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Coherence refers to correlations in waves. Because matter has a wave-particle nature, it is unsurprising that coherence has deep connections with the most contemporary issues in chemistry research (e.g., energy harvesting, femtosecond spectroscopy, molecular qubits and more). But what does the word "coherence" really mean in the context of molecules and other quantum systems? We provide a review of key concepts, definitions, and methodologies, surrounding coherence phenomena in chemistry, and we describe how the terms "coherence" and "quantum coherence" refer to many different phenomena in chemistry. Moreover, we show how these notions are related to the concept of an interference pattern. Coherence phenomena are indeed complex, and ambiguous definitions may spawn confusion. By describing the many definitions and contexts for coherence in the molecular sciences, we aim to enhance understanding and communication in this broad and active area of chemistry.
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Molecular electron spin qubits arranged in precise arrays have great potential for use in quantum information science applications. Molecular qubits are synthetically versatile and can be placed in ordered arrangements upon incorporation into a new class of materials known as paired-ion frameworks (PIFs). A PIF composed of vanadyl porphyrin molecular qubits, VOTCPP-PIF-1, was synthesized as single crystals. Electron paramagnetic resonance spectroscopy was used to study their spin coherence at temperatures up to 293 K. A suspension of VOTCPP-PIF-1 at 5 K in dimethylformamide (DMF) had a spin-spin relaxation time (Tm) of 270 ns. In DMF-d7 and at 5 K, the coherence time of this material increased to 370 ns. This increase in Tm is attributed to the lower gyromagnetic ratio of 2H compared to 1H, which results in weaker electron-nuclear dipolar coupling that reduces the effect of nuclear spin flips on electron spin coherence. In toluene, crystals of VOTCPP-PIF-1 had a Tm of 31 ns at 293 K, demonstrating that PIFs are a promising platform for creating materials for quantum information science applications.
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We report on new donor-chromophore-acceptor triads BDX-ANI-NDI and BDX-ANI-xy-NDI where the BDX donor is 2,2,6,6-tetramethylbenzo[1,2-d;4,5-d]bis[1,3]dioxole, the ANI chromophore is 4-(N-piperidinyl)naphthalene-1,8-dicarboximide, the NDI acceptor is naphthalene-1,8:4,5-bis(dicarboximide), and xy is a 2,5-xylyl spacer. The results on these compounds are compared to the analogous derivatives having a p-methoxyaniline (MeOAn) as the donor. BDXâ¢+ has no nitrogen atoms and only a single hydrogen atom coupled to its unpaired electron spin, and therefore has significantly decreased hyperfine interactions compared to MeOAnâ¢+. We use femtosecond transient absorption (fsTA) and nanosecond TA (nsTA) spectroscopies, the latter with an applied static magnetic field, to study the charge transfer dynamics and determine the spin-spin exchange interaction (J) for BDXâ¢+-ANI-NDIâ¢- and BDXâ¢+-ANI-xy-NDIâ¢- at both ambient and cryogenic temperatures. Time-resolved electron paramagnetic resonance (EPR) and pulse-EPR measurements on these spin-correlated radical pairs (SCRPs) were used to probe their spin dynamics. We demonstrate that BDXâ¢+-ANI-xy-NDIâ¢- has an unusually long lifetime of â¼550 µs in glassy butyronitrile (PrCN) at 85 K, which makes it useful for pulse-EPR studies that target quantum information science (QIS) applications. We also show that rotation of the BDX group about the single bond linking it to the neighboring phenyl group has a significant impact on the spin dynamics, and in particular the magnitude of J. By comparing the results on these compounds to the analogous MeOAn series, insights into design principles for creating improved spin-correlated radical pair systems for QIS studies are obtained.
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The excitation of carbonyl compounds by light to generate radical intermediates has historically been restricted to ketones and aldehydes; carboxylic acids have been overlooked because of high energy requirements and low quantum efficiency. A successful activation strategy would necessitate a bathochromic shift in the absorbance profile, an increase in triplet diradical lifetime, and ease of further functionalization. We present a single-flask transformation of carboxylic acids to acyl phosphonates that can access synthetically useful triplet diradicals under visible light or near-ultraviolet irradiation. The use of phosphorus circumvents unproductive Norrish type I processes, promoting selectivity that enables hydrogen-atom transfer reactivity. Use of this strategy promotes the efficient scaffold remodeling of carboxylic acids through various annulation, contraction, and expansion manifolds.
