Delayed fluorescence from inverted singlet and triplet excited states

Hund’s multiplicity rule states that a higher spin state has a lower energy for a given electronic configuration1. Rephrasing this rule for molecular excited states predicts a positive energy gap between spin-singlet and spin-triplet excited states, as has been consistent with numerous experimental observations over almost a century. Here we report a fluorescent molecule that disobeys Hund’s rule and has a negative singlet–triplet energy gap of −11 ± 2 meV. The energy inversion of the singlet and triplet excited states results in delayed fluorescence with short time constants of 0.2 μs, which anomalously decrease with decreasing temperature owing to the emissive singlet character of the lowest-energy excited state. Organic light-emitting diodes (OLEDs) using this molecule exhibited a fast transient electroluminescence decay with a peak external quantum efficiency of 17%, demonstrating its potential implications for optoelectronic devices, including displays, lighting and lasers.

Hund's multiplicity rule states that a higher spin state has a lower energy for a given electronic configuration 1 . Rephrasing this rule for molecular excited states predicts a positive energy gap between spin-singlet and spin-triplet excited states, as has been consistent with numerous experimental observations over almost a century. Here we report a fluorescent molecule that disobeys Hund's rule and has a negative singlettriplet energy gap of −11 ± 2 meV. The energy inversion of the singlet and triplet excited states results in delayed fluorescence with short time constants of 0.2 μs, which anomalously decrease with decreasing temperature owing to the emissive singlet character of the lowest-energy excited state. Organic light-emitting diodes (OLEDs) using this molecule exhibited a fast transient electroluminescence decay with a peak external quantum efficiency of 17%, demonstrating its potential implications for optoelectronic devices, including displays, lighting and lasers.
The spin multiplicity of molecular excited states plays a crucial role in organic optoelectronic devices. In the case of OLEDs, recombination of charge carriers leads to the formation of singlet and triplet excited states in a 1:3 ratio. This spin statistics limits the internal quantum efficiency of OLEDs and leads to the energy loss owing to the spin-forbidden nature of triplet excited states to emit photons. To overcome this issue, two strategies for harvesting the 'dark' triplet excited states as photons have been established. The first relies on organometallic complexes with transition metals, such as iridium and platinum, which induce a large spin-orbit coupling to allow triplet states to emit photons as phosphorescence [2][3][4] . The other uses organic molecules that exhibit thermally activated delayed fluorescence (TADF) [5][6][7] . This class of materials has energetically close singlet and triplet excited states, in which ambient thermal energy upconverts the triplet states into the singlet states through reverse intersystem crossing (RISC). Although the concept of TADF has the advantage of eliminating the need for transition metals, the resultant temporally delayed fluorescence typically has a time constant in the microsecond or even millisecond range, which is long enough for detrimental bimolecular annihilations, such as triplet-triplet annihilation and tripletpolaron annihilation, to compete with delayed fluorescence. These bimolecular annihilations lead to the decrease in device efficiency under high current densities, known as efficiency roll-off in OLEDs 8,9 , and also generate high-energy excitons that are suspected to cause chemical degradation of materials, particularly in blue OLEDs 10 . The research community has thus focused on minimizing the singlettriplet energy gap (ΔE ST ) to accelerate the upconversion by thermal activation 7 . Alternatively, an ideal case would be thermodynamically favourable downconversion with negative ΔE ST , which is not expected if applying Hund's multiplicity rule to the lowest-energy excited state.
Herein, we demonstrate experimental evidence of the existence of highly fluorescent organic molecules that disobey Hund's rule and possess negative ΔE ST for constructing efficient OLEDs.
Numerous observations of positive ΔE ST in molecular excited states are generally understood by the exchange interaction, the quantum-mechanical effect involving Pauli repulsion, which stabilizes triplet states relative to singlet states 11 . ΔE ST is simply equal to twice the positive exchange energy if the lowest-energy singlet and triplet excited states (S 1 and T 1 ) have the same single-excitation configuration 11 . Although there is general agreement that ΔE ST must be positive, potentially negative ΔE ST has been discussed in nitrogen-substituted phenalene analogues, such as cycl [3.3.3]azine and heptazine, during the past two decades [12][13][14][15][16][17][18][19][20][21] . Recent theoretical studies have also suggested the possibility of negative ΔE ST in these molecules by accounting for double-excitation configurations in which two electrons of occupied orbitals have been promoted out to virtual orbitals [15][16][17][18][19] ( Supplementary  Fig. 1). Because the Pauli exclusion principle restricts the accessible double-excitation configurations in T 1 , an effective admixture of such configurations stabilizes S 1 relative to T 1 . If this stabilization overcomes the exchange energy, ΔE ST could be a negative value (Fig. 1a). However, to the best of our knowledge, none of the molecules has been experimentally identified with negative ΔE ST and the resultant delayed fluorescence from inverted singlet and triplet excited states (DFIST). We note that the accounting for double-excitation configurations has proved crucial to theoretically reproduce the small but positive ΔE ST of 5,9-diphenyl-5,9-diaza-13b-boranaphtho[3,2,1-de]anthracene (DABNA-1) (0.15 eV) 22,23 .
