Time dependent correlations of entangled states with nondegenerate branches and possible experimental realization using singlet fission

Intramolecular singlet fission: Quantum dynamical simulations including the effect of the laser field

In the previous work [Reddy et al., J. Chem. Phys. 151, 044307 (2019)], we have analyzed the dynamics of the intramolecular singlet fission process in a series of prototypical pentacene-based dimers, where the pentacene monomers are covalently bonded to a phenylene linker in ortho, meta, and para positions. The results obtained were qualitatively consistent with the experimental data available, showing an ultrafast population of the multiexcitonic state that mainly takes place via a mediated (superexchange-like) mechanism involving charge transfer and doubly excited states. Our results also highlighted the instrumental role of molecular vibrations in the process as a sizable population of the multiexcitonic state could only be obtained through vibronic coupling. Here, we extend these studies and investigate the effect of the laser field on the dynamics of intramolecular singlet fission by explicitly including the coupling to the laser field in our model. In this manner, and by selectively tuning the laser field to the different low-lying absorption bands of the systems investigated, we analyze the wavelength dependence of the intramolecular singlet fission process. In addition, we have also analyzed how the nature of the initially photoexcited electronic state (either localized or delocalized) affects its dynamics. Altogether, our results provide new insights into the design of intramolecular singlet fission-active molecules.

Elucidating Singlet-Fission-Born Multiexciton Dynamics via Molecular Engineering: A Dilution Principle Extended to Quintet Triplet Pair

Multiexciton in singlet exciton fission represents a critical quantum state with significant implications for both solar cell applications and quantum information science. Two distinct fields of interest explore contrasting phenomena associated with the geminate triplet pair: one focusing on the persistence of long-lived correlation and the other emphasizing efficient decorrelation. Despite the pivotal nature of multiexciton processes, a comprehensive understanding of their dependence on the structural and spin properties of materials is currently lacking in experimental realizations. To address this gap in knowledge, molecular engineering was employed to modify the TIPS-tetracene structures, enabling an investigation of the structure-property relationships in spin-related multiexciton processes. In lieu of the time-resolved electron paramagnetic resonance technique, two time-resolved magneto-optical spectroscopies were implemented for quantitative analysis of spin-dependent multiexciton dynamics. The utilization of absorption and fluorescence signals as complementary optical readouts, in the presence of a magnetic field, provided crucial insights into geminate triplet pair dynamics. These insights encompassed the duration of multiexciton correlation and the involvement of the spin state in multiexciton decorrelation. Furthermore, simulations based on our kinetic models suggested a role for quintet dilution in multiexciton dynamics, surpassing the singlet dilution principle established by the Merrifield model. The integration of intricate model structures and time-resolved magneto-optical spectroscopies served to explicitly elucidate the interplay between structural and spin properties in multiexciton processes. This comprehensive approach not only contributes to the fundamental understanding of these processes but also aligns with and reinforces previous experimental studies of solid states and theoretical assessments.

Efficient Spin Interconversion by Molecular Conformation Dynamics of a Triplet Pair for Photon Up-Conversion in an Amorphous Solid

Solid-state materials with improved light-to-energy conversions in organic photovoltaics and in optoelectronics are expected to be developed by realizing efficient triplet-triplet annihilation (TTA) by manipulating the spin conversion processes to the singlet state. In this study, we elucidate the spin conversion mechanism for delayed fluorescence by TTA from a microscopic view of the molecular conformations. We examine the time evolution of the electron spin polarization of the triplet-pair state (TT state) in an amorphous solid-state system exhibiting highly efficient up-conversion emission by using time-resolved electron paramagnetic resonance. We clarified that the spin-state population of the singlet TT increased through the spin interconversion from triplet and quintet TT states during exciton diffusion with random orientation dynamics between the two triplets for the modulation of the exchange interaction, achieving a high quantum yield of up-conversion emission. This understanding provides us with a guide for the development of efficient light-to-energy conversion devices utilizing TTA.

