (see Figure 13). ΔE_ST for this TTM-mPh-TTM diradical has been determined by DFT to be positive, indicating a triplet ground state; however, the value is smaller than the error of the calculation method, so it is fair to say that effectively, the energies of the singlet and triplet ground states can be considered degenerate. TTM-mPh-TTM has a ϕ of 0.6% and the authors have shown that ODMR can be performed on an ensemble of molecules [103]. The next electronic homologue has been synthesized as a 3,6-fluorene-bridged diradical ((Mes₂-TTM)₂-mFl, see Figure 13). This molecule is capped with electron-donating mesityl groups and exhibits a high ϕ of 92% in toluene solution. However, the molecule exhibits a singlet ground state. Again, ΔE_ST is so small that the singlet and triplet states have to be considered effectively degenerate (see Figure 13) [104]. Nevertheless, ODMR could be performed on the ensemble of diradicals, with a thermally accessible triplet state. The concept of meta-coupling of trityl radicals to produce non-Kekulé diradicals has also been followed by coupling two trityl radicals to the 1 and 6 positions of a perylene bisimide (1,6-TTM-PBI, see Figure 13), as well as through the 3 and 6 positions of N-phenylcarbazole (carbazole can be considered non-Kekulé, see explanation below) [105,106]. Despite the meta-coupling, these diradicals also exhibit negative ΔE_ST, meaning that the ground state is a singlet. From this series of diradicals with extending bridge length the spin state of the ground state can be rationalized, when considering that the dipolar coupling strength between the two radical electrons decays quickly. While the distance between the methine groups, at which the radical electrons reside in m-PTH are approximately 0.5 nm apart, in 1,6-TTM-PBI the distance between the radical sites is about 1.4 nm (also 1.4 nm in the (Mes₂-TTM)₂-mFl). Apparently, the interaction between the electrons is too weak at these distances to allow them to assume a triplet state. However, the meta-coupling effectively hinders conjugation and so 1,6-TTM-PBI has a strong diradical character of y₀ = 0.966 (see Figure 13).

While triarylamines are typically sp²-hybridized and the electrons on the nitrogen are delocalized to a substantial degree, in triphenylamine- or carbazole-bridged diradicals it is impossible to draw a correct Kekulé structure (see Figure 13). Therefore, such triphenylamine- or carbazole-bridged diradicals, can be considered non-Kekulé hydrocarbons. Triphenylamine-bridged PyBTM diradicals have been synthesized and the para-substitution in the free phenylamine ring has been functionalized with varying electron-accepting or donating units (see Figure 13). It has been shown that the absolute ΔE_ST value increases when going from electron-withdrawing units – which reduce the UB3LYP calculated spin-density at the trityl sites and increase the exchange coupling – to electron-donating units (see Figure 13). Altogether, ΔE_ST is negative, corroborating a singlet ground state at the large distance (≈1.6 nm) between the radical centers [107]. Since triphenylamine has an overall electron-donating effect, it is not surprising that all TPA(PyBTM)₂ diradicals exhibit acceptable ϕ of up to 7.9% for the methyl-substituted TPA(Me)(PyBTM)_2, where the triphenylamine has the strongest electron donor character [107]. The variation of the electron directing unit in the para-position of the free phenylamine ring also allows shifting of the emission color from λ_em ≈ 700 nm for TPA(CN)(PyBTM)₂ to λ_em ≈ 790 nm for TPA(OMe)(PyBTM)₂ (see Figure 14b)_. This bathochromic shift for electron-donating units is analogous to the well-studied effect of increasing electron donation in monoradicals [63,65].

