Singlet-triplet Gap Research Articles

The inverted singlet-triplet gap: a vanishing myth?

Molecules with an inverted singlet-triplet gap (STG) between the first excited singlet and triplet states, for example, heptazine, have recently been reported and gained substantial attention since they violate the famous Hund's rule. Utilizing state-of-the-art high-level ab initio methods, the singlet-triplet gap vanishes and approaches zero from below whatever is improved in the theoretical description of the molecules: the basis set or the level of electron correlation. Seemingly, the phenomenon of inverted singlet-triplet gaps tends to vanish the closer we observe.

Beobachtung der ersten Schlüsselschritte eines titanbasierten Photoredox‐Katalysezyklus in Echtzeit

AbstractDie titanbasierte Katalyse mit Ein‐Elektronentransfer‐Schritten (SET) hat sich zu einem vielseitigen Ansatz für die Synthese von Feinchemikalien entwickelt. Kürzlich wurden erste Versuche unternommen, ihre Nachhaltigkeit zu verbessern, indem sie mit der Photoredox (PR) Katalyse kombiniert wird. Hier untersuchen wir die photochemischen Prinzipien der SET‐PR‐Katalyse auf Basis von Ti und in Abwesenheit eines Edelmetall PR−Co‐Katalysators. Durch Kombination von zeitaufgelöster Emissionsspektroskopie mit Ultraviolett‐Anregungs‐/Infrarot‐Abfrage‐Spektroskopie auf Zeitskalen von Femtosekunden bis Mikrosekunden quantifizieren wir die Dynamik der kritischen Ereignisse bei der Initiierung des Katalysezyklus, nämlich die Singulett‐Triplett‐Umwandlung des Titanocen(IV) PR‐Universalkatalysators und seine Ein‐Elektronen‐Reduktion durch einen Amin‐Elektronendonator. Die Ergebnisse unterstreichen die Bedeutung der Singulett‐Triplett‐Energielücke des PR‐Katalysators als Leitfaden für künftige Verbesserungen.

Observing theEntry Events of a Titanium-Based PhotoredoxCatalytic Cycle in Real Time.

Titanium-based catalysis in single electron transfer (SET) steps has evolved into a versatile approach for the synthesis of fine chemicals and first attempts have recently been made to enhance its sustainability by merging it with photo-redox (PR) catalysis. Here, we explore the photochemical principles of all-Ti-based SET-PR-catalysis, i.e. in the absence of a precious metal PR-co-catalyst. By combining time-resolved emission with ultraviolet-pump/mid-infrared-probe (UV/MIR) spectroscopy on femtosecond-to-microsecond time scales we quantify the dynamics of the critical events of entry into the catalytic cycle; namely, the singlet-triplet interconversion of the do-it-all titanocene(IV) PR-catalyst and its one-electron reduction by a sacrificial amine electron donor. The results highlight the importance of the PR-catalyst's singlet-triplet gap as a design guide for future improvements.

Fused Indacene Dimers.

Polycyclic hydrocarbons consisting of two or more directly fused antiaromatic subunits are rare due to their high reactivity. However, it is important to understand how the interactions between the antiaromatic subunits influence the electronic properties of the fused structure. Herein, we present the synthesis of two fused indacene dimer isomers: s-indaceno[2,1-a]-s-indacene (s-ID) and as-indaceno[3,2-b]-as-indacene (as-ID), containing two fused antiaromatic s-indacene or as-indacene units, respectively. Their structures were confirmed by X-ray crystallographic analysis. 1 H NMR/ESR measurements and DFT calculations revealed that both s-ID and as-ID have an open-shell singlet ground state. However, while localized antiaromaticity was observed in s-ID, as-ID showed weak global aromaticity. Moreover, as-ID exhibited a larger diradical character and a smaller singlet-triplet gap than s-ID. All the differences can be attributed to their distinct quinoidal substructures.

Connections and performances of Green's function methods for charged and neutral excitations.

In recent years, Green's function methods have garnered considerable interest due to their ability to target both charged and neutral excitations. Among them, the well-established GW approximation provides accurate ionization potentials and electron affinities and can be extended to neutral excitations using the Bethe-Salpeter equation (BSE) formalism. Here, we investigate the connections between various Green's function methods and evaluate their performance for charged and neutral excitations. Comparisons with other widely known second-order wave function methods are also reported. Additionally, we calculate the singlet-triplet gap of cycl[3,3,3]azine, a model molecular emitter for thermally activated delayed fluorescence, which has the particularity of having an inverted gap thanks to a substantial contribution from the double excitations. We demonstrate that, within the GW approximation, a second-order BSE kernel with dynamical correction is required to predict this distinctive characteristic.

