Coupling Matrix Elements Research Articles

Insights into mechanistic interpretation of crystalline-state reddish phosphorescence of non-planar π-conjugated organoboron compounds.

Metal-free room-temperature phosphorescent (RTP) materials are attracting attention in such applications as organic light-emitting diodes and bioimaging. However, the chemical structures of RTP materials reported thus far are mostly predominantly based on π-conjugated systems incorporating heavy atoms such as bromine atoms or carbonyl groups, resulting in limited structural diversity. On the other hand, triarylboranes are known for their strong Lewis acidity and deep LUMO energy levels, but few studies have reported on their RTP properties. In this study, we discovered that compounds based on a tetracyclic structure containing boron, referred to as benzo[d]dithieno[b,f]borepins, exhibit strong solid-state reddish phosphorescence even in air. Quantum chemical calculations, including those for model compounds, revealed that the loss of planarity of the tetracyclic structure increases spin-orbit coupling matrix elements, thereby accelerating the intersystem crossing process. Moreover, single-crystal X-ray structural analysis and natural energy decomposition analysis suggested that the borepin compounds without bromine or oxygen atoms, unlike typical RTP materials, exhibit red-shifted phosphorescence in the crystalline state owing to structural relaxation in the T1 state. Additionally, the borepin compounds showed potential application as bioimaging dyes.

A multi-resonance emitter with five-membered thiophene as the π-core enables efficient, narrowband and reduced efficiency roll-off OLEDs.

Efficient, narrowband multi-resonance thermally activated delayed fluorescence (MR-TADF) emitters have recently sparked significant interest in high-resolution organic light-emitting diode (OLED) displays. However, almost all the progress in MR-TADF materials has been accomplished using a six-membered ring as the π-core to date. Herein, we present the first example of a five-membered ring π-core-based MR-TADF emitter named Th-BN developed by introducing thiophene instead of hexagonal benzene as the π-core. The introduction of thiophene significantly enhances intramolecular charge transfer intensity and the spin-orbit coupling matrix elements but does not change the intrinsic MR properties. As a result, Th-BN exhibits a narrowband green emission at 512 nm, with a high luminous efficiency of 97%, a narrow full-width at half maximum of 41 nm/0.20 eV, and a rapid reverse intersystem crossing rate of 18.7 × 104 s-1, which is 10 times higher than that of its benzenoid counterpart DtBuCzB. The corresponding green OLEDs based on Th-BN achieve excellent electroluminescence performance with an external quantum efficiency (EQE) of 34.6% and a reduced efficiency roll-off with an EQE of 26.8% at a high luminance of 1000 cd m-2.

Achieving pure room temperature phosphorescence (RTP) in phenoselenazine-based organic emitters through synergism among heavy atom effect, enhanced n → π* transitions and magnified electron coupling by the A-D-A molecular configuration.

The weak spin-orbit coupling (SOC) in metal-free organic molecules poses a challenge in achieving phosphorescence emission. To attain pure phosphorescence in RTP organic emitters, a promising molecular design concept has been proposed. This involves incorporating n → π* transitions and leveraging the heavy atomic effect within the spin-orbit charge transfer-induced intersystem crossing (SOCT-ISC) mechanism of bipolar molecules. Following this design concept, two bipolar metal-free organic molecules (PhSeB and PhSeDB) with donor-acceptor (D-A) and acceptor-donor-acceptor (A-D-A) configurations have been synthesized. When the molecular configuration changes from D-A to A-D-A, PhSeDB exhibits stronger electron coupling and n → π* transitions, which can further enhance the spin-orbit coupling (SOC) together with the heave atom effect from the selenium atom. By the advanced synergism among enhanced n → π* transitions, heavy atom effect and magnified electron coupling to efficiently promote phosphorescence emission, PhSeDB can achieve pure RTP emission in both the solution and doped solid film. Thanks to the higher spin-orbit coupling matrix elements (SOCMEs) for T1 ↔ S0, PhSeDB attains the highest phosphorescence quantum yield (ca. 0.78) among all the RTP organic emitters reported. Consequently, the purely organic phosphorescent light-emitting diodes (POPLEDs) based on PhSeDB achieve the highest external quantum efficiencies of 18.2% and luminance of 3000 cd m-2. These encouraging results underscore the significant potential of this innovative molecular design concept for highly efficient POPLEDs.