Interestingly, when two TTM radicals are coupled via a carbazole unit, ΔE_ST shrinks to −0.022 kcal mol⁻¹, while y₀ ≈ 1 as expected for non-Kekulé diradicals (see DR1 in Figure 13) [108]. DR1 shows ϕ of 16% and relatively short luminescence decay of τ = 10.6 ns compared to TTM-Cz with τ ≈ 40 ns (ϕ = 88–91%, see Figure 8). Knowing that the luminescence decay scales with the ϕ in donor-functionalized trityl radicals, the performance of the carbazole-bridged diradical can be rationalized. The photoluminescence spectrum of DR1 (λ_em = 654 nm) is red-shifted against that of TTM-Cz (λ_em = 628 nm) and its shape resembles more the spectrum of TTM-3PCz (λ_em = 664 nm), which is also a structural sub-motif of DR1 (cf. Figures 6, 13 and 14c) [108]. DR1 shows magnetoluminescence, meaning that the films of 0.5 wt % of DR1 in PMMA show increasing photoluminescence, when increasing the magnetic field from 0 to 7 T at 2 K. The authors explain the magnetoluminescence by improved radiative relaxation from excited triplet states than singlet states and the spin-forbidden ISC between these excited states. In the magnetic field, the spins align and the triplet state population is increased (similar to temperature dependent photoluminescence). Population of the lowest triplet state allows reaching of excited triplet states that exhibit better radiative relaxation rates than the corresponding singlet excitons.

Bridging of two TTM-Cz with an anthracene unit does not deliver a photoluminescence spectrum that can be explained by a single substructure of this molecule. Instead, the emission of (TTM-Cz)₂-An is much further red-shifted than TTM-Cz or any other sub-fragment (see Figure 13 and Figure 14d) [109]. The ϕ of 3% is surprisingly low, considering that the other diradicals with donor–acceptor subunits have produced much higher values. Apparently, the first electronically excited state is not the expected CT state between the carbazole fragment and the TTM unit, but instead an excited triplet state on the anthracene unit. Since the distance between the radical sites is ≈2.2 nm it is not surprising that the ground state of this molecule represents a singlet state, as there is little to no dipolar coupling between the radical electrons. However, once excited the molecule exists in a quintet state, which explains the broad and redshifted emission spectrum. The excited anthracene in its triplet state leads to spin-polarization of the neighboring TTM-Cz units to an overall (four-spins) quintet state (the TTM radical site to anthracene distance is ≈1 nm). Interestingly, the two radical electrons on the TTM sites remain correlated for about 30 µs even after the molecule has electronically relaxed and the anthracene has returned to its singlet ground state. This ground state polarization is possible at room temperature with the (TTM-Cz)₂-An molecules dispersed in a PMMA matrix [109]. These properties render the molecule capable for application as a spin-optical interface for optical initialization of qubits and potentially optical readout of the spin-state.

Bridges between trityl radicals can also be employed to align the radical centers in a cage geometry so that the trityl units are oriented on top of one another, with the radical p-orbitals pointing towards each other (see PTM-C in Figure 13) [110]. The crystal structure of this molecule allows determination of the distance (0.99 nm) between the two (bridgehead) carbons, where the radical electrons reside. Because there is no conjugation possible through the biscarbazole bridges and because the distance between the radical sites is small, the ground state of this molecule is a triplet as indicated by the positive ΔE_ST = 0.005 kcal mol⁻¹ determined experimentally. By contrast, unrestricted DFT delivered a singlet ground state with a similarly small energy gap, substantiating that the triplet and singlet states can be considered degenerate. Despite the threefold carbazole substitution, there is no photoluminescence reported for this diradical.

Summary: diradicals based on the triarylmethyl motif

In diradical systems, the conjugation between the radical centers plays an important role. In the family of Kekulé diradicals we see a clear correlation between the number of phenyl rings between the radical centers and the diradical index y₀ (see Table 3). The diradical character is small for TTH (y₀ ≈ 0.4) and steadily grows for TTM-TTM (y₀ = 0.58), TTM-PhTTM (y₀ = 0.9) to bPTM (y₀ ≈ 1). By contrast, non-Kekulé diradicals, which do not allow conjugation have in principle higher diradical character.

Diradicals may present the smallest viable building blocks for organic quantum technology. bPTM exhibits coherence times that can rival or even outperform state-of-the-art solid-state inorganic systems for quantum computing [98]. By contrast, non-Kelulé diradicals bear the potential of exhibiting a triplet ground state, and therefore an electronic structure that resembles that of nitrogen vacancies (NV) in diamond. Such molecular NV-centers represent an interesting platform for quantum sensing, where for example small magnetic fields can be detected. This magnetic field sensing is important for applications ranging from future navigation to medical imaging systems.

