A Practicable Real-Space Measure and Visualization of Static Electron-Correlation Effects

The inclusion of dynamical and static electron correlation (SEC) is mandatory for accurate quantum chemistry (QC). SEC is particularly difficult to calculate and hence a qualitative understanding is important to judge the applicability of approximate QC methods. Existing scalar SEC diagnostics, however, lack the important information where the SEC effects occur in a molecule. We introduce an analysis tool based on a fractional occupation number weighted electron density (rho(FOD)) that is plotted in 3D for a pre-defined contour surface value. The scalar field is obtained by finite-temperature DFT calculations with pre-defined electronic temperature (e.g. TPSS at 5000 K). FOD plots only show the contribution of the "hot" (strongly correlated) electrons. We discuss illustrative plots for a broad range of chemical systems from small molecules to large conjugated molecules with polyradicaloid character. Spatial integration yields a single number which can be used to globally quantify SEC.