Incorporating anionic ligands in chemical space exploration with new ligand additivity relationships

Chemical space exploration motivates the development of data-driven models that bypass explicit computation or experiment. Cost-efficient strategies include the concept of additivity via the many-body expansion that treats a molecule as the sum of its parts. In the context of transition metal chemistry, ligand-wise additivity has been established as a powerful tool to infer the properties of heteroleptic transition metal complexes (TMCs) from homoleptic TMCs to excellent accuracy, including spin-splitting, orbital energies, and reaction energies. Nevertheless, this framework is incompatible with anionic ligands, because a stable homoleptic, polyanionic parent complex cannot be simulated readily. Here, I explore alternative approaches, first identifying the limits of stability of heteroleptic TMCs when successive Cl- anions are added in representative complexes formed with neutral H2O and CO ligands. I establish that expected linear relationships are preserved, albeit not as strongly as in complexes with neutral ligands. I propose data-efficient interpolation and extrapolation schemes for TMCs that achieve root mean square errors as low as 0.15–0.36 eV on HOMO/LUMO levels and gaps or ionization potentials and electron affinities and 4 kcal/mol on adiabatic spin-splitting energies for Fe(II) complexes. I show that this approach generalizes well across TMCs with 14 other 3d, 4d, and 5d metals. Finally, I extend this approach to predict properties of thousands of binary and ternary Fe(II) or Zn(II) complexes involving a single neutral ligand and up to two unique anionic ligands by leveraging a handful of calculations. I show how this interpolated space can be used to infer the limits of stable and valid complexes and to discover complexes with novel properties.