Intramolecular Singlet Fission: Insights from Quantum Dynamical Simulations

mpsqd: A matrix product state based Python package to simulate closed and open system quantum dynamics

We introduce a Python package based on matrix product states (MPS) to simulate both the time-dependent Schrödinger equation (TDSE) and the hierarchical equations of motion (HEOM). The wave function in the TDSE or the reduced density operator/auxiliary density operators in the HEOM are represented using MPS. A matrix product operator (MPO) is then constructed to represent the Hamiltonian in the TDSE or the generalized Liouvillian in the HEOM. The fourth-order Runge-Kutta method and the time-dependent variational principle are used to propagate the MPS. Several examples, including the nonadiabatic interconversion dynamics of the pyrazine molecule, excitation energy transfer dynamics in molecular aggregates and photosynthetic light-harvesting complexes, the spin-boson model, a laser driven two-state model, the Holstein model, and charge transport in the Anderson impurity model, are presented to demonstrate the capability of the package.

Photoionization of aziridine: Nonadiabatic dynamics of the first six low-lying electronic states of the aziridine radical cation

In this article, the theoretical photoionization spectroscopy of the aziridine (C2H5N) molecule is investigated. To start with, we have optimized the geometry of this molecule at the neutral electronic ground state at the density functional theory/augmented correlation-consistent polarized valence triple zeta level of theory using the G09 program. The electronic structure calculations were restricted to the first six low-lying electronic states in order to account for the experimental photoelectron spectrum of the C2H5N molecule. The first six low-lying electronic states (X̃2A', Ã2A', B̃2A″, C̃2A″, D̃2A', and Ẽ2A') of the potential energy surfaces (PESs) are calculated by both equation of motion-ionization potential-coupled cluster singles and doubles and multi-configuration quasi-degenerate perturbation theory ab initio quantum chemistry methods along the dimensionless normal displacement coordinates in which multiple conical intersections were established among the considered electronic states. A (6 × 6) model vibronic Hamiltonian is constructed on a diabatic electronic basis, using the symmetry selection rules and Taylor series expansion. The Cs symmetry point group of the aziridine molecule leads to electronic states symmetry of either A' or A″, and these states are close in energy, due to which the same symmetry electronic states avoid each other. To get a smooth diabatic PES, a fourfold diabatization scheme is used, which is implemented in the General Atomic and Molecular Electronic Structure Systems suite of programs. All the parameters used in the diabatic vibronic coupling model Hamiltonian are calculated in terms of the normal modes of vibrational coordinates. Finally, the vibronic model Hamiltonian constructed for the coupled six electronic states is used to solve both time-independent and time-dependent Schrödinger equations using the multi-configuration time-dependent Hartree program module to obtain the dynamical observables. The theoretical vibronic band structure is found to be in good accord with the available experimental results.

Photo-induced dynamics with continuous and discrete quantum baths

The ultrafast quantum dynamics of photophysical processes in complex molecules is an extremely challenging computational problem with a broad variety of fascinating applications in quantum chemistry and biology. Inspired by recent developments in open quantum systems, we introduce a pure-state unraveled hybrid-bath method that describes a continuous environment via a set of discrete, effective bosonic degrees of freedom using a Markovian embedding. Our method is capable of describing both, a continuous spectral density and sharp peaks embedded into it. Thereby, we overcome the limitations of previous methods, which either capture long-time memory effects using the unitary dynamics of a set of discrete vibrational modes or use memoryless Markovian environments employing a Lindblad or Redfield master equation. We benchmark our method against two paradigmatic problems from quantum chemistry and biology. We demonstrate that compared to unitary descriptions, a significantly smaller number of bosonic modes suffices to describe the excitonic dynamics accurately, yielding a computational speed-up of nearly an order of magnitude. Furthermore, we take into account explicitly the effect of a δ-peak in the spectral density of a light-harvesting complex, demonstrating the strong impact of the long-time memory of the environment on the dynamics.