Doping-mediated excited state dynamics of diphosphine-protected M@Au12 (M = Au, Ir) superatom nanoclusters.

Doping heterometal atoms into ligand-protected gold superatom nanoclusters (Aun NCs) is proposed to further diversify their geometrical and electronic structures and enhance their photoluminescence properties, which is attributed to the mixing and effects between atoms. However, the fundamental principles that govern the optoelectronic properties of the doped Aun NCs remain elusive. Herein, we systematically explored two prototypical 8-electron Aun (n = 11 and 13) NCs with and without Ir dopant atoms using comprehensive ab initio calculations and real-time nonadiabatic molecular dynamics simulations. These doped Aun NCs maintain their parent geometrical structures and 8-electron superatomic configuration (1S21P6). Strong core-shell (Ir-Aun) electronic coupling significantly expands the energy gap, resulting in a weak nonadiabatic coupling matrix element, which in turn increases the carrier lifetime. This increase is mainly governed by the low-frequency vibration mode. We uncovered the relationship between electronic structures, electron-vibration, and carrier dynamics for these doped Aun NCs. These calculated results provide crucial insights for the atomically precise design of metal NCs with superior optoelectronic properties.

Anthracene derivatives with strong spin-orbit coupling and efficient high-lying reverse intersystem crossing beyond the El-Sayed rule.

The attention to materials with hot exciton channel and triplet-triplet fusion (TTF) mediated high-lying reverse intersystem crossing (hRISC) has been raised for their ability to convert non-emissive 'dark' triplets into radiative singlet excitons. This spin conversion process results in high exciton utilization efficiency (EUE) that exceeds the theoretical limits. Notably, it is known that such spin conversion processes from the high-lying excited triplet to the singlet state are facilitated by the orthogonal orbital transition effect governed by the El-Sayed's rule. In this study, an anthracene derivative with indenoquinoline substituent 7,7-dimethyl-9-(10-(4-(naphthalen-1-yl)phenyl)anthracen-9-yl)-7H-indeno[1,2-f]quinoline (2MIQ-NPA) was synthesized and analyzed to investigate whether the hRISC process occurs in these molecules, even when the El-Sayed's rule is not followed. The hRISC channels of the emitter were fully unraveled through DFT calculations and experiments, which were quantitatively subdivided using transient electroluminescence measurements. The results showed that 2MIQ-NPA, which does not follow the El-Sayed's rule and has a relatively strong spin-orbit coupling matrix element of 0.116 cm-1 between the high-lying triplet state of T4 and the lowest singlet state of S1, effectively converted triplet excitons into singlet excitons with an EUE of 64.3%, contributed by a direct hot exciton channel of 19.2% and a TTF-mediated hot exciton channel of 15.1%. Despite the low outcoupling efficiency, the non-doped device with 2MIQ-NPA achieved an excellent device performance with an external quantum efficiency of 7.0%.

The effect of heavy atoms on the deactivation of electronic excited states of dye molecules near the surface of metal nanoparticles.

The influence of a heavy atom and the plasmon field on the efficiency of populating the lowest triplet state (T1) and on the phosphorescence intensity has been studied for fluorescein, 2Br-fluorescein, eosin and erythrosine, which have an increasing number of substituted heavy atoms. We show that the heavy atoms affect not only the rate constant of intersystem crossing (kISC) but also the rate constant of internal conversion (kIC). The calculations show that the C-H bonds in the meso position are the primary acceptors of the excitation energy of the lowest excited electronic singlet state (S1). Substitution of the meso hydrogen atoms with I or Br leads to a smaller kIC rate constant of 1 × 108 s-1 for fluorescein to 8 × 106 s-1 for eosin. Substitution with heavy atoms also leads to a larger ISC rate constant (kISC) between the T2 and S1 states because the spin-orbit coupling matrix element 〈S1|HSO|T2〉 increases by two orders of magnitude from 0.36 cm-1 for fluorescein to 35.0 cm-1 for erythrosine. The phosphorescence rate constant increases by three orders of magnitude from 4.8 × 10 s-1 for fluorescein to 3.3 × 104 s-1 for erythrosine, which is supported by experimental data. The plasmon effect increases the intensity of the xanthene dye emissions. The intensity and the quantum yield of fluorescence increase in the series fluorescein < 2Br-fluorescein < eosin < erythrosine. The intensity of the delayed fluorescence and phosphorescence grows in the same way. The enhancement factor of the phosphorescence intensity increases from 1.8 to 5.6 in the series from fluorescein to erythrosine. The differences in the plasmon effect originate from intensity borrowing to the radiative triplet-singlet transition (T1 → S0) from the singlet-singlet transitions (Sn → S0), which is more efficient when molecules have heavy atoms in the meso position.