Unfortunately, only few of the diradicals present today exhibit photoluminescence and those that do have no distinct triplet ground state. Photoluminescence is an important means for reading out the spin state in such molecular quantum systems, which is why this property should be reflected in future research endeavors in this field. The cases of TTH, with the highest ϕ among the Kekulé radicals and (Mes₂-TTM)₂-mFl among the non-Kekulé radicals show that it requires CT excited states for efficient emission. The strong emission of open-shell molecules that exhibit CT states is known from the trityl monoradicals; however, to date only few attempts have been reported, where CT excited states have been designed into trityl-derived diradicals.

Triarylmethyl multiradicals

For molecules with more than two unpaired electrons, the singlet and triplet ground states nomenclature is no longer correct. For such multiradicals the concepts of ferro-, antiferro-, and paramagnetism are more accurate descriptors [111]. On the one hand, in ferromagnetic molecules neighboring magnetic moments align parallel to each other, resulting in a strong overall magnetic alignment. In typical ferromagnets this alignment persists even in the absence of an external magnetic field (this state would correspond to a diradical with triplet ground state). On the other hand, antiferromagnetic molecules exhibit neighboring magnetic moments that align antiparallel to each other. This leads to a cancellation of the overall magnetic moment, resulting in minimal macroscopic magnetization (corresponding to what we discussed for diradicals with a singlet ground state). By contrast, in paramagnetic materials, no alignment without the presence of an external magnetic field can be observed.

Often, ferromagnetic and antiferromagnetic molecules exhibit strong magnetic interactions between adjacent electron spins only at low temperatures but lack a net magnetic moment at room temperature where they behave as paramagnets.

In the past, much effort has been steered into the synthesis of trityl-derived multiradicals. Meta-linked multiradicals are of special interest as their broken conjugation should help facilitate high-spin ground states and therefore ferromagnetic coupling. In meta-linked diradicals this has already been observed in the form of triplet ground states in the aforementioned m-PTH [112-114]. By contrast, meta-linked multiradicals have proven to be rather elusive, due to their impressive steric congestion [115]. Despite these synthetic challenges, three meta-linked tetraradicals m-4BTH, m-4TTH and m-4PTH have been reported, which exhibit the proposed high spin (quintet) ground state (see Figure 15) [100,111,115,116]. Moreover, a similar para-linked p-4BTM terminated with galvinoxyl groups has been realized [117]. No photoluminescence has been reported for these tetraradicals.

The above described triphenylamine bridged diradicals, have also been reported in the form of triradicals, either with triphenylamine or with triphenylborane as non-Kekulé coupling nodes for the radical moieties [107]. While TPB(PyBTM)₃ exhibits a ϕ of only 0.3%, TPA(PyBTM)₃ features a much better ϕ of 6.1%. This is due to the electron-donating character of the triphenylamine moiety, as opposed to the electron-poor triphenylborane node. The electron-accepting character of triphenylborane in the triradicals therefore induces a photoluminescence maximum at shorter wavelengths TPA(PyBTM)₃ (<700 nm), as compared to the emission maximum of the triradical with the electron-donating triphenylamine node (>700 nm) (cf. purple and dark green photoluminescence spectra in Figure 13b). While for both triradicals the high and low spin states are almost degenerate in energy, the multiplicity has almost no effect on the photoluminescence, rendering such weakly coupled multiradicals useful for optoelectronic applications [107].

Polymer chains

Polymerization of radical-containing monomers represents a complementary approach to produce multiradicals without running into problems of steric congestion.

