Development and Application of Quantum Mechanical Tight-Binding Methods for the Exploration of Chemical Space

Abstract

This thesis centrally focuses on the systematic exploration of the so-called "chemical space" using fast quantum chemical methods. In computational chemistry any calculation requires a detailed knowledge about a molecules spatial three-dimensional structure which defines the potential energy surface (PES). The prediction of molecular properties is therein directly linked to the populated (local) minima on the PES for a given connectivity. Because finding these minima requires a systematic sampling of the PES, the use of conventional quantum mechanical (QM) methods is often prohibitively expensive and other methodologies have to be pursued. The reason for this can easily be seen for typical molecules up to a size of roughly 200 atoms, where thousands to millions of energy evaluations are required to thoroughly explore the PES. One of the few suitable schemes for this are extended tight-binding (xTB) methods, which are derived from ab initio density functional theory (DFT) and introduce semiempirical approximations to accelerate calculations. <br /> The combination of semiempirical quantum mechanical (SQM) calculations at the xTB levels with automatized sampling workflows and sophisticated sorting procedures led to the development of a computer code called CREST, to which major parts of this thesis are dedicated. As implied by the name CREST, an abbreviation for conformer-rotamer ensemble sampling tool, this program was initially introduced as a procedure to identify molecular conformers, but now adapts procedures for the screening of other representatives of the low-energy chemical space such as protonation sites and tautomers. The automated sampling procedures in CREST profit from the use of the so-called GFNn-xTB methods, purpose specific xTB schemes that are parametrized for all elements up to radon (Z ≤ 86). It is shown that CREST and GFNn-xTB can be employed to a wide variety of chemical systems, including drug like molecules and polypeptides, organometallic compounds, transition state conformers and small molecular clusters. Due to a high robustness of the calculations and low computational times, the program is a sophisticated foundation in multilevel approaches for the calculation of molecular properties. <br /> In an extension to the basic capabilities of CREST, a connection to a fundamental thermostatistical property, the entropy, is established. For molecules, the entropy describes a temperature dependent energy measure for the internal molecular degrees of freedom (DOF). It is commonly associated with a state of disorder and is usually obtained from partition functions for molecular motions (vibrations) in a rigid-rotor harmonic-oscillator (RRHO) approximation. In the respective chapter of this thesis, the often missing conformational dependence in typical QM calculations of the entropy is investigated, which can be obtained from partition functions for the conformer ensemble. The problem herein is that a detailed knowledge of the (full) conformational space is required for these contributions to the entropy and so far no generally applicable procedures existed for their calculation. A revised workflow of the CREST conformational sampling procedure is presented that provides an automated and numerically stable algorithm for the treatment of conformational entropies of flexible molecules. From thermodynamic expressions closely related to the entropy also conformational molecular heat capacities are obtained. Both quantities are benchmarked in comparison with experimental data and the computational robustness of the procedure is tested for large, flexible molecules up to roughly 100 atoms. Furthermore, the significance of the conformational terms is exemplified for some prototypical chemical reactions. <br /> The last part of this thesis is devoted to the applications of low cost DFT, GFNn-xTB and CREST for calculation of gas-phase infrared (IR) spectra and acid dissociation constants (pKa). Vibrational spectroscopy such as IR spectroscopy is used to characterize molecules and can identify unknown compounds when supplemented with other experiments or theoretical calculations. Theoretical IR spectra are obtained in a harmonic approximation from second derivatives of the energy and first derivatives of the molecular dipole moment with respect to nuclear positions, respectively, providing the vibrational frequencies and IR intensities. In comparison with over seven thousand experimental gas-phase IR spectra the performance of GFNn-xTB and the composite DFT method B3LYP-3c is evaluated. It is found that B3LYP-3c as a representative of DFT provides excellent, almost quantitative predictions of IR spectra. GFNn-xTB also shows reasonable accuracy and much better performance than force field or competitor SQM methods. Furthermore, an empirical correction of vibrational frequencies based on modification of atomic masses is introduced and conformational effects are studied by the use of CREST. <br /> Acid dissociation constants are obtained from the eponymous acid dissociation reaction of molecules in solution and the associated Gibbs free energies. These energies are calculated using QM total energies from DFT or SQM, solvation free energies from implicit solvation models and free energy contributions from GFNn-xTB vibrational frequencies. By fitting empirical parameters of free energy relationship to experimental reference values a generally applicable and efficient composite protocol for the calculation of pKa values is formulated. It is found that rather independently of the underlying DFT method errors below one pKa unit can be achieved for flexible drug like molecules, but a strong conformational dependence is observed. CREST is herein used to identify (de-)protonation sites and to sample conformers. pKa values calculated entirely at the GFNn-xTB level typically do not reach this accuracy and require corrections for heterolytic dissociation free energies. However, due to the low computational cost and high generalizability, they are still useful for pKa pre-screening applications. <br /> In summary, this thesis provides a broadly applicable framework for computational studies of conformational effects and other representatives of the low-energy chemical space. The CREST program is already being used by several computational chemistry groups, but due to sophisticated automatization and robustness of calculations is also aimed at the general chemistry community.