Revision of Quantum Chemistry Valence Formulas based on Density Matrix Analysis

Sammanfattning

Valence is a fundamental yet ambiguously defined concept in chemistry, playing a central role in the description of molecular structure, bonding, and reactivity. This thesis examines the quantum mechanical Veryazov valence formula (referred to as the original formula), which determines atomic valence based on density matrix analysis. The aim of this work is to assess the robustness of this valence formula with respect to different computational methods and basis sets and to investigate the consequences of modifications of the original formula. As a first step, the original formula was applied to a diverse database comprising molecular and crystalline systems. This analysis revealed that the behavior of the formula depends strongly on the system. For a first group of molecules, consisting mainly of small and chemically simple systems, the valence values obtained with the original formula agree with expected valence values and show only minor sensitivity to methods and basis sets. For these systems, valence can be regarded as a well-defined and stable property within the framework of the original formula. This group therefore serves as a reference set for further analysis. In contrast, for a second group of larger and chemically more complex systems, including heavier elements, hypervalent species, ionic compounds, and transition-metal molecules, the valence values obtained show a more pronounced dependence on the method and basis sets. In these cases, valence emerges as a less well-defined property. Expected valence values for this second group are therefore used for comparative analysis rather than as reference data. Further investigations were focused primarily on the reference group of molecules with well-defined valence. Based on this reference set, four approaches were undertaken in order to modify the original formula and evaluate the resulting consequences on the valence: (i) variations of the ionic and covalent contributions using alternative charge analyses and modified weighting functions in the covalent term, (ii) fitted valence formulas with parameters optimized for selected groups of molecules, (iii) targeted adaptations of the original formula for classes of molecules sharing common chemical features such as hypervalency or lone pairs, and (iv) modifications of the density matrix, including the orbital occupation scheme. Among the investigated modifications, changes to the treatment of the covalent contribution have the strongest impact on the resulting valence values, whereas modifications of the density matrix itself do not lead to increased stability.