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TY  - THES
AU  - Reuter, Leonard
TI  - Probability density analysis: a real space valence bond theory
PB  - RWTH Aachen University
VL  - Dissertation
CY  - Aachen
M1  - RWTH-2024-02189
SP  - 1 Online-Ressource : Illustrationen
PY  - 2023
N1  - Veröffentlicht auf dem Publikationsserver der RWTH Aachen University 2024
N1  - Dissertation, RWTH Aachen University, 2023
AB  - Chemists have two separate toolboxes at hand to rationalize and predict the stability and reactivity of molecules: the field of quantum chemistry and the realm of structural formulas, qualitative diagrams and empiric rules. There exists already a plethora of methods that strive to connect these two conceptually distinct worlds and to find traces or images of the empirical concepts within the mathematics of quantum mechanics. Among these methods are valence bond theory, molecular orbital localization algorithms, energy decomposition analyses, and the quantum theory of atoms in molecules. However, all of these schemes are either restricted to specific wave function ansatzes or are unable to describe many-particle effects. Here, probability density analysis is presented, with which we strive to define method-agnostic quantities by analyzing the many-electron probability density  - Ψ - ². These quantities are—by design—many-particle descriptors. Most likely electron arrangements, which often resemble well-known resonance structures, are identified as local maxima of  - Ψ - ². These arrangements furthermore allow for partitioning the many-electron coordinate space and calculating structure probabilities, which are in good agreement with resonance structure weights from valence bond theory. A probability potential is defined in order to quantify delocalization by calculating barriers on paths describing the exchange between different locally most likely electron arrangements. Already a qualitative discussion of these barriers leads directly from the antisymmetry of Fermionic wave functions to a generalized Hückel rule for cyclic systems. Furthermore, these barriers reveal both the role of ionic resonance structures and a clear real space fingerprint of charge-shift bonds. In short, probability density analysis allows for obtaining valence bond theoretical quantities from any wave function and offers new, insightful perspectives onto fundamental concepts of chemical bonding.
LB  - PUB:(DE-HGF)11
DO  - DOI:10.18154/RWTH-2024-02189
UR  - https://publications.rwth-aachen.de/record/980328
ER  -