The topology of the ground-state potential energy surface of M(CN)₆ with orbitally degenerate ²T_2g (M = Ti^III (t_2g¹), Fe^III and Mn^II (both low-spin t_2g⁵)) and ³T_1g ground states (M = V^III (t_2g²), Mn^III and Cr^II (both low-spin t_2g⁴)) has been studied with linear and quadratic Jahn−Teller coupling models in the five-dimensional space of the ε_g and τ_2g octahedral vibrations (T_g⊗(ε_g+τ_2g) Jahn−Teller coupling problem (T_g = ²T_2g, ³T_1g)). A procedure is proposed to give access to all vibronic coupling parameters from geometry optimization with density functional theory (DFT) and the energies of a restricted number of Slater determinants, derived from electron replacements within the t_2g^1,5 or t_2g^2,4 ground-state electronic configurations. The results show that coupling to the τ_2g bending mode is dominant and leads to a stabilization of D_3d structures (absolute minima on the ground-state potential energy surface) for all complexes considered, except for [Ti(CN)₆]^3-, where the minimum is of D_4h symmetry. The Jahn−Teller stabilization energies for the D_3d minima are found to increase in the order of increasing CN−M π back-donation (Ti^III < V^III < Mn^III < Fe^III < Mn^II < Cr^II). With the angular overlap model and bonding parameters derived from angular distortions, which correspond to the stable D_3d minima, the effect of configuration interaction and spin−orbit coupling on the ground-state potential energy surface is explored. This approach is used to correlate Jahn−Teller distortion parameters with structures from X-ray diffraction data. Jahn−Teller coupling to trigonal modes is also used to reinterpret the anisotropy of magnetic susceptibilities and g tensors of [Fe(CN)₆]^3-, and the ³T_1g ground-state splitting of [Mn(CN)₆]^3-, deduced from near-IR spectra. The implications of the pseudo Jahn−Teller coupling due to t_2g−e_g orbital mixing via the trigonal modes (τ_2g) and the effect of the dynamic Jahn−Teller coupling on the magnetic susceptibilities and g tensors of [Fe(CN)₆]^3- are also addressed.

Copper(II) complexes of the pentadentate bispidine ligands exist in two isomeric forms (see structure) with bond-length differences up to 0.5 Å. The stabilization of either isomer may be achieved by a variation of the substituent at N7.