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At least 37 records · Page 2

Charge transfer states impact the triplet pair dynamics of singlet fission polymers

Polymers are desirable optoelectronic materials, stemming from their solution processability, tunable electronic properties, and large absorption coefficients. An exciting development is the recent discovery that singlet fission (SF), the conversion of a singlet exciton to a pair of triplet states, can occur along the backbone of an individual conjugated polymer chain. Here, compared to other intramolecular SF compounds, the nature of the triplet pair state in SF polymers remains poorly understood, hampering the development of new materials with optimized excited state dynamics.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

Elucidation of complex triplet excited state dynamics in Pd(ii) biladiene tetrapyrroles

Pd(II) biladienes have been developed over the last five years as non-aromatic oligotetrapyrrole complexes that support a rich triplet photochemistry. In this work, we have undertaken the first detailed photophysical interrogation of three homologous Pd(II) biladienes bearing different combinations of methyl- and phenyl-substituents on the frameworks’ sp 3 -hybridized meso-carbon (i.e., the 10-position of the biladiene framework). These experiments have revealed unexpected excited-state dynamics that are dependent on the wavelength of light used to excite the biladiene. More specifically, transient absorption spectroscopy revealed that higher-energy excitation (λ exc ~ 350–500 nm) led to an additional lifetime (i.e., an extra photophysical process) compared to experiments carried out following excitation into the lowest-energy excited states (λ exc = 550 nm). Each Pd(II) biladiene complex displayed an intersystem crossing lifetime on the order of tens of ps and a triplet lifetime of ~20 μs, regardless of the excitation wavelength. However, when higher-energy light is used to excite the complexes, a new lifetime on the order of hundreds of ps is observed. The origin of the ‘extra’ lifetime observed upon higher energy excitation was revealed using density functional theory (DFT) and time-dependent DFT (TDDFT). These efforts demonstrated that excitation into higher-energy metal-mixed-charge-transfer excited states with high spin–orbit coupling to higher energy metal-mixed-charge-transfer triplet states leads to the additional excitation deactivation pathway. Furthermore, the results of this work demonstrate that Pd(II) biladienes support a unique triplet photochemistry that may be exploited for development of new photochemical schemes and applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Electron Affinity and Electronic Structure of Hexafluoroacetone (HFA) Revealed by Photodetaching the [HFA] •– Radical Anion

A great deal of effort has been focused on developing a metal-free catalytic system for epoxidation of unreactive alkenes. Fluoroketones are thought as remarkably promising catalysts for epoxidation reactions. The combination of fluorinated alcohols and catalytic amounts of hexafluoroacetone (HFA) gives a versatile and effective medium for epoxidation of various olefins with hydrogen peroxide. However, the fundamental physicochemical properties of HFA remained largely unclear, although they were very important to understand the related interactions. Here, in this study, we performed a joint study on the electron affinity and electronic structure of HFA employing negative ion photoelectron (NIPE) spectroscopy and quantum chemistry calculations. Two distinct bands with complicated vibrational progressions were observed in the 193 nm NIPE spectrum. The adiabatic/vertical detachment energies (ADE/VDE) were derived to be 1.42/2.06 and 4.43/4.86 eV for the ground singlet state and excited triplet state, respectively. Using the optimized geometries and vibrational frequencies of the anion and the neutral, the Franck–Condon factors were calculated for electron detachments to produce HFA in its lowest singlet and triplet states. Good agreements are obtained hereby for both bands between the experimental and calculated NIPE spectra, when taking into account combination vibrational excitations, unequivocally revealing that HFA possesses a singlet ground state with a giant singlet–triplet energy difference (ΔE ST ). The electron affinity (EA) and ΔE ST of HFA were therefore determined to be EA = 1.42 ± 0.02 eV and ΔE ST = −3.01 eV.