Interestingly, co-polymerization with non-radical molecules allows for dilution of the spin species or dedicated charge- or energy transfer phenomena between these units and the respective trityl radical. This way, a styrenyl TTM-Cz monomer has been incorporated into a polystyrene backbone and employed as the light-emitting layer in an OLED (see Figure 16a) [118,119]. Moreover, PTM has been employed to terminate a polyphosphorhydrazone dendrimer, which can be reversibly switched electrochemically between a multiradical state and a multi-anionic state with optical readout [120]. In a different approach, 2,7-dibromocarbazole with N-coupled TTM has been subjected to a C–C cross-coupling reaction to obtain conjugated polymer nano- and microparticles (see Figure 16b) [121]. The particles exhibit a ϕ of up to 28.1% and those with 50 mol % of radical are paramagnetic even at low temperatures, documenting the amorphous morphology and the resulting magnetic anisotropy of the radical species inside the particles.

Incorporation of TTM into the backbone of polymeric materials can be achieved by co-polymerization using fluorene and dithiophene compounds by Sonogashira, Stille, and Suzuki coupling (see Figure 17a). Incorporation of trityl radicals into the conjugated backbone can lead to conjugation effects, in which some of the radicals may become consumed in closed-shell quinoidal structures [50,122]. This effect becomes apparent in the luminescence spectra of the particles that are much broader than expected from the monomeric units. The resulting polymers exhibit weak emission between 600–1100 nm [50,122].

This problem of radical combination through quinoid formation in conjugated radical polymers has been investigated in a theoretical approach. Using DFT calculations, conjugated trityl polymers have been investigated with regard to their geometry, dihedral angles, and ground state energies for both the open- and closed-shell variations (see Figure 17b). Interestingly, the authors of the study include different structural changes to tune the dihedral angle ‹ω› between two radical methyl planes. The ether-annulated p-oxTAM is completely flat (‹ω› = 0°), whereas the perchlorinated p-PTM polymer has the largest dihedral angle (‹ω› = 45.8°) due to steric demand of the large chlorine substituents (see Figure 17b). Naturally, p-TPM exhibits the greatest degree of freedom and the minimal energy ground state geometry exhibits a dihedral angle (‹ω› = 26.5°) between those of p-oxTAM and p-PTM [123]. In analogy to the diradical character y₀, in polyradicals we can express the radical–quinoidal balance as the average spin population ‹|µ_αC|›. ‹|µ_αC|› increases with ‹ω›, indicating that planarity and conjugation favor the quinoidal structure and radical combination. Non-symmetric substitution like in p-BCM leads to variable dihedral angles, seemingly favoring the quinoidal structure as well.

Dendritic calixarenes m-DCxA-TPM and m-TCxA-TPM composed of para- and meta-connected trityls exhibit ferromagnetic domains within the molecules, which are termed spin clusters with large S (see Figure 17c). The calixarene radical clusters (blue in Figure 17b) possess total spin S = 7/2 or 6/2 and are bridged by triarylmethyl monoradical linkers (red in Figure 17b) with S = 1/2. The spin clusters are randomly coupled ferro- and antiferromagnetically through the triarylmethyl linkers [124]. m-DCxA-TPM and m-TCxA-TPM can be viewed as di- and trimeric subunits of a longer spin-chain, and could therefore present an interesting future endeavor for potential conjugated polymers with strong magnetic ordering.

Supramolecular frameworks

While oligomers and polymers often assume a disordered coiled geometry or an amorphous morphology in the solid state, trityl-based radicals can also be assembled into highly ordered molecular frameworks. Such supramolecular frameworks are a class of material, formed under reversible association conditions using non-covalent interactions, like hydrogen bonds, π–π interactions, metal-coordination, or electrostatic forces. The resulting molecular scaffolds can vary in their dimensionality (two- or three-dimensional), in size and their homogeneity, and in their properties. Molecular frameworks exhibit a porous structure, rendering these materials interesting for gas adsorption and catalysis. Moreover, spin interaction between the unpaired electrons of radical-containing molecular frameworks can be useful for their application in spintronics or quantum information processing. In the following, we will discuss hydrogen-bonded radical supramolecular organic frameworks (SOFs) and metal coordinated organic frameworks (MOFs).

Hydrogen-bonded frameworks: Trityl-derived radicals with carboxylic acid moieties in para- or meta-positions of the phenyl groups have been employed regularly to design and produce different types of hydrogen bonded trityl SOFs (see PTMDC, PTMTC and PTMHC in Figure 18a and resulting network structures in Figure 18b).