Simulating the full spin manifold of triplet-pair states in a series of covalently linked TIPS-pentacenes

Combined density functional theory and multireference configuration interaction methods have been used to elucidate singlet fission (SF) pathways and mechanisms in three regioisomers of side-on linked pentacene dimers. In addition to the optically bright singlets (S1 $$ {}_1 $$ and S2 $$ {}_2 $$ ) and singly excited triplets (T1 $$ {}_1 $$ and T2 $$ {}_2 $$ ), the full spin manifold of multiexcitonic triplet-pair states (1 $$ {}^1 $$ ME,3 $$ {}^3 $$ ME,5 $$ {}^5 $$ ME) has been considered. In the ortho- and para-regioisomers, the1 $$ {}^1 $$ ME and S1 $$ {}_1 $$ potentials intersect upon geometry relaxation of the S1 $$ {}_1 $$ excitation. In the meta-regioisomer, the crossing occurs upon delocalization of the optically bright excitation. The energetic accessibility of these conical intersections and the absence of low-lying charge-transfer states suggests a direct SF mechanism, assisted by charge-resonance effects in the1 $$ {}^1 $$ ME state. While the5 $$ {}^5 $$ ME state does not appear to play a role in the SF mechanism of the ortho- and para-regioisomers, its participation in the disentanglement of the triplet pair is conceivable in the meta-regioisomer.

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.

Simultaneous Intra- and Intermolecular Singlet Fission in Bipentacene Macrocycle Aggregates

Singlet fission (SF) is a process where a singlet state splits into two triplet states, which is essential for enhancing optoelectronic devices. Macrocyclic structures allow for precise control of chromophore orientation and facilitate singlet fission in solutions. However, the behavior of these structures in thin films, crucial for solid-state device optimization, remains underexplored. This study examines the aggregation and singlet fission processes of bipentacene macrocycles (BPc) in thin films using molecular dynamics simulations and electronic structure calculations. Findings indicate that BPc aggregates more rapidly with less chloroform, aligning parallel to the substrate. Intramolecular singlet fission (iSF) rates are rarely changed during evaporation, but the efficiency of intermolecular singlet fission (xSF) improves due to the increase in packing domains, suggesting that orderly crystal domains are not necessary for device efficiency. This opens avenues for varied device designs and traditional solution-based methods for optimal device development.

The Lack of Triplet Fusion for an Intramolecular Singlet Fission Chromophore: The Expected, the Unexpected, and a Reconciliation

Singlet fission (SF) has the potential to play a key role in photovoltaics since it generates a larger number of longer-lived triplet excitons after photoabsorption. Intramolecular SF (iSF) is of special interest since it enables tuning of SF efficiency by adjusting interchromophore configuration through covalent interaction. However, as elaborated in the present work, iSF chromophores are doomed to dissatisfy one general thermodynamic criterion for all SF chromophores, intramolecular or not: E(T2) ≥ 2E(T1), and therefore, the fusion of two triplet excitons to one triplet exciton is thermodynamically favorable. In our nonadiabatic quantum dynamics simulation for a model iSF chromophore, this expected fusion does not occur, because of the inefficient intersystem crossing hidden under the cover of internal conversion of the triplet fusion. A reconciliation is achieved between the dissatisfaction of E(T2) ≥ 2E(T1) and the large tetraradical character for general iSF chromophores.

Intramolecular Singlet Fission in Pentacene Oligomers via an Intermediate State

Intramolecular singlet fission (iSF) is an efficient strategy of multiexciton generation via a singlet exciton splitting into a correlated triplet pair in one organic molecule with more than two chromophores. Propeller-shaped iptycene-linked triisopropylsilyl(TIPS)-ethynyl functionalized pentacene oligomers (pent-monomer, pent-dimer, and pent-trimer) were synthesized, and the iSF dynamics of pent-dimer and -trimer were monitored by a visible-near-IR transient absorption (TA) spectroscopy. Quantum yields of the triplet pair, ∼80%, of both estimated by near-IR TA spectral analysis are in good agreement with the results of global analysis and triplet sensitization experiments. The iSF rate of pent-trimer is slightly faster than that of pent-dimer even with one more chromophore site. The unexpectedly weak difference indicates the existence of an intermediate process to realize iSF. The intermediate process might be determined by through-bond electronic coupling of the homoconjugation bridge in the pentacene oligomers. Our results suggest the importance of the rigid bridge to the fast iSF rate and the elongated lifetime of the correlated triplet pair in pentacene oligomers.

