Ligand Many-Body Expansion as a General Approach for\nAccelerating Transition Metal Complex Discovery

Methods\nthat accelerate the evaluation of molecular properties\nare essential for chemical discovery. While some degree of ligand\nadditivity has been established for transition metal complexes, it\nis underutilized in asymmetric complexes, such as the square pyramidal\ncoordination geometries highly relevant to catalysis. To develop predictive\nmethods beyond simple additivity, we apply a many-body expansion to\noctahedral and square pyramidal complexes and introduce a correction\nbased on adjacent ligands (i.e., the <i>cis</i> interaction\nmodel). We first test the <i>cis</i> interaction model on\nadiabatic spin-splitting energies of octahedral Fe(II) complexes,\npredicting DFT-calculated values of unseen binary complexes to within\nan average error of 1.4 kcal/mol. Uncertainty analysis reveals the\noptimal basis, comprising the homoleptic and <i>mer</i> symmetric\ncomplexes. We next show that the <i>cis</i> model (i.e.,\nthe <i>cis</i> interaction model solved for the optimal\nbasis) infers both DFT- and CCSD(T)-calculated model catalytic reaction\nenergies to within 1 kcal/mol on average. The <i>cis</i> model predicts low-symmetry complexes with reaction energies outside\nthe range of binary complex reaction energies. We observe that <i>trans</i> interactions are unnecessary for most monodentate\nsystems but can be important for some combinations of ligands, such\nas complexes containing a mixture of bidentate and monodentate ligands.\nFinally, we demonstrate that the <i>cis</i> model may be\ncombined with Δ-learning to predict CCSD(T) reaction energies\nfrom exhaustively calculated DFT reaction energies and the same fraction\nof CCSD(T) reaction energies needed for the <i>cis</i> model,\nachieving around 30% of the error from using the CCSD(T) reaction\nenergies in the <i>cis</i> model alone.