Entropy displacement and information distance analysis of electron distributions in molecules and their Hirshfeld atoms

The displacements of the Shannon entropy and its density, relative to the corresponding reference values for the overlapping densities of the free atoms of the isoelectronic promolecule, are investigated for selected small molecules and propellane systems. A similar analysis is carried out for the Hirshfeld constituent atoms. The entropy difference maps are shown to be qualitatively similar to the corresponding plots of the density difference function and the entropy deficiency density, with respect to the same reference distributions. A use of these quantities as complementary tools for monitoring changes in electronic structure due to the bond formation is advocated. The entropy displacement plots for small-ring propellanes are used to examine the nature of the central bond between the bridgehead carbons. These results are compared with predictions of the previous bond multiplicity study. The [1.1.1]- and [2.1.1]propellanes are found to exhibit a partial through-bridge bond and lowering of the electron density and the entropy/entropy deficiency densities between the bridgehead atoms. Larger bridges in the [2.2.1]- and [2.2.2]propellanes generate an increase of the electron and information densities in the central bond region, thus introducing a partial through-space bond component.