Spin–Vibronic Model for Quantitative Prediction of Reverse Intersystem Crossing Rate in Thermally Activated Delayed Fluorescence Systems

Achieving efficient and stable blue thermally activated delayed fluorescence organic light-emitting diodes based on four-coordinate fluoroboron emitters by simple substitution molecular engineering

Achieving both high efficiency and high stability in blue thermally activated delayed fluorescence organic light-emitting diodes (TADF-OLEDs) is challenging for practical displays and lighting. Here, we have successfully developed a series of sky-blue to pure-blue emitting donor-acceptor (D-A) type TADF materials featuring a four-coordinated boron with 2,2'-(pyridine-2,6-diyl)diphenolate (dppy) ligands, i.e.1-8. Synergistic engineering of substituents on the phenyl bridge as well as the electronic properties and the attached positions of heteroatom N-donors not only enables fine-tuning of the emission colors, but also modulates the nature and energies of their triplet excited states that are important for the reverse intersystem crossing (RISC). Particularly for the compound with two methyl substituents on the phenyl bridge (compound 8), RISC is significantly facilitated through the vibronic coupling of the energetically close-lying triplet charge transfer (3CT) and the triplet local excited (3LE) states, when compared to analogue 7. Efficient sky-blue to pure-blue OLEDs with electroluminescence peaks (λ EL) at 460-492 nm have been obtained, in which ca. five-fold higher external quantum efficiencies (EQEs) of 18.9% have been demonstrated by 8 than that by 7. Moreover, ca. thirty times longer device operational half-lifetimes (LT50) of 9113 hours for 8 than that for 7 as well as satisfactory LT50 reaching 26 643 hours for 6 at an initial luminance of 100 cd m-2 have also been demonstrated. To the best of our knowledge, these results represent one of the best high-performance blue OLEDs based on tetracoordinated boron TADF emitters. Moreover, the design strategy presented here has provided an attractive strategy for enhancing the device performance of blue TADF-OLEDs.

Reverse Intersystem Crossing Dynamics in Vibronically Modulated Inverted Singlet-Triplet Gap System: A Wigner Phase Space Study

We inspect the origin of the inverted singlet-triplet gap (INVEST) and slow change in the reverse intersystem crossing (rISC) rate with temperature, as recently observed. A Wigner phase space study reveals that, though INVEST is found at equilibrium geometry, variation in the exchange interaction and the doubles-excitation for other geometries in the harmonic region leads to non-INVEST behavior. This highlights the importance of nuclear degrees of freedom for the INVEST phenomenon, and in this case, geometric puckering of the studied molecule determines INVEST and the associated rISC dynamics.

Charge Transfer and Intersystem Crossing in Compact Naphthalenediimide-Phenothiazine Triads: Synthesis and Study of the Photophysical Property with Transient Optical and Electron Paramagnetic Resonance Spectroscopic Methods

In order to obtain a long-lived charge separation (CS) state in compact electron donor-acceptor molecular systems, we prepared a series of naphthalenediimide (NDI)-phenothiazine (PTZ) triads, with phenylene as the linker between the donor and acceptor. Conformation restriction is imposed to control the mutual orientation of the NDI and PTZ units by attaching methyl groups on the phenylene linker to tune the electronic coupling between the donor and the acceptor. Moreover, the PTZ moiety was oxidized to sulfoxide to tune the ordering of the CS state and the 3LE state (LE: locally excited state). UV-vis absorption spectra indicate electronic coupling between NDI with the phenylene linker as well as the PTZ units, manifested by the appearance of a charge-transfer (CT) absorption band, whereas this coupling is devoid in the triads with conformation restriction imposed. Fluorescence is strongly quenched in the triads compared to the reference compound, indicating electron transfer upon photoexcitation. Femtosecond transient absorption spectra indicate that the CS takes 0.8 ps, and then the 3LE state is formed by charge recombination in 83 ps. Nanosecond transient absorption (ns-TA) spectra show that the 3NDI state was observed in nonpolar solvents such as cyclohexane (triplet state lifetime: 95.7 μs), whereas the CS state was observed in more polar solvents. The CS state lifetimes are up to 1.2 μs (in toluene). Time-resolved electron paramagnetic resonance spectra of the triads in toluene consist of two types of signals: CS states (narrower signals, ∼10 mT) and 3LE states (broader signals, ∼50 to 200 mT). In the spectra of the triads containing PTZ, the CS state signals dominate, whereas for the triads containing oxidized PTZ, the 3NDI signals (zero-field splitting D ≈ 2000 MHz) prevail, both observations being in agreement with the ns-TA spectral studies. The electron spin polarization phase pattern of the 3NDI states of the triads indicates that the intersystem crossing (ISC) mechanism is spin-orbit charge-transfer ISC. Considering the 3CS state as ion pairs, the electron-exchange energy (J) is determined to be -39 to -59 MHz, and the electron spin dipolar interaction is 83-92 MHz.