The implementation of these open-shell building blocks with supramolecular (carboxylic acid) recognition motifs shows several benefits. The bulky structure of highly chlorinated TPM radicals prevents a close packing between units and enables exchange interaction via the hydrogen bond without leading to radical combination and quinoid formation, as is often the case for para-coupled trityl radicals. POROF-1, which has been crystallized from (twofold carboxylated) PTMDC, forms 2-dimensional hexagonal structures with smaller hydrophilic pores, due to the connecting carboxylic acid groups. The local hexagonal structures organize into regular patterns with long range regularity, forming also larger hydrophobic pores (see Figure 18b, yellow shading). These 2-dimensional layers stack on top of each other, forming channels, large enough to host for example n-hexane solvent molecules [125]. The (threefold carboxylated) PTMTC also forms layered hexagonal structures of similar pore size [126]. However, here the larger pores are hydrophilic, preventing the ingress of non-polar solvent guest molecules into the channels of this POROF-2 framework (see Figure 18b, red shading).

Magnetic susceptibility (χ) measurements show mostly paramagnetic behavior of both POROF-1 [125] and POROF-2 [126], with effectively identical χT values of 0.38 emu K mol⁻¹ at 300 K (χT for uncorrelated spins (S = 1/2) is expected at 0.375 emu K mol⁻¹). At temperatures below 50 K weak antiferromagnetic exchange interactions can be observed for POROF-1. The magnetic properties are impervious to the presence of solvent guest molecules. By contrast, POROF-2 reveals slightly increased χT-values at 5 K and a ferromagnetic ordering of the unpaired radical electrons at 0.11 K [126].

The crystalline structure of hexa-meta-carboxlyated PTMHC framework POROF-3 has been observed to incorporate solvent molecules during the crystallization process via hydrogen bonding (see Figure 18b). Different framework morphologies can be obtained depending on the solvent system, from which the frameworks are crystallized [127]. In the case of THF, every carboxylic acid group is bound to one THF molecule and the resulting [PTMHC∙(THF)₆] clusters self-assemble into a honeycomb lattice.

For Et₂O as a solvent, only half of the carboxylic acid groups are bound to the solvent, rendering three of these units (one per phenyl ring) accessible for hydrogen bonding between neighboring [PTMHC∙(Et₂O)₃] clusters. Due to the lack of direct hydrogen bonding between the PTMTC units, [PTMHC∙(THF)₆] exhibits purely paramagnetic behavior between 10–200 K and very weak antiferromagnetic behavior below 10 K, whereas [PTMHC∙(Et₂O)₃] shows weak ferromagnetic interactions at low temperatures.

Unfortunately, photoluminescence has not been reported for any of the mentioned hydrogen-bonded frameworks, although one could assume that the emission behavior would be similar to the photoluminescence of the respective building blocks, which has been reported to be around 6% (in CHCl₃) [128]. The rigidity of the produced SOF material could lead to enhanced ϕ, considering that radicals are immobilized in a crystalline environment of their hydrogenated closed-shell parent molecules, which reduces non-radiative (vibrational) relaxation pathways [43].

Metal-coordinated radical frameworks: The above discussed carboxylic acid functionalized PTM derivatives have not only been used in hydrogen bonded SOFs, but also for the generation of MOFs [128-133]. Copper (Cu) and cobalt (Co) ions form honeycomb arrangements together with PTMTC, with the metal center residing on the hexagonal grid (see MOF-1 in Figure 18c). While the planar coordination to Cu ions results in 2-dimensional layers of MOF-1, the coordination to Co ions yields a helical tertiary structure in MOF-2 (see Figure 18c) [130,131]. When a second 4,4’-bipyridine ligand is admixed, the Co ions restrict the PTMTC radical building blocks into quasi-1-dimensional strands, where the Co ions are coordinated octahedrally (see MOF-3 in Figure 18). Each metal is additionally bound to one PTMTC radical ligand and three water molecules (omitted in Figure 18 for clarity). The non-coordinated carboxylic acid groups bind to water molecules of neighboring strands, bridging and aligning the chains into a quasi-parallel, stacked fashion [132].