Decorrelated singlet and triplet exciton delocalization in acetylene-bridged Zn-porphyrin dimers

The controlled delocalization of molecular excitons remains an important goal towards the application of organic chromophores in processes ranging from light-initiated chemical transformations to classical and quantum information processing. In this study, we present a methodology to couple optical and magnetic spectroscopic techniques and assess the delocalization of singlet and triplet excitons in model molecular chromophores. By comparing the steady-state and time-resolved optical spectra of Zn-porphyrin monomers and weakly coupled dimers, we show that we can use the identity of substituents bound at specific positions of the macromolecules' rings to control the inter-ring delocalization of singlet excitons stemming from their B states through acetylene bridges. While broadened steady-state absorption spectra suggest the presence of delocalized B state excitons in mesityl-substituted Zn-tetraphenyl porphyrin dimers (Zn2U-D), we confirm this conclusion by measuring an enhanced ultrafast non-radiative relaxation from these inter-ring excitonic states to lower lying electronic states relative to their monomer. In contrast to the delocalized nature of singlet excitons, we use time-resolved EPR and ENDOR spectroscopies to show that the triplet states of the Zn-porphyrin dimers remain localized on one of the two macrocyclic sub-units. We use the analysis of EPR and ENDOR measurements on unmetallated model porphyrin monomers and dimers to support this conclusion. The results of DFT calculations also support the interpretation of localized triplet states. These results demonstrate researchers cannot conclude triplet excitons delocalize in macromolecular based on the presence of spatially extended singlet excitons, which can help in the design of chromophores for application in spin conversion and information processing technologies.

Molecular Control of Triplet-Pair Spin Polarization and Its Optoelectronic Magnetic Resonance Probes

ConspectusPreparing and manipulating pure magnetic states in molecular systems are the key initial requirements for harnessing the power of synthetic chemistry to drive practical quantum sensing and computing technologies. One route for achieving the requisite higher spin states in organic systems exploits the phenomenon of singlet fission, which produces pairs of triplet excited states from initially photoexcited singlets in molecular assemblies with multiple chromophores. The resulting spin states are characterized by total spin (quintet, triplet, or singlet) and its projection onto a specified molecular or magnetic field axis. These excited states are typically highly polarized but exhibit an impure spin population pattern. Herein, we report the prediction and experimental verification of molecular design rules that drive the population of a single pure magnetic state and describe the progress toward its experimental realization.A vital feature of this work is the close partnership among theory, chemical synthesis, and spectroscopy. We begin by presenting our theoretical framework for understanding spin manifold interconversion in singlet fission systems. This theory makes specific testable predictions about the intermolecular structure and orientation relative to an external magnetic field that should lead to pure magnetic state preparation and provides a powerful tool for interpreting magnetic spectra. We then test these predictions through detailed magnetic spectroscopy experiments on a series of new molecular architectures that meet one or more of the identified structural criteria. Many of these architectures rely on the synthesis of molecules with features unique to this effort: rigid bridges between chromophores in dimers, heteroacenes with tailored singlet/triplet-pair energy level matching, or side-group engineering to produce specific crystal structures. The spin evolution of these systems is revealed through our application and development of several magnetic resonance methods, each of which has different sensitivities and relevance in environments relevant to quantum applications.Our theoretical predictions prove to be remarkably consistent with our experimental results, though experimentally meeting all the structural prescriptions demanded by theory for true pure-state preparation remains a challenge. Our magnetic spectra agree with our model of triplet-pair behavior, including funneling of the population to the ms = 0 magnetic sublevel of the quintet under specified conditions in dimers and crystals, showing that this phenomenon is subject to control through molecular design. Moreover, our demonstration of novel and/or highly sensitive detection mechanisms of spin states in singlet fission systems, including photoluminescence (PL), photoinduced absorption (PA), and magnetoconductance (MC), points the way toward both a deeper understanding of how these systems evolve and technologically feasible routes toward experiments at the single-molecule quantum limit that are desirable for computational applications.

