Accurate Computation of Structures and Strain Energies of Cyclophanes with Modern DFT Methods

Four contemporary density functionals of meta-GGA, hybrid-GGA, meta-GGA-hybrid, and double-hybrid type connected with two versions of our recent dispersion correction (DFT-D3) are tested for the description of the geometric and electronic structures of typical cyclophanes. Strain energies (SE) as well as aromatic interaction energies (AIE) are considered. The systems [2.2]para- and [2.2]metacyclophane, [2.2.2.2.2.2]cyclophane, [2.2]paracyclonaphthane, [2.2](9,10)anthracenophane, and [2.2](1,4)anthracenophane are investigated. Computed structures are compared to experimental X-ray data. For the three smallest cyclophanes, accurate CCSD(T)/CBS reference SE and AIE values are computed to assess the accuracy of the DFT methods. It is found that medium-range dispersion (correlation) effects are important for all cyclophanes. Dispersion corrections in the BeckeJohnson damping (BJ) variant of the DFT-D3 method provide the most accurate results. The best density functionals yield relative (strain) energies accurate to within about 510?%. Inter-ring distances can be computed very accurately with errors less than about 0.003 angstrom while, for example, uncorrected B3LYP yields large average errors of almost 0.1 angstrom for this property. The PW6B95-D3(BJ) and TPSS-D3(BJ) general purpose quantum chemical methods overall perform best and can be recommended also for studies of cyclophanes. The strain energies are partitioned to chemically meaningful components and the effect of the crystal environment is discussed.