Wang, Lei↗

Development of (NO)Fe(N 2 S 2 ) as a Metallodithiolate Spin Probe Ligand: A Case Study Approach

The ubiquity of sulfur–metal connections in nature inspires the design of bi- and multimetallic systems in synthetic inorganic chemistry. Common motifs for biocatalysts developed in evolutionary biology include the placement of metals in close proximity with flexible sulfur bridges as well as the presence of π-acidic/delocalizing ligands. This Account will delve into the development of a (NO)Fe(N 2 S 2 ) metallodithiolate ligand that harnesses these principles. The Fe(NO) unit is the centroid of a N 2 S 2 donor field, which as a whole is capable of serving as a redox-active, bidentate S-donor ligand. Its paramagnetism as well as the ν(NO) vibrational monitor can be exploited in the development of new classes of heterobimetallic complexes. We offer four examples in which the unpaired electron on the {Fe(NO)} 7 unit is spin-paired with adjacent paramagnets in proximal and distal positions. First, the exceptional stability of the (NO)Fe(N 2 S 2 )-Fe(NO) 2 platform, which permits its isolation and structural characterization at three distinct redox levels, is linked to the charge delocalization occurring on both the Fe(NO) and the Fe(NO) 2 supports. This accommodates the formation of a rare nonheme {Fe(NO)} 8 triplet state, with a linear configuration. A subsequent FeNi complex, featuring redox-active ligands on both metals (NO on iron and dithiolene on nickel), displayed unexpected physical properties. Our research showed good reversibility in two redox processes, allowing isolation in reduced and oxidized forms. Various spectroscopic and crystallographic analyses confirmed these states, and Mössbauer data supported the redox change at the iron site upon reduction. Oxidation of the complex produced a dimeric dication, revealing an intriguing magnetic behavior. The monomer appears as a spin-coupled diradical between {Fe(NO)} 7 and the nickel dithiolene monoradical, while dimerization couples the latter radical units via a Ni 2 S 2 rhomb. Magnetic data (SQUID) on the dimer dication found a singlet ground state with a thermally accessible triplet state that is responsible for magnetism. A theoretical model built on an H 4 chain explains this unexpected ferromagnetic low-energy triplet state arising from the antiferromagnetic coupling of a four-radical molecular conglomerate. For comparison, two (NO)Fe(N 2 S 2 ) were connected through diamagnetic group 10 cations producing diradical trimetallic complexes. Antiferromagnetic coupling is observed between {Fe(NO)} 7 units, with exchange coupling constants (J) of -3, -23, and -124 cm –1 for Ni II , Pd II , and Pt II , respectively. This trend is explained by the enhanced covalency and polarizability of sulfur-dense metallodithiolate ligands. A central paramagnetic trans-Cr(NO)(MeCN) receiver unit core results in a cissoid structural topology, influenced by the stereoactivity of the lone pair(s) on the sulfur donors. This {Cr(NO)} 5 radical bridge, unlike all previous cases, finds the coupling between the distal Fe(NO) radicals to be ferromagnetic (J = 24 cm –1 ). The stability and predictability of this S = 1/2 moiety and the steric/electronic properties of the bridging thiolate sulfurs suggest it to be a likely candidate for the development of novel molecular (magnetic) compounds and possibly materials. The role of synthetic inorganic chemistry in designing synthons that permit connections of the (NO)Fe(N 2 S 2 ) metalloligand is highlighted as well as the properties of the heterobi- and polymetallic complexes derived therefrom.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Long-Lived Triplet Excited State in a Heterogeneous Modified Carbon Nitride Photocatalyst

Heterogeneous carbon nitrides have numerous advantages as photocatalysts, including strong light absorption, tunable band edges, and scalability, but their performance and continued development are limited by fast charge recombination and an under-developed mechanistic understanding of photodriven interfacial electron transfer. These shortcomings are a result of complex photophysics, leading to rate asynchrony between oxidation and reduction, as well as redox processes driven out of electronic trap states rather than excited states. We show that a well-defined triplet excited state in cyanamide-modified carbon nitride is realized with appropriately sized particles. The utility of this long-lived excited state is demonstrated by its ability to drive a hydroamidation photoredox cycle. By the tuning of the particle size of CN x , the oxidation–reduction photochemistry of carbon nitride may be balanced to achieve a redox-neutral closed photocatalytic cycle. Here, these results uncover a triplet excited state chemistry for appropriately sized CNx particles that preludes a rich energy and electron transfer photochemistry for these materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Visible-Light-Driven, Iridium-Catalyzed Hydrogen Atom Transfer: Mechanistic Studies, Identification of Intermediates, and Catalyst Improvements

