Energy Gap Law Research Articles

The Energy Gap Law at Work: Emission Yield and Rate Fluctuations of Single NIR Emitters.

Internal conversion (IC) often is the dominating relaxation pathway in NIR emitters, lowering their fluorescence quantum yield. Here, we investigate dibenzoterrylene (DBT) by bulk and single molecule spectroscopy. With increasing solvent polarity, the S1-S0 energy gap decreases leading to a decrease of the fluorescence quantum yield and an increase of the IC rate in full accordance with the energy gap law. Making use of the unexpectedly strong fluorescence solvatochromism of this aromatic hydrocarbon, the validity of the energy gap law could also be demonstrated at the single molecule level. The S1-S0 energy gap not only controls the fluorescence lifetime and quantum yield of single molecules but also dictates how these quantities develop during spectral fluctuations. Our results open new avenues into unexplored single molecule photophysics and appear as a promising tool for nanoscale probing of dynamic heterogeneities.

Delocalization suppresses nonradiative charge recombination in polymer solar cells

Suppressing nonradiative deactivation of charge transfer (CT) states is pivotal to realizing further improvements in the power conversion efficiencies of polymer solar cells (PSCs). According to the energy gap law, the nonradiative decay rate constant knr scales exponentially with decreasing CT state energy ECT; thereby, as long as knr is governed by the energy gap law, a decrease in ECT will inevitably increase nonradiative deactivation of CT states and hence decrease the power conversion efficiency. Here, we report the nonradiative decay dynamics of CT states generated in various nonfullerene-acceptor-based PSCs by using transient absorption spectroscopy. The absence of a strong correlation between knr and ECT indicates that the energy gap law is not valid for these PSCs and that parameters other than ECT contribute significantly to knr. We found that knr decreased with an increase in materials’ crystallinities, indicating that increasing crystallinity leads to CT state delocalization, which in turn mitigates the nonradiative deactivation of CT states. We report the nonradiative decay dynamics of charge transfer (CT) states generated in nonfullerene-acceptor-based polymer solar cells. The nonradiative decay rate constants knr decreased with an increase in the efficiency for dissociation of CT states into free carriers, indicating that nonradiative decay of CT states can be mitigated by increasing the delocalization of the CT state wave function.

Recent Progress of Novel Organic Near‐Infrared‐Emitting Materials

Organic near‐infrared (NIR) emissive materials integrating the intrinsic NIR light advantages and organic semiconductor characters have generated immense scientific interest in fundamental science and practical application, including optical communications, night vision, surveillance, and biomedical applications. Nevertheless, the intrinsic energy gap law engenders a huge challenge to simultaneously meet longer emission wavelength and higher luminescence efficiency for organic NIR emitters. Herein, it is suggested that the purposefully molecular design and crystal engineering for novel organic NIR materials are urgently studied and explored. Herein, recent advances in novel organic NIR materials, mainly focusing on the hybridized local and charge transfer (HLCT) compounds, thermally activated delayed fluorescence (TADF) emitters, CT cocrystals, neutral π‐radicals, and excited‐state intramolecular proton transfer (ESIPT)‐active materials, are summarized. It is hoped that this perspective can afford a new insight into the fine design and synthesis of the desired organic NIR emitters.

Deepening Insights into Near‐Infrared Excited‐State Intramolecular Proton Transfer Lasing: The Charm of Resonance‐Assisted Hydrogen Bonds

AbstractExcited‐state intramolecular proton transfer (ESIPT)‐active organic semiconductor materials, characterized by a or several resonance‐assisted hydrogen bonds (RAHBs), are supposed to be ideal candidates for achieving high‐performance near‐infrared (NIR) lasers. However, according to the energy gap law, the development of ESIPT‐active gain materials is still limited by the serious nonradiative decays. Herein, it is demonstrated that RAHBs can activate ESIPT lasing by inhibiting nonradiative decays. A new ESIPT‐active material 1,5‐dihydroxy‐2,6‐diphenylanthraquinone (DP‐DHAQ) containing two centrosymmetric RAHBs is developed, which exhibits a ≈100‐fold higher radiative decay rate (kr = 1.1 × 1010 s–1) in doped polystyrene (PS) film than that of 1‐hydroxy‐5‐methoxy‐2,6‐diphenylanthraquinone (DP‐HMAQ) and 1,5‐dimethoxy‐2,6‐diphenylanthraquinone (DP‐DMAQ), in which one and two RAHBs are broken, respectively, by introducing methyl groups. Both DP‐DHAQ and DP‐HMAQ can form four‐level systems based on the ESIPT processes, but only DP‐DHAQ doped PS microspheres exhibit laser emission at 710 nm under the test conditions. It is worth mentioning that single‐crystal microplates of DP‐DHAQ can realize NIR laser emission at 725 nm. The results suggest that RAHBs can effectively activate the gain property of ESIPT‐active materials, which deepens insights into NIR ESIPT lasing and provides a new proposal for the design of organic laser‐active molecules.

Endowing deep-red BODIPY luminophors with enhanced aggregation-induced emission by installing miniature rotor of trifluoromethyl for solution-processed OLEDs

Highly efficient deep-red (DR) organic materials in aggregated state are fundamentally restricted by the serious nonradiative decay rates (k nr ) due to the energy gap law, and the aggregation induced quenching in view of significant intermolecular interaction. Here, two new BODIPY chromophores owning donor−acceptor−donor (D−A−D) structure, namely CF 3 -2TPA and 2CF 3 -2TPA, were designed and synthesized. Trifluoromethyl (CF 3 )-substituted phenyl group was introduced to the meso-position of the BODIPY core, tuning red to DR emission and suppressing intermolecular interaction with the utilization of the steric hindrance of CF 3 . Besides, CF 3 -2TPA and 2CF 3 -2TPA show enhanced aggregation-induced emission (AIE) characteristic, which was ascribed to the CF 3 rotor dissipating the excited-state energy. The OLEDs are fabricated by combining a thermally assisted delayed fluorescence host with a deep-red dye, showing a DR cut-on wavelength of 668 nm and external quantum efficiency of 2.3%. This work provided a rotor strategy to convert BODIPY molecule with obvious AIE property, providing their promising applications in DR-OLEDs. The miniature rotor of trifluoromethyl (CF 3 ) introduced to the meso-position of BODIPY, induced redshifted to deep-red emission, prevented obvious intermolecular interaction and achieved remarkably enhanced aggregation induced emission feature. Deep-red OLED showed an emission wavelength of 668 nm and an EQE max of 2.3%. • The CF 3 units, modifying the meso position of BODIPY, assisted in the deep-red emission. • Depending on the steric hindrance of CF 3 groups, the intermolecular interaction and packing were suppressed. • The enhanced AIE feature of BODIPYs was realized due to the miniature rotor of CF 3 substitutes. • Deep-red OLED showed an emission wavelength of 668 nm and an external quantum efficiency of 2.3%.

High Performance NIR OLEDs with Emission Peak Beyond 760 nm and Maximum EQE of 6.39%

AbstractAdvances in achieving high external quantum efficiency (EQE) of near‐infrared (NIR) organic light‐emitting diodes (OLEDs) are lagging behind that of the visible‐light OLEDs, according to the energy gap law. Herein, two structurally simple NIR‐phosphorescent Ir(III) complexes, DTCNIr and PTCNIr, with the cyclometalated ligands functionalized by the 1‐phenylisoquinoline‐4‐carbonitrile moiety and thieno/benzo[b]thiophene moiety are handily accessed within three synthetic steps. The introduction of the cyano unit can significantly lower the lowest unoccupied molecular orbitals whereas incorporating the conjugated group can elevate the highest occupied molecular orbitals of the newly designed Ir(III) complexes. The intramolecular charge transfer (ICT) transitions are enhanced due to the increased donor–acceptor interaction inside the metallophosphor. As a result, the emissions are red‐shifted to the NIR region with fast radiative decay. A maximum external quantum efficiency (EQE) of 8.11% with the emission peak at 726 nm for DTCNIr and a maximum EQE of 6.39% with the emission peak at 763 nm for PTCNIr are achieved in the NIR OLEDs by using these Ir(III) materials as the dopant emitters, a champion efficiency in the Ir(III)‐based OLEDs with the emission peak exceeding 760 nm.

Modulation of Thermally Stable Photoluminescence in Cr3+-Based Near-Infrared Phosphors

Broadband near-infrared (NIR) light sources based on phosphor-converted light-emitting diodes (pc-LEDs) are desirable for various photonics applications, while developing thermally stable NIR phosphors remains a great challenge. Increasing the temperature accelerates the severe nonradiative relaxation process gorverned by the intrinsic energy gap law, which further suspends the efficient low-energy emission of Cr3+ emitters in the inorganic lattice. To address this rule, several state-of-the-art strategies have been put forward in this perspective to modulate the critical law from the viewpoints of (1) crystal structure design, (2) defect engineering, (3) strengthened rigidity, and (4) energy transfer. This perspective suggests avenues for exploring novel broadband NIR phosphors with high thermal stability and will also stimulate further studies on NIR spectroscopy for high-power applications.

Radiative relaxation in isolated large carbon clusters: Vibrational emission versus recurrent fluorescence.

Recurrent fluorescence (RF) from isolated carbon clusters containing between 24 and 60 atoms is theoretically investigated as a function of internal energy, cluster size, and structural features. The vibrational relaxation kinetics and the associated IR emission spectra are determined by means of a Monte Carlo approach with vibrational density of states computed in the harmonic approximation. RF is generally found to be highly competitive with vibrational emission. The behaviors predicted for clusters of various sizes and archetypal structures indicate that the IR emission spectra are strongly influenced by RF, an energy gap law being obtained for the evolution of the RF rate constant depending on the electronic excitation state. The present results are relevant to the photophysics of the interstellar medium and could contribute to elucidating the carriers of the extended red emission bands and the continuum emission lying below the aromatic infrared bands believed to originate from mixed aromatic-aliphatic compounds.

Beyond the Energy Gap Law: The Influence of Selection Rules and Host Compound Effects on Nonradiative Transition Rates in Boltzmann Thermometers

AbstractApart from the energy gap law, control parameters over nonradiative transitions are so far only scarcely regarded. In this work, the impact of both covalence of the lanthanoid–ligand bond and varying bond distance on the magnitude of the intrinsic nonradiative decay rate between the excited 6P5/2 and 6P7/2 spin–orbit levels of Gd3+ is investigated in the chemically related compounds Y2[B2(SO4)6] and LaBO3. Analysis of the temperature‐dependent luminescence spectra reveals that the intrinsic nonradiative transition rates between the excited 6PJ ( J = 5/2, 7/2) levels are of the order of only 10 ms−1 (Y2[B2(SO4)6]:Gd3+: 8.9 ms−1; LaBO3:Gd3+: 10.5 ms−1) and differ due to the different degree of covalence of the GdO bonds in the two compounds. Comparison to the established luminescent Boltzmann thermometer Er3+ reveals, however, that the nonradiative transition rates between the excited levels of Gd3+ are over three orders of magnitude slower despite a similar energy gap and the presence of a single resonant phonon mode. This hints to a fundamental magnetic dipolar character of the nonradiative coupling in Gd3+. These findings can pave a way to control nonradiative transition rates and how to tune the dynamic range of luminescent Boltzmann thermometers.

Rational design of CN substituted dibenzo[a,c]phenazine acceptor for color tuning of thermally activated delayed fluorescent emitters

• Rational color tuning of thermally activated delayed fluorescence emitters by molecular engineering. • CN substituent management of dibenzophenazine acceptor to manage the light-emitting properties. • High external quantum efficiency from yellow to deep red organic light-emitting diodes. Thermally activated delayed fluorescent (TADF) emitters with emission wavelength beyond 600 nm and high external quantum efficiency (EQE) above 20 % are rarely reported because of the inherent limitation of the energy gap law. Rigid and planar dibenzo[ a,c ]phenazine (BP) core was proven to be a useful acceptor to develop highly efficient red TADF emitters by minimizing non-radiative loss mechanism. In this work, by varying the number and substitution position of donor/acceptor unit attached to the BP acceptor, four long wavelength TADF emitters (3-AcBPmCN, 3-AcBPdCN, 3-AcBPtCN and 11-ACBPdCN) were developed to control the emission wavelength from yellow (552 nm) to deep-red (637 nm) region. A directly attached 9,9-dimethyl-9,10-dihydroacridine (Ac) donor and newly developed 3-CNBP, 11,12-CNBP, 3,11,12-CNBP and 3,6-CNBP acceptor units were utilized in the synthesis of TADF emitters of 3-AcBPmCN, 3-AcBPdCN, 3-AcBPtCN and 11-AcBPdCN respectively. With the increasing number of cyano units on BP acceptor, decreased HOMO-LUMO energy gap and singlet–triplet energy gap (Δ E ST ) were reported for three TADF emitters of 3-AcBPmCN, 3-AcBPdCN and 3-AcBPtCN. Further, it was demonstrated that in between the two donor-substitution positions of BP acceptor (3 and 11), 11-position substituted 11-AcBPdCN TADF emitter exhibited higher EQE (23.1 %) than the 3-position substituted 3-AcBPdCN TADF emitter (17.3 %) with the similar color coordinate (0.53, 0.46).

Guest-host doped strategy for constructing ultralong-lifetime near-infrared organic phosphorescence materials for bioimaging

Organic near-infrared room temperature phosphorescence materials have unparalleled advantages in bioimaging due to their excellent penetrability. However, limited by the energy gap law, the near-infrared phosphorescence materials (>650 nm) are very rare, moreover, the phosphorescence lifetimes of these materials are very short. In this work, we have obtained organic room temperature phosphorescence materials with long wavelengths (600/657–681/732 nm) and long lifetimes (102–324 ms) for the first time through the guest-host doped strategy. The guest molecule has sufficient conjugation to reduce the lowest triplet energy level and the host assists the guest in exciton transfer and inhibits the non-radiative transition of guest excitons. These materials exhibit good tissue penetration in bioimaging. Thanks to the characteristic of long lifetime and long wavelength emissive phosphorescence materials, the tumor imaging in living mice with a signal to background ratio value as high as 43 is successfully realized. This work provides a practical solution for the construction of organic phosphorescence materials with both long wavelengths and long lifetimes.

Recent advances in D–A–D based Pdots with NIR-II fluorescence for deep-tissue imaging

This mini-review outlines the recent designs of D–A–D based Pdots with NIR-II fluorescence. Several strategies for molecular engineering are summarized to overcome the emission energy gap law. Their applications of bio-imaging are also included.

Highly Efficient TADF‐Type Organic Afterglow of Long Emission Wavelengths

AbstractDue to the energy gap law, the direct fabrication of efficient organic afterglow materials with long emission wavelengths at ambient conditions remains challenging. Here, luminescent dopants with moderate kRISC values of 100–101 s−1 are designed to harvest triplet energies, simultaneously improving afterglow efficiency and maintaining emission lifetimes >0.1 s. Organic matrices with large dipole moments are selected to populate the triplet excited states of the luminescent dopants and suppress their nonradiative decay and quenching. The dopant‐matrix systems exhibit TADF‐type organic afterglow with quantum efficiency of 20% to 60% and emission wavelengths exceeding 600 nm. Because of their singlet excited state nature, the TADF‐type afterglow emitters can efficiently transfer excited energy to rhodamine B or cyanine 5.5 fluorescence dyes for the construction of red and near‐infrared afterglow materials which display promising bioimaging applications.

Stable Diarylamine-Substituted Tris(2,4,6-trichlorophenyl)methyl Radicals: One-Step Synthesis, Near-Infrared Emission, and Redox Chemistry

Stable Diarylamine-Substituted Tris(2,4,6-trichlorophenyl)methyl Radicals: One-Step Synthesis, Near-Infrared Emission, and Redox Chemistry

Hexaphenylbenzene based push-pull fluorophores displaying intriguing polarity-dependent fluorescence behavior, AIE(E) characteristics and mega-large Stokes shifts

In general, most donor-acceptor type fluorophores are known to exhibit solvatochromic behavior and obey the energy gap law simultaneously, showing decreased emission with increasing solvent polarity. In this work, four push-pull hexaphenylbenzene (HPB) derivatives 1–4 have been designed and synthesized by introducing methoxy and dicyanovinyl groups at the tip of aromatic blades, which behave exceptionally polarity-dependent emission properties. In the low to medium solvent polarity region, the four dipole fluorophores display gradually enhanced fluorescence, whereas a reverse trend is observed with the further increase of solvent polarity. Meanwhile, 1–4 are found to exhibit the strongest emission at the same wavelength remarkably, which appears to be somewhat relevant to the intrinsic characteristics of dicyanovinyl-phenyl acceptor. A mechanistic scheme containing a conical intersection (CI) has been proposed to explain the up-down emission of 1–4 with increasing solvent polarity. Large Stokes shifts (up to 254 nm) and AIE(E) characteristics have also been achieved in these four HPB fluorophores. Besides, fluorophores 1–4 exhibit obvious freezing-solution induced chromism (FSIC), demonstrating an enhancement of the local matrix polarity upon freezing solutions.

Ruthenium (II) Complexes Bearing Heteroleptic Terpyridine Ligands: Synthesis, Photophysics and Solar Energy Conversion

AbstractHeteroleptic ruthenium (II) complexes featuring donor functionalized phenyl‐terpyridine (ph‐tpy) and a monocarboxylic‐(ph‐tpy)/(tpy) are synthesized and characterized. Reactions of ruthenium (II) precursors at 80 °C favored heteroleptic complexes formation over the homoleptic side products. Visible light excitation of these complexes resulted in the metal‐to‐ligand charge transfer (MLCT) transitions. The inter‐planar torsional angle between the atoms of donor functionalized phenyl ring and the central pyridine (py) of the tpy core strongly influences visible light absorption and photovoltaic properties. The lower inter‐ring py‐ph torsion in the acceptor end of the MLCT structures and its increase in the oxidized doublets could prevent the back electron transfer. The ruthenium atom and the acceptor functionalized tpy host the triplet‐MLCT spin density. Ambient temperature excited‐state decay followed the energy gap law and occurred in the order of a few nanoseconds. Herein, we evaluate the photosensitizing ability of these complexes via a combined experimental and computational approach.

