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

Abstract

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.

Interpreting geometric preferences in π‐stacking interactions through molecular orbital analysis

“…Translation along the V‐PD coordinate is accompanied by conversion of the character of the antibonding π B − dimer MO to “bonding” at Bz 2 V‐PD ( R slip = 1.7 Å, Figure B) for an SBO of 2 and an attractive interaction. The inter‐ring density as measured by TWBI was maximized at this point in agreement with extrema in the DF‐DFT‐SAPT interaction energies and its components (ie, dispersion, electrostatics, and induction) . The combinations of the π B Bz MOs are involved in the dimer MOs that change character because its node is perpendicular to the V‐PD direction such that the overlap of the monomer lobes varies as the rings slip relative to one another.…”

“…However, these studies as yet do not provide an intuitive model of conformational preferences in p-stacking interactions that would allow for the prediction and design of materials.We have introduced qualitative molecular orbital (MO) analysis as a means to explain the preference for PD and twisted geometries (TW) over the S structure in p-stacked dimers in terms of the character of the dimer MOs as built from the constituent monomer MOs. [24] To paraphrase Coulson (p. 90, [25] ) the monomer MOs are used as building blocks to visualize the inter-ring density by breaking it down into linear combinations of the easier-to-understand monomer MOs to rationalize why the interactions prefer certain conformations. This intuitive Int J Quantum Chem.…”

“…Repulsions between these MOs are consistent with the longer inter-ring distances obtained in stacks constrained to S. When the rings are displaced or twisted, one or more of the p-type MOs convert from antibonding to nonbonding or bonding inter-ring character, leading to a non-zero SBO and a favorable interaction. [24] Note that the SBO is not equivalent to the bond orderno covalent bonds are impliedand the strength of the actual interaction will be proportional to the overlap of the densities of the rings.…”

Enhancement of the physicochemical properties of [Pt(dien)(nucleobase)]2+ for HIVNCp7 targeting

“…28,29 A combination of electrostatic, hydrophobic, solvation, charge-transfer, induction, and dispersion interactions accounts for the three-dimensional arrangements observed in biochemical recognition processes mediated through π-stacking interactions, such as the interaction of purine and pyrimidine rings with aromatic amino-acid residues such as tryptophan. 30–33 We have previously used the relative energy difference between the frontier orbitals of isolated molecules as a predictive tool for the strength of the π-stacking interaction of the nucleobase/tryptophan pair. 13 The analysis correlated well with experimental association constants, measured by fluorescence spectroscopy, of metallated (Pt, Pd) and methylated nucleobases with tryptophan in comparison to free nucleobases.…”

Hydrogen bonding and π–π interactions in imidazolium-chloride ionic liquid clusters

“…89,90 Moreover, qualitative molecular orbital (MO) analysis has been employed to understand πtype interactions. 55,91 QTAIM and NBO analysis has been reported for several ILs. These studies have focussed primarily on the H-bonding interactions between the cation-anion IPs and have been restricted to limited conformers with emphasis placed on the lowest energy conformer.…”