Comprehensive Benchmark of Association (Free) Energies of Realistic Host–Guest Complexes


The S12L test set for supramolecular Gibbs free energies of association Δ<i>G</i><sub><i>a</i></sub> (Grimme, S. Chem. Eur. J. 2012, 18, 9955−9964) is extended to 30 complexes (S30L), featuring more diverse interaction motifs, anions, and higher charges (−1 up to +4) as well as larger systems with up to 200 atoms. Various typical noncovalent interactions like hydrogen and halogen bonding, π–π stacking, nonpolar dispersion, and CH−π and cation–dipolar interactions are represented by “real” complexes. The experimental Gibbs free energies of association (Δ<i>G</i><sub><i>a</i></sub><sup><i>exp</i></sup>) cover a wide range from −0.7 to −24.7 kcal mol<sup>–1</sup>. In order to obtain a theoretical best estimate for Δ<i>G</i><sub><i>a</i></sub>, we test various dispersion corrected density functionals in combination with quadruple-ζ basis sets for calculating the association energies in the gas phase. Further, modern semiempirical methods are employed to obtain the thermostatistical corrections from energy to Gibbs free energy, and the COSMO-RS model with several parametrizations as well as the SMD model are used to include solvation contributions. We investigate the effect of including counterions for the charged systems (S30L-CI), which is found to overall improve the results. Our best method combination consists of PW6B95-D3 (for neutral and charged systems) or ωB97X-D3 (for systems with counterions) energies, HF-3c thermostatistical corrections, and Gibbs free energies of solvation obtained with the COSMO-RS 2012 parameters for nonpolar solvents and 2013-fine for water. This combination gives a mean absolute deviation for Δ<i>G</i><sub><i>a</i></sub> of only 2.4 kcal mol<sup>–1</sup> (S30L) and 2.1 kcal mol<sup>–1</sup> (S30L-CI), with a mean deviation of almost zero compared to experiment. Regarding the relative Gibbs free energies of association for the 13 pairs of complexes which share the same host, the correct trend in binding affinities could be reproduced except for two cases. The MAD compared to experiment amounts to 1.2 kcal mol<sup>–1</sup>, and the MD is almost zero. The best-estimate theoretical corrections are used to back-correct the experimental Δ<i>G</i><sub><i>a</i></sub> values in order to get an empirical estimate for the “experimental”, zero-point vibrational energy exclusive, gas phase binding energies. These are then utilized to benchmark the performance of various “low-cost” quantum chemical methods for noncovalent interactions in large systems. The performance of other common DFT methods as well as the use of semiempirical methods for structure optimizations is discussed

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