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Journal of Statistical Physics

, Volume 160, Issue 6, pp 1684–1695 | Cite as

A Sensible Estimate for the Stability Constant of the Lennard-Jones Potential

  • Sergio A. Yuhjtman
Article

Abstract

We show that the stability constant of the Lennard-Jones potential in \(\mathbb {R}^{3}\), \(\Phi (x)=\Vert x\Vert _2^{-12}-2\Vert x\Vert _2^{-6}\), is smaller than 14.316. This is remarkably smaller than the best previously known bound. Our method is very elementary, and probably applicable to other similar potentials such as the Morse potentials. We also improve slightly, in the Lennard-Jones case, the lower bound for the minimum interparticle distance of an optimal n-particle configuration to 0.684.

Keywords

Stability constant Lennard-Jones potential Statistical mechanics 

Notes

Acknowledgments

I am totally grateful to Aldo Procacci. He taught me about this problem and much more. This work has been supported by the argentinian state organism Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET).

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Departamento de Matemática Intendente Guiraldes 2160, FCENUniversidad de Buenos AiresBuenos AiresArgentina

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