Deep Learning-Based Chemical Similarity for Accelerated Organic Light-Emitting Diode Materials Discovery

Thermally activated delayed fluorescence (TADF) material has attracted great attention as a promising metal-free organic light-emitting diode material with a high theoretical efficiency. To accelerate the discovery of novel TADF materials, computer-aided material design strategies have been developed. However, they have clear limitations due to the accessibility of only a few computationally tractable properties. Here, we propose TADF-likeness, a quantitative score to evaluate the TADF potential of molecules based on a data-driven concept of chemical similarity to existing TADF molecules. We used a deep autoencoder to characterize the common features of existing TADF molecules with common chemical descriptors. The score was highly correlated with the four essential electronic properties of TADF molecules and had a high success rate in large-scale virtual screening of millions of molecules to identify promising candidates at almost no cost, validating its feasibility for accelerating TADF discovery. The concept of TADF-likeness can be extended to other fields of materials discovery.

Accidental triplet harvesting in donor-acceptor dyads with low spin-orbit coupling

We present an accidental mechanism for efficient intersystem crossing (ISC) between singlet and triplet states with low spin-orbit coupling (SOC) in molecules having donor-acceptor (D-A) moieties separated by a Sigma bond. Our study shows that SOC between the lowest singlet excited state and the higher-lying triplet states, together with nuclear motion-driven coupling of this triplet state with lower-lying triplet states during the free rotation about a Sigma bond, is one of the possible ways to achieve the experimentally observed ISC rate for a class of D-A type photoredox catalysts. This mechanism is found to be the dominant contributor to the ISC process with the corresponding rate reaching a maximum at a dihedral angle in the range of 72°-78° between the D-A moieties of 10-(naphthalen-1-yl)-3,7-diphenyl-10H-phenoxazine and other molecules included in the study. We have further demonstrated that the same mechanism is operative in a specific spirobis[anthracene]dione molecule, where the D and A moieties are interlocked near to the optimal dihedral angle, indicating the plausible effectiveness of the proposed mechanism. The present finding is expected to have implications in strategies for the synthesis of new generations of triplet-harvesting organic molecules.

Theoretical Insight into the Effect of Phosphorus Oxygenation on Nonradiative Decays: Comparative Analysis of P-Bridged Stilbene Analogs

Incorporation of the phosphorus element into a π-conjugated skeleton offers valuable prospects for adjusting the electronic structure of the resulting functional π-electron systems. Trivalent phosphorus has the potential to decrease the LUMO level through σ*-π* interaction, which is further enhanced by its oxygenation to the pentavalent P center. This study shows that utilizing our computational analysis to examine excited-state dynamics based on radiative/nonradiative rate constants and fluorescence quantum yield (ΦF) is effective for analyzing the photophysical properties of P-containing organic dyes. We theoretically investigate how the trivalent phosphanyl group and pentavalent phosphine oxide moieties affect radiative and nonradiative decay processes. We evaluate four variations of P-bridged stilbene analogs. Our analysis reveals that the primary decay pathway for photoexcited bis-phosphanyl-bridged stilbene is the intersystem crossing (ISC) to the triplet state and nonradiative. The oxidation of the phosphine moiety, however, suppresses the ISC due to the relative destabilization of the triplet states. The calculated rate constants match an increase in experimental ΦF from 0.07 to 0.98, as simulated from 0.23 to 0.94. The reduced HOMO-LUMO gap supports a red shift in the fluorescence spectra relative to the phosphine analog. The thiophene-fused variant with the nonoxidized trivalent P center exhibits intense emission with a high ΦF, 0.95. Our prediction indicates that the ISC transfer is obstructed owing to the relatively destabilized triplet state induced by the thiophene substitution. Conversely, the thiophene-fused analog with the phosphine oxide moieties triggers a high-rate internal conversion mediated by conical intersection, leading to a decreased ΦF.

The photophysical properties of sulfone-based TADF emitters in relation to their structural properties

In this work, thermally activated delayed fluorescence (TADF) of a series of emitters with sulfone-based acceptor moieties was studied by density functional theory (DFT) methods. Sulfone derivatives were shown to be high performing TADF emitters over recent years. When discussing the TADF efficiency, various properties, such as the singlet-triplet energy gap (ΔEST), spin-orbit coupling (SOC) and the nature of states, stand out due to their roles in reverse intersystem crossing (RISC). Here, we mainly focused on three important structural parameters that affect the intersystem crossing (ISC) and RISC pathways and their efficiencies. These three parameters are: (1) the effect of meta- and para-conjugation, (2) the effect of rigid acceptor moieties and (3) the effect of the phenyl bridge on photophysical properties.

The Unified Hamiltonian Formalism of Spin-Orbit Jahn-Teller and Pseudo-Jahn-Teller Problems in All Axial Symmetries

Spatial degeneracy of electronic states closely connects spin-orbit coupling and vibronic coupling, which together determine properties of materials, especially heavy element compounds. Accurate description of those materials entails accurate mathematical formulas for spin-orbit vibronic Hamiltonians. For the first time ever, we in this work derive the Hamiltonian formalism to describe all spin-orbit Jahn-Teller and pseudo-Jahn-Teller vibronic problems in all axial symmetries. The conventional one-electron approximation of spin-orbit coupling, which was the foundation of all previous studies in this field, is not involved in the present work. Actually, the present formalism is applicable to all time-reversal symmetric hermitian Hamiltonian that has a Rank-1 dependence on the spin operator, without any restriction on the type and the number of term symbols and vibrational modes.

