Comparative Analysis of Molecular Conformers Using Localization–Delocalization Matrices and Frobenius Distance

We quantify electronic similarity across conformers of eight sulfur-containing systems using localization– delocalization matrices (LDMs) from Quantum Theory of Atoms in Molecule (QTAIM) and the Frobenius distance (FD) as a matrix-based metric. After conformer sampling and wB97X-D/6-311G(2d,p) optimization, we analyzed 630 unique conformers (allyl mercaptan, 2-propenesulfenic acid, diallyl monosulfide, diallyl disulfide, diallyl trisulfide, allicin, and the E/Z isomers of ajoene. Conformers were grouped according to their QTAIM molecular-graph classification as acyclic, ring critical point (RCP), or cyclic critical point (ccp) types. Pairwise FDs within and across classes are generally small (typically ≤ 0.10–0.15), indicating that electron density is largely preserved over geometrical variation. Boltzmann weighting at 298 K confirms that ensemble-averaged LDMs are very close to those of the lowest-energy conformers. These results support the use of an LDM-based FD as a compact descriptor of conformer similarity and clarify when single-conformer approximations are adequate and may be extended in future work to explore structural conformations relevant to protein binding.