The harvesting of visible light is a powerful strategy for the synthesis of weak chemical bonds involving hydrogen that are below the thermodynamic threshold for spontaneous H 2 evolution. Piano-stool iridium hydride complexes are effective for the bluelight- driven hydrogenation of organic substrates and contrathermodynamic dearomative isomerization. In this work, a combination of spectroscopic measurements, isotopic labeling, structure–reactivity relationships, and computational studies has been used to explore the mechanism of these stoichiometric and catalytic reactions. Photophysical measurements on the iridium hydride catalysts demonstrated the generation of long-lived excited states with principally metal-to-ligand charge transfer (MLCT) character. Transient absorption spectroscopic studies with a representative substrate, anthracene revealed a diffusion-controlled dynamic quenching of the MLCT state. The triplet state of anthracene was detected immediately after the quenching events, suggesting that triplet–triplet energy transfer initiated the photocatalytic process. The key role of triplet anthracene on the post-energy transfer step was further demonstrated by employing photocatalytic hydrogenation with a triplet photosensitizer and a HAT agent, hydroquinone. DFT calculations support a concerted hydrogen atom transfer mechanism in lieu of stepwise electron/proton or proton/electron transfer pathways. Kinetic monitoring of the deactivation channel established an inverse kinetic isotope effect, supporting reversible C(sp 2 )–H reductive coupling followed by rate-limiting ligand dissociation. Mechanistic insights enabled design of a piano-stool iridium hydride catalyst with a rationally modified supporting ligand that exhibited improved photostability under blue light irradiation. The complex also provided improved catalytic performance toward photoinduced hydrogenation with H 2 and contra-thermodynamic isomerization.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Conversion between triplet pair states is controlled by molecular coupling in pentadithiophene thin films

In singlet fission (SF) the initially formed correlated triplet pair state, 1 (TT), may evolve toward independent triplet excitons or higher spin states of the (TT) species. The latter result is often considered undesirable from a light harvesting perspective but may be attractive for quantum information sciences (QIS) applications, as the final exciton pair can be spin-entangled and magnetically active with relatively long room temperature decoherence times. In this study we use ultrafast transient absorption (TA) and time-resolved electron paramagnetic resonance (TR-EPR) spectroscopy to monitor SF and triplet pair evolution in a series of alkyl silyl-functionalized pentadithiophene (PDT) thin films designed with systematically varying pairwise and long-range molecular interactions between PDT chromophores. The lifetime of the (TT) species varies from 40 ns to 1.5 μs, the latter of which is associated with extremely weak intermolecular coupling, sharp optical spectroscopic features, and complex TR-EPR spectra that are composed of a mixture of triplet and quintet-like features. On the other hand, more tightly coupled films produce broader transient optical spectra but simpler TR-EPR spectra consistent with significant population in 5 (TT) 0 . These distinctions are rationalized through the role of exciton diffusion and predictions of TT state mixing with low exchange coupling J versus pure spin substate population with larger J. The connection between population evolution using electronic and spin spectroscopies enables assignments that provide a more detailed picture of triplet pair evolution than previously presented and provides critical guidance for designing molecular QIS systems based on light-induced spin coherence.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Transient resonant Auger–Meitner spectra of photoexcited thymine

In this paper, we present the first investigation of excited state dynamics by resonant Auger–Meitner spectroscopy (also known as resonant Auger spectroscopy) using the nucleobase thymine as an example. Thymine is photoexcited in the UV and probed with X-ray photon energies at and below the oxygen K-edge. After initial photoexcitation to a ππ* excited state, thymine is known to undergo internal conversion to an nπ* excited state with a strong resonance at the oxygen K-edge, red-shifted from the ground state π* resonances of thymine. We resolve and compare the Auger–Meitner electron spectra associated both with the excited state and ground state resonances, and distinguish participator and spectator decay contributions. Furthermore, we observe simultaneously with the decay of the nπ* state signatures the appearance of additional resonant Auger–Meitner contributions at photon energies between the nπ* state and the ground state resonances. We assign these contributions to population transfer from the nπ* state to a ππ* triplet state via intersystem crossing on the picosecond timescale based on simulations of the X-ray absorption spectra in the vibrationally hot triplet state. Moreover, we identify signatures from the initially excited ππ* singlet state which we have not observed in our previous study.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Spin dynamics of [1,2- 13 C 2 ]pyruvate hyperpolarization by parahydrogen in reversible exchange at micro Tesla fields

