Open Access Article
This Open Access Article is licensed under a
Creative Commons Attribution 3.0 Unported Licence

Enhancing the statistical probability factor in triplet–triplet annihilation photon upconversion via TIPS functionalization

Lukas Naimovičiusabc, Manvydas Dapkevičiusb, Edvinas Radiunasb, Mila Miroshnichenkoa, Gediminas Kreizab, Carles Alcaided, Paulius Baronase, Yoichi Sasakif, Nobuhiro Yanaif, Nobuo Kimizukaf, Andrew B. Punc, Miquel Solàd, Pankaj Bharmoria*a, Karolis Kazlauskasb and Kasper Moth-Poulsen*aegh
aInstitute of Materials Science of Barcelona (ICMAB-CSIC), Universitat Autònoma de Barcelona, Bellaterra, Barcelona, 08193, Spain. E-mail: kasper.moth-poulsen@upc.edu; pbharmoria@icmab.es
bInstitute of Photonics and Nanotechnology, Vilnius University, Saulėtekio av. 3, LT-10257 Vilnius, Lithuania
cDepartment of Chemistry and Biochemistry, University of California San Diego, 92093 La Jolla, CA, USA
dInstitute of Computational Chemistry and Catalysis (IQCC) and Department of Chemistry, Universitat de Girona, M. Aurèlia Capmany 69, 17003 Girona, Spain
eDepartment of Chemical Engineering, Universitat Politècnica de Catalunya EEBE Eduard Maristany 10–14, 08019 Barcelona, Spain
fDepartment of Applied Chemistry, Graduate School of Engineering Kyushu University 744 Moto-oka, Nishi-ku, Fukuoka 819-0395, Japan
gCatalan Institution for Research & Advanced Studies (ICREA), Pg. Lluís Companys 23, Barcelona, Spain
hDepartment of Chemistry and Chemical Engineering, Chalmers University of Technology, Kemivagen 4, Gothenburg 412 96, Sweden

Received 15th July 2025 , Accepted 6th October 2025

First published on 7th October 2025


Abstract

We investigated the influence of triisopropylsilyl (TIPS) functionalization on annihilators in triplet–triplet annihilation photon upconversion, specifically focusing on their spin statistical probability factor. A new green-emitting annihilator 3,9-bis((triisopropylsilyl)ethynyl)perylene (TIPS-PY) displaying a record red-to-green TTA-UC quantum yield of 13.7% (50% theoretical maximum) was synthesized. This remarkable efficiency was achieved due to the following features of the TIPS functionalization of PY: (1) retaining a high fluorescence quantum yield of 95%, (2) reduced triplet energy to 1.29 eV enabling efficient triplet energy transfer (∼100%) from the sensitizer PdTPBP (T1 = 1.55 eV), and (3) a high efficiency of singlet generation after triplet coupling, indicated by the statistical probability factor, f = 39.2% ± 2.4%. Notably, the f value of TIPS-PY surpasses other annihilators in the 470–570 nm emission range. Excited state computational analysis using TheoDORE revealed a higher percentage of charge transfer character in S0S1 in TIPS-PY compared to PY, indicative of higher singlet-like character in their triplet-pair state 1(T1T1), which can enhance the coupling of the triplet-pair state with the excited singlet-state, thereby increasing the efficiency of singlet generation, a phenomenon undisclosed before. Furthermore, the suitable T1 of TIPS-PY enables upconversion of 730 nm light when sensitized with Os(m-peptpy)2(TFSI)2 (T1 = 1.63 eV), demonstrating the broad upconversion range of TIPS-PY in the phototherapeutic window desired for biological applications.


Introduction

Triplet–triplet annihilation photon upconversion (TTA-UC) is a molecular nonlinear optical process that converts two photons with low-energy into one photon with high energy (Scheme 1a).1 This phenomenon is attractive compared to other UC processes2 due to its operation under incoherent low energy density excitations3 which opens many potential applications such as photocatalysis, biological photoactivation, 3D printing, and photovoltaics.4–11 A typical TTA-UC system consists of a sensitizer and an annihilator ensemble. The sensitizer absorbs low-energy photons and generates triplet states via intersystem crossing (ISC). The annihilator accumulates the triplets through Dexter triplet energy transfer (TET) from the sensitizer and undergoes TTA-UC, generating a photon-emitting high-energy singlet state (Scheme 1a). The efficiency of singlet generation is evaluated by TTA-UC quantum yield (ϕUC), which is the product of all operational processes within the TTA-UC system (eqn (1)) and the spin-statistical probability factor (f). The f determines the probability of singlet generation after triplet coupling (Scheme 1b).
 
image file: d5sc05248c-t1.tif(1)
In the eqn (1), ϕUC, ϕISC, ϕTET, ϕTTA, ϕFL represent the quantum yields of upconversion (UC), intersystem crossing (ISC), triplet energy transfer (TET), triplet–triplet annihilation (TTA), and annihilator fluorescence (FL), respectively.

image file: d5sc05248c-s1.tif
Scheme 1 (a) Scheme of TTA-UC indicating conversion of two low-energy photons into one high-energy photon through a series of energy transfer processes. ISC – intersystem crossing, TET – triplet energy transfer, TTA – triplet–triplet annihilation and UC – upconversion (b) schematic illustration of the post-TTA events resulting in the formation of the TT pair with singlet (S1, f = 1/9), triplet (T2, 3/9) and quintet (Q1, 5/9) states due to the anti-ferromagnetic coupling (AFC) between triplet-pairs. Further recycling via quintet dissociation (Q1 diss.) or internal conversion (IC) can increase the f of S1 formation to 1/2. A higher singlet character of the TT pair increases the coupling between the TT pair and the singlet state, which further increases the f.

