Are Heptazine-Based Organic Light-Emitting Diode Chromophores Thermally Activated Delayed Fluorescence or Inverted Singlet-Triplet Systems?

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.

ΔDFT Predicts Inverted Singlet-Triplet Gaps with Chemical Accuracy at a Fraction of the Cost of Wave Function-Based Approaches

Efficient OLEDs need to quickly convert singlet and triplet excitons into photons. Molecules with an inverted singlet-triplet energy gap (INVEST) are promising candidates for this task. However, typical INVEST molecules have drawbacks like too low oscillator strengths and excitation energies. High-throughput screening could identify suitable INVEST molecules, but existing methods are problematic: The workhorse method TD-DFT cannot reproduce gap inversion, while wave function-based methods are too slow. This study proposes a state-specific method based on unrestricted Kohn-Sham DFT with common hybrid functionals. Tuned on the new INVEST15 benchmark set, this method achieves an error of less than 1 kcal/mol, which is traced back to error cancellation between spin contamination and dynamic correlation. Applied to the larger and structurally diverse NAH159 set in a black-box fashion, the method maintains a small error (1.2 kcal/mol) and accurately predicts gap signs in 83% of cases, confirming its robustness and suitability for screening workflows.

Computational design of boron-free triangular molecules with inverted singlet-triplet energy gap

A novel, computationally designed, class of triangular-shape organic molecules with an inverted singlet-triplet (IST) energy gap is investigated with ab initio electronic structure methods. The considered molecular systems are cyclic oligomers and their common feature is electronic conjugation along the molecular rim. Vertical excitation energies from the electronic ground state to the lowest singlet and triplet excited states were computed, as well as vertical emission energies from these states to the ground state. The results underscore the significance of optimizing excited-state geometries to accurately describe the optoelectronic properties of IST molecules, in particular with respect to their application in OLEDs.

Spectroscopic Quantification of the Inverted Singlet-Triplet Gap in Pentaazaphenalene

We report the direct and accurate spectroscopic quantification of the inverted singlet-triplet gap in 1,3,4,6,9b-pentaazaphenalene. This measurement is achieved by directly probing the lowest singlet and triplet states via high-resolution cryogenic anion photoelectron spectroscopy. The assignment of the first excited singlet state is confirmed by visible absorption spectroscopy in an argon matrix at 20 K. Our measurements yield an inverted singlet-triplet gap with ΔEST= -0.047(7) eV. The accurate quantification of the singlet-triplet gap presented here allows for direct evaluation of various computational electronic structure methods and highlights the critical importance of the proper description of the double excitation character of these electronic states. Overall, this study validates the idea that despite Hund's multiplicity rule, useful organic chromophores can have inherently inverted singlet-triplet gaps.

Resilience of Hund's rule in the chemical space of small organic molecules

We embark on a quest to identify small molecules in the chemical space that can potentially violate Hund's rule. Utilizing twelve TDDFT approximations and the ADC(2) many-body method, we report the energies of S1 and T1 excited states of 12 880 closed-shell organic molecules within the bigQM7ω dataset with up to 7 CONF atoms. In this comprehensive dataset, none of the molecules, in their minimum energy geometry, exhibit a negative S1-T1 energy gap at the ADC(2) level while several molecules display values <0.1 eV. The spin-component-scaled double-hybrid method, SCS-PBE-QIDH, demonstrates the best agreement with ADC(2). Yet, at this level, a few molecules with a strained sp3-N center turn out as false-positives with the S1 state lower in energy than T1. We investigate a prototypical cage molecule with an energy gap <-0.2 eV, which a closer examination revealed as another false positive. We conclude that in the chemical space of small closed-shell organic molecules, it is possible to identify geometric and electronic structural features giving rise to S1-T1 degeneracy; still, there is no evidence of a negative gap. We share the dataset generated for this study as a module, to facilitate seamless molecular discovery through data mining.

Computational Investigations of the Detailed Mechanism of Reverse Intersystem Crossing in Inverted Singlet-Triplet Gap Molecules

