Excited Singlet Research Articles

Dual Triplet Sensitization Strategy for Efficient and Stable Triplet–Triplet Annihilation Upconversion Perovskite Solar Cells

Dual Triplet Sensitization Strategy for Efficient and Stable Triplet–Triplet Annihilation Upconversion Perovskite Solar Cells

Down-conversion-induced delayed fluorescence via an inverted singlet-triplet channel

Inverted singlet-triplet molecules possessing a down-conversion process from the lowest excited triplet state (T1) to the lowest excited singlet state (S1) have recently roused much attention on account of potential merits in organic optoelectronics and photocatalysis. Nevertheless, investigations on inverted singlet-triplet molecules predominantly depend on the sophisticated ab initio calculations, while experimental attempts are extremely rare. In this work, we experimentally demonstrate the inverted singlet-triplet character of a heptazine derivative (HAP-3MF) which exhibits negative S1-T1 energy gaps (ΔEST) of −0.22 eV in toluene and −0.19 eV in acetonitrile based on meticulous photophysical investigations. To the best of our knowledge, this is the first time to directly obtain negative ΔEST based on fluorescence and phosphorescence spectra. Moreover, to better evaluate and reveal the photophysical features of extremely weak delayed emission in HAP-3MF, a mixed solution system of HAP-3MF:1,3-di(9H-carbazol-9-yl)benzene (mCP) in toluene at various molar ratios was subtly designed, and the energy transition mechanism involving a down-converted triplet-to-singlet channel was carefully elucidated.

An efficient implementation of time-dependent linear-response theory for strongly orthogonal geminal wave function models.

We present an implementation of time-dependent linear-response equations for strongly orthogonal geminal wave function models: the time-dependent generalized valence bond (TD-GVB) perfect-pairing theory and the antisymmetrized product of strongly orthogonal geminals. The geminal wave functions are optimized using a restricted-step second-order algorithm suitable for handling many geminals, and the linear-response equations are solved in an efficient way using a direct iterative approach. The wave function optimization algorithm features an original scheme to create initial orbitals for the geminal functions in a black-box fashion. The implementation is employed to examine the accuracy of the geminal linear response for singlet excitation energies of small and medium-sized molecules. In systems dominated by dynamic correlation, geminal models constitute only a minor improvement with respect to time-dependent Hartree-Fock. Compared to the linear-response complete active space self-consistent field, TD-GVB either misses or gives large errors for states dominated by double excitations.

Thermodynamics of the spin-half square kagome lattice antiferromagnet

Over the last decade, the interest in the spin-$1/2$ Heisenberg antiferromagnet (HAF) on the square kagome (also called shuriken) lattice has been growing as a model system of quantum magnetism with a quantum paramagnetic ground state, flat-band physics near the saturation field, and quantum scars. A further motivation to study this model comes from the recent discovery of a gapless spin liquid in the square kagome magnet $\mathrm{K}{\mathrm{Cu}}_{6}\mathrm{Al}\mathrm{Bi}{\mathrm{O}}_{4}{(\mathrm{S}{\mathrm{O}}_{4})}_{5}\mathrm{Cl}$ [M. Fujihala et al., Nat. Commun. 11, 3429 (2020)]. Here, we present large-scale numerical investigations of the specific heat $C(T)$, the entropy $S(T),$ as well as the susceptibility $\ensuremath{\chi}(T)$ by means of the finite-temperature Lanczos method for system sizes of $N=18,24,30,36,42,48$, and $N=54$. We find that the specific heat exhibits a low-temperature shoulder below the major maximum which can be attributed to low-lying singlet excitations filling the singlet-triplet gap, which is significantly larger than the singlet-singlet gap. This observation is further supported by the behavior of the entropy $S(T)$, where a change in curvature is present just at about $T/J=0.2$, the same temperature where the shoulder in $C$ sets in. For the susceptibility the low-lying singlet excitations are irrelevant, and the singlet-triplet gap leads to an exponentially activated low-temperature behavior. The maximum in $\ensuremath{\chi}(T)$ is found at a pretty low temperature ${T}_{\mathrm{max}}/J=0.146$ (for $N=42$) compared to ${T}_{\mathrm{max}}/J=0.935$ for the unfrustrated square-lattice HAF signaling the crucial role of frustration also for the susceptibility. We find a striking similarity of our square kagome data with the corresponding ones for the kagome HAF down to very low $T$. The magnetization process featuring plateaus and jumps and the field dependence of the specific heat that exhibits characteristic peculiarities attributed to the existence of a flat one-magnon band are discussed as well.

