Machine learning and statistical analysis for catalyst structure prediction and design

Disclosed is a heteroatomic ligand-metal compound complex transition-state model which has been developed for activity, purity, and/or selectivity for selective ethylene oligomerizations, and density functional theory calculations for determining heteroatomic ligand-metal compound complex reactivity, product purity, and/or selectivity for ethylene trimerizations and/or tetramerizations. Using reaction ground states and transition states, and/or reaction ground states and transition states in combination with the energetic span model, this disclosure reveals that a chromium chromacycle mechanism, there are multiple ground states and multiple transition states, which can account for activity, purity, and/or selectivity for selective ethylene oligomerizations. Based on the reaction ground states and transition states, and/or reaction ground states and transition states in combination with the energetic span model, the methods disclosed herein can qualitatively and semi-quantitatively used to predict relative heteroatomic ligand-metal compound complex activity, purity, and/or selectivity and lead to a successful process for catalyst design and implementation, in which new ligands can be successfully identified and experimentally validated.