Electron Density Redistribution as a Descriptor for Excited-State Reactivity

This study introduces the electronic redistribution function, <i>Δρ</i>_<i>ij</i>(<b>r</b>), as a descriptor for analyzing excited-state reactivity in photochemical processes. Building upon the Quantum Theory of Atoms in Molecules (QTAIM) and state-specific density partitioning, <i>Δρ</i>_<i>ij</i>(<b>r</b>) quantifies electron density changes between two electronic states (<i>i</i> and <i>j</i>) and identifies reactive sites by integrating charge redistribution over atomic basins. This approach includes state weights (<i>c</i>_<i>i</i>², <i>c</i>_<i>j</i>²) to ensure physically meaningful interpretations of density differences. Applied to diverse systems─including the [2 + 2] cycloaddition of ethylene, Paternò-Büchi reactions of carbonyl/thiocarbonyl compounds, and photocyclizations of 1,3-butadiene─the descriptor reveals distinct reactivity patterns. For instance, <i>Δρ</i>_<i>ij</i>(<b>r</b>) delineates charge depletion (δ⁺) and accumulation (δ^-) sites, predicting interactions that drive photoproduct formation. The framework is further extended to analyze conical intersection regions, offering insights into bond-forming mechanisms for processes such as benzene isomerization and ethylene cycloaddition.