Quantum topological resolution of catalyst proficiency

The purpose of this exploratory investigation is to characterize, contrast, and explain the differences between efficient Ni(π‐allyl) 2 and inefficient Pd(π‐allyl) 2 systems in the catalyzed cross‐coupling of alkanes. Within the framework of the quantum theory of atoms in molecules, we have created quantum topology phase diagrams (QTPDs) for nonisomeric species by the creation of aggregate‐isomers; simple sum rules are introduced to ensure that the Poincaré‐Hopf relation is obeyed. We show that the catalyzed reaction cycles can be represented as a directed QTPD where each species of the main reaction cycle forms a closed loop. The topological position of the unwanted side products relative to the main reaction cycle for each catalyst is also considered. We find the more efficient Ni(π‐allyl) 2 catalyst produces a reaction cycle on the QTPD that contains no “missing” topologies, preferentially proceeding to desired product at 94% yield, while avoiding wasteful side‐product pathways, disconnected from the major pathway by “missing” topologies. The converse is true for the less efficient Pd(π‐allyl) 2 catalyst, whose reaction pathway markedly bifurcates to final yields of 56% and 44% for product and side‐product, respectively. We subsequently used our nearest neighbor ring‐critical point approach to show that the species of the main reaction cycle of the efficient Ni(π‐allyl) 2 catalyst facilitates the desired chemical transformation whilst more effectively barring the formation of unwanted side product, with respect to the inefficient Pd(π‐allyl) 2 catalyst. The findings from the QTPD analysis are in agreement with traditional energetic‐barrier interpretations of reaction pathway preference. © 2015 Wiley Periodicals, Inc.