Intermolecular interactions involving aromatic pi-electron density are widely believed to be governed by the aromatic molecular quadrupole moment, Theta(zz). Arene-cation binding is believed to occur primarily with negative Theta(zz) aromatics, and arene-anion binding is believed to occur largely with positive Theta(zz) aromatics. We have performed quantum mechanical computations that show the cation binding of positive Theta(zz) aromatics and the anion binding of negative Theta(zz) aromatics is quite common in the gas phase. The pi-electron density of hexafluorobenzene, the prototypical positive Theta(zz) aromatic (experimental Theta(zz) = +9.5 +/- 0.5 D angstrom), has a Li+ binding enthalpy of -4.37 kcal/mol at the MP2(full)/6-311G** level of theory. The RHF/6-311G** calculated Theta(zz) value of 1,4-dicyanobenzene is +11.81 D angstrom, yet it has an MP2(full)/6-311G**Li+ binding enthalpy of -12.65 kcal/mol and a Na+ binding enthalpy of -3.72 kcal/mol. The pi-electron density of benzene, the prototypical negative Theta(zz) aromatic (experimental Theta(zz) = -8.7 +/- 0.5 D angstrom), has a F- binding enthalpy of -5.51 kcal/mol. The RHF/6-311G** calculated Theta(zz) of C6H2I4 is -10.45 D angstrom, yet it has an MP2(full)/6-311++G** calculated F- binding enthalpy of -20.13 kcal/mol. Our results show that as the aromatic Theta(zz) value increases the cation binding enthalpy decreases; a plot of cation binding enthalpies versus aromatic Theta(zz) gives a line of best of fit with R-2 = 0.778. No such correlation exists between the aromatic Theta(zz) value and the anion binding enthalpy; the line of best fit has R-2 = 0.297. These results are discussed in terms of electrostatic and polarizability contributions to the overall binding enthalpies.