Inverted singlet-triplet gap (INVEST) materials have promising photophysical properties for optoelectronic applications due to an inversion of their lowest singlet (S1) and triplet (T1) excited states. This results in an exothermic reverse intersystem crossing (rISC) process that potentially enhances triplet harvesting, compared to thermally activated delayed fluorescence (TADF) emitters with endothermic rISCs. However, the processes and phenomena that facilitate conversion between excited states for INVEST materials are underexplored. We investigate the complex potential energy surfaces (PESs) of the excited states of three heavily studied azaphenalene INVEST compounds, namely, cyclazine, pentazine, and heptazine using two state-of-the-art computational methodologies, namely, RMS-CASPT2 and SCS-ADC(2) methods. Our findings suggest that ISC and rISC processes take place directly between the S1 and T1 electronic states in all three compounds through a minimum-energy crossing point (MECP) with an activation energy barrier between 0.11 to 0.58 eV above the S1 state for ISC and between 0.06 and 0.36 eV above the T1 state for rISC. We predict that higher-lying triplet states are not populated, since the crossing point structures to these states are not energetically accessible. Furthermore, the conical intersection (CI) between the ground and S1 states is high in energy for all compounds (between 0.4 to 2.0 eV) which makes nonradiative decay back to the ground state a relatively slow process. We demonstrate that the spin-orbit coupling (SOC) driving the S1-T1 conversion is enhanced by vibronic coupling with higher-lying singlet and triplet states possessing vibrational modes of proper symmetry. We also rationalize that the experimentally observed anti-Kasha emission of cyclazine is due to the energetically inaccessible CI between the bright S2 and the dark S1 states, hindering internal conversion. Finally, we show that SCS-ADC(2) is able to qualitatively reproduce excited state features, but consistently overpredict relative energies of excited state structural minima compared to RMS-CASPT2. The identification of these excited state features elaborates design rules for new INVEST emitters with improved emission quantum yields.

Reverse intersystem crossing mechanisms in doped triangulenes

Thermally activated delayed fluorescence (TADF) has emerged as one of the most promising strategies in the quest for organic light emitting diodes with optimal performance. This computational study dissects the mechanistic intricacies of the central photophysical step, reverse intersystem crossing (rISC) in N and B doped triangulenes as potential multi-resonance TADF compounds. Optimal molecular patterns conducive to efficient rISC, encompassing dopant atom size, number, and distribution, are identified. Additionally, we assess various electronic structure methods for characterizing TADF-relevant molecular systems. The findings identify the distinct role of the direct and mediated mechanisms in rISC, and provide insights into the design of advanced TADF chromophores for next-generation OLED technology.

Ultrafast Computational Screening of Molecules with Inverted Singlet-Triplet Energy Gaps Using the Pariser-Parr-Pople Semiempirical Quantum Chemistry Method

Molecules with an inverted energy gap between their first singlet and triplet excited states have promising applications in the next generation of organic light-emitting diode (OLED) materials. Unfortunately, such molecules are rare, and only a handful of examples are currently known. High-throughput virtual screening could assist in finding novel classes of these molecules, but current efforts are hampered by the high computational cost of the required quantum chemical methods. We present a method based on the semiempirical Pariser-Parr-Pople theory augmented by perturbation theory and show that it reproduces inverted gaps at a fraction of the cost of currently employed excited-state calculations. Our study paves the way for ultrahigh-throughput virtual screening and inverse design to accelerate the discovery and development of this new generation of OLED materials.

Excited-state dynamics of C3-symmetric heptazine-based thermally activated delayed-fluorescence emitters

Heptazine-based materials have recently emerged as a promising motif for thermally activated delayed fluorescence, as their near-zero or negative singlet-triplet energy gaps enable extremely fast reverse intersystem crossing (rISC) rates. Another method for achieving a high rate of rISC is through the use of highly symmetric emitters, which benefit from energy-level degeneracies and a high density of states. Here, we investigate the effect of combining these two design strategies on the excited-state dynamics of C3-symmetric emitters containing heptazine cores. We find that in two of the four emitters studied, the S1 state has a high degree of locally excited (LE) character with density on the heptazine moiety, preventing excited-state localization and a loss of symmetry in the energy-minimized S1 geometry. Surprisingly, these symmetric molecules still suffer from a loss of density of triplet states below the S1 state. Overall, we find that maintaining C3 symmetry will not necessarily maintain density of states, but that heptazine-based materials with LE S1 states still benefit from maximized rISC rates via increased spin-orbit coupling with low-lying charge-transfer triplet states and exhibit advantageous photophysical properties, such as near-unity photoluminescence quantum yields and high colour purity.

Luminescence mechanism analysis of a TADF molecule showing peculiar thermal behavior

In recent years, much attention has been paid to the development of thermally activated delayed fluorescence (TADF) materials with short delayed-fluorescence lifetimes to improve the device performances of OLEDs. In principle, by reducing the highest occupied molecular orbital (HOMO)-lowest unoccupied molecular orbital (LUMO) overlap, while the energy difference between S1-T1 (ΔEST) and activation energy (Ea) can be reduced, and the reverse intersystem crossing rate constant (kRISC) can be accelerated, a decrease in the radiative rate constant happens, necessitating an advanced molecular design. Furthermore, a molecule based on heptazine as a parent skeleton has recently been found to have a peculiar temperature dependence of luminescence decay, suggesting a negative gap (NG) material. In this report, we show that 9-[1,4]benzoxaborino[2,3,4-kl]phenoxaborine-7-yl-1,3,6,8-tetramethyl-9H-carbazole (TMCz-BO), a donor-acceptor linked TADF molecule with a very short delay lifetime of 750 ns, exhibits a peculiar thermal behavior similar to that of NG materials based on the temperature dependence of its luminescence decay in solution.

