Linear alpha olefins (LAOs) are key petrochemical precursors for the synthesis of larger polymers, detergents, plasticizers, and lubricants. Most catalytic ethylene oligomerization processes generate a wide distribution of LAO carbon chain lengths. A major ongoing industrial challenge is to develop homogeneous catalysts that result in selective and tunable ethylene oligomerization to 1-hexene and 1-octene alkenes. Quantum mechanical calculations coupled with rapidly advancing technology have enabled the ability to calculate small molecule systems with high accuracy. Employing computational models to advance from empirical to quantitative prediction of product selectivities has become an active area of exploration. In this work, we demonstrate the development and use of a density-functional theory (DFT) transition-state model that provides highly accurate quantitative prediction of phosphinoamidine (P,N) Cr catalysts for controllable selective ethylene trimerization and tetramerization. This model identified a new family of highly selective catalysts that through computational-based ligand design results in a predictable shift from 1-hexene selectivity to 1-octene. Subsequent experimental ligand synthesis and catalyst testing verified the quantitative computational predictions. DFT calculations also provide key insights to factors controlling catalytic activity and present important design criteria for the development of active Cr-based ethylene oligomerization systems. Non-selective ethylene transformations, referred to as full range processes, provide access to a range of LAOs (C4-C20) that are used to produce polyethylene, surfactants, and other commercial products. During full-range oligomerizations, undesired byproducts degrade the purity of LAOs mostly consisting of branched oligomers. Computational mechanistic investigations reveal the origin of linear versus branched selectivity in Fe-catalyzed ethylene oligomerization reactions.