Triplet Gap Research Articles

Isomeric Effects of Au28(S-c-C6H11)20 Nanoclusters on Photoluminescence: Roles of Electron-Vibration Coupling and Higher Triplet State.

The exploration of near-infrared photoluminescence (PL) from atomically precise nanoclusters is currently a prominent area of interest owing to its importance in both fundamental research and diverse applications. In this work, we investigate the near-infrared (NIR) photoluminescence mechanisms of two structural isomers of atomically precise gold nanoclusters of 28 atoms protected by cyclohexanethiolate (CHT) ligands, i.e., Au28i(CHT)20 and Au28ii(CHT)20. Based on their structures, analysis of 3O2 (triplet oxygen) quenching of the nanocluster triplet states, temperature-dependent photophysical studies, and theoretical calculations, we have elucidated the intricate processes governing the photoluminescence of these isomeric nanoclusters. For Au28i(CHT)20, its emission characteristics are identified as phosphorescence plus thermally activated delayed fluorescence (TADF) with a PL quantum yield (PLQY) of 0.3% in dichloromethane under ambient conditions. In contrast, the Au28ii(CHT)20 isomer exhibits exclusive phosphorescence with a PLQY of 3.7% in dichloromethane under ambient conditions. Theoretical simulations reveal a larger singlet (S1)-triplet (T1) gap in Au28ii than that in Au28i, and the higher T2 state plays a critical role in both isomers' photophysical processes. The insights derived from this investigation not only contribute to a more profound comprehension of the fundamental principles underlying the photoluminescence of atomically precise gold nanoclusters but also provide avenues for tailoring their optical properties for diverse applications.

Enhanced quantum efficiency of dicyano BODIPYs over difluoro BODIPYs: A DFT approach

The modified BODIPY (pyrromethene) dyes with cyano (-CN), substituting usual fluorine (-F), at the 4-position may give enhanced photochemical stability and quantum yield of fluorescence (QYF) when compared to the corresponding fluoro derivative. We have investigated and discussed comparatively the structural parameters of the ground (S0) and excited (S1) state geometries of a few widely used BODIPY dyes, both 4-cyano and 4-fluoro pyrromethene (PM), through DFT and TD-DFT studies and established the reasons for improved QYF of the cyano derivatives. The electrophilicity index indicates the stability of the excited geometry of the cyanated BODIPY and the calculated transition dipole moments reveal a longer lifetime of the excited state (S1) for the cyano BODIPY. The higher singlet and triplet gap in cyanated BODIPY accounts for higher QYF due to restricted transition from singlet to triplet state. This suggests that a population inversion, crucial for laser action, is easier to build up for cyano derivative than for the commonly used fluoro analogue while other gain/loss parameters of the PM dye lasers remain similar. Hence, 4-cyano derivatives of the PM dyes may be useful for more efficient lasing applications. The non-linear optical properties of the PM dyes are also investigated.

Cyano disubstituted tetrabenzoindeno[2,1-a]fluorene: open-shell or closed-shell?

Organic diradicaloids have lately emerged as potential spintronic materials. We report the unprecedented synthesis of a near-IR absorbing indeno[2,1-a]fluorene derivative that displays remarkably low LUMO (-4.15 eV) and a small HOMO-LUMO gap (0.85 eV). NMR/EPR studies indicated its open-shell diradical property, which was supported by DFT calculations while suggesting a 30% diradical character and a small singlet (S)-triplet (T) gap (-2.52 kcal mol-1). A large bond length alternation of the as-indacene core for its single-crystals indicated a quinoidal contribution with greater antiaromaticity, which is in line with the small diradical character despite showing a small S-T gap.

