On the performance of DFT/MRCI-R and MR-MP2 in spin–orbit coupling calculations on diatomics and polyatomic organic molecules

We have investigated the performance of different multi-reference quantum chemical methods with regard to electronic excitation energies and spin–orbit matrix elements (SOMES). Among these methods are two variants of the combined density functional theory and multi-reference configuration interaction method (DFT/MRCI and DFT/MRCI-R) and a multi-reference second-order Møller–Plesset perturbation theory (MR-MP2) approach. Two variants of MR-MP2 have been tested based on either Hartree–Fock orbitals or Kohn–Sham orbitals of the BH-LYP density functional. In connection with the MR-MP2 approaches, the first-order perturbed wave functions have been employed in the evaluation of spin–orbit coupling. To validate our results, we assembled experimental excitation energies and SOMES of eight diatomic and fifteen polyatomic molecules. For some of the smaller molecules, we carried out calculations at the complete active space self-consistent field (CASSCF) level to obtain SOMEs to compare with. Excitation energies of the experimentally unknown states were assessed with respect to second-order perturbation theory corrected (CASPT2) values where available. Overall, we find a very satisfactory agreement between the excitation energies and the SOMEs obtained with the four approaches. For a few states, outliers with regard to the excitation energies and/or SOMEs are observed. These outliers are carefully analysed and traced back to the wave function composition. </p

Exciton Dynamics of a Diketo-Pyrrolopyrrole Core for All Low-Lying Electronic Excited States Using Density Functional Theory-Based Methods

Ab initio treatments of interexcited state internal conversion (IC) are more often than not missing from exciton dynamic descriptions, because of their inherent complexity. Here, we define ”interexcited state IC” as a same-spin nonradiative transition between states i and j, where i ≠ j ≠ 0. Competing directly with multiexciton processes such as singlet fission or triplet photoupconversion, inclusion of this mechanism in the narrative of molecular photophysics would allow for strategic synthesis of chromophores for more efficient photon-harvesting applications. Herein, we present a robust formalism which can model these rates using density functional theory (DFT)-based methods within the Franck–Condon and Herzberg–Teller regime. Using an unsubstituted diketo-pyrrolopyrrole (DPP) core as a case study, we illustrate the exciton dynamics along the first four excited states for both singlet and triplet manifolds, showing ultrafast same-spin transfer mechanisms due to all excited states, excluding the first triplet level, being in close energetic proximity (within 0.8 eV of each other). The resulting electron same-spin rates outcompete the electron spin-flipping intersystem crossing (ISC) rates, with excitons firmly obeying Kasha’s rule as they cascade down from the high-lying excited states toward the lower states. Furthermore, we calculated that only the first singlet excited state displayed a reasonable probability of triplet exciton generation, of ∼40%, with a near-zero chance of the exciton reverting to the singlet manifold once the electron–hole pair are of parallel spin

Singlet Fission in Quinoidal Oligothiophenes

The electronic properties of quinoidal oligithiophenes make them interesting for applications in semiconductor technology. Because of their very large singlet–triplet splitting, they are promising candidates for singlet fission (SF), a process in which an initially excited singlet state is converted into two triplet excitons. Thus, the efficiency of solar cells could be increased to overcome the Shockley-Queisser limit. Here, we investigate the ability of a quinoidal bithiophene to undergo SF in solution. We calculated the ground state and low-lying excited states using a combined density functional theory and multireference configuration interaction approach including dispersion corrections. Potential energy curves along normal mode displacements were computed to detect avoided crossings between the initially excited bright singlet state and a dark doubly excited state which can be interpreted as a triplet pair overall coupled to a singlet ¹(TT). The studied quinoidal bithiophene meets the energetic requirement for SF. A path enabling <i>intramolecular</i> SF could not be found. In contrast, we were able to identify two vibrational modes relevant for an <i>intermolecular</i> SF process in the slip-stacked dimer: A promoting coordinate that couples a bright singlet state with the ¹(TT) state and a separating coordinate that localizes the triplet states on the respective monomers. These results elucidate the mechanism underlying the formation of a triplet pair and the separation of the triplet excitons after initial photoexcitation of the bright singlet state

Charge Transfer-Mediated Multi-exciton Mechanisms in Weakly Coupled Perylene Dimers

The role of charge transfer states in multi-exciton mechanisms has recently become a point of discussion due to the difficulty associated with modeling their contributions accurately. Intermolecular packing has been shown experimentally to heavily influence multi-exciton mechanisms, and therefore understanding how this affects the coupling is key to controlling these processes. Using a gas phase perylene dimer in a weakly coupled configuration as a case study, we employ two separate methods to model the coupling between the bright and correlated triplet 1TT states as a function of relative displacement. For singlet fission, displaced geometries are found to yield large charge transfer contributions within a wavefunction overlap paradigm, unlike for aligned geometries. Triplet–triplet annihilation charge transfer couplings are conversely very weak due to a large energy gap. We found that slipping of the dimer cofacial geometry is beneficial to both charge transfer-mediated processes within a wavefunction overlap scheme. However, within a fragment excitation difference (FED) scheme, a 1 Å slip is more beneficial than a 2 Å one. The resulting rates for singlet fission are in the femtosecond range, up to 22 ps–1, while for triplet fusion they are in the nanosecond range, up to 707 μs–1. By studying the dynamics of the triplet pair following singlet fission, we show that the decorrelation time scale depends on the nature of the relative molecular motion, ranging from picoseconds for fluctuations in the monomer orientations to microseconds for coplanar fluctuations. The direct comparison of the wavefunction overlap and FED methods yields an expected differential due to the method of calculation (linear-response vs multireference) but still strong agreement, suggesting that the more exact wavefunction overlap method can be substituted for the FED method in larger systems with minimal loss in accuracy vs computational complexity. These results provide a good stepping stone for further investigations into singlet fission related problems, correlating well with experiments despite the weakly coupled nature of the dimer

Machine learning-assisted exploration of a versatile polymer platform with charge transfer-dependent full-color emission

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