Dynamic and static behavior of the H⋯π and E⋯π interactions in EH2 adducts of benzene π-system (E = O, S, Se and Te), elucidated by QTAIM dual functional analysis

Abstract

Dynamic and static behavior of the interactions in the EH₂ adducts of a benzene π-system (E = O, S, Se and Te) is elucidated by applying QTAIM-DFA (QTAIM dual functional analysis). Two types of H-*-π and E-*-π interactions are detected in the adducts, where the asterisk (*) emphasizes the existence of the bond critical point (BCP) on the interaction in question. Total electron energy densities H_b(r_c) are plotted versus H_b(r_c) − V_b(r_c)/2 [=(ℏ²/8m)∇²ρ_b(r_c)] at BCPs in QTAIM-DFA, where V_b(r_c) are the potential energy densities at BCPs. Data from the fully optimized structures are analyzed by polar (R, θ) coordinate representation. Each plot for an interaction, containing data from the perturbed structures with those of the fully optimized one, shows a specific curve, which provides important information. The plot is expressed by (θ_p, κ_p): θ_p corresponds to the tangent line for the plot and κ_p is the curvature. θ and θ_p are measured from the y-axis and y-direction, respectively. Moreover, (R, θ) corresponds to the static nature, (θ_p, κ_p) represents the dynamic nature of interactions. While θ classifies the interaction in question, θ_p characterizes it. Both values are less than 90° for all H-*-π and E-*-π interactions examined in this study; therefore, they are all classified by the pure closed-shell interactions and predicted to have the character of vdW nature. However, it is suggested that E-*-π has the nature of the stronger interaction than the case of H-*-π for dynamic behavior in the same species evaluated at the MP2 and M06-2X levels. The nature of the interactions is well analyzed and specified by applying QTAIM-DFA.