Accessing blue-room-temperature phosphorescence from pyridine-fused extended coumarins

Coumarin derivatives have potential applications in sensing, laser dyes, fluorescent probes, and dye−sensitized solar cells due to their unique photophysical properties. However, the realization of room-temperature phosphorescence (RTP) under ambient conditions in coumarin derivatives remains unexplored. Extended coumarins can therefore be used to achieve RTP under ambient conditions. Here, we report two pyridine-fused coumarins (CPP, CPPCz); CPPCz contains a 9-phenyl carbazole unit that is covalently attached to the 5-position of CPP via a C–C single bond. Spectroscopic studies and quantum chemistry calculations reveal that CPPCz exhibits local emission (LE) and charge transfer (CT) emission in solution, while only LE emission is realized in CPP. In films, both compounds show fluorescence and blue-RTP under ambient conditions due to the low singlet-triplet gap (0.07–0.14 eV). The photoluminescence quantum yields are found to be 29–43%. Phosphorescence quantum yield was found to be 1.3–3%. This design principle reveals a method to understand RTP in extended coumarins.

Magnetism of the S=12 J1−J2 square-kagome lattice antiferromagnet

The spin-$1/2$ Heisenberg antiferromagnet on the square-kagome (SK) lattice has attracted growing attention as a model system of highly frustrated quantum magnetism. A further motivation for theoretical studies comes from the recent discovery of SK spin-liquid compounds. The SK antiferromagnet exhibits two non-equivalent nearest-neighbor bonds $J_1$ and $J_2$. One may expect that in SK compounds $J_1$ and $J_2$ are of different strength. We present a numerical study of finite systems by means of the finite-temperature Lanczos method. We discuss the temperature dependence of the specific heat $C(T)$, the entropy $S(T)$, and of the susceptibility $X(T)$ of the $J_1$-$J_2$ SK Heisenberg antiferromagnet varying $J_2/J_1$ in the range $0 \le J_2/J_1 \le 4$. We also discuss the zero-field ground state of the model. We find indications for a magnetically disordered singlet ground state for $0 \le J_2/J_1 \lesssim 1.65$. Beyond $J_2/J_1 \sim 1.65$ the singlet ground state gives way for a ferrimagnetic ground state. In the region $0.77 \lesssim J_2/J_1 \lesssim 1.65$ the low-temperature thermodynamics is dominated by a finite singlet-triplet gap filled with low-lying singlet excitations leading to an exponentially activated low-temperature behavior of $X(T)$. On the other hand, the low-lying singlets yield an extra maximum or a shoulder-like profile below the main maximum in the $C(T)$ curve. For $J_2/J_1 \lesssim 0.7$ the low-temperature thermodynamics is characterized by a large fraction of $N/3$ weakly coupled spins leading to a sizable amount of entropy at very low temperatures. In an applied magnetic field the magnetization process features plateaus and jumps in a wide range of $J_2/J_1$.

Understanding remarkably high triplet quantum yield in thione analogs of perylenediimide: A detailed theoretical study.

The diverse and tunable electronic structures of perylenediimide (PDI), together with its high thermal and chemical stability, make the compound suitable for applications in bioimaging, electrical, and optical devices. However, a large singlet-triplet gap (ΔES-T) and almost zero spin-orbit coupling (SOC) between the lowest excited singlet (S1) and triplet (T1) restrict intersystem crossing (ISC) in highly fluorescent pristine PDI, yielding a near zero triplet quantum yield (ΦT). Interestingly, a thione analogs of PDI with varied S content (mS-PDIs, m = 1-4) was experimentally shown to yield ΦT ∼ 1.0 through efficient ISC. Time-dependent optimally-tuned range-separated hybrid calculations are performed to rationalize the experimentally observed red-shifted optical absorption and also the remarkably high ISC with almost zero radiative fluorescence reported for these mS-PDIs. To this end, the relative energies of low-lying excited singlets Sn (n = 1, 2) and a few triplets Tn(n = 1-3), along with their nature (nπ* or ππ*), are assessed for each of the mS-PDIs studied in chloroform. To our surprise and contrary to the earlier reports, both S1 and T1 are found to be of the same ππ* character, originating from the highest occupied to lowest unoccupied orbital transition, which, therefore, leads to a still large ΔES-T and vanishingly small SOC, as expected from the identical wavefunction symmetry. Increasing S content lowers S1(ππ*) due to a greater extent of π-delocalization, which well complements and supports the observed red-shift. More importantly, the T2 (or T3) closely lying to the S1 is of nπ* and, therefore, produces a relatively smaller ΔES-T and larger SOC. Detailed kinetics analysis suggests S1(ππ*) → T2(nπ*) is the primary ISC channel for all mS-PDIs, which is responsible for the remarkably high ΦT observed. In addition, comparable SOC and ΔES-T produce similar ISC rates for all mS-PDIs.

