Arne Lüchow

E-mail address: luechow@pc.rwth-aachen.de It is demonstrated that a topological analysis of the many-electron probability density |Ψ|2 (PDA) is useful for the analysis of chemical bonding. The stationary points of the probability density can be visualized in ordinary space. Additionally, basins, or attractor domains, are defined for the maxima of the probability density analogously to the 3D analysis of the electron density in the quantum theory of atoms in molecules by Bader and coworkers. The maxima of the probability density correspond to the locally most probable electron arrangements. They can be analyzed in many cases in terms of electron arrangements of the atoms. A local spin of the atom in the molecule can be defined easily and is discussed with respect to the covalent bond. The saddle points of the probability density connect two basins of maxima and thus describe the electron exchange between atoms. A probability barrier is defined describing the electron delocalization via the saddle points. The topological analysis of the probability density is based on the efficient sampling of |Ψ|2 with quantum Monte Carlo methods and is possible with arbitrary wave functions. The favorable scaling allows analysis of fairly large molecules. New results regarding the local spin in molecules and their relation to chemical bonding are discussed as well the delocalization via probability barriers in aromatic molecules. Additionally, a comparison of first-row and second-row covalent bonding is presented from a probability density perspective.