Electronic Structure Study of Singlet Fission in Tetracene Derivatives

Non-adiabatic electronic relaxation of tetracene from its brightest singlet excited state

The ultrafast relaxation dynamics of tetracene following UV excitation to the bright singlet state S6 has been studied with time-resolved photoelectron spectroscopy. With the help of high-level ab initio multireference perturbation theory calculations, we assign photoelectron signals to intermediate dark electronic states S3, S4, and S5 as well as to a low-lying electronic state S2. The energetic structure of these dark states has not been determined experimentally previously. The time-dependent photoelectron yields assigned to the states S6, S5, and S4 have been analyzed and reveal the depopulation of S6 within 60 fs, while S5 and S4 are populated with delays of about 50 and 80 fs. The dynamics of the lower-lying states S3 and S2 seem to agree with a delayed population coinciding with the depopulation of the higher-lying states S4-S6 but could not be elucidated in full detail due to the low signal levels of the corresponding two-photon ionization probe processes.

Electronic Couplings for Triplet-Triplet Annihilation Upconversion in Crystal Rubrene

Triplet-triplet annihilation photon upconversion (TTA-UC) is a process able to repackage two low-frequency photons into light of higher energy. This transformation is typically orchestrated by the electronic degrees of freedom within organic compounds possessing suitable singlet and triplet energies and electronic couplings. In this work, we propose a computational protocol for the assessment of electronic couplings crucial to TTA-UC in molecular materials and apply it to the study of crystal rubrene. Our methodology integrates sophisticated yet computationally affordable approaches to quantify couplings in singlet and triplet energy transfer, the binding of triplet pairs, and the fusion to the singlet exciton. Of particular significance is the role played by charge-transfer states along the b-axis of rubrene crystal, acting as both partial quenchers of singlet energy transfer and mediators of triplet fusion. Our calculations identify the π-stacking direction as holding notable triplet energy transfer couplings, consistent with the experimentally observed anisotropic exciton diffusion. Finally, we have characterized the impact of thermally induced structural distortions, revealing their key role in the viability of triplet fusion and singlet fission. We posit that our approaches are transferable to a broad spectrum of organic molecular materials, offering a feasible means to quantify electronic couplings.

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.

Spin-Orbit Couplings of Open-Shell Systems with Restricted Active Space Configuration Interaction

In this work we perform electronic structure calculations to unravel the origin of spin-orbit couplings (SOCs) in open-shell molecules. For that, we select systems displaying di or polyradical character, e.g., trimethylene, and analyze the changes in the magnitude of SOC constants along molecular distortions of ethylene and in the presence of intermolecular interactions between open and closed-shell moieties in the O₂-C₂H₄ system. Calculations were performed by using nonrelativistic wave functions obtained with the restricted active space configuration interaction (RASCI) method, in conjunction with a recent implementation for the calculation of SOC based on the spin-orbit mean field approximation. Our results demonstrate the suitability of RASCI in the calculation of SOCs of open-shell systems, while providing a deep understanding of the relationship between couplings and the nature of the electronic states. Moreover, we introduce a new definition of the SOC constant for the study of molecular aggregates.

Revealing the Contest between Triplet-Triplet Exchange and Triplet-Triplet Energy Transfer Coupling in Correlated Triplet Pair States in Singlet Fission

Understanding the separation of the correlated triplet pair state ¹(TT) intermediate is critical for leveraging singlet fission to improve solar cell efficiency. This separation mechanism is dominated by two key interactions: (i) the exchange interaction (K) between the triplets which leads to the spin splitting of the biexciton state into ¹(TT),³(TT) and ⁵(TT) states, and (ii) the triplet-triplet energy transfer integral (t) which enables the formation of the spatially separated (but still spin entangled) state ¹(T···T). We develop a simple ab initio technique to compute both the biexciton exchange (K) and biexciton transfer coupling. Our key findings reveal new conditions for successful correlated triplet pair state dissociation. The biexciton exchange interaction needs to be ferromagnetic or negligible to the triplet energy transfer for favorable dissociation. We also explore the effect of chromophore packing to reveal geometries where these conditions are achieved for tetracene.

Vacancy control in acene blends links exothermic singlet fission to coherence

The fission of singlet excitons into triplet pairs in organic materials holds great technological promise, but the rational application of this phenomenon is hampered by a lack of understanding of its complex photophysics. Here, we use the controlled introduction of vacancies by means of spacer molecules in tetracene and pentacene thin films as a tuning parameter complementing experimental observables to identify the operating principles of different singlet fission pathways. Time-resolved spectroscopic measurements in combination with microscopic modelling enables us to demonstrate distinct scenarios, resulting from different singlet-to-triplet pair energy alignments. For pentacene, where fission is exothermic, coherent mixing between the photoexcited singlet and triplet-pair states is promoted by vibronic resonances, which drives the fission process with little sensitivity to the vacancy concentration. Such vibronic resonances do not occur for endothermic materials such as tetracene, for which we find fission to be fully incoherent; a process that is shown to slow down with increasing vacancy concentration.

