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

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.

High-Throughput Screening of Molecule/Polymer Photocatalysts for the Hydrogen Evolution Reaction

Although there has been progress in designing organic photocatalysts, identifying and designing structurally distinct polymeric or molecular photocatalysts with high performance is still challenging. Using the properties of a set of well-known polymer photocatalysts, we performed a virtual screening of a large data set of around 50 000 organic semiconductors. In the initial stage, we looked for candidates with electronic properties similar to those of the best-performing photocatalysts. Next, we screened the data set using reactivity descriptors based on mechanisms derived from quantum chemical calculations for selected cases. We identified 33 candidates with high potential as photocatalysts for the hydrogen evolution reaction.

An efficient reverse intersystem crossing process exploiting non-bonding states in an inverted singlet-triplet gap system

Reverse intersystem crossing (rISC) is an essential process in organic light-emitting diodes to populate singlet excited states from non-emissive triplet states. A small or negative singlet-triplet energy gap and a large spin-orbit coupling between low-lying singlet and triplet states are key requirements to enhance the rISC rate. Here, we present a molecular design exploiting the n-π* excited state to maximize the efficacy of the rISC process for efficient light emitters using thermodynamic and kinetic calculations validated with high-level quantum chemical methods. Heptazine-based molecules with carbonyl groups attached are shown to possess a reasonable singlet energy gap for blue-light emission with the energy level of the n-π* triplet state modulated by addition of electron withdrawing or donating groups to achieve the optimal energy level ordering of T(π-π*) > T(n-π*) > S1, leading to enhanced spin-orbit coupling between the lowest triplet and singlet states with an inverted energy gap.

Enhancing the prediction of TADF emitter properties using Δ-machine learning: A hybrid semi-empirical and deep tensor neural network approach

This study presents a machine learning (ML)-augmented framework for accurately predicting excited-state properties critical to thermally activated delayed fluorescence (TADF) emitters. By integrating the computational efficiency of semi-empirical PPP+CIS theory with a Δ-ML approach, the model overcomes the inherent limitations of PPP+CIS in predicting key properties, including singlet (S1) and triplet (T1) energies, singlet-triplet gaps (ΔEST), and oscillator strength (f). The model demonstrated exceptional accuracy across datasets of varying sizes and diverse molecular features, notably excelling in predicting oscillator strength and ΔEST values, including negative regions relevant to TADF molecules with inverted S1-T1 gaps. This work highlights the synergy between physics-inspired models and machine learning in accelerating the design of efficient TADF emitters, providing a foundation for future studies on complex systems and advanced functional materials.

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 Importance of High-Frequency Modes in the Prediction of RISC Rates for TADF Molecules

The reverse intersystem crossing (RISC) rate determines the efficiency of dyes displaying thermally activated delayed fluorescence (TADF). Such a rate can be predicted at the full quantum level by considering all the vibrational normal modes or adopting an approximated methodology which relies on single classical modes. We evaluated the importance of considering all of the vibrational degrees of freedom in computations for targeting the design of novel emissive materials from first principles. We computed the RISC rate for 17 molecules of interest for TADF by comparing a full quantum mechanics treatment based on Fermi's golden rule with Marcus-based semiclassical approaches. The results are quantitatively and sometimes qualitatively different in the two approaches, especially when the reorganization energy is small, a common occurrence for molecules exhibiting TADF. The importance of high-frequency modes varies across the set of molecules considered, suggesting that their evaluation should become part of the molecular design process.

Can ΔSCF and ROKS DFT-Based Methods Predict the Inversion of the Singlet-Triplet Gap in Organic Molecules?

Inverted singlet-triplet gap systems (INVEST) have emerged as an intriguing class of materials with potential applications as emitters in Organic Light Emitting Diodes (OLEDs). Indeed, this type of material exhibits a negative singlet-triplet energy gap (ΔEST), i.e., an inversion of the lowest singlet (S1) and triplet (T1) excited states, that goes against Hund's rule. In this study, the ΔEST of a set of 15 INVEST molecules has been computed within the framework of Restricted Open-Shell Kohn-Sham (ROKS) and Delta Self-Consistent Field (ΔSCF) methods and the results were benchmarked against wavefunction-based calculations performed at the EOM-CCSD, NEVPT2, and SCS-CC2 levels. We find that ROKS always (and wrongly) predicts a positive ΔEST with global hybrid, meta-GGA, and long-range corrected functionals and that this is almost functional-independent. We also show that the only way to obtain an inverted gap was to resort to double hybrid functionals. In contrast, using the above-mentioned functionals, ΔSCF usually gives a negative ΔEST, although the results are largely functional-dependent. Overall, applying a ΔSCF method based on the PBE0 functional provides the lowest MSD and MAD with respect to the EOM-CCSD results. We further show that the singlet-triplet inversion is driven by different degrees of orbital relaxation in the singlet versus triplet state and that this is well captured by ΔSCF calculations. As a matter of fact, this orbital relaxation in ΔSCF somehow mimics the involvement of double and higher-order excitations in EOM-CCSD, which leads to a difference in spatial localization of the α and β spins, and thus introduces (local) spin polarization effects sourcing the negative ΔEST. However, care should be taken when using the ΔSCF method to screen materials with potential INVEST behavior in view of their limited quantitative correlation with reference EOM-CCSD results on the molecular data basis used here.