Color Stable Deep Blue Multi-Resonance Organic Emitters with Narrow Emission and High Efficiency

The development of highly efficient and deep blue emitters satisfying the color specification of the commercial products has been a challenging hurdle in the organic light-emitting diodes (OLEDs). Here, deep blue OLEDs with a narrow emission spectrum with good color stability and spin-vibronic coupling assisted thermally activated delayed fluorescence are reported using a novel multi-resonance (MR) emitter built on a pure organic-based molecular platform of fused indolo[3,2,1-jk]carbazole structure. Two emitters derived from 2,5,11,14-tetrakis(1,1-dimethylethyl)indolo[3,2,1-jk]indolo[1',2',3':1,7]indolo[3,2-b]carbazole (tBisICz) core are synthesized as the MR type thermally activated delayed fluorescence emitters realizing a very narrow emission spectrum with a full-width-at-half-maximum (FWHM) of 16 nm with suppressed broadening at high doping concentration. The tBisICz core is substituted with a diphenylamine or 9-phenylcarbazole blocking group to manage the intermolecular interaction for high efficiency and narrow emission. The deep blue OLEDs achieve high external quantum efficiency (EQE) of 24.9%, small FWHM of 19 nm, and deep blue color coordinate of (0.16, 0.04) with good color stability with increase in doping concentration. To the authors' knowledge, the EQE in this work is one of the highest values reported for the deep blue OLEDs that achieve the BT.2020 standard.

Long-Lived Charge-Separated State in Naphthalimide-Phenothiazine Compact Electron Donor-Acceptor Dyads: Effect of Molecular Conformation Restriction and Solvent Polarity

To study the charge separation (CS) and long-lived CS state, we prepared a series of dyads based on naphthalimide (NI, electron acceptor) and phenothiazine (PTZ, electron donor), with an intervening phenyl linker attached on the N-position of both moieties. The purpose is to exploit the electron spin control effect to prolong the CS-state lifetime by formation of the 3CS state, instead of the ordinary 1CS state, the spin-correlated radical pair (SCRP), or the free ion pairs. The electronic coupling magnitude is tuned by conformational restriction exerted by the methyl groups on the phenyl linker. Differently from the previously reported NI-PTZ analogues containing long and flexible linkers, we observed a significant CS emission band centered at ca. 600 nm and thermally activated delayed fluorescence (TADF) with a lifetime of 13.8 ns (population ratio: 42%)/321.6 μs (56%). Nanosecond transient absorption spectroscopy indicates that in cyclohexane (CHX), only the 3NI* state was observed (lifetime τ = 274.7 μs), in acetonitrile (ACN), only the CS state was observed (τ = 1.4 μs), whereas in a solvent with intermediate polarity, such as toluene (TOL), both the 3NI* (shorter-lived) and the CS states were observed. Observation of the long-lived CS state in ACN, yet lack of TADF, confirms the spin-vibronic coupling theoretical model of TADF. Femtosecond transient absorption spectroscopy indicates that charge separation occurs in both nonpolar and polar solvents, with time constants ranging from less than 1 ps in ACN to ca. 60 ps in CHX. Time-resolved electron paramagnetic resonance (TREPR) spectra indicate the existence of the 3NI* and CS states for the dyads upon photoexcitation. The electron spin-spin dipole interaction magnitude of the radical anion and cation of the CS state is intermediate between that of a typical SCRP and a 3CS state, suggesting that the long CS-state lifetime is partially due to the electron spin control effect.

Overcoming the Limitation of Spin Statistics in Organic Light Emitting Diodes (OLEDs): Hot Exciton Mechanism and Its Characterization

Triplet harvesting processes are essential for enhancing efficiencies of fluorescent organic light-emitting diodes. Besides more conventional thermally activated delayed fluorescence and triplet-triplet annihilation, the hot exciton mechanism has been recently noticed because it helps reduce the efficiency roll-off and improve device stability. Hot exciton materials enable the conversion of triplet excitons to singlet ones via reverse inter-system crossing from high-lying triplet states and thereby the depopulation of long-lived triplet excitons that are prone to chemical and/or efficiency degradation. Although their anti-Kasha characteristics have not been clearly explained, numerous molecules with behaviors assigned to the hot exciton mechanism have been reported. Indeed, the related developments appear to have just passed the stage of infancy now, and there will likely be more roles that computational elucidations can play. With this perspective in mind, we review some selected experimental studies on the mechanism and the related designs and then on computational studies. On the computational side, we examine what has been found and what is still missing with regard to properly understanding this interesting mechanism. We further discuss potential future points of computational interests toward aiming for eventually presenting in silico design guides.

The effect of dark states on the intersystem crossing and thermally activated delayed fluorescence of naphthalimide-phenothiazine dyads

