Spin-orbit Coupling Matrix Elements Research Articles

Theoretical studies of new iridium-based terpolymer donors for high-efficiency triplet-material-based organic photovoltaics: Incorporation of different iridium(III) complexes

Screening potential terpolymer donors for high-performance triplet-material-based organic photovoltaics (T-OPVs) has been a challenge. Herein, four terpolymer donors, with different bis-tridentate iridium(III) complexes incorporated into the backbone of PTB7Ir, were designed and investigated by DFT and TD-DFT methods. The results show that, for designed 1–4 molecules, the bis-tridentate architecture in iridium complexes contributes to the formation of the orbital transitions involving iridium atoms, and promotes the enhancement of spin-orbit coupling (SOC) in heavy metals. Based on the efficient exciton transformation channel from the lowest singlet (S1) state to the third triplet (T3) state, the designed 1–3 have smaller energy differences (ΔES1−T3) and larger SOC matrix elements (⟨S1|HSOC|T3⟩) between S1 and T3, resulting in the faster intersystem crossing (ISC) and triplet exciton formation. Furthermore, 1–3/PC71BM heterojunctions with –ΔGCRT<−0.1 eV (–ΔGCRT refers to the driving force of triplet charge recombination) could exhibit suppressed triplet charge recombination (CRT) processes. The calculation results suggest that designed 1–3 systems can present enhanced inter-facial charge transfer and photovoltaic performance, and become promising candidates for iridium-based terpolymer donors in T-OPVs. This work will provide valuable guidance for the molecular design of T-OPV terpolymer donors.

Low-Temperature Luminescence in Organic Helicenes: Singlet versus Triplet State Circularly Polarized Emission.

The experimental measurement of the photophysical and chiroptical properties of helicene-based π-conjugated emitters with electron-accepting (-CN, -py, -NO2) or donating (TMS, NMe2, NH2) moieties is reported at low temperature (77 K). The samples exhibit strong circularly polarized phosphorescence in frozen solution of 2-MeTHF, with a luminescence dissymmetry factor reaching 1.6 × 10-2 and a lifetime of over 0.46 s for the most active molecule, the nitro compound. The theoretical investigation shows that although the singlet (S1) and triplet (T1) excited-state emissions mainly arise from the helicene core, the rotatory strengths of the spin-allowed versus spin-forbidden emission have opposite signs. Further analysis of the spin-orbit coupling matrix elements shows that there is no strong mixing between S1 and T1, justifying the different signs of the rotatory strengths. In the case of the nitro compound, the enhanced phosphorescence emission is due to an efficient intersystem crossing.

Theoretical Insights into the Optical and Excited State Properties of Donor–Phenyl Bridge–Acceptor Containing Through-Space Charge Transfer Molecules

A comparative new strategy to enhance thermally activated delayed fluorescence (TADF) of through-space charge transfer (CT) molecules in organic light-emitting diodes (OLEDs) is investigated. Generally, TADF molecules adopt a twisted donor and acceptor structure to get a sufficiently small ΔEST and a higher value of the spin-orbit coupling matrix element (SOCME). However, molecules containing donor-phenyl bridge-acceptor (D-p-A) units and featuring π-stacked architectures have intramolecular CT contribution through space and exhibit high TADF efficiency. We have explored the insights into the TADF mechanism in D-p-A molecules using the density functional theory (DFT) and time-dependent DFT methods. The calculated optical absorption and ΔEST values are found to be in good agreement with available experimental data. Interestingly, we found the origin of the SOCME to be the twisted orientation of the donor and bridge moieties. Also, we predicted similar molecules with enhanced OLED efficiency with different substitutions.

Unveiling the intersystem crossing dynamics in N-annulated perylene bisimides.