Exciton Delocalization Counteracts the Energy Gap: A New Pathway toward NIR-Emissive Dyes.

Exciton coupling between the transition dipole moments of ordered dyes in supramolecular assemblies, so-called J/H-aggregates, leads to shifted electronic transitions. This can lower the excited state energy, allowing for emission well into the near-infrared regime. However, as we show here, it is not only the excited state energy modifications that J-aggregates can provide. A bay-alkylated quaterrylene was synthesized, which was found to form J-aggregates in 1,1,2,2-tetrachloroethane. A combination of superradiance and a decreased nonradiative relaxation rate made the J-aggregate four times more emissive than the monomeric counterpart. A reduced nonradiative relaxation rate is a nonintuitive consequence following the 180 nm (3300 cm–1) red-shift of the J-aggregate in comparison to the monomeric absorption. However, the energy gap law, which is commonly invoked to rationalize increased nonradiative relaxation rates with increasing emission wavelength, also contains a reorganization energy term. The reorganization energy is highly suppressed in J-aggregates due to exciton delocalization, and the framework of the energy gap law could therefore reproduce our experimental observations. J-Aggregates can thus circumvent the common belief that lowering the excited state energies results in large nonradiative relaxation rates and are thus a pathway toward highly emissive organic dyes in the NIR regime.

A simple generalization of the energy gap law for nonradiative processes.

For more than 50 years, an elegant energy gap (EG) law developed by Englman and Jortner [Mol. Phys. 18, 145 (1970)] has served as a key theory to understand and model the nearly exponential dependence of nonradiative transition rates on the difference of energy between the initial and final states. This work revisits the theory, clarifies the key assumptions involved in the rate expression, and provides a generalization for the cases where the effects of temperature dependence and low-frequency modes cannot be ignored. For a specific example where the low-frequency vibrational and/or solvation responses can be modeled as an Ohmic spectral density, a simple generalization of the EG law is provided. Test calculations demonstrate that this generalized EG law brings significant improvement over the original EG law. Both the original and generalized EG laws are also compared with the stationary phase approximations developed for electron transfer theory, which suggests the possibility of a simple interpolation formula valid for any value of EG.

Increasing the Energy Gap between Band‐Edge and Trap States Slows Down Picosecond Carrier Trapping in Highly Luminescent InP/ZnSe/ZnS Quantum Dots

Non-toxic InP-based nanocrystals have been developed for promising candidates for commercial optoelectronic applications and they still require further improvement on photophysical properties, compared to Cd-based quantum dots (QDs), for better device efficiency and long-term stability. It is, therefore, essential to understand the precise mechanism of carrier trapping even in the state-of-the-art InP-based QD with near-unity luminescence. Here, it is shown that using time-resolved spectroscopic measurements of systematically size-controlled InP/ZnSe/ZnS core/shell/shell QDs with the quantum yield close to one, carrier trapping decreases with increasing the energy difference between band-edge and trap states, indicating that the process follows the energy gap law, well known in molecular photochemistry for nonradiative internal conversion between two electronic states. Similar to the molecular view of the energy gap law, it is found that the energy gap between the band-edge and trap states is closely associated with ZnSe phonons that assist carrier trapping into defects in highly luminescent InP/ZnSe/ZnS QDs. These findings represent a striking departure from the generally accepted view of carrier trapping mechanism in QDs in the Marcus normal region, providing a step forward understanding how excitons in nanocrystals interact with traps, and offering valuable guidance for making highly efficient and stable InP-based QDs.

Photophysics and spectroscopy of 1,2-Benzazulene

The electronic spectroscopy and photophysics of 1,2-benzazulene (BzAz) have been examined in solution and in thin solid films, with the objective of comparing its intramolecular and intermolecular excited state decay processes with those of azulene. Unlike azulene, the S2 – S0 absorption and fluorescence spectra exhibit a clear mirror image relationship dominated by a single strong Franck-Condon active progression. Picosecond transient absorption spectra and non-linear S2 fluorescence upconversion experiments reveal lifetimes that follow a well-established energy gap law correlation, indicative of a dominant S2 – S1 decay route. Mechanistic interpretations, including the possibility of S2 singlet fission in aggregates, are discussed.