Sensitized Singlet Fission in Rigidly Linked Axial and Peripheral Pentacene-Subphthalocyanine Conjugates

The goal of harnessing the theoretical potential of singlet fission (SF), a process in which one singlet excited state is split into two triplet excited states, has become a central challenge in solar energy research. Covalently linked dimers provide crucial models for understanding the role of chromophore arrangement and coupling in SF. Sensitizers can be integrated into these systems to expand the absorption bandwidth through which SF can be accessed. Here, we define the role of the sensitizer-chromophore geometry in a sensitized SF model system. To this end, two conjugates have been synthesized consisting of a pentacene dimer (SF motif) connected via a rigid alkynyl bridge to a subphthalocyanine (the sensitizer motif) in either an axial or a peripheral arrangement. Steady-state and time-resolved photophysical measurements are used to confirm that both conjugates operate as per design, displaying near unity energy transfer efficiencies and high triplet quantum yields from SF. Decisively, energy transfer between the subphthalocyanine and pentacene dimer occurs ca. 26 times faster in the peripheral conjugate, even though the two chromophores are ca. 3 Å farther apart than in the axial conjugate. Following a theoretical evaluation of the dipolar coupling, V_dip², and the orientation factor, κ², of both the axial (V_dip² = 140 cm^-2; κ² = 0.08) and the peripheral (V_dip² = 724 cm^-2; κ² = 1.46) arrangements, we establish that this rate acceleration is due to a more favorable (nearly co-planar) relative orientation of the transition dipole moments of the subphthalocyanine and pentacenes in the peripheral constellation.

Quest for singlet fission of organic sulfur-containing systems in the higher lying singlet excited state: application prospects of anti-Kasha's rule

In this study, we explore the possibilities of the deactivating pathways of organic thione containing systems through first-principles calculations. We particularly pay attention to the second lying singlet excited state, S₂, due to its large energy difference from the lowest lying S₁ state in the sulfur-containing systems. Several theoretical models including the previously synthesized thiones and the strategically designed molecules are investigated to search for the basic conjugation unit that exhibits the prospect of S₂ fission. Various molecular motifs and different substituents are combined to maneuver the relative alignment of the relevant low excited energy states. The results lead us to conclude that the thione derivatives, under rational and delicate molecular designs, may be engineered to possess a sufficiently high S₂-S₁ energy gap as high as 2 eV and that these systems may exhibit S₂ fission to triplet excitons in the red to near infrared region.

Hierarchical Mapping for Efficient Simulation of Strong System-Environment Interactions

Quantum dynamics (QD) simulation is a powerful tool for interpreting ultrafast spectroscopy experiments and unraveling their microscopic mechanism in out-of-equilibrium excited state behaviors in various chemical, biological, and material systems. Although state-of-the-art numerical QD approaches such as the time-dependent density matrix renormalization group (TD-DMRG) already greatly extended the solvable system size of general linearly coupled exciton-phonon models with up to a few hundred phonon modes, the accurate simulation of larger system sizes or strong system-environment interactions is still computationally highly challenging. Based on quantum information theory (QIT), in this work, we realize that only a small number of effective phonon modes couple to the excitonic system directly regardless of a large or even infinite number of modes in the condensed phase environment. On top of the identified small number of direct effective modes, we propose a hierarchical mapping (HM) approach through performing block Lanczos transformations on the remaining indirect modes, which transforms the Hamiltonian matrix to a nearly block-tridiagonal form and eliminates the long-range interactions. Numerical tests on model spin-boson systems and realistic singlet fission models in a rubrene crystal environment with up to 7000 modes and strong system-environment interactions indicate HM can reduce the system size by 1-2 orders of magnitude and accelerate the calculation by ∼80% without losing accuracy.