Pushing the Limits of the Donor-Acceptor Copolymer Strategy for Intramolecular Singlet Fission

Donor-acceptor (D-A) copolymers have shown great potential for intramolecular singlet fission (iSF). Nonetheless, very few design principles exist for optimizing these systems for iSF, with very little knowledge about how to engineer them for this purpose. In recent work, a fundamental trade-off between the main electronic ingredients required for iSF capable D-A coplanar copolymers was revealed. Still, further investigations are needed to understand these limitations and learn how to bypass them. In this work, we propose to induce torsion as an effective way to circumvent the limits of the coplanar approach. We disclose the potential of noncoplanar copolymers with inherently low triplet energies that encompass all the characteristics required for iSF beyond the limiting values associated with fully coplanar systems. Our findings shed some light on the electronic structure aspects of D-A copolymers for iSF and offer a new avenue for the rational design of novel promising candidates.

Short-range DFT energy correction to multiconfigurational wave functions for open-shell systems

Electronic structure methods emerging from the combination of multiconfigurational wave functions and density functional theory (DFT) aim to take advantage of the strengths of the two nearly antagonistic theories. One of the common strategies employed to merge wave function theory (WFT) with DFT relies on the range separation of the Coulomb operator in which DFT functionals take care of the short-distance part, while long-range inter-electronic interactions are evaluated by using the chosen wave function method (WFT-srDFT). In this work, we uncover the limitations of WFT-srDFT in the characterization of open-shell systems. We show that spin polarization effects have a major impact on the (short-range) DFT exchange energy and are of vital importance in order to provide a balanced description between closed and open-shell configurations. We introduce different strategies to account for spin polarization in the short range based on the definition of a spin polarized electron density and with the use of short-range exact exchange. We test the performance of these approaches in the dissociation of the hydrogen molecule, the calculation of energy gaps in spin-triplet atoms and molecular diradicals, and the characterization of low-lying states of the gallium dimer. Our results indicate that the use of short-range DFT correlation in combination with a (full-range) multiconfigurational wave function might be an excellent approach for the study of open-shell molecules and largely improves the performance of WFT and WFT-srDFT.

Electronic couplings for singlet fission: Orbital choice and extrapolation to the complete basis set limit

For the search for promising singlet fission candidates, the calculation of the effective electronic coupling, which is required to estimate the singlet fission rate between the initially excited state (S0S1) and the multiexcitonic state (1TT, two triplets on neighboring molecules, coupled into a singlet), should be sufficiently reliable and fast enough to explore the configuration space. We propose here to modify the calculation of the effective electronic coupling using a nonorthogonal configuration interaction approach by: (a) using only one set of orbitals, optimized for the triplet state of the molecules, to describe all molecular electronic states, and (b) only taking the leading configurations into consideration. Furthermore, we also studied the basis set convergence of the electronic coupling, and we found, by comparison to the complete basis set limit obtained using the cc-pVnZ series of basis sets, that both the aug-cc-pVDZ and 6-311++G** basis sets are a good compromise between accuracy and computational feasibility. The proposed approach enables future work on larger clusters of molecules than dimers.

Singlet fission relevant energetics from optimally tuned range-separated hybrids

As a promising idea to design high-efficiency organic photovoltaics, singlet fission (SF) mechanism, i.e., generating two triplet excitons out of a single photon absorption, has recently come into the spotlight. Even though much effort has been devoted to this arena, accurately accounting for the SF process from the theoretical perspective has proven to be challenging. Herein, the SF energetics have thoroughly been investigated with the help of optimally tuned range-separated hybrid functionals (OT-RSHs) in both gas and solvent phases. Taking a series of experimentally known SF chromophores as working models, we have proposed and validated several variants of OT-RSH approximations for the reliable prediction of the energy levels which match the crucial criteria for the SF process, namely, the negative singlet-triplet and triplet-triplet energy gaps. We scrutinize the role of the OT-RSH ingredients, i.e., the underlying density functional approximations, short- and long-range exact-like exchange, as well as the range-separation parameter, for our purpose. The newly designed OT-RSHs outperform the standard RSHs and other related schemes such as screened-exchange approximations as well as other density functionals from different rungs for describing the SF energetics. More importantly, it is unveiled that although the OT-RSH coupled with the polarizable continuum model, OT-RSH-PCM, as well as the screened versions, OT-SRSHs, which account for the screening effect by the electron correlation through the scalar dielectric constant have some advantages over gas-phase computations using OT-RSHs, the energetics criteria of the SF process may not necessarily be satisfied. This in turn corroborates the idea of performing both the optimal tuning procedure and subsequent computations of the SF relevant energetics using OT-RSHs as a more reliable and affordable framework, at least for the present purpose. The applicability of the proposed models is also put into broader perspective, where they are used for the computational design of several chromophores as promising candidates prone to utilization in the SF-based materials. Hopefully, our recommended OT-RSHs can function as efficient models for both the theoretical modeling of SF chromophores and confirming the experimental observations in the field.