The f plays an essential role in TTA-UC by defining the maximum achievable ϕUC as f/2 when all other processes approach unity. As follows, the f allows us to assess the intrinsic potential of the annihilator triplets to generate an emissive singlet state (Scheme 1b). It can be altered by suitable molecular engineering of annihilator chromophores to control the triplet coupling strength, which has been investigated in this work. The TTA results in the formation of a triplet-pair (T1⋯T1) whose net spin can be S = 0, 1, or 2, hence possessing singlet, triplet, or quintet character. According to the adapted Merrifield model including exchange interactions (J), under zero-field splitting, coupling results in the formation of 9 spin eigenstates of T1T1 pairs with an overall fraction of 1/9, 3/9, and 5/9 of singlet, triplet, and quintet pair states (Scheme 1b). Triplet coupling can be expressed simply by Heisenberg's spin-only Hamiltonian (Ĥ) using eqn 2

 
Ĥ = −2JŜ1·Ŝ2 (2)
where Ŝ1 and Ŝ2 are individual spin operators of the two individual interacting triplets, and J is the magnetic exchange parameter that also defines the strength of inter-triplet exchange interactions.1,5 In the case of strong electronic coupling, the quintet state (Q1) is energetically inaccessible and cannot form the excited singlet state. This limits the f of singlet formation to 1/4, leading to low UC efficiencies. However, the quintet and triplet (T2) states may re-participate in singlet formation via other channels like Q1 to T1 dissociation, and T2 to T1 internal conversion (IC).12,13 This recycling can increase the experimentally obtained f value even up to ∼1/2.5,14,15 The TTA-UC (1(T1T1) > S1S0) is the reverse process of singlet fission (S1S0 > 1(T1T1)) with an intermediate correlated triplet-pair state, 1(T1T1) as per the Johnson–Merrifield model eqn (3).16,17
 
SF → S0S1 ⇌ T1T1 ⇌ T1 + T1 ← TTA-UC (3)

It is according to the Merrifield model that the singlet character of the T1T1 pair determines its coupling to the singlet state.18 Hence, annihilators with a triplet-pair state exhibiting a significant singlet character can have a high probability of singlet formation and consequently, a higher f factor19 which has been investigated in this work by calculating the percentage of charge resonance/transfer character in the S0S1 dimer.

Another way to increase the f factor is to avoid secondary loss channels such as 2T1 to Tn non-radiative decay (Scheme 1b). This can be achieved via the molecular engineering of an annihilator with 2T1 ≈ S1 and Qn and Tn states higher in energy than the 2T1 state. This prevents 2T1 decay to Qn or Tn states due to the energy gap law relation5 (eqn (3)). This results in preferential decay of 2T1 to the S1 state, leading to more efficient singlet generation.

 
image file: d5sc05248c-t2.tif(4)
where knr is the rate of non-radiative decay and ΔE is the energy gap between electronic states.

Several derivatives of naphthalene,14,20 anthracene,21–23 perylene,24,25 rubrene,26–30 and diketopyrrolopyrrole31,32 based compounds have been investigated to achieve high f values to boost the overall ϕUC.5 The UC emission of these compounds spans across the majority of the UV-visible spectrum. However, the lack of an efficient annihilator emitting within the 470–540 nm range impedes important biological applications which can be photoactivated with upconverted green light upon excitation within or close to the phototherapeutic window (650–850 nm,33 These applications include targeted drug delivery,34 light–gated ion channel control,35 light-activated CRISPR,36 photo-pharmacology,37 and photosynthesis.38 While 9,10-bis(phenylethynyl)anthracene (BPEA) is a well-known commercially available green annihilator, its low UC quantum yield due to the small f = 5.6 to 6.3% is an issue.21 Therefore, an efficient annihilator within the 470–540 emission range could serve as a powerful photoactivation tool in biological applications upon low-density red or NIR excitation via TTA-UC for embracing higher penetration into biological tissue.

Herein, we report the synthesis of a new perylene (PY) based annihilator functionalized with triisopropylsilyl (TIPS) groups, TIPS-PY (Fig. 1a). TIPS-PY demonstrates highly efficient TTA-UC, with experimental ϕUC of 13.7% (out of 50%), with f = 39.2% upon combining with Pd(II) meso-tetraphenyl tetrabenzoporphine (PdTPBP) as sensitizer (λex = 640 nm CW laser). The ϕUC is shown to be greater compared to unfunctionalized PY due to the increase in f value implying enhanced triplet-pair-singlet coupling, which may be governed by the singlet-like character of the triplet-pair state of TIPS-PY, revealed from the higher percentage charge resonance or charge transfer character of the S0S1 excitations of the TIPS-PY compared to PY using TheoDORE program.19,39 To our knowledge, an efficient annihilator in 470–540 nm emission range with a high f value of 39.2% ± 2.4% and ϕUC up to 19.6% (theoretical limit) has not been reported before.40 This study demonstrates the value of TIPS-functionalization in engineering the triplet energy, singlet-triplet character, and T1T1 coupling of annihilator triplets to yield a high statistical probability factor for upconverted singlet-state generation, which is a key limiting factor in TTA-UC. When combined with Os(m-peptpy)2(TFSI)2 as a sensitizer, TIPS-PY upconverted the 730 nm light into yellow-green light, thus reaching deep into the phototherapeutic window33 that is highly sought after for various biological applications.34–38


image file: d5sc05248c-f1.tif
Fig. 1 Molecular structures and T1 energies (a), and absorption and emission spectra (b) of annihilators (PY, TIPS-PY, BPEA), and sensitizer (PdTPBP) at concentrations of 20 μM and 1 μM in THF, respectively.

Results and discussion

Synthesis of 3,9-bis((triisopropylsilyl)ethynyl)perylene (TIPS-PY)

The annihilator TIPS-PY was synthesized in a two-step reaction as depicted in Scheme 2. A mixture of 3,9- and 3,10-dibromoperylene was obtained via an electrophilic aromatic bromination reaction between PY, and n-bromosuccinimide (NBS).41 The final compound, TIPS-PY, was obtained via a Sonogashira coupling between the mixture of 3,9- and 3,10-dibromoperylene and TIPS-acetylene. The purified-orange colored compound was characterized by 1H NMR, 13C {1H} NMR, MALDI-TOF, and single-crystal X-ray diffraction analysis (for detailed synthesis procedure and characterization see Annexure 1, Fig. S1–S5) and found to be 3,9-bis(TIPS)perylene.
image file: d5sc05248c-s2.tif
Scheme 2 Synthesis of 3,9-bis(TIPS)perylene (TIPS-PY).

Photophysical properties

The photophysical properties of TIPS-PY were studied in comparison to other competitive annihilators, PY and BPEA in the 470 to 540 nm emission range. The molecular structures of TIPS-PY, PY,42 and BPEA (ref. 21) are shown in Fig. 1a along with PdTPBP, the sensitizer used in this study for red-to-green upconversion.43

TIPS-PY demonstrated absorption and emission peaks at 483 nm (ε ∼73[thin space (1/6-em)]000 M−1 cm−1, Fig. S6) and 489 nm (ϕFL = 95% and τFL = 5.5 ns), respectively (Fig. 1b, S7, and S8). Compared to PY, the emission spectrum of TIPS-PY is red-shifted by 0.29 eV due to the extension of conjugation upon introduction of TIPS-acetylene moieties (Fig. 1b). However, the ΦFL remained almost the same (96% and 95%). This red shift in the emission spectrum of TIPS-PY overcame the secondary inner filter issue caused by reabsorption of UC light by the PdTPBP Soret band to boost the ϕUC (Fig. S9). When compared to BPEA, the emission spectrum of TIPS-PY is red-shifted by just 0.1 eV (Fig. 1b). However, the lower ϕFL = 85%21 of BPEA implies a negative effect on the overall ϕUC according to eqn (1). Besides ϕFL, our previous time-dependent density functional theory (TD-DFT) investigations (Gray et al.21) found that the difference in geometry of singlet and triplet surfaces of BPEA makes the triplet-state energetically inefficient to generate the first excited singlet-state to yield low ϕUC.21 Hence, prior to TTA-UC experiments, molecular geometry optimization, and excited state modeling studies of TIPS-PY in comparison to PY were conducted (Fig. 1 and S10).

