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@PHDTHESIS{Reuter:980328,
      author       = {Reuter, Leonard},
      othercontributors = {Lüchow, Arne and Bannwarth, Christoph Nils},
      title        = {{P}robability density analysis: a real space valence bond
                      theory},
      school       = {RWTH Aachen University},
      type         = {Dissertation},
      address      = {Aachen},
      publisher    = {RWTH Aachen University},
      reportid     = {RWTH-2024-02189},
      pages        = {1 Online-Ressource : Illustrationen},
      year         = {2023},
      note         = {Veröffentlicht auf dem Publikationsserver der RWTH Aachen
                      University 2024; Dissertation, RWTH Aachen University, 2023},
      abstract     = {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.},
      cin          = {153420 / 150000},
      ddc          = {540},
      cid          = {$I:(DE-82)153420_20140620$ / $I:(DE-82)150000_20140620$},
      typ          = {PUB:(DE-HGF)11},
      doi          = {10.18154/RWTH-2024-02189},
      url          = {https://publications.rwth-aachen.de/record/980328},
}