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We present the first microscopic model for the chirality-induced spin selectivity effect in electron-transfer, in which the internal degrees of freedom of the chiral bridge are explicitly included. By exactly solving this model on short chiral chains we demonstrate that a sizable spin polarization on the acceptor arises from the interplay of coherent and incoherent dynamics, with strong electron-electron correlations yielding many-body states on the bridge as crucial ingredients. Moreover, we include the coherent and incoherent dynamics induced by interactions with vibrational modes and show that they can play an important role in determining the long-time polarized state probed in experiments.
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Optical-spin interfaces that enable the photoinitialization, coherent microwave manipulation, and optical read-out of ground state spins have been studied extensively in solid-state defects such as diamond nitrogen vacancy (NV) centers and are promising for quantum information science applications. Molecular quantum bits (qubits) offer many advantages over solid-state spin centers through synthetic control of their optical and spin properties and their scalability into well-defined multiqubit arrays. In this work, we report an optical-spin interface in an organic molecular qubit consisting of two luminescent tris(2,4,6-trichlorophenyl)methyl (TTM) radicals connected via the meta-positions of a phenyl linker. The triplet ground state of this system can be photoinitialized in its |T0⟩ state by shelving triplet populations as singlets through spin-selective excited-state intersystem crossing with 80% selectivity from |T+⟩ and |T-⟩. The fluorescence intensity in the triplet manifold is determined by the ground-state polarization, and we show successful optical read-out of the ground-state spin following microwave manipulations by fluorescence-detected magnetic resonance spectroscopy. At 85 K, the lifetime of the polarized ground state is 45 ± 3 µs, and the ground state phase memory time is Tm = 5.9 ± 0.1 µs, which increases to 26.8 ± 1.6 µs at 5 K. These results show that luminescent diradicals with triplet ground states can serve as optically addressable molecular qubits with long spin coherence times, which marks an important step toward the rational design of spin-optical interfaces in organic materials.
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A complex interplay of structural, electronic, and vibrational degrees of freedom underpins the fate of molecular excited states. Organic assemblies exhibit a myriad of excited-state decay processes, such as symmetry-breaking charge separation (SB-CS), excimer (EX) formation, singlet fission, and energy transfer. Recent studies of cofacial and slip-stacked perylene-3,4:9,10-bis(dicarboximide) (PDI) multimers demonstrate that slight variations in core substituents and H- or J-type aggregation can determine whether the system follows an SB-CS pathway or an EX one. However, questions regarding the relative importance of structural properties and molecular vibrations in driving the excited-state dynamics remain. Here, we use a combination of two-dimensional electronic spectroscopy, femtosecond stimulated Raman spectroscopy, and quantum chemistry computations to compare the photophysics of two PDI dimers. The dimer with 1,7-bis(pyrrolidin-1'-yl) substituents (5PDI2) undergoes ultrafast SB-CS from a photoexcited mixed state, while the dimer with bis-1,7-(3',5'-di-t-butylphenoxy) substituents (PPDI2) rapidly forms an EX state. Examination of their quantum beating features reveals that SB-CS in 5PDI2 is driven by the collective vibronic coupling of two or more excited-state vibrations. In contrast, we observe signatures of low-frequency vibrational coherence transfer during EX formation by PPDI2, which aligns with several previous studies. We conclude that key electronic and structural differences between 5PDI2 and PPDI2 determine their markedly different photophysics.