Sensitization of Nd3+ Luminescence by Simultaneous Two-Photon Excitation through a Coordinating Polymethinic Antenna.

We have designed and synthesized two new cyaninic Nd3+ complexes where the lanthanide emission can be induced from simultaneous two-photon absorption followed by energy migration. These complexes correspond to a molecular design that uses an antenna ligand formed by the functionalization of a heptamethine dye with 5-ol-phenanthroline or 4-phenyl-terpyridine derivatives. These complexes employ the important nonlinear optical properties of symmetric polymethines to sensitize the lanthanide ion. We verified that simultaneous biphotonic excitation indirectly induces the 4F3/2 → 4I11/2 Nd3+ emission using femtosecond laser pulses tuned below the first electronic transition of the antenna. The simultaneous two-photon excitation events initially form the nonlinear-active second excited singlet of the polymethine antenna, which rapidly evolves into its first excited singlet. This state in turn induces the formation of the emissive Nd3+ states through energy transfer. The role of the first excited singlet of the antenna as the donor state in this process was verified through time resolution of the antenna's fluorescence. These measurements also provided the rates for antenna-lanthanide energy transfer, which indicate that the phenanthroline-type ligand is approximately five times more efficient for energy transfer than the phenyl-terpyridine derivative due to their relative donor-acceptor distances. The simultaneous two-photon excitation of this polymethine antenna allows for high spatial localization of the Nd3+excitation events.

Comprehensive understanding of multiple resonance thermally activated delayed fluorescence through quantum chemistry calculations

Molecules that exhibit multiple resonance (MR) type thermally activated delayed fluorescence (TADF) are highly efficient electroluminescent materials with narrow emission spectra. Despite their importance in various applications, the emission mechanism is still controversial. Here, a comprehensive understanding of the mechanism for a representative MR-TADF molecule (5,9-diphenyl-5,9-diaza-13b-boranaphtho[3,2,1-de]anthracene, DABNA-1) is presented. Using the equation-of-motion coupled-cluster singles and doubles method and Fermi’s golden rule, we quantitatively reproduced all rate constants relevant to the emission mechanism; prompt and delayed fluorescence, internal conversion (IC), intersystem crossing, and reverse intersystem crossing (RISC). In addition, the photoluminescence quantum yield and its prompt and delayed contributions were quantified by calculating the population kinetics of excited states and the transient photoluminescence decay curve. The calculations also revealed that TADF occurred via a stepwise process of 1) thermally activated IC from the electronically excited lowest triplet state T1 to the second-lowest triplet state T2, 2) RISC from T2 to the lowest excited singlet state S1, and 3) fluorescence from S1.

Exploring the water hydrogen-bonding effects on the ground and low-lying excited states of serotonin