Unraveling the delayed fluorescence mechanism of copper(I) halide-phosphine emitters from DFT calculations

Several copper complexes exhibiting luminescent properties have been studied. In this context, the possibility of incorporating them into the architecture of organic light-emitting diode (OLED) devices has been investigated to improve their efficiency and photophysical stability for predicting the suitability and character of the emissive material. Specifically, we unraveled the excitation mechanism of the Cu(I)X(dppt)(PPh3) complex [X = Br, I, dppt = 3,4-bis(diphenylphosphino)thiophene]. Since the intersystem crossing (ISC) depicts a necessary process, where the knowledge of the rate constant value enables the assessment of the suitability of the material, we calculated the reverse and intersystem crossing rates for the Cu(I) complexes contrasting with pure organic thermally activated delayed fluorescence (TADF) emitters, with the goal to emphasize that the structural design of the mononuclear copper(I) complexes results in similar singlet–triplet gaps, ΔEST, values (∼0.1 eV). Moreover, it shows a remarkable enhancement of spin–orbit coupling, which allows achieving ISC rates in the ns scale. The calculations were made in the Time-Dependent Density Functional Theory (TD-DFT) level framework with the accurate response of large molecules studied here.

Theoretical Evaluation of the Properties of Nitrogen-Doped C24 Fullerenes and Their Interactions with Two Adamantane-Derived Antivirals

The replacement of carbon with a heteroatom within the structure of a fullerene gives the possibility of obtaining compounds with adjustable properties. The influence of aza-substitution on C24 fullerenes was investigated and a comparison of HF and DFT calculations was performed. Various substitution patterns were proposed and the characterization of C22N2 and C20N4 structures was performed. Global reactivity descriptors like chemical potential, hardness, HOMO–LUMO gap and singlet–triplet gap were computed. Aromaticity descriptors like delocalization indices and NICS(0) index were employed for the characterization of each six-membered ring of the studied fullerenes. The possible use of aza-fullerenes as drug delivery systems for two adamantane-derived antivirals was evaluated through molecular docking studies. The best results were obtained for the fullerenes with a pronounced hydrophobic character, the favored configuration of the antiviral drugs being the one oriented toward the side consisting of carbon atoms of the fullerenes.

Triplet Pairing in Neutron Matter

The presence of superfluidity in neutron star interiors can affect the cooling of neutron stars in intricate ways, enhancing certain mechanisms and suppressing others. Model calculations employing realistic nuclear potentials in Bardeen–Cooper–Schrieffer theory generally suggest the development of a 3P2–3F2 pairing gap, and therefore the presence of superfluidity in dense neutron star matter. Improved models that go beyond conventional mean-field calculations by including polarization effects suggest a suppression of the triplet gap. We have evaluated the pairing interaction by summing the “parquet” Feynman diagrams, which include both ladder and ring diagrams systematically, plus a set of important nonparquet diagrams, making this the most comprehensive diagram-based approach presently available. Our results suggest a radical suppression of the 3P2–3F2 triplet pairing gap and an enhancement of 3P0 pairing.

Dinor[7]helicene and Beyond: Divergent Synthesis of Chiral Diradicaloids with Variable Open‐Shell Character

AbstractDiradicaloid helicenes constructed formally by non‐benzenoid double π‐extension of phenanthrene were synthesized by a common strategy involving double electrophilic benzannulation. Steric effects in the second benzannulation step led to considerable structural diversity among the products, yielding a symmetrical dinor[7]helicene 1 and two isomeric unsymmetrical double helicenes 2 and 3, containing a nor[5]helicene and [4]helicene fragment, respectively, in addition to a common nor[6]helicene motif. Geometries, configurational dynamics, and electronic structure of these helicenes were analyzed using solid‐state structures, spectroscopic methods, and computational analyses. The open‐shell character of the singlet states of these helicenes increases in the order 3<1<2, with strongly varying diradicaloid indexes and singlet–triplet gaps. Compounds 1–3 displayed narrow optical gaps of 0.79–1.25 eV, resulting in significant absorption in the near infrared (NIR) region. They also exhibit reversible redox chemistry, each of them yielding stable radical cations, radical anions, and dianions, in some cases possessing intense NIR absorptions extending beyond 2500 nm.

