Atoms-in-Molecules Dual Functional Analysis of Weak to Strong Interactions

Atoms-in-molecules (AIM) dual functional analysis is reviewed after brief introduction of AIM. Total electron energy densities (Hb(rc)) are plotted versus Laplacian of electron densities (▽2ρb(rc)) at bond critical points (BCPs). The plots draw a helical stream as a whole. For the better understanding of weak to strong interactions, polar coordinate (R, o) representation is employed for the plot of Hb(rc) versus (ħ2/8m)▽2ρb(rc). Both x- and y-axes are expressed in the common unit of energy in this treatment: Hb(rc) = Gb(rc) + Vb(rc) and (ħ2/8m)▽2ρb(rc) = Hb(rc) - Vb(rc)/2 where Gb(rc) and Vb(rc) are kinetic energy densities and potential energy densities, respectively. Interactions examined are those in van der Waals adducts, hydrogen bonded complexes, molecular complexes and hypervalent adducts through charge-transfer, and some classical covalent bonds. Data employed for the plots are calculated at BCPs for full-optimized structures and optimized structures with the fixed distances r around the full-optimized distances, ro: r = ro + wao where ao is the Bohr radius with w = ±0.1 and ±0.2. The helical stream is well described by (R, o): R is given in the energy unit and o in degree is measured from the y-axis. The ratio of Vb(rc)/Gb(rc) (= k) controls o of which acceptable range is 45.0° > o > 206.6°. Each plot for an interaction gives a curve, which supplies important information. It is expressed by op and κp: op corresponds to the tangent line measured from the ydirection and κp is the curvature of the plot at w = 0. The treatment enables us to classify, evaluate, and understand well the weak to strong interactions.