Improved parameterization of the bridge function of one-component plasma liquids
Abstract
• The newly-proposed isomorph-based empirically modified hypernetted-chain (IEMHNC) approach is capable of reproducing the structural and thermodynamic properties of Yukawa liquids with unprecedented combination of accuracy and computational speed. This integral equation theory approach utilizes an isentropic mapping between Yukawa and Coulomb states but requires the bridge function of the one-component plasma (OCP) as input. “Exact” OCP bridge functions were previously extracted from Monte Carlo simulations and closed form expressions were proposed via the coupling parameter in works by Ichimaru & collaborators.
• Concerning the aforementioned works, our recent investigations indicated that: (a) the bin widths used in the determination of radial distribution functions were too large translating to small grid errors in the radial distribution function but unacceptably large grid errors in the highly sensitive bridge function, (b) the reduced excess entropy constitutes a better independent state variable than the coupling parameter concerning parameterization, (c) the four reference states considered are inadequate for accurate parameterization, (d) the artificial decay assumed beyond the first coordination cell leads to inaccuracies in the longer range structure.
• The objective of this project is to provide a substantially improved parameterization of the OCP bridge function based on our tested combination of large-statistics NVT MD simulations with short, long & ultra-long specially designed cavity MD simulations.
• As detailed in the activity report for the initial proposal: the large-statistics NVT, short cavity and long cavity MD simulations have been completed for 17 state points that span the entire OCP liquid range from the uncorrelated limit up to the liquid - crystal transition. Post processing led to highly accurate bridge functions in the entire range apart from very small separations. Despite its small extent (less than 1/10 of interparticle distance), the noise-afflicted short range has substantial impact on structural predictions, courtesy of the nature of the Ornstein-Zernike equation. In this very short range, ultra-long cavity MD simulations are necessary to decrease the fluctuation level originating from insufficient pair statistics. We should note that the necessity for the missing ultra-long cavity simulations was foreseen in the original proposal and computational resources were requested for them in the initial proposal. However, only half of the requested resources was ultimately allocated (150000 core hours vs 75000 core hours per month). Furthermore, we ran into rather unexpected problems concerning the Ewald sum implementation and, thus, under-utilized resources for few months, until these issues were resolved.
• With this proposal, we request for the resources that are necessary to complete this study. Note that there is zero risk involved, since missing runs concern increased statistics and involve tested scripts. The missing input will allow for a highly accurate parameterization of the exact OCP bridge function, with important consequences for classical liquids (where it should further increase the already impressive accuracy of the IEMHNC approach on par with computer simulations) and for quantum liquids (where it can increase the accuracy of successful STLS-like dielectric formalisms that are based on RPA quantum effects and classical correlations).