Assessing Intersystem Crossing Rates in Donor- and/Acceptor-Functionalized Corroles: A Computational Study

Small singlet-triplet gap (ΔES-T) and large spin-orbit coupling (SOC) between the low-lying excited spin singlet and triplet states greatly promote the intersystem crossing (ISC) and reverse intersystem crossing (RISC) processes that are keys to harvest the triplet population. The electronic structure of a molecule, which strongly depends on its geometry, governs the ISC/RISC. Herein, we have studied visible-light-absorbing freebase corrole and its electron donor/acceptor functional derivatives to explore and understand the effect of homo/hetero meso-substitution in the modulation of corrole photophysical characteristics using time-dependent density functional theory implementing optimally tuned range-separated hybrid. Dimethylaniline and pentafluorophenyl are considered as the representative donor and acceptor functional groups, respectively. Solvent effects are accounted for using a polarizable continuum model with the dichloromethane dielectric. Calculations reproduce the experimentally measured 0-0 energies for some of the functional corroles studied here. Importantly, results reveal that both the homo- and hetero-substituted corroles including the unsubstituted one show substantial ISC rates (∼108 s-1) that are comparable to the fluorescence rates (∼108 s-1). On the other hand, while homo-substituted corroles exhibit modest RISC rates (∼104 - 106 s-1), hetero-substituted ones show relatively lower RISC rates (∼103 - 104 s-1). These results together suggest that both homo- and hetero-substituted corroles could act as triplet photosensitizers, which is also evident from some experimental reports on modest singlet oxygen quantum yield. Calculated rates are analyzed with respect to the variation of ΔES-T and SOC, and their dependence on the molecular electronic structure was evaluated in detail. The research findings reported in this study will add to understanding rich photophysical properties of functional corroles and also aid in devising molecular-level design strategies for developing heavy-atom free functional corroles or related macrocycles for applications in lighting, photocatalysis, photodynamic therapy, etc.

Building on the strengths of a double-hybrid density functional for excitation energies and inverted singlet-triplet energy gaps.

It is demonstrated that a double hybrid density functional approximation, ωB88PTPSS, that incorporates equipartition of density functional theory and the non-local correlation, however with a meta-generalized gradient approximation correlation functional, as well as with the range-separated exchange of ωB2PLYP, provides accurate excitation energies for conventional systems, as well as correct prescription of negative singlet-triplet gaps for non-conventional systems with inverted gaps, without any necessity for parametric scaling of the same-spin and opposite-spin non-local correlation energies. Examined over "safe" excitations of the QUESTDB set, ωB88PTPSS performs quite well for open-shell systems, correctly and fairly accurately [relative to equation-of-motion coupled-cluster singles and doubles (EOM-CCSD) reference] predicts negative gaps for 50 systems with inverted singlet-triplet gaps, and is one of the leading performers for intramolecular charge-transfer excitations and achieves near-second-order approximate coupled cluster (CC2) and second-order algebraic diagrammatic construction quality for the Q1 and Q2 subsets. Subsequently, we tested ωB88PTPSS on two sets of real-life examples from recent computational chemistry literature-the low energy bands of chlorophyll a (Chl a) and a set of thermally activated delayed fluorescence (TADF) systems. For Chl a, ωB88PTPSS qualitatively and quantitatively achieves DLPNO-STEOM-CCSD-level performance and provides excellent agreement with experiment. For TADF systems, ωB88PTPSS agrees quite well with spin-component-scaled CC2 (SCS-CC2) excitation energies, as well as experimental values, for the gaps between the S1 and T1 excited states.

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

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

Breaking bonds and breaking rules: inert-bond activation by [(iPr3P)Ni]5H4 and catalytic stereospecific norbornene dimerization.