Like in hydrogen bonded frameworks, there is virtually no information about the luminescence of trityl radical containing MOFs. PTMTC has been reported to bind to lanthanides, such as europium (see MOF-4 in Figure 18) [129]. However, when introducing a TTM radical derivative as a linker for Ln-MOFs, the broad absorption of PTMTC at 500–575 nm overlaps with the characteristic emission bands of lanthanides, which may be the reason for emission quenching in these systems. Only for MOF-5 photoluminescence is reported. MOF-5 exhibits photoluminescence that is similar to that of the PTMTC building block in CHCl₃ solution [128]. The Zn ions force the PTMTC ligands into ribbons, which stack in an off-set fashion (see Figure 18c). MOF-5 is paramagnetic irrespective of the temperature. The paramagnetic nature might be caused by the low concentration of actual radical units, which are dispersed in a matrix of the α-hydrogenated PTMTC-H and the diamagnetic Zn(II) ions.

In MOFs-1, -2 and -3 a transition between ferro- and antiferromagnetic effects is typically observed at low temperatures. For the MOF-4 (with Ln = Eu, Gd, Tb) antiferromagnetic behavior at low temperatures is reported, with a minimum χT-value at around 2 K each. For the MOF-4 with Ln = Eu a smooth decrease between 300 and 10 K is ascribed to a depopulation to close-to-ground-state excited states, whereas the more sharp decrease below 10 K is believed to be caused by antiferromagnetic radical–radical interaction through the lanthanide ions, as the distances are assumed to be too long to sustain through-space coupling [129].

The variety in trityl-derived MOFs has been further increased by using coordinating groups other than carboxylic acid units. TTM radicals have been para-substituted by imidazole units (TTMDI, TTMTI), or alternatively, the phenyl groups have been replaced by pyridines, which exhibit superior photostability as discussed above (see Figure 19a, and cf. to PyBTM in Figure 3). Using Co ions, a linear coordination polymer CoCP-1 and a two-dimensional CoCP-2 can be achieved with TTMDI and TTMTI, respectively (see Figure 19b) [134]. While no photoluminescence is reported for these MOFs, UV–vis spectra show broad absorption bands around 385 nm and 600 nm, resulting from the typical (in-phase and out-of-phase combinations of) HDMO–SOMO and SOMO–LUMO transitions of the trityl-based radical ligands [134]. Moreover, bands at 470 and 508 nm and a shoulder at 720 nm can be attributed to the octahedrally coordinated, high-spin Co(II) ions and the band at 553 nm to a coexistence between absorption of the radical and heavy atom effects of Co(II) [134].

Magnetic susceptibility measurements reveal higher χT-values than expected, due to significant orbital contribution of the octahedral Co(II) ions. Lower temperature generates a continuous decrease in χT down to 1.66 emu K mol⁻¹ at 3 K for CoCP-1 and 1.55 emu K mol⁻¹ at 4 K for CoCP-2, indicating an antiferromagnetic coupling between ions and ligands, which is supported by DFT calculations [134].

The Py₂MTM and Py₃TM ligands produce two intriguing MOFs coordinated by Zn ions (see bisZn and trisZn in Figure 19b). While Py₂MTM yields a linear metal-coordination polymer, Py₃TM delivers a hexagonal 2-dimensional MOF [133]. Although the unpaired electrons of the trityl radicals are in even closer proximity to the coordinated metal center and towards each other than in the imidazole based frameworks CoCP-1 and CoCP-2, χT magnetic susceptibility reveals antiferromagnetic behavior at low temperature [133].

Photoluminescence of bisZn and trisZn at 4.2 K is negligible with ϕ values of <0.001 and 0.02%, respectively. However interestingly, magnetoluminescence is observed when an external magnetic field is applied [56,135,136]. It is proposed that the rigidity of the MOF reduces radical–radical interactions at low temperatures so that modulation of the spin sublevel population can be achieved by a magnetic field and read out by fluorescence [133]. By contrast, greater spacings between radical units do not seem to result in a similar effect, as magnetoluminescence has not been reported for any of the other SOFs or MOFs.