A series of 1,8-naphthalimide (NI)-phenothiazine (PTZ) electron donor-acceptor dyads were prepared to study the thermally activated delayed fluorescence (TADF) properties of the dyads, from a point of view of detection of the various transient species. The photophysical properties of the dyads were tuned by changing the electron-donating and the electron-withdrawing capability of the PTZ and NI moieties, respectively, by oxidation of the PTZ unit, or by using different aryl substituents attached to the NI unit. This tuning effect was manifested in the UV-vis absorption and fluorescence emission spectra, e.g., in the change of the charge transfer absorption bands. TADF was observed for the dyads containing the native PTZ unit, and the prompt and delayed fluorescence lifetimes changed with different aryl substituents on the imide part. In polar solvents, no TADF was observed. For the dyads with the PTZ unit oxidized, no TADF was observed as well. Femtosecond transient absorption spectra showed that the charge separation takes ca. 0.6 ps, and admixtures of locally excited (3LE) state and charge separated (1CS/3CS) states formed (in n-hexane). The subsequent charge recombination from the 1CS state takes ca. 7.92 ns. Upon oxidation of the PTZ unit, the beginning of charge separation is at 178 fs and formation of 3LE state takes 4.53 ns. Nanosecond transient absorption (ns-TA) spectra showed that both 3CS and 3LE states were observed for the dyads showing TADF, whereas only 3LE or 3CS states were observed for the systems lacking TADF. This is a rare but unambiguous experimental evidence that the spin-vibronic coupling of 3CS/3LE states is crucial for TADF. Without the mediating effect of the 3LE state, no TADF is resulted, even if the long-lived 3CS state is populated (lifetime τCS ≈ 140 ns). This experimental result confirms the 3CS → 1CS reverse intersystem crossing (rISC) is slow, without coupling with an approximate 3LE state. These studies are useful for an in-depth understanding of the photophysical mechanisms of the TADF emitters, as well as for molecular structure design of new electron donor-acceptor TADF emitters.

Modified Fermi's golden rule rate expressions

Fermi's golden rule (FGR) serves as the basis for many expressions of spectroscopic observables and quantum transition rates. The utility of FGR has been demonstrated through decades of experimental confirmation. However, there still remain important cases where the evaluation of a FGR rate is ambiguous or ill-defined. Examples are cases where the rate has divergent terms due to the sparsity in the density of final states or time dependent fluctuations of system Hamiltonians. Strictly speaking, assumptions of FGR are no longer valid for such cases. However, it is still possible to define modified FGR rate expressions that are useful as effective rates. The resulting modified FGR rate expressions resolve a long standing ambiguity often encountered in using FGR and offer more reliable ways to model general rate processes. Simple model calculations illustrate the utility and implications of new rate expressions.

A Thermally Activated Delayed Fluorescence Emitter Investigated by Time-Resolved Near-Infrared Spectroscopy

Emitters for organic light-emitting diodes (OLEDs) based on thermally activated delayed fluorescence (TADF) require small singlet (S₁ )-triplet (T₁ ) energy gaps as well as fast intersystem crossing (ISC) transitions. These transitions can be mediated by vibronic mixing with higher excited states S_n and T_n (n=2, 3, 4, …). For a prototypical TADF emitter consisting of a triarylamine and a dicyanobenzene moiety (TAA-DCN) it is shown that these higher states can be located energetically by time-resolved near-infrared (NIR) spectroscopy.

TDDFT versus GW/BSE Methods for Prediction of Light Absorption and Emission in a TADF Emitter

Design concepts for organic light emitting diode (OLED) emitters, which exhibit thermally activated delayed fluorescence (TADF) and thereby achieve quantum yields exceeding 25%, depend on singlet-triplet splitting energies of order kT to allow reverse intersystem crossing at ambient temperatures. Simulation methods for these systems must be able to treat relatively large organic molecules, as well as predict their excited state energies, transition energies, singlet-triplet splittings, and absorption and emission cross sections with reasonable accuracy, in order to prove useful in the design process. Here we compare predictions of TDDFT with M06-2X and ωB97X-D exchange-correlation functionals and a G_oW_o@HF/BSE method for these quantities in the well-studied DPTZ-DBTO2 TADF emitter molecule. Geometry optimization is performed for ground state (GS) and lowest donor-acceptor charge transfer (CT) state for each functional. Optical absorption and emission cross sections and energies are calculated at these geometries. Relaxation energies are on the order of 0.5 eV, and the importance of obtaining excited state equilibrium geometries in predicting delayed fluorescence is demonstrated. There are clear trends in predictions of G_oW_o@HF/BSE, and TDDFT/ωB97X-D and M06-2X methods in which the former method favors local exciton (LE) states while the latter favors DA CT states and ωB97X-D makes intermediate predictions. G_oW_o@HF/BSE suffers from triplet instability for LE states but not CT states relevant for TADF. Shifts in HOMO and LUMO levels on adding a conductor-like polarizable continuum model dielectric background are used to estimate changes in excitation energies on going from the gas phase to a solvated molecule.

Combining machine learning and quantum chemical calculations for high-throughput virtual screening of thermally activated delayed fluorescence molecular materials: the impact of selection strategy and structural mutations

