Gradient Bundle Analysis: A Full Topological Approach to Chemical   Bonding
  The "chemical bond" is a central concept in molecular sciences, but there is no consensus as to what a bond actually is. Therefore, a variety of bonding models have been developed, each defining the structure of molecules in a different manner with the goal of explaining and predicting chemical properties. This thesis describes the initial development of gradient bundle analysis (GBA), a chemical bonding model that creates a high resolution picture of chemical interactions within the charge density framework. GBA is based on concepts from the quantum theory of atoms in molecules (QTAIM), but uses a more complete picture of the topology and geometry of the electron charge density to understand and predict bonding interactions. Gradient bundles are defined as volumes bounded by zero-flux surfaces (ZFSs) in the gradient of the charge density with well-defined energies. The structure of gradient bundles provides an avenue for detecting the locations of valence electrons, which correspond to reactive regions in a molecule. The number of electrons in bonding regions, which are defined by the lowering of kinetic energy in gradient bundles, is found to correlate to bond dissociation energy in diatomic molecules. Furthermore, site reactivity can be understood and predicted by observing the motion of ZFSs bounding gradient bundles and calculating condensed gradient bundle Fukui functions. Using only the ground state charge density, I present preliminary results for a method that predicts which regions in a molecule are most likely to undergo nucleophilic and electrophilic attack, effectively locating the HOMO and LUMO. 
Amanda Morgenstern
physics.chem-ph