Functionalization of Clar's Goblet Diradical with Heteroatoms: Tuning the Excited-State Energies to Promote Triplet-to-Singlet Conversion

The ground-state spin multiplicity as well as the energy difference between the lowest-energy spin-singlet (S1) and spin-triplet (T1) excited states of topologically frustrated organic (diradical) molecules can be tuned by doping with a pair of heteroatoms (N or B atoms). We have thus systematically studied here a set of Clar's Goblet derivatives upon a controlled substitution at different C sites, to alter the electronic structure of the molecules and disclose the positions at which: (i) the ground-state multiplicity becomes a closed-shell singlet and (ii) the energy difference between S1 and T1 is considerably small (i.e., below 0.1-0.2 eV to induce a triplet exciton recovery upon thermal effects). This electronic structure outcome is driven by strong correlation effects; therefore, we have here applied a variety of single-reference [TD-DFT, CIS(D), SCS-CC2] and multireference [CASSCF, NEVPT2, RAS-srDFT] methods. For TD-DFT, we have covered global hybrid (PBE0, M06-2X), range-separated hybrid (ωB97X), and double-hybrid (PBE-QIDH, SOS1-PBE-QIDH, and PBE0-2) functionals to ascertain whether the results were highly dependent on the functional choice. Overall, we found that the heterosubstitution strategy could largely modify the electronic and optical properties of the pristine diradical system, with these organic forms thus constituting a new set of compounds with further optoelectronic applications.

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.

Machine Learning-Corrected Simplified Time-Dependent DFT for Systems With Inverted Single-t-o-Triplet Gaps of Interest for Photocatalytic Water Splitting

Hydrogen gas (H2) can be produced via entirely solar-driven photocatalytic water splitting (PWS). A promising set of organic materials for facilitating PWS are the so-called inverted singlet-triplet, INVEST, materials. Inversion of the singlet (S1) and triplet (T1) energies reduces the population of triplet states, which are otherwise destructive under photocatalytic conditions. Moreover, when INVEST materials possess dark S1 states, the excited state lifetimes are maximized, facilitating energy transfer to split water. In the context of solar-driven processes, it is also desirable that these INVEST materials absorb near the solar maximum. Many aza-triangulenes possess the desired INVEST property, making it beneficial to describe an approach for systematically and efficiently predicting the INVEST property as well as properties that make for efficient photocatalytic water splitting, while exploring the large chemical space of the aza-triangulenes. Here, we utilize machine learning to generate post hoc corrections to simplified Tamm-Dancoff approximation density functional theory (sTDA-DFT) for singlet and triplet excitation energies that are within 28-50 meV of second-order algebraic diagrammatic construction, ADC(2), as well as the singlet-to-triplet, ΔES1T1, gaps of PWS systems. Our Δ-ML model is able to recall 85% of the systems identified by ADC(2) as candidates for PWS. Further, with a modest database of ADC(2) excitation energies of 4025 aza-triangulenes, we identified 78 molecules suitable for entirely solar-driven PWS.

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.

Excited-State Hund's Rule Violations in Bridged [10]- and [14]Annulene Perimeters

Molecules with Hund's rule violations between low-lying singlet and triplet states may enable a new generation of fluorescent emitters. However, only a few classes of molecules are known with this property at the current time. Here, we use a high-throughput screening algorithm of the FORMED database to uncover a class of compounds where the first excited state violates Hund's rule. We examine this class of bridged [10]- and [14]annulene perimeters with saturated bridges, and relate them to known conjugated polycyclic systems with Hund's rule violations. Despite the structural similarities with the related class of nonalternant polycyclic hydrocarbons, the mechanism is different in these bridged annulene perimeters. Here, two molecular orbital configurations contribute to each excited state. Consequently, a Hund's rule violation can only be unambiguously assigned based on the symmetry of the lowest excited singlet and triplet states. With several examples of synthetically realistic molecules, the class of bridged [10]- and [14]annulenes thus provides a structural link between the known nonalternant and alternant (azaphenalene) classes of molecules violating Hund's rule. These design principles may open avenues for the identification of new types of molecules where the order of the photophysically relevant first excited singlet and triplet states are inverted.

