New insights into the use of (TD-)DFT for geometries and electronic structures of constrained pi-stacked systems: [n.n]paracyclophanes.

We have evaluated the performance of three (TD-)DFT functionals with the 6-31+G(d,p) basis set for the reproduction of experimental geometries, vertical ionization potentials, and low excitation energies of a selection of [2.2] and [3.3]paracyclophanes. Overall, (TD-)BH&H outperforms both (TD-)B3LYP and (TD-)PBE0. Some shortcomings are shown by B3LYP for geometries and by BH&H for ionization potentials. Most notably, whereas TD-B3LYP and TD-PBE0 reproduce the wavelength for the first electronic excitation of [n.n]paracyclophanes with weakly interacting aromatic rings, neither handles the strong donor-acceptor interactions in certain substituted [n.n]paracyclophanes, and both seriously underestimate the energy for their first electronic excitation. As the former systems are in many ways similar to stacked nucleic acid bases, we recommend the use of (TD-)PBE0/6-31+G(d,p) for further studies on pi-stacking interactions in constrained systems, such as the base pairs in oligonucleotides.