Pioneering computational calculations 15 inspired us to focus on heptazine as a potential class of molecules that exhibit DFIST. Correlated wave function theories suggested that S 1 of heptazine lies 0.2-0.3 eV below T 1 , although S 1 is a 'dark' state, meaning that the electronic transition to the ground state (S 0 ) is dipole-forbidden and the oscillator strength (f) is zero in the D 3h symmetry point group. Notably, the heptazine core is shared by several synthesized molecules that exhibit intense TADF 24,25 with positive ΔE ST (refs. 26,27 ). Furthermore, the recent computational screening by Pollice et al. has demonstrated that appropriate chemical modifications of heptazine recover f while retaining negative ΔE ST (ref. 19 ). As such, we introduced 186 different substituents to heptazine to generate 34,596 candidate molecules for computational screening. The structures of all substituents are available in Supplementary  Fig. 2. To ensure the synthetic feasibility, at most two distinct types of substituents were introduced to the heptazine core as R 1 and R 2 (Fig. 1b). We used standard linear-response time-dependent density functional theory (TDDFT) to calculate ΔE ST and f, which are more affordable in computational cost than those calculated by correlated wave function theories. Although the commonly used adiabatic approximation in TDDFT does not account for double-excitation character 16,28 , the properties calculated by TDDFT are still useful to prescreening for narrowing the list of the candidate molecules before the high-cost calculations and experimental evaluation, as both S 1 and T 1 of heptazine are almost dominated by the single-excitation configuration between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) 15 . Figure 1c shows the statistics of the screened molecules as a function of ΔE ST and f calculated by TDDFT. A well-known trade-off between small ΔE ST and large f is evident from this particular dataset of heptazine analogues. Although balancing such a trade-off is a key concern in recent synthetic efforts on TADF materials, Fig. 1c demonstrates the optimal combinations of ΔE ST and f for which one parameter can no longer be improved without sacrificing the other. Figure 1d further visualizes the trade-off between ΔE ST and f for each fluorescence colour. The screening data suggest 5,264 promising candidates to show fluorescence across the entire visible spectrum, with ΔE ST < 0.35 eV and f > 0.01. Setting the range of the vertical S 1 -S 0 energy gap to 2.70-2.85 eV for blue fluorescence further narrows down the candidates to 1,028 molecules, corresponding to 2.97% of all the screened molecules. We then assessed their synthetic feasibility and selected two heptazine analogues HzT-FEX 2 and HzPipX 2 ( Fig. 2a) for further evaluation. We note that these molecules recover f while retaining small ΔE ST (f = 0.010 and 0.015 and ΔE ST = 210 and 334 meV for HzTFEX 2 and HzPipX 2 , respectively). This trend is consistent with the recent computational screening on heptazine analogues with asymmetrical substitutions 19 .

Article
To examine whether HzTFEX 2 and HzPipX 2 could have negative ΔE ST , we computed their S 1 and T 1 by correlated wave function theories. Equation-of-motion coupled cluster with single and double excitation (EOM-CCSD) 29 calculations predict HzTFEX 2 to possess negative ΔE ST of −12 meV, affirming its potential for exhibiting DFIST. In comparison, ΔE ST calculated for HzPipX 2 remains at a positive value of 10 meV, which is comparable with those of the current state-of-the-art TADF materials [30][31][32][33][34][35][36][37][38] . Figure 2b,c shows the dominant pair of natural transition orbitals (NTOs) 39 for S 1 and T 1 . In both molecules, the hole orbitals are exclusively localized on the peripherical six nitrogen atoms of the heptazine core, whereas the electron orbitals are localized on the central nitrogen atom and the carbon atoms of the core, as well as on the substituents. The spatial separation of these orbitals indicates that the exchange interaction is weak, resulting in nearly degenerate S 1 and T 1 in the single-excitation picture. Similar spatial separations of NTOs have also been found in the multi-resonant TADF materials, such