Partial Information Decomposition of Electronic Observables Along a Reaction Coordinate

Abstract

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 $\xi=d_{\mathrm{C}\!-\!\mathrm{nuc}}-d_{\mathrm{C}\!-\!\mathrm{LG}}$, 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 $\mathrm{F^-+CH_3F}$, halide substitution $\mathrm{F^-+CH_3Br}$, and hydroxide substitution $\mathrm{OH^-+CH_3CH_2Br}$) 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.