Electronic structure aspects of singlet fission process are discussed. Correlated adiabatic wave functions of the bright singlet and dark multiexciton states of tetracene and pentacene dimers are analyzed in terms of their character (excitonic, charge-resonance, multiexciton). At short interfragment separation (3.5−4 Å), both multiexcitonic and singly excited singlet states have noticeable charge-resonance contributions that fall off quickly at longer distances. Nonadiabatic couplings between the states are discussed. The limitations of diabatic framework in the context of singlet fission are explained. Based on the Cauchy−Schwarz inequality, we propose using the norm of one-particle transition density matrix, ∥γ∥, as a proxy for couplings. The analysis of ∥γ∥ and state characters reveals that the couplings between the multiexciton and singly excited states depend strongly on the weights of charge-resonance configurations in these states. To characterize energetics relevant to triplets separation step, we consider multiexciton binding energy (E b ) defined as the difference between the quintet and singlet multiexciton states. The effect of fragment orientation on the couplings and E b is analyzed.

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ABSTRACT:We revisit the interpretative scheme (Luzanov et al., Theor Exp Chem 1974, 10, 354) of singly excited configuration interaction (CIS) model given earlier at semiempirical level. Detailed computations and spectral (natural orbital) treatment of the CIS density matrices of various types are presented. The corresponding hole-particle densities and related excitation localization indices are described. All the quantities are extended to the excited states calculated in the random phase approximation and closely related time-dependent density functional theory (TDDFT). The localization indices and charge transfer numbers which are invoked to describe interfragment interactions provide a basis for our scheme which is referred to as the excited state structural analysis for electronic transitions. The proposed analysis is exemplified by various moderate and large-size conjugated molecules treated within ab initio TDDFT and the Parizer-Parr-Pople approximation. Finally, we propose a possible generalization to the electronic transitions between CIS-like states followed by applications to singlet organic biradicals treated within the -electron spin-flip CIS.

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.

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.