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The formation of "Russian doll" complexes consisting of [n]cycloparaphenylenes was predicted using quantum chemistry tools. The electronic structures of multiple inclusion complexes containing up to four macrocycles were explored at the M06-2X/6-31G* level of theory. The binding energy between the macrocycles increases from the center to the periphery of the complex and can be >60 kcal mol(-1) for macrocycles containing 14 and 19 repeating units. It has been demonstrated that additional electrostatic interactions originating from the asymmetric electron density distribution observed when comparing the concave and convex macrocycle sides are responsible for the high binding energies in these Russian doll complexes. Oxidation or reduction of the Russian doll complexes creates polarons that are delocalized across the complexes. In the case of polaron cations, most of the polarons are localized at the macrocycle with the smallest ionization potential; for polaron anions, the negative charge is localized across the outer rings of the complex. Because anion polarons are more delocalized than cation polarons, the relaxation energies of the polaron anions were found to be smaller than those of the polaron cations.

The geometries of neutral, mono-, and dioxidized tubular aggregates of cyclo[8]thiophenes containing up to 5 repeating units were fully optimized at the MPWB1K/3-21G* level of theory. Calculated interplane distances between macrocycles were found to be close to 3.1 A for neutral and charged aggregates. The binding energies between macrocycles in neutral intermediates were in the range of 40-45 kcal/mol, increasing for monocations and dropping strongly for dicationic species due to electrostatic repulsion between polarons. It was established that there exists a noticeable interaction between pi-orbitals of individual macrocycles in tubular aggregates as follows from decreasing of the band gap with a number of repeating units in aggregates and the polaron delocalization toward tube axes in oxidized species. A polaron pair is the most stable dicationic state for all studied molecules according to the calculations. A singlet polaron pair is more stable than a triplet one. The energy difference between singlet and triplet states is growing smaller with the size of the system, becoming zero for the pentamer corresponding to a completely dissociated bipolaron.

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Benzene, pyrimidine, and naphthalene dimers have been studied at canonical MP2, LMP2, and MP4(SDTQ) levels of theory. It has been shown that the LMP2 method is superior to canonical MP2 due to reduced BSSE. Thus, basis set limit-extrapolated LMP2 binding energies of T-shaped and parallel displaced (PD) benzene dimers are nearly the same, as has been found in higher level ab initio calculations. MP4(SDTQ) binding energies calculated at LMP2 optimized geometries are always more negative than those calculated for MP2-optimized geometries. MP4(SDTQ)/CC-pVDZ-corrected complete basis set-extrapolated LMP2 binding energies of T-shaped and PD dimers of benzene and naphthalene were found to be -2.80, -2.59 and -4.39, -6.29 kcal/mol, respectively.