Calibration of several first excited state properties for organic molecules through systematic comparison of TDDFT with experimental spectra

Time-dependent density functional theory (TDDFT) is a powerful computational tool for investigating excitation properties in organic electronics, and it holds significant potential for high-throughput virtual screening (HTVS) in this field. While most benchmarks focus on excitation energies, less attention has been paid to evaluating the accuracy of computed oscillator strengths and exciton reorganization energies against experimental data. In this work, we provide a systematic approach to evaluate in parallel the accuracy of these three quantities on the basis of a suitable fitting of the experimental absorption spectra of 71 molecules in solution. After considering 18 computational methodologies, the results from the M06-2X/def2-TZVP/PCM method demonstrate the strongest correlation with experimental data across the desired properties. For HTVS, the M06-2X/6-31G(d)/PCM method appears to be a particularly convenient choice among all methodologies due to its balance of computational efficiency and accuracy. Our results provide an additional benchmark needed before employing TDDFT methods for the discovery and design of organic electronic molecules.

Design of Anti-Hund Organic Emitters Based on Heptazine

Hund's rule, which is powerful in governing the first excited states of closed-shell organic materials, can hardly be violated to get inverted singlet-triplet gap (INVEST) molecules with negative singlet-triplet energy gaps (ΔEST), although INVEST materials have shown extraordinary photophysical properties and promising device performance especially in light-emitting diodes. Here, we propose a facile strategy to construct emissive INVEST molecules by introducing different types of substituents to heptazine in various modes, which can effectively tune the ΔEST to be negative with the enlarged oscillator strength (f) for the high fluorescence rate of the heptazine derivatives. Systematic computational studies show that the double substitution of electron-donating units with another nonconjugated substituent in hybrid substitution mode is the most favorable way in achieving slightly negative ΔEST and large f values; the conjugated substituent will compete with heptazine to make the molecule deviate from the INVEST feature. Especially, a series of high-performance heptazine-based INVEST emitters were constructed, exhibiting ΔEST low to -0.362 eV, f up to 0.0436, as well as a wide range emission color from 339 to 716 nm. Also, the designed molecules were predicted to have fluorescence radiative rates up to 106 s-1, along with efficient reverse intersystem crossing rates reaching 108 s-1. Importantly, the figure of merit (FM) was first proposed as a parameter to wholly evaluate the performance of INVEST emitters, and the highest FM of 0.198 was found in the triazine and double nonconjugated amine-substituted heptazine. These results highlight the great potential of the heptazine chromophore in constructing INVEST emitters, revealing fundamental structure-property understandings for the material design of efficient anti-Hund organic molecules with improved emission properties.

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.

Singlet-Triplet Inversions in Through-Bond Charge-Transfer States

Molecules where the lowest excited singlet state is lower in energy than the lowest triplet are highly promising for a number of organic materials applications as efficiency limitations stemming from spin statistics are overcome. All molecules known to possess such singlet-triplet inversions exhibit a pattern of spatially alternating but nonoverlapping HOMO and LUMO orbitals, meaning the lowest excited states are of a local character. Here, we demonstrate that derivatives of the bicyclic hydrocarbon calicene exhibit Hund's rule violations in charge-transfer (CT) states between its rings. These CT states can be tuned with substituents, so that the first excited singlet and triplet state are energetically inverted. This provides a conceptual connection between the emerging fields of inverted gap molecules and existing molecular design rules for state-of-the-art thermally activated delayed fluorescence materials.

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.

