Orbital-based insights into parallel-displaced and twisted conformations in π–π interactions

Dispersion and electrostatics are known to stabilize π-π interactions, but the preference for parallel-displaced (PD) and/or twisted (TW) over sandwiched (S) conformations is not well understood. Orbital interactions are generally believed to play little to no role in π-stacking. However, orbital analysis of the dimers of benzene, pyridine, cytosine and several polyaromatic hydrocarbons demonstrates that PD and/or TW structures convert one or more π-type dimer MOs with out-of-phase or antibonding inter-ring character at the S stack to in-phase or bonding in the PD/TW stack. This change in dimer MO character can be described in terms of a qualitative stack bond order (SBO) defined as the difference between the number of occupied in-phase/bonding and out-of-phase/antibonding inter-ring π-type MOs. The concept of an SBO is introduced here in analogy to the bond order in molecular orbital theory. Thus, whereas the SBO of the S structure is zero, parallel displacement or twisting the stack results in a non-zero SBO and overall bonding character. The shift in bonding/antibonding character found at optimal PD/TW structures maximizes the inter-ring density, as measured by intermolecular Wiberg bond indices (WBIs). Values of WBIs calculated as a function of the parallel-displacement are found to correlate with the dispersion and other contributions to the π-π interaction energy determined by the highly accurate density-fitting DFT symmetry adapted perturbation theory (DF-DFT-SAPT) method. These DF-DFT-SAPT calculations also suggest that the dispersion and other contributions are maximized at the PD conformation rather than the S when conducted on a potential energy curve where the inter-ring distance is optimized at fixed slip distances. From these results of this study, we conclude that descriptions of the qualitative manner in which orbitals interact within π-stacking interactions can supplement high-level calculations of the interaction energy and provide an intuitive tool for applications to crystal design, molecular recognition and other fields where non-covalent interactions are important.