Deriving the vibronic coupling constants of the cyclopentadienyl radical with density functional theory and G₀W₀

The vibronic coupling constants of the cyclopentadienyl radical have been calculated with G₀W₀, HF, and density functional theory (DFT) with various exchange-correlation functionals such as PBE, PBE0, LC-ωPBE, and the non-empirically tuned LC-ωPBE^*. The vibronic coupling constants for HF and DFT were derived using the gradients of the eigenvalues of the degenerate HOMOs of the closed-shell cyclopentadienyl anion, while the gradients of the corresponding quasiparticle energy levels were used in the case of G₀W₀. The differences between the linear vibronic constants obtained using HF and DFT were found to be small and reduced further when the G₀W₀ correction is applied to HF and DFT. Finally, the linear vibronic coupling constants calculated with G₀W₀ were found to agree well with the values obtained using high level wave function methods in the literature, which suggests that G₀W₀ can be a useful tool toward the study of vibronic coupling.