Origin of Fluorescence from Boranils in the Crystalline Phase

A small series of boranil complexes has been studied by fluorescence spectroscopy. Weakly fluorescent in most organic solvents at room temperature, the target compounds display bright emission in the crystalline phase. X-ray diffraction patterns obtained for single crystals indicate a distorted tetrahedral geometry around the O-B-N center with the boron atom being displaced from the plane of the heterobicyclic ring. Consideration of the various bond lengths in comparison with those of reference compounds indicates that the ancillary phenyl ring, bearing different para-substituents, does not make a prominent contribution to the molecular dipole moment in the solid state. Absorption and fluorescence spectra recorded for the crystals remain remarkably similar to those for liquid solutions and display large Stokes shifts. Proximity broadening is observed in one case. The nitrophenyl derivative exhibits additional absorption and emission bands unique to the solid state and could be indicative of an intermolecular charge-transfer transition. The optical properties are discussed in terms of the crystal packing diagrams.

Spin-flip methods in quantum chemistry

This Perspective discusses salient features of the spin-flip approach to strong correlation and describes different methods that sprung from this idea. The spin-flip treatment exploits the different physics of low-spin and high-spin states and is based on the observation that correlation is small for same-spin electrons. By using a well-behaved high-spin state as a reference, one can access problematic low-spin states by deploying the same formal tools as in the excited-state treatments (i.e., linear response, propagator, or equation-of-motion theories). The Perspective reviews applications of this strategy within wave function and density functional theory frameworks as well as the extensions for molecular properties and spectroscopy. The utility of spin-flip methods is illustrated by examples. Limitations and proposed future directions are also discussed.

Design of singlet fission chromophores with cyclic (alkyl)(amino) carbene building blocks

We use MRSF-TDDFT and NEVPT2 methods to design singlet fission chromophores with the building blocks of cyclic (alkyl)(amino)carbenes (CAACs). CAAC dimers with C₂, C₄, and p-phenylene spacers are considered. The substitutions with trifluoromethyls and fluorine atoms at the α C position are investigated. The electronegative substituents enhance the π accepting capability of the α C while maintaining it as a quaternary C atom. The phenylene-connected dimers with the two substitutions are identified as promising candidates for singlet fission chromophores. The cylindrically symmetric C₂ and C₄ spacers allow for substantial structural reorganizations in the S₀-to-S₁ and S₀-to-T₁ excitations. Although the two substituted dimers with the C₄ spacer satisfy (or very close to satisfy) the primary thermodynamics criterion for singlet fission, the significant structural reorganizations result in high barriers so that the fission is kinetically unfavorable.

Triplet Pair States in Singlet Fission

This account aims at providing an understanding of singlet fission, i.e., the photophysical process of a singlet state ( S₁) splitting into two triplet states (2 × T₁) in molecular chromophores. Since its discovery 50 years ago, the field of singlet fission has enjoyed rapid expansion in the past 8 years. However, there have been lingering confusion and debates on the nature of the all-important triplet pair intermediate states and the definition of singlet fission rates. Here we clarify the confusion from both theoretical and experimental perspectives. We distinguish the triplet pair state that maintains electronic coherence between the two constituent triplets, ¹(TT), from one which does not, ¹(T···T). Only the rate of formation of ¹(T···T) is defined as that of singlet fission. We present distinct experimental evidence for ¹(TT), whose formation may occur via incoherent and/or vibronic coherent mechanisms. We discuss the challenges in treating singlet fission beyond the dimer approximation, in understanding the often neglected roles of delocalization on singlet fission rates, and in realizing the much lauded goal of increasing solar energy conversion efficiencies with singlet fission chromophores.

