Atoms-in-Molecules Dual Parameter Analysis of Weak to Strong Interactions: Behaviors of Electronic Energy Densities versus Laplacian of Electron Densities at Bond Critical Points

Abstract

AIM dual parameter analysis is proposed for the better understanding of weak to strong interactions: Total electron energy densities (H(b)(r(c))) are plotted versus Laplacian of electron densities (Delta rho(b)(r(c))) at bond critical points (BCPs). Interactions examined in this work are those in van der Waals adducts, hydrogen bonded complexes, molecular complexes and hypervalent adducts through charge transfer (CT) interactions, and some classical covalent bonds. Data calculated at BCPs for the optimized distances (r(o)), together with r(o) - 0.1 A, r(o) + 0.1 A, and r(o) + 0.2 A, are employed for the plots. The plots of H(b)(r(c)) versus Delta rho(b)(r(c)) start from near origin (H(b)(r(c)) = Delta rho(b)(r(c)) = 0) and turn to the right drawing a helical stream as a whole. The helical nature is demonstrated to be controlled by the relative magnitudes of kinetic energy densities (G(b)(r(c))) and potential energy densities (V(b)(r(c))), where G(b)(r(c)) + V(b)(r(c)) = H(b)(r(c)). Requirements for the data to appear in the specified quadrant are clarified. Points corresponding to the data will appear in the first quadrant (Delta rho(b)(r(c)) > 0 and H(b)(r(c)) > 0) when -V(b)(r(c)) < G(b)(r(c)), they drop in the forth one (Delta rho(b)(r(c)) > 0 and H(b)(r(c)) < 0) if -(1/2)V(b)(r(c)) < G(b)(r(c)) < -V(b)(r(c)), and they appear in the third quadrant (Delta rho(b)(r(c)) < 0 and H(b)(r(c)) < 0) when G(b)(r(c)) < -(1/2)V(b)(r(c)). No points will appear in the second quadrant (Delta rho(b)(r(c)) < 0 and H(b)(r(c)) > 0). The physical meanings of the plots proposed in this work are also considered. The helical nature of the interactions in the plots helps us to understand the interactions in a unified way.