In summary, one ferromagnetic and one magnetoluminescent MOF have been reported in the literature. A clear understanding of what causes ferromagnetism in MOFs has not been reached. Ground state population of the Kramer’s doublet of Co(II) ions at very low temperature with S_eff = 1/2 could help as an explanation for the increased correlation of MOF-4 at 1.8 K [131]. But as a coexistence of ferro- and antiferromagnetic interactions is reported for this compound, it is still elusive what causes such behavior. So far it is only clear that for magnetoluminescence to occur, a spatial separation of radicals needs to take place. But it remains unclear, at which distance this response breaks down. More insight needs to be gained on these topics and a design strategy needs to be developed to help improve magnetic and fluorescent properties of radical MOFs in the future. Concepts from the discrete radical constructs could help to improve the performance, like incorporation of donor moieties in the radical synthons to achieve higher quantum yields and possibly a combination of ferromagnetic and emissive properties.

Covalent organic radical frameworks: Covalent organic frameworks (COFs) with covalent and non-reversible connections between trityl radical building blocks have been of particular interest, as they – much like SOFs and MOFs – combine tunable pore sizes and predictable geometry to address a wide set of potential applications. In contrast to SOFs and MOFs, the covalent connection comes with the well-known problem of the equilibrium between benzenoid multiradical and quinoidal closed-shell electronic structure in para-connected trityl building blocks. However, para-connection delivers the most predictable hexagonal COFs, which is why most reported COFs are based on para-connected building blocks. For this reason, there are several theoretical studies, which discuss whether the assembly delivers a significant fraction of unpaired (non-quinoid) radical electrons and what magnetic properties to expect from the material [137-140]. In theoretically explored COFs the change of the dihedral angles upon uniaxial stretching or out-of-plane compression is studied in chlorinated and non-chlorinated trityl units connected through 1,3,5-benzene (see m-TPM-Ph-COF and m-PTM-Ph-COF in Figure 20). It is observed that stretching of these COFs causes a flattening of the dihedral angles between neighboring phenyl rings, resulting in a higher orbital overlap. This orbital overlap gives rise to a shift from the open-shell to the closed-shell quinoidal structure. All ring-sharing, para-connected COFs, which represent an extension to the formerly discussed Thiele diradicals, have been explored theoretically and show an antiferromagnetic ground state in their open-shell configuration (see p-TPH-COF, p-PTH-COF, p-DTH-COF in Figure 20) [137,139,140]. For all these para-connected COFs, this open-shell ground state solution is lower in energy, except p-TPH-COF where both multi-radical and quinoidal solutions are nearly degenerated [137]. Interestingly, for p-oxTAM-COF with its fully planarized geometry (cf. p-oxTAM in Figure 17b), the localized quinoidal state spontaneously produces a delocalized semi-metallic state that could not be stabilized during the calculations [137]. However, when we introduce trifunctional crosslinkers so that the conjugation between trityl radicals becomes broken through the meta-connection (m-TPM-Ph-COF and m-PTM-Ph-COF discussed before) ferromagnetic exchange interactions are found. However, the necessary spin alignment into high spin materials is expected only at temperatures below 10 K [138].

PTMAc-COF has been synthesized in 2018 by two independent research groups [141,142]. Both groups observed Mott insulating properties, arising from the antiferromagnetic behavior below 42.5 K, which were also predicted by independent theoretical studies (see Figure 21) [140]. Decrease of spin localization from PTMAc-COF to oxTAMAc-COF and TOTAc-COF (due to their coplanar structures) has been observed to lead to higher exchange values and therefore more stable antiferromagnetic configuration compared to PTMAc-COF [140].

