The topology of the ground-state potential energy surface of M(CN) 6 with orbitally degenerate 2 T 2g (M ) Ti III (t 2g 1 ), Fe III and Mn II (both low-spin t 2g 5 )) and 3 T 1g ground states (M ) V III (t 2g 2 ), Mn III and Cr II (both low-spin t 2g 4 )) has been studied with linear and quadratic Jahn-Teller coupling models in the five-dimensional space of the g and τ 2g octahedral vibrations (T g X( g +τ 2g ) Jahn-Teller coupling problem (T g ) 2 T 2g , 3 T 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 3 T 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.
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