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Using Symbolic Computing in Building Probabilistic Models for Atoms

Journal / Anthology

International Journal of Quantum Chemistry
Year: 2006
Volume: 106
Page range: 4-26

This article shows how symbolic computing and the mathematical formalism induced by maximizing entropy and minimizing the mean deviation from statistical equilibrium may be effectively applied to obtaining probabilistic models for the structure of atoms, using trial wave functions compatible with an average shell picture of the atom. The objective is not only to recover the experimental value of the ground state mean energy of the atom, but rather to better approximate the unknown parameters of these trial functions and to calculate both correlations between electrons and the amount of interdependence among different subsets of electrons of the atoms. The examples and numerical results refer to the hydrogen, helium, lithium, and beryllium atoms. The main computer programs, using the symbolic computing software Mathematica, are also given.

*Science > Chemistry
*Science > Physics > Quantum Physics

symbolic computing, trial wave functions, maximum entropy principle, minimum mean deviation from statistical equilibrium, correlations between electrons, amount of interdependence between subsets of electrons, weighted mean orbits of subshells of atoms