Twisted Carotenoids Do Not Support Efficient Intramolecular Singlet Fission in the Orange Carotenoid Protein

Singlet exciton fission is the spin-allowed generation of two triplet electronic excited states from a singlet state. Intramolecular singlet fission has been suggested to occur on individual carotenoid molecules within protein complexes provided that the conjugated backbone is twisted out of plane. However, this hypothesis has been forwarded only in protein complexes containing multiple carotenoids and bacteriochlorophylls in close contact. To test the hypothesis on twisted carotenoids in a "minimal" one-carotenoid system, we study the orange carotenoid protein (OCP). OCP exists in two forms: in its orange form (OCPo), the single bound carotenoid is twisted, whereas in its red form (OCPr), the carotenoid is planar. To enable room-temperature spectroscopy on canthaxanthin-binding OCPo and OCPr without laser-induced photoconversion, we trap them in a trehalose glass. Using transient absorption spectroscopy, we show that there is no evidence of long-lived triplet generation through intramolecular singlet fission despite the canthaxanthin twist in OCPo.

Intramolecular Charge Transfer and Ultrafast Nonradiative Decay in DNA-Tethered Asymmetric Nitro- and Dimethylamino-Substituted Squaraines

Molecular (dye) aggregates are a materials platform of interest in light harvesting, organic optoelectronics, and nanoscale computing, including quantum information science (QIS). Strong excitonic interactions between dyes are key to their use in QIS; critically, properties of the individual dyes govern the extent of these interactions. In this work, the electronic structure and excited-state dynamics of a series of indolenine-based squaraine dyes incorporating dimethylamino (electron donating) and/or nitro (electron withdrawing) substituents, so-called asymmetric dyes, were characterized. The dyes were covalently tethered to DNA Holliday junctions to suppress aggregation and permit characterization of their monomer photophysics. A combination of density functional theory and steady-state absorption spectroscopy shows that the difference static dipole moment (Δd) successively increases with the addition of these substituents while simultaneously maintaining a large transition dipole moment (μ). Steady-state fluorescence and time-resolved absorption and fluorescence spectroscopies uncover a significant nonradiative decay pathway in the asymmetrically substituted dyes that drastically reduces their excited-state lifetime (τ). This work indicates that Δd can indeed be increased by functionalizing dyes with electron donating and withdrawing substituents and that, in certain classes of dyes such as these asymmetric squaraines, strategies may be needed to ensure long τ, e.g., by rigidifying the π-conjugated network.

Symmetry Breaking Charge Transfer in DNA-Templated Perylene Dimer Aggregates

Molecular aggregates are of interest to a broad range of fields including light harvesting, organic optoelectronics, and nanoscale computing. In molecular aggregates, nonradiative decay pathways may emerge that were not present in the constituent molecules. Such nonradiative decay pathways may include singlet fission, excimer relaxation, and symmetry-breaking charge transfer. Singlet fission, sometimes referred to as excitation multiplication, is of great interest to the fields of energy conversion and quantum information. For example, endothermic singlet fission, which avoids energy loss, has been observed in covalently bound, linear perylene trimers and tetramers. In this work, the electronic structure and excited-state dynamics of dimers of a perylene derivative templated using DNA were investigated. Specifically, DNA Holliday junctions were used to template the aggregation of two perylene molecules covalently linked to a modified uracil nucleobase through an ethynyl group. The perylenes were templated in the form of monomer, transverse dimer, and adjacent dimer configurations. The electronic structure of the perylene monomers and dimers were characterized via steady-state absorption and fluorescence spectroscopy. Initial insights into their excited-state dynamics were gleaned from relative fluorescence intensity measurements, which indicated that a new nonradiative decay pathway emerges in the dimers. Femtosecond visible transient absorption spectroscopy was subsequently used to elucidate the excited-state dynamics. A new excited-state absorption feature grows in on the tens of picosecond timescale in the dimers, which is attributed to the formation of perylene anions and cations resulting from symmetry-breaking charge transfer. Given the close proximity required for symmetry-breaking charge transfer, the results shed promising light on the prospect of singlet fission in DNA-templated molecular aggregates.