Enhanced inverted singlet-triplet gaps in azaphenalenes and non-alternant hydrocarbons

Inverted singlet-triplet gaps may lead to novel molecular emitters if a rational design approach can be achieved. We uncover a substituent strategy that enables tuning of the gap and succeed in inducing inversion in near-gapless molecules. Based on known inverted-gap emitters, we design substituted analogs with even more negative singlet-triplet gaps than in the parent systems. The inversion is lost if the reverse substituent-strategy is used. We thus demonstrate a definite set of conceptual design rules for inverted gap molecules.

Experimental and computational studies of the optical properties of 2,5,8-tris(phenylthiolato)heptazine with an inverted singlet-triplet gap

Photophysical properties of the three-fold symmetric 2,5,8-tris(phenylthiolato)heptazine molecule (1) are studied from combined experimental and computational viewpoints. The intense blue photoemission of 1 in the solid state and in toluene solution is proposed to have a fluorescent origin on the basis of a relatively short emission lifetime and no detectable triplet decay. Calculations at correlated ab initio levels of theory also show that 1 has a large inverted singlet-triplet (IST) gap, a non-vanishing spin-orbit coupling matrix element between the first excited singlet and triplet states, and a fast intersystem crossing rate constant that leads to singlet population from the higher-lying triplet state. The IST gap implies that the first excited singlet state is the lowest excited one, agreeing with the measured fluorescent behaviour of 1. IST gaps are also obtained for the oxygen-containing (2) and selenium-containing (3) analogues of 1 at the ADC(2) level of theory, but not for the tellurium one (4). Calculations of the magnetically induced current density demonstrate that the heptazine core of 1 is globally non-aromatic due to the alternation of carbon and nitrogen atoms along its external rim.

Shining Light on Inverted Singlet-Triplet Emitters

The inversion of the lowest singlet and triplet excited states, observed in several triangle-shaped organic molecules containing conjugated carbon and nitrogen atoms, is an astonishing result that implies the breakdown of Hund's rule. The phenomenon attracted interest for its potential toward triplet harvesting in organic LEDs. On a more fundamental vein, the singlet-triplet (ST) inversion sheds new light on the role of electron correlations in the excited-state landscape of π-conjugated molecules. Relying on the celebrated Pariser-Parr-Pople model, the simplest model for correlated electrons in π-conjugated systems, we demonstrate that the ST inversion does not require triangle-shaped molecules nor any specific molecular symmetry. Indeed, the ST inversion does not require strictly non-overlapping HOMO and LUMO orbitals but rather a small gap and a small exchange integral between the frontier orbitals.

Computational Design of Multiple Resonance-Type BN Molecules for Inverted Singlet and Triplet Excited States

A computational design of linearly extended multiple resonance (MR)-type BN molecules based on DABNA-1 is proposed herein in the quest to find potential candidates that exhibit a negative singlet-triplet gap (ΔEST) and a large oscillator strength value. The impact of a proper account of the electron correlation in the lowest singlet and triplet excited states is systematically investigated by using double-hybrid functionals within the TD-DFT framework, as well as wavefunction-based methods (EOM-CCSD and SCS-CC2), since this contribution plays an essential role in driving the magnitude of the ΔEST in MR-TADF and inverted singlet-triplet gap compounds. Our results point out a gradual reduction of the ΔEST gap with respect to the increasing sum of the number of B and N atoms, reaching negative ΔEST values for some molecules as a function of their size. The double-hybrid functionals reproduce the gap with only slight deviation compared to available experimental data for DABNA-1, ν-DABNA, and mDBCz and nicely agree with high-level quantum mechanical methods (e.g., EOM-CCSD and SCS-CC2). Larger oscillator strengths are found compared to the azaphenalene-type molecules, also exhibiting the inversion of their singlet and triplet excited states. We hope this study can serve as a motivation for further design of the molecules showing negative ΔEST based on boron- and nitrogen-doped polyaromatic hydrocarbons.

Heptazine, Cyclazine, and Related Compounds: Chemically-Accurate Estimates of the Inverted Singlet-Triplet Gap

Molecules that violate Hund's rule and exhibit an inverted gap between the lowest singlet S1 and triplet T1 excited states have attracted considerable attention due to their potential applications in optoelectronics. Among these molecules, the triangular-shaped heptazine, and its derivatives, have been in the limelight. However, conflicting reports have arisen regarding the relative energies of S1 and T1. Here, we employ highly accurate levels of theory, such as CC3, to not only resolve the debate concerning the sign but also quantify the magnitude of the S1-T1 gap. We also determined the 0-0 energies to evaluate the significance of the vertical approximation. In addition, we compute reference S1-T1 gaps for a series of 10 related molecules. This enables us to benchmark lower-order methods for future applications in larger systems within the same family of compounds. This contribution can serve as a foundation for the design of triangular-shaped molecules with enhanced photophysical properties.

