On the ground state Tg ⊗ εg (Tg = 2T2g, 3T1g) Jahn–Teller-coupling in hexacyano complexes of 3d-transition metals

The linear and quadratic Tg ⊗ εg Jahn–Teller effect in the Tg (Tg = 2T2g, 3T1g) ground states of low-spin octahedral cyano complexes of 3d-transition metals (M = TiIII, VIII, MnIII, FeIII, CrII, MnII) has been studied. Vibronic coupling parameters have been derived using density functional theory to calculate energies of Slater determinants, which result from various electron distributions within the t 2 g n configuration due to the metal based t2g(3d) molecular orbitals (n = 1, 2, 3, 4). Tetragonal elongations are found in the case of TiIII, MnIII and CrII, and compressions for VIII, FeIII and MnII, and these establish the metal–ligand π-back donation as the dominant effect and driving force for the geometry distortions and energy stabilizations towards non-degenerate 2 B 2 g ( t 2 g 1 , t 2 g 5 ) and 3 A 2 g ( t 2 g 2 , t 2 g 4 ) ground states. The strength of the Jahn–Teller coupling is very weak and found not to follow a monotonic trend across the transition metal series but is shown to be weakest for TiIII, VIII and FeIII, slightly larger for MnIII, increases further to MnII and is found to be the strongest but is still weak for CrII.