Azaborine as a Versatile Weak Donor for Thermally Activated Delayed Fluorescence

Extensive research has been devoted to the development of thermally activated delayed fluorescence emitters, especially those showing pure-blue emission for use in lighting and full-color display applications. Toward that goal, herein we report a novel weak donor, 1,4-azaborine (AZB), with complementary electronic and structural properties compared to the widely used dimethylacridan (DMAC) or carbazole (Cz) donors. Coupled with a triazine acceptor, AZB-Ph-TRZ is the direct structural analogue of the high-performance and well-studied green TADF emitter DMAC-TRZ and has ΔEST = 0.39 eV, a photoluminescence quantum yield (ΦPL) of 27%, and λPL = 415 nm in 10 wt % doped mCP films. The shortened analogue AZB-TRZ possesses red-shifted emission with a reduced singlet-triplet gap (ΔEST = 0.01 eV) and fast reverse intersystem crossing (kRISC of 5 × 106 s-1) in mCP. Despite a moderate ΦPL of 34%, OLEDs with AZB-TRZ in mCP showed sky-blue emission with CIE1931(x,y) of (0.22,0.39) and a maximum external quantum efficiency (EQEmax) of 10.5%. Expanding the chemist's toolkit for the design of blue donor-acceptor TADF materials will enable yet further advances in the future, as AZB is paired with a wider range of acceptor groups.

Crystal structure, stability, spectroscopy, electronic structure, and ultrafast excited-state dynamics of the elusive iron(II) phthalocyanine axially coordinated with DABCO ligands

The elusive PcFe(DABCO)2 (Pc = phthalocyaninato(2-) ligand; DABCO = 1,4-diazabicyclo[2.2.2]octane) complex was prepared and characterized by UV-Vis, MCD, 1H NMR, and Mössbauer spectroscopies. The X-ray crystal structure of this complex indicates the longest Fe-N(DABCO) bond distance among all known PcFeL2 complexes with nitrogen donors as the axial ligands. The target compound is only stable in the presence of large access of the axial ligand and rapidly converts into the (PcFe)2O [Formula: see text]-oxo dimer even at a modest temperature. The electronic structure of the PcFe(DABCO)2 complex was elucidated by DFT and TDDFT methods. The DFT calculations predicted a very small singlet-triplet gap in this compound. The femtosecond transient absorption spectroscopy is indicative of extremely fast ([Formula: see text]200 fs) deactivation of the first excited state in PcFe(DABCO)2 with a lack of formation of the long-lived low-energy triplet state.

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.

Captodative Effect Facilitates the Excitation in Diboron Molecule (CAAC)2 B2 (SH)2.

Given the extraordinary versatility in chemical reactions and applications, boron compounds have gained increasing attentions in the past two decades. One of the remarkable advances is the unprecedented preparation of unsaturated boron species. Notably, Braunschweig et al. found that the cyclic (alkyl)(amino) carbenes (CAACs) stabilized diboron molecules (CAAC)2 B2 (SR)2 host unpaired electrons and exist in the 90°-twisted diradical form, while other analogues, such as N-heterocyclic carbenes (NHCs), stabilized diboron molecules prefer a conventional B=B double bond. Since previous studies recognized the differences in the steric effect between CAAC and NHC carbenes, here we focused on the role of thiol substituents in (CAAC)2 B2 (SR)2 by gradually localizing involved electrons. The co-planarity of the thiol groups and the consequent captodative effect were found to be the culprit for the 90°-twisted diradical form of (CAAC)2 B2 (SR)2 . Computational analyses identified two forces contributing to the π electron movements. One is the "push" effect of lone pairs on the sulfur atoms which boosts the π electron delocalization between the BB center and CAACs. The other is the π electron delocalization within each (CAAC)B(SR) fragment where the pull effect originates from the π electron withdrawal by CAACs. There are two such independent and orthogonal push-pull channels which function mainly in individual (CAAC)B(SR) fragments. This enhanced π push-pull effect in the triplet state facilitates the electronic excitation in (CAAC)2 B2 (SR)2 by reducing the singlet-triplet gap.