Inverted Lowest Singlet and Triplet Excitation Energy Ordering of Graphitic Carbon Nitride Flakes

In organic light-emitting diodes (OLEDs), only 25% of electrically generated excitons are in a singlet state, S1, and the remaining 75% are in a triplet state, T1. In thermally activated delayed fluorescence (TADF) chromophores the transition from the nonradiative T1 state to the radiative S1 state can be thermally activated, which improves the efficiency of OLEDs. Chromophores with inverted energy ordering of S1 and T1 states, S1 < T1, are superior to TADF chromophores, thanks to the absence of an energy barrier for the transition from T1 to S1. We benchmark the performance of time-dependent density functional theory using different exchange-correlation functionals and find that scaled long-range corrected double-hybrid functionals correctly predict the inverted singlet-triplet gaps of N-substituted phenalene derivatives. We then show that the inverted energy ordering of S1 and T1 is an intrinsic property of graphitic carbon nitride flakes. A design strategy of new chromophores with inverted singlet-triplet gaps is proposed. The color of emitted light can be fine-tuned through flake size and amine substitution on flake vertices.

Theoretical Research and Photodynamic Simulation of Aggregation-Induced Thermally Activated Delayed Fluorescence Materials for Organic Light-Emitting Diodes

The discovery and utilization of pure organic thermally activated delayed fluorescence (TADF) materials provide a major breakthrough in obtaining high-performance and low-cost organic light-emitting diodes (OLEDs). In spite of recent research progress in TADF emitters, highly efficient and stable TADF emitters in high-concentration solutions and in the solid state have been rarely reported, and most of them suffer from aggregation-induced quenching (ACQ). To resolve this issue, the aggregation-induced delayed fluorescence (AIDF) mechanism was studied in depth by the simulation of excited-state dynamic processes, and the effect of geometric modifications on optical properties was minutely investigated based on molecular modeling. TD-DFT calculations demonstrate that it is the key point for the transformation between prompt fluorescence and TADF to effectively regulate singlet-triplet energy difference and electron-vibration coupling by the aggregation effect. Then, excellent green and red TADF materials with very small singlet-triplet energy differences of 0.05 and 0.06 eV, high TADF quantum yields up to 57.53% and 39.19%, and suitable fluorescence lifetimes of 0.99 and 1.67 us, respectively, were designed and obtained, which demonstrate the potential application of these two TADF materials in OLEDs.

Role of Spin Polarization and Dynamic Correlation in Singlet-Triplet Gap Inversion of Heptazine Derivatives

The new generation of proposed light-emitting molecules for organic light-emitting diodes (OLEDs) has raised considerable research interest due to its exceptional feature─a negative singlet-triplet (ST) gap violating Hund's multiplicity rule in the excited S1 and T1 states. We investigate the role of spin polarization in the mechanism of ST gap inversion. Spin polarization is associated with doubly excited determinants of certain types, whose presence in the wave function expansion favors the energy of the singlet state more than that of the triplet. Using a perturbation theory-based model for spin polarization, we propose a simple descriptor for prescreening of candidate molecules with negative ST gaps and prove its usefulness for heptazine-type molecules. Numerical results show that the quantitative effect of spin polarization decreases linearly with the increasing highest occupied molecular orbital-lowest unoccupied molecular orbital (HOMO-LUMO) exchange integral. Comparison of single- and multireference coupled-cluster predictions of ST gaps shows that the former methods provide good accuracy by correctly balancing the effects of doubly excited determinants and dynamic correlation. We also show that accurate ST gaps may be obtained using a complete active space model supplemented with dynamic correlation from multireference adiabatic connection theory.

Large area inkjet-printed OLED fabrication with solution-processed TADF ink

This work demonstrates successful large area inkjet printing of a thermally activated delayed fluorescence (TADF) material as the emitting layer of organic light-emitting diodes (OLEDs). TADF materials enable efficient light emission without relying on heavy metals such as platinum or iridium. However, low-cost manufacturing of large-scale TADF OLEDs has been restricted due to their incompatibility with solution processing techniques. In this study, we develop ink formulation for a TADF material and show successful ink jet printing of intricate patterns over a large area (6400 mm2) without the use of any lithography. The stable ink is successfully achieved using a non-chlorinated binary solvent mixture for a solution processable TADF material, 3-(9,9-dimethylacridin-10(9H)-yl)-9H-xanthen-9-one dispersed in 4,4'-bis-(N-carbazolyl)-1,1'-biphenyl host. Using this ink, large area ink jet printed OLEDs with performance comparable to the control spin coated OLEDs are successfully achieved. In this work, we also show the impact of ink viscosity, density, and surface tension on the droplet formation and film quality as well as its potential for large-area roll-to-roll printing on a flexible substrate. The results represent a major step towards the use of TADF materials for large-area OLEDs without employing any lithography.