Hyperpolarization of 13 C-pyruvate via Signal Amplification By Reversible Exchange (SABRE) is an important recent discovery because of both the relative simplicity of hyperpolarization and the central biological relevance of pyruvate as a biomolecular probe for in vitro or in vivo studies. Here, we analyze the [1,2- 13 C 2 ]pyruvate-SABRE spin system and its field dependence theoretically and experimentally. We provide first-principles analysis of the governing 4-spin dihydride- 13 C 2 Hamiltonian and numerical spin dynamics simulations of the 7-spin dihydride- 13 C 2 –CH 3 system. Furthermore, the analytical and the numerical results are compared to matching systematic experiments. With these methods we unravel the observed spin state mixing of singlet states and triplet states at microTesla fields and we also analyze the dynamics during transfer from micro-Tesla field to high field for detection to understand the resulting spectra from the [1,2- 13 C 2 ]pyruvate-SABRE system.

13C pyruvate↗

Metallofullerene photoswitches driven by photoinduced fullerene-to-metal electron transfer

We report on the discovery and detailed exploration of the unconventional photo-switching mechanism in metallofullerenes, in which the energy of the photon absorbed by the carbon cage π-system is transformed to mechanical motion of the endohedral cluster accompanied by accumulation of spin density on the metal atoms. Comprehensive photophysical and electron paramagnetic resonance (EPR) studies augmented by theoretical modelling are performed to address the phenomenon of the light-induced photo-switching and triplet state spin dynamics in a series of Y x Sc 3-x N@C 80 (x = 0–3) nitride clusterfullerenes. Variable temperature and time-resolved photoluminescence studies revealed a strong dependence of their photophysical properties on the number of Sc atoms in the cluster. All molecules in the series exhibit temperature-dependent luminescence assigned to the near-infrared thermally-activated delayed fluorescence (TADF) and phosphorescence. The emission wavelengths and Stokes shift increase systematically with the number of Sc atoms in the endohedral cluster, whereas the triplet state lifetime and S 1 –T 1 gap decrease in this row. For Sc 3 N@C 80 , we also applied photoelectron spectroscopy to obtain the triplet state energy as well as the electron affinity. Spin distribution and dynamics in the triplet states are then studied by light-induced pulsed EPR and ENDOR spectroscopies. The spin–lattice relaxation times and triplet state lifetimes are determined from the temporal evolution of the electron spin echo after the laser pulse. Well resolved ENDOR spectra of triplets with a rich structure caused by the hyperfine and quadrupolar interactions with 14 N, 45 Sc, and 89 Y nuclear spins are obtained. The systematic increase of the metal contribution to the triplet spin density from Y 3 N to Sc 3 N found in the ENDOR study points to a substantial fullerene-to-metal charge transfer in the excited state. These experimental results are rationalized with the help of ground-state and time-dependent DFT calculations, which revealed a substantial variation of the endohedral cluster position in the photoexcited states driven by the predisposition of Sc atoms to maximize their spin population.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

OLED with hybrid emissive layer

A hybrid emissive layer and OLED incorporating the same are provided. The hybrid emissive layer includes a first material having a triplet state energy level T1 H and a singlet state energy level S1 H , a second material having a triplet state energy level T1 F and a singlet state energy level S1 F ; and a third material having a triplet state energy level T1 P and a single state energy level S1 P , where T1 F $\geqslant$ T1 H ; S1 F $\leqslant$ S1 H ; and T1 P < T1 H

