Xintian Feng

Singlet Fission in a Covalently Linked Cofacial Alkynyltetracene Dimer

Singlet fission is a process in which a singlet exciton converts into two triplet excitons. To investigate this phenomenon, we synthesized two covalently linked 5-ethynyl-tetracene (ET) dimers with differing degrees of intertetracene overlap: BET-X, with large, cofacial overlap of tetracene π-orbitals, and BET-B, with twisted arrangement between tetracenes exhibits less overlap between the tetracene π-orbitals. The two compounds were crystallographically characterized and studied by absorption and emission spectroscopy in solution, in PMMA and neat thin films. The results show that singlet fission occurs within 1 ps in an amorphous thin film of BET-B with high efficiency (triplet yield: 154%). In solution and the PMMA matrix the S1 of BET-B relaxes to a correlated triplet pair (1)(T1T1) on a time scale of 2 ps, which decays to the ground state without forming separated triplets, suggesting that triplet energy transfer from (1)(T1T1) to a nearby chromophore is essential for producing free triplets. In support of this hypothesis, selective excitation of BET-B doped into a thin film of diphenyltetracene (DPT) leads to formation of the (1)(T1T1) state of BET-B, followed by generation of both DPT and BET-B triplets. For the structurally cofacial BET-X, an intermediate forms in <180 fs and returns to the ground state more rapidly than BET-B. First-principles calculations predict a 2 orders of magnitude faster rate of singlet fission to the (1)(T1T1) state in BET-B relative to that of crystalline tetracene, attributing the rate increase to greater coupling between the S1 and (1)(T1T1) states and favorable energetics for formation of the separated triplets.

General implementation of the resolution-of-the-identity and Cholesky representations of electron repulsion integrals within coupled-cluster and equation-of-motion methods: Theory and benchmarks

We present a general implementation of the resolution-of-the-identity (RI) and Cholesky decomposition (CD) representations of electron repulsion integrals within the coupled-cluster with single and double substitutions (CCSD) and equation-of-motion (EOM) family of methods. The CCSD and EOM-CCSD equations are rewritten to eliminate the storage of the largest four-index intermediates leading to a significant reduction in disk storage requirements, reduced I/O penalties, and, as a result, improved parallel performance. In CCSD, the number of rate-determining contractions is also reduced; however, in EOM the number of operations is increased because the transformed integrals, which are computed once in the canonical implementation, need to be reassembled at each Davidson iteration. Nevertheless, for large jobs the effect of the increased number of rate-determining contractions is surpassed by the significantly reduced memory and disk usage leading to a considerable speed-up. Overall, for medium-size examples, RI/CD CCSD calculations are approximately 40% faster compared with the canonical implementation, whereas timings of EOM calculations are reduced by a factor of two. More significant speed-ups are obtained in larger bases, i.e., more than a two-fold speed-up for CCSD and almost five-fold speed-up for EOM-EE-CCSD in cc-pVTZ. Even more considerable speedups (6-7-fold) are achieved by combining RI/CD with the frozen natural orbitals approach. The numeric accuracy of RI/CD approaches is benchmarked with an emphasis on energy differences. Errors in EOM excitation, ionization, and electron-attachment energies are less than 0.001 eV with typical RI bases and with a 10(-4) threshold in CD. Errors with 10(-2) and 10(-3) thresholds, which afford more significant computational savings, are less than 0.04 and 0.008 eV, respectively.

What We Can Learn from the Norms of One-Particle Density Matrices, and What We Can't: Some Results for Interstate Properties in Model Singlet Fission Systems

The utility of the norms of one-particle density matrices, ∥γ∥, for understanding the trends in electronic properties is discussed. Using several model systems that are relevant in the context of singlet fission (butadiene, octatetraene, and ethylene dimer), the dependence of interstate properties (such as transition dipole moments and nonadiabatic couplings, NACs) on molecular geometries is investigated. ∥γ∥ contains the principal information about the changes in electronic states involved, such as varying degree of one-electron character of the transition; thus, it captures leading trends in one-electron interstate properties (i.e., when ∥γ∥ is small, the respective interstate matrix elements are also small). However, finer variations in properties that arise due to the dependence of the matrix elements of the respective operators may not be reproduced. Analysis of NACs in ethylene dimer reveals that intermolecular components of NACs follow the trends in ∥γ∥ well, as they are determined primarily by the characters of the two wave functions; however, intramolecular components depend on the relative orientation of the two moieties via the dependence in the derivative of the electron-nuclear Coulomb operator. Therefore, intramolecular NACs may exhibit large variations even when the changes in ∥γ∥ are small. We observe large NACs at perfectly stacked geometry; however, larger values (by a factor of 1.6) are observed at slip-stacked (along the long axis) geometries. Larger values of NACs at slip-stacked configurations are due to the breaking of symmetry of the local environment of the heavy atoms and not due to the wave function composition. We found that the variations in ∥γ∥ for ethylene dimer are due to a varying admixture of the charge-resonance configurations in the S1 state, whereas the (1)ME state retains its pure multiexciton character.

Quantifying charge resonance and multiexciton character in coupled chromophores by charge and spin cumulant analysis

We extend excited-state structural analysis to quantify the charge-resonance and multi-exciton character in wave functions of weakly interacting chromophores such as molecular dimers. The approach employs charge and spin cumulants which describe inter-fragment electronic correlations in molecular complexes. We introduce indexes corresponding to the weights of local, charge resonance, and biexciton (with different spin structure) configurations that can be computed for general wave functions thus allowing one to quantify the character of doubly excited states. The utility of the approach is illustrated by applications to several small dimers, e.g., He-H2, (H2)2, and (C2H4)2, using full and restricted configuration interaction schemes. In addition, we present calculations for several systems relevant to singlet fission, such as tetracene, 1,6-diphenyl-1,3,5-hexatriene, and 1,3-diphenylisobenzofuran dimers.

Linker-Dependent Singlet Fission in Tetracene Dimers

Separation of triplet excitons produced by singlet fission is crucial for efficient application of singlet fission materials. While earlier works explored the first step of singlet fission, the formation of the correlated triplet pair state, the focus of recent studies has been on understanding the second step of singlet fission, the formation of independent triplets from the correlated pair state. We present the synthesis and excited-state dynamics of meta- and para-bis(ethynyltetracenyl)benzene dimers that are analogues to the ortho-bis(ethynyltetracenyl)benzene dimer reported by our groups previously. A comparison of the excited-state properties of these dimers allows us to investigate the effects of electronic conjugation and coupling on singlet fission between the ethynyltetracene units within a dimer. In the para isomer, in which the two chromophores are conjugated, the singlet exciton yields the correlated triplet pair state, from which the triplet excitons can decouple via molecular rotations. In contrast, the meta isomer in which the two chromophores are cross-coupled predominantly relaxes via radiative decay. We also report the synthesis and excited-state dynamics of two para dimers with different bridging units joining the ethynyltetracenes. The rate of singlet fission is found to be faster in the dimer with the bridging unit that has orbitals closer in energy to that of the ethynyltetracene chromophores.