Regulation of photoinduced charge transfer in all-small-molecule organic solar cells through the synergistic effect of external electric field and solvent

The donor (BTR-Cl) and acceptor (BTP-FCl-FCl) have well-defined small molecule properties and excellent repeatability, and they can form charge transfer complexes with a wide spectral absorption range. Using density functional theory (DFT), we simulate the photoinduced charge transfer of bulk-heterojunction (BHJ) organic solar cell (OSC) materials modulated by the external electric field (Fext) at the microscopic level. The excited-state properties, reorganization energy (λ), Gibbs free energy (ΔG), electron coupling matrix elements (VDA) and intermolecular charge transfer (ICT) rate dependent on Fext are systematically analyzed. The results manifest that Fext has apparent positive regulation on the charge separation rate (KCS), and VDA is the main factor affecting KCS. The synergistic effect of solvent and Fext on charge transfer process is further investigated. It is found that the charge transfer rate in solvent is lower than that in solvent-free conditions, and the charge transfer rate in chlorobenzene (CB) solvent does not change significantly under the control of Fext. At the same time, Fext has a positive effect on the charge transfer rate in tetrahydrofuran (THF) solvent. Considering the charge transfer rate under different solvents and Fext intensities, it is found that the solvent and Fext play an essential role in determining the KCS and charge recombination rate (KCR).

Spreading Widths of Giant Monopole Resonance in the Lead Region: Random Matrix Approach

The microscopic calculation of the decay width of giant monopole resonance (GMR) anticipates the mixing of one-phonon states with configurations of increasing complexity. To this aim we develop the effective approach for description of monopole excited states that are obtained in the quasiparticle random phase approximation (QRPA), with regard of the coupling between one- and two-phonon states. Based on the QRPA one-phonon states, we generate the coupling and two-phonon states by means of the Gaussian orthogonal ensemble (GOE) distribution. Within our approach the spreading width of the GMRs in 204,206,208Pb are described by means of a random matrix approach on two energy scales. It is demonstrated that the main contribution into the decay of the GMR is determined by a small number of two-phonon states strongly coupled to low-energy surface vibrations. While a vast majority of the coupling matrix elements (that are small in value and following the GOE distribution) are responsible for the fine structure of the GMR spreading width. A remarkable agreement between the results of the full microscopic calculations (based on QRPA phonons coupled by means of the microscopic coupling matrix elements with calculated two-phonon states) with those of the developed approach confirms the vitality of the proposed ideas.

Theoretical investigation of electron capture processes in slow O7+–H collisions

Aims. The total and n-, l-, and S -resolved single-electron-capture cross sections for the collisions of O7+ with atomic hydrogen are studied in the energy region from 10−3eV u−1−5keV u−1. Methods. These state-selective cross sections were calculated by employing the full quantum-mechanical molecular-orbital close-coupling (QMOCC) method. The ab initio multireference single- and double-excitation configuration interaction approach, with optimized atomic basis sets to accurately describe the highly excited states, was used to obtain the adiabatic potentials and the radial and rotational coupling matrix elements that are required in the QMOCC calculation. Results. Our results are compared with other available theoretical and experimental data. The n = 5 manifold is the dominant reaction channel for the chasrge-transfer process for this collision system over the entire energy range, and our results agree better with the experimental data than the other theoretical results in the energy region in which they overlap because we included the necessary highly excited states in the expansion basis set. These charge-exchange cross-section data are useful for understanding and modeling the X-ray emission in astrophysical environments.

