Dispersion-Corrected Density Functional Theory for Aromatic Interactions in Complex Systems

Abstract

Aromatic interactions play a key role in many chemical and biological systems. However, even if very simple models are chosen, the systems of interest are often too large to be handled with standard wave function theory (WFT). Although density functional theory (DFT) can easily treat systems of more than 200 atoms, standard semilocal (hybrid) density functional approximations fail to describe the London dispersion energy, a factor that is essential for accurate predictions of inter- and intramolecular noncovalent interactions. Therefore dispersion-corrected DFT provides a unique tool for the investigation and analysis of a wide range of complex aromatic systems. In this Account, we start with an analysis of the noncovalent interactions in simple model dimers of hexafluorobenzene (HFB) and benzene, with a focus on electrostatic and dispersion interactions. The minima for the parallel-displaced dimers of HFB/HFB and HFB/benzene can only be explained when taking into account all contributions to the interaction energy and not by electrostatics alone. By comparison of saturated and aromatic model complexes, we show that increased dispersion coefficients for sp²-hybridized carbon atoms play a major role in aromatic stacking. Modern dispersion-corrected DFT yields accurate results (about 5–10% error for the dimerization energy) for the relatively large porphyrin and coronene dimers, systems for which WFT can provide accurate reference data only with huge computational effort. In this example, it is also demonstrated that new nonlocal, density-dependent dispersion corrections and atom pairwise schemes mutually agree with each other. The dispersion energy is also important for the complex inter- and intramolecular interactions that arise in the molecular crystals of aromatic molecules. In studies of hexahelicene, dispersion-corrected DFT yields “the right answer for the right reason”. By comparison, standard DFT calculations reproduce intramolecular distances quite accurately in single-molecule calculations while inter- and intramolecular distances become too large when dispersion-uncorrected solid-state calculations are carried out. Dispersion-corrected DFT can fix this problem, and these results are in excellent agreement with experimental structure and energetic (sublimation) data. Uncorrected treatments do not even yield a bound crystal state. Finally, we present calculations for the formation of a cationic, quadruply charged dimer of a porphyrin derivative, a case where dispersion is required in order to overcome strong electrostatic repulsion. A combination of dispersion-corrected DFT with an adequate continuum solvation model can accurately reproduce experimental free association enthalpies in solution. As in the previous examples, consideration of the electrostatic interactions alone does not provide a qualitatively or quantitatively correct picture of the interactions of this complex.