Coupled double triplet state in singlet fission

The highly unusual state, 1(TT), is a coupled, double triplet state that has recently garnered significant attention. This multiexcitonic state can be formed by a quantum transition from a single-photon bright state in a variety of organic semiconducting materials. 1(TT)'s transient nature and similarity to independent triplets, however, has led to significant difficulties in characterization and prediction of its properties. Recent progress describing 1(TT) from theory and experiment are breaking through these difficulties, and have greatly advanced our comprehension of this state. Starting from the early description of 1(TT) in polyenes, this perspective discusses formation mechanisms, spectroscopic signatures, and the scope of intertriplet interactions. When employing singlet fission to generate charge carriers in a solar cell, 1(TT) has a central role. Due to the variety of coupling strengths between triplet states in 1(TT) amongst different chromophores, two different strategies are discussed to enable efficient charge carrier extraction. Continued growth in our understanding of 1(TT) may lead to control over complex quantum states for intriguing applications beyond high-efficiency, organic solar cells.

Intramolecular Singlet Fission: Insights from Quantum Dynamical Simulations

We investigate the dynamics of intramolecular singlet fission in a dimer consisting of two pentacene-based chromophores covalently bonded to a phenylene spacer using an approach that combines high-level ab initio multireference perturbation theory methods and quantum dynamical simulations. The results show that the population of the multiexcitonic state, corresponding to the first step of singlet fission, is facilitated by the existence of higher-lying doubly excited and charge transfer states that participate in a superexchange-like way. The important role played by high-frequency ring-breathing molecular vibrations in the process is also discussed.

Vibronic exciton theory of singlet fission. I. Linear absorption and the anatomy of the correlated triplet pair state

Recent time-resolved spectroscopic experiments have indicated that vibronic coupling plays a vital role in facilitating the process of singlet fission. In this work, which forms the first article of a series, we set out to unravel the mechanisms underlying singlet fission through a vibronic exciton theory. We formulate a model in which both electronic and vibrational degrees of freedom are treated microscopically and non-perturbatively. Using pentacene as a prototypical material for singlet fission, we subject our theory to comparison with measurements on polarization-resolved absorption of single crystals, and employ our model to characterize the excited states underlying the absorption band. Special attention is given to the convergence of photophysical observables with respect to the basis size employed, through which we determine the optimal basis for more expensive calculations to be presented in subsequent work. We furthermore evaluate the energetic separation between the optically prepared singlet excited state and the correlated triplet pair state, as well as provide a real-space characterization of the latter, both of which are of key importance in the discussion of fission dynamics. We discuss our results in the context of recent experimental studies.

Identifying (BN)2-pyrenes as a New Class of Singlet Fission Chromophores: Significance of Azaborine Substitution

Singlet fission converts one photoexcited singlet state to two triplet excited states and raises photoelectric conversion efficiency in photovoltaic devices. However, only a handful of chromophores have been known to undergo this process, which greatly limits the application of singlet fission in photovoltaics. We hereby identify a recently synthesized diazadiborine-pyrene ((BN)₂-pyrene) as a singlet fission chromophore. Theoretical calculations indicate that it satisfies the thermodynamics criteria for singlet fission. More importantly, the calculations provide a physical chemistry insight into how the BN substitution makes this happen. Both calculation and transient absorption spectroscopy experiments indicate that the chromophore has a better absorption than pentacene. The convenient synthesis pathway of the (BN)₂-pyrene suggests an in situ chromophore generation in photovoltaic devices. Two more (BN)₂-pyrene isomers are proposed as singlet fission chromophores. This study sets a step forward in the cross-link of singlet fission and azaborine chemistry.

Theoretical Modeling of Singlet Fission

Singlet fission is a photophysical reaction in which a singlet excited electronic state splits into two spin-triplet states. Singlet fission was discovered more than 50 years ago, but the interest in this process has gained a lot of momentum in the past decade due to its potential as a way to boost solar cell efficiencies. This review presents and discusses the most recent advances with respect to the theoretical and computational studies on the singlet fission phenomenon. The work revisits important aspects regarding electronic states involved in the process, the evaluation of fission rates and interstate couplings, the study of the excited state dynamics in singlet fission, and the advances in the design and characterization of singlet fission compounds and materials such as molecular dimers, polymers, or extended structures. Finally, the review tries to pinpoint some aspects that need further improvement and proposes future lines of research for theoretical and computational chemists and physicists in order to further push the understanding and applicability of singlet fission.

