The nature of EH₂-*-π(C₁₄H₁₀) interactions (E = O, S, Se and Te) of an anthracene system was elucidated by applying QTAIM dual functional analysis (QTAIM-DFA) after clarification of the structural features with quantum chemical (QC) calculations. π-HB (hydrogen bond) interactions were detected for E = O, S, Se and Te, whereas π-EB (chalcogen bond) interactions were observed for E = O in (EH₂)-*-π(C₁₄H₁₀), where the bond paths connected H in EH₂ to C₁₄H₁₀ in π-HB, and they connected E in EH₂ to C₁₀H₈ in π-EB. The QTAIM-DFA parameters of (R, θ) and (θ_p, κ_p) were evaluated for the interactions via analysing the plots of H_b(r_c) versus H_b(r_c) − V_b(r_c)/2 for the interactions at the bond critical points. Data obtained from the perturbed structures around the fully optimized structures were employed for the plots, in addition to the fully optimized structures. Data obtained from the fully optimized structures were analysed using (R, θ), which corresponded to the static nature, and those obtained from the perturbed structures were analysed using (θ_p, κ_p), which represented the dynamic nature of the interactions, where θ_p corresponds to the tangent line of the plot and κ_p is the curvature. The θ and θ_p values are less than 90° for all the interactions examined, except for the ⁱH-*-¹¹C(π) interaction in TeH₂-*-C₁₄H₁₀ (C₁: IIB_Atc), where ⁱH is located closer to the centre of C₁₄H₁₀. Therefore, the interactions examined were predicted to have vdW nature, appeared in the pure-CS (closed shell) interaction region, although ⁱH-*-¹¹C(π) was predicted to have the pure-CS/typical-HB nature without covalency. Additionally, the π-HB interaction seems to be slightly stronger than π-EB in (OH₂)-*-π(C₁₄H₁₀).