Juan Carlos Castro Ramírez

Relationships between Jaynes entropy of the one-particle density matrix and Shannon entropy of the electron densities

Relationships between the Jaynes and Shannon information entropies, both of which are related to the correlation energy, are given and the physical implications are explored. Evidence is provided from a study of the Be and Ne isoelectronic sequences that the Shannon entropy is more sensitive to the effects of the nuclear charge than is the Jaynes entropy. It is shown that the Jaynes entropy may be considered as the difference between the mean orbital Shannon entropy per electron and the mean orbital Shannon entropy of one electron. These mean orbital entropies display the same functional behavior as the total Shannon entropy throughout the isoelectronic sequence. We demonstrate that the Jaynes entropy may be considered as the sum of the Kullback–Leibler distance entropies occurring between natural spin orbital densities and a reference point whose occupation number is one. The large Z asymptotic behavior of the Jaynes and Shannon entropies is discussed. From a study of a Ne isonuclear sequence, it is show...