Ab initio studies on the van der Waals complexes of polycyclic aromatic hydrocarbons. II. Naphthalene dimer and naphthalene–anthracene complex

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Abstract
Ab initio calculations were carried out for the naphthalene dimer and naphthalene–anthracene complex to determine their stable geometries and binding energies. Two medium-size basis sets of 6-31 G * (0.25) and 6-31+ G * were employed at the MP2 level. Five local minima were found for the naphthalene dimer, three of which were parallel-displaced type and the other two T-shaped type. The global minimum geometry was a parallel-displaced structure of a two-layer graphitic type (C i point group), not the crossed form (D 2d ). Its energy calculated by the 6-31 G * (0.25) and 6-31+ G * basis sets was −7.62 and −6.36 kcal/mol, respectively. The naphthalene–anthracene complex showed four local minima, two of which were parallel-displaced type and the other two T-shaped type. The global minimum was a twisted parallel-displaced form (C 2 ), in which the centers of both molecules lie on the same z-axis with their two long axes skewed at an angle of ≈40°. Its energy was −11.30 and −9.52 kcal/mol with the 6-31 G * (0.25) and 6-31+ G * basis sets, respectively. From these results a set of general rules for the stable geometry of the polycyclic aromatic hydrocarbon clusters were derived, which turned out to be the same as those previously deduced from other systems less directly relevant to polycyclic aromatic hydrocarbons: (1) a face-to-face configuration is unstable, (2) the T-shaped structure is stable, (3) the parallel-displaced structure is also stable. We also found some additional rules: (4) the energies of the T-shaped and parallel-displaced structures are quite comparable when the molecules are small, but (5) the parallel-displaced structure becomes more stable than the T-shaped one as the molecules become larger due to the nature of the π–π interaction. The interplanar distance of stable parallel-displaced structures was about 3.3–3.4 Å, while the plane-to-center distances of T-shaped structures was about 5.0–5.1 Å. We also discovered what we would call the integer rule for the binding energy of the polycyclic aromatic hydrocarbon clusters in that the binding energy varied linearly as the number of overlapping hexagons in the parallel-displaced structures. The ratio of binding energies for the benzene dimer, benzene–naphthalene complex, naphthalene dimer, and naphthalene–anthracene complex were nearly 1:2:3:4.