Article pubs.acs.org/JPCA
Properties of Complexes Formed by Na+, Mg2+, and Fe2+ Binding with Benzene Molecules Sujitha Kolakkandy,† Subha Pratihar,† Adelia J. A. Aquino,† Hai Wang,‡ and William L. Hase*,† †
Department of Chemistry and Biochemistry, Texas Tech University, Lubbock, Texas 79409, United States Department of Mechanical Engineering, Stanford University, Stanford, California 94305, United States
‡
S Supporting Information *
ABSTRACT: A theoretical investigation was performed to study cation−π interactions in complexes of benzene (Bz) with cations, that is, Mz+(Bz)n for Mz+ = 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 complex’s structure. All of the Mz+(Bz) complexes prefer a half-sandwich geometry. A geometry with the cation sandwiched between the two benzene rings was found for the Mz+(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 Mz+(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 former’s 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.
I. INTRODUCTION
Overwhelming experimental evidence shows that the dominant molecular species in small carbon particles extracted from flames start from three- to four-ring aromatics and extend to sizes somewhere beyond coronene.20−25 Molecular dynamics simulations of pyrene dimerization at 1600 K were carried out by Schuetz and Frenchlach.26 They proposed that pyrene dimerization is possible at flame conditions, and the lifetime and collision frequency for the dimers are sufficiently large that they can survive long enough to form carbon nuclei in high temperature flames. However, this suggestion is not supported by later studies. A combined experimental and theoretical investigation of pyrene dimerization and nucleation was performed by Sabbah et al.27 The results of their study indicated that pyrene dimerization cannot be a key step in soot formation, since the equilibrium for the dimerization at high temperatures favors dissociation of the weakly bonded complex due to the low concentration of pyrene in the flame environment. This result is supported by molecular dynamics simulations,27 which indicate that the free energy barrier for pyrene association favors dissociation of the resulting dimer.
Particulate carbon formation, during gas-phase high-temperature hydrocarbon pyrolysis and oxidation, is a common phenomenon.1 However, the particle inception step of carbon formation is not well understood, though it is widely accepted that polyaromatic hydrocarbon (PAH) molecules are precursors for carbon formation.1−4 Conceptually PAH molecules may aggregate, forming clusters as precursors to soot,4 and experimental and computational binding energies for benzene, naphthalene, pyrene, and coronene dimers are summarized in Table 1.5−16 In general, the dispersive and electrostatic interaction is weak, and even for a larger system, like the coronene dimer, this interaction only gives rise to a relatively small binding energy (