as DABNA-1 (refs. 22,23 ). In this situation, the stabilization of S 1 by including the double-excitation configurations becomes more dominant to determine the sign of ΔE ST . Indeed, S 1 of both molecules comprise double-excitation configurations with weights of around 1% described as the sum of the squares of the doubles amplitudes in EOM-CCSD, which are slightly higher than those of T 1 . Two other wave-function-based calculations using second-order algebraic diagrammatic construction (ADC(2)) 40 and complete active space with second-order perturbation theory (CASPT2) 41 further validate the inversion of S 1 and T 1 in HzTFEX 2 with calculated ΔE ST of −34 meV and −184 meV, respectively. However, for HzPipX 2 , the two methods also invert ΔE ST (−12 meV with ADC(2) and −171 meV with CASPT2) as compared with the positive value of 10 meV predicted with EOM-CCSD (Supplementary Table 1). This variation in estimates of ΔE ST highlights the current limitations of excited-state calculations and demands conclusive experimental evaluation. We note that ΔE ST calculated by other second-order methods are given in the Supplementary Information, as well as the dependence of the choice of the guess orbitals and the size of the active space on the CASPT2 results.  Table 1). The steady-state absorption spectra of HzTFEX 2 and HzPipX 2 comprise the lowest-energy absorption band centred at 441 nm and 429 nm, respectively, with small molar absorption coefficients on the order of 10 3 M −1 cm −1 , reflecting the spatial separation between the hole and electron NTOs computed for S 1 of each molecule. On photoexcitation, HzTFEX 2 exhibits blue emission with a peak wavelength (λ PL ) of 449 nm and a photoluminescence (PL) quantum yield (Φ PL ) of 74%, whereas slightly blue-shifted λ PL of 442 nm and similar Φ PL of 67% are observed for HzPipX 2 . These energy differences in absorption and emission are also predicted by TDDFT calculations and are attributed to the stronger electron-donating effect of the piperidyl group in HzPipX 2 than that of 2,2,2-trifluoroethoxy group in HzTFEX 2 . In aerated toluene solutions, Φ PL of HzTFEX 2 and HzPipX 2 decrease to 54% and 37%, respectively. Because atmospheric O 2 can quench molecular triplet excited states and the change in Φ PL is reversible, we ascribe the blue emissions of the two molecules, at least partially, to delayed fluorescence through forward intersystem crossing (ISC) and RISC between S 1 and T 1 . This assumption is supported by transient absorption decay measurements on HzTFEX 2 , which scrutinized ISC from S 1 to T 1 as the signal decay of S 1 at 700 nm and the signal growth of T 1 at 1,600 nm, followed by the persistent signal decays of both S 1 and T 1 (Extended Data Fig. 1). We also note that both decays have similar time constants (223 ns for S 1 and 210 ns for T 1 ), indicating the steady-state condition with the constant population ratio maintained by ISC and RISC.
To show the excited-state kinetics of the two molecules in detail, we performed transient PL decay measurements at varying temperatures (Fig. 3b,c and Supplementary Fig. 3 for the log-log representation). Both molecules exhibit biexponential transient PL decays, which comprise nanosecond-order prompt fluorescence followed by sub-microsecond delayed fluorescence with temperature-dependent time constants. Remarkably, the time constant of delayed fluorescence (τ DF ) of HzTFEX 2 gradually decreases from 217 ns to 195 ns with decreasing temperature from 300 K to 200 K (Fig. 3d). This anomalous temperature dependence of τ DF indicates that S 1 lies energetically below T 1 , for which lowering the temperature shifts the steady-state population towards emissive S 1 relative to dark T 1 and thus accelerates the delayed fluorescence (that is, decreases τ DF ). In comparison, τ DF of HzPipX 2 increases from 565 ns to 1,372 ns by the same temperature decrease, as has been similarly observed in conventional TADF materials [5][6][7] . It is worth noting that τ DF of HzTFEX 2 is much shorter than emission time constants ever reported for TADF materials [30][31][32][33][34][35][36][37][38] and phosphorescent materials 2-4 used for efficient OLEDs, which are typically in the microsecond range.
