The Fractional Occupation Number Weighted Density as a Versatile Analysis Tool for Molecules with a Complicated Electronic Structure.

The fractional occupation number weighted density (FOD) analysis is explored as a general theoretical diagnostic for complicated electronic structures. Its main feature is to provide robustly and quickly the information on the localization of "hot" (strongly correlated and chemically active) electrons in a molecule. We demonstrate its usage in four different prototypical applications: 1) As a new and fast measure of the biradical character of polycyclic aromatic hydrocarbons, 2) for the selection of active orbital spaces in multiconfigurational or complete active space self consistent field (MCSCF/CASSCF) treatments, 3) as a possibility to describe molecular-energy landscapes consistently in regions with varying biradical character, as exemplified by partial double-bond torsions, and 4) as a powerful visualization method for static electron correlation effects in large biomolecules in connection with an efficient semi-empirical tight-binding molecular orbital scheme. The last application opens a full quantum-mechanical, unbiased route to the automatic detection of errors in experimental protein X-ray structures, such as false protonation states or misplaced atoms. In the first example, the complete (unfragmented) quantum-chemical calculation of the FOD for an entire metalloprotein with more than 7500 atoms is described.