Stationary Points on Potential Energy Surface of Cyclic C₃H₃ with Coupled-Cluster Approaches and Density Functional...

Cyclic C₃H₃ is the simplest cyclic hydrocarbon, but its configuration is complicated. The ground ²E″ state at the equilateral triangle geometry with D₃ symmetry undergoes both Jahn-Teller (JT) distortion and pseudo-Jahn-Teller (PJT) distortion to structures with C₃, C₂, C, or C₂ symmetry. Previous works using complete active space self-consistent field (CASSCF) or multiconfiguration SCF (MCSCF) differ on the characteristics of these structures. To clarify the characteristics of these stationary points on the potential energy surface (PES) of this radical, coupled-cluster methods CCSD, CCSD(T), and EOMEA/IP-CCSD as well as density functional theory are employed to calculate their geometries, harmonic frequencies, and relative energies. Deformations between these stationary points due to JT and PJT effects are analyzed in detail. Most of the results with these methods are consistent with each other, except for the b₂ mode of the ²B₁ state with C₂ symmetry. CCSD and CCSD(T) provide an imaginary frequency for this vibrational mode, while it is calculated to be real with the other methods as well as with EOM-CCSDT-3. This may be related to unstable reference in CCSD and CCSD(T) calculations. On the other hand, most of the employed exchange-correlation functionals provide reliable results on the characteristics of these stationary points. Our results show that the ²A' state with C symmetry is the only minimum structure on the PES of cyclic C₃H₃. The ²A₂ and ²B₁ states of the C₂ structure are second-order saddle points, while both the ²A state of the C₂ structure and the ²A″ state of the C structure are transition states connecting the global minimum ²A' state.