In view of the theoretical importance and huge application potential of Thermally Activated Delayed Fluorescence (TADF) materials, it is of great significance to conduct High-Throughput Virtual Screening (HTVS) on compound libraries to find TADF candidate molecules. This research focuses on the computational design of pure organic TADF molecules. By combining machine learning and quantum chemical calculations, using cheminformatics tools, and introducing the concept of selection and mutation from evolutionary theory, we have designed a computational program for HTVS of TADF molecular materials, especially the impact of selection strategy and structural mutations on the results of HTVS was explored. An initial compound library (size = 103) constructed by enumeration of typical donors and acceptors was used to evolve by successively applying selection and 10 different structural mutations. And a group fingerprint similarity (ΔMSPR) index was proposed to account for the similarity between two compound libraries with comparable sizes. Based on the computed data, we have found that the mix of selection and mutations into the evolution map does have great impact on the HTVS results: (a) except the fast mutation Sub2, all the rest of the mutations can effectively concentrate 'good' molecules in a compound library, and hence give large material abundance (typically >0.8) for high mutation generations (n g ≥ 6). (b) The mean energy gap can exhibit a fast convergent trend toward very low values, hence the studied mutations (except Sub2) can cooperate very well with the studied DA substrates to generate optimal molecules, and the group fingerprint similarity can retain high enough values for large n g, which can be associated with the apparent convergence in molecular skeletons as n g increases. (c) The distribution of skeleton frequencies for a specific mutation is generally uneven with one dominant skeleton. The overall numbers of common and generic cores for all mutations are 11 and 7 as n g = 9. Hence, in a sense, the 'optimal' skeletons seem unique and useful in realizing low energy gaps. With these observations and the development of related HTVS software, we expect to provide insight and tools to the research community of HTVS of molecular (TADF) materials.

Multiple-Resonance Extension and Spin-Vibronic-Coupling-Based Narrowband Blue Organic Fluorescence Emitters with Over 30% Quantum Efficiency

Achieving narrow-bandwidth emission and high external quantum efficiency (EQE) simultaneously is a challenge for next-generation blue-emitting organic light-emitting diodes (OLEDs). In this study, novel multiple-resonance thermally activated delayed fluorescence (MR-TADF) emitters are developed by fusing an indolocarbazole unit with two carbazole skeletons using para-oriented nitrogen atoms. The resulting rigid and planar π-system without electron-accepting atoms exhibits pure blue photoluminescence at 470 nm, reaching a 100% quantum yield with a full-width-at-half-maximum (FWHM) of 25 nm. Higher-level quantum chemistry calculations confirm an MR effect within the extended π-conjugation and an enhanced triplet-to-singlet crossover (10⁴ s^-1 ) through a reduced energy gap (ΔE_ST ) coupled with large spin-vibronic coupling mediated by low-lying triplet excited states. An OLED fabricated using the MR-TADF emitter with CIE color coordinates of (0.12, 0.16) exhibits a record high EQE of 30.9% and a small FWHM of 23 nm. With further optimization of the device structure, a high EQE of 33.8% is achieved without additional outcoupling enhancements owing to the near-perfect horizontal alignment of the emitting dipoles.

Unified one-electron Hamiltonian formalism of spin-orbit Jahn-Teller and pseudo-Jahn-Teller problems in tetrahedral and octahedral symmetries

Heavy element compounds with high symmetries often feature both spin-orbit coupling and vibronic coupling. This is especially true for systems with tetrahedral and octahedral symmetries, whose electronic states may be three-fold degenerate and experience complicated Jahn-Teller and pseudo-Jahn-Teller interactions. To accurately describe these interactions, high quality spin-orbit vibronic Hamiltonian operators are needed. In this study, we present a unified one-electron Hamiltonian formalism for spin-orbit vibronic interactions for systems in all tetrahedral and octahedral symmetries. The formalism covers all spin-orbit Jahn-Teller and pseudo-Jahn-Teller problems in the symmetries with arbitrary types and arbitrary numbers of vibrational modes, and generates Hamiltonian expansion formulas of arbitrarily high order.

Vibronic Coupling Effect on the Vibrationally Resolved Electronic Spectra and Intersystem Crossing Rates of a TADF Emitter: 7-PhQAD

Assessing and improving the performance of organic light-emitting diode (OLED) materials require quantitative prediction of rate coefficients for the intersystem crossing (ISC) and reverse ISC (RISC) processes, which are determined not only by the energy gap and the direct spin-orbit coupling (SOC) between the first singlet and triplet excited-states at a thermal equilibrium position of the initial electronic state but also by the non-Condon effects such as the Herzberg-Teller-like vibronic coupling (HTVC) and the spin-vibronic coupling (SVC). Here we apply the time-dependent correlation function approaches to quantitatively calculate the vibrationally resolved absorption and fluorescence spectra and ISC/RISC rates of a newly synthesized multiple-resonance-type (MR-type) thermally activated delayed fluorescence (TADF) emitter, 7-phenylquinolino[3,2,1-de]acridine-5,9-dione (7-PhQAD), with the inclusion of the Franck-Condon (FC), HTVC, and Duschinsky rotation (DR) effects. The SVC effect on the rates has also been approximately evaluated. We find that the experimentally measured ISC rates of 7-PhQAD originate predominantly from the vibronic coupling, consistent with the previous reports on other MR-type TADF emitters. The SVC effect on ISC rates is about 10 times larger than the HTVC effect, and the latter increases the ISC rates by more than 1 order of magnitude while it slightly affects the vibrationally resolved absorption and fluorescence spectra. The discrepancy between the theoretical and experimental results is attributed to inaccurately describing excited-states calculated by the time-dependent density functional theory as well as to not fully accounting for the complex experimental conditions. This work provides a demonstration of what proportion of ISC and RISC rate coefficients of a MR-type TADF emitter can be covered by the HTVC effect, and it opens design routes that go beyond the FC approximation for the future development of high-performance OLED devices.

