All-Electron Path Integral Monte Carlo Simulations of Warm Dense Matter: Application to Water and Carbon Plasmas

Abstract

We develop an all-electron path integral Monte Carlo method with free-particle nodes for warm dense matter and apply it to water and carbon plasmas. We thereby extend path integral Monte Carlo studies beyond hydrogen and helium to elements with core electrons. Path integral Monte Carlo results for pressures, internal energies, and pair-correlation functions compare well with density functional theory molecular dynamics calculations at temperatures of (2.5-7.5)×10(5) K, and both methods together form a coherent equation of state over a density-temperature range of 3-12 g/cm(3) and 10(4)-10(9) K.

Multiphase equation of state for carbon addressing high pressures and temperatures

“…In order to minimize finite-size errors, the total energy was converged to better than 0.2% for a 24 atom cubic cell. Though this may seem like a small number of atoms, we stress that the number of atoms/cell needed to accurately compute energy and pressure decreases rapidly for condensed systems as T is increased into the plasma regime [14,34,51].…”

“…In this approach, unlike in typical implementations of DFT, there is no mean-field assumption made for the many-electron problem, and the imaginary time treatment makes high-T simulations more efficient to perform than low-T simulations. Although assumptions regarding the nodal surface of the many electron density matrix necessarily introduce approximations for the treatment of atomic shells, it is very encouraging that recent work on the C plasma has demonstrated that EOS predictions can be made with this method which smoothly interpolate between DFT-MD results at the lower temperatures and the high-T Debye-Hückel limit [14].…”

“…Fermionic PIMC simulations have been applied to study hydrogen [31][32][33][34][35][36][37][38][39], helium [40,41], hydrogen-helium mixtures [42], and one-component plasmas [43,44], and most recently to simulate carbon and water plasmas [14]. In PIMC simulations, electrons and nuclei are treated equally as Feynman paths in a stochastic framework for solving the full, finite-temperature, quantum many-body problem.…”

“…However, within any given set of nodes, the restricted path method will obtain the best possible solution that includes all interaction and correlation effects. The PIMC method used here employs a free-particle nodal structure, which has been shown to be sufficient for carbon at temperatures where atoms still have occupied 1s states but partially occupied 2s states (T 2.5×10 5 K) [14]. Using the restricted-path, free-particle nodal framework, we use all-electron PIMC to compute equations of state for carbon at densities of 0.1, 3.18, 8.5, and 11.18 g cm −3 over a temperature range of 10 5 -10 9 K (though we present data pertaining to all four isochores in the Supplemental Material [19], we stress that 0.1 g/cc is below the low-density limit of applicability of the EOS model described below) [50].…”

“…[15], the inclusion of these extra phases allows our EOS to be in accord with ab initio predictions for pressures up to well over 100 Mbar. The EOS of the high-temperature liquid is elucidated by performing DFT-MD for C up to 100 000 K and PIMC calculations [14] from ∼200 000 K (depending on the density) to over 10 8 K. We establish that the best fit to these EOS predictions requires a liquid free energy model in which (1) electronic excitations are treated in an average-atom picture which includes atomic shell structure, and (2) the decay of the ion-thermal specific heat from 3k B /atom to 3k B /2/atom as T → ∞ is much faster than previously expected. In what follows, we describe the details of our DFT and PIMC calculations of the EOS of C, present the models we use to fit these ab initio data, and compare various thermodynamic tracks through our resulting EOS with the findings of recent experiments performed on high-energy laser platforms [1,6,7].…”