Information theoretic properties from the quantum theory of atoms in molecules

Information theoretic atomic properties within the quantum theory of atoms in molecules (QTAIM) are discussed. The fate of the dimensions of the electron density inserted into the logarithm of Shannon’s entropy is examined. It is shown that referencing the atomic missing information function to the corresponding uniform electron gas captures most of the size-dependence and converts the non-transferable atomic missing information into a transferable property. A striking trend relates an atom’s contribution to the overall Coulombic correlation energy and that atom’s Shannon’s entropy. The information theoretic atomic properties obtained from MP2, DFT, or Hartree–Fock (H–F) are almost perfectly correlated.