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

Addressing the High-Throughput Screening Challenges of Inverted Singlet-Triplet Materials by MRSF-TDDFT

A new computational protocol utilizing mixed-reference spin-flip time-dependent density functional theory (MRSF-TDDFT) and the DTCAM-STG exchange-correlation functional has been developed to identify materials with inverted singlet-triplet (INVEST) energy levels. This protocol surpasses existing quantum chemical methods in both accuracy and computational efficiency for predicting ΔEST, addressing challenges in high-throughput screening for INVEST materials. Based on this approach, novel heptazine derivatives have been proposed, which are anticipated to outperform currently known systems. Additionally, dynamic spin polarization (DSP) has been identified as a critical factor influencing INVEST phenomena. This insight provides a foundation for new design principles, enabling the discovery of materials with superior performance compared to existing alternatives.

Quantifying Design Principles for Light-Emitting Materials with Inverted Singlet-Triplet Energy Gaps

Molecular engineering of organic emitter molecules with inverted singlet-triplet energy gaps (INVEST) has emerged as a powerful approach for enhancing fluorescence efficiency through triplet harvesting. In these unique materials, the first excited singlet state (S1) lies below the lowest triplet state (T1), enabling efficient reverse intersystem crossing. Previous computational studies have focused on accurately calculating the inverted energy gap and establishing qualitative structure-property relationships. Here, we present quantitative relationships that link the molecular structure to the S1-T1 energy gap, ΔEST, by introducing a benchmark set of 15 heptazine-based INVEST molecules (HEPTA-INVEST15). We identify a strong linear correlation (R2 > 0.94) between ΔEST and both the degree of intramolecular charge transfer and the deviation from a single-excitation character, as quantified by %R1 values and transition density matrix norms. These trends persist across our expanded set of 44 mono-, di-, and tri-substituted heptazines (HEPTA-INVEST44), underscoring the generality of our findings. Notably, strongly electron-donating groups, such as -NH2, minimize the magnitude of inverted gaps in mono-substituted heptazines yet produce the most negative ΔEST in certain tri-substituted derivatives, a result arising from competing resonance effects and excited-state aromaticity. Although ΔEST shows no clear correlation with Hammett parameters, our results reveal that physically meaningful, computable descriptors offer a mechanistic foundation for the future data-driven design of INVEST emitters. These findings pave the way for machine-learning approaches that connect the molecular structure to ΔEST without requiring high-level excited-state calculations.

Tripodal Heptazine Core-Based C3-Symmetric Multi-Azo(Hetero)Arenes: Photoswitching, Supramolecular Sol-Gel Behavior, and Base Sensing Prospects

Electron-deficient heptazine-based molecular and polymeric materials are a fast-growing area of research with their exciting electronic and optical properties, finding potential applications in catalysis, optoelectronics etc. However, the continuous thirst for the design of heptazine-core-based molecular systems has grown in interest in the search for a new class of materials. Herein, we have synthesized two heptazine core-based C3-symmetric tripodal molecular systems decorated with three azobenzene and phenylazo-3,5-dimethylisoxazole as photoswitchable units connected through ─NH linker. The photoswitching characteristics and thermal half-lives of photoswitched states were studied using UV-vis and nuclear magnetic resonance (NMR) spectroscopy. In addition, for azobenzene derivative 1, intriguing properties such as reversible sonication-induced gelation and base sensing ability have been demonstrated and supported by computations.