Ground States of Heisenberg Spin Clusters from a Cluster-Based Projected Hartree–Fock Approach

Recent work on approximating ground states of Heisenberg spin clusters by projected Hartree–Fock theory (PHF) is extended to a cluster-based ansatz (cPHF). Whereas PHF variationally optimizes a site–spin product state for the restoration of spin- and point-group symmetry, cPHF groups sites into discrete clusters and uses a cluster-product state as the broken-symmetry reference. Intracluster correlation is thus already included at the mean-field level, and intercluster correlation is introduced through symmetry projection. Variants of cPHF differing in the broken and restored symmetries are evaluated for ground states and singlet-triplet gaps of antiferromagnetic spin rings for various cluster sizes, where cPHF in general affords a significant improvement over ordinary PHF, although the division into clusters lowers the cyclical symmetry. In contrast, certain two- or three-dimensional spin arrangements permit cluster groupings compatible with the full spatial symmetry. We accordingly demonstrate that cPHF yields approximate ground states with correct spin- and point-group quantum numbers for honeycomb lattice fragments and symmetric polyhedra.

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.

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.

9-Borafluoren-9-yl and diphenylboron tetracoordinate complexes of F- and Cl-substituted 8-quinolinolato ligands: synthesis, molecular and electronic structures, fluorescence and application in OLED devices.

Six new four-coordinate tetrahedral boron complexes, containing 9-borafluoren-9-yl and diphenylboron cores attached to orthogonal fluorine- and chlorine-substituted 8-quinolinolato ligand chromophores, have been synthesised, characterised, and applied as emitters in organic light-emitting diodes (OLEDs). An extensive steady-state and time-resolved photophysical study, in solution and in the solid state, resulted in the first-time report of delayed fluorescence (DF) in solid films of 8-quinolinolato boron complexes. The DF intensity dependence on excitation dose suggests that this emission originates from triplet-triplet annihilation (TTA). Density functional theory (DFT) and time-dependent density functional theory (TDDFT) studies give insight into the ground and excited state geometries, electronic structures, absorption energies, and singlet-triplet gaps in these new organoboron luminophores. Finally, given their highly luminescent behaviour, organic light-emitting diode (OLED) devices were produced using the synthesised organoboron compounds as emissive fluorescent dopants. The best OLED displays green-blue (λmaxEL = 489 nm) electroluminescence with an external quantum efficiency (EQE) of 3.3% and a maximum luminance of 6300 cd m-2.

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).

Dimethylnonacethrene - en route to a magnetic switch.

Dimethylnonacethrene is the first derivative of the cethrene family that is energetically more stable than the product of its electrocyclic ring closure. Compared to the shorter homologue dimethylcethrene, the new system is EPR-active, because of a significantly lowered singlet-triplet gap, and displays remarkable stability. Our results suggest that adjustment of the steric bulk in the fjord region can enable realisation of diradicaloid-based magnetic photoswitches.

Multiple stable redox states and tunable ground states via the marriage of viologens and Chichibabin's hydrocarbon.

Chichibabin's hydrocarbon and viologens are among the most famous diradicaloids and organic redox systems, respectively. However, each has its own disadvantages: the instability of the former and its charged species, and the closed-shell nature of the neutral species derived from the latter, respectively. Herein, we report that terminal borylation and central distortion of 4,4'-bipyridine allow us to readily isolate the first bis-BN-based analogues (1 and 2) of Chichibabin's hydrocarbon with three stable redox states and tunable ground states. Electrochemically, both compounds exhibit two reversible oxidation processes with wide redox ranges. One- and two-electron chemical oxidations of 1 afford the crystalline radical cation 1˙+ and dication 12+, respectively. Moreover, the ground states of 1 and 2 are tunable with 1 as a closed-shell singlet and the tetramethyl-substituted 2 as an open-shell singlet, the latter of which could be thermally excited to its triplet state because of the small singlet-triplet gap.