Theoretical Studies of Singlet Fission: Searching for Materials and Exploring Mechanisms

In this Review article, a survey is given for theoretical studies in the subject of singlet fission. Singlet fission converts one singlet exciton to two triplet excitons. With the doubled number of excitons and the longer lifetime of the triplets, singlet fission provides an avenue to improve the photoelectric conversion efficiency in organic photovoltaic devices. It has been a subject of intense research in the past decade. Theoretical studies play an essential role in understanding singlet fission. This article presents a Review of theoretical studies in singlet fission since 2006, the year when the research interest in this subject was reignited. Both electronic structure and dynamics studies are covered. Electronic structure studies provide guidelines for designing singlet fission chromophores and insights into the couplings between single- and multi-excitonic states. The latter provides fundamental knowledge for engineering interchromophore conformations to enhance the fission efficiency. Dynamics studies reveal the importance of vibronic couplings in singlet fission.

The role of topology in organic molecules: origin and comparison of the radical character in linear and cyclic oligoacenes and related oligomers

We discuss the nature of electron-correlation effects in carbon nanorings and nanobelts by a combined approach based on FT-DFT and RAS-SF methods.

Vibronically coherent ultrafast triplet-pair formation and subsequent thermally activated dissociation control efficient endothermic singlet fission

Singlet exciton fission (SF), the conversion of one spin-singlet exciton (S₁) into two spin-triplet excitons (T₁), could provide a means to overcome the Shockley-Queisser limit in photovoltaics. SF as measured by the decay of S₁ has been shown to occur efficiently and independently of temperature, even when the energy of S₁ is as much as 200 meV less than that of 2T₁. Here we study films of triisopropylsilyltetracene using transient optical spectroscopy and show that the triplet pair state (TT), which has been proposed to mediate singlet fission, forms on ultrafast timescales (in 300 fs) and that its formation is mediated by the strong coupling of electronic and vibrational degrees of freedom. This is followed by a slower loss of singlet character as the excitation evolves to become only TT. We observe the TT to be thermally dissociated on 10-100 ns timescales to form free triplets. This provides a model for 'temperature-independent' efficient TT formation and thermally activated TT separation.

Intermolecular Packing Effects on Singlet Fission in Oligorylene Dimers

Using the density functional theory method, the crystalline packing effect on the singlet fission (SF) rate of oligorylenes, some of which are found to exhibit SF in crystal forms, is revealed by evaluating the effective electronic coupling (|V_eff|), the square of which is proportional to the SF rate. The |V_eff| values for terrylene and quaterrylene dimer models are investigated for a variety of slip-stacked forms. It is found that these values show similar dependences on the intermolecular packing as a function of lateral and longitudinal displacements of monomer frameworks, and that they are maximized in several configurations of one monomer slipped from another along the longitudinal axis. The present estimation method of the SF rate is also found to qualitatively explain the experimental SF rate difference between terrylene derivatives with different packing forms. Furthermore, by analyzing the effect of electronic couplings on the adiabatic electronic states related to SF, we predict several favorable molecular packings leading to a fast SF with a high triplet yield.

Effect of Off-Diagonal Exciton-Phonon Coupling on Intramolecular Singlet Fission

Intramolecular singlet fission (iSF) materials provide remarkable advantages in terms of tunable electronic structures, and quantum chemistry studies have indicated strong electronic coupling modulation by high frequency phonon modes. In this work, we formulate a microscopic model of iSF with simultaneous diagonal and off-diagonal coupling to high-frequency modes. A nonperturbative treatment, the Dirac-Frenkel time-dependent variational approach is adopted using the multiple Davydov trial states. It is shown that both diagonal and off-diagonal coupling can aid efficient singlet fission if excitonic coupling is weak, and fission is only facilitated by diagonal coupling if excitonic coupling is strong. In the presence of off-diagonal coupling, it is found that high frequency modes create additional fission channels for rapid iSF. Results presented here may help provide guiding principles for design of efficient singlet fission materials by directly tuning singlet-triplet interstate coupling.

The entangled triplet pair state in acene and heteroacene materials

Entanglement of states is one of the most surprising and counter-intuitive consequences of quantum mechanics, with potent applications in cryptography and computing. In organic materials, one particularly significant manifestation is the spin-entangled triplet-pair state, which mediates the spin-conserving fission of one spin-0 singlet exciton into two spin-1 triplet excitons. Despite long theoretical and experimental exploration, the nature of the triplet-pair state and inter-triplet interactions have proved elusive. Here we use a range of organic semiconductors that undergo singlet exciton fission to reveal the photophysical properties of entangled triplet-pair states. We find that the triplet pair is bound with respect to free triplets with an energy that is largely material independent (∼30 meV). During its lifetime, the component triplets behave cooperatively as a singlet and emit light through a Herzberg-Teller-type mechanism, resulting in vibronically structured photoluminescence. In photovoltaic blends, charge transfer can occur from the bound triplet pairs with >100% photon-to-charge conversion efficiency.