Calculation of high-order virial coefficients for the square-well potential

Do, Hainam; Feng, Chao; Schultz, Andrew J.; Kofke, David A.; Wheatley, Richard J.

Abstract

Accurate virial coefficients BN(λ,ε) (where ε is the well depth) for the three-dimensional square-well and square-step potentials are calculated for orders N = 5–9 and well widths λ = 1.1−2.0 using a very fast recursive method. The efficiency of the algorithm is enhanced significantly by exploiting permutation symmetry and by storing integrands for reuse during the calculation. For N = 9 the storage requirements become sufficiently large that a parallel algorithm is developed. The methodology is general and is applicable to other discrete potentials. The computed coefficients are precise even near the critical temperature, and thus open up possibilities for analysis of criticality of the system, which is currently not accessible by any other means.

Citation

Do, H., Feng, C., Schultz, A. J., Kofke, D. A., & Wheatley, R. J. (2016). Calculation of high-order virial coefficients for the square-well potential. Physical Review E, 94(1), Article 013301. https://doi.org/10.1103/PhysRevE.94.013301

• Journal Article Type: Article
• Acceptance Date: Jul 1, 2016
• Publication Date: Jul 5, 2016
• Deposit Date: Jul 20, 2016
• Publicly Available Date: Jul 20, 2016
• Journal: Physical Review E
• Print ISSN: 2470-0045
• Electronic ISSN: 2470-0053
• Publisher: American Physical Society
• Peer Reviewed: Peer Reviewed
• Volume: 94
• Issue: 1
• Article Number: 013301
• DOI: https://doi.org/10.1103/PhysRevE.94.013301
• Public URL: https://nottingham-repository.worktribe.com/output/802242
• Publisher URL: http://journals.aps.org/pre/abstract/10.1103/PhysRevE.94.013301
• Additional Information: ©2016 American Physical Society
• Contract Date: Jul 20, 2016