Triplet-pair spin signatures from macroscopically aligned heteroacenes in an oriented single crystal

The photo-driven process of singlet fission generates coupled triplet pairs (TT) with fundamentally intriguing and potentially useful properties. The quintet ⁵TT₀ sublevel is particularly interesting for quantum information because it is highly entangled, is addressable with microwave pulses, and could be detected using optical techniques. Previous theoretical work on a model Hamiltonian and nonadiabatic transition theory, called the JDE model, has determined that this sublevel can be selectively populated if certain conditions are met. Among the most challenging, the molecules within the dimer undergoing singlet fission must have their principal magnetic axes parallel to one another and to an applied Zeeman field. Here, we present time-resolved electron paramagnetic resonance (TR-EPR) spectroscopy of a single crystal sample of a tetracenethiophene compound featuring arrays of dimers aligned in this manner, which were mounted so that the orientation of the field relative to the molecular axes could be controlled. The observed spin sublevel populations in the paired TT and unpaired (T+T) triplets are consistent with predictions from the JDE model, including preferential ⁵TT₀ formation at z ‖ B₀, with one caveat-two ⁵TT spin sublevels have little to no population. This may be due to crossings between the ⁵TT and ³TT manifolds in the field range investigated by TR-EPR, consistent with the intertriplet exchange energy determined by monitoring photoluminescence at varying magnetic fields.

Spin Statistics for Triplet-Triplet Annihilation Upconversion: Exchange Coupling, Intermolecular Orientation, and Reverse Intersystem Crossing

Triplet-triplet annihilation upconversion (TTA-UC) has great potential to significantly improve the light harvesting capabilities of photovoltaic cells and is also sought after for biomedical applications. Many factors combine to influence the overall efficiency of TTA-UC, the most fundamental of which is the spin statistical factor, η, that gives the probability that a bright singlet state is formed from a pair of annihilating triplet states. The value of η is also critical in determining the contribution of TTA to the overall efficiency of organic light-emitting diodes. Using solid rubrene as a model system, we reiterate why experimentally measured magnetic field effects prove that annihilating triplets first form weakly exchange-coupled triplet-pair states. This is contrary to conventional discussions of TTA-UC that implicitly assume strong exchange coupling, and we show that it has profound implications for the spin statistical factor η. For example, variations in intermolecular orientation tune η from to through spin mixing of the triplet-pair wave functions. Because the fate of spin-1 triplet-pair states is particularly crucial in determining η, we investigate it in rubrene using pump-push-probe spectroscopy and find additional evidence for the recently reported high-level reverse intersystem crossing channel. We incorporate all of these factors into an updated model framework with which to understand the spin statistics of TTA-UC and use it to rationalize the differences in reported values of η among different common annihilator systems. We suggest that harnessing high-level reverse intersystem crossing channels in new annihilator molecules may be a highly promising strategy to exceed any spin statistical limit.

Using temperature dependent fluorescence to evaluate singlet fission pathways in tetracene single crystals