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Chirality-induced spin selectivity (CISS) has the potential to control the spin dynamics of chiral molecules for applications in quantum information science. Here we investigate the effect of CISS on the spin dynamics of radical pair formation following photodriven hole transfer in a pair of donor-chiral bridge-acceptor (D-Bχ-A) enantiomers, where D = 2,2,6,6-tetramethyl[1,3]-dioxolo[4,5-f][1,3]benzodioxole, Bχ = (R)- or (S)-2,2'-dimethoxy-4,4'-diphenyl-5,5',6,6',7,7',8,8'-octahydro-1,1'-binaphthalene, and A = naphthalene-(1,4:5,8)-bis(dicarboximide). The results are compared to those obtained on the corresponding achiral D-B-A reference molecule in which B = 2â³,3',5',6â³-tetramethyl-1,1':4',1â³:4â³,1â´-quaterphenyl. Photoexcitation of A in a randomly oriented sample of D-Bχ-A in glassy butyronitrile at 85 K results in subnanosecond two-step hole transfer from 1*A to D to form Dâ¢+-Bχ-Aâ¢-, which was characterized using time-resolved electron paramagnetic resonance (TREPR) spectroscopy at X (9.6 GHz), Q (34 GHz), and W (94 GHz) bands. The spectra show line shape changes that are characteristic of a â¼38% contribution of CISS to the spin dynamics of Dâ¢+-Bχ-Aâ¢- formation. The line shape changes resulting from CISS are particularly apparent in the TREPR spectra at X-band as predicted by recent theory. These results show that (1) CISS has a significant influence on radical pair dynamics initiated by photodriven hole transfer, which is complementary to our recent electron transfer results, and (2) CISS can be detected using TREPR on radical pairs that are randomly oriented relative to an external magnetic field.
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We report the synthesis and characterization of a covalently linked asymmetric cyclophane comprising a 1,7-di(pyrrolidin-1'-yl)perylene-3,4,9,10-bis(dicarboximide) (pyrPDI) and 1,6,7,12-tetra(4'-t-butylphenoxy)perylene-3,4,9,10-bis(dicarboximide) (tpPDI), which absorbs light from 400-750 nm. Single crystals of pyrPDI-tpPDI were analyzed by using X-ray diffraction and transient absorption microscopy. The crystal structure contains several types of intermolecular donor-acceptor interactions (pyrPDI-pyrPDI, tpPDI-tpPDI, and pyrPDI-tpPDI) in addition to the covalently installed intramolecular interaction. Following photoexcitation of the pyrPDI-tpPDI single crystal, the transient absorption data show that charge separation occurs in τ = 21 ps, which is about nine times faster than in toluene solution, while charge recombination occurs in τ > 2 µs, which is more than 400 times longer than in solution. The faster charge separation in the single crystals results from the intermolecular donor-acceptor pyrPDI-tpPDI interactions, while the greatly enhanced charge-separated state lifetime is a consequence of charge transport through the intermolecular π-stacks. These results demonstrate the utility of pre-organizing donor-acceptor structural motifs to elicit specific crystal morphologies that can lead to enhanced photogenerated charge carrier lifetimes for solar energy conversion.
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The development of architecturally unique molecular nanocarbons by bottom-up organic synthesis is essential for accessing functional organic materials awaiting technological developments in fields such as energy, electronics, and biomedicine. Herein, we describe the design and synthesis of a triptycene-based three-dimensional (3D) nanocarbon, GFN-1, with geometrical flexibility on account of its three peripheral π-panels being capable of interconverting between two curved conformations. An effective through-space electronic communication among the three π-panels of GFN-1 has been observed in its monocationic radical form, which exhibits an extensively delocalized spin density over the entire 3D π-system as revealed by electron paramagnetic resonance and UV-vis-NIR spectroscopies. The flexible 3D molecular architecture of GFN-1, along with its densely packed superstructures in the presence of fullerenes, is revealed by microcrystal electron diffraction and single-crystal X-ray diffraction, which establish the coexistence of both propeller and tweezer conformations in the solid state. GFN-1 exhibits strong binding affinities for fullerenes, leading to host-guest complexes that display rapid photoinduced electron transfer within a picosecond. The outcomes of this research could pave the way for the utilization of shape and electronically complementary nanocarbons in the construction of functional coassemblies.