Computational Design of Molecules Having Less Overlapping HOMO and LUMO in the Same Plane

The negative energy difference between singlet and triplet excited states (ΔEST) is currently attracting significant attention; however, molecular designs remain largely confined to azaphenalene structures, as reported by Leupin and Wirz in 1980. To show negative ΔEST, a maximally separated highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) arrangement is crucial to minimizing the exchange interaction in the excited state. We revisited the electronic structure of cyclazine, consisting of cyclododecahexaene ([12]annulene) and a central nitrogen atom. The 12 π-electrons of the peripheral cyclic oligoene play an important role in achieving the less overlapping HOMO and LUMO arrangement, and the bridging by the nitrogen atom inside produces the energy difference between HOMO and LUMO while maintaining a stable planar structure. Based on these insights, we designed a set of 10 molecules in which the number of π-electrons (N) in the peripheral cyclic oligoene is 16, 20, and 24, satisfying N = 4·n (n = 4, 5, 6), and a further set of 11 molecules in which N in the peripheral cyclic oligoene is extended to 14, 18, 22, and 26, satisfying N = 4·n + 2 (n = 3, 4, 5, 6). HOMO, LUMO, exchange interaction (K), and ΔEST were calculated using configuration interaction singles, TD-DFT, and equation of motion coupled-cluster singles and doubles (EOM-CCSD), with the structure optimized without any symmetry constraint. Among the molecular structures with N = 4·n, only the molecules without bond alternation exhibit less overlapping HOMO and LUMO and a small K and ΔEST. In contrast, among the molecular structures with N = 4·n + 2, none of the molecules exhibit less overlapping HOMO and LUMO arrangement. The molecules with both N = 4·n and no bond alternation show negative ΔEST in the EOM-CCSD calculation. The findings of this study will pave the way for broader molecular designs of molecules exhibiting negative ΔEST, where a less overlap of HOMO and LUMO is essential.

Singlet-Triplet Inversion

The inversion of singlet and triplet states is a rare phenomenon, where, in opposition to Hund's first rule, singlet electronic states are stabilized relative to their triplet counterparts. The recent discovery of organic molecules exhibiting this inversion presents exciting new technological opportunities, such as addressing stability issues in organic light-emitting diodes (OLEDs). In this review, we describe fundamental molecular properties that can yield singlet-triplet inversion, generally ascribed to a phenomenon known as dynamic spin polarization. We discuss the systems in which singlet-triplet inversion was theoretically proposed, experimentally verified, and first implemented in an OLED device. We highlight key insights from the extensive computational work being carried out to understand the intricacies of these systems. Finally, we consider the outlook for future inverted singlet-triplet (IST) emitters.

The Best of Both Worlds: ΔDFT Describes Multiresonance TADF Emitters with Wave-Function Accuracy at Density-Functional Cost

With their narrow-band emission, high quantum yield, and good chemical stability, multiresonance thermally activated delayed fluorescence (MR-TADF) emitters are promising materials for OLED technology. However, accurately modeling key properties, such as the singlet-triplet (ST) energy gap and fluorescence energy, remains challenging. While time-dependent density functional theory (TD-DFT), the workhorse of computational materials science, suffers from fundamental issues, wave function-based coupled-cluster (CC) approaches, like approximate CC of second-order (CC2), are accurate but suffer from high computational cost and unfavorable scaling with system size. This work demonstrates that a state-specific ΔDFT approach based on unrestricted Kohn-Sham (ΔUKS) combines the best of both worlds: on a diverse benchmark set of 35 MR-TADF emitters, ΔUKS performs as good as or better than CC2, recovering experimental ST gaps with a mean absolute deviation (MAD) of 0.03 eV at a small fraction of the computational cost of CC2. When combined with a tuned range-separated LC-ωPBE functional, the excellent performance extends to fluorescence energies and ST gaps of MR- and donor-acceptor TADF emitters and even molecules with an inverted ST gap (INVEST), rendering this approach a jack of all trades for organic electronics.

