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 (Ebind or ΔH298) and common parameters for describing cation–π binding (∑σm, ∑σp, ∑(σm + σp), or Θzz) are decent (r2 between 0.79 and 0.90). SAPT calculations show that variations in the electrostatic (Eele), exchange (Eexch), induction (Eind), and dispersion (Edisp) component energies to the overall binding are almost entirely due to differences in arene–cation distances (dAr–cat). Eele varies most with dAr–cat; however, Eind seems to be the primary term responsible for the ∑σm, ∑σp, ∑(σm + σp) and Θzz parameters not accurately predicting the cation–π Ebind 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 Ebind 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.