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Study of an approximate relation between the energy of an atom and the electronic potential at the nucleus
Author(s) -
Alonso J. A.,
González D. J.,
Balbás L. C.
Publication year - 1982
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.560220510
Subject(s) - thomas–fermi model , formalism (music) , physics , electronic density , atom (system on chip) , term (time) , atomic physics , density functional theory , orbital free density functional theory , electron , krypton , local density approximation , quantum mechanics , argon , art , musical , computer science , visual arts , embedded system
This paper provides an analysis of the reasons for the approximate validity of the relation \documentclass{article}\pagestyle{empty}\begin{document}$ E = \frac{3}{7}NV(0) $\end{document} , between the total energy E of a neutral atom, the number N of electrons, and the electronic potential at the nucleus V (0). Using the density functional formalism we find that the right‐hand side of the above equation also appears (and is the leading term) in density functional approximations more sophisticated than the Thomas–Fermi ( TF ) approximation (the above equation is exact in the TF approximation). Systematic improvements to the equation appear to be difficult because the main corrections come from those terms which are more difficult to handle in the density functional formalism. After this analysis we propose a kinetic energy functional for neutral atoms in the Hartree–Fock approximation. The first term of this new functional is a rescaled Thomas–Fermi term\documentclass{article}\pagestyle{empty}\begin{document}$$ T_0^\gamma = (1 + \gamma)\int {\frac{3}{{10}}(3\pi ^2){}^{2/3}\rho ^{5/3} d{\rm r}} $$\end{document} , where γ = −0.0063 for light atoms and γ = 0.0085 for the others. The second term is the first gradient correction due to Kirzhnits\documentclass{article}\pagestyle{empty}\begin{document}$$ T_2 = \frac{1}{{72}}\int {\frac{{(\nabla \rho)^2 }}{\rho }d{\rm r}} $$\end{document} . For lithium to krypton atoms, this new functional gives an average error of 0.22%.