Benchmark computations of nearly degenerate singlet and triplet states of N-heterocyclic chromophores. II. Density-based methods

In this paper, we demonstrate the performance of several density-based methods in predicting the inversion of S1 and T1 states of a few N-heterocyclic triangulene based fused ring molecules (popularly known as INVEST molecules) with an eye to identify a well performing but cost-effective preliminary screening method. Both conventional linear-response time-dependent density functional theory (LR-TDDFT) and ΔSCF methods (namely maximum overlap method, square-gradient minimization method, and restricted open-shell Kohn-Sham) are considered for excited state computations using exchange-correlation (XC) functionals from different rungs of Jacob's ladder. A well-justified systematism is observed in the performance of the functionals when compared against fully internally contracted multireference configuration interaction singles and doubles and/or equation of motion coupled-cluster singles and doubles (EOM-CCSD), with the most important feature being the capture of spin-polarization in the presence of correlation. A set of functionals with the least mean absolute error is proposed for both the approaches, LR-TDDFT and ΔSCF, which can be more cost-effective alternatives for computations on synthesizable larger derivatives of the templates studied here. We have based our findings on extensive studies of three cyclazine-based molecular templates, with additional studies on a set of six related templates. Previous benchmark studies for subsets of the functionals were conducted against the domain-based local pair natural orbital-similarity transformed EOM-CCSD (STEOM-CCSD), which resulted in an inadequate evaluation due to deficiencies in the benchmark theory. The role of exact-exchange, spin-contamination, and spin-polarization in the context of DFT comes to the forefront in our studies and supports the numerical evaluation of XC functionals for these applications. Suitable connections are drawn to two and three state exciton models, which identify the minimal physics governing the interactions in these molecules.

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.

Toward Efficient Modeling of Nonradiative Decay in Extended INVEST: Overcoming Computational Challenges in Quantum Dynamics Simulations

In recent years, an increasing number of fully organic molecules capable of thermally activated delayed fluorescence (TADF) have been reported, often with very small or even inverted singlet-triplet (INVEST) energy gaps. These molecules typically exhibit complex photophysics due to the close energy levels of multiple singlet and triplet states, which create various transition pathways toward emission. A predictive model for the rates of these transitions is thus essential for assessing the suitability of new materials for light-emitting devices. Quantum Dynamics (QD) calculations are ideal for this purpose, as they include quantum effects, without the limitations of first-order perturbative approaches, also allowing taking into account more than two electronic states at once. However, the huge computational demands of QD methodologies, especially for large molecules, currently limit their use as a standard tool. To address this problem, we here employ a strategy that allows us to include almost the whole set of the vibrational coordinates by selecting the key elements of the Hilbert space that significantly impact dynamics, thereby hugely reducing the computational burden. Application of this protocol to two relatively large INVEST molecules reveals that internal conversion in these systems is very fast, making indirect emissive pathways a possible channel for the population of the S1 state. More importantly, this study demonstrates that the dynamics can be accurately described even with a significantly reduced vibrational space, thus allowing quantum dynamics calculations that yield accurate transition rates in a few minutes of computational time.

Benchmark computations of nearly degenerate singlet and triplet states of N-heterocyclic chromophores. I. Wavefunction-based methods

In this paper, we investigate the role of electron correlation in predicting the S1-S0 and T1-S0 excitation energies and, hence, the singlet-triplet gap (ΔEST) in a set of cyclazines, which act as templates for potential candidates for fifth generation organic light emitting diode materials. This issue has recently garnered much interest with the focus being on the inversion of the ΔEST, although experiments have indicated near degenerate levels with both positive and negative being within the experimental error bar [J. Am. Chem. Soc. 102, 6068 (1980), J. Am. Chem. Soc. 108, 17(1986)]. We have carried out a systematic and exhaustive study of various excited state electronic structure methodologies and identified the strengths and shortcomings of the various approaches and approximations in view of this challenging case. We have found that near degeneracy can be achieved either with a proper balance of static and dynamic correlation in multireference theories or with state-specific orbital corrections, including its coupling with correlation. The role of spin contamination is also discussed. Eventually, this paper seeks to produce benchmark numbers for establishing cost-effective theories, which can then be used for screening derivatives of these templates with desirable optical and structural properties. Additionally, we would like to point out that the use of domain-based local pair natural orbital-similarity transformed EOM-coupled cluster singles and doubles as the benchmark for ΔEST [as used in J. Phys. Chem. A 126(8), 1378 (2022), Chem. Phys. Lett. 779, 138827 (2021)] is not a suitable benchmark for these classes of molecules.

