Effective fragment orbitals for chemical applications

The effective fragment orbitals (EFOs) are uniquely, basis set-independent orbitals of any chemically defined atom or molecular fragment, obtained without the requirement of an external reference state, Lewis structure assumption, or population threshold. The EFOs are capable of rationalising bond polarisation, charge transfer, and back-donation at the bond level, and form an effective minimal basis for any atom or fragment regardless of the basis-set employed in the underlying calculation. Building on this foundation, the effective oxidation state (EOS) method assigns formal oxidation states directly from wave function analysis. This review presents the theoretical foundations of the EFOs and surveys a selected variety of chemical applications organised in four themes: formal oxidation state evaluation in ambiguous inorganic and organometallic systems, metal-ligand bonding characterisation in non-innocent and reactive complexes, quantification of donor-acceptor interactions, and prediction of macroscopic chemical properties including spin-crossover transition temperatures and Hammett substituent constants.