In this work, we examined the ground and low-lying excited states of the serotonin (SERO) molecule and of four of its water hydrogen-bonded complexes (SERO-(H2O)n, with n = 1 and 2). Density functional theory (DFT) and its time-dependent variant (TD-DFT) were used for determining, respectively, ground state properties (such as equilibrium structures and relative energetics, when applicable) and excited state parameters (vertical excitation energies, generalized oscillator strengths (GOS), and structures). The CAM-B3LYP exchange–correlation functional with the def2-TZVP basis set was used and all the computations were performed in the gas-phase and in water (through the use of the integral equation formalism polarizable continuum model, IEF-PCM). In terms of ground-state, the existence of the H⋯O–H⋯N interaction in one of the SERO-H2O conformations contributed to the stabilization of the system when compared to its corresponding counterpart, with solvation decreasing (from 3.43 kcal/mol in the gas-phase to 1.75 kcal/mol in water) the differences regarding their relative energies. While no major differences regarding the excitation energies associated to an accessible state are suggested from the comparison between the results obtained for a given system through the consideration of solvation and those corresponding determined in the gas-phase, the hydrogen-bond interactions (originating from the explicit water molecules) combined with the implicit (water) solvation may be responsible for providing synergic effects in terms of increasing both the GOS related to a given open state as well as the number of excited states accessible, suggesting an enhancement in the photoabsorption. Taking one of the SERO-(H2O)2 conformations as instance, all the five lowest-lying excited singlets of the system were determined as being accessible (having GOS from 0.1036 to 0.5664) in water while only a single excited state (with GOS = 0.1150) is expected to be open in the gas-phase environment.

Long-Lived Organic Room-Temperature Phosphorescence from Amorphous Polymer Systems.

Long-lived organic room-temperature phosphorescence (RTP) materials have recently drawn extensive attention because of their promising applications in information security, biological imaging, optoelectronic devices, and intelligent sensors. In contrast to conventional fluorescence, the RTP phenomenon originates from the slow radiative transition of triplet excitons. Thus, enhancing the intersystem crossing (ISC) rate from the lowest excited singlet state (S1) to the excited triplet state and suppressing the nonradiative relaxation channels of the lowest excited triplet state (T1) are reasonable methods for realizing highly efficient RTP in purely organic materials. Over the past few decades, many strategies have been designed on the basis of the above two crucial factors. The introduction of heavy atoms, aromatic carbonyl groups, and other heteroatoms with abundant lone-pair electrons has been demonstrated to strengthen the spin-orbit coupling, thereby successfully facilitating the ISC process. Furthermore, the rigid environment is commonly constructed through crystal engineering to restrict intramolecular motions and intermolecular collisions to decrease excited-state energy dissipation. However, most crystal-based organic RTP materials suffer from poor processability, flexibility, and reproducibility, becoming a thorny obstacle to their practical application.Amorphous organic polymers with long-lived RTP characteristics are more competitive in materials science. The intertwined structures and long chains of polymers not only ensure the rigid environment with multiple interactions but also protect triplet excitons from the surroundings, which are conducive to realizing ultralong and bright RTP emission. Exploring the fabrication strategies, intrinsic mechanisms, and practical applications of organic long-lived RTP polymers is highly desirable but remains a formidable challenge. In particular, intelligent organic RTP polymer systems that are capable of dynamically responding to external stimuli (e.g., light, temperature, oxygen, and humidity) have been rarely reported. To develop multifunctional RTP materials and expand their potential applications, a great amount of effort has been expended.This Account gives a summary of the significant advances in amorphous organic RTP polymer systems, especially smart stimulus-responsive ones, focusing on the construction of a rigid environment to suppress nonradiative deactivation by abundant inter/intramolecular interactions. The typical interactions in RTP polymer systems mainly include hydrogen bonding, ionic bonding, and covalent bonding, which can change the molecular electronic structures and affect the energy dissipation channels of the excited states. An in-depth understanding of intrinsic mechanisms and an extensive exploration of potential applications for excitation-dependent color-tunable, ultraviolet (UV) irradiation-activated, temperature-dependent, water-responsive, and circularly polarized RTP polymer systems are distinctly illustrated in this Account. Furthermore, we propose some detailed perspectives in terms of materials design, mechanism exploration, and promising application potential with the hope to provide helpful guidance for the future development of amorphous organic RTP polymers.

Wave function identity: A new symmetry for 2-electron systems in an electromagnetic field

Stationary-state Schr{\"o}dinger-Pauli theory is a description of electrons with a spin moment in an external electromagnetic field. For 2-electron systems as described by the Schr{\"o}dinger-Pauli theory Hamiltonian with a symmetrical binding potential, we report a new symmetry operation of the electronic coordinates. The symmetry operation is such that it leads to the equality of the transformed wave function to the wave function. This equality is referred to as the Wave Function Identity. The symmetry operation is a two-step process: an interchange of the spatial coordinates of the electrons whilst keeping their spin moments unchanged, followed by an inversion. The Identity is valid for arbitrary structure of the binding potential, arbitrary electron interaction of the form $w(|{\bf{r}} - {\bf{r}}'|)$, all bound electronic states, and arbitrary dimensionality. It is proved that the exact wave functions satisfy the Identity. On application of the permutation operation for fermions to the identity, it is shown that the parity of the singlet states is even and that of triplet states odd. As a consequence, it follows that at electron-electron coalescence, the singlet state wave functions satisfy the cusp coalescence constraint, and triplet state wave functions the node coalescence condition. Further, we show that the parity of the singlet state wave functions about all points of electron-electron coalescence is even, and that of the triplet state wave functions odd. The Wave Function Identity and the properties on parity, together with the Pauli principle, are then elucidated by application to the $2$-dimensional $2$-electron `artificial atoms' or semiconductor quantum dots in a magnetic field in their first excited singlet $2^{1}S$ and triplet $2^{3} S$ states.

Manifestations of strong electron correlation in polyacene: Fundamental gap, density of states, and photoconductivity

The quasi-particle (QP) bands of polyacene (PAC) – an infinite linear chain of fused benzene rings – are reconstructed from the QP spectra of oligoacenes (OACs) with N ∈ [ 5 , 30 ] ( N is the number of fused rings) obtained using a computational methodology capable of incorporating the effect of strong non-dynamic electron correlation into the computation of the QP (electrons and holes) energy levels. As the result of mixing with the doubly excited electronic configuration, the fundamental gap in the ground electronic state of PAC widens to ca. 1.8 – 2.2 eV depending on the density functional employed. In the excited singlet electronic state, the band gap closes; thus, leading to photoconductivity of PAC, as well as longer ( N ≳ 9 ) OACs. The calculated optical gap of OACs converges to a finite value of ca. 1 eV in a reasonable agreement with the experiment. The experimentally observed sudden opening of the transmission gap in scanning tunneling spectroscopy of dodecacene ( N = 12) is explained by the effect of strong correlation, which shifts the first maxima of the density of states of the ground and excited states towards larger electron binding energies.

Identification of excimer delayed fluorescence by Protoporphyrin IX: A novel access to local chromophore concentration?

Protoporphyrin IX (PpIX) is a molecule produced in the mitochondria following the administration of its approved precursor, aminolevulinic acid (ALA). Strong light absorber at different wavelengths in the visible range, PpIX is extensively used as a photosensitizer (PS) for Photodynamic Therapy (PDT). PpIX is also an ideal molecular probe for the quantification of the tissue oxygen partial pressure (pO2), as its delayed fluorescence (DF) is quenched by oxygen, creating a direct relationship between the DF lifetime and the pO2. A limitation of both techniques is the ignorance of the PpIX concentration in tissues when the pO2 is measured or during PDT. In this study, the prompt (PF) and delayed fluorescence of PpIX dissolved in DiMethylFormamide (DMF) were acquired, in absence of oxygen, at different PpIX concentrations. Measurements of the PpIX emission for different excitation energies and temperatures, as well as spectral considerations led to the conclusion that E-type (thermal) DF was the dominant DF mechanism at low PpIX excited states concentrations (density of absorbed energy Hε[PpIX]<1 μJ. cm-3, H:excitation radiant exposure per pulse, ε: molar extinction coefficient at excitation wavelength) while P-type (Triplet Triplet Annihilation) DF took place at higher excited states concentrations (Hε[PpIX]>10 μJ. cm-3). The gradual development of a strong, red-shifted structureless DF peak at 670nm, invisible in the PF and absorption spectra, strongly points towards the first observation of PpIX excimer DF (EDF). It appears that, similarly to other aromatic molecules, PpIX excimers can be formed either by the encounter of two molecules in the first excited triplet state T1, or by the reaction of an excited singlet S1 with a triplet T1. Excimer DF could be beneficially used to determine the local concentration of PpIX, as the initial DF intensity ratio I0670/I0630 is linearly correlated with the local PpIX concentration, and thus rises up to the challenge of PpIX based pO2 measurement and PDT. This work could also pave the way for a fine comprehension of the production, diffusion and catabolization of PpIX in biological tissues.