Excited-state modeling studies

The DFT and TD-DFT calculations carried out at the (U)PBE0-D3(BJ)/6-311G(d,p) level of theory have shown the T1 states of PY and TIPS-PY at 1.49 eV and 1.29 eV, respectively (see SI for a more detailed description of the computational method). The calculated T1 of PY is almost similar to the reported experimental8 and theoretical values ∼1.5 eV.42 The calculated singlet-state (S1) energies of PY and TIPS-PY (Fig. S10) are also in agreement with the experimental S1 values. Due to the T1 of TIPS-PY at 1.29 eV, PdTPBP having T1 at 1.55 eV42 (Fig. 1a) was selected as a sensitizer to ensure the feasible sensitization of TIPS-PY via an exothermic triplet energy transfer pathway. Moreover, the non-overlapping of the emission spectrum of TIPS-PY with the absorption spectrum of PdTPBP (Fig. 1b and S9), and a high ϕISC of PdTPBP approaching unity44 were other key factors for PdTPBP selection as a sensitizer.

The calculated energy level distributions (Fig. S10) demonstrate that TIPS-PY complies with the 2T1 > S1 energetic condition for TTA-UC to occur.5 However, the proximity of 2T1 to higher energy triplet-states (Tn = T2, T3) plays a crucial role in the probability of singlet generation due to the energy gap law relation (eqn (4)), imposing a non-radiative decay channel if 2T1 is in the vicinity of T2 and further from S1.45,46 We investigated the implication of the energy gap law in affecting the f factor of TIPS-PY and found a 2ET1-ET2 energy gap of +70 meV. The gap is significant enough to substantially reduce the non-radiative decay.45–47 Hence, it could be one of the key contributors to the high f factor of TIPS-PY. However, when compared with the 2ET1ET2 = −140 meV of PY having f value of 17.9%42 this parameter does not seem enough to explain the high f factor observed of TIPS-PY. Hence, we explored another possible channel to understand the high f factor of TIPS-PY. One key argument of the Merrifield model of triplet–triplet coupling is that the efficiency of singlet generation depends on the triplet pair-singlet coupling.18,29,48 Hence, a higher singlet character of the triplet-state can increase the singlet-triplet coupling post triplet–triplet annihilation to generate a high singlet population.18 Therefore, we calculated the charge resonance or charge transfer character of S1S0, commonly shared by 1(T1T1), of TIPS-PY compared to that of PY to assess the singlet character using TheoDORE program (Fig. 2).39 Fig. 2a shows the change in electron density from the ground state to the excited state, resulting from a linear combination of orbital replacement involving charge transfer (blue arrows) and local excitations (black arrows). The HOMO-1 to LUMO+1 transition in TIPS-PY, which contributes the strongest (92.39%), has charge transfer (CT) character, moving one electron each from left to right and from right to left. Contrary to this, the HOMO−1 to LUMO+1 transition in PY, which contributes the strongest (88.24%), has a charge resonance (CR) character. The percentage of CT or CR character is indicative of the singlet character of the dimer.39 These results indicate that TIPS-functionalization increases the singlet character of the TIPS-PY dimer, which is likely to have a positive effect on f value (Scheme 1b)16,49–51 and UC quantum yield.


image file: d5sc05248c-f2.tif
Fig. 2 (a) Illustration of the contribution of the linear combination of orbital replacement in TIPS-PY. (b) Plot showing comparative electron (E), and hole (H) contributions during orbital replacement in PY and TIPS-PY. (c) Percentage of charge resonance (CR) or charge transfer (CT) calculated from E and H contributions during orbital replacement in PY and TIPS-PY.

To substantiate these results, we also investigated biphenyl (BP) and bis-TIPS-biphenyl (TIPS-BP), having a similar transition dipole axis as that of PY (Fig. S11a and b)52,53 using the TheoDORE program (Fig. S12). Similar to PY, the CT character of BP increased upon TIPS-functionalization (Fig. S12d), thus supporting the proposed argument. Recently, TIPS-BP was shown to demonstrate superior UC performance compared to BP, confirming our prediction experimentally.54 Seeking further generalization of this argument, we also calculated the CT or CR character for highly efficient TIPS-functionalized annihilators such as TIPS-anthracene (TIPS-An) (ref. 23) and TIPS-naphthalene (TIPS-Naph).55 However, the CT or CR character decreased for these molecules upon TIPS-functionalization (Fig. S13a–d). This could be due to the difference in the main transition dipole axis of Naph and An (1Lα), which unlike BP and PY is along the horizontal axis (Fig. S11b). It is to mention that the transition dipole axis plays a key role in the electronic interactions of the molecules in the excited state.56 Nevertheless, it shows that the singlet character of the triplet pair may not be the sole criterion to evaluate the high TTA-UC quantum yields in molecules with different transition dipole axes. Therefore, we also investigated the role of energy gap law5 in TIPS-An and TIPS-Naph and found 2ET1ET2 of −103 meV, and +186 meV, respectively (Table S2), which is in synergy with results obtained upon application of the energy gap law in the case of PY and TIPS-PY. Therefore, the energy gap law could be the common factor contributing to high ϕUC (27%)23 of TIPS-An and high f value (54%)55 of TIPS-Naph chromophores, as well as TIPS-PY. Seeking further insights, we also computed the S0S0 and T1T1 states for PY and TIPS-PY and found a smaller dimerization energy for TIPS-PY (−31.6 kcal mol−1) compared to that of PY (−20.43 kcal mol−1) (see Fig. S14).57 In both cases, the potential energy surface is relatively flat, allowing for easy rotation and translation of the dimers. In the particular case of PY, we have also computed the S0S1, S0T1, S0T2, and T1T2 states (Fig. S15). As the emission of TIPS-PY is red-shifted due to the presence of TIPS moieties, the extended conjugation leads to a decrease of excited state energies (Fig. 1a) as well as the polarization of the C[triple bond, length as m-dash]C bond in the opposite direction by the triplet spin compared to PY (Fig. S16). The higher stability of the T1 state in TIPS-PY can be attributed to the reduction of the HOMO–LUMO gap by 0.37 eV in TIPS-PY compared to PY.57 Given the extension of conjugation, the T1 energy of TIPS-PY (1.29 eV) decreased by 0.24 eV compared to PY (1.53 eV) making it suitable for exothermic triplet-energy transfer.

