Evaluation and Development of Quantum Chemical Methodologies for Noncovalent Interactions and Supramolecular Thermochemistry

Abstract

This thesis focuses on the application and development of electronic structure methods for noncovalent interactions in general and the evaluation of multilevel methodologies for an accurate description of supramolecular thermochemistry in particular. Noncovalent interactions are omnipresent in systems of various domains of science, such as supramolecular chemistry, structural biology, and surface science. Within supramolecular chemistry, host-guest complexes are of particular importance due to their diverse applicability in various fields like molecular recognition or self-assembly. <br /> The binding situation in a supramolecular complex is often unknown and sampling many different conformations is desired. Therefore, the first part of this thesis is concerned with cost-efficient density functional theory (DFT) and Hartree-Fock (HF) based electronic structure methods for noncovalent interactions, which are about a factor of 50 to 100 faster than calculations in a large basis set. <br /> The main errors in a DFT or HF calculation with small atomic orbital basis sets are the missing London dispersion and the basis set superposition error (BSSE). An exemplary benchmark study shows that modern correction strategies clearly outperform plain DFT or HF for energies and geometries of small dimers, large supramolecular complexes, and molecular crystals. Further, the development and evaluation of a minimal basis set Hartree--Fock method with three atom-pairwise corrections for London dispersion, BSSE, and basis set incompleteness (HF-3c) is presented. With nine global parameters, the empiricism of HF-3c is moderate, the method is self-interaction error free, and noiseless analytical frequencies can be obtained.<br /> HF-3c provides accurate geometries of organic supramolecular systems and small proteins, and good noncovalent interaction energies. The mean absolute deviations (MADs) for the S22 set of small noncovalently bound dimers and the S12L set of supramolecular host-guest association energies are 0.6 and 4.4 kcal mol^-1, respectively. This is excellent compared to dispersion corrected DFT methods whose MADs are in the range of 0.3-0.5 and 2-5 kcal mol^-1, respectively.<br /> The second part focuses on the application and evaluation of multilevel methodologies for an accurate description of Gibbs free energies of association (Δ G_a) for supramolecular host-guest complexes in solution. First, state-of-the-art dispersion corrected DFT (DFT-D3^ATM) is used together with a large quadruple-zeta (QZ) basis set to obtain association energies in the gas phase. A semiempirical method is utilized to compute the thermostatistical corrections from energy to free energy and last, a continuum solvation model is employed. <br /> The general procedure is illustrated with a case study on eight typical complexes. The SAMPL4 blind test challenge provides a unique opportunity to test this methodology in a realistic setting. Relative Δ G_a in water are predicted for a cucurbit[7]uril host and 14 guest molecules containing ammonia groups. The HF-3c method was employed to sample possible binding conformations and the final Δ G_a were calculated on the PW6B95-D3^ATM/QZ level with HF-3c thermal corrections and COSMO-RS solvation contributions. Compared to other methods theses predictions rank in the top three of all statistical measurements. The MAD and RMSD are only 2.0 and 2.6 kcal mol^-1, respectively.<br /> Further, the S30L benchmark set is proposed as an extension of the S12L set for association (free) energies of host-guest complexes. Larger systems with up to 200 atoms, more divers interaction motifs, and higher charges are represented by experimentally measured complexes with Δ G_a values in the range from -0.7 to -24.7 kcal mol^-1. In order to obtain a theoretical best estimate for Δ G_a different dispersion corrected density functionals, semiempirical methods, and continuum solvation models are tested. The best method combination is similar to the one used for the SAMPL4 bind test and yields an MAD with respect to experiment of only 2.4 kcal mol^-1. Inclusion of counterions for the charged systems (S30L-CI) were found to improve the results overall.<br /> Synergy between theory and experiment is demonstrated in the last part of this thesis with the application of quantum chemical methods to two specific chemical problems related to supramolecular chemistry.<br /> Experimentally, it was found that titanocene(III) catalysts can be stabilized by chloride additives and the calculations reveal that the stabilities of these adducts are determined by the extent of hydrogen bonding between the catalyst and the ammonium cation. <br /> 1,1'-Binaphthol based ligands can be used to obtain enantiomerically pure double- and triple-stranded helicates with transition-metal ions in a completely diastereoselective self-assembly process. Electronic circular dichroism spectra of precursors for paracyclophane based ligands have been investigated computationally in order to identify their absolute configuration.