Photodissociation dynamics of N3.

The photodissociation dynamics of N3 + excited from its (linear) 3Σg -/(bent) 3A″ ground to the first excited singlet and triplet states is investigated. Three-dimensional potential energy surfaces for the 1A', 1A″, and 3A' electronic states, correlating with the 1Δg and 3Πu states in linear geometry, for N3 + are constructed using high-level electronic structure calculations and represented as reproducing kernels. The reference ab initio energies are calculated at the MRCI+Q/aug-cc-pVTZ level of theory. For following the photodissociation dynamics in the excited states, rotational and vibrational distributions P(v') and P(j') for the N2 product are determined from vertically excited ground state distributions. Due to the different shapes of the ground state 3A″ potential energy surface and the excited states, appreciable angular momentum j' ∼ 60 is generated in diatomic fragments. The lifetimes in the excited states extend to at least 50ps. Notably, results from sampling initial conditions from a thermal ensemble and from the Wigner distribution of the ground state wavefunction are comparable.

Cisoid-cis intermediate plays a crucial role in decolouration rate in photochromic reaction of 8H-pyranoquinazolines and 3H-naphthopyrans

The photochromic reaction of 8H-pyranoquinazoline shows intriguing aspects in comparison to 3H-naphthopyrans. These come from a stabilized excited singlet state for 8 H-pyranoquinazoline, which has a longer lifetime and is strongly sensitive to the solvent. The polar solvent acetonitrile reduces the quantum yield of coloured isomer formation (transoid-cis species). Colour fading related to the decay of transoid-cis population is faster than that for 3H-naphthopyran family and occurs within few seconds time-window in solution at room temperature. Theoretical calculations show the crucial role in fading process played by the potential energy landscape, with the cisoid-cis intermediate located in a shallow high-energy minimum.

Phosphorescence and Photophysical Parameters of Porphycene in Cryogenic Matrices

Matrix isolation studies were carried out for porphycene, an isomer of porphyrin, embedded in solid nitrogen and xenon. The external heavy atom effect resulted in nearly a 100% population of the triplet state and in the appearance of phosphorescence, with the origin located at 10163 cm−1. This energy is much lower than that corresponding to the T1 position in porphyrin. This difference could be explained by postulating that the orbital origin corresponds in both isomers to the second excited singlet state, which lies much closer to S1 in porphycene. Most of the vibrational frequencies observed in the phosphorescence spectrum correspond to totally symmetric modes, but several ones were assigned to the out-of-plane Bg vibrations. These bands are not observed in fluorescence, which suggests their possible role in vibronic-spin-orbit coupling.

Rapid Computational Approach Towards Designing Singlet-Fission Chromophores by Tuning the Diradical Character of Heteroatom-Doped Polycyclic Aromatic Hydrocarbons Using the Atom-Specific Fukui Function.

