Role of DG/dw and DV/dw in AIM Analysis: an Approach to the Nature of Weak to Strong Interactions

Role of dG(b)(r(c))/dw and dV(b)(r(c))/dw is revealed as the basic atoms-in-molecules (AIM) functions to evaluate, classify, and understand the nature of interactions, as well as G(b)(r(c)) and V(b)(r(c)). The border area between van der Waals (vdW) adducts and hydrogen-bonded (HB) adducts is shown to appear at around dG(b)(r(c))/dw = -dV(b)(r(c))/dw and that between molecular complexes (MC) and trigonal bipyramidal adducts (TBP) of chalcogenide dihalides appears at around 2dG(b)(r(c))/dw = -dV(b)(r(c))/dw. H(b)(r(c)) are plotted versus H(b)(r(c)) - V(b)(r(c))/2 at bond critical points (BCPs) in the AIM dual functional analysis. The plots incorporate the classification of interactions by the signs of ∇(2)ρ(b)(r(c)) and H(b)(r(c)). R [= (x(2) + y(2))(1/2)] corresponds to the energy for the interaction in question at BCPs, where (x, y) = (H(b)(r(c)), H(b)(r(c)) - V(b)(r(c))/2) and (x, y) = (0, 0) at the origin. The segment of lines for the plots (S) should correspond to energy, if the segment is substantially linear. The first derivative of S (dS) is demonstrated to be proportional to R. Relations between AIM functions, such as dV(b)(r(c))/dw, dG(b)(r(c))/dw, dH(b)(r(c))/d[H(b)(r(c)) - V(b)(r(c))/2], d(2)V(b)(r(c))/dw(2), d(2)G(b)(r(c))/dw(2), and d(2)H(b)(r(c))/d[H(b)(r(c)) - V(b)(r(c))/2](2), are also discussed. The results help us to understand the nature of interactions.