Influence of pseudo-Jahn-Teller activity on the singlet-triplet gap of azaphenalenes

We analyze the possibility of symmetry-lowering induced by pseudo-Jahn-Teller interactions in six previously studied azaphenalenes that are known to have their first excited singlet state (S1) lower in energy than the triplet state (T1). The primary aim of this study is to explore whether Hund's rule violation is observed in these molecules when their structures are distorted from C2v or D3h point group symmetries by vibronic coupling. Along two interatomic distances connecting these point groups to their subgroups Cs or C3h, we relaxed the other internal degrees of freedom and calculated two-dimensional potential energy subsurfaces. The many-body perturbation theory (MP2) suggests that the high-symmetry structures are the energy minima for all six systems. However, single-point energy calculations using the coupled-cluster method (CCSD(T)) indicate symmetry lowering in four cases. The singlet-triplet energy gap plotted on the potential energy surface also shows variations when deviating from high-symmetry structures. A full geometry optimization at the CCSD(T) level with the cc-pVTZ basis set reveals that the D3h structure of cyclazine (1AP) is a saddle point, connecting two equivalent minima of C3h symmetry undergoing rapid automerization. The combined effects of symmetry lowering and high-level corrections result in a nearly zero singlet-triplet gap for the C3h structure of cyclazine. Azaphenalenes containing nitrogen atoms at electron-deficient sites - 2AP, 3AP, and 4AP - exhibit more pronounced in-plane structural distortion; the effect is captured by the long-range exchange-interaction corrected DFT method, ωB97XD. Excited state calculations of these systems indicate that in their low-symmetry energy minima, T1 is indeed lower in energy than S1, upholding the validity of Hund's rule. Jahn-Teller analysis predicts the symmetries of the in-plane distortion vibrational modes as or B2: C2v → Cs agreeing with the vibrational frequencies of the saddle-points.

Rank-Reduced Equation-of-Motion Coupled Cluster Triples: an Accurate and Affordable Way of Calculating Electronic Excitation Energies

In the present work, we report an implementation of the rank-reduced equation-of-motion coupled cluster method with approximate triple excitations (RR-EOM-CC3). The proposed variant relies on tensor decomposition techniques in order to alleviate the high cost of computing and manipulating the triply excited amplitudes. In the RR-EOM-CC3 method, both ground-state and excited-state triple-excitation amplitudes are compressed according to the Tucker-3 format. This enables factorization of the working equations such that the formal scaling of the method is reduced to N6, where N is the system size. An additional advantage of our method is the fact that the accuracy can be strictly controlled by proper choice of two parameters defining sizes of triple-excitation subspaces in the Tucker decomposition for the ground and excited states. Optimal strategies of selecting these parameters are discussed. The developed method has been tested in a series of calculations of electronic excitation energies and compared to its canonical EOM-CC3 counterpart. Errors several times smaller than the inherent error of the canonical EOM-CC3 method (in comparison to FCI) are straightforward to achieve. This conclusion holds both for valence states dominated by single excitations and for states with pronounced doubly excited character. Taking advantage of the decreased scaling, we demonstrate substantial computational costs reductions (in comparison with the canonical EOM-CC3) in the case of two large molecules - l-proline and heptazine. This illustrates the usefulness of the RR-EOM-CC3 method for accurate determination of excitation energies of large molecules.

