Density-functional theory investigation of the geometric, energetic, and optical properties of the cobalt(II)tris(2,2′-bipyridine) complex in the high-spin and the Jahn-Teller active low-spin states

State-of-the-art generalized gradient approximation (GGA) (PBE, OPBE, RPBE, OLYP, and HCTH), meta-GGA (VSXC and TPSS), and hybrid (B3LYP, B3LYP*, O3LYP, and PBE0) functionals are compared for the determination of the structure and the energetics of the D₃ [Co(bpy)₃]²⁺ complex in the ⁴A₂ and ⁴E trigonal components of the high-spin ⁴T_1g(t_2g⁵ e _g²) state and in the low-spin ²E state of octahedral ²E_g(t_2g⁶ e _g¹) parentage. Their comparison extends also to the investigation of the Jahn-Teller instability of the ²E state through the characterization of the extrema of C₂ symmetry of this spin state's potential energy surface. The results obtained for [Co(bpy) ₃]²⁺ in either spin manifold are very consistent among the functionals used and are in good agreement with available experimental data. The functionals, however, perform very differently with respect to the spin-state energetics because the calculated values of the high-spin/low-spin energy difference ΔE_HL^el vary between -3212 and 3919 cm^-1. Semilocal functionals tend to give too large ΔE _HL^el values and thus fail to correctly predict the high-spin state as the ground state of the isolated complex, while hybrid functionals tend to overestimate the stability of the high-spin state with respect to the low-spin state. Reliable results are, however, obtained with the OLYP, HCTH, B3LYP*, and O3LYP functionals which perform best for the description of the isolated complex. The optical properties of [Co(bpy) ₃]²⁺ in the two spin states are also analyzed on the basis of electronic excitation calculations performed within time-dependent density functional response theory. The calculated absorption and circular dichroism spectra agree well with experimental results.