Properties of complexes formed by Na⁺, Mg²⁺, and Fe²⁺ binding with benzene molecules

A theoretical investigation was performed to study cation-π interactions in complexes of benzene (Bz) with cations, that is, M^z+(Bz)_n for M^z+ = Na⁺, Mg²⁺, Fe²⁺ and n = 1-3, using MP2 theory with the 6-31+G∗ and 6-311++G ∗ basis sets and the DFT/(B3LYP and B3LYP-D)/6-311++G ∗ methods. Binding energies and structures of the complexes are reported. The splitting between the quintet and single states of the Fe²⁺ complexes was found to depend on the number of benzene molecules in the complex and the complexs structure. All of the M^z+(Bz) complexes prefer a half-sandwich geometry. A geometry with the cation sandwiched between the two benzene rings was found for the M^z+(Bz)₂ complexes, with the benzene rings either in an eclipsed or staggered conformation. An approximate cyclic structure, with the cation at its center, was found for three benzene molecules interacting with the cation. The cation-benzene binding energy is substantial and equal to 22, 108, and 151 kcal/mol for the Na⁺(Bz), Mg²⁺(Bz), and Fe²⁺(Bz) complexes, respectively. The strength of the interaction of the cation with an individual benzene molecule decreases as the number of benzene molecules bound to the cation increases; for example, it is 108 kcal/mol for Mg²⁺(Bz), but only 71 kcal/mol for Mg²⁺(Bz)₃. There is a range of values for the M^z+(Bz)_n intermolecular vibrational frequencies; for example, they are ∼230-360 and ∼10-330 cm^-1 for the Mg²⁺(Bz) and Mg²⁺(Bz)₃ complexes, respectively. Binding of the cation to benzene both red and blue shifts the benzene vibrational frequencies. This shifting is larger for the Mg²⁺ and Fe²⁺ complexes, as compared to those for Na⁺, as a result of the formers stronger cation-benzene binding. The present study is an initial step to understand the possible importance of cation-π interactions for polycyclic aromatic hydrocarbon aggregation processes during soot formation.