Correlation vs. exchange competition drives the singlet-triplet excited-state inversion in non-alternant hydrocarbons

In this work, we focus on the understanding of the driving force behind the S1-T1 excited-state energy inversion (which would thus violate Hund's rule, making the S1 state lower in energy than the T1 state) of two non-benzenoid non-alternant hydrocarbons, composed of odd-membered rings. The molecules considered here have identical chemical composition but different atomic configuration in space. The delicate interplay between structural and electronic factors that might induce inversion and its energy extension, only by a few meV, is systematically investigated here by state-of-the-art calculations. Qualitative and quantitative accurate predictions are obtained employing post-HF methods, thanks to the balanced and careful inclusion of electron correlation effects. The obtained results might guide and rationalize new searches for molecules violating Hund's rule, concomitantly demonstrating the importance of key contributions from the theoretical method of choice.

Double-bond delocalization in non-alternant hydrocarbons induces inverted singlet-triplet gaps

Molecules where the first excited singlet state is lower in energy than the first excited triplet state have the potential to revolutionize OLEDs. This inverted singlet-triplet gap violates Hund's rule and currently there are only a few molecules which are known to have this property. Here, we screen the complete set of non-alternant hydrocarbons consisting of 5-, 6-, 7-membered rings fused into two-, three- and four-ring polycyclic systems. We identify several molecules where the symmetry of the ground-state structure is broken due to bond-length alternation. Through symmetry-constrained optimizations we identify several molecular cores where the singlet-triplet gap is inverted when the structure is in a higher symmetry, pentalene being a known example. We uncover a strategy to stabilize the molecular cores into their higher-symmetry structures with electron donors or acceptors. We design several substituted pentalenes, s-indacenes, and indeno[1,2,3-ef]heptalenes with inverted gaps, among which there are several synthetically known examples. In contrast to known inverted gap emitters, we identify the double-bond delocalized structure of their conjugated cores as the necessary condition to achieve the inverted gap. This strategy enables chemical tuning and paves the way for the rational design of polycyclic hydrocarbons with inverted singlet-triplet gaps. These molecules are prospective emitters if their properties can be optimized for use in OLEDs.

Identification of Unknown Inverted Singlet-Triplet Cores by High-Throughput Virtual Screening

Molecules where the energy of the lowest excited singlet state is found below the energy of the lowest triplet state (inverted singlet-triplet molecules) are extremely rare. It is particularly challenging to discover new ones through virtual screening because the required wavefunction-based methods are expensive and unsuitable for high-throughput calculations. Here, we devised a virtual screening approach where the molecules to be considered with advanced methods are pre-selected with increasingly more sophisticated filters that include the evaluation of the HOMO-LUMO exchange integral and approximate CASSCF calculations. A final set of 7 candidates (0.05% of the initial 15 000) were verified to possess inversion between singlet and triplet states with state-of-the-art multireference methods (MS-CASPT2). One of them is deemed of particular interest because it is unrelated to other proposals made in the literature.

The inverted singlet-triplet gap: a vanishing myth?

Molecules with an inverted singlet-triplet gap (STG) between the first excited singlet and triplet states, for example, heptazine, have recently been reported and gained substantial attention since they violate the famous Hund's rule. Utilizing state-of-the-art high-level ab initio methods, the singlet-triplet gap vanishes and approaches zero from below whatever is improved in the theoretical description of the molecules: the basis set or the level of electron correlation. Seemingly, the phenomenon of inverted singlet-triplet gaps tends to vanish the closer we observe.

R2022: A DFT/MRCI Ansatz with Improved Performance for Double Excitations

A reformulation of the combined density functional theory and multireference configuration interaction method (DFT/MRCI) is presented. Expressions for ab initio matrix elements are used to derive correction terms for a new effective Hamiltonian. On the example of diatomic carbon, the correction terms are derived, focusing on the doubly excited ¹Δ_g state, which was problematic in previous formulations of the method, as were double excitations in general. The derivation shows that a splitting of the parameters for intra- and interorbital interactions is necessary for a concise description of the underlying physics. Results for ¹L_a and ¹L_b states in polyacenes and ¹A_u and ¹A_g states in mini-β-carotenoids suggest that the presented formulation is superior to former effective Hamiltonians. Furthermore, statistical analysis reveals that all the benefits of the previous DFT/MRCI Hamiltonians are retained. Consequently, the here presented formulation should be considered as the new standard for DFT/MRCI calculations.

