Thermally activated delayed fluorescence: A critical assessment of environmental effects on the singlet-triplet energy gap

Unveiling the photophysical and excited state properties of multi-resonant OLED emitters using combined DFT and CCSD method

Multi-resonance thermally-activated delayed fluorescence (MR-TADF) is predominantly observed in organoboron heteroatom-embedded molecules, featuring enhanced performance in organic light-emitting diodes (OLEDs) with high color purity, chemical stability, and excellent photoluminescence quantum yields. However, predicting the impact of any chemical change remains a challenge. Computational methods including density functional theory (DFT) still require accurate descriptions of photophysical properties of MR-TADF emitters. To circumvent this drawback, we explored recent investigations on the CzBX (Cz = carbazole, X = O, S, or Se) molecule as a central building block. We constructed a series of MR-TADF molecules by controlling chalcogen atom embedding, employing a combined approach of DFT and coupled-cluster (CCSD) methods. Our predicted results for MR-TADF emitter molecules align with the reported experimental data in the literature. The variation in the positions of chalcogen atoms embedded within the CzBX2X framework imparts unique photophysical properties.

Shedding light on thermally-activated delayed fluorescence

Thermally activated delayed fluorescence (TADF) is a hot research topic in view of its impressive applications in a wide variety of fields from organic LEDs to photodynamic therapy and metal-free photocatalysis. TADF is a rare and fragile phenomenon that requires a delicate equilibrium between tiny singlet-triplet gaps, sizable spin-orbit couplings, conformational flexibility and a balanced contribution of charge transfer and local excited states. To make the picture more complex, this precarious equilibrium is non-trivially affected by the interaction of the TADF dye with its local environment. The concurrent optimization of the dye and of the embedding medium is therefore of paramount importance to boost practical applications of TADF. Towards this aim, refined theoretical and computational approaches must be cleverly exploited, paying attention to the reliability of adopted approximations. In this perspective, we will address some of the most important issues in the field. Specifically, we will critically review theoretical and computational approaches to TADF rates, highlighting the limits of widespread approaches. Environmental effects on the TADF photophysics are discussed in detail, focusing on the major role played by dielectric and conformational disorder in liquid solutions and amorphous matrices.

Visualizing and characterizing excited states from time-dependent density functional theory

Time-dependent density functional theory (TD-DFT) is the most widely-used electronic structure method for excited states, due to a favorable combination of low cost and semi-quantitative accuracy in many contexts, even if there are well recognized limitations. This Perspective describes various ways in which excited states from TD-DFT calculations can be visualized and analyzed, both qualitatively and quantitatively. This includes not just orbitals and densities but also well-defined statistical measures of electron-hole separation and of Frenkel-type exciton delocalization. Emphasis is placed on mathematical connections between methods that have often been discussed separately. Particular attention is paid to charge-transfer diagnostics, which provide indicators of when TD-DFT may not be trustworthy due to its categorical failure to describe long-range electron transfer. Measures of exciton size and charge separation that are directly connected to the underlying transition density are recommended over more ad hoc metrics for quantifying charge-transfer character.

Solid state solvation: a fresh view

The design of efficient organic electronic devices, including OLEDs, OPVs, luminescent solar concentrators, etc., relies on the optimization of relevant materials, often constituted by an active (functional) dye embedded in a matrix. Understanding solid state solvation (SSS), i.e. how the properties of the active dye are affected by the matrix, is therefore an issue of fundamental and technological relevance. Here an extensive experimental and theoretical investigation is presented shedding light on this, somewhat controversial, topic. The spectral properties of the dye at equilibrium, i.e. absorption and Raman spectra, are not affected by the matrix dynamics. Reliable estimates of the matrix polarity are then obtained from an analysis of the micro-Raman spectra of polar dyes. Specifically, to establish a reliable polarity scale, the spectra of DCM or NR dispersed in amorphous matrices are compared with the spectra of the same dyes in liquid solvents with known polarity. On the other hand, steady-state emission spectra obtained in solid matrices depend in a highly non-trivial way on the matrix polarity and its dynamics. An extensive experimental and theoretical analysis of the time-resolved emission spectra of NR in a very large time window (15 fs-15 ns) allows us to validate this dye as a good probe of the dielectric dynamics of the surrounding medium. We provide a first assessment of the relaxation dynamics of two matrices (mCBPCN and DPEPO) of interest for OLED application, unambiguously demonstrating that the matrix readjusts for at least 15 ns after the dye photoexcitation.

