Topological Electronic Sensitivity Index (TESI): Weighted Graph Spectral Analysis of Molecular Systems with Electron Delocalization Indices

This work introduces the Topological Electronic Sensitivity Index (TESI), a response-based descriptor that combines quantum chemical topology with molecular spectral graph theory to characterize global electronic redistribution in extended pi-systems. TESI is constructed from a Laplacian matrix derived from atomic delocalization indices and augmented by Non-local Second-order Fukui Indices (NSFI), enabling identification of the dominant connectivity channels governing changes in the molecular charge state. The findings reveal that TESI goes beyond the limitations of static bonding descriptors by identifying how the global molecular architecture constrains or facilitates electronic connectivity. This approach demonstrates that algebraic connectivity, as captured by the Fiedler eigenvalue and vector, provides a robust descriptor of the electronic sensitivity of the molecular skeleton. It reveals preferential connectivity pathways and channels of electronic redistribution that are not necessarily apparent from conventional delocalization indices alone. Within this framework, charge-redistribution channels in complex pi-networks can be systematically characterized, offering a quantitative and formal link between QCT theory and molecular spectral graph theory