Singlet fission (SF) is proposed as a promising method to circumvent the Shockley-Queisser threshold of single junction photovoltaics. Progress towards realizing efficient SF-based devices has been impeded by the fact that only a handful of molecules and their derivatives practically exhibit efficient SF. In the present work, we demonstrate a TDDFT-based rapid and cost-effective computational approach for designing SF chromophores by doping various atomic sites (substituting carbon atoms) of polycyclic aromatic hydrocarbons with nitrogen, phosphorus, and silicon. We establish a hitherto unexplored, direct correlation between the atom-specific chemical reactivity parameter─Fukui function─of these molecules with their frontier molecular orbital energies, diradical characters, and vertical singlet and triplet excitation energies. These quantitative correlations show exactly opposite trends for nitrogen-doped molecules and phosphorus- or silicon-doped molecules. The doped derivatives that have the Fukui function falling in a range of 0.03-0.14 possess the required intermediate diradical character and suitable singlet-triplet energies to qualify for SF candidature. Our findings enable one, at reasonable computational times and cost, to easily assess the doping criteria and to develop design rules for SF molecules in particular and for diradicaloids in general.

Urbach Rule in the Red-Shifted Absorption Edge of PET Films Irradiated with Swift Heavy Ions.

This paper presents a new analysis of the experimental transmission spectra of polyethylene terephthalate (PET) films before and after irradiation with swift heavy ions (SHI) films, as reported previously by the authors. It is shown that the absorption edge red shift for irradiated films contains two regions of exponential form, one of which is located in the UV region and the other at lower energy, mainly in the visible part of the spectrum. The behaviour of the transmission curves under different irradiating fluences demonstrates that these two regions reflect respectively the electron-enriched core of the latent track and its electron-depleted peripheral halo. The focal point method yields a bandgap energy of 4.1 eV for the electron-enriched core of the latent track, which is similar to n-doped semiconductors, and a bandgap of about 1.3–1.5 eV for the electron-depleted halo, similar to p-doped semiconductors. The boundary between the latent track cores and halos corresponds to a conventional semiconductor p-n junction. The values of the characteristic Urbach energy determined from experimental data correspond to the nonradiative transition energy between the excited singlet and triplet levels of benzene-carboxyl complexes in repeat units of the PET chain molecule. A parallel is drawn between the SHI-induced redistribution of electrons held in structural traps in the PET film and chemical redox reactions, which involve the redistribution of electrons in chemical bonds. It is suggested that alkali etching triggers the release of excess electrons in the latent track cores, which act as a catalyst for the fragmentation of PET chain molecules along the latent tracks of the SHI irradiation.

Role of NOM in the Photolysis of Chlorine and the Formation of Reactive Species in the Solar/Chlorine System.

The solar/chlorine system has been proposed as a novel advanced oxidation process (AOP) for efficient pollutant degradation and water disinfection by producing a series of reactive species including hydroxyl radicals (HO•), chlorine radicals (Cl•), and so forth. In this study, the role of natural organic matter (NOM) in the photolysis of free available chlorine (FAC) and the formation of HO• and Cl• in the solar/chlorine system was investigated employing nitrobenzene and benzoic acid as selective chemical probes. The decay rate of FAC was significantly accelerated in the presence of NOM at pH 5.5 under simulated solar irradiation, likely due to the photoreaction between FAC and the photoexcited NOM. The decay rate of FAC increased upon increasing the electron-donating capacity of NOM, which indicated that phenolic components play a significant role in the photodegradation of FAC. This acceleration mechanism was further verified using 4-nitrophenol as a model phenolic compound. NOM promoted Cl• formation and quenched HO• in the solar/chlorine system. The proposed reaction mechanism included the reaction of excited singlet phenolic compounds in NOM with FAC, which yielded Cl•. This study provides a useful insight into future applications for using the solar/chlorine system as a novel AOP for wastewater treatment or disinfection.

Dissolved Organic Matter Enhanced the Aggregation and Oxidation of Nanoplastics under Simulated Sunlight Irradiation in Water.

