Deriving the Vibronic Coupling Constants of the Cyclopentadienyl Radical with Density Functional Theory and G0W0

<div>The vibronic coupling constants of the cyclopentadienyl radical have been calculated with G₀W₀, HF, and DFT with various exchange-correlation functionals. 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 towards the study of vibronic coupling.</div>

Deriving the Vibronic Coupling Constants of the Cyclopentadienyl Radical with Density Functional Theory and G0W0

<div>The vibronic coupling constants of the cyclopentadienyl radical have been calculated with G₀W₀, HF, and DFT with various exchange-correlation functionals. 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 towards the study of vibronic coupling.</div>

An aminotetracyanocyclopentadienide system: light-induced formation of a thermally stable cyclopentadienyl radical

Crystals of the aminotetracyanocyclopentadienyl radical were obtained from the reaction of CaCl2 with Ag[C5(CN)4(NH2)] and recrystallization in MeOH was performed in sunlight.

The Gas-Phase Formation Mechanism of Dibenzofuran (DBF), Dibenzothiophene (DBT), and Carbazole (CA) from Benzofuran (BF), Benzothiophene (BT), and Indole (IN) with Cyclopentadienyl Radical

Benzofuran (BF), benzothiophene (BT), indole (IN), dibenzofuran (DBF), dibenzothiophene (DBT), and carbazole (CA) are typical heterocyclic aromatic compounds (NSO-HETs), which can coexist with polycyclic aromatic hydrocarbons (PAHs) in combustion and pyrolysis conditions. In this work, quantum chemical calculations were carried out to investigate the formation of DBF, DBT, and CA from the reactions of BF, BT, and IN with a cyclopentadienyl radical (CPDyl) by using the hybrid density functional theory (DFT) at the MPWB1K/6-311+G(3df,2p)//MPWB1K/6-31+G(d,p) level. The rate constants of crucial elementary steps were deduced over 600−1200 K, using canonical variational transition state theory with a small-curvature tunneling contribution (CVT/SCT). This paper showed that the production of DBF, DBT, and CA from the reactions of BF, BT, and IN with CPDyl involved six elementary steps: the addition reaction, ring closure, the first H shift, C–C cleavage, the second H shift, and elimination of CH3 or H. The cleavage of the C–C bond was regarded as the rate-determining step for each pathway due to the extremely high barrier. The 1-methyl substituted products were more easily formed than the 4-methyl substituted products. The main products were DBF and 1-methyl-DBF, DBT and 1-methyl-DBT, and CA and 1-methyl-CA for reactions of BF, BT, and IN with CPDyl, respectively. The ranking of DBF, DBT, and CA formation potential was as follows: DBT and methyl-DBT formation > DBF and methyl-DBF formation > CA, and methyl-CA formation. Comparison with the reaction of naphthalene with CPDyl indicated that the reactions of CPDyl attacking a benzene ring and a furan/thiophene/pyrrole ring could be inferred to be comparable under high temperature conditions.