Triplet–triplet annihilation photon upconversion

Following photophysical characterization and excited-state modeling studies, the TIPS-PY annihilator was applied in TTA-UC in combination with PdTPBP as a sensitizer in deaerated THF. The investigated TIPS-PY: PdTPBP UC system demonstrated UC emission upon 640 nm laser excitation (Fig. 3a, b and S17), confirming the DFT prediction of the most favourable energetic condition (2T1 ≥ S1) for TTA-UC.5 To demonstrate the full potential of TIPS-PY, the annihilator concentration was varied from 0.1 mM to 100 mM while the PdTPBP concentration was maintained at 0.01 mM (Fig. 3a and c). The TIPS-PY: PdTPBP system demonstrated a high experimental ϕUC varying from 7.0% to 13.7% (Fig. 3c and Table 1) at 100 mM and 1 mM annihilator concentrations, respectively. The ϕUC and UC threshold (Ith) were estimated from ϕUC vs. excitation power density (Iex) profile according to previously reported procedures58 (Fig. S18 and Table 1).
image file: d5sc05248c-f3.tif
Fig. 3 (a) TIPS-PY: PdTPBP upconversion spectra at 0.1 mM, 1 mM, 10 mM, and 100 mM annihilator concentrations. 640 nm laser excitation indicated. (b) Digital image of TTA-UC emission, and (c) ϕFL, ϕTET, ϕUC, and f dependence on TIPS-PY concentration. All solutions were prepared in deaerated THF. PdTPBP concentration in all UC solutions was maintained at 0.01 mM. The grey lines serve as a guide to the eyes.
Table 1 UC parameters of TIPS-PY-PdTPBP UC solutions in deaerated THF at 0.1 mM, 1 mM, 10 m M, 100 mM, and 0.01 mM concentrations of TIPS-PY and PdTPBP
TIPS-PY ϕFLa, % ϕUCb, % ϕUCc, % ϕTETd, % Ithe, W cm−2 τTf, μs fg, %
a FL quantum yield of annihilator in UC solution.b Reabsorption corrected maximum measured UC quantum yield values.c Maximum attainable UC quantum yield values.d TET quantum yield.e UC threshold at 38.2% of ϕUC.f Triplet lifetime (=2 × τUC).g Statistical probability of singlet generation from two triplets via TTA, calculated according to eqn (1). τUC values in Table 1 were determined from the tail fit of the UC emission decay profiles in Fig. S21.
0.1 mM 73.5 11.1 14.4 96 0.19 1250 40.8
1 mM 75.5 13.7 14.9 99 0.29 914 39.8
10 mM 73.7 13.0 13.6 100 0.43 741 36.9
100 mM 65.5 7.0 8.0 100 4.94 30–80 24.4


The Ith values for TIPS-PY: PdTPBP vary from 0.19 W cm−2 to 0.43 W cm−2, a low threshold barrier desired for most applications. The difference in ϕUC at varying TIPS-PY concentrations can be explained by concentration effects on ϕFL and ϕTET according to eqn (1). While the ϕFL (75.5–73.5%) for 0.1 mM to 10 mM concentrations are similar, the 100 mM concentration sample demonstrates a decrease in ϕFL to 65.5% owing to the aggregation of the annihilator species (Fig. 3a and S19). This suggests an enhanced non-radiative decay channel, potentially due to the aggregation. It was also reflected in the anti-Stokes shifts, which varied from 0.56 to 0.21 eV between 0.1 to 100 mM TIPS-PY (Table S3).59 No significant aggregation is observed up to a concentration of 10 mM, as evidenced by the absence of changes in the low-energy shoulder of the absorption spectra (Fig. S20). The growth of ϕTET from 96% to 100% is explained by the higher concentration of acceptor chromophores surrounding sensitizer molecules. The longest triplet-lifetime, τT = 1250 μs was observed at the lowest TIPS-PY concentration (0.1 mM), and decreased further upon increasing the concentration (Table 1 and Fig. S21).

This decreases the average distance between PdTPBP and TIPS-PY, inferring higher TET probability. ϕTET was evaluated via rise time (τr) of TTA-UC transients (Fig. S22 and Table S4) according to the following relation:

 
image file: d5sc05248c-t3.tif(5)
where τ0 – intrinsic (unquenched) triplet lifetime of the sensitizer that, in the case of PdTPBP, is 175.5 μs.42 A high ϕTET = 96% was also confirmed from the quenching of the phosphorescence spectrum of PdTPBP by TIPS-PY (Fig. S22).

To further understand the higher TTA-UC quantum yields obtained with TIPS-PY, the f value of 39.2% ± 2.4% was evaluated according to eqn (1) as the average of 3 measurements at 0.1 mM, 1 mM, and 10 mM annihilator concentrations (Fig. 3b and Table 1). The results obtained at 0.1 mM, 1 mM, and 10 mM support that f value is an intrinsic property of a molecule that does not experience a change due to the change in concentration. The f value of 24.4% recorded at 100 mM was omitted from the calculation due to the presence of TIPS-PY aggregates (Fig. 3a and S19) in the UC solution enabling non-radiative decay channels.

For a reliable comparison of f values between studied PY,42 TIPS-PY, and BPEA, we conducted additional measurements at identical conditions with BPEA:PdTPBP UC system to determine the f value resulting in 6.3% (Fig. S23, S24, and Table S6). The reported f value of 39.2% ± 2.4% for TIPS-PY outperforms all previously studied annihilators within the 470–570 nm emission region and is among the top values in the entire spectrum (Fig. 4).5,40,54,60–62 This leads to a high experimental ϕUC of 13.7% with a possibility to approach the intrinsic limit ϕUC ∼19.6% if all energy transfer processes approach unity. The main reason for the high f value of TIPS-PY is the TIPS functional groups, which increase the stability of the triplet state as well as form a singlet-like character of the triplet dimer (T1T1) species, as revealed from the charge resonance or charge transfer studies. This may exhibit a positive impact on T1⋯T1 pair state and S1 coupling to generate the singlet-state with high efficiency according to the Merrifield model.18,29,48 Additionally, the favourable energy distribution prevents 2T1-to-T2 non-radiative decay from favouring the S1 formation.


image file: d5sc05248c-f4.tif
Fig. 4 Plot showing variation in statistical probability factor of various annihilators emitting across the visible spectral range. TIPS-PY synthesized in this work tops the list in the 470–570 nm range.