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We report on an electron donor-electron acceptor-stable radical (D-A-Râ¢) molecule in which an electron spin state first prepared on R⢠is followed by photogeneration of an entangled singlet 1[Dâ¢+-Aâ¢-] spin pair to produce Dâ¢+-Aâ¢--Râ¢. Since the Aâ¢- and R⢠spins within Dâ¢+-Aâ¢--R⢠are uncorrelated, spin teleportation from R⢠to Dâ¢+ occurs with a maximal 25% efficiency only for the singlet pair 1(Aâ¢--Râ¢) by spin-allowed electron transfer from Aâ¢- to Râ¢. However, since 1[Dâ¢+-Aâ¢-] is sufficiently long-lived, coherent spin mixing involving the unreactive 3(Aâ¢--Râ¢) population affects entanglement and teleportation within Dâ¢+-Aâ¢--Râ¢. Pulse electron paramagnetic resonance experiments show a direct correlation between electron spin flip-flops and entanglement loss, providing information for designing molecular materials to serve as nanoscale quantum device interconnects.
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The inherently low sensitivity of nuclear magnetic resonance (NMR) spectroscopy is the major limiting factor for its application to elucidate structure and dynamics in solids. In the solid state, nuclear spin hyperpolarization methods based on microwave-induced dynamic nuclear polarization (DNP) provide a versatile platform to enhance the bulk NMR signal of many different sample formulations, leading to significant sensitivity improvements. Here we show that 1H NMR hyperpolarization can also be generated in solids at high magnetic fields by optical irradiation of the sample. We achieved this by exploiting a donor-chromophore-acceptor molecule with an excited state electron-electron interaction similar to the nuclear Larmor frequency, enabling solid-state 1H photochemically induced DNP (photo-CIDNP) at high magnetic fields. Through hyperpolarization relay, we obtained bulk NMR signal enhancements εH by factors of â¼100 at both 9.4 and 21.1 T for the 1H signal of o-terphenyl in magic angle spinning (MAS) NMR experiments at 100 K. These findings open a pathway toward a general light-induced hyperpolarization approach for dye-sensitized high-field NMR in solids.
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Solid-state photochemically induced dynamic nuclear polarization (photo-CIDNP) is a nuclear magnetic resonance spectroscopy technique in which nuclear spin hyperpolarization is generated upon optical irradiation of an appropriate donor-acceptor system. Until now, solid-state photo-CIDNP at high magnetic fields has been observed only in photosynthetic reaction centers and flavoproteins. In the present work, we show that the effect is not limited to such biomolecular samples, and solid-state 13C photo-CIDNP can be observed at 9.4 T under magic angle spinning using a frozen solution of a synthetic molecular system dissolved in an organic solvent. Signal enhancements for the source molecule larger than a factor of 2300 are obtained. In addition, we show that bulk 13C hyperpolarization of the solvent can be generated via spontaneous 13C-13C spin diffusion at natural abundance.
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Engineering asymmetric transmission between left-handed and right-handed circularly polarized light in planar Fabry-Pérot (FP) microcavities would enable a variety of chiral light-matter phenomena, with applications in spintronics, polaritonics, and chiral lasing. Such symmetry breaking, however, generally requires Faraday rotators or nanofabricated polarization-preserving mirrors. We present a simple solution requiring no nanofabrication to induce asymmetric transmission in FP microcavities, preserving low mode volumes by embedding organic thin films exhibiting apparent circular dichroism (ACD); an optical phenomenon based on 2D chirality. Importantly, ACD interactions are opposite for counter-propagating light. Consequently, we demonstrated asymmetric transmission of cavity modes over an order of magnitude larger than that of the isolated thin film. Through circular dichroism spectroscopy, Mueller matrix ellipsometry, and simulation using theoretical scattering matrix methods, we characterize the spatial, spectral, and angular chiroptical responses of this 2D chiral microcavity.
