FeO (wüstite), which exhibits complex electronic and structural properties with increasing pressure and temperature, is a key mineralogical phase for understanding deep planetary interiors. However, direct measurements of its spin state at high-pressure and temperature remain challenging in static compression experiments. Here, we employ laser-driven shock compression to extend the FeO principal Hugoniot up to ∼900 GPa and perform in situ X-ray diffraction and X-ray emission spectroscopy up to 250 GPa, probing FeO's crystal structure and spin state. We demonstrate a continuous spin crossover of iron in FeO over a broad pressure range, with the high-spin state persisting beyond Earth's core-mantle boundary (CMB) conditions. These observations provide new experimental constraints on iron spin state at extreme conditions essential for geophysical models of (exo)planetary interiors.

The expanded warm dense matter regime, an intermediate state between condensed matter and high-energy-density plasma at low density, remains poorly constrained experimentally, particularly regarding transport properties across the metal-to-nonmetal transition. Here, we explore expanded warm dense aluminum using a newly developed pulsed Joule heating platform combined with first-principles simulations. Using a largely model-independent approach with time-resolved diagnostics, we measure thermodynamic and transport properties from ambient density down to 0.6 g ⋅ cm−3 and temperatures exceeding 37 kK, providing benchmark data for electrical conductivity and equation-of-state models. Our results reveal electronic state localization associated with the onset of the metal-to-nonmetal transition and show distinct conductivity behaviors depending on the thermodynamic path followed during expansion. Crucially, electronic relaxation time – rather than ionization – dominates conduction in this supercritical regime. These observations advance our understanding of expanded warm dense matter and open perspectives for future studies on alloys and high-Z elements relevant to giant impact modeling and fusion energy. Despite the ubiquity of warm dense matter states, there is lack of well-established models describing the expanded regime. To address this gap, the authors provide theoretical and experimental analysis of warm dense aluminium by means of pulse Joule heating. This provides constraints to the equation of state and insight into the electrical conductivity behaviour.

This roadmap presents the state-of-the-art, current challenges and near future developments anticipated in the thriving field of warm dense matter physics. Originating from strongly coupled plasma physics, high pressure physics and high energy density science, the warm dense matter physics community has recently taken a giant leap forward. This is due to spectacular developments in laser technology, diagnostic capabilities, and computer simulation techniques. Only in the last decade has it become possible to perform accurate enough simulations & experiments to truly verify theoretical results as well as to reliably design experiments based on predictions. Consequently, this roadmap discusses recent developments and contemporary challenges that are faced by theoretical methods, and experimental techniques needed to create and diagnose warm dense matter. A large part of this roadmap is dedicated to specific warm dense matter systems and applications in astrophysics, inertial confinement fusion and novel material synthesis.

We computed the equation of state of iron using extended first-principles molecular dynamics simulations, ranging from 7.874 g/cm3 and 5500 K up to 47.2 g/cm3 and 109 K. We compared the principal Hugoniot curve with semiempirical models, average atom-based model predictions, and shock experiment results. We derived the Helmholtz free energy and the entropy via thermodynamic integration along isochores. We explore the ionization processes at play along the Hugoniot curve by analyzing the evolution of the electronic densities of states in the gigabar regime.

Abinit is a widely used scientific software package implementing density functional theory and many related functionalities for excited states and response properties. This paper presents the novel features and capabilities, both technical and scientific, which have been implemented over the past 5 years. This evolution occurred in the context of evolving hardware platforms, high-throughput calculation campaigns, and the growing use of machine learning to predict properties based on databases of first-principle results. We present new methodologies for ground states with constrained charge, spin, or temperature; for density functional perturbation theory extensions to flexoelectricity and polarons; and for excited states in many-body frameworks including GW, dynamical mean field theory, and coupled cluster. Technical advances have extended Abinit high-performance execution to graphical processing units and intensive parallelism. Second-principles methods build effective models on top of first-principle results to scale up in length and time scales. Finally, workflows have been developed in different community frameworks to automate Abinit calculations and enable users to simulate hundreds or thousands of materials in controlled and reproducible conditions.

The dynamics of an inertial confinement fusion capsule, or of a stellar or planet interior, obey a very similar set of equations: magneto-radiative-hydrodynamic equations. The solutions of these equations, however, depend entirely on the transport properties associated with the different materials at play. To properly model the dynamics of these systems, it is necessary to determine with high accuracy the transport coefficients of several materials over a large range of thermodynamic conditions. Experimental capabilities in this respect are still limited due to the nature of the microphysics at play and the extreme conditions involved. Numerical simulations are thus necessary, and in this respect, molecular dynamics simulations based on density functional theory offer exquisite possibilities to constrain the transport properties in the warm to hot dense matter regime. In this paper, we report the methodology used to extract different transport properties based on molecular dynamics performed with the software Abinit. The examples shown are based on the specific cases identified for the purpose of the second charged-particle transport code comparison workshop.

We report the results of the second charged-particle transport coefficient code comparison workshop, which was held in Livermore, California on 24–27 July 2023. This workshop gathered theoretical, computational, and experimental scientists to assess the state of computational and experimental techniques for understanding charged-particle transport coefficients relevant to high-energy-density plasma science. Data for electronic and ionic transport coefficients, namely, the direct current electrical conductivity, electron thermal conductivity, ion shear viscosity, and ion thermal conductivity were computed and compared for multiple plasma conditions. Additional comparisons were carried out for electron–ion properties such as the electron–ion equilibration time and alpha particle stopping power. Overall, 39 participants submitted calculated results from 18 independent approaches, spanning methods from parameterized semi-empirical models to time-dependent density functional theory. In the cases studied here, we find significant differences—several orders of magnitude—between approaches, particularly at lower temperatures, and smaller differences—roughly a factor of five—among first-principles models. We investigate the origins of these differences through comparisons of underlying predictions of ionic and electronic structure. The results of this workshop help to identify plasma conditions where computationally inexpensive approaches are accurate, where computationally expensive models are required, and where experimental measurements will have high impact.

We investigate the material properties of a mixture of hydrogen, helium, and oxygen representative of Saturn’s interior at pressure–temperature conditions of a recent Saturn model (see Mankovich & Fortney) with molecular dynamics simulations based on density functional theory. Their model considers the demixing of hydrogen and helium and predicts a He-rich layer above a diluted core. We calculate the thermodynamic and transport properties and discuss the impact on Saturn’s evolution and interior structure. We find a significant impact of the He-rich layer on the specific heat capacity, speed of sound, viscosity, diffusion coefficients, thermal and electrical conductivity, Lorenz number, and magnetic and thermal diffusivities.

The Wigner-Kirkwood expansion of the quantum correction to the classical free energy is generally said to be in powers of ℏ2 and only its first few terms are presented. In this work, we use the Bloch differential equation to obtain a general description of all terms in a dimensionless form. The first corrective term turns out to be proportional to the product of λ2/a2, where λ is the thermal de Broglie wavelength and a3 is the volume per particle, by an effective coupling constant. This dimensionless parameter can be used to assess the magnitude of the quantum correction. Using the one-component plasma as an illustration we highlight the importance of the magnitude of the potential on the quantum correction. The results presented are not formally new; the emphasis is placed on a simple and didactic presentation.

The determination of the ionization of a system in the hot dense regime is a long standing issue. Recent studies have shown inconsistencies between standard predictions using average atom models and evaluations deduced from electronic transport properties computed with quantum molecular dynamics simulations [Bethkenhagen et al., Phys. Rev. Res. 2, 023260 (2020)]2643-156410.1103/PhