Shannon entropy and Fisher information are key quantities in information theory.These quantities involve only the electron density and its gradient,so,according to density functional theory,they are natural descriptors of a molecular system and thus should be able to determine all its properties including chemical reactivity.We investigated these quantities from the perspective of density functional reactivity theory at both molecular and atomic levels.To that end,a new basin-based integration algorithm has been implemented,whose reliability and effectiveness have been extensively examined.Our results show that(i)strong correlations between Shannon entropy and Fisher information at both atomic and molecular levels have been confirmed;(ii)different partition schemes(Bader and Hirshfeld)have been implemented for different quantities involving electron density and gradients;(iii)these quantities have been applied to a number of chemical processes such as bonding/rotation,electrophilicity/nucleophilicity,etc.,(iv)interesting changing patterns for the atomic and molecular values of these quantities for different systems have been observed,and(v)they are remarkably strongly correlates with experimental scales of both electrophilicity and nucleophilicity.Based on these results,a new theoretical framework has been proposed to quantify reactivity properties and justify regioselectivity using the quantities from information theory.