The efficient population of the triplet excited states in heavy metal-free organic chromophores has been one of the long-standing research problems to molecular photochemists. The negligible spin-orbit coupling matrix elements in the purely organic chromophores and the large singlet-triplet energy gap (ΔES-T) pose a hurdle for ultrafast intersystem crossing (ISC). Herein we report the unprecedented population of triplet manifold in a series of nitrogen-annulated perylene bisimide chromophores (NPBI and Br-NPBI). NPBI is found to have a moderate fluorescence quantum yield (Φf = 68 ± 5%), whereas Br-NPBI showcased a low fluorescence quantum yield (Φf = 2.0 ± 0.6%) in toluene. The femtosecond transient absorption measurements of Br-NPBI revealed ultrafast ISC (kISC = 1.97 × 1010 s-1) from the initially populated singlet excited state to the long-lived triplet excited states. The triplet quantum yields (ΦT = 95.2 ± 4.6% for Br-NPBI, ΦT = 18.7 ± 2.3% for NPBI) calculated from nanosecond transient absorption spectroscopy measurements showed the enhancement in triplet population upon bromine substitution. The quantum chemical calculations revealed the explicit role of nitrogen annulation in tuning the excited state energy levels to favor the ISC. The near degeneracy between the singlet and triplet excited states observed in NPBI and Br-NPBI (ΔES-T = -0.01 eV for NPBI, ΔES-T = 0.03 eV for Br-NPBI) facilitates the spin flipping in the molecules. Nitrogen annulation emerges as a design strategy to open up the ISC pathway and the rate of which can be further enhanced by the substitution of a heavier element.

Ultra-fast triplet-triplet-annihilation-mediated high-lying reverse intersystem crossing triggered by participation of nπ*-featured excited states

The harvesting of ‘hot’ triplet excitons through high-lying reverse intersystem crossing mechanism has emerged as a hot research issue in the field of organic light-emitting diodes. However, if high-lying reverse intersystem crossing materials lack the capability to convert ‘cold’ T1 excitons into singlet ones, the actual maximum exciton utilization efficiency would generally deviate from 100%. Herein, through comparative studies on two naphthalimide-based compounds CzNI and TPANI, we revealed that the ‘cold’ T1 excitons in high-lying reverse intersystem crossing materials can be utilized effectively through the triplet-triplet annihilation-mediated high-lying reverse intersystem crossing process if they possess certain triplet-triplet upconversion capability. Especially, quite effective triplet-triplet annihilation-mediated high-lying reverse intersystem crossing can be triggered by endowing the high-lying reverse intersystem crossing process with a 3ππ*→1nπ* character. By taking advantage of the permanent orthogonal orbital transition effect of 3ππ*→1nπ*, spin–orbit coupling matrix elements of ca. 10 cm−1 can be acquired, and hence ultra-fast mediated high-lying reverse intersystem crossing process with rate constant over 109 s−1 can be realized.

The Interplay between ESIPT and TADF for the 2,2'-Bipyridine-3,3'-diol: A Theoretical Reconsideration.

Organic molecules with excited-state intramolecular proton transfer (ESIPT) and thermally activated delayed fluorescence (TADF) properties have great potential for realizing efficient organic light-emitting diodes (OLEDs). Furthermore, 2,2'-bipyridine-3,3'-diol (BP(OH)2) is a typical molecule with ESIPT and TADF properties. Previously, the double ESIPT state was proved to be a luminescent state, and the T2 state plays a dominant role in TADF for the molecule. Nevertheless, whether BP(OH)2 undergoes a double or single ESIPT process is controversial. Since different ESIPT channels will bring different TADF mechanisms, the previously proposed TADF mechanism based on the double ESIPT structure for BP(OH)2 needs to be reconsidered. Herein, reduced density gradient, potential energy surface, IR spectra and exited-state hydrogen-bond dynamics computations confirm that BP(OH)2 undergoes the barrierless single ESIPT process rather than the double ESIPT process with a barrier. Moreover, based on the single ESIPT structure, we calculated spin-orbit coupling matrix elements, nonradiative rates and electron-hole distributions. These results disclose that the T3 state plays a predominant role in TADF. Our investigation provides a better understanding on the TADF mechanism in hydrogen-bonded molecular systems and the interaction between ESIPT and TADF, which further provides a reference for developing efficient OLEDs.

Dynamics of the Energy Transfer Process in Eu(III) Complexes Containing Polydentate Ligands Based on Pyridine, Quinoline, and Isoquinoline as Chromophoric Antennae.