Novel Method for the Synthesis of Merocyanines: New Photophysical Possibilities for a Known Class of Fluorophores

A new, transformative method for the preparation of rhodols and other merocyanines from readily available tetrafluorohydroxybenzaldehyde and aminophenols has been developed. It is now possible to prepare merocyanines bearing three fluorine atoms and additional conjugated rings, and the whole one-pot process occurs under neutral, mild conditions. Three heretofore unknown merocyanine-based architectures were prepared using this strategy from aminonaphthols and 4-hydroxycoumarins. The ability to change the structure of original rhodol chromophore into π-expanded merocyanines translates to a comprehensive method for the modulation of photophysical properties, such as shifting the absorption and emission bands across almost the entire visible spectrum, reaching a huge Stokes shift i. e. 4800 cm-1 , brightness approximately 80.000 M-1  cm-1 , two-photon absorption cross-section above 150 GM and switching-on/off solvatofluorochromism. A detailed investigation allowed to rationalize the different spectroscopic behavior of rhodols and new merocyanines, addressing solvatochromism and two-photon absorption.

Anomalous deep-red luminescence of perylene black analogues with strong π-π interactions

Perylene bisimide (PBI) dyes are known as red, maroon and black pigments, whose colors depend on the close π-π stacking arrangement. However, contrary to the luminescent monomers, deep-red and black PBI pigments are commonly non- or only weakly fluorescent due to (multiple) quenching pathways. Here, we introduce N-alkoxybenzyl substituted PBIs that contain close π stacking arrangement (exhibiting d_π-π ≈ 3.5 Å, and longitudinal and transversal displacements of 3.1 Å and 1.3 Å); however, they afford deep-red emitters with solid-state fluorescence quantum yields (Φ_F) of up to 60%. Systematic photophysical and computational studies in solution and in the solid state reveal a sensitive interconversion of the PBI-centred locally excited state and a charge transfer state, which depends on the dihedral angle (θ) between the benzyl and alkoxy groups. This effectively controls the emission process, and enables high Φ_F by circumventing the common quenching pathways commonly observed for perylene black analogues.

From symmetry breaking to symmetry swapping: is Kasha's rule violated in multibranched phenyleneethynylenes?

The phenomenon of excited-state symmetry breaking is often observed in multipolar molecular systems, significantly affecting their photophysical and charge separation behavior. As a result of this phenomenon, the electronic excitation is partially localized in one of the molecular branches. However, the intrinsic structural and electronic factors that regulate excited-state symmetry breaking in multibranched systems have hardly been investigated. Herein, we explore these aspects by adopting a joint experimental and theoretical investigation for a class of phenyleneethynylenes, one of the most widely used molecular building blocks for optoelectronic applications. The large Stokes shifts observed for highly symmetric phenyleneethynylenes are explained by the presence of low-lying dark states, as also established by two-photon absorption measurements and TDDFT calculations. In spite of the presence of low-lying dark states, these systems show an intense fluorescence in striking contrast to Kasha's rule. This intriguing behavior is explained in terms of a novel phenomenon, dubbed "symmetry swapping" that describes the inversion of the energy order of excited states, i.e., the swapping of excited states occurring as a consequence of symmetry breaking. Thus, symmetry swapping explains quite naturally the observation of an intense fluorescence emission in molecular systems whose lowest vertical excited state is a dark state. In short, symmetry swapping is observed in highly symmetric molecules having multiple degenerate or quasi-degenerate excited states that are prone to symmetry breaking.

Theoretical Insights into the Optical and Excited State Properties of Donor-Phenyl Bridge-Acceptor Containing Through-Space Charge Transfer Molecules

A comparative new strategy to enhance thermally activated delayed fluorescence (TADF) of through-space charge transfer (CT) molecules in organic light-emitting diodes (OLEDs) is investigated. Generally, TADF molecules adopt a twisted donor and acceptor structure to get a sufficiently small ΔE_ST and a higher value of the spin-orbit coupling matrix element (SOCME). However, molecules containing donor-phenyl bridge-acceptor (D-p-A) units and featuring π-stacked architectures have intramolecular CT contribution through space and exhibit high TADF efficiency. We have explored the insights into the TADF mechanism in D-p-A molecules using the density functional theory (DFT) and time-dependent DFT methods. The calculated optical absorption and ΔE_ST values are found to be in good agreement with available experimental data. Interestingly, we found the origin of the SOCME to be the twisted orientation of the donor and bridge moieties. Also, we predicted similar molecules with enhanced OLED efficiency with different substitutions.