Parallel versus Twisted Pentacenes: Conformational Impact on Singlet Fission

We placed two pentacene chromophores at the termini of a diacetylene linker to investigate the impact of excitation wavelength, conformational flexibility, and vibronic coupling on singlet fission. Photoexcitation of the low-energy absorption results in a superposed mixture of states, which transform on an ultrafast time-scale into a spin-correlated and vibronically coupled/hot delocalized triplet pair 1(T1T1)deloc. Regardless of temperature, the lifetime for 1(T1T1)deloc is less than 2 ps. In contrast, photoexcitation of the high-energy absorption results in the formation of 1(T1T1)deloc lasting 1.0 ps, which then decays at room temperature within 4 ps via triplet-triplet annihilation. Lowering the temperature enables 1(T1T1)deloc to delocalize and vibronically decouple, in turn affording 1(T1T1)loc. In addition, our results suggest that the quasi-free rotation at the diacetylene spacer may lead to twisted conformations with very low SF quantum yields, highlighting the need of controlling this structural aspect in the design of new singlet fission active molecules.

Optimizing the Thermodynamics and Kinetics of the Triplet-Pair Dissociation in Donor-Acceptor Copolymers for Intramolecular Singlet Fission

Singlet fission (SF) is a two-step process in which a singlet splits into two triplets throughout the so-called correlated triplet-pair (1TT) state. Intramolecular SF (iSF) materials, in particular, have attracted growing interest as they can be easily implemented in single-junction solar cells and boost their power conversion efficiency. Still, the potential of iSF materials such as polymers and oligomers for photovoltaic applications has been partially hindered by their ability to go beyond the 1TT intermediate and generate free triplets, whose mechanism remains poorly understood. In this work, the main aspects governing the 1TT dissociation in donor-acceptor copolymers and the key features that optimize this process are exposed. First, we show that both thermodynamics and kinetics play a crucial role in the intramolecular triplet-pair separation and second, we uncover the inherent flexibility of the donor unit as the fundamental ingredient to optimize them simultaneously. Overall, these results provide a better understanding of the intramolecular 1TT dissociation process and establish a new paradigm for the development of novel iSF active materials.

Carotenoid Single-Molecular Singlet Fission and the Photoprotection of a Bacteriochlorophyll b-Type Core Light-Harvesting Antenna

Carotenoid (Car) in photosynthesis plays the major roles of accessary light harvesting and photoprotection, and the underlying structure-function relationship attracts continuing research interests. We have attempted to explore the dynamics of Car triplet excitation (³Car*) in the bacteriochlorophyll b (BChl b)-type light harvesting reaction center complex (LH1-RC) of photosynthetic bacterium Halorhodospira halochloris. We show that the LH1 antenna binds a single Car that was identified as a lycopene derivative. Although the Car is hardly visible in the LH1-RC stationary absorption, it shows up conspicuously in the triplet excitation profile with distinct vibronic features. This and the ultrafast formation of ³Car* on direct photoexcitation of Car unequivocally manifest the unimolecular singlet fission reaction of the Car. Moreover, the Car with even one molecule per complex is found to be rather effective in quenching ³BChl b*. The implications of different ³Car* formation mechanisms are discussed, and the self-photoprotection role of BChl b are proposed for this extremophilic species.

Altering singlet fission pathways in perylene-dimers; perylene-diimide versus perylene-monoimide

We used a systematic approach to shed light on the inherent differences in perylenes, namely monoimides versus diimides, including coplanarity and dipole moment, and their impact on singlet fission (SF) by designing, synthesizing, and probing a full fledged series of phenylene- and naphthalene-linked dimers. Next to changing the functionality of the perylene core, we probed the effect of the spacers and their varying degrees of rotational freedom, molecular electrostatic potentials, and intramolecular interactions on the SF-mechanism and -efficiencies. An arsenal of spectroscopic techniques revealed that for perylene-monoimides, a strong charge-transfer mixing with the singlet and triplet excited states restricts SF and yields low triplet quantum yields. This is accompanied by an up-conversion channel that includes geminate triplet-triplet recombination. Using perylene-diimides alters the SF-mechanism by populating a charge-separated-state intermediate, which either favors or shuts-down SF. Napthylene-spacers bring about higher triplet quantum yields and overall better SF-performance for all perylene-monoimides and perylene-diimides. The key to better SF-performance is rotational freedom because it facilitates the overall excited-state polarization and amplifies intramolecular interactions between chromophores.

