Investigation and Development of Quantum Chemical Solvation Models

Abstract

The main topic of this thesis is the investigation and development of quantum chemical solvation models. In combination with modern quantum chemical methods, these models can predict various molecular properties for complex and chemically diverse systems in solution. A special focus lies thereby on the creation and application of automatic multi-level workflows to combine various levels of theory for an efficient and accurate calculation that is readily usable even by non-expert users. These multi-level workflows use carefully chosen combinations of semi-empirical methods for cheap screening in combination with higher-level quantum chemical methods to yield an accurate prediction for all parts of the free energy. The computed free energy, in turn, can be used to calculate molecular properties, like partition coefficients or vapor pressures from thermodynamic relationships. To give a full picture of this topic, Chapter 2 of this thesis will cover the fundamental theory behind the calculation of the total free energy. The total free energy thereby includes the electronic energy, which describes the energy of a molecule in the gas phase at a temperature of 0 K, but also additional contributions to account for finite temperature and conformational effects. Finally, the theory behind implicit solvation models, which are used to approximate solvent-solute interactions in a computationally efficient way, will be briefly introduced. Chapters 3 and 4 will deal with the application of an automated multi-level workflow for environmentally relevant and other highly complex systems (e.g., frustrated Lewis pairs), which are largely dominated by non-covalent interactions. <br /> While most of the contributions to the free energy are already rather accurate, or (in the case of electronic structure theory) at least systematically improvable, solvation contributions can still be a major source of error. Because solvation effects can have a large impact on both, the final energy, as well as the molecular structure of a system, an accurate and robust solvation description is important in all parts of a multi-level workflow, even for the cheap screening parts. <br /> This thesis will, therefore, propose different approaches to improve the accuracy of solvation models used on all levels of theory. Chapter 5 will introduce a post-SCF solvation model for semi-empirical methods based on an efficient implementation of a polarizable continuum model (PCM) into the xTB program package. The calculated results are then post-processed by a combination of literature-known approaches. This combined method yields a significant improvement of the solvation description on the "low-level" side of the quantum chemical hierarchy in comparison with the analytical linearized Poisson Boltzmann (ALPB) solvation model used as default in the xTB program package. While this eXtended Conductor-like Polarizable Continuum Model (CPCM-X) is specifically designed for the GFN2-xTB method, it can, in theory, be used as a post-processing method with a variety of PCM class solvation models, given that enough reference data for training is available. However, despite the use of sophisticated solvation models, it is still challenging to produce enough suitable reference data given the aforementioned inaccuracies in the description of solvation effects. <br /> In Chapter 6, therefore, an efficient approach for the dynamic adjustment of radii for continuum solvation (the DRACO approach) is presented to improve existing solvation models. This approach dynamically scales the atomic radii used for a solvation evaluation based on an atoms-in-molecules approach. To do this, it uses an interface to efficient charge models to obtain atomic partial charges and fractional coordination numbers, which are used to model the chemical environment of the atoms. Incorporating dynamic radii in existing solvation models improves their accuracy significantly, especially for highly polar and ionic solutes. The DRACO method is tested on various versatile benchmark sets and published as an open source library on GitHub. It introduces no additional computational overhead and can be used with any solvation model that allows a custom modification of solute radii. <br /> Although this thesis already yields significant improvements to the description of solvation interactions, the development of new solvation models is an ongoing process. Nonetheless, the physical insights gained through this thesis may contribute to further improvements if incorporated into future research.