We further analysed the temperature-dependent PL decay kinetics with the underlying rate equation. In the absence of phosphorescence and non-radiative decay of T 1 to S 0 , the rate equation for the populations of S 1 and T 1 is given by in which k r , k nr , k ISC and k RISC are the rate constants of radiative decay of S 1 to S 0 , non-radiative decay of S 1 to S 0 , ISC of S 1 to T 1 and RISC of T 1 to S 1 , respectively. By numerically fitting equation (1) to the PL decay data at 300 K, we found that RISC is faster than ISC in HzTFEX 2 (k RISC = 4.2 × 10 7 s −1 versus k ISC = 2.3 × 10 7 s −1 ), whereas RISC is slower than ISC in HzPipX 2 (k RISC = 2.2 × 10 7 s −1 versus k ISC = 8.9 × 10 7 s −1 ) (Fig. 3e,f). These parameters simulate that the population of T 1 is lower than that of S 1 in HzTFEX 2 under the steady-state condition, indicating that S 1 lies energetically below T 1 (Extended Data Fig. 2). Furthermore, the temperature dependence of k ISC and k RISC follows the Arrhenius equation, k = Aexp(−E a /k B T), in which k is the rate constant, A is the pre-exponential factor, E a is the activation energy, k B is the Boltzmann constant and T is the absolute temperature (Extended Data Fig. 3). The best-fit parameters of the Arrhenius equation yield the activation energies of ISC and RISC (E a,ISC and E a,RISC ) (Extended Data Table 1). Subtracting E a,ISC from E a,RISC , we determined ΔE ST of HzTFEX 2 to be −11 ± 2 meV, which is in marked contrast to positive ΔE ST ever observed in numerous molecules, as well as in HzPipX 2 (ΔE ST = 52 ±1 meV). We note that the change in k r + k nr at varying temperatures is negligible compared with those in k ISC and k RISC (Supplementary Fig. 4) and thus the decreasing trend of τ DF of HzTFEX 2 is more reasonably attributed to the inverted S 1 and T 1 . The negative ΔE ST of HzTFEX 2 is retained in a solid-state host matrix (see Extended Data Fig. 4 and the Supplementary Information for details).
Having experimentally determined negative ΔE ST , we conclude that HzTFEX 2 exhibits DFIST. Further synthetic efforts replacing the xylyl groups in HzTFEX 2 with either phenyl or tolyl groups led to HzTFEP 2 and HzTFET 2 , which similarly show DFIST with measured ΔE ST of −14 ± 3 meV and −13 ± 3 meV, respectively (see Extended Data Table 1 and Supplementary Fig. 5 for details), indicating the potential of heptazines for further developing efficient DFIST materials. In common with the three materials, ISC from S 1 to T 1 competes with the inherently slow radiative decay of heptazines, followed by faster RISC, leading to a significant S 1 population relative to T 1 and sub-microsecond DFIST. Thus, we propose to refer to the present type of emissions as 'H (heptazine)-type delayed fluorescence' by analogy with 'E (eosin)-type delayed fluorescence' referred to as TADF 42 and 'P (pyren)-type delayed fluorescence' involving triplet-triplet annihilation 43 .
Finally, we evaluated the electroluminescence (EL) properties of HzTFEX 2 in OLEDs fabricated by thermal evaporation. The details of the fabrication procedures and the device structures are given in the Supplementary Information. Figure 4a,b shows the EL spectra, current density-voltage-luminance characteristics and external quantum efficiency-luminance characteristics of the OLED. Intense blue EL originating from HzTFEX 2 was observed with spectral peak wavelengths (λ EL ) at 450 nm and 479 nm and Commission internationale de l'éclairage (CIE) coordinates of (0.17, 0.24). The maximum external quantum efficiency reached 17%, corresponding to the internal quantum efficiency of 80% for a bottom-emission OLED with a typical light-outcoupling efficiency of 20% 44 . We note that the viewing-angle dependence of the luminance followed the Lambertian distribution ( Fig. 4b inset), ensuring accurate estimation of the external quantum efficiency from the forward emission. Remarkably, HzTFEX 2 exhibited fast transient EL decay, reflecting the sub-microsecond H-type delayed fluorescence (Fig. 4c). In comparison, much slower transient EL decays were observed for E-type delayed fluorescence of 2,4,5,6-tetra(carbazol-9-yl)isophthalonitrile (4CzIPN) 6 and P-type delayed fluorescence of 2-methyl-9,10-bis(naphthalen-2-yl) anthracene (MADN) 45 , although the EL of MADN initially decayed faster by the prompt fluorescence solely from S 1 (ref. 46 ). It is thus evident that the fast triplet harvesting of HzTFEX 2 with negative ΔE ST can be retained even in actual OLEDs. Although the efficiency roll-off is still marked in this preliminary device concerning the large hole injection barrier caused by the high ionization potential of HzTFEX 2 (6.3 eV), we anticipate that further optimization of molecular design will address this issue and allow a conclusive exploration of the effects of negative ΔE ST on efficiency roll-off and device stability.
In conclusion, we have demonstrated fluorescent heptazine molecules that possess negative ΔE ST . We observed their blue delayed fluorescence in both PL and EL with anomalous features: (1) the very short decay time constants (τ DF ≈ 0.2 μs), (2) the decreasing trend of τ DF with decreasing temperature and (3) the rate inversion of RISC and ISC (k RISC > k ISC ). These features indeed arise from negative ΔE ST and led to the terminology 'delayed fluorescence from inverted singlet and triplet Article excited states (DFIST)' or 'H (heptazine)-type delayed fluorescence'. We predict that further development of DFIST materials will offer stable and efficient OLEDs based on the fast triplet-to-singlet downconversion, with great implications for displays, lighting and lasers.

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