The facile carbon atom abstraction reaction by [(iPr3P)Ni]5H6 (1) with various terminal alkenes to give [(iPr3P)Ni]5H4(μ5-C) (2) occurs via a common highly reactive intermediate [(iPr3P)Ni]5H4 (3), which was isolated by the reaction of 1 with norbornene. Temperature dependent 1H and 31P{1H} NMR chemical shifts of 3 are consistent with a thermally populated triplet excited state only 2 kcal mol-1 higher energy than the diamagnetic ground state. Complex 3 catalyzes the dimerization of norbornene to stereoselectively provide exclusively (Z) anti-(bis-2,2'-norbornylidene).

Curious Case of Singlet Triplet Gaps in Nonlinear Polyaromatic Hydrocarbons

The singlet triplet (ST) gap of linear polyacenes decays exponentially with the system size as a result of extended conjugation and reducing highest occupied molecular orbital (HOMO)-lowest unoccupied molecular orbital (LUMO) gaps. These low ST gaps can ideally be leveraged toward energy applications but are hindered by the decreasing stability of the systems. Thus, there is the need to understand the ST gap of nonlinear polyacenes, which are markedly more stable than their linear counterparts. Here, we show that the ST gaps of the nonlinear polyacenes do not decrease with the system size and have no correlation with the HOMO-LUMO gaps or increased conjugation. The reason behind this is identified as the high multireference character of the triplet high-spin state. These unprecedented results are in stark contrast to the observations in linear polyacenes and are due to the combined effects of topology and geometrical factors.

Design and Synthesis of Kekulè and Non-Kekulè Diradicaloids via the Radical Periannulation Strategy: The Power of Seven Clar’s Sextets

This work introduces an approach to uncoupling electrons via maximum utilization of localized aromatic units, i.e., the Clar's π-sextets. To illustrate the utility of this concept to the design of Kekulé diradicaloids, we have synthesized a tridecacyclic polyaromatic system where a gain of five Clar's sextets in the open-shell form overcomes electron pairing and leads to the emergence of a high degree of diradical character. According to unrestricted symmetry-broken UCAM-B3LYP calculations, the singlet diradical character in this core system is characterized by the y0 value of 0.98 (y0 = 0 for a closed-shell molecule, y0 = 1 for pure diradical). The efficiency of the new design strategy was evaluated by comparing the Kekulé system with an isomeric non-Kekulé diradical of identical size, i.e., a system where the radical centers cannot couple via resonance. The calculated singlet-triplet gap, i.e., the ΔEST values, in both of these systems approaches zero: -0.3 kcal/mol for the Kekulé and +0.2 kcal/mol for the non-Kekulé diradicaloids. The target isomeric Kekulé and non-Kekulé systems were assembled using a sequence of radical periannulations, cross-coupling, and C-H activation. The diradicals are kinetically stabilized by six tert-butyl substituents and (triisopropylsilyl)acetylene groups. Both molecules are NMR-inactive but electron paramagnetic resonance (EPR)-active at room temperature. Cyclic voltammetry revealed quasi-reversible oxidation and reduction processes, consistent with the presence of two nearly degenerate partially occupied molecular orbitals. The experimentally measured ΔEST value of -0.14 kcal/mol confirms that K is, indeed, a nearly perfect singlet diradical.

Either Accurate Singlet-Triplet Gaps or Excited-State Structures: Testing and Understanding the Performance of TD-DFT for TADF Emitters.

The energy gap between the lowest singlet and triplet excited states (ΔEST) is a key property of thermally activated delayed fluorescence (TADF) emitters, where these states are dominated by charge-transfer (CT) character. Despite its well-known shortcomings concerning CT states, time-dependent density functional theory (TD-DFT) is widely used to predict this gap and study TADF. Moreover, polar CT states exhibit a strong interaction with their molecular environment, which further complicates their computational description. Addressing these two major challenges, this work studies the performance of Tamm-Dancoff-approximated TD-DFT (TDA-DFT) on the recent STGABS27 benchmark set,1 exploring different strategies to include orbital and structural relaxation, as well as dielectric embedding. The results show that the best-performing strategy is to calculate ΔEST at the ground-state structure using functionals with a surprisingly small amount of Fock exchange of ≈10% and without a (complete) solvent model. However, as this approach heavily relies on error cancellation to mimic dielectric relaxation, it is not robust and exhibits large systematic deviations in excited state energies, state characters, and structures. More rigorous approaches, including state-specific solvation, do not share these systematic deviations, but their predicted ΔEST values exhibit larger statistical errors. We thus conclude that for the description of CT states in dielectric environments, none of the tested TDA-DFT methods is competitive with the recently presented ROKS/PCM approach regarding robustness, accuracy, and computational efficiency.