In this work, we investigated from a theoretical point of view the dynamics of the energy transfer process from the ligand to Eu(III) ion for 12 isomeric species originating from six different complexes differing by nature of the ligand and the total charge. The cationic complexes present the general formula [Eu(L)(H2O)2]+ (where L = bpcd2– = N,N′-bis(2-pyridylmethyl)-trans-1,2-diaminocyclohexane N,N′-diacetate; bQcd2– = N,N′-bis(2-quinolinmethyl)-trans-1,2-diaminocyclohexane N,N′-diacetate; and bisoQcd2– = N,N′-bis(2-isoquinolinmethyl)-trans-1,2-diaminocyclohexane N,N′-diacetate), while the neutral complexes present the Eu(L)(H2O)2 formula (where L = PyC3A3– = N-picolyl-N,N′,N′-trans-1,2-cyclohexylenediaminetriacetate; QC3A3– = N-quinolyl-N,N′,N′-trans-1,2-cyclohexylenediaminetriacetate; and isoQC3A3– = N-isoquinolyl-N,N′,N′-trans-1,2-cyclohexylenediaminetriacetate). Time-dependent density functional theory (TD-DFT) calculations provided the energy of the ligand excited donor states, distances between donor and acceptor orbitals involved in the energy transfer mechanism (RL), spin-orbit coupling matrix elements, and excited-state reorganization energies. The intramolecular energy transfer (IET) rates for both singlet-triplet intersystem crossing and ligand-to-metal (and vice versa) involving a multitude of ligand and Eu(III) levels and the theoretical overall quantum yields (ϕovl) were calculated (the latter for the first time without the introduction of experimental parameters). This was achieved using a blend of DFT, Judd–Ofelt theory, IET theory, and rate equation modeling. Thanks to this study, for each isomeric species, the most efficient IET process feeding the Eu(III) excited state, its related physical mechanism (exchange interaction), and the reasons for a better or worse overall energy transfer efficiency (ηsens) in the different complexes were determined. The spectroscopically measured ϕovl values are in good agreement with the ones obtained theoretically in this work.

A theoretical study on the electronically excited-state spectroscopic properties of phosphorus nitride

ABSTRACT The potential energy curves of 103 Ω states generated from the 39 Λ–S states of PN have been calculated using the internally contracted multireference configuration interaction method with the Davidson modification. Core-valence correlation and scalar relativistic corrections, as well as the basis-set extrapolation to the complete basis set limit are considered. The spin–orbit coupling is computed using the state interaction approach with the Breit-Pauli Hamiltonian. The spectroscopic parameters and molecular constants of bound and quasibound Λ–S and Ω states are evaluated. Our calculated spectroscopic results agree quite well with the available experimental data. The interactions among different electronic states in curve crossing regions have been discussed with the help of computed spin–orbit coupling matrix elements. The perturbations and predissociation phenomena of the A1 , b3 , D1Δ, E1Σ+, and 21 states and so on have been revealed.

Multiple resonance type thermally activated delayed fluorescence by dibenzo [1,4] azaborine derivatives.

We studied the photophysical and electroluminescent (EL) characteristics of a series of azaborine derivatives having a pair of boron and nitrogen aimed at the multi-resonance (MR) effect. The computational study with the STEOM-DLPNO-CCSD method clarified that the combination of a BN ring-fusion and a terminal carbazole enhanced the MR effect and spin-orbit coupling matrix element (SOCME), simultaneously. Also, we clarified that the second triplet excited state (T2) plays an important role in efficient MR-based thermally activated delayed fluorescence (TADF). Furthermore, we obtained a blue–violet OLED with an external EL quantum efficiency (EQE) of 9.1%, implying the presence of a pronounced nonradiative decay path from the lowest triplet excited state (T1).

Towards Efficient Blue Delayed-Fluorescence Molecules by Modulating Torsion Angle Between Electron Donor and Acceptor

Towards Efficient Blue Delayed-Fluorescence Molecules by Modulating Torsion Angle Between Electron Donor and Acceptor

Microscopic origin of magnetism in monolayer 3d transition metal dihalides

Motivated by the recent wealth of exotic magnetic phases emerging in two-dimensional frustrated lattices, we investigate the origin of possible magnetism in the monolayer family of triangular lattice materials $M{X}_{2}$ ($M$=V, Mn, Ni and $X$=Cl, Br, I). We first show that consideration of general properties such as filling and hybridization enables to formulate the trends for the most relevant magnetic interaction parameters. In particular, we observe that the effects of spin-orbit coupling (SOC) can be effectively tuned through the ligand elements as the considered $3d$ transition metal ions do not strongly contribute to the anisotropic component of the intersite exchange interaction. Consequently, we find that the corresponding SOC matrix elements differ significantly from the atomic limit. In the next step and by using two ab initio based complementary approaches, we extract realistic effective spin models and find that in the case of heavy ligand elements, SOC effects manifest in anisotropic exchange and single-ion anisotropy only for specific fillings.

Facile access to high-performance reverse intersystem crossing OLED materials through an unsymmetrical D-A-D’ molecular scaffold

Organic light-emitting diode (OLED) materials based on a reverse intersystem crossing (RISC) triplet harvesting mechanism have attracted tremendous attention. Currently, many research efforts have been devoted to the construction of D-A or D-A-D RISC-OLED materials whose charge-transfer-featured singlet excited states (1CTD-A) are very close to the local triplet excited states of their D or/and A moieties (3LED or/and 3LEA), so that a small singlet–triplet energy splitting and a large spin–orbit coupling matrix element can be acquired concurrently. However, the chief technical difficulty lies in the accurate prediction and delicate tuning of the 1CTD–A energy levels of these compounds. Herein, by using PCz-TXO2 as an example, we demonstrated that high-performance RISC-OLED materials can be readily achieved by integrating an appropriate D’ subunit into a traditional D-A fluorophore that lacks RISC property, i.e., constructing a D–A–D’ triad whose 1CTD-A is close to its 3LED’. In comparison with its D-A or D-A-D counterpart of P-TXO2 or DP-TXO2 showing satisfactory photoluminescence efficiency, pure blue gamut but poor RISC, the presence of a carbazole-based D’ subunit has negligible influence on the transition feature of its lowest singlet excited state (S1), but triggers significantly enhanced RISC property. Consequently, PCz-TXO2 shows pure blue electroluminescence (EL) inherited from DP-TXO2 [CIE1931: (0.160, 0.089) vs. (0.154, 0.102)], but significantly enhanced external quantum efficiency (EQEmax: 9.5% vs. 6.1%) and exciton utilization efficiency (EUEmax: 93% vs. 42%). Our results present a new method to facilely access RISC materials and can greatly extend the design rationales for high-performance OLED materials.

Theoretical study for the TADF nature of through-space conjugated [2.2]paracyclophane derivatives and the design for red-light emission

The thermally activated delayed fluorescence (TADF) nature of a series of [2.2]paracyclophane derivatives with spatially conjugated structures were studied by DFT/TD-DFT method. Through-space charge transfer, rather than the usual through-bond charge transfer exist between the frontier molecular orbitals of these molecules. The singlet-triplet energy gaps which affect the reverse intersystem crossing (RISC) process were compared among the molecules reported in the experimental study to explain why 2 and 4 are more likely to show TADF emission than 1 and 3. Especially, when discussing the intersystem crossing (ISC) process according to the excited states properties and the spin-orbit coupling matrix elements, the influence of the spatially conjugated structure was also analyzed detailedly. Transition dipole moments of the absorption states were greatly enhanced in the conjugated structure and the ISC between some high-energy states was promoted in consequence, indirectly leading to the promotion of the RISC process which generates S1 excitons. In addition, we designed 5–8 by replacing the benzophenone group with the thianthrene-9,9′,10,10′-tetraoxide group, in order to obtain red-light emission through decreasing the LUMO energy level. The calculation results show that the new molecules have larger radiation rate and smaller internal conversion rate, which indicates that the designed molecules are potential efficient red-light TADF materials.

Geometry Dependence of Spin-Orbit Coupling in Complexes of Molecular Oxygen with Atoms, H2, or Organic Molecules.

