Visualizing electron flow at transition states by natural reaction orbitals.

Abstract

Transition-state analysis in quantum chemistry provides structural and energetic information but does not directly reveal how electron density is redistributed at the onset of bond reorganization. Although frontier-orbital theory is highly effective for predicting reactivity from reactant molecules, it is less suited to transition states, where bond-breaking and bond-forming processes are already underway. Here, we show that natural reaction orbital (NRO) analysis provides a response-based framework for directly visualizing electron flow at transition states. By extracting the dominant occupied-virtual mixing induced by nuclear displacement along the imaginary vibrational mode, NRO analysis reveals the electronic response that drives bond reorganization. Applications to representative pericyclic reactions show that the essential electron-density redistribution is captured by only a few dominant NRO pairs, which closely reproduces conventional curved-arrow descriptions. In a more complex system, NRO analysis automatically extracts localized, reaction-relevant orbital responses even when canonical frontier orbitals are extensively delocalized. NRO analysis thus provides a compact and chemically intuitive framework for transition-state electron-flow analysis.