Rational Design of Organic Emitters with Inverted Singlet-Triplet Gaps for Enhanced Exciton Management

In organic light-emitting diodes (OLEDs), the pursuit of efficient molecular emitters has led to the development of thermally activated delayed fluorescence (TADF) molecules. While TADF compounds have promising properties, they face challenges such as energy gap constraints and uphill exciton transfer. Inverted emitters (INVEST) offer a novel solution with an inverted singlet-triplet energy (ΔEST) gap, enabling efficient utilization of excitons. This study examines the design and computational analysis of an array of molecules, including 23 INVEST emitters and remaining with positive energy gaps. Within the STEOM-DLPNO-CCSD framework, we explore the role of various molecular fragments in determining ΔEST. We also assess the importance of dynamic spin-polarization (DSP) obtained via the Pariser-Parr-Pople (PPP) scheme in energy gap determination. Exciting trends emerged from our results, with pentalene-containing compounds consistently manifesting negative ΔEST values while their naphthalene counterparts exhibited contrasting behavior. Moreover, we observed a negative DSP correlates with inverted singlet-triplet gaps. Overall, this research advances OLED materials through molecular design and computational analysis, offering avenues for optimizing exciton management and enhancing device performance.

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.

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.

From Chemical Drawing to Electronic Properties of Semiconducting Polymers in Bulk: A Tool for Chemical Discovery

A quantum chemistry (QC)/molecular dynamics (MD) scheme is developed to calculate electronic properties of semiconducting polymers in three steps: (i) constructing the polymer force field through a unified workflow, (ii) equilibrating polymer models, and (iii) calculating electronic structure properties (e.g., density of states and localization length) from the equilibrated models by QC approaches. Notably, as the second step of this scheme is generally the most time-consuming one, we introduce an alternative method to compute thermally averaged electronic properties in bulk, based on the simulation of a polymer chain in the solution of its repeat units, which is shown to reproduce the microstructure of polymer chains and their electrostatic effect (successfully tested for five benchmark polymers) 10 times faster than state-of-the-art methods. In fact, this scheme offers a consistent and speedy way of estimating electronic properties of polymers from their chemical drawings, thus ensuring the availability of a homogeneous set of simulations to derive structure-property relationships and material design principles. As an example, we show how the electrostatic effect of the polymer chain environment can disturb the localized electronic states at the band tails and how this effect is more significant in the case of diketopyrrolopyrrole polymers as compared to indacenodithiophene and dithiopheneindenofluorene ones.

Revisiting Hafner's Azapentalenes: The Chemistry of 1,3-Bis(dimethylamino)-2-azapentalene

Stable azaheterocyclic derivatives of pentalene have been reported by the group of Hafner in the 1970s. However, these structures remained of low interest until recently, when they started to be investigated in the context of organic light-emitting diodes' (OLEDs') development. Herein, we revisit the synthesis of stable azapentalene derivative 1,3-bis(dimethylamino)-2-azapentalene and further explore its properties both computationally and experimentally. Beyond the reproduction and optimization of some previously reported transformations, such as formylation and amine substitution, the available scope of reactions was expanded with azo-coupling, selective halogenations, and cross-coupling reactions.

A Computational Perspective on the Reactivity of π-spacers in Self-Immolative Elimination Reactions

The controlled release of chemicals, especially in drug delivery, is crucial, often employing "self-immolative" spacers to enhance reliability. These spacers separate the payload from the protecting group, ensuring a more controlled release. Over the years, design rules have been proposed to improve the elimination process's reaction rate by modifying spacers with electron-donating groups or reducing their aromaticity. The spacer design is critical for determining the range of functional groups released during this process. This study explores various strategies from the literature aimed at improving release rates, focusing on the electronic nature of the spacer, its aromaticity, the electronic nature of its substituents, and the leaving groups involved in the elimination reaction. Through computational analysis, I investigate activation free energies by identifying transition states for model reactions. My calculations align qualitatively with experimental results, demonstrating the feasibility and reliability of computationally pre-screening model self-immolative eliminations. This approach allows proposing optimal combinations of spacer and leaving group for achieving the highest possible release rate.

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.

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.

Artificial design of organic emitters via a genetic algorithm enhanced by a deep neural network

The design of molecules requires multi-objective optimizations in high-dimensional chemical space with often conflicting target properties. To navigate this space, classical workflows rely on the domain knowledge and creativity of human experts, which can be the bottleneck in high-throughput approaches. Herein, we present an artificial molecular design workflow relying on a genetic algorithm and a deep neural network to find a new family of organic emitters with inverted singlet-triplet gaps and appreciable fluorescence rates. We combine high-throughput virtual screening and inverse design infused with domain knowledge and artificial intelligence to accelerate molecular generation significantly. This enabled us to explore more than 800 000 potential emitter molecules and find more than 10 000 candidates estimated to have inverted singlet-triplet gaps (INVEST) and appreciable fluorescence rates, many of which likely emit blue light. This class of molecules has the potential to realize a new generation of organic light-emitting diodes.

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.

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.

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.