Partial Information Decomposition of Electronic Observables Along a Reaction Coordinate

A reaction-coordinate–resolved information-theoretic analysis of chemical reactivity is developed using mutual information and partial information decomposition (PID). Along an intrinsic reaction coordinate (IRC), a local empirical distribution is constructed at each position $s$ that couples a coarse-grained geometric progress variable (target) to two electronic readouts (sources), and the joint mutual information $I(T;X,Y)$ is decomposed into redundant, unique, and synergistic contributions using the Williams–Beer PID formalism. In the numerical demonstrations, the target is a binned bond-asymmetry coordinate $\xi =d_{\mathrm{C}\text{\hspace{0.17em}⁣}-\text{\hspace{0.17em}⁣}\mathrm{n}\mathrm{u}\mathrm{c}}-d_{\mathrm{C}\text{\hspace{0.17em}⁣}-\text{\hspace{0.17em}⁣}\mathrm{L}\mathrm{G}}$, while the sources are DDEC6 net atomic charges on the nucleophile and leaving-group centres. Application to three prototypical S${}_{\mathrm{N}}$2 reactions (identity exchange ${\mathrm{F}}^{-}+\mathrm{C}{\mathrm{H}}_3\mathrm{F}$, halide substitution ${\mathrm{F}}^{-}+\mathrm{C}{\mathrm{H}}_3\mathrm{B}\mathrm{r}$, and hydroxide substitution $\mathrm{O}{\mathrm{H}}^{-}+\mathrm{C}{\mathrm{H}}_3\mathrm{C}{\mathrm{H}}_2\mathrm{B}\mathrm{r}$) yields compact, symmetry-sensitive signatures of bonding evolution: the identity reaction exhibits mirror-related information profiles with exchange of unique-information contributions between equivalent centres, whereas asymmetric reactions show shifted, centre-specific redistribution among redundancy and synergy as C–X cleavage couples to C–Nu formation. This Supplementary Information provides the formal construction, chemically motivated limiting toy models, a solvable analytic symmetric-transfer model, and the computational protocol used to obtain IRC-resolved PID curves.