The temperature-dependent fluorescence spectrum, decay rate, and spin quantum beats are examined in single tetracene crystals to gain insight into the mechanism of singlet fission. Over the temperature range of 250 K-500 K, the vibronic lineshape of the emission indicates that the singlet exciton becomes localized at 400 K. The fission process is insensitive to this localization and exhibits Arrhenius behavior with an activation energy of 550 ± 50 cm^-1. The damping rate of the triplet pair spin quantum beats in the delayed fluorescence also exhibits an Arrhenius temperature dependence with an activation energy of 165 ± 70 cm^-1. All the data for T > 250 K are consistent with direct production of a spatially separated ¹(T⋯T) state via a thermally activated process, analogous to spontaneous parametric downconversion of photons. For temperatures in the range of 20 K-250 K, the singlet exciton continues to undergo a rapid decay on the order of 200 ps, leaving a red-shifted emission that decays on the order of 100 ns. At very long times (≈1 µs), a delayed fluorescence component corresponding to the original S₁ state can still be resolved, unlike in polycrystalline films. A kinetic analysis shows that the redshifted emission seen at lower temperatures cannot be an intermediate in the triplet production. When considered in the context of other results, our data suggest that the production of triplets in tetracene for temperatures below 250 K is a complex process that is sensitive to the presence of structural defects.

Singlet fission for quantum information and quantum computing: the parallel JDE model

Singlet fission is a photoconversion process that generates a doubly excited, maximally spin entangled pair state. This state has applications to quantum information and computing that are only beginning to be realized. In this article, we construct and analyze a spin-exciton hamiltonian to describe the dynamics of the two-triplet state. We find the selection rules that connect the doubly excited, spin-singlet state to the manifold of quintet states and comment on the mechanism and conditions for the transition into formally independent triplets. For adjacent dimers that are oriented and immobilized in an inert host, singlet fission can be strongly state-selective. We make predictions for electron paramagnetic resonance experiments and analyze experimental data from recent literature. Our results give conditions for which magnetic resonance pulses can drive transitions between optically polarized magnetic sublevels of the two-exciton states, making it possible to realize quantum gates at room temperature in these systems.

Analysis of Photosynthetic Systems and Their Applications with Mathematical and Computational Models

In biological and life science applications, photosynthesis is an important process that involves the absorption and transformation of sunlight into chemical energy. During the photosynthesis process, the light photons are captured by the green chlorophyll pigments in their photosynthetic antennae and further funneled to the reaction center. One of the most important light harvesting complexes that are highly important in the study of photosynthesis is the membrane-attached Fenna–Matthews–Olson (FMO) complex found in the green sulfur bacteria. In this review, we discuss the mathematical formulations and computational modeling of some of the light harvesting complexes including FMO. The most recent research developments in the photosynthetic light harvesting complexes are thoroughly discussed. The theoretical background related to the spectral density, quantum coherence and density functional theory has been elaborated. Furthermore, details about the transfer and excitation of energy in different sites of the FMO complex along with other vital photosynthetic light harvesting complexes have also been provided. Finally, we conclude this review by providing the current and potential applications in environmental science, energy, health and medicine, where such mathematical and computational studies of the photosynthesis and the light harvesting complexes can be readily integrated.

Modular Tensor Diagram Approach for the Construction of Spin Eigenfunctions: The Case Study of Exciton Pair States

Mapping out the high-dimensional state space would be valuable for better understanding the multistate quantum systems. Here, we demonstrate that high-dimensional spin state space can be mapped onto a tensor diagram in full dimension or self-similarly onto the reduced base state space. Based on the tensor diagram, a modular approach is proposed to construct spin eigenfunctions taking the basis of the lower-dimensional space as modules. The implementation of the approach on exciton pair states results in 16 spin eigenstates including 2 singlet states, 3 triplet states, and 1 quintet state with proper symmetry, in contrast to the ones generated using the conventional branching diagram method. The corresponding state energies obtained show the order of spin eigenstates reverses with respect to spin multiplicity. Interestingly, the state space can be decomposed into three subspaces corresponding to the singlet-singlet pair, singlet-triplet pair, and triplet-triplet pair, resulting in a modular structure that is invariant as intermolecular interactions diminish. The proposed approach offers a new perspective on the state space structure of multiple spin states, featuring a hierarchical symmetry, which could be extended to general high-dimensional quantum multistate systems.