The β-cyclodextrin/benzene complex and its hydrogen bonds – a theoretical study using molecular dynamics, quantum mechanics and COSMO-RS

Four highly ordered hydrogen-bonded models of β-cyclodextrin (β-CD) and its inclusion complex with benzene were investigated by three different theoretical methods: classical quantum mechanics (QM) on AM1 and on the BP/TZVP-DISP3 level of approximation, and thirdly by classical molecular dynamics simulations (MD) at different temperatures (120 K and 273 to 300 K). The hydrogen bonds at the larger O2/O3 rim of empty β-CDs prefer the right-hand orientation, e.g., O3-H(…)O2-H in the same glucose unit and bifurcated towards (…)O4 and O3 of the next glucose unit on the right side. On AM1 level the complex energy was −2.75 kcal mol(−1) when the benzene molecule was located parallel inside the β-CD cavity and −2.46 kcal mol(−1) when it was positioned vertically. The AM1 HOMO/LUMO gap of the empty β-CD with about 12 eV is lowered to about 10 eV in the complex, in agreement with data from the literature. AM1 IR spectra displayed a splitting of the O–H frequencies of cyclodextrin upon complex formation. At the BP/TZVP-DISP3 level the parallel and vertical positions from the starting structures converged to a structure where benzene assumes a more oblique position (−20.16 kcal mol(−1) and −20.22 kcal mol(−1), resp.) as was reported in the literature. The character of the COSMO-RS σ-surface of β-CD was much more hydrophobic on its O6 rim than on its O2/O3 side when all hydrogen bonds were arranged in a concerted mode. This static QM picture of the β-CD/benzene complex at 0 K was extended by MD simulations. At 120 K benzene was mobile but always stayed inside the cavity of β-CD. The trajectories at 273, 280, 290 and 300 K certainly no longer displayed the highly ordered hydrogen bonds of β-CD and benzene occupied many different positions inside the cavity, before it left the β-CD finally at its O2/O3 side.