Triplet–Triplet Coupling in Chromophore Dimers: Theory and Experiment

Distance and Orientation Dependence of Triplet-Triplet Energy Transfer Couplings Based on Nonorthogonal Multireference Wave Functions

Triplet-triplet energy transfer (TEnT) is of particular interest in various photochemical, photobiological, and energy science processes. It involves the exchange of spin and energy of electrons between two molecular fragments. Here, quasi-diabatic self-consistent field solutions were used to obtain the diabatic states involved in TEnT. The resonant Hartree-Fock approach was used to compute the nonorthogonal matrix elements for the two-state or four-state effective Hamiltonian and the overlap matrix. From the symmetric orthogonalized Hamiltonian, electronic coupling elements between the diabatic states in the TEnT process can be obtained. Two structural models, namely, naphthalene dimer and the 2,2'-bifluorene molecule, were employed to investigate the role of distance and orientation of the molecular fragments on the energy transfer process. It is observed that the inclusion of charge transfer states is critical to obtain the correct description of TEnT couplings. We discuss the effectiveness of the two-state model and four-state model in the successful evaluation of TEnT couplings. Spin density plots and biorthogonal orbitals were utilized to verify that the correct diabatic electronic structure of the TEnT states was determined.

Investigation of excited states of BODIPY derivatives and non-orthogonal dimers from the perspective of singlet fission

We report state of the art electronic structure calculations RICC2 and XMCQDPT of BODIPY nonorthogonal dimers to understand the photophysical processes from the intramolecular singlet fission (iSF) perspective. We have calculated singlet, triplet and quintet states at the XMCQDPT(8,8)/cc-pVDZ level of theory and diabatic singlet states at the XMCQDPT(4,4)/cc-pVDZ level of theory. In all the systems studied, charge transfer states (1(CA) and 1(AC)) couple strongly with locally excited (1(S1S0)) and multiexcitonic (1(T1T1)) states. The rates of formation of the multiexcitonic state from the locally excited state are very low on account of large activation energy (E(1(T1T1)) - E(1(S1S0))). A relaxed scan along the torsional angle revealed contrasting results for axial and orthogonal conformers. We proposed a probable mechanism for contrasting photophysical properties of dimers B[3,3] and B[2,8]. We also found that substitution of CN, NH2 and BH2 at meso, β and α positions reduces the energy gap (ΔSF = 2E(T1) - E(S1)) significantly, making iSF a competing process in triplet state generation. Intrigued by the success of the CN group at the meso position in reducing the energy gap, we also studied the azaBODIPY monomer and its derivatives using the same methodology. The iSF is slightly endoergic with ΔSF ∼ 0.2 eV in these systems and iSF may play an important role in their photophysical responses.

Singlet Fission as the Gateway to Triplet Generation in Heavy Atom-Free Organic Molecules

Triplet generations in heavy atom-free organic molecules are primarily revealed to proceed through singlet fissions (SFs) by investigating the contributions of SFs and intersystem crossings to the generation rates. The spin-flip long-range corrected time-dependent density functional theory calculations on 11 organic molecules known for triplet generation under photoirradiation are performed. The correlation between the descriptors for SF and the experimental singlet-to-triplet conversion rates strongly supports the predominance of SF progressions in all these molecules, corroborated by experimental observations of their triplet-triplet annihilations. Based on these findings, we propose updated conditions for SF progression: There is a high-absorption singlet state just above the triplet-triplet excitation of the chromophore dimer, or the singlet (triplet-triplet) excitation itself is responsible for photoabsorption. To the best of our knowledge, all organic molecules known for rapid triplet state generation fulfill these conditions.