New HATNA(CN)6 ligand in the design of dianion magnetic assemblies with lanthanides {Cryptand(K+)}2{HATNA(CN)6·3LnIII(TMHD)3}2− (Ln = Gd, Tb and Dy)

Hexaazatrinaphthylenehexacarbonitrile ligand, HATNA(CN)6, when reduced to dianion state, forms crystalline {Cryptand[2.2.2](K+)}2{HATNA(CN)6}2−·2C6H4Cl2 (1) salt whose structure, optical and magnetic properties are studied. The HATNA(CN)6}2− dianions absorb light in the whole visible and a wide NIR range from 900 up to 2200 nm and have singlet EPR silent ground state. The dianions form trinuclear {Cryptand[2.2.2](K+)}2{HATNA(CN)6·3LnIII(TMHD)3}2−·3C6H5CH3 complexes where Ln is Gd (2), Tb (3) and Dy (4), and TMHD is 2,2,6,6-tetramethyl-3,5-heptanedionate. The {HATNA(CN)6}2− dianions are strongly distorted in coordination assemblies and have the length of the La-N{HATNA(CN)6} bonds of 2.58–2.66 Å. Dianions preserve low-energy absorption at the coordination of three metal complexes with maxima of the bands at 1440–1460 nm. DFT calculations support strong acceptor properties of HATNA(CN)6 and the non-degenerated LUMO for this ligand. As a result, dianions have singlet ground state whereas triplet state is positioned higher by 139 meV only (1620 K) and is thermally unattainable at 300 K. Coordination of the lanthanide complexes increases the singlet–triplet gap up to 210 meV (2440 K). Complexes 2–4 show weak antiferromagnetic coupling between high-spin lanthanide ions. J value estimated by PHI program for the gadolinium-complex is close to zero. Among 2–4 only gadolinium-containing complex 2 manifests an EPR signal with a complicated structure which can be approximated with D = 0.19 and E = 0.02 cm−1.

Benchmarking the semi-stochastic CC(P;Q) approach for singlet-triplet gaps in biradicals.

We recently proposed a semi-stochastic approach to converging high-level coupled-cluster (CC) energetics, such as those obtained in the CC calculations with singles, doubles, and triples (CCSDT), in which the deterministic CC(P;Q) framework is merged with the stochastic configuration interaction Quantum Monte Carlo propagations [J. E. Deustua, J. Shen, and P. Piecuch, Phys. Rev. Lett. 119, 223003 (2017)]. In this work, we investigate the ability of the semi-stochastic CC(P;Q) methodology to recover the CCSDT energies of the lowest singlet and triplet states and the corresponding singlet-triplet gaps of biradical systems using methylene, (HFH)-, cyclobutadiene, cyclopentadienyl cation, and trimethylenemethane as examples.

The effect of nonmagnetic disorder in the superconducting energy gap of strontium ruthenate

We have performed for the strontium ruthenate compound, a disordered tight-binding numerical study in the unitary and intermedia scattering regimes analyzing the imaginary part of the self-consistent elastic scattering cross-section at zero temperature as a function of the superconducting gap parameter using the anisotropic limit of the γ sheet. We start this research, mentioning a set of different zero energy superconducting spectrum values inferred from experimental data. Furthermore, it is reproduced the Miyake–Narikiyo tiny triplet gap by varying the zero energy superconducting microscopic parameter. Additionally, using the finite temperature Matsubara Green functions formalism, it is investigated the energy gap as a function temperature and disorder. We conclude that the evolution of the reduced phase space using the elastic scattering cross-section for a triplet order parameter is a useful numerical technique and predicts the two elastic scattering regimes for strontium ruthenate.

