Supramolecular Binding Thermodynamics by Dispersion-Corrected Density Functional Theory

The equilibrium association free enthalpies ?Ga for typical supramolecular complexes in solution are calculated by ab initio quantum chemical methods. Ten neutral and three positively charged complexes with experimental ?Ga values in the range 0 to -21 kcal?mol-1 (on average -6 kcal?mol-1) are investigated. The theoretical approach employs a (nondynamic) single-structure model, but computes the various energy terms accurately without any special empirical adjustments. Dispersion corrected density functional theory (DFT-D3) with extended basis sets (triple-? and quadruple-? quality) is used to determine structures and gas-phase interaction energies (?E), the COSMO-RS continuum solvation model (based on DFT data) provides solvation free enthalpies and the remaining ro-vibrational enthalpic/entropic contributions are obtained from harmonic frequency calculations. Low-lying vibrational modes are treated by a free-rotor approximation. The accurate account of London dispersion interactions is mandatory with contributions in the range -5 to -60 kcal?mol-1 (up to 200?% of ?E). Inclusion of three-body dispersion effects improves the results considerably. A semilocal (TPSS) and a hybrid density functional (PW6B95) have been tested. Although the ?Ga values result as a sum of individually large terms with opposite sign (?E vs. solvation and entropy change), the approach provides unprecedented accuracy for ?Ga values with errors of only 2 kcal?mol-1 on average. Relative affinities for different guests inside the same host are always obtained correctly. The procedure is suggested as a predictive tool in supramolecular chemistry and can be applied routinely to semirigid systems with 300400 atoms. The various contributions to binding and enthalpyentropy compensations are discussed.