Decay Rate of Correlated Real-Space Delocalization Measures: Insights into Chemical Bonding and Mott Transitions from Hydrogen Chains

We study in this contribution the spatial decay rate of real-space localization and delocalization indices in correlated systems. To that end, we examine Hubbard and quantum chemical models of simple cyclic hydrogen chains, showing that all descriptors of delocalization converge quickly toward the infinite chain limits. It is then shown that the localization index may be understood as a generalization of the standard order parameter in Mott insulator transitions and that the origin of the enigmatic sigmoidal profile of delocalization indices in chemical bond-breaking processes lies in the nonlinear mapping between intersite distances and correlation parameters. Although the long-range asymptotic decay of delocalization indices is exponential, we show that as the correlation parameter decreases quantum mechanical interference sets in and a switch to an oscillating pattern, related to core chemical concepts such as resonance or mesomerism, appears.