Magnetization process and ordering of the S=12 pyrochlore Heisenberg antiferromagnet in a magnetic field

We study the $S=\frac{1}{2}$ pyrochlore Heisenberg antiferromagnet in a magnetic field. Using large-scale density-matrix renormalization group calculations for clusters with up to 128 spins, we find indications of a finite triplet gap, causing a threshold field to nonzero magnetization in the magnetization curve. We obtain a robust saturation field consistent with a magnon crystal, although the corresponding $5/6$ magnetization plateau is very slim and possibly unstable. Most remarkably, there is a pronounced and apparently robust $1/2$ magnetization plateau where the ground state breaks the rotational symmetry of the lattice, exhibiting oppositely polarized spins on alternating kagome and triangular planes. Reminiscent of the kagome ice plateau of the pyrochlore Ising antiferromagnet known as spin ice, it arises via a much more subtle ``quantum order by disorder'' mechanism.

Modular design for constructing narrowband deep-blue multiresonant thermally activated delayed fluorescent emitters for efficient organic light emitting diodes

The simultaneous achievement of high efficiency and deep blue narrowband emission in multi resonant thermally activated delayed fluorescence (MR-TADF) materials are crucial and challenging. Herein we report two deep blue MR-TADF emitters, namely, TPD4PA and tBu-TPD4PA, using double boron, three nitrogen and two oxygen atoms. The design is based on amalgamating the high charge transfer (CT) characteristic moiety into MR-type fragments towards efficient MR-TADF emitters with improved CT characteristics. Both the materials show deep blue photo luminescent emissions of ∼450 nm with a high photoluminescence quantum yield (PLQY) of ∼90 %. These materials showed very small singlet–triplet gap (≤0.06 eV) and a high rate of reverse intersystem crossing of ∼2.5 × 105 s−1. The TADF devices based on TPD4PA and tBu-TPD4PA showed maximum external quantum efficiencies of 30.7 and 32.5 %, respectively. Furthermore, both devices exhibited narrow band deep blue emissions and corresponding CIE y coordinates 0.06 and 0.07, which match near NTSC and BT2020 blue color requirements.

Fast and Accurate Determination of the Singlet–Triplet Gap in Donor–Acceptor and Multiresonance TADF Molecules by Using Hole–Hole Tamm–Dancoff Approximated Density Functional Theory

AbstractOne of the requirements to design efficient emitters based on the multiresonance (MR)‐ or donor–acceptor (D‐A) thermally activated delayed fluorescence (TADF) materials is a relatively small energy gap between the lowest singlet and triplet excited states (ΔEST). High‐level ab initio calculations of their ΔEST provide benchmark results, but they are very time consuming and little practical for large‐size systems. Here, the performances of hole–hole Tamm–Dancoff approximated density functional theory (hh‐TDA‐DFT) and the functional dependent accuracy of hh‐TDA are examined on ΔEST of a large number of MR‐ and D‐A TADF molecules. The results indicate that hh‐TDA combined with the hybrid functional B3LYP can predict ΔEST values for a wide number of MR‐TADF molecules with mean absolute error (MAE) within 0.04 eV with correlation as high as 0.75. For D‐A TADF molecules, ΔEST is less sensitive to the nature of the functionals, with MAE as low as 0.07 eV. The larger discrepancy between ΔEST obtained from hh‐TDA‐DFT and experimental data in several oxygen‐containing MR‐TADF molecules is assumed to stem from the aggregation tendency of these compounds in solution. These findings provide important insights on the role of aggregation in reducing the ΔEST of MR‐TADF compounds.