Quantum topological resolution of catalyst proficiency

Abstract

The purpose of this exploratory investigation is to characterize, contrast, and explain the differences between efficient Ni(π-allyl)<inf>2</inf> and inefficient Pd(π-allyl)<inf>2</inf> 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)<inf>2</inf> 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)<inf>2</inf> 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)<inf>2</inf> catalyst facilitates the desired chemical transformation whilst more effectively barring the formation of unwanted side product, with respect to the inefficient Pd(π-allyl)<inf>2</inf> catalyst. The findings from the QTPD analysis are in agreement with traditional energetic-barrier interpretations of reaction pathway preference.