Symmetry-Induced Singlet-Triplet Inversions in Non-Alternant Hydrocarbons

Molecules with inversion of the singlet and triplet excited-state energies are highly promising for the development of organic light-emitting diodes (OLEDs). To date, azaphenalenes are the only class of molecules where these inversions have been identified. Here, we screen a curated database of organic crystal structures to identify existing compounds for violations of Hund's rule in the lowest excited states. We identify two further classes with this behavior. The first, a class of zwitterions, has limited relevance to molecular emitters as the singlet-triplet inversions occur in the third excited singlet state. The second class consists of two D_2h -symmetry non-alternant hydrocarbons, a fused azulene dimer and a bicalicene, whose lowest excited singlet states violate Hund's rule. Due to the connectivity of the polycyclic structure, they achieve this symmetry through aromatic stabilization. These hydrocarbons show promise as the next generation of building blocks for OLED emitters.

Gold(i)-containing light-emitting molecules with an inverted singlet–triplet gap†

Delayed fluorescence from molecules with an inverted singlet–triplet gap (DFIST) is the consequence of the unusual reverse order of the lowest excited singlet (S₁) and triplet (T₁) states of thermally activated delayed fluorescence (TADF) emitters. Heptazine (1,3,4,6,7,9,9b-heptaazaphenalene) derivatives have an inverted singlet–triplet gap thanks to the combination of multiple resonance (MR) effects and a significant double excitation character. Here, we study computationally the effect of gold(i) metalation and coordination on the optical properties of heptazine (molecule 4) and the phosphine-functionalized 2,5,8-tris(dimethylphosphino)heptazine derivatives (molecules 1–3). Ab initio calculations at the approximate second-order coupled cluster (CC2) and extended multiconfigurational quasi degenerate perturbation theory at the second order (XMC-QDPT2) levels show that molecules 1–4 have an inverted singlet–triplet gap due to the alternating spatial localization of the electron and hole of the exciton in the heptazine core. A non-vanishing one-electron spin–orbit coupling operator matrix element between T₁ and and a fast S₁ ← T₁ intersystem crossing rate constant (k_ISC) calculated at the XMC-QDPT2(12,12) level of theory for molecule 4 suggest that this new family of complexes may be the first organometallic DFIST emitters reported.

Substitution with gold(i)-containing moieties results in non-vanishing oscillator strengths and spin–orbit coupling leading to fast intersystem crossing in light-emitting heptazine derivates with an inverted singlet–triplet gap.

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.

Organic molecules with inverted singlet-triplet gaps

According to Hund’s multiplicity rule, the energy of the lowest excited triplet state (T₁) is always lower than that of the lowest excited singlet state (S₁) in organic molecules, resulting in a positive singlet-triplet energy gap (ΔE_ST). Therefore, the up-converted reverse intersystem crossing (RISC) from T₁ to S₁ is an endothermic process, which may lead to the quenching of long-lived triplet excitons in electroluminescence, and subsequently the reduction of device efficiency. Interestingly, organic molecules with inverted singlet-triplet (INVEST) gaps in violation of Hund’s multiplicity rule have recently come into the limelight. The unique feature has attracted extensive attention in the fields of organic optoelectronics and photocatalysis over the past few years. For an INVEST molecule possessing a higher T₁ with respect to S₁, namely a negative ΔE_ST, the down-converted RISC from T₁ to S₁ does not require thermal activation, which is possibly conducive to solving the problems of fast efficiency roll-off and short lifetime of organic light-emitting devices. By virtue of this property, INVEST molecules are recently regarded as a new generation of organic light-emitting materials. In this review, we briefly summarized the significant progress of INVEST molecules in both theoretical calculations and experimental studies, and put forward suggestions and expectations for future research.

On the origin of the inverted singlet-triplet gap of the 5th generation light-emitting molecules

Excitation energies of the lowest singlet and triplet state of molecules whose first excited singlet state lies energetically below the first triplet state have been studied computationally at (time-dependent) density functional theory, coupled-cluster, and second-order multiconfiguration perturbation theory levels. The calculations at the ab initio levels show that the singlet-triplet gap is inverted as compared to the one expected from Hund's rule, whereas all density functionals yield the triplet state as the lowest excited state. Double excitations responsible for the inverted singlet-triplet gap have been identified. Employing the spin-flip and ΔSCF methods, singlet-triplet inversion was obtained at the density functional theory level for some of the studied molecules.

Virtual Screening for Organic Solar Cells and Light Emitting Diodes

The field of organic semiconductors is multifaceted and the potentially suitable molecular compounds are very diverse. Representative examples include discotic liquid crystals, dye-sensitized solar cells, conjugated polymers, and graphene-based low-dimensional materials. This huge variety not only represents enormous challenges for synthesis but also for theory, which aims at a comprehensive understanding and structuring of the plethora of possible compounds. Eventually computational methods should point to new, better materials, which have not yet been synthesized. In this perspective, it is shown that the answer to this question rests upon the delicate balance between computational efficiency and accuracy of the methods used in the virtual screening. To illustrate the fundamentals of virtual screening, chemical design of non-fullerene acceptors, thermally activated delayed fluorescence emitters, and nanographenes are discussed.