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Crystalline donor-acceptor (D-A) systems serve as an excellent platform for studying CT exciton creation, migration, and dissociation into free charge carriers for solar energy conversion. Donor-acceptor cocrystals have been utilized to develop an understanding of CT exciton formation in ordered organic solids; however, the strong electronic coupling of the D and A units can sometimes limit charge separation lifetimes due to their close proximity. Covalent D-A systems that preorganize specific donor-acceptor structures can assist in engineering crystal morphologies that promote long-lived charge separation to overcome this limitation. Here we investigate photogenerated CT exciton formation in a single crystal of a 2,5,8,11-tetraphenylperylene (PerPh4) donor to which four identical naphthalene-(1,4:5,8)-bis(dicarboximide) (NDI) electron acceptors are covalently attached at the para positions of the PerPh4 phenyl groups to yield PerPh4-NDI4. X-ray crystallography shows that the four NDIs pack pairwise into two distinct motifs. Two NDI acceptors of one PerPh4-NDI4 are positioned over the PerPh4 donors of adjacent PerPh4-NDI4 molecules with the donor and acceptor π-systems having a large dihedral angle between them, while the other two NDIs of PerPh4-NDI4 form xylene-NDI van der Waals π-stacks with the corresponding NDIs in adjacent PerPh4-NDI4 molecules. Upon selective photoexcitation of PerPh4 in the single crystal, CT exciton formation occurs in <300 fs yielding electron-hole pairs that live for more than â¼16 µs. This demonstrates the effectiveness of covalently linked D-A systems for engineering single crystal structures that promote efficient and long-lived charge separation for solar energy conversion.
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Two-dimensional cadmium selenide nanoplatelets (NPLs) exhibit large absorption cross sections and homogeneously broadened band-edge transitions that offer utility in wide-ranging optoelectronic applications. Here, we examine the temperature-dependence of amplified spontaneous emission (ASE) in 4- and 5-monolayer thick NPLs and show that the threshold for close-packed (neat) films decreases with decreasing temperature by a factor of 2-10 relative to ambient temperature owing to extrinsic (trapping) and intrinsic (phonon-derived line width) factors. Interestingly, for pump intensities that exceed the ASE threshold, we find development of intense emission to lower energy in particular provided that the film temperature is ≤200 K. For NPLs diluted in an inert polymer, both biexcitonic ASE and low-energy emission are suppressed, suggesting that described neat-film observables rely upon high chromophore density and rapid, collective processes. Transient emission spectra reveal ultrafast red-shifting with the time of the lower energy emission. Taken together, these findings indicate a previously unreported process of amplified stimulated emission from polyexciton states that is consistent with quantum droplets and constitutes a form of exciton condensate. For studied samples, quantum droplets form provided that roughly 17 meV or less of thermal energy is available, which we hypothesize relates to polyexciton binding energy. Polyexciton ASE can produce pump-fluence-tunable red-shifted ASE even 120 meV lower in energy than biexciton ASE. Our findings convey the importance of biexciton and polyexciton populations in nanoplatelets and show that quantum droplets can exhibit light amplification at significantly lower photon energies than biexcitonic ASE.
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Semiconductor nanocrystals (NCs) offer prospective use as active optical elements in photovoltaics, light-emitting diodes, lasers, and photocatalysts due to their tunable optical absorption and emission properties, high stability, and scalable solution processing, as well as compatibility with additive manufacturing routes. Over the course of experiments, during device fabrication, or while in use commercially, these materials are often subjected to intense or prolonged electronic excitation and high carrier densities. The influence of such conditions on ligand integrity and binding remains underexplored. Here, we expose CdSe NCs to laser excitation and monitor changes in oleate that is covalently attached to the NC surface using nuclear magnetic resonance as a function of time and laser intensity. Higher photon doses cause increased rates of ligand loss from the particles, with upward of 50% total ligand desorption measured for the longest, most intense excitation. Surprisingly, for a range of excitation intensities, fragmentation of the oleate is detected and occurs concomitantly with formation of aldehydes, terminal alkenes, H2, and water. After illumination, NC size, shape, and bandgap remain constant although low-energy absorption features (Urbach tails) develop in some samples, indicating formation of substantial trap states. The observed reaction chemistry, which here occurs with low photon to chemical conversion efficiency, suggests that ligand reactivity may require examination for improved NC dispersion stability but can also be manipulated to yield desired photocatalytically accessed chemical species.