We also investigated the rate of TTA (kTTA) as a possible reason for higher UC performance in TIPS-PY compared to PY in THF. To determine kTTA of TIPS-PY, UC intensity decay profiles of TIPS-PY: PdTPBP and PY: PdTPBP solutions containing 0.1 mM of annihilator were measured at increasing excitation power densities (Fig. 5) and fitted using the following relation.63

 
image file: d5sc05248c-t4.tif(6)
 
image file: d5sc05248c-t5.tif(7)
Here, [3A*]0 denotes the initial triplet exciton concentration within the annihilator, and τT (=1/kT) is the spontaneous triplet decay lifetime. τT was obtained from the tails of the transients, assuming that the condition kT >> kTTA[3A*]0 is met at low triplet exciton concentration, where TTA is negligible.


image file: d5sc05248c-f5.tif
Fig. 5 Normalized UC transients of PY and TIPS-PY on a log–log scale at different excitation densities (indicated) upon sensitization with PdTPBP at 640 nm. Circles present experimental data, while solid lines show global fits with a shared τT.

The obtained β values, which describe TTA efficiency at particular excitation densities, are listed in Table S5, along with τT values. Since pulsed nanosecond excitation with a pulse duration much shorter than triplet lifetime was used, quasi-steady-state conditions could not be achieved, preventing direct determination of [3A*]0 from these measurements. However, given that the τT is known and remains invariant with excitation density, [3A*]0 at each pump level was estimated utilizing the reported kTTA value for PY (19 × 108 M−1 s−1 (ref. 64) according to the eqn (7). Considering the similar TET efficiencies for PY: PdTPBP (ϕTET = 92%)42 and TIPS-PY: PdTPBP (ϕTET = 96%; this work) at equivalent annihilator and sensitizer concentrations, the [3A*]0 values derived for PY: PdTPBP were also employed to estimate kTTA in TIPS-PY. The estimated kTTA for TIPS-PY is approximately 5 × 108 M−1 s−1, which is 4-fold lower than that of PY. Hence, kTTA may not be the reason for higher UC performance in TIPS-PY compared to PY. This observation is different from what has been reported by Han et al.40 where the higher normalized triplet–triplet annihilation efficiency of 3,10-di-o-tolylperylene (mB-PY) triplets, due to the restricted motion of o-tolyl rings was cited as the key reason for enhanced UC quantum yield.40 Nevertheless, the enhancement of UC performance by TIPS groups provides a novel strategy for molecular design for future annihilators as well as demonstrates the potential of TIPS-PY as another suitable compound to be implemented in numerous applications, especially in biology requiring 470–540 nm emission upon excitation with deep tissue penetrative red/far-red light.

To further demonstrate the potential of the TIPS-PY for long-wavelength far-red light upconversion, we performed TTA-UC study by combining TIPS-PY with Os(m-peptpy)2(TFSI)2 as sensitizer in deaerated DMF (Fig. 6a). The absorption spectrum of Os(m-peptpy)2(TFSI)2 shows vibronic peaks at 291, 318, 422, 447 nm due to ligand centred, at 494 nm due to singlet metal-to-ligand charge transfer (1MLCT), and at 648 nm and 673 nm due to triplet MLCT (3MLCT) (Fig. 6b).65 Furthermore, Os(m-peptpy)2(TFSI)2 shows 3MLCT emission at 759 nm (1.63 eV) and phosphorescence emission due to meta-substituted perylene units at 827 nm (1.5 eV), respectively.65 Unlike other Os-complexes, it shows a long phosphorescence lifetime (τPo) of 98 μs (Fig. S25), which is among the key requirements for an efficient sensitizer in TTA-UC.5 Upon excitation with a 730 nm CW laser, the TIPS-PY:Os(m-peptpy)2(TFSI)2 (1 mM:0.01 mM) system demonstrated bright yellow-green UC emission (Fig. 6c and d), thus expanding the upconversion range into the phototherapeutic window to the far-red region.33 The phosphorescence transients (Fig. S25) were used to determine the ϕTET = 99.7%, indicating almost complete quenching of TIPS-PY:Os(m-peptpy)2(TFSI)2 phosphorescence by TIPS-PY. Despite the high ϕTET, long triplet lifetime, τT = 846 μs (Fig. S26) and high ϕFL = 71% of TIPS-PY in this system, a low absolute ϕUC = 0.62%[thin space (1/6-em)]was observed. This could be due to 1) the secondary inner filter effect caused by fast reabsorption of the upconverted light by Os(m-peptpy)2(TFSI)2 due to the high spectral overlap of its absorption spectrum with the emission spectrum of TIPS-PY (Fig. 6b and Fig. S27), or 2) aggregated UC emission due to complexation of TIPS-PY with Os(m-peptpy)2(TFSI)2 confirmed from the distorted UC emission spectrum showing shift in emission maxima to 572 nm in the yellow emission range (Fig. 6c). Comparatively low solubility of TIPS-PY in DMF also support the possible aggregated UC emission. A better far-red absorbing sensitizer with higher transparency window in the TIPS-PY emission range may yield higher ϕUC.


image file: d5sc05248c-f6.tif
Fig. 6 (a) Molecular structure of Os(m-peptpy)2(TFSI)2. (b) Absorption spectrum of Os(m-peptpy)2(TFSI)2 and fluorescence emission spectrum of TIPS-PY (1 mM) in the presence of Os(m-peptpy)2(TFSI)2 (0.01 mM) in DMF (λex = 420 nm). (c) Upconversion emission spectrum of TIPS-PY: Os(m-peptpy)2(TFSI)2 (1 mM:0.01 mM) system (λex = 730 nm CW laser). (d) Digital image of the yellow-green UC emission upon 730 nm CW laser excitation.

Conclusions

We synthesized a new green-emitting annihilator TIPS-PY, which exhibits the highest absolute TTA-UC quantum yield of 13.7% (50% theoretical maximum) for red-to-green (640 nm to 489 nm) TTA-UC upon combining with PdTPBP as a sensitizer. Such a high UC quantum yield is enabled by the combined effects of: (1) a high ϕFL = 95% of TIPS-PY, (2) ϕTET ∼100% due to exothermic triplet energy transfer from PdTPBP to TIPS-PY, (3) minuscule secondary inner filter effects due to minimum spectral overlap of PdTPBP absorption and TIPS-PY emission, and (4) a high f value of 39.2% ± 2.4% of TIPS-PY, which generated a high singlet population after triplet-coupling. Further investigations of the f factor from the TheoDORE program revealed a singlet-like character of the triplet-pair state of TIPS-PY induced by the higher charge transfer character of the S0S1 excitations of TIPS-PY compared to PY. This may increase the coupling of the triplet-pair state with the excited singlet state of TIPS-PY to generate a high singlet population after triplet–triplet annihilation according to the Merrifield model. Interestingly, this behaviour was also observed for other TIPS-functionalized annihilators like TIPS-BP, having a similar transition dipole axis to that of PY, which was not previously explored. The obtained ϕUC and f values for TIPS-PY are among the highest for annihilators in the green-to-red spectral range and outperform well-known annihilators such as PY, BPEA, mB-PY, rubrene, or DPPs.