Water Oxidation and Hydrogen Evolution with Organic Photooxidants: A Theoretical Perspective

In this Perspective, we discuss a novel water-splitting scenario, namely the direct oxidation of water molecules by organic photooxidants in hydrogen-bonded chromophore-water complexes. In comparison with the established scenario of semiconductor-based water splitting, the distance of electron transfer processes is thereby reduced from mesoscopic scales to the Ångström scale, and the time scale is reduced from milliseconds to femtoseconds, which suppresses competing loss processes. The concept is illustrated by computational studies for the heptazine-H₂O complex. The excited-state landscape of this complex has been characterized with ab initio electronic-structure methods and the proton-coupled electron-transfer dynamics has been explored with nonadiabatic dynamics simulations. A unique feature of the heptazine chromophore is the existence of a low-lying and exceptionally long-lived ¹ππ* state in which a substantial part of the photon energy can be stored for hundreds of nanoseconds and is available for the oxidation of water molecules. The calculations reveal that the absorption spectra and the photochemical functionalities of heptazine chromophores can be systematically tailored by chemical substitution. The options of harvesting hydrogen and the problems posed by the high reactivity of OH radicals are discussed.

Origin of the Failure of Density Functional Theories in Predicting Inverted Singlet-Triplet Gaps

Recent experimental and theoretical studies have shown several new organic molecules that violate Hund’s rule and have the first singlet excited state lower in energy than the first triplet excited state. While many correlated single reference wave function methods have successfully predicted excited-state energetics of these low-lying states, conventional linear-response time-dependent density functional theory (TDDFT) fails to predict the correct excited-state energy ordering. In this article, we have explored the performance of combined DFT and wave function methods like doubles-corrected TDDFT and multiconfiguration pair-density functional theory for the calculation of inverted singlet–triplet gaps. We have also tested the performance of the excited-state DFT (eDFT) method for this problem. Our results have shown that it is possible to obtain inverted singlet–triplet gaps both by using doubles-corrected TDDFT with a proper choice of double-hybrid functionals or by using eDFT.

Organic Emitters Showing Excited-States Energy Inversion: An Assessment of MC-PDFT and Correlation Energy Functionals Beyond TD-DFT

The lowest-energy singlet (S1) and triplet (T1) excited states of organic conjugated chromophores are known to be accurately calculated by modern wavefunction and Time-Dependent Density Functional Theory (TD-DFT) methods, with the accuracy of the latter heavily relying on the exchange-correlation functional employed. However, there are challenging cases for which this cannot be the case, due to the fact that those excited states are not exclusively formed by single excitations and/or are affected by marked correlation effects, and thus TD-DFT might fall short. We will tackle here a set of molecules belonging to the azaphenalene family, for which research recently documented an inversion of the relative energy of S1 and T1 excited states giving rise to a negative energy difference (ΔEST) between them and, thereby, contrary to most of the systems thus far treated by TD-DFT. Since methods going beyond standard TD-DFT are not extensively applied to excited-state calculations and considering how challenging this case is for the molecules investigated, we will prospectively employ here a set of non-standard methods (Multi-Configurational Pair Density Functional Theory or MC-PDFT) and correlation functionals (i.e., Lie–Clementi and Colle–Salvetti) relying not only on the electronic density but also on some modifications considering the intricate electronic structure of these systems.

Narrowband Deep-Blue Multi-Resonance Induced Thermally Activated Delayed Fluorescence: Insights from the Theoretical Molecular Design

Multi-resonance thermal activated delayed fluorescence (MR-TADF) has been promising with large oscillator strength and narrow full width at half maxima of luminescence, overcoming the compromise of emission intensity and energy criteria of traditional charge transfer TADF frameworks. However, there are still limited theoretical investigations on the excitation mechanism and systematic molecular manipulation of MR-TADF structures. We systematically study the highly localized excitation (LE) characteristics based on typical blue boron-nitrogen (BN) MR-TADF emitters and prove the potential triangular core with theoretical approaches. A design strategy by extending the planar π-conjugate core structure is proposed to enhance the multiple resonance effects. Moreover, several substituted groups are introduced to the designed core, achieving color-tunable functions with relatively small energy split and strong oscillator strength simultaneously. This work provides a theoretical direction for molecular design strategy and a series of potential candidates for highly efficient BN MR-TADF emitters.

Local Constraints on Junctions to Strengthen Near-Infrared Phosphorescence of Organic Dyes

A strategy involving the effect of the local constraint on junctions for doping-induced phosphorescence was proposed to increase the rigidity of hydrogen-bonded polymer to inhibit the nonradiative decay of the organic phosphorescent dyes and was verified by bromophenol blue (BPB) derivatives as the near-infrared (NIR) phosphorescent dye. It is shown that the effect of local constraints on junctions of β-cyclodextrin in the poly(vinyl alcohol) (PVA-LCPN) matrix can effectively improve the quantum yields of NIR phosphorescence of BPB derivatives. On the basis of the verification and optimization of the system through response surface analysis, the quantum yield of TBPB@PVA-LCPN film based on NIR emission could be increased up to 77% compared with that of TBPB@PVA, reaching 5.3%, and the quantum yield in the NIR region could be improved to 3.6%. The results of response surface analysis are consistent with the phenomenon of our proposed strategy, which can inspire the production of organic materials with NIR RTP emission. Together, this could inform efficient and cheap strategies for increasing the quantum yield of the doping RTP materials.

