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