Quantum dynamics simulation of intramolecular singlet fission in covalently linked tetracene dimer

In this work, we study singlet fission in tetracene para-dimers, covalently linked by a phenyl group. In contrast to most previous studies, we account for the full quantum dynamics of the combined excitonic and vibrational system. For our simulations, we choose a numerically unbiased representation of the molecule's wave function, enabling us to compare with experiments, exhibiting good agreement. Having access to the full wave function allows us to study in detail the post-quench dynamics of the excitons. Here, one of our main findings is the identification of a time scale t₀ ≈ 35 fs dominated by coherent dynamics. It is within this time scale that the larger fraction of the singlet fission yield is generated. We also report on a reduced number of phononic modes that play a crucial role in the energy transfer between excitonic and vibrational systems. Notably, the oscillation frequency of these modes coincides with the observed electronic coherence time t₀. We extend our investigations by also studying the dependency of the dynamics on the excitonic energy levels that, for instance, can be experimentally tuned by means of the solvent polarity. Here, our findings indicate that the singlet fission yield can be doubled, while the electronic coherence time t₀ is mainly unaffected.

Dynamic emissive signatures of intramolecular singlet fission during equilibration to steady state revealed from stochastic kinetic simulations

We investigate the ability of dynamic fluorescence probes to accurately track populations of multi-excitonic states in molecular dyads based on conjugated acenes capable of intramolecular singlet fission (iSF). Stochastic simulations of reported photophysical models from time-resolved spectroscopic studies of iSF dyads based on large acenes (e.g., tetracene and pentacene) are used to extrapolate population and fluorescence yield dynamics. The approach entails the use of repetitive rectangular-shaped excitation waveforms as a stimulus, with durations comparable to triplet lifetimes. We observe unique dynamics signatures that can be directly related to relaxation of multi-exciton states involved over the entire effective time of singlet fission in the presence and absence of an excitation light stimulus. In particular, time-dependent fluorescence yields display an abrupt decay followed by slower rise dynamics appearing as a prominent "dip" feature in responses. The initial fast decrease in the fluorescence yield arises from the formation of triplet pairs and separated triplets that do not produce emission resembling a complete ground state bleach effect. However, relaxation of one separated triplet allows the system to absorb, and in some cases, this increases the fluorescence yield, causing rise dynamics in the emissive response. Our approach also permits extrapolation of all multi-exciton state population dynamics up to steady state conditions in addition to the ability to explore consequences of alternative relaxation channels. The results demonstrate that it is possible to resolve unique signatures of singlet fission events from dynamic fluorescence studies, which can augment detection capabilities and extend sensitivity limits and accessible time scales.

Direct, Mediated, and Delayed Intramolecular Singlet Fission Mechanism in Donor-Acceptor Copolymers

Donor-acceptor (D-A) extended copolymers have shown great potential to be exploited for intramolecular singlet fission (iSF) because of their modular tunability and intrinsic ability to incorporate low-lying charge-transfer (CT) and a triplet-pair (¹TT) states. While the SF mechanism has been widely debated in homo- and heterodimers, little is known about the singlet splitting process in A-D-A copolymer trimers. Unlike traditional two-site SF, the process of iSF in D-A copolymers involves three molecular units consisting of two A's and one D following an A-D-A polymeric chain. This scenario is, therefore, different from that of the homodimer analogues in terms of which states (if any) may drive the SF process. In this work, we identify how singlet splitting occurs in prototypical iSF D-A copolymer poly(benzodithiophene-alt-thiophene-1,1-dioxide) by means of wave packet propagations on the basis of the linear vibronic coupling model Hamiltonian. Our results reveal that three different mechanisms drive the S₁ → ¹TT population transfer via antisymmetric and symmetric vibrational motion, including two favorable mechanisms of direct and mediated interactions, as well as a parasitic decay pathway that potentially delays the process. Remarkably, we uncover the interplay between an upper state of marked multiexcitonic character and a low-lying CT state in balancing the splitting efficiency, which anticipates their major role in defining future guidelines for the molecular design of D-A copolymers for iSF.