Author contributions

P. B., L. N., and K. M. P. conceptualized the idea of this work. M.M. synthesized the TIPS-Perylene. P. B. and M. M. carried out primary photophysical characterization. L. N., M. D., E. R, G. K., P. B., and K. K. carried out UC and time resolved measurements. C. A. and M. S. carried out computational calculations. Y. S., N. Y., and N. K. synthesized Os-complex. P.B., L. N., and K. M. P. wrote the first draft of the manuscript. All authors contributed to the analysis of results in their respective parts and editing of the manuscript.

Conflicts of interest

There are no conflicts to declare.

Data availability

The original datasets generated and analyzed during the current study are available from the corresponding authors on reasonable request and also available via open access on Zenodo at https://doi.org/10.5281/zenodo.3755810.

Supplementary information: synthesis, NMR, MALDI-TOF, and X-Ray diffraction analysis of TIPS-PY together with photophysical and upconversion measurements and DFT calculations. The authors have cited additional references within the SI.66–84 Cartesian coordinates of the species studied for computational calculations. See DOI: https://doi.org/10.1039/d5sc05248c.

Acknowledgements

L. N. acknowledges the Erasmus + Traineeship Program, P. B. and M. M. acknowledge financial support from the La-Caixa junior research leadership-post doctoral program (ID: 100010434, fellowship code: LCF/BQ/P122/11910023) the State Investigation Agency, through the Severo Ochoa Programme for Centres of Excellence in R&D (CEX2023-001263-S) and project PID2021-123873NB-I00 for financial support. L. N. and A. B. P. acknowledge the start-up funds provided by the University of California San Diego and the use of facilities and instrumentation supported by NSF through the UC San Diego Materials Research Science and Engineering Center (UCSD MRSEC), grant # DMR-2011924. K. M. P. acknowledges funding from the European Research Council (No. 101002131), the Swedish Energy Agency, the Göran Gustafsson Foundation, the Swedish Research Council, Swedish Research Council Formas, the European Research Council (ERC) under grant agreement CoG, PHOTHERM – 101002131, the Catalan Institute of Advanced Studies (ICREA), and the European Union's Horizon 2020 Framework Programme under grant agreement no. 951801. M. D., G. K., K. K., acknowledge the “Universities” Excellence Initiative” programme by the Ministry of Education, Science and Sports of the Republic of Lithuania under the agreement with the Research Council of Lithuania (project No. S-A-UEI-23-6). M. S. is grateful for financial support from the Agencia Española de Investigación (MCIN/AEI/10.13039/501100011033) for projects RED2024-154178-T and PID2023-147424NB-I00 and from the Generalitat de Catalunya for Project 2021SGR623 and ICREA Academia 2025 prize to M. S. N. Y. acknowledges the support by JSPS KAKENHI (JP23H00304). N. K. acknowledges the support by JSPS KAKENHI (JP20H05676).

