Quantum Calculations of Anion-Benzene Interactions

The DFT and MP2 calculations were carried out using the Gaussian 09 program.⁴² The hybrid density functional ωB97X-D/6-31+G(d,p),^{43 (link)} which includes empirical dispersion corrections, was used for geometry optimizations and to calculate the interaction energies. This method was also featured in a recent, extensive study of anions interacting with benzenoid surfaces.^{28 (link)} Subsequently, MP2/6-311G(d,p) energies were obtained from single-point calculations on the ωB97X-D geometries.^{44 –47} The corresponding calculations with the OPLS-AA⁷ and OPLS-AAP^{13 –15 (link)} force fields were carried out with the MCPRO program.^{41 (link)} The OPLS-AA parameters for aromatic hydrocarbons were used;³¹ specifically, carbon atoms with attached hydrogen atoms have a partial charge q_C = −0.115 e and Lennard-Jones parameters σ_CC = 3.55 Å and ε_CC = 0.07 kcal/mol, while the corresponding parameters for the hydrogen atoms are q_H = +0.115 e, σ_CH = 3.55 Å, and ε_CH = 0.07 kcal/mol. All other carbons are uncharged Lennard-Jones particles with σ_CC = 3.55 Å and ε_CC = 0.07 kcal/mol. Standard OPLS-AA parameters were used for chloride ion, potassium ion, and TIP3P and TIP4P water.^{48 ,49} The polarizable OPLS-AAP force field is obtained from OPLS-AA by adding inducible dipoles, μ_i = α_iE^q_i, which are calculated for each non-hydrogen atom i in the presence of the electric field E^q_i generated by the permanent charges. The polarization energy is then given by E_pol = −(1/2)Σμ_i·E^q_i. For aromatic carbon atoms, α_C was assigned as 1.0 Å^3.14