Intermolecular Interactions and Charge Resonance Contributions to Triplet and Singlet Exciton States of Oligoacene Aggregates

Intermolecular interactions modulate the electro-optical properties of molecular materials and the nature of low-lying exciton states. Molecular materials composed by oligoacenes are extensively investigated for their semiconducting and optoelectronic properties. Here, we analyze the exciton states derived from time-dependent density functional theory (TDDFT) calculations for two oligoacene model aggregates: naphthalene and anthracene dimers. To unravel the role of inter-molecular interactions, a set of diabatic states is selected, chosen to coincide with local (LE) and charge-transfer (CT) excitations within a restricted orbital space including two occupied and two unoccupied orbitals for each molecular monomer. We study energy profiles and disentangle inter-state couplings to disclose the (CT) character of singlet and triplet exciton states and assess the influence of inter-molecular orientation by displacing one molecule with respect to the other along the longitudinal translation coordinate. The analysis shows that (CT) contributions are relevant, although comparably less effective for triplet excitons, and induce a non-negligible mixed character to the low-lying exciton states for eclipsed monomers and for small translational displacements. Such (CT) contributions govern the L_a/L_b state inversion occurring for the low-lying singlet exciton states of naphthalene dimer and contribute to the switch from H- to J-aggregate type of the strongly allowed B_b transition of both oligoacene aggregates.

Impact of Charge-Resonance Excitations on CT-Mediated J-Type Aggregation in Singlet and Triplet Exciton States of Perylene Di-Imide Aggregates: A TDDFT Investigation

The modulation of intermolecular interactions upon aggregation induces changes in excited state properties of organic molecules that can be detrimental for some optoelectronic applications but can be exploited for others. The time-dependent density functional theory (TDDFT) is a cost-effective approach to determining the exciton states of molecular aggregates, and it has been shown to provide reliable results when coupled with the appropriate choice of the functional. Here we apply a general procedure to analyze the aggregates’ exciton states derived from TDDFT calculations in terms of diabatic states chosen to coincide with local (LE) and charge-transfer (CT) excitations within a restricted orbital space. We apply the approach to study energy profiles, interstate couplings, and the charge-transfer character of singlet and triplet exciton states of perylene di-imide aggregates (PDI). We focus on the intermolecular displacement along the longitudinal translation coordinate, which mimics different amounts of slip-stacking observed in PDI crystals. The analysis, in terms of symmetry-adapted Frenkel excitations (FE) and charge-resonance (CR) states and their interactions, discloses how the interchange of the H/J character for small longitudinal shifts, previously reported for singlet exciton states, also occurs for triplet excitons.

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.

Geometry dependence of excitonic couplings and the consequences for configuration-space sampling

Excitonic coupling plays a key role for the understanding of excitonic energy transport (EET) in, for example, organic photovoltaics. However, the calculation of realistic systems is often beyond the applicability range of accurate wavefunction methods so that lower-scaling semi-empirical methods are used to model EET events. In the present work, the distance and angle dependence of excitonic couplings of dimers of selected organic molecules are evaluated for the semi-empirical long-range corrected density functional based tight binding (LC-DFTB) method and spin opposite scaled second order approximate coupled cluster singles and doubles (SOS-CC2). While semi-empirically scaled methods can lead to slightly increased deviations for excitation energies, the excitonic couplings and their dependence on the dimer geometry are reproduced. LC-DFTB yields a similar accuracy range as density-functional theory (DFT) employing the ωB97X functional while the computation time is reduced by several orders of magnitude. The dependence of the exchange contributions to the excitonic couplings on the dimer geometry is analyzed assessing the calculation of Coulombic excitonic couplings from monomer local excited states only, which reduces the computational effort significantly. The present work is a necessary first step toward the simulation of excitonic energy transport using semi-empirical methods.

GIWAXS-SIIRkit: scattering intensity, indexing and refraction calculation toolkit for grazing-incidence wide-angle X-ray scattering of organic materials

Grazing-incidence wide-angle X-ray scattering (GIWAXS) has become an increasingly popular technique for quantitative structural characterization and comparison of thin films. For this purpose, accurate intensity normalization and peak position determination are crucial. At present, few tools exist to estimate the uncertainties of these measurements. Here, a simulation package is introduced called GIWAXS-SIIRkit, where SIIR stands for scattering intensity, indexing and refraction. The package contains several tools that are freely available for download and can be executed in MATLAB. The package includes three functionalities: estimation of the relative scattering intensity and the corresponding uncertainty based on experimental setup and sample dimensions; extraction and indexing of peak positions to approximate the crystal structure of organic materials starting from calibrated GIWAXS patterns; and analysis of the effects of refraction on peak positions. Each tool is based on a graphical user interface and designed to have a short learning curve. A user guide is provided with detailed usage instruction, tips for adding functionality and customization, and exemplary files.