References

  1. P. Bharmoria, H. Bildirir and K. Moth-Poulsen, Chem. Soc. Rev., 2020, 49, 6529–6554 RSC.
  2. F. Auzel, Chem. Rev., 2004, 104, 139–174 CrossRef PubMed.
  3. M. Wu, D. N. Congreve, M. W. B. Wilson, J. Jean, N. Geva, M. Welborn, T. Van Voorhis, V. Bulovic, M. G. Bawendi and M. A. Baldo, Nat. Photonics, 2016, 10, 31–34 CrossRef.
  4. T. Schloemer, P. Narayanan, Q. Zhou, E. Belliveau, M. Seitz and D. N. Congreve, ACS Nano, 2023, 17(4), 3259–3288 CrossRef PubMed.
  5. L. Naimovičius, P. Bharmoria and K. Moth-Poulsen, Mater. Chem. Front., 2023, 7, 2297–2315 RSC.
  6. B. D. Ravetz, A. B. Pun, E. M. Churchill, D. N. Congreve, T. Rovis and L. M. Campos, Nature, 2019, 565, 343–346 CrossRef PubMed.
  7. Q. Liu, M. Xu, T. Yang, B. Tian, X. Zhang and F. Li, ACS Appl. Mater. Interfaces, 2018, 10, 9883–9888 CrossRef PubMed.
  8. Y. Sasaki, M. Oshikawa, P. Bharmoria, H. Kouno, A. Hayashi-Takagi, M. Sato, I. Ajioka, N. Yanai and N. Kimizuka, Angew. Chem., Int. Ed., 2019, 58, 17827–17833 CrossRef PubMed.
  9. S. N. Sanders, T. H. Schloemer, M. K. Gangishetty, D. Anderson, M. Seitz, A. O. Gallegos, R. C. Stokes and D. N. Congreve, Nature, 2022, 604, 474–478 CrossRef PubMed.
  10. D. K. Limberg, J. H. Kang and R. C. Hayward, J. Am. Chem. Soc., 2022, 144, 5226–5232 CrossRef PubMed.
  11. A. J. Carrod, V. Gray and K. Börjesson, Energy Environ. Sci., 2022, 15, 4982–5016 RSC.
  12. R. E. Merrifield, J. Chem. Phys., 1968, 48, 4318–4319 CrossRef CAS.
  13. R. E. Merrifield, Pure Appl. Chem., 1971, 27, 481–498 CrossRef CAS.
  14. A. Olesund, J. Johnsson, F. Edhborg, S. Ghasemi, K. Moth-Poulsen and B. Albinsson, J. Am. Chem. Soc., 2022, 144, 3706–3716 CrossRef CAS PubMed.
  15. A. Monguzzi, R. Tubino, S. Hoseinkhani, M. Campione and F. Meinardi, Phys. Chem. Chem. Phys., 2012, 14, 4322–4332 RSC.
  16. D. Casanova, Theoretical modeling of singlet fission, Chem. Rev., 2018, 118, 7164–7207 CrossRef CAS PubMed.
  17. A. J. Carrod, V. Gray and K. Börjesson, Energy Environ. Sci., 2022, 15, 4982–5016 RSC.
  18. D.-G. Ha, R. Wan, C. A. Kim, T.-A. Lin, L. Yang, T. Van Voorhis, M. A. Baldo and M. Dincă, Nat. Mater., 2022, 21, 1275–1281 CrossRef CAS PubMed.
  19. M. B. Smith and J. Michl, Chem. Rev., 2010, 110, 6891–6936 CrossRef CAS PubMed.
  20. N. Harada, Y. Sasaki, M. Hosoyamada, N. Kimizuka and N. Yanai, Angew. Chem., Int. Ed., 2021, 60, 142–147 CrossRef CAS PubMed.
  21. V. Gray, A. Dreos, P. Erhart, B. Albinsson, K. Moth-Poulsen and M. Abrahamsson, Phys. Chem. Chem. Phys., 2017, 19, 10931–10939 RSC.
  22. A. Olesund, V. Gray, J. Mårtensson and B. Albinsson, J. Am. Chem. Soc., 2021, 143, 5745–5754 CrossRef CAS PubMed.
  23. D. Beljonne and A. Rao, ACS Mater. Lett., 2019, 1, 660–664 CrossRef.
  24. A. J. Carrod, A. Cravcenco, C. Ye and K. Börjesson, J. Mater. Chem. C, 2022, 10, 4923–4928 RSC.
  25. C. Ye, V. Gray, K. Kushwaha, S. Kumar Singh, P. Erhart and K. Börjesson, Phys. Chem. Chem. Phys., 2020, 22, 1715–1720 RSC.
  26. E. Radiunas, S. Raišys, S. Juršenas, A. Jozeliunaite, T. Javorskis, U. Šinkeviciute, E. Orentas and K. Kazlauskas, J. Mater. Chem. C, 2020, 8, 5525–5534 RSC.
  27. E. Radiunas, L. Naimovičius, S. Raišys, A. Jozeliūnaitė, E. Orentas and K. Kazlauskas, J. Mater. Chem. C, 2022, 10, 6314–6322 RSC.
  28. E. Radiunas, M. Dapkevičius, L. Naimovičius, P. Baronas, S. Raišys, S. Juršėnas, A. Jozeliūnaitė, T. Javorskis, U. Šinkevičiūtė, E. Orentas and K. Kazlauskas, J. Mater. Chem. C, 2021, 9, 4359–4366 RSC.
  29. D. G. Bossanyi, Y. Sasaki, S. Wang, D. Chekulaev, N. Kimizuka, N. Yanai and J. Clark, JACS Au, 2021, 1, 2188–2201 CrossRef CAS PubMed.
  30. W. S. Y. Cheng, B. Fuckel, T. Khoury, R. G. C. R. Clady, M. J. Y. Tayebjee, N. J. Ekins-Daukes and M. J. Crossley, J. Phys. Chem. Lett., 2010, 1, 1795–1799 CrossRef.
  31. A. B. Pun, L. M. Campos and D. N. Congreve, J. Am. Chem. Soc., 2019, 141, 3777–3781 CrossRef CAS.
  32. L. Naimovičius, E. Radiunas, B. Chatinovska, A. Jozeliūnaitė, E. Orentas and K. Kazlauskas, J. Mater. Chem. C, 2023, 11, 698–704 RSC.
  33. G. Alachouzos, A. M. Schulte, A. Mondal, W. Szymanski and B. L. Feringa, Angew. Chem., Int. Ed., 2022, 61, e202201308 CrossRef CAS PubMed.
  34. A. K. Singh, S. Banerjee, A. V Nair, S. Ray, M. Ojha, A. Mondal and N. D. P. Singh, ACS Appl. Bio. Mater., 2022, 5, 1202–1209 CrossRef CAS PubMed.
  35. K. R. Konrad, S. Gao, M. D. Zurbriggen and G. Nagel, Annu. Rev. Plant Biol., 2023, 74, 313–339 CrossRef CAS PubMed.
  36. K.-N. Chen and B.-G. Ma, ACS Synth. Biol., 2023, 12, 1708–1715 CrossRef CAS PubMed.
  37. S. H. C. Askes, M. Kloz, G. Bruylants, J. T. M. Kennis and S. Bonnet, Phys. Chem. Chem. Phys., 2015, 17, 27380–27390 RSC.
  38. I. Terashima, T. Fujita, T. Inoue, W. S. Chow and R. Oguchi, Plant Cell Physiol., 2009, 50, 684–697 CrossRef CAS PubMed.
  39. F. Plasser, J. Chem. Phys., 2020, 152, 084108 CrossRef CAS.
  40. L. Zeng, L. Huang, W. Lin, L. H. Jiang and G. Han, Nat. Commun., 2023, 14, 1102 CrossRef CAS PubMed.
  41. M. Tracy, S. Singh and Sony Corp, WO2017197144A1, 2016.
  42. L. Naimovičius, E. Radiunas, M. Dapkevičius, P. Bharmoria, K. Moth-Poulsen and K. Kazlauskas, J. Mater. Chem. C, 2023, 11, 14826–14832 RSC.
  43. A. J. Carrod, A. Cravcenco, C. Ye and K. Börjesson, J. Mater. Chem. C, 2022, 10, 4923–4928 RSC.
  44. J. E. Rogers, K. A. Nguyen, D. C. Hufnagle, D. G. McLean, W. Su, K. M. Gossett, A. R. Burke, S. A. Vinogradov, R. Pachter and P. A. Fleitz, J. Phys. Chem. A, 2003, 107, 11331–11339 CrossRef.