"H-Type" Like Constructed Dimer: Another Way to Enhance the Thermally Activated Delayed Fluorescence Effect

Thermally activated delayed fluorescence (TADF) materials are an essential part of TADF-based organic light-emitting diodes (OLEDs). All the reported methods to improve the performance of TADF materials were focused on achieving a high reverse intersystem crossing rate (k_RISC) and oscillator strength (f), but most of them were studies on single molecular states. In this paper, we have discovered a new dimer architecture called the "H-type" like dimer and proved that the "H-type" like dimer is another way to improve the performance of TADF materials by calculation and experiment. The calculated energy levels of excited states only provided 1.72-5.46% relative errors (RE) compare with the measured values, which indicated that the methods we chose were suitable for predicting the properties. The intermolecular interactions of the "H-type" like dimer endow it with much larger f and k_RISC properties than monomer states, proving that the "H-type" like dimer could improve the performance of TADF emitters.

Large Inverted Singlet-Triplet Energy Gaps Are Not Always Favorable for Triplet Harvesting: Vibronic Coupling Drives the (Reverse) Intersystem Crossing in Heptazine Derivatives

Heptazine derivatives are promising dopants for electroluminescent devices. Recent studies raised the question whether heptazines exhibit a small regular or an inverted singlet-triplet (IST) gap. It was argued that the S₁ ← T₁ reverse intersystem crossing (RISC) is a downhill process in IST emitters and therefore does not require thermal activation, thus enabling efficient harvesting of triplet excitons. Rate constants were not determined in these studies. Modeling the excited-state properties of heptazine proves challenging because fluorescence and intersystem crossing (ISC) are symmetry-forbidden in first order. In this work, we present a comprehensive theoretical study of the photophysics of heptazine and its derivative HAP-3MF. The calculations of electronic excitation energies and vibronic coupling matrix elements have been conducted at the density functional theory/multireference configuration interaction (DFT/MRCI) level of theory. We have employed a finite difference approach to determine nonadiabatic couplings and derivatives of spin-orbit coupling and electric dipole transition matrix elements with respect to normal coordinate displacements. Kinetic constants for fluorescence, phosphorescence, internal conversion (IC), ISC, and RISC have been computed in the framework of a static approach. Radiative S₁ ↔ S₀ transitions borrow intensity mainly from optically bright E' π → π* states, while S₁ ↔ T₁ (R)ISC is mediated by E″ states of n → π* character. Test calculations show that IST gaps as large as those reported in the literature are counterproductive and slow down the S₁ ← T₁ RISC process. Using the adiabatic DFT/MRCI singlet-triplet splitting of -0.02 eV, we find vibronically enhanced ISC and RISC to be fast in the heptazine core compound. Nevertheless, its photo- and electroluminescence quantum yields are predicted to be very low because S₁ → S₀ IC efficiently quenches the luminescence. In contrast, fluorescence, IC, ISC, and RISC proceed at similar time scales in HAP-3MF.

Thermally activated delayed fluorescence materials with aggregation-induced emission properties: a QM/MM study

Organic molecules with thermally activated delayed fluorescence (TADF) and aggregation induced emission (AIE) properties have attracted increasing research interest due to their great potential applications in organic light emitting diodes (OLEDs), especially for those with multicolor mechanochromic luminescence (MCL) features. Theoretical research on the luminescence characteristics of organic TADF emitters based on the aggregation states is highly desired to quantify the relationship between the TADF properties and aggregation states. In this work, we study the 4,4'-(6-(9,9-dimethylacridine-10(9H)-yl)quinoline-2,3-dibenzonitrile (DMAC-CNQ) emitter with TADF and AIE properties, and calculate the photophysical properties in gas, solid and amorphous states by using the quantum mechanics and molecular mechanics (QM/MM) method. Our simulations demonstrate that the aggregation states enhance obviously the reverse intersystem crossing rates and transition dipole moments of the DMAC-CNQ emitter, and suppress the non-radiative rates from the lowest excited singlet state (S₁) to ground state (S₀). Specifically, the molecular stacking of DMAC-CNQ in solid phases can mainly restrict the geometric torsion of the DMAC moiety for decreasing non-radiative decay rates, and the torsion of the CNQ moiety for increasing the reverse intersystem crossing rates. As a result, the calculated fluorescence efficiencies of the DMAC-CNQ emitter in the crystal and amorphous states are 67% and 26% respectively, and in good agreement with the experimental results.