A chiral spirofluorene‐embedded multiple‐resonance thermally activated delayed fluorescence emitter for efficient pure‐green circularly polarized electroluminescence

AbstractThe simultaneous achievement of chiral multiple‐resonance thermally activated delayed fluorescence (MR‐TADF) emitters with narrowband and circularly polarized electroluminescence (CPEL) poses a challenge. Herein, a MR‐TADF emitter, Spiro‐BNCz, embedding spirofluorene structure was developed and chiral separated, whose emission peaks at 528 nm in toluene with Commission Internationale de L'Eclairage coordinates of (0.26, 0.69). The conjugation extension caused by embedding sulfur substituted spirofluorene on B/N framework shortens the singlet‐triplet energy gap and increases spin‐orbital coupling matrix element. Therefore, a fast reverse intersystem crossing rate constant of 2.8 × 106 s−1 and a high photoluminescence efficiency of 92% in film were achieved. The organic light‐emitting diode (OLED) exhibits a maximum external quantum efficiency of 32.3%. Particularly, the circularly polarized OLEDs based on Spiro‐BNCz enantiomers show symmetric CPEL with dissymmetry factors (|gEL|) ≈ 10−3.

Machine Learning Representations of the Three Lowest Adiabatic Electronic Potential Energy Surfaces for the ArH2+ Reactive System.

In this work, we present Gaussian process regression machine learning representations of the three lowest coupled 2A' adiabatic electronic potential energy surfaces of the ArH2+ reactive system in full dimensionality. Additionally, the nonadiabatic coupling matrix elements were calculated. These adiabatic potentials and their nonadiabatic couplings are necessary ingredients in the theoretical investigation of the nonadiabatic reaction dynamics of the Ar + H2+ → ArH+ + H and Ar+ + H2 → ArH+ + H reactions, as well as the competing charge transfer process, Ar + H2+↔ Ar+ + H2. Accurate ab initio electronic structure calculations (ic-MRCI+Q/aug-cc-pVQZ), whereby the effect of spin-orbit coupling in Ar+ has been accounted for through the state interaction method, serve as input for the machine learning training process. The potential energy surfaces are fitted with high accuracies, with root-mean-square errors on the order of 10-7 eV for the three surfaces, which meet the requirements for chemical dynamics at low temperature. It was found that quite a large number of training points (of the order of 5000 ab initio points) are needed in order to achieve these accuracies due to the complex topography of these electronic surfaces.

Electron–phonon physics from first principles using the EPW code

EPW is an open-source software for ab initio calculations of electron–phonon interactions and related materials properties. The code combines density functional perturbation theory and maximally localized Wannier functions to efficiently compute electron–phonon coupling matrix elements, and to perform predictive calculations of temperature-dependent properties and phonon-assisted quantum processes in bulk solids and low-dimensional materials. Here, we report on significant developments in the code since 2016, namely: a transport module for the calculation of charge carrier mobility under electric and magnetic fields using the Boltzmann transport equation; a superconductivity module for calculations of phonon-mediated superconductors using the anisotropic multi-band Eliashberg theory; an optics module for calculations of phonon-assisted indirect transitions; a module for the calculation of small and large polarons without supercells; and a module for calculating band structure renormalization and temperature-dependent optical spectra using the special displacement method. For each capability, we outline the methodology and implementation and provide example calculations.

