d-orbital energy levels in planar [MIIF4]2−, [MII(NH3)4]2+ and [MII(CN)4]2− complexes: the nature of M–L π bonding and the implications for ligand field theory

Abstract

Qualitative MO theory predicts degenerate dπ orbitals for planar coordination complexes with formally σ-only ligands and the splitting energy, ΔE_π = E(d_xy) − E(d_xz,d_yz), should be zero. For π-donor ligands, ΔE_π should be positive (d_xy > d_xz,yz) while for π-acceptors, ΔE_π should be negative (d_xy < d_xz,yz). However, experimental d–d spectra, ab initio ligand field theory (AI LFT) and crystal field theory for σ-only [M(NH₃)₄]²⁺ complexes give pronounced dπ splittings with ΔE_π around +2500 cm⁻¹ for first-row, divalent metal ions. AI LFT further suggests ΔE_π values around +4500 cm⁻¹ for [MF₄]²⁻ and +1000 cm⁻¹ for [M(CN)₄]²⁻ species. The origins of these dπ orbital splittings can be traced to the effects of the ligand field potential surrounding the metal centre which includes not only the intrinsic metal–ligand π bonding but also substantial contributions from the ‘void’ regions above and below the molecular plane. The π component of the ‘void cell’ potentials increases ΔE_π which, if not explicitly taken into account, artificially enhances the apparent π-donor strength of the ligands. With the inclusion of void cell π interactions, even though the AI LFT d orbital sequence always places d_xz,yz below d_xy, the ligand field analysis provides a chemically-reasonable description of the M–L π interactions with cyanide being a weak π acceptor, ammonia being π-neutral and fluoride being a strong π donor. In the case of [Ni(CN)₄]²⁻, ligand field calculations further show that, contrary to the recent claims of Oppenheim et al. (Inorg. Chem., 2019, 58, 15202) the sequence of the many-electron excited states is not a definitive guide to the underlying order of one-electron d orbital energies and that the observed sequence of ⁿA_2g > ⁿE_g > ⁿB_1g, n = 1 or 3, does not guarantee a d-orbital sequence of d_xy < d_xz,yz < d_z².