Theoretical Molecular Design of Phenanthrenes for Singlet Fission by Diazadibora-Substitution

Based on the valence configuration interaction (VCI) model and quantum chemical calculations, we theoretically investigate the potential of diazadibora-substituted phenanthrenes [(BN)₂-phenanthrenes] as novel singlet fission (SF) chromophores. (BN)₂-substitution to phenanthrene is performed to exhibit a captodative effect, which is found to enhance both diradical character and exchange integral. These enhanced parameters induced by (BN)₂-substitution are shown to bring energetically favorable SF with high triplet excitation energies. In order to reveal the relationship between diradical character and positions replaced by (BN)₂, analyses based on the VCI model, odd-electron density, and resonance structures are conducted. Accordingly, a concrete design principle, which is inherent in and is understandable from the topology of (BN)₂-phenanthrene, is presented. Furthermore, design strategies to fine-tuning of the diradical character are newly demonstrated based on the additional introduction of π-donor and π-acceptor. The present results provide feasible candidate molecules and novel design strategies toward the discovery of bright SF chromophores for the application to efficient organic solar cells.

Electronic Communication as a Transferable Property of Molecular Bridges?

Electronic communication through molecular bridges is important for different types of experiments, such as single-molecule conductance, electron transfer, superexchange spin coupling, and intramolecular singlet fission. In many instances, the chemical structure of the bridge determines how the two parts it is connecting communicate, and does so in ways that are transferable between these different manifestations (for example, high conductance often correlates with strong antiferromagnetic spin coupling, and low conductance due to destructive quantum interference correlates with ferromagnetic coupling). Defining electronic communication as a transferable property of the bridge can help transfer knowledge between these different areas of research. Examples and limits of such transferability are discussed here, along with some possible directions for future research, such as employing spin-coupled and mixed-valence systems as structurally well-controlled proxies for understanding molecular conductance and for validating first-principles theoretical methodologies, building conceptual understanding for the growing experimental work on intramolecular singlet fission, and developing measures for the transferability of electronic communication as a bridge property.

Fluctuating exchange interactions enable quintet multiexciton formation in singlet fission

Several recent electron spin resonance studies have observed a quintet multiexciton state during the singlet fission process. Here, we provide a general theoretical explanation for the generation of this state by invoking a time-varying exchange coupling between pairs of triplet excitons and subsequently solving the relevant time-varying spin Hamiltonian for different rates at which the exchange coupling varies. We simulate experimental ESR spectra and draw qualitative conclusions about the adiabatic and diabatic transitions between triplet pair spin states.

A molecular movie of ultrafast singlet fission

The complex dynamics of ultrafast photoinduced reactions are governed by their evolution along vibronically coupled potential energy surfaces. It is now often possible to identify such processes, but a detailed depiction of the crucial nuclear degrees of freedom involved typically remains elusive. Here, combining excited-state time-domain Raman spectroscopy and tree-tensor network state simulations, we construct the full 108-atom molecular movie of ultrafast singlet fission in a pentacene dimer, explicitly treating 252 vibrational modes on 5 electronic states. We assign the tuning and coupling modes, quantifying their relative intensities and contributions, and demonstrate how these modes coherently synchronise to drive the reaction. Our combined experimental and theoretical approach reveals the atomic-scale singlet fission mechanism and can be generalized to other ultrafast photoinduced reactions in complex systems. This will enable mechanistic insight on a detailed structural level, with the ultimate aim to rationally design molecules to maximise the efficiency of photoinduced reactions.

Singlet Fission from Upper Excited Electronic States of Cofacial Perylene Dimer

Singlet fission directly from the upper excited vibrational and electronic states of cofacial perylene dimers, bypassing the relaxed state S₁, was detected within 50 fs. This process competes well with vibrational cooling in S₁ (4.7-7.0 ps) and S₂ → S₁ internal conversion (380 fs). The singlet fission has the energy threshold E = 3.06 eV. Other competitive relaxation processes are excimer and dimer cation formation on an ultrafast time scale. Excitation to higher energy levels (4.96 eV) leads to a higher efficiency of singlet fission.