Simplification of the electron-ion many-body problem: N -representability of pair densities obtained via a classical map for the electrons

Abstract

The classical map hypernetted-chain (CHNC) method for interacting electrons uses a kinetic energy functional in the form of a classical-fluid temperature. Here, we show that the CHNC generated two-body densities and pair-distribution functions (PDFs) correspond to $N$-representable densities. Comparisons of results from CHNC with quantum Monte Carlo (QMC) and path-integral Monte Carlo (PIMC) are used to validate the CHNC results. Since the PDFs are sufficient to obtain the equation of state or linear response properties of electron-ion systems, we apply the CHNC method for fully classical calculations of electron-ion systems in the quantum regime, using hydrogen at 4000 K and 350 times the solid density as an example since QMC comparisons are available. We also present neutral pseudoatom (NPA) calculations which use rigorous density functional theory (DFT) to reduce the many nuclear problem to an effective one-ion problem. The CHNC PDFs and NPA results agree well with the ion-ion, electron-ion, and electron-electron PDFs from QMC, PIMC, or DFT coupled to molecular dynamics simulations where available. The PDFs of a two-dimensional (2D) electron-hole system at 5 K are given as an example of 2D ``warm dense'' matter where the electrons and the counterparticles (holes) are all in the quantum regime. Basic methods such as QMC, PIMC, or even DFT become prohibitive while CHNC methods, being independent of the number of particles or the temperature, prove to be easily deployable.