Thompson, Mark E.↗

Tunable Spin Qubit Pairs in Quantum Dot–Molecule Conjugates

Organic molecules and quantum dots (QDs) have both shown promise as materials that can host quantum bits (qubits). This is in part because of their synthetic tunability. The current work employs a combination of both materials to demonstrate a series of tunable quantum dot–organic molecule conjugates that can both host photogenerated spin-based qubit pairs (SQPs) and sensitize molecular triplet states. The photogenerated qubit pairs, composed of a spin-correlated radical pair (SCRP), are particularly intriguing since they can be initialized in well-defined, nonthermally populated, quantum states. Additionally, the radical pair enables charge recombination to a polarized molecular triplet state, also in a well-defined quantum state. The materials underlying this system are an organic molecular chromophore and electron donor, 9,10-bis(phenylethynyl)anthracene, and a quantum dot acceptor composed of ZnO. We prepare a series of quantum dot–molecule conjugates that possess variable quantum dot size and two different linker lengths connecting the two moieties. Optical spectroscopy revealed that the QD–molecule conjugates undergo photoexcited charge separation to generate long-lived charge-separated radical pairs. The resulting spin states are probed using light-induced time-resolved electron paramagnetic resonance (TR-EPR) spectroscopy, revealing the presence of singlet-generated SCRPs and molecular triplet states. Notably, the EPR spectra of the radical pairs are dependent on the geometry of this highly tunable system. The g value of the ZnO QD anion is size tunable, and the line widths are influenced by radical pair separation. Overall, this work demonstrates the power of synthetic tunability in adjusting the spin specific addressability, satisfying a key requirement of functional qubit systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Ruthenium Dye Excitations and Relaxations in Natural Sunlight

Solar harvesting devices using dyes convert the sun's energy to usable forms. The photophysics involved are generally investigated using time-resolved spectroscopic experiments with femtosecond to nanosecond resolution. We show that a kinetic framework constructed from transient and linear absorption measurements of metal-ligand charge transfer states for a set of ruthenium complexes in solution can be used to simulate the steady-state dynamics of dyes adsorbed on a substrate under diffuse solar radiation. Even though the intensity of sunlight is relatively low, double excitations to higher excited states can occur. The steady-state populations show that the dyes' triplet state is the main species present besides the ground state. While small, these persistent excited populations can influence reactivity over the extended periods of time that the systems operate. The results show that non-radiative and optical events (dye -1 s -1 ) within the singlet manifold and from the triplet state exhibit a dependence on ligand substituents.

14 SOLAR ENERGY↗

Strong-field ionization of the triplet ground state of O 2

Using strong-field ionization as a probe, we observe highly nonperiodic evolution of the spin-rotation wave packet launched by a nonionizing femtosecond pulse in oxygen. The nonperiodicity is readily apparent only in rotationally cold molecules that are pumped with a weak alignment pulse. We show that this behavior is a consequence of the spin-rotation and the spin-spin couplings in the triplet ground state of the neutral molecule. A model that includes these couplings in the field-free Hamiltonian but in neither the alignment nor the ionization step explains most of the observed dynamics, suggesting that neither process depends explicitly on the electronic spin. We also show that the angle dependence of strong-field ionization can be retrieved from the delay-dependent signal even when coupling to spin complicates the rotational dynamics.

74 ATOMIC AND MOLECULAR PHYSICS↗

B—N–Bond–Embedded Triplet Terpolymers with Small Singlet–Triplet Energy Gaps for Suppressing Non–Radiative Recombination and Improving Blend Morphology in Organic Solar Cells

Suppressing the photon energy loss (E loss ), especially the non-radiative loss, is of importance to further improve the device performance of organic solar cells (OSCs). However, typical π-conjugated semiconductors possess a large singlet–triplet energy gap (ΔE ST ), leading to a lower triplet state than charge transfer state and contributing to a non-radiative loss channel of the photocurrent by the triplet state. Herein, a series of triplet polymer donors are developed by introducing a BNIDT block into the PM6 polymer backbone. Further, the high electron affinity of BNIDT and the opposite resonance effect of the B—N bond in BNIDT results in a lowered highest occupied molecular orbital (HOMO) and a largely reduced ΔE ST . Moreover, the morphology of the active blends is also optimized by fine-tuning the BNIDT content. Therefore, non-radiative recombination via the terminal triplet loss channels and morphology traps is effectively suppressed. The PNB-3 (with 3% BNIDT):L8-BO device exhibits both small ΔE ST and optimized morphology, favoring more efficient charge transfer and transport. Finally, the simultaneously enhanced V oc of 0.907 V, J sc of 26.59 mA cm –2 , and FF of 78.86% contribute to a champion PCE of 19.02%. Therefore, introducing B—N bonds into benchmark polymers is a possible avenue toward higher-performance of OSCs.

