A simple method for the evaluation of the information content and complexity in atoms. A proposal for scalability

We present a very simple method for the calculation of Shannon, Fisher and Onicescu entropies in atoms, as well as SDL and LMC complexity measures, as functions of the atomic number Z. Fractional occupation probabilities of electrons in atomic orbitals are employed, instead of the more complicated continuous electron probability densities in position- and momentum-spaces, used so far in the literature. Our main conclusions are compatible with the results of more sophisticated approaches and correlate fairly with experimental data. A practical way towards scalability of the quantification of complexity for systems with more components than the atom is indicated. We also discuss the issue if the complexity of the electronic structure of atoms increases with Z. A Pair (α,β) of Order-Disorder Indices (PODI), which can be introduced for any quantum many-body system, is evaluated in atoms (α=0.085, β=1.015). We conclude, by observing the trend of closed shells atoms, that 'atoms are ordered systems, which grow in complexity as Z increases'.