Rational designs of structurally similar TADF and HLCT emitters with benzo- or naphtho-carbazole units as electron donors

Structurally similar D–A type molecules with the combination of benzo- or naphtho-carbazole units as electron donors and tunable electron acceptors with different electron-withdrawing ability are designed to realize HLCT and TADF emissions.

Unified one-electron Hamiltonian formalism of spin-orbit Jahn-Teller and pseudo-Jahn-Teller problems in axial symmetries

Spin-orbit coupling and vibronic coupling are both closely related to orbital degeneracy of electronic states. Both types of coupling play significant roles in determining properties of heavy element compounds and shall be treated on the same footing. In this work, we derive a unified one-electron Hamiltonian formalism for spin-orbit and vibronic interactions for systems in all axial symmetries. The one-electron formalism is usually adequate as the spin-orbit interaction can often be approximated as a one-electron interaction. For the first time, the formalism covers spin-orbit and vibronic couplings in all axial symmetries from C₁ to D_∞h, arbitrary types of vibrational modes in those symmetries, and an arbitrary number of those modes and gives Hamiltonian expansions up to an arbitrary order.

Simulation of Low-Lying Singlet and Triplet Excited States of Multiple-Resonance-Type Thermally Activated Delayed Fluorescence Emitters by Delta Self-Consistent Field (ΔSCF) Method

The delta self-consistent field (ΔSCF) method was applied to the simulation of low-lying singlet and triplet excited states of multiple-resonance (MR)-type thermally activated delayed fluorescence (TADF) molecules, which form a promising group for organic light-emitting diode (OLED) emitters. A comparison with the experimental values of 13 emitters from the literature showed that ΔSCF gave fairly accurate S₁ and T₁ excitation energies (mean absolute errors (MAEs) of 0.092 and 0.055 eV, respectively) as well as quite accurate ΔE_ST (S₁-T₁ gap, MAE of 0.041 eV), which could not be calculated with sufficient accuracy by the conventional time-dependent density functional theory (TDDFT). ΔSCF also demonstrated its utility for the analysis of photophysical properties through a simulation of the reverse intersystem crossing (RISC) process of an MR-type emitter.

A simple generalization of the energy gap law for nonradiative processes

For more than 50 years, an elegant energy gap (EG) law developed by Englman and Jortner [Mol. Phys. 18, 145 (1970)] has served as a key theory to understand and model the nearly exponential dependence of nonradiative transition rates on the difference of energy between the initial and final states. This work revisits the theory, clarifies the key assumptions involved in the rate expression, and provides a generalization for the cases where the effects of temperature dependence and low-frequency modes cannot be ignored. For a specific example where the low-frequency vibrational and/or solvation responses can be modeled as an Ohmic spectral density, a simple generalization of the EG law is provided. Test calculations demonstrate that this generalized EG law brings significant improvement over the original EG law. Both the original and generalized EG laws are also compared with the stationary phase approximations developed for electron transfer theory, which suggests the possibility of a simple interpolation formula valid for any value of EG.

Simultaneously Enhanced Reverse Intersystem Crossing and Radiative Decay in Thermally Activated Delayed Fluorophors with Multiple Through-space Charge Transfers

Thermally activated delayed fluorescence (TADF) materials with through-space charge transfers (CT) have attracted particularly interest recently. However, the slow reverse intersystem crossing (RISC) and radiative decay always limit their electroluminescence performances. Herein, TADF molecules with ortho-linked multiple donors-acceptor (ortho-D_n -A) motif are developed to create near-degenerate excited states for the reinforcement of spin-orbit coupling. The incorporation of both through-bond and through-space CT enlarges oscillator strength. The optimal ortho-D₃ -A compound exhibits a photoluminescence quantum yield of ca. 100 %, a high RISC rate of 2.57×10⁶  s^-1 and a high radiative decay rate of 1.00×10⁷  s^-1 simultaneously. With this compound as the sensitizer, a TADF-sensitized-fluorescent organic light-emitting diode shows a maximum external quantum efficiency of 31.6 % with an ultrapure green Commission Internationale de L'Eclairage y coordinate value of 0.69.

Theoretical Determination of Rate Constants from Excited States: Application to Benzophenone

A cost-effective method of theoretically predicting electronic-transition rate constants from the excited states of molecules is reported. This method is based on density functional theory calculations of electronic states and quantitative rate constant determination with the Fermi golden rule. The method is applied to the theoretical determination of the excited-state decay mechanism of photoexcited benzophenone, a representative molecule in photochemistry and biochemistry. Calculated rate constants for benzophenone are quantitatively consistent with experimental ones, which validates the reliability of our rate constant calculation. The calculated population kinetics indicate that S₁ → T₂ → T₁ → S₀ is the predominant decay pathway.