36 MATERIALS SCIENCE↗

Differential sensitivity to oxygen among the bacteriochlorophylls g in the type-I reaction centers of Heliobacterium modesticaldum

The type-I, homodimeric photosynthetic reaction center (RC) of Heliobacteria (HbRC) is the only known RC in which bacteriochlorophyll g (BChl g) is found. It is also simpler than other RCs, having the smallest number of protein subunits and bound chromophores of any type-I RC. In the presence of oxygen, BChl g isomerizes to 8 1 -hydroxychlorophyll aF (Chl a F ). This naturally occurring process provides a way of altering the chlorophylls and studying the efect of these changes on energy and electron transfer. Transient absorbance diference spectroscopy reveals that triplet-state formation occurs in the antenna chlorophylls of HbRCs but does not provide site-specifc information. Herein, we report on an extended optically detected magnetic resonance (ODMR) study of the antenna triplet states in HbRCs with difering levels of conversion of BChl g to Chl a F . The data reveal pools of BChl g molecules with diferent triplet zero-feld splitting parameters and diferent susceptibilities to chemical oxidation. Finally, by relating the detailed spectroscopic characteristics derived from the ODMR data to the recently solved crystallographic structure, we have tentatively identifed BChl g molecules in which the probability of triplet formation is high and sites at which BChl g conversion is more likely, providing useful information about the fate of the excitation in the complex.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Interligand Coupling Drives Fast Triplet Energy Transfer Routes in PbS/Tetracene Quantum Dot Hybrids

The binding of photoactive organic ligands to inorganic quantum dots (QDs) creates a versatile hybrid architecture that allows access to photophysical processes such as efficient triplet exciton generation with near-infrared radiation. Here we report the subnanosecond generation of a hybrid triplet state with mixed ligand-QD character by replacing native oleate ligands on small PbS QDs with 5,12-tetracenepropiolic acid, a bifunctional ligand with two carboxylic acids that tends to lie face-on with the QD surface at low loadings. The face-on geometry engenders a regime of strong electronic coupling that is evident in steady-state absorption and hastens triplet energy flow by several orders of magnitude compared with more typical tetracene-based ligands exhibiting weak coupling. We further determined via Fourier transform infrared (FTIR) and supported by density functional theory (DFT)-based geometry optimizations that high ligand loading causes a shift in QD-ligand mutual disposition toward an edge-on geometry that instigates the formation of intermolecular excited states characterized by triplet excimer-like features in photoluminescence and transient absorption. Our results demonstrate the ability to control strongly coupled ligand-QD systems toward ultrafast generation of photophysically relevant species such as triplets that are valuable for photon upconversion and catalysis.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Systems for Transducing Entanglement Between Photons and Electron Spins

The transfer of quantum properties and entanglement between photons and matter (transduction) is a major challenge in QIS, especially with regard to networking quantum information processing. In order to overcome this challenge, it is important to know how non-classical light (single or entangled photons) interacts with matter. This project specifically addresses fundamental questions about the interaction of single and entangled photons with molecules and nanostructures to produce electrons with prescribed spin polarizations and pairs of electrons with entangled spins, thus resulting in transduction by addressing two major objectives: (2) In Objective 1, we will investigate the formation of polarization-encoded radical (spin qubit) pairs and molecular triplet states photoexcited by single quantum emitter light sources. (2) In Objective 2, we will demonstrate the use of two entangled photons, generated by spontaneous parametric down conversion (SPDC) or by the coherent biexcitonic states of perovskite NPLs, to produce two entangled radical (spin qubit) pairs or molecular triplet states.

74 ATOMIC AND MOLECULAR PHYSICS↗