Singlet-Triplet Inversion in Triangular Boron Carbon Nitrides

The discovery of singlet-triplet (ST) inversion in some π-conjugated triangle-shaped boron carbon nitrides is a remarkable breakthrough that defies Hund's first rule. Deeply rooted in strong electron-electron interactions, ST inversion has garnered significant interest due to its potential to revolutionize triplet harvesting in organic LEDs. Using the well-established Pariser-Parr-Pople model for correlated electrons in π-conjugated systems, we employ a combination of CISDT and restricted active space configuration interaction calculations to investigate the photophysics of several triangular boron carbon nitrides. Our findings reveal that ST inversion in these systems is primarily driven by a network of alternating electron-donor and electron-acceptor groups in the molecular rim, rather than by the triangular molecular structure itself.

Reference CC3 Excitation Energies for Organic Chromophores: Benchmarking TD-DFT, BSE/GW, and Wave Function Methods

To expand the QUEST database of highly accurate vertical transition energies, we consider a series of large organic chromogens ubiquitous in dye chemistry, such as anthraquinone, azobenzene, BODIPY, and naphthalimide. We compute, at the CC3 level of theory, the singlet and triplet vertical transition energies associated with the low-lying excited states. This leads to a collection of more than 120 new highly accurate excitation energies. For several singlet transitions, we have been able to determine CCSDT transition energies with a compact basis set, finding minimal deviations from the CC3 values for most states. Subsequently, we employ these reference values to benchmark a series of lower-order wave function approaches, including the popular ADC(2) and CC2 schemes, as well as time-dependent density-functional theory (TD-DFT), both with and without applying the Tamm-Dancoff approximation (TDA). At the TD-DFT level, we evaluate a large panel of global, range-separated, local, and double hybrid functionals. Additionally, we assess the performance of the Bethe-Salpeter equation (BSE) formalism relying on both G0W0 and evGW quasiparticle energies evaluated from various starting points. It turns out that CC2 and ADC(2.5) are the most accurate models among those with respective O ( N 5 ) and O ( N 6 ) scalings with system size. In contrast, CCSD does not outperform CC2. The best performing exchange-correlation functionals include BMK, M06-2X, M06-SX, CAM-B3LYP, ωB97X-D, and LH20t, with average deviations of approximately 0.20 eV or slightly below. Errors on vertical excitation energies can be further reduced by considering double hybrids. Both SOS-ωB88PP86 and SOS-ωPBEPP86 exhibit particularly attractive performances with overall quality on par with CC2, whereas PBE0-DH and PBE-QIDH are only slightly less efficient. BSE/evGW calculations based on Kohn-Sham starting points have been found to be particularly effective for singlet transitions, but much less for their triplet counterparts.

Development of an Organic Emitter Exhibiting Reverse Intersystem Crossing Faster than Intersystem Crossing

In thermally activated delayed fluorescence (TADF)-based organic light-emitting diodes (OLEDs), acceleration of reverse intersystem crossing (RISC) and suppression of intersystem crossing (ISC) are demanded to shorten a lifetime of triplet excitons. As a system realizing RISC faster than ISC, inverted singlet-triplet excited states (iST) with a negative energy difference (ΔEST) between the lowest excited singlet and the lowest triplet states have been gathering much attention recently. Here, we have focused on an asymmetric hexa-azaphenalene (A6AP) core to obtain a new insight into iST. Based on A6AP, we have newly designed A6AP-Cz with the calculated ΔEST of -44 meV. The experimental studies of a synthesized A6AP-Cz revealed that the lifetime of delayed fluorescence (τDF) was only 54 ns, which was the shortest among all organic materials. The rate constant of RISC (kRISC=1.9×107 s-1) was greater than that of ISC (kISC=1.0×107 s-1). The negative ΔEST of A6AP-Cz was experimentally confirmed from 1) the kRISC and kISC (-45 meV) and 2) the temperature-dependent τDF. 3) The onsets of fluorescence and phosphorescence spectra at 77 K also supported the evidence of negative ΔEST (-73 meV). This study demonstrated the potential of A6AP as an iST core for the first time.

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.

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.

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.

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.