{"id":120731,"date":"2021-03-20T15:23:36","date_gmt":"2021-03-20T22:23:36","guid":{"rendered":"https:\/\/lifeboat.com\/blog\/2021\/03\/efficacy-of-the-radial-pair-potential-approximation-for-molecular-dynamics-simulations-of-dense-plasmas"},"modified":"2021-03-20T15:23:36","modified_gmt":"2021-03-20T22:23:36","slug":"efficacy-of-the-radial-pair-potential-approximation-for-molecular-dynamics-simulations-of-dense-plasmas","status":"publish","type":"post","link":"https:\/\/lifeboat.com\/blog\/2021\/03\/efficacy-of-the-radial-pair-potential-approximation-for-molecular-dynamics-simulations-of-dense-plasmas","title":{"rendered":"Efficacy of the radial pair potential approximation for molecular dynamics simulations of dense plasmas"},"content":{"rendered":"

<\/a><\/p>\n

In this work, we carry out KS-MD simulations for a range of elements, temperatures, and densities, allowing for a systematic comparison of three RPP models. While multiple RPP models can be selected, 7\u201311<\/sup><\/a> 7. J. Vorberger and D. Gericke, \u201cEffective ion\u2013ion potentials in warm dense matter,\u201d High Energy Density Phys. 9<\/b>, 178 (2013). https:\/\/doi.org\/10.1016\/j.hedp.2012.12.009<\/a><\/a> 8. Y. Hou, J. Dai, D. Kang, W. Ma, and J. Yuan, \u201cEquations of state and transport properties of mixtures in the warm dense regime,\u201d Phys. Plasmas 22<\/b>, 022711 (2015). https:\/\/doi.org\/10.1063\/1.4913424<\/a><\/a> 9. K. W\u00fcnsch, J. Vorberger, and D. Gericke, \u201cIon structure in warm dense matter: Benchmarking solutions of hypernetted-chain equations by first-principle simulations,\u201d Phys. Rev. E 79<\/b>, 010201 (2009). https:\/\/doi.org\/10.1103\/PhysRevE.79.010201<\/a><\/a> 10. L. Stanton and M. Murillo, \u201cUnified description of linear screening in dense plasmas,\u201d Phys. Rev. E 91<\/b>, 033104 (2015). https:\/\/doi.org\/10.1103\/PhysRevE.91.033104<\/a><\/a> 11. W. Wilson, L. Haggmark, and J. Biersack, \u201cCalculations of nuclear stopping, ranges, and straggling in the low-energy region,\u201d Phys. Rev. B 15<\/b>, 2458 (1977). https:\/\/doi.org\/10.1103\/PhysRevB.15.2458<\/a><\/a> we choose to compare the widely used Yukawa potential, which accounts for screening by linearly perturbing around a uniform density in the long-wavelength (Thomas\u2013Fermi) limit, a potential constructed from a neutral pseudo-atom (NPA) approach, 12\u201315<\/sup><\/a> 12. L. Harbour, M. Dharma-wardana, D. D. Klug, and L. J. Lewis, \u201cPair potentials for warm dense matter and their application to x-ray Thomson scattering in aluminum and beryllium,\u201d Phys. Rev. E 94<\/b>, 053211 (2016). https:\/\/doi.org\/10.1103\/PhysRevE.94.053211<\/a><\/a> 13. M. Dharma-wardana, \u201cElectron-ion and ion-ion potentials for modeling warm dense matter: Applications to laser-heated or shock-compressed Al and Si,\u201d Phys. Rev. E 86<\/b>, 036407 (2012). https:\/\/doi.org\/10.1103\/PhysRevE.86.036407<\/a><\/a> 14. F. Perrot and M. Dharma-Wardana, \u201cEquation of state and transport properties of an interacting multispecies plasma: Application to a multiply ionized al plasma,\u201d Phys. Rev. E 52<\/b>, 5352 (1995). https:\/\/doi.org\/10.1103\/PhysRevE.52.5352<\/a><\/a> 15. L. Harbour, G. F\u00f6rster, M. Dharma-wardana, and L. J. Lewis, \u201cIon-ion dynamic structure factor, acoustic modes, and equation of state of two-temperature warm dense aluminum,\u201d Phys. Rev. E 97<\/b>, 043210 (2018). https:\/\/doi.org\/10.1103\/PhysRevE.97.043210<\/a><\/a> and the optimal force-matched RPP that is constructed directly from KS-MD simulation data.<\/p>\n

Each of the models we chose impacts our physics understanding and has clear computational consequences. For example, success of the Yukawa model reveals the insensitivity to choices in the pseudopotential and screening function and allows for the largest-scale simulations. Large improvements are expected from the NPA model, which makes many fewer assumptions with a modest cost of pre-computing and tabulating forces. (See the Appendix<\/a> for more details on the NPA model.) The force-matched RPP requires KS-MD data and is therefore the most expensive to produce, but it reveals the limitations of RPPs themselves since they are by definition the optimal RPP.<\/p>\n

Using multiple metrics of comparison between RPP-MD and KS-MD including the relative force error, ion\u2013ion equilibrium radial distribution function g <\/i>(r<\/i>), Einstein frequency, power spectrum, and the self-diffusion transport coefficient, the accuracy of each RPP model is analyzed. By simulating disparate elements, namely, an alkali metal, multiple transition metals, a halogen, a nonmetal, and a noble gas, we see that force-matched RPPs are valid for simulating dense plasmas at temperatures above fractions of an eV and beyond. We find that for all cases except for low temperature carbon, force-matched RPPs accurately describe the results obtained from KS-MD to within a few percent. By contrast, the Yukawa model appears to systematically fail at describing results from KS-MD at low temperatures for the conditions studied here validating the need for alternate models such as force-matching and NPA approaches at these conditions.<\/p>\n","protected":false},"excerpt":{"rendered":"

In this work, we carry out KS-MD simulations for a range of elements, temperatures, and densities, allowing for a systematic comparison of three RPP models. While multiple RPP models can be selected, 7\u201311 7. J. Vorberger and D. Gericke, \u201cEffective ion\u2013ion potentials in warm dense matter,\u201d High Energy Density Phys. 9, 178 (2013). https:\/\/doi.org\/10.1016\/j.hedp.2012.12.009 8. [\u2026]<\/p>\n","protected":false},"author":427,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1523,41,873,48],"tags":[],"class_list":["post-120731","post","type-post","status-publish","format-standard","hentry","category-computing","category-information-science","category-nuclear-energy","category-particle-physics"],"_links":{"self":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/posts\/120731","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/users\/427"}],"replies":[{"embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/comments?post=120731"}],"version-history":[{"count":0,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/posts\/120731\/revisions"}],"wp:attachment":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/media?parent=120731"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/categories?post=120731"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/tags?post=120731"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}