Nanoplastics (NPs) have become a new type of pollutant of high concern that is ubiquitous in aqueous environments. However, the transport and transformation of NPs in natural waters are not yet fully understood. In this study, the aggregation and photooxidation of NPs were assessed with nanosized polystyrene (PS) as an example, and the effects of dissolved organic matter (DOM) were investigated with Suwannee River fulvic acid (SRFA) as representative DOM. The results showed that simulated sunlight irradiation exhibited negligible effects on the aggregation of PS, while SRFA enhanced its heteroaggregation through hydrophobic interactions. In SRFA solutions, photooxidation of PS with a particle size of 200 nm was observed, which led to an increase in the O/C ratio on its surface at a rate of (2.20 ± 0.40) × 10-2 h-1. This indicates the promotional effect of SRFA on the oxidation of nanosized PS, which is attributed to the generation of the excited triplet state (3SRFA*), hydroxyl radicals (•OH), and singlet oxygen (1O2). Among these reactive species, 1O2 played a crucial role in the oxidation of PS. The findings in this study are helpful for an in-depth understanding of the environmental behavior of NPs in natural waters.

Kinetic specific features of singlet fission in highly anisotropic organic semiconductors.

Kinetics of singlet fission (SF) in molecular semiconductors, i.e., spontaneous splitting of the excited singlet state into a pair of triplet (T) excitons, is known to be strongly affected by geminate annihilation of created TT-pairs. In our work, we analyze in detail the specific properties of SF-kinetics in highly anisotropic molecular crystals (in which T-excitons undergo strongly anisotropic hopping migration) within the earlier proposed two-state model (TSM). This model allows for accurate treatment of the characteristic effects of anisotropic relative migration of T-excitons and TT-interaction on SF-kinetics, describing these effects within the approximation, that assumes kinetic coupling of two states: the [TT]-state of interacting TT-pairs and the [T + T]-state of freely migrating T-excitons. The TSM makes it possible to represent the TT-migration and interaction effects in terms of lattice-migration Green's functions, accurate analytical formulas that are obtained in this work. The TSM is applied to the analysis of SF-kinetics in rubrene single crystals, recently measured in a wide range of times (0.1ns < t < 104ns). The analysis enables one to obtain important information on specific properties of SF-kinetics in highly anisotropic crystals. In particular, the observed specific "hump" of SF-kinetics at intermediate times can be treated as a manifestation of the TT-coupling in the [TT]-state. It is also found that the characteristic asymptotic time-dependence of SF-kinetics (∼t-3/2) can markedly be distorted by spin relaxation in TT-pairs.

Theoretical Studies on the Photophysical Properties of the Ag(I) Complex for Thermally Activated Delayed Fluorescence Based on TD-DFT and Path Integral Dynamic Approaches.

Theoretical calculation not only is a powerful tool to deeply explore photophysical processes of the emitters but also provides a theoretical basis for material renewal and design strategy in the future. In this work, the interconversion and decay rates of the thermally activated delayed fluorescence (TADF) process of the rigid Ag(dbp)(P2-nCB) complex are quantitatively calculated by employing the optimally tuned range-separated hybrid functional (ω*B97X-D3) method combined with the path integral approach to dynamics considering the Herzberg–Teller and the Duschinsky rotation effects within a multimode harmonic oscillator model. The calculated results show that the small energy splitting ΔE(S1–T1) = 742 cm–1 (experimental value of 650 cm–1) of the lowest singlet S1 and triplet T1 state and proper vibrational spin–orbit coupling interactions facilitate the reverse intersystem crossing (RISC) processes from the T1 to S1 states. The kRISC rate is estimated to be 1.72 × 108 s–1 that is far more than the intersystem crossing rate kISC of 7.28 × 107 s–1, which will greatly accelerate the RISC process. In addition, the multiple coupling routes of zero-field splitting (ZFS) interaction can provide energetically nearby lying states, to speed up the RISC pathway, and restrict the phosphorescence decay rate. A smaller ZFS D-tensor of 0.143 cm–1, E/D ≈ 0.094 ≪ 1/3, and Δg > 0 are obtained, indicating that the excited singlet states are hardly mixed into the T1 state; thus, a lower phosphorescence decay rate (kp = 9.29 × 101 s–1) is expected to occur, and the T1 state has a long lifetime, which is helpful for the occurrence of the RISC process. These works are in excellent agreement with the experimental observation and are useful for improving and designing efficient TADF materials.