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

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

Dielectric control of reverse intersystem crossing in thermally activated delayed fluorescence emitters

Thermally activated delayed fluorescence enables organic semiconductors with charge transfer-type excitons to convert dark triplet states into bright singlets via reverse intersystem crossing. However, thus far, the contribution from the dielectric environment has received insufficient attention. Here we study the role of the dielectric environment in a range of thermally activated delayed fluorescence materials with varying changes in dipole moment upon optical excitation. In dipolar emitters, we observe how environmental reorganization after excitation triggers the full charge transfer exciton formation, minimizing the singlet-triplet energy gap, with the emergence of two (reactant-inactive) modes acting as a vibrational fingerprint of the charge transfer product. In contrast, the dielectric environment plays a smaller role in less dipolar materials. The analysis of energy-time trajectories and their free-energy functions reveals that the dielectric environment substantially reduces the activation energy for reverse intersystem crossing in dipolar thermally activated delayed fluorescence emitters, increasing the reverse intersystem crossing rate by three orders of magnitude versus the isolated molecule.

Thermally Activated Delayed Fluorescence: Polarity, Rigidity, and Disorder in Condensed Phases

We present a detailed and comprehensive picture of the photophysics of thermally activated delayed fluorescence (TADF). The approach relies on a few-state model, parametrized ab initio on a prototypical TADF dye, that explicitly accounts for the nonadiabatic coupling between electrons and vibrational and conformational motion, crucial to properly address (reverse) intersystem crossing rates. The Onsager model is exploited to account for the medium polarity and polarizability, with careful consideration of the different time scales of relevant degrees of freedom. TADF photophysics is then quantitatively addressed in a coherent and exhaustive approach that accurately reproduces the complex temporal evolution of emission spectra in liquid solvents as well as in solid organic matrices. The different rigidity of the two environments is responsible for the appearance in matrices of important inhomogeneous broadening phenomena that are ascribed to the intertwined contribution from (quasi)static conformational and dielectric disorder.

Quantum simulations of thermally activated delayed fluorescence in an all-organic emitter

We investigate the prototypical NAI-DMAC thermally activated delayed fluorescence (TADF) emitter in the gas phase- and high-packing fraction limits at finite temperature, by combining first principles molecular dynamics with a quantum thermostat to account for nuclear quantum effects (NQE). We find a weak dependence of the singlet-triplet energy gap (ΔE_ST) on temperature in both the solid and the molecule, and a substantial effect of packing. While the ΔE_ST vanishes in the perfect crystal, it is of the order of ∼0.3 eV in the molecule, with fluctuations ranging from 0.1 to 0.4 eV at 300 K. The transition probability between the HOMOs and LUMOs has a stronger dependence on temperature than the singlet-triplet gap, with a desirable effect for thermally activated fluorescence; such temperature effect is weaker in the condensed phase than in the molecule. Our results on ΔE_ST and oscillator strengths, together with our estimates of direct and reverse intersystem crossing rates, show that optimization of packing and geometrical conformation is critical to increase the efficiency of TADF compounds. Our findings highlight the importance of considering thermal fluctuations and NQE to obtain robust predictions of the electronic properties of NAI-DMAC.

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.

Intersystem Crossing in Boron-Based Donor-Spiro-Acceptor Organic Chromophore: A Detailed Theoretical Study

Intersystem crossing and reverse intersystem crossing (rISC) processes were investigated in a boron-based donor-spiro-acceptor organic chromophore which shows thermally activated delayed fluorescence. Due to the perpendicular arrangement between donor and acceptor moieties, the HOMO and the LUMO are spatially separated, and the compound shows charge transfer (CT) transitions. We found both S₁ and T₁ excited states are CT in nature (i.e., electron and hole wave functions are localized on acceptor and donor units, respectively) and T₂, which is higher in energy than S₁ and T₁, is locally excited in nature (i.e., both electron and hole wave functions are localized on an acceptor unit). Because of the same nature of excitation (i.e., CT here), the spin-orbit coupling matrix element between S₁ and T₁ is very low and insignificant exciton conversion occurs from the T₁ state to the S₁ state (and vice versa). Our combined time-dependent density functional theory and quantum dynamics simulation shows that the rISC process from the T₁ state to the S₁ state can be enhanced by the presence of a nearby local excited triplet state (i.e., T₂ state here). A smaller gap between the T₁ and T₂ states efficiently establishes the rISC route.