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Spin-correlated radical pairs generated by photoinduced electron transfer are characterised by a distinctive spin polarisation and a unique behaviour in pulse electron paramagnetic resonance (EPR) spectroscopy. Under non-selective excitation, an out-of-phase echo signal modulated by the dipolar and exchange coupling interactions characterising the radical pair is observed and allows extraction of geometric information in the two-pulse out-of-phase electron spin echo envelope modulation (ESEEM) experiment. The investigation of the role of spin-correlated radical pairs in a variety of biological processes and in the fundamental mechanisms underlying device function in optoelectronics, as well as their potential use in quantum information science, relies on the ability to precisely address and manipulate the spins using microwave pulses. Here, we explore the use of shaped pulses for controlled narrowband selective and broadband non-selective excitation of spin-correlated radical pairs in two model donor-bridge-acceptor triads, characterised by different spectral widths, at X- and Q-band frequencies. We demonstrate selective excitation with close to rectangular excitation profiles using BURP (band-selective, uniform response, pure-phase) pulses and complete non-selective excitation of both spins of the radical pair using frequency-swept chirp pulses. The use of frequency-swept pulses in out-of-phase ESEEM experiments enables increased modulation depths and, combined with echo transient detection and Fourier transformation, correlation of the dipolar frequencies with the EPR spectrum and therefore the potential to extract additional information on the donor-acceptor pair geometry.
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Photoexcitation of molecular electron donor and/or acceptor chromophore aggregates can greatly affect their charge-transfer dynamics. Excitonic coupling not only alters the energy landscape in the excited state but may also open new photophysical pathways, such as symmetry-breaking charge separation (SB-CS). Here, we investigate the impact of excitonic coupling on a covalent donor-acceptor-acceptor system comprising a perylene donor (Per) and two perylenediimide (PDI) acceptor chromophores in which the three components are π-stacked in a geometry that is slipped along their long axes (Per-PDI2). Following selective photoexcitation of PDI, femtosecond transient absorption data for Per-PDI2 is compared to that for the single-donor, single-acceptor Per-PDI system, and the PDI2 dimer, which both have the same interchromophore geometry as Per-PDI2. The data show that electron transfer from Per to the lower exciton state of the PDI dimer is slower than that of the single PDI acceptor system. This is due to the lower free energy of the reaction for charge separation because of the electronic stabilization afforded by the excitonic coupling between the PDIs. While PDI2 was shown previously to undergo ultrafast SB-CS, the strong π-π electronic interaction of Per with the adjacent PDI in Per-PDI2 breaks the electronic symmetry of the PDI dimer, resulting in the oxidation of Per rather than SB-CS. These results show that the electronic coupling between molecules designed to accept charges produced by SB-CS in molecular dimers and the chromophores comprising the dimer must be balanced to favor SB-CS.
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The photogeneration of multiple unpaired electron spins within molecules is a promising route to applications in quantum information science because they can be initialized into well-defined, multilevel quantum states (S > 1/2) and reproducibly fabricated by chemical synthesis. However, coherent manipulation of these spin states is difficult to realize in typical molecular systems due to the lack of selective addressability and short coherence times of the spin transitions. Here, these challenges are addressed by using donor-acceptor single cocrystals composed of pyrene and naphthalene dianhydride to host spatially oriented triplet excitons, which exhibit promising photogenerated qutrit properties. Time-resolved electron paramagnetic resonance (TREPR) spectroscopy demonstrates that spatially orienting triplet excitons in a single crystal platform imparts narrow, well-resolved, tunable resonances in the triplet EPR spectrum, allowing selective addressability of the spin sublevel transitions. Pulse-EPR spectroscopy reveals that at temperatures above 30 K, spin decoherence of these triplet excitons is driven by exciton diffusion. However, coherence is limited by electronic spin dipolar coupling below 30 K, where T2 varies nonlinearly with the optical excitation density due to exciton annihilation. Overall, an optimized coherence time of T2 = 7.1 µs at 20 K is achieved. These results provide important insights into designing solid-state molecular excitonic materials with improved spin qutrit properties.