Purely Spin-Vibronic Coupling Assisted Triplet to Singlet Up-Conversion for Real Deep Blue Organic Light-Emitting Diodes with Over 20% Efficiency and y Color Coordinate of 0.05

Finding narrow-band, ultrapure blue thermally activated delayed fluorescence (TADF) materials is extremely important for developing highly efficient organic light-emitting diodes (OLEDs). Here, spin-vibronic coupling (SVC)-assisted ultrapure blue emitters obtained by joining two carbazole-derived moieties at a para position of a phenyl unit and performing substitutions using several blocking groups are presented. Despite a relatively large singlet-triplet gap (∆EST ) of >0.2 eV, efficient triplet-to-singlet crossover can be realized, with assistance from resonant SVC. To enhance the spin crossover, electronic energy levels are fine-tuned, thereby causing ∆EST to be in resonance with a triplet-triplet gap (∆ETT ). A sizable population transfer between spin multiplicities (>103 s-1 ) is achieved, and this result agrees well with theoretical predictions. An OLED fabricated using a multiple-resonance-type SVC-TADF emitter with CIE color coordinates of (0.15, 0.05) exhibits ultrapure blue emissions, with a narrow full-width-at-half-maximum of 21 nm and a high external quantum efficiency of 23.1%.

Three States Involving Vibronic Resonance is a Key to Enhancing Reverse Intersystem Crossing Dynamics of an Organoboron-Based Ultrapure Blue Emitter

The recently developed narrow-band blue-emitting organoboron chromophores based on the multiple-resonance (MR) effect have now become one of the most important components for constructing efficient organic light emitting diodes (OLEDs). While they basically emit through fluorescence, they are also known for showing substantial thermally activated delayed fluorescence (TADF) even with a relatively large singlet-triplet gap (ΔE _ST). Indeed, understanding the reverse intersystem crossing (RISC) dynamics behind this peculiar TADF will allow judicious molecular designs toward achieving better performing OLEDs. Explaining the underlying nonadiabatic spin-flip mechanism, however, has often been equivocal, and how the sufficiently fast RISC takes place even with the sizable ΔE _ST and vanishingly small spin-orbit coupling is not well understood. Here, we show that a vibronic resonance, namely the frequency matching condition between the vibration and the electronic energy gap, orchestrates three electronic states together and this effect plays a major role in enhancing RISC in a typical organoboron emitter. Interestingly, the mediating upper electronic state is quite high in energy to an extent that its thermal population is vanishingly small. Through semiclassical quantum dynamics simulations, we further show that the geometry dependent non-Condon coupling to the upper triplet state that oscillates with the frequency ΔE _ST/ℏ is the main driving force behind the peculiar resonance enhancement. The existence of an array of vibrational modes with strong vibronic rate enhancements provides the ability to sustain efficient RISC over a range of ΔE _ST in defiance of the energy gap law, which can render the MR-emitters peculiar in comparison with more conventional donor-acceptor type emitters. Our investigation may provide a new guide for future blue emitting molecule developments.

Unified Hamiltonian Formalism of Jahn-Teller and Pseudo-Jahn-Teller Problems in Axial Symmetries

A formalism for expansions of all Jahn-Teller and pseudo-Jahn-Teller Hamiltonian operators in all axial symmetries is presented. The formalism provides Hamiltonian expansions up to arbitrarily high order and including an arbitrary number of vibrational modes, which are of arbitrary types. It consists of three equations and two tables. The formalism is user-friendly since it can be used without understanding its derivation. An example of E₃^″⊗e₁^' Jahn-Teller interaction is used to demonstrate the correctness of the formalism. A Python program is developed to automate the generation of Hamiltonian expansions for all axial Jahn-Teller and pseodo-Jahn-Teller problems and interface the expansions to the MCTDH quantum dynamics simulation program. This is the first unified Hamiltonian formalism for axial Jahn-Teller and pseudo-Jahn-Teller problems. Also it is the only one.

Vibrational Damping Reveals Vibronic Coupling in Thermally Activated Delayed Fluorescence Materials

We investigate a series of D-A molecules consisting of spiro[acridan-9,9'-fluorene] as the donor and 2-phenylenepyrimidine as the acceptor. In two of the materials, a spiro center effectively electronically isolates the D unit from (consequently) optically innocent yet structurally influential adamantyl side groups. In a third material, adamantyl groups attached directly to the acceptor strongly influence the electronic properties. Steady-state and time-resolved photophysical studies in solution, Zeonex polymer matrix, and neat films reveal that the substituents impact the efficiency of vibronic coupling between singlet and triplet states relevant to reverse intersystem crossing (rISC) and thermally activated delayed fluorescence (TADF), without significantly changing the singlet-triplet gap in the materials. The adamantyl groups serve to raise the segmental mass and inertia, thereby damping intramolecular motions (both vibrational and rotational). This substitution pattern reveals the role of large-amplitude (primarily D-A dihedral angle rocking) motions on reverse intersystem crossing (rISC), as well as smaller contributions from low-amplitude or dampened vibrations in solid state. We demonstrate that rISC still occurs when the high-amplitude motions are suppressed in Zeonex and discuss various vibronic coupling scenarios that point to an underappreciated role of intersegmental motions that persist in rigid solids. Our results underline the complexity of vibronic couplings in the mediation of rISC and provide a synthetic tool to enable future investigations of vibronic coupling through selective mechanical dampening with no impact on electronic systems.

