Predicting the cation–π binding of substituted benzenes: energy decomposition calculations and the development of a cation–π substituent constant

Abstract

This work proposes a new substituent constant, termed Π⁺, to describe cation–π binding using computational methods at the MP2(full)/6-311++G** level of theory with Symmetry Adapted Perturbation Theory (SAPT) calculations on selected cation–π complexes. The correlations between binding strength (E_bind or ΔH₂₉₈) and common parameters for describing cation–π binding (∑σ_m, ∑σ_p, ∑(σ_m + σ_p), or Θ_zz) are decent (r² between 0.79 and 0.90). SAPT calculations show that variations in the electrostatic (E_ele), exchange (E_exch), induction (E_ind), and dispersion (E_disp) component energies to the overall binding are almost entirely due to differences in arene–cation distances (d_Ar–cat). E_ele varies most with d_Ar–cat; however, E_ind seems to be the primary term responsible for the ∑σ_m, ∑σ_p, ∑(σ_m + σ_p) and Θ_zz parameters not accurately predicting the cation–π E_bind and ΔH₂₉₈ values. The Π⁺ parameter largely reflects electrostatics, but it also includes the impact of exchange, induction, and dispersion on cation–π binding of aromatics, and the resulting correlation between ΔH₂₉₈ or E_bind and Π⁺ is excellent (r² of 0.97 and 0.98, respectively). Importantly, the Π⁺ parameter is general to cation–π systems other than those reported here, and to studies where the cation–π binding strength is determined using computational levels different from those employed in this study.