All six configurations in a two-level diradical model.
The structures of trimethylenemethane, cyclobutadiene, and octacene.
Plots of PBE singlet-triplet (ΔE ST = E S(c p ) − E T) and orbital () energy gaps as functions of c p for six diradicals. The adiabatic ΔE ST is used for all cases, except cyclobutadiene, where the vertical ΔE ST is used. All data were calculated in ADF with the TZP basis set.
Plots of PBE vertical singlet-triplet (ΔE ST = E S(c p ) − E T) and orbital () energy gaps as functions of c p for stretched H2 and the ·CH2CH2CH2· diradical. All data were calculated in ADF with the TZP basis set.
Fractional spin error of a carbon atom as the two electrons in the p shell become depolarized. The fractional spin error is defined as , with 1s and 2s doubly occupied. At ξ = 0, two electrons in the p shell are fully polarized, while at ξ = 1, two electrons in the p shell are fully spin-compensated. The energy at ξ = 0 is set to zero for each functional. The calculations are performed with the 6-311++G(2d,2p) basis set in a modified version of NWChem package.71
PBE fractional scan profiles for selected bond angles for the CH2 and molecules using ADF. Potential-energy surfaces obtained with a combined FS-DFT and VFS-DFT approach are compared to literature MRCI data.73–75 All calculations used fixed bond lengths for the 1 A 1 state, adapted from Ref. 86 in Slipchenko and Krylov's work,33 which are 1.1089 Å and 1.0459 Å for CH2 and , respectively. The ΔE ST is the adiabatic energy gap.
Plots of PBE vertical singlet-triplet (ΔE ST = E S(c p ) − E T) and orbital (Δεgap = ε q − ε p ) energy gaps as a function of c p for octacene. All data were calculated in ADF with the TZP basis set.
Singlet-triplet energy gaps (in kcal/mol) calculated with VFS-DFT using the LDA and PBE functionals with the 6-311++G(2d,2p) basis set calculated by QM4D. The numbers in the parentheses indicate the optimal occupation number, c p .
Adiabatic singlet-triplet energy gaps for C 2v diradicals in kcal/mol by QM4D.
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