Elucidating the Electronic Structure of a Delayed Fluorescence Emitter via Orbital Interactions, Excitation Energy Components, Charge-Transfer Numbers, and Vibrational Reorganization Energies

Recently, Wang and co-workers carried out frontier molecule orbital engineering in the design of m-Cz-BNCz, a thermally activated delayed fluorescence (TADF) molecule that emits pure green light at an external quantum efficiency of 27%. To further understand the underlying molecular design principles, we employed four advanced electronic structure analysis tools. First, an absolutely localized molecular orbitals (ALMO-) based analysis indicates an antibonding combination between the highest occupied molecular orbitals (HOMOs) of the donor 3,6-di-tert-butylcarbazole fragment and the acceptor BNCz fragment, which raises the HOMO energy and red-shifts the fluorescence emission wavelength. Second, excitation energy component analysis reveals that the S₁-T₁ gap is dominated by two-electron components of the excitation energies. Third, charge transfer number analysis, which is extended to use fragment-based Hirshfeld weights, indicates that the S₁ and T₁ excited states of m-Cz-BNCz (within time-dependent density functional theory) have notable charge transfer characters (27% for S₁ and 12% for T₁). This provides a balance between a small single-triplet gap and a substantial fluorescence intensity. Last, a vibrational reorganization energy analysis pinpoints the torsional motion between the BNCz and Cz moieties of m-Cz-BNCz as the source for its wider emission peak than that of p-Cz-BNCz. These four types of analyses are expected to be very valuable in the study and design of other TADF and functional dye molecules.

Vibrationally Assisted Direct Intersystem Crossing between the Same Charge-Transfer States for Thermally Activated Delayed Fluorescence: Analysis by Marcus-Hush Theory Including Reorganization Energy

Thermally activated delayed fluorescence (TADF) has recently become an extensively investigated phenomenon due to its high potential for application in organic optoelectronics. Currently, there is still lack of a model describing correctly basic photophysical parameters of organic TADF emitters. This article presents such a photophysical model describing the rates of intersystem crossing (ISC), reverse ISC (rISC), and radiative deactivation in various media and emphasizing key importance of molecular vibrations on the example of a popular TADF dye 9,10-dihydro-9,9-dimethyl-10-(4-(4,6-diphenyl-1,3,5-triazin-2-yl)phenyl)-acridine (DMAC-TRZ). The presented experimental and theoretical investigations prove that ISC and rISC can occur efficiently between the singlet and triplet states of the same charge-transfer nature (¹CT and ³CT, respectively). In emitters with the orthogonal donor and acceptor fragments, such spin-forbidden ¹CT ↔ ³CT transitions are activated by molecular vibrations. Namely, the change of dihedral angle between the donor and the acceptor affords reasonable spin–orbit coupling, which together with a small energy gap and reorganization energy enable ¹CT ↔ ³CT transition rates reaching 1 × 10⁷ s^–1. Evidence of direct ¹CT ↔ ³CT spin-flip and negligible role of a second triplet state, widely believed as a key parameter in the design of (r)ISC materials, change significantly the current understanding of TADF mechanism. In authors’ opinion, photophysics, and molecular design principles of TADF emitters should be revised considering the importance of vibrationally enhanced ¹CT ↔ ³CT transitions.

Behind the scenes of spin-forbidden decay pathways in transition metal complexes

The interpretation of the ultrafast photophysics of transition metal complexes following photo-absorption is quite involved as the heavy metal center leads to a complicated and entangled singlet-triplet manifold. This opens up multiple pathways for deactivation, often with competitive rates. As a result, intersystem crossing (ISC) and phosphorescence are commonly observed in transition metal complexes. A detailed understanding of such an excited-state structure and dynamics calls for state-of-the-art experimental and theoretical methodologies. In this review, we delve into the inability of non-relativistic quantum theory to describe spin-forbidden transitions, which can be overcome by taking into account spin-orbit coupling, whose importance grows with increasing atomic number. We present the quantum chemical theory of phosphorescence and ISC together with illustrative examples. Finally, a few applications are highlighted, bridging the gap between theoretical studies and experimental applications, such as photofunctional materials.

Molecular engineering of carbazole–acrylonitrile fluorophores: substituent-dependent optical properties and mechanochromism

Controlling the fluorescence properties of organic molecules in the aggregation state and understanding the structure–activity relationship are important for developing excellent luminophors with tunable solid emission.

Effect of Perturbative Vibronic Correction for Weak Fluorescence in Thermally Activated Delayed Fluorescence Systems

Minimizing the energy difference between the lowest singlet (S₁) and the lowest triplet states, ΔE_ST, is the main strategy to design thermally activated delayed fluorescence (TADF) molecules, and spatially separating the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) is the general method in the design. However, such a separation also tends to reduce the oscillator strength of the S₁ state. In real systems, vibrations change the S₁ oscillator strength, and thus one needs to consider the vibronic coupling toward searching for TADF candidate molecules. Here, we evaluate the importance of vibronic coupling by including the first-order perturbative correction to the transition dipole moments of carbazolyl-phthalonitrile derivatives. Indeed, some molecules display large enhancements in their oscillator strengths, with their fluorescence lifetimes reduced by 2 orders of magnitude. The twisting mode between the carbazole groups and phthalonitrile is the most important mode in inducing the perturbations. Thus, performing the perturbative correction is crucial in attaining more reliable predictions on their fluorescence propensities. We also observe that some other molecules, whose zeroth-order predicted fluorescence rates are much slower than the actual experimental data, are affected little by the same first-order correction. For these molecules, we deduce that the geometry-dependent excited-state switching kicks in. Our results demonstrate the significance of vibronic coupling in TADF molecules and the importance of adopting correction schemes as the guidelines for screening of useful TADF molecules.