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

Abstract

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.