High‐Performance Multi‐Resonance Thermally Activated Delayed Fluorescence Emitters for Narrowband Organic Light‐Emitting Diodes

AbstractMulti‐resonance thermally activated delayed fluorescence (MR‐TADF) emitters have drawn considerable attention because of their remarkable optoelectronic properties of high emission efficiency and narrow emission profile, and represent an active subject of cutting‐edge research in the organic electroluminescence (EL). However, the slow reverse intersystem crossing (RISC) rate of MR‐TADF emitter caused by the large energy gap (ΔEST) and small spin‐orbit coupling (SOC) matrix elements between the singlet and triplet excited states limits their further development in organic EL devices. Currently, innovative molecular design strategies have been developed including heavy atom integration, π‐extended MR framework and metal perturbation, and so on to improve the RISC process of MR‐TADF emitters for high‐performance EL devices. Here, an overview is presented on the recent progress of MR‐TADF emitters with fast RISC rate ( &gt; 10−5 s−1), with particular attention to the molecular design, optoelectronic properties, and device performance of organic light‐emitting diodes (OLEDs), which intends to systematize the knowledge in this subject for the thriving development of highly efficient MR‐TADF emitters. Finally, the challenges and future prospects of MR‐TADF materials are discussed comprehensively.

Impact of Molecular Orientation on Lateral and Interfacial Electron Transfer at Oxide Interfaces.

Molecular dyes, called sensitizers, with a cis-[Ru(LL)(dcb)(NCS)2] structure, where dcb is 4,4'-(CO2H)2-2,2'-bipyridine and LL is dcb or a different diimine ligand, are among the most optimal for application in dye-sensitized solar cells (DSSCs). Herein, a series of five sensitizers, three bearing two dcb ligands and two bearing one dcb ligand, were anchored to mesoporous thin films of conducting tin-doped indium oxide (ITO) or semiconducting TiO2 nanocrystallites. The number of dcb ligands impacts the surface orientation of the sensitizer; density functional theory (DFT) calculations revealed an ∼1.6 Å smaller distance between the oxide surface and the Ru metal center for sensitizers with two dcb ligands. Interfacial electron transfer kinetics from the oxide material to the oxidized sensitizer were measured as a function of the thermodynamic driving force. Analysis of the kinetic data with Marcus-Gerischer theory indicated that the electron coupling matrix element, Hab, was sensitive to distance and ranged from Hab = 0.23 to 0.70 cm-1, indicative of nonadiabatic electron transfer. The reorganization energies, λ, were also sensitive to the sensitizer location within the electric double layer and were smaller, with one exception, for sensitizers bearing two dcb ligands λ = 0.40-0.55 eV relative to those with one λ = 0.63-0.66 eV, in agreement with dielectric continuum theory. Electron transfer from the oxide to the photoexcited sensitizer was observed when the diimine ligand was more easily reduced than the dcb ligand. Lateral self-exchange "hole hopping" electron transfer between surface-anchored sensitizers was found to be absent for sensitizers with two dcb ligands, while those with only one were found to hop with rates similar to those previously reported in the literature, khh = 47-89 μs-1. Collectively, the kinetic data and analysis reveal that interfacial kinetics are highly sensitive to the surface orientation and sensitizers bearing two dcb ligands are most optimal for practical applications of DSSCs.

He+ +N2 Charge Transfer Reaction: An Ab initio Analysis.

An ab initio analysis on the involved potential energy surfaces is presented for the investigation of the charge transfer mechanism for the He+ +N2 system. At high collision energy, as many as seven low-lying electronic states are observed to be involved in the charge transfer mechanism. Potential energy surfaces for these low-lying electronic states have been computed in the Jacobi scattering coordinates, applying multireference configuration interaction level of theory and aug-cc-pVQZ basis sets. Asymptotes for the ground and various excited states are assigned to mark the entrance (He+ +N2 ) and charge transfer channels (He+N2 + ). Nonadiabatic coupling matrix elements and quasi-diabatic potential energy surfaces have been computed for all seven states to rationalize the available experimental data on the charge transfer processes and to facilitate dynamics studies.

Intensity-Borrowing Mechanisms Pertinent to Laser Cooling of Linear Polyatomic Molecules.

