Contribution of Different Crystal Packing Forces in π-Stacking: From Noncovalent to Covalent Multicentric Bonding

The present review is aimed to compare crystal packing interactions contributing to stacking arrangements of primarily nonaromatic systems referring only briefly to classical aromatic stacking. The classical aromatic stacking is mainly based on weak dispersion interactions (E <= 1 kcal mol (-1)) whereas heteroaromatics reveal more electrostatic (or specifically dipolar) contributions (E = 5-10 kcal mol(-1)). Based mainly on our charge density studies and DFT calculations, the results show that (i) all planar rings stack, regardless of aromaticity (or delocalization of pi electrons) and (ii) stacking interactions cover a wide continuum ranging from weak, mainly dispersion interactions (E < 5 kcal mol(-1)) to unlocalized two-electron multicentric (2e/mc) covalent bonds ("pancake bonds", E > 15 kcal mol -1 ). Our recent studies showed that quinones form face-to-face stacks and the energies of interactions exceed 10 kcal mol(-1); ours and other authors' results indicate that interactions between planar radicals involve a significant contribution of covalent bonding. Thus, pi-interactions cover a broad range of energies, ranging from <= 1 to >= 20 kcal mol(-1), and the interactions span from weak dispersion to multicentric covalent bonding. Therefore, development of a universal model of stacking is needed. In this respect, stacking can be compared to hydrogen bonding, which also ranges between dispersion (weakest hydrogen bonds, such as C-H center dot center dot center dot S and C-H center dot center dot center dot Cl) and two-electron/three-centric covalent bonding (the strongest "symmetrical" hydrogen bonds).