Quantification of the Donor-Acceptor Character of Ligands by the Effective Fragment Orbitals

Metal-ligand interactions are at the heart of transition metal complexes. The Dewar-Chat-Duncanson model is often invoked, whereby the metal-ligand bonding is decomposed into the simultaneous ligand→metal electron donation and the metal→ligand back-donation. The separate quantification of both effects is not a trivial task, neither from experimental nor computational exercises. In this work we present the effective fragment orbitals (EFOs) and their occupations as a general procedure beyond the Kohn-Sham density functional theory (KS-DFT) framework for the identification and quantification of donor-acceptor interactions, using solely the wavefunction of the complex. Using a common Fe(II) octahedral complex framework, we quantify the σ-donor, π-donor, and π-acceptor character for a large and chemically diverse set of ligands, by introducing the respective descriptors σ^d, π^d, and π^a. We also explore the effect of the metal size, coordination number, and spin state on the donor/acceptor features. The spin-state is shown to be the most critical effect, inducing a systematic decrease of the sigma donation and π-backdonation going from low spin to high spin. Finally, we illustrate the ability of the EFOs to rationalize the Tolman electronic parameter and the trans influence in planar square complexes in terms of these new descriptors.