A study of the intensity-borrowing mechanisms important to optical cycling transitions in laser-coolable polyatomic molecules arising from non-adiabatic coupling, contributions beyond the Franck-Condon approximation, and Fermi resonances is reported. It has been shown to be necessary to include non-adiabatic coupling to obtain computational accuracy that is sufficient to be useful for laser cooling of molecules. The predicted vibronic branching ratios using perturbation theory based on the non-adiabatic mechanisms have been demonstrated to agree well with those obtained from variational discrete variable representation calculations for representative molecules including CaOH, SrOH, and YbOH. The electron-correlation and basis-set effects on the calculated transition properties, including the vibronic coupling constants, the spin-orbit coupling matrix elements, and the transition dipole moments, and on the calculated branching ratios have been thoroughly studied. The vibronic branching ratios predicted using the present methodologies demonstrate that RaOH is a promising radioactive molecule candidate for laser cooling.

Ultrafast Electronic Coupling Estimators: Neural Networks versus Physics-Based Approaches.

Fast and accurate estimation of electronic coupling matrix elements between molecules is essential for the simulation of charge transfer phenomena in chemistry, materials science, and biology. Here we investigate neural-network-based coupling estimators combined with different protocols for sampling reference data (random, farthest point, and query by committee) and compare their performance to the physics-based analytic overlap method (AOM), introduced previously. We find that neural network approaches can give smaller errors than AOM, in particular smaller maximum errors, while they require an order of magnitude more reference data than AOM, typically one hundred to several hundred training points, down from several thousand required in previous ML works. A Δ-ML approach taking AOM as a baseline is found to give the best overall performance at a relatively small computational overhead of about a factor of 2. Highly flexible π-conjugated organic molecules like non-fullerene acceptors are found to be a particularly challenging case for ML because of the varying (de)localization of the frontier orbitals for different intramolecular geometries sampled along molecular dynamics trajectories. Here the local symmetry functions used in ML are insufficient, and long-range descriptors are expected to give improved performance.

Elastic and electron capture processes in slow He+–He collision

Aims. The elastic and electron-capture processes of He+ ions with ground helium atoms are very important for studies in astrophysics. It is essential to have reliable state-selective charge transfer, elastic, and transport cross-sections, along with the corresponding reaction rate coefficient data, especially for low collision energies. Methods. We investigated the elastic and non-radiative electron-capture processes in He+(1s)–He(1s2) collisions are investigated employing the full quantum-mechanical molecular orbital close-coupling method. The adopted ab initio adiabatic potentials and coupling matrix elements were obtained by a multi-reference single- and double-excitation configuration interaction approach. Results. We computed the elastic, charge-transfer, and transport cross-sections in the energy range of 0.01–2500eVamu−1 and the reaction rate coefficient in the temperature range of 10–109 K. Good agreement was achieved when compared to the available experimental and theoretical results. Shape resonance, Regge, and Glory oscillations were also found in the elastic and charge transfer cross-sections in the energy region considered here.

Non-adiabatic interactions in H[formula omitted] + C[formula omitted] system: An ab initio study

Diabatic surfaces generated for the ground state 11Σ+(11A′) as well as for the first excited electronic state 21Σ+(21A′) have been quantified for the C3 collision with H+ system employing the MRCI/aug-cc-pVQZ method. These collisions are significant in understanding the mechanism of energy transfer in astrophysics and molecular physics. For studying the dynamics of the interaction between the charge transfer and inelastic processes, properties such as non-adiabatic coupling matrix elements, and mixing angle have been determined. The computed surface and their properties will be useful in studying charge partitioning between the inelastic and charge transfer channels by wave packet quantum dynamics.

Probability of charge transport through al/GaAs interfaces system using quantum model

The focus of this paper is on the investigation and the understanding of transition probability of charge at the metal/semiconductor interface depending on the calculation of the rate constant. For this system we can suppose two localized quantum vector states system with a conduction electron state vector l 〉 interacting with an acceptor state vector l 〉 of electron in band of metal with the interacting described by the coupling matrix element. Expression of rate constant of charge transfer for metal/semiconductor system derived upon the quantum model and perturbation theory for transition between l 〉 and I state when the coupling matrix element coefficient smaller than . The probability of the charge transfer rate constant for the metal/semiconductor interface in this context, is basically defined as a relatively to potential barrier between a metal and a semiconductor The probability of charge transfer rate constant evaluated with reorganization energy using a matlap program. Theoretical results obtained for our mode show that the probability of charge transfer is more probable with decreasing the reorganization energy.