The above discussed experimentally investigated radical COF examples have been synthesized through C–C cross-coupling reactions [141-144]. Interestingly, when an additional coupling agent is included, the radical centers can be diluted in the “matrix” of electron-accepting crosslinker units, as is the case in PTMTAz-COF (see Figure 21) [145]. Paramagnetic behavior has been reported for this triazine-linked PTMTAz-COF [145]. Here the distance between neighboring spins, which is nearly 20 Å, is too large for significant spin–spin interactions to persist. Again, no emissive behavior is reported for these COFs. By contrast, the distance between unpaired electrons is significantly smaller in p-PTM-COF than in the triazine-linked PTMTAz-COF; however, p-PTM-COF shows paramagnetic behavior as well, arising from a coexistence of both ferro- and antiferromagnetic interactions at low temperatures [144]. Despite theoretical calculations predicting an open-shell conformation for small molecular PTM radicals, it is likely that not every sp²-carbon of the p-PTM-COF is in its radical form. Of course, quenching by π–π-stacking – often observed in these 2-dimensional COFs – is another prominent factor inhibiting emissive behavior.

Interestingly, TTMAc-PCz-COF has been synthesized using electropolymerisation [143]. The incorporated electron-donating unit could induce interesting optical and magnetic properties. However, neither photoluminescence nor magnetic susceptibility measurements have been performed for this material. It is to be expected that either antiferromagnetic coupling, due to conjugation between radical centers, or paramagnetic coupling for greater distances between two neighboring spin-centers will be observed.

Summary: triarylmethyl multiradicals

Molecular multiradicals, like diradical systems, are significantly influenced by the connectivity between the radical centers and their potential to form quinoidal or delocalized structures. In Kekulé-type multiradicals, the delocalization of unpaired spins determines the formation of open- or closed-shell structures and is affected by dihedral angles between the sp²-plane of the central carbons and the neighboring phenyl rings, as well as by steric effects. Increasing the distance between radical centers leads to transitions from ferro- or antiferromagnetic to paramagnetic behavior.

In covalent materials, Kekulé multiradicals often exhibit antiferromagnetic behavior, due to quinoidal structure formation, while non-Kekulé multiradicals show ferromagnetic interactions when spatial distances are small. Hydrogen-bonded radical frameworks generally display ferromagnetism or paramagnetism, with solvent molecules influencing the latter.

Predicting the magnetic properties of MOFs remains challenging, due to the influence of the metal ions on the geometry and the electronic properties. Optical properties, particularly emission and quantum yields, are understudied, with π–π stacking in 3D COFs often quenching the emissive pathways. Adjusting framework dimensions, dihedral angles, or functionalizing TTM with donor moieties like carbazole may enable luminescent behavior.

Magnetoluminescence, as seen in frameworks like bisZn and trisZn, stems from radical ordering and invites further investigation into whether similar mechanisms apply to other MOFs. Incorporating TTM radicals into non-radical matrices has been shown to enhance ϕ by mitigating self-quenching, suggesting that precisely tailored introduction of radical units into otherwise inert framework materials could reveal new insights into the interplay of magnetic and optical properties.

Conclusion

Organic radicals with their long electron spin coherence times and diverse opportunities for functionalization, represent interesting molecular qubit materials for advanced optoelectronic applications and as novel molecular quantum materials. Their luminescence, tunable electronic ground state conformation, and their ability to be connected into 1, 2, and 3-dimensional frameworks renders trityl-based radicals interesting for quantum sensing, quantum computing, and quantum communication applications.

Whereas trityl monoradicals have been widely investigated and the effect of the donor moiety on the emission and photostability is well-understood, there remain open questions on how to implement high ϕ into diradicals and multiradicals.

While molecular color centers have been produced in metal-organic complexes [146,147], highly luminescent diradicals with a distinct triplet ground state remain unattainable to date.

While light emission is becoming an objective of active research for diradicals, it is not yet a topic for the higher dimensional assemblies of trityl radicals. If light emission of individual radical species inside of a 2D or 3D framework could be achieved, it could represent the starting point for quantum computing using organic radicals. Virtually there would be no limits in scalability for the number of qubits per framework. While electrical connectivity and readout will not be possible in a large 2D or 3D framework, optical strategies might be suitable for reading out the radical spin states.

Despite being an old molecule, after Gomberg’s first report in 1900 [31], the trityl radical represents an extremely timely class of molecules with many prospective uses in high technology applications.