What Is Special about Aromatic-Aromatic Interactions? Significant Attraction at Large Horizontal Displacement

Abstract

High-level ab initio calculations show that the most stable stacking for benzene-cyclohexane is 17% stronger than that for benzene-benzene. However, as these systems are displaced horizontally the benzene-benzene attraction retains its strength. At a displacement of 5.0 Å, the benzene-benzene attraction is still ∼70% of its maximum strength, while benzene-cyclohexane attraction has fallen to ∼40% of its maximum strength. Alternatively, the radius of attraction (>2.0 kcal/mol) for benzene-benzene is 250% larger than that for benzene-cyclohexane. Thus, at relatively large distances aromatic rings can recognize each other, a phenomenon that helps explain their importance in protein folding and supramolecular structures.

Figure 1

Areas in which attractive interaction energy is larger than −2.0 kcal/mol for benzene–benzene (left) and benzene–cyclohexane (right).

Figure 2

Geometric parameters used in calculations of benzene–benzene and cyclohexane–benzene interactions. Ω_a and Ω_b denote benzene or cyclohexane ring centers. R denotes distance between parallel mean planes of the rings, while Ω_b′ are benzene and cyclohexane ring centers projections onto the benzene rings planes; r denotes displacement of the second ring projection on the benzene.

Figure 3

Calculated interaction energies averaged over the three possible orientations and two directions for cyclohexane–benzene and benzene–benzene (Figures S1 and S2) plotted as a function of the displacement (r) (Figure 1).

Figure 4

(a) Parallel benzene–benzene interaction with a large offset (r = 4.81 Å) in the crystal structure of EREYUV. Both benzene molecules, involved in parallel interaction, also form CH/π and stacking interactions on both sides of the rings with molecules from the environment. (b) Histogram of the offset values r for phenyl–cyclohexyl (blue, left bars) and benzene–benzene (orange, right bars) interactions. N is the number of interactions.

Figure 5

Results of SAPT analysis and CCSD(T)/CBS calculations for (a) benzene–benzene and (b) cyclohexane–benzene at several offset values. All interaction energies and selected energy components are average (Tables 1 and 2) and given in kcal/mol.

Figure 6

Overlaid electrostatic potentials for benzene–benzene and cyclohexane–benzene interactions at 5.0 Å. Electrostatic potentials for cyclohexane and benzene were plotted on a contour with an electron density of 0.001 e^–/(a.u.).