An unexpected bridge between chemical bonding indicators and electrical conductivity through the localization tensor

While the modern theory of the insulating state shows that the conducting or insulating properties of a system can be extracted solely from the ground state properties via the so-called localization tensor (LT), no chemical reading of this important quantity has ever been offered. Here, a remarkable link between the LT and the bond orders as described by the delocalization indices (DIs) of chemical bonding theory is reported. This is achieved through a real space partition of the LT into intra- and interatomic contributions. We show that the convergence or divergence of the LT in the thermodynamic limit, which signals the insulating or conducting nature of an extended system, respectively, can be nailed down to DIs. This allows for the exploitation of traditional chemical intuition to identify essential and spectator atomic groups in determining electrical conductivity. The thermodynamic limit of the LT is controlled by the spatial decay rate of the interatomic DIs, exponential in insulators and power-law in conductors. Computational data of a few selected toy systems corroborate our results.