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Statistical representation of atomic systems structure. II. classification of the representation; entropy dependence of the total energy for isoelectronic series
Author(s) -
Fraczak Marek
Publication year - 1985
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560270605
Subject(s) - series (stratigraphy) , electronic structure , ground state , statistical physics , representation (politics) , chemistry , quantum mechanics , atomic physics , physics , paleontology , politics , political science , law , biology
The energies of the ground states of the mononuclear atomic systems, until now determined merely by approximate methods, turn out to exhibit some almost exact interdependencies. A simple statistical functional of the electronic structure (the “γ representation”) turns out to be decisive for the system energy. In this paper that interdependence is further traced for the N ‐electron systems in isoelectronic series (with constant N and varying Z ). The resulting “combinatorial formula” reproduces the experimental data with the errors at least ten times smaller than those of the conventional Hartree–Fock approximation. The reason why there is such an exact formula for the ground‐state energy remains to be clarified. The limiting behavior of our energy formula for large Z exhibits consistency with the Thomas–Fermi and the Z −1 perturbation expansion models.