PMID: 15244893Jul 13, 2004Paper

Stable method for the calculation of partition functions in the superconfiguration approach

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Franck Gilleron, Jean-Christophe Pain

Abstract

A general method for the calculation of the partition function of a canonical ensemble of noninteracting bound electrons is presented. It consists in a doubly recursive procedure with respect to the number of electrons and the number of orbitals. Contrary to existing approaches, this recursion relation contains no alternate summation of positive and negative numbers, which was the main source of numerical uncertainties. It is accompanied with a normalization of partition function through the determination of a free parameter consistent with the zeroth-order saddle-point approximation. The recursion relation allows one to calculate accurately partition functions for ions with a large number of orbitals, and is therefore important for calculations relying on the superconfiguration approximation.

References

Sep 15, 1989·Physical Review A: General Physics·A Bar-ShalomA Zigler
Apr 24, 2002·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·G Faussurier

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Citations

Oct 13, 2007·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Brian G WilsonJean-Christophe Pain
Jul 30, 2011·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Jean-Christophe PainQuentin Porcherot
Mar 21, 2008·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·D S KosovA I Vdovin
Oct 2, 2009·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Jean-Christophe PainGérald Faussurier
Apr 18, 2021·Physical Review. E·Menahem Krief

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