This work explores the electronic structure as well as the reactivity of singlet diradicals, making use of multistate density functional theory (MSDFT). In particular, we show that a minimal active space of two electrons in two orbitals is adequate to treat the relative energies of the singlet and triplet adiabatic ground state as well as the first singlet excited state in many cases. This is plausible because dynamic correlation is included in the first place in the optimization of orbitals in each determinant state via block-localized Kohn–Sham density functional theory. In addition, molecular fragment, i.e., block-localized Kohn–Sham orbitals, are optimized separately for each determinant, providing a variational diabatic representation of valence bond-like states, which are subsequently used in nonorthogonal state interactions (NOSIs). The computational procedure and its performance are illustrated on some prototypical diradical species. It is shown that NOSI calculations in MSDFT can be used to model bond dissociation and hydrogen-atom transfer reactions, employing a minimal number of configuration state functions as the basis states. For p- and s-types of diradicals, the closed-shell diradicals are found to be more reactive than the open-shell ones due to a larger diabatic coupling with the final product state. Such a diabatic representation may be useful to define reaction coordinates for electron transfer, proton transfer and coupled electron and proton transfer reactions in condensed-phase simulations.
Phosphorescent material is widely used in light-emitting devices and in the monitoring of cell phenomena. Anthraquinone compounds (AQs), as important phosphorescent materials, have potential applications as emitters for highly efficient organic light-emitting diodes (OLEDs). Therefore, the accurate calculation of the phosphorescence energy of anthraquinone compounds is particularly important. This study mainly analyzes the phosphorescence energy calculation method of anthraquinone compounds. The time-dependent density functional theory (TDDFT) and the unrestricted density functional theory (UDFT) with seven functionals are selected to calculate the phosphorescence of AQs, taking the high-precision coupled-cluster singles and doubles (CC2) method as a reference. The results showed that the mean unsigned error (MUE) of UDFT was 0.14 eV, which was much smaller than that of TDDFT at 0.29 eV. Therefore, UDFT was more suitable for calculating the phosphorescence energy of AQs. The results obtained by different functionals indicate that the minimum MUE obtained by M06-2X was 0.14 eV. More importantly, the diffuse function in the basis set played an important role in calculating the phosphorescence energy in the M06-HF functional. In the BDBT, FBDBT, and BrBDBT, when M06-HF selected the basis set containing a diffuse function, the differences with CC2 was 0.02 eV, which is much smaller than the one obtained without a diffuse function at 0.80 eV. These findings might be of great significance for the future study of the phosphorescence energy of organic molecules.
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