  45. R. Englman and J. Jortner, Mol. Phys., 1970, 18, 145 CrossRef.
  46. W. Siebrand, J. Chem. Phys., 1967, 47, 2411–2422 CrossRef.
  47. S. J. Jang, J. Chem. Phys., 2021, 155, 1641061–1641069 Search PubMed.
  48. R. C. Johnson and R. E. Merrifield, Phys. Rev. B, 1970, 1, 896–902 CrossRef.
  49. M. Gudem and M. Kowalewski, Chem.–Eur. J., 2022, 28, e202200781 CrossRef PubMed.
  50. K. C. Krishnapriya, P. Roy, B. Puttaraju, U. Salzner, A. J. Musser, M. Jain, J. Dasgupta and S. Patil, Nat. Commun., 2019, 10, 33 CrossRef PubMed.
  51. K. Miyata, F. S. Conrad-Burton, F. L. Geyer and X.-Y. Zhu, Chem. Rev., 2019, 119, 4261–4292 CrossRef PubMed.
  52. H.-S. lm and E. R. Bernstein, J. Chem. Phys., 1988, 88, 7337–7347 CrossRef.
  53. P. Yan, A. Chowdhury, M. W. Holman and D. M. Adams, J. Phys. Chem. B, 2005, 109, 724–730 CrossRef PubMed.
  54. J. A. Moghtader, M. Uji, T. J. B. Zähringer, M. Schmitz, L. M. Carrella, A. Heckel, E. Rentschler, N. Yanai and C. Kerzig, ChemRxiv, 2025 DOI:10.26434/chemrxiv-2025-9prp7.
  55. A. Olesund, J. Johnsson, F. Edhborg, S. Ghasemi, K. Moth-Poulsen and B. Albinsson, J. Am. Chem. Soc., 2022, 144, 3706–3716 CrossRef PubMed.
  56. C. Brand, W. L. Meerts and M. Schmitt, J. Phys. Chem. A, 2011, 115, 9612–9619 CrossRef CAS PubMed.
  57. P. Kimbert and F. Plasser, J. Chem. Theory Comput., 2023, 19, 2340–2352 CrossRef PubMed.
  58. Y. Murakami and K. Kamada, Phys. Chem. Chem. Phys., 2021, 23, 18268–18282 RSC.
  59. Y. Zhou, F. N. Castellano, T. W. Schmidt and K. Hanson, ACS Energy Lett., 2020, 5, 2322–2326 CrossRef CAS.
  60. P. Baronas, J. Lekavičius, M. Majdecki, J. L. Elholm, K. Kazlauskas, P. Gaweł and K. Moth-Poulsen, ACS Cent. Sci., 2025, 11, 413–421 CrossRef CAS PubMed.
  61. E. Radiunas, L. Naimovičius, P. Baronas, A. Jozeliūnaitė, E. Orentas and K. Kazlauskas, Adv. Opt. Mater., 2025, 13, 2403032 CrossRef CAS.
  62. L. Naimovičius, S. K. Zhang and A. B. Pun, J. Mater. Chem. C, 2024, 12, 18374–18380 RSC.
  63. F. Edhborg, A. Olesund and B. Albinsson, Photochem. Photobiol. Sci., 2022, 21, 1143–1158 CrossRef CAS PubMed.
  64. A. J. Carrod, A. Cravcenco, C. Ye and K. Börjesson, J. Mater. Chem. C, 2022, 10, 4923–4928 RSC.
  65. Y. Sasaki, N. Yanai and N. Kimizuka, Inorg. Chem., 2022, 61, 5982–5990 CrossRef CAS.
  66. J.-H. Kim, C. E. Song, I.-N. Kang, W. S. Shind and D.-H. Hwang, Chem. Commun., 2013, 49, 3248–3250 RSC.
  67. G. M. Sheldrick, Acta Crystallogr., Sect. A: Found. Crystallogr., 2015, 71, 3–8 CrossRef.
  68. G. M. Sheldrick, Acta Crystallogr., Sect. C: Struct. Chem., 2015, 71, 3–8 Search PubMed.
  69. O. V. Dolomanov, L. J. Bourhis, R. J. Gildea, J. A. K. Howard and H. Puschmann, J. Appl. Crystallogr., 2009, 42, 339–341 CrossRef CAS.
  70. C. Adamo and V. Barone, J. Chem. Phys., 1999, 110, 6158–6170 CrossRef CAS.
  71. S. Grimme, J. Antony, S. Ehrlich and H. Krieg, J. Chem. Phys., 2010, 132, 154104 CrossRef PubMed.
  72. E. R. Johnson and A. D. Becke, J. Chem. Phys., 2005, 123, 024101 CrossRef PubMed.
  73. A. D. Becke and E. R. Johnson, J. Chem. Phys., 2005, 123, 154101 CrossRef.
  74. R. Krishnan, J. S. Binkley, R. Seeger and J. A. Pople, J. Chem. Phys., 1980, 72, 650–654 CrossRef CAS.
  75. M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, G. Scalmani, V. Barone, G. A. Petersson, H. Nakatsuji, X. Li, M. Caricato, A. V Marenich, J. Bloino, B. G. Janesko, R. Gomperts, B. Mennucci, H. P. Hratchian, J. V Ortiz, A. F. Izmaylov, J. L. Sonnenberg, D. Williams-Young, F. Ding, F. Lipparini, F. Egidi, J. Goings, B. Peng, A. Petrone, T. Henderson, D. Ranasinghe, V. G. Zakrzewski, J. Gao, N. Rega, G. Zheng, W. Liang, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, T. Vreven, K. Throssell, J. A. Montgomery Jr., J. E. Peralta, F. Ogliaro, M. J. Bearpark, J. J. Heyd, E. N. Brothers, K. N. Kudin, V. N. Staroverov, T. A. Keith, R. Kobayashi, J. Normand, K. Raghavachari, A. P. Rendell, J. C. Burant, S. S. Iyengar, J. Tomasi, M. Cossi, J. M. Millam, M. Klene, C. Adamo, R. Cammi, J. W. Ochterski, R. L. Martin, K. Morokuma, O. Farkas, J. B. Foresman and D. J. Fox, Gaussian 16 Rev. C.01, Wallingford, CT, 2016soft Search PubMed.
  76. C. Lee, W. Yang and R. G. Parr, Phys. Rev. B: Condens. Matter Mater. Phys., 1988, 37, 785–789 CrossRef CAS PubMed.
  77. A. D. Becke, J. Chem. Phys., 1993, 98, 5648–5652 CrossRef CAS.
  78. M. R. Padhye, S. P. McGlynn and M. Kasha, J. Chem. Phys., 1956, 24, 588–594 CrossRef CAS.
  79. J. S. Brinen and J. G. Koren, Chem. Phys. Lett., 1968, 2, 671–672 CrossRef CAS.
  80. J. K. H. Pun, J. K. Gallaher, L. Frazer, S. K. K. Prasad, C. B. Dover, R. W. MacQueen and T. W. Schmidt, J. Photonics Energy, 2018, 8, 1 Search PubMed.
  81. R. H. Clarke and R. M. Hochstrasser, J. Mol. Spectrosc., 1969, 32, 309–319 CrossRef CAS.
  82. E. M. Gholizadeh, S. K. K. Prasad, Z. L. Teh, T. Ishwara, S. Norman, A. J. Petty, J. H. Cole, S. Cheong, R. D. Tilley, J. E. Anthony, S. Huang and T. W. Schmidt, Nat. Photonics, 2020, 14, 585–590 CrossRef CAS.
  83. T. N. Singh-Rachford and F. N. Castellano, J. Phys. Chem. A, 2008, 112, 3550–3556 CrossRef CAS PubMed.
  84. J. C. De Mello, H. F. Wittmann and R. H. Friend, Adv. Mater., 1997, 230–232 CrossRef CAS.

This journal is © The Royal Society of Chemistry 2025
Click here to see how this site uses Cookies. View our privacy policy here.