Studies of the interactions between molecular oxygen and a perturbing species, such as an organic solvent, have been an active research area for at least 70 years. In particular, interaction with a neighboring molecule or atom may perturb the electronic states of oxygen to such an extent that the O2(a1Δg) → O2(X3Σg-) transition, formally forbidden as an electric dipole process, achieves significant transition probability. We present a computational study of how the geometry of complexes consisting of molecular oxygen and different perturbing species influences the magnitude of spin-orbit coupling that facilitates the O2(a1Δg) → O2(X3Σg-) transition. We rationalize our results using a model based on orbital interactions: a non-zero spin-orbit coupling matrix element results from asymmetric transfer of charge to or from the 1πg orbitals on oxygen. Our results indicate that the atoms in a perturbing species closest to oxygen are responsible for the majority of the spin-orbit interactions, suggesting that large systems can be simplified appreciably. Furthermore, we infer and confirm that an estimate of the spin-orbit coupling matrix element can be obtained from the magnitude of the induced energy splitting of oxygen's 1πg orbitals. These results should provide further momentum in the long-standing issue of understanding phenomena that influence the O2(a1Δg) → O2(X3Σg-) transition.

Spin–orbit coupling matrix elements from the explicitly connected expressions of the response functions within the coupled-cluster theory

In this work, we present a coupled cluster-based approach to the computation of the spin–orbit coupling matrix elements. The working expressions are derived from the quadratic response function with the coupled-cluster parametrisation, using the auxiliary excitation operator S. Systematic approximations are proposed with the CCSD and CC3 levels of theory. The new method is tested by computing lifetimes of several electronic states of Ca, Sr and Ba atoms, with Gaussian and Slater basis sets. The results are compared with available theoretical and experimental data.

Characterization of Excited States in a Multiple-Resonance-Type Thermally Activated Delayed Fluorescence Molecule Using Time-Resolved Infrared Spectroscopy

Abstract We investigated the correlation between the photophysical properties and detailed excited-state characteristics of a multiple-resonance-type thermally activated delayed fluorescence (TADF) molecule, DABNA-1, using time-resolved infrared vibrational spectroscopy. By comparing the distinctive vibrational spectra in the fingerprint region (1000–1700 cm−1) to the simulated spectra, we found the optimal calculation conditions for density functional theory calculations to retrieve the vibrational spectra. Based on the calculations, the excited-state geometries and molecular orbitals in the lowest excited singlet (S1) and triplet (T1) states, as well as the ground state (S0), were determined. Consequently, we revealed that the similarity between the potential surfaces of T1 and S0 suppressed non-radiative decay and improved the high fluorescence quantum yield via TADF. Furthermore, we calculated the spin-orbit coupling matrix elements (SOCMEs) considering the experimentally confirmed geometries, and revealed that twisting of the main skeleton increases the SOCMEs.

The involvement of triplet states in the isomerization of retinaloids.

Rhodopsins form a family of photoreceptor proteins which utilize the retinal chromophore for light energy conversion. Upon light absorption the retinal chromophore undergoes a photoisomerization. This reaction involves a non-radiative relaxation through a conical intersection between the singlet excited state and the ground state. In this work we studied the possible involvement of triplet states in the photoisomerization of retinaloids using the extended multistate (XMS) version of CASPT2. To this end, truncated models of three retinaloids were considered: protonated Schiff base, deprotonated Schiff base and the aldehyde form. The optimized geometries of the reactant, the product and the conical intersection were connected by a linear interpolation of internal coordinates to describe the isomerization. The energetic position of the low-lying singlet and triplet states as well as their spin-orbit coupling matrix elements (SOCME) were calculated along the isomerization profile. The SOCME values peaked in vicinity of the conical intersection for all the retinaloids. Furthermore, the magnitude of SOCME is invariant to the number of double bonds in the model. The SOCME for the protonated Schiff base is negligible (1.5 cm-1) which renders the involvement of the triplet state as improbable. However, the largest SOCME value of 30 cm-1 was found for the aldehyde form, followed by 15 cm-1 for the deprotonated Schiff base.

Temperature Dependent Emission Properties of ReI Tricarbonyl Complexes with Dipyrido-Quinoxaline and Phenazine Ligands

In this work, the emission properties of fac-[Re(CO)3(NN)(py)]+, NN = 1,10-phenanthroline (phen), dipyrido[3,2-f:2’,3’-h]quinoxaline (dpq) and dipyrido[3,2-a:2’3’-c]phenazine (dppz); py = pyridine were investigated in different temperatures, ranging from 80 to 300 K, and in different solvent mixtures and in polymethyl methacrylate. The changes observed in the emission quantum yields were rationalized based on a two-level excited state model, in which the nonemissive upper state is thermally populated and decays faster than the lowest lying emissive state. fac‑[Re(CO)3(dpq)(py)]+ is a metal-to-ligand charge transfer (MLCT) emitter as the complex with phen but exhibits smaller emission quantum yields, being more sensitive to the solvent. This behavior was rationalized by quantum-mechanical calculations including the spin-orbit coupling matrix elements, revealing that intersystem crossing from the lowest singlet excited state in fac- [Re(CO)3(dpq)(py)]+ likely occurs to triplet states lying at higher energies. Similar behavior were observed for fac-[Re(CO)3(dppz)(py)]+, although the later exhibits intraligand emission that are strongly quenched in fluid solutions by low-lying MLCT states. The fundamental studies carried out here provide new insights on the excited state dynamics of ReI complexes with dipyridoquinoxaline and phenazine ligands and can contribute for further advances on their application as luminescent probes.

Large Inverted Singlet–Triplet Energy Gaps Are Not Always Favorable for Triplet Harvesting: Vibronic Coupling Drives the (Reverse) Intersystem Crossing in Heptazine Derivatives

Heptazine derivatives are promising dopants for electroluminescent devices. Recent studies raised the question whether heptazines exhibit a small regular or an inverted singlet-triplet (IST) gap. It was argued that the S1 ← T1 reverse intersystem crossing (RISC) is a downhill process in IST emitters and therefore does not require thermal activation, thus enabling efficient harvesting of triplet excitons. Rate constants were not determined in these studies. Modeling the excited-state properties of heptazine proves challenging because fluorescence and intersystem crossing (ISC) are symmetry-forbidden in first order. In this work, we present a comprehensive theoretical study of the photophysics of heptazine and its derivative HAP-3MF. The calculations of electronic excitation energies and vibronic coupling matrix elements have been conducted at the density functional theory/multireference configuration interaction (DFT/MRCI) level of theory. We have employed a finite difference approach to determine nonadiabatic couplings and derivatives of spin-orbit coupling and electric dipole transition matrix elements with respect to normal coordinate displacements. Kinetic constants for fluorescence, phosphorescence, internal conversion (IC), ISC, and RISC have been computed in the framework of a static approach. Radiative S1 ↔ S0 transitions borrow intensity mainly from optically bright E' π → π* states, while S1 ↔ T1 (R)ISC is mediated by E″ states of n → π* character. Test calculations show that IST gaps as large as those reported in the literature are counterproductive and slow down the S1 ← T1 RISC process. Using the adiabatic DFT/MRCI singlet-triplet splitting of -0.02 eV, we find vibronically enhanced ISC and RISC to be fast in the heptazine core compound. Nevertheless, its photo- and electroluminescence quantum yields are predicted to be very low because S1 → S0 IC efficiently quenches the luminescence. In contrast, fluorescence, IC, ISC, and RISC proceed at similar time scales in HAP-3MF.

Extensive spin–orbit multi-reference study on low-lying electronic states of HgI

The multireference configuration interaction (MRCI) method with inclusion of Davidson correction (+Q) and spin-orbit coupling (SOC) effects is adopted to compute the electronic structures of the low-lying states of HgI. The potential energy curves (PECs) of 14 Λ-S states correlated with the first and second dissociation limits together with 30 low-lying Ω states are calculated. The spectroscopic constants of bound states are obtained, which agree well with the available experimental values. With the assistance of calculated SOC matrix elements, the perturbations on the vibrational levels of the C2Π caused by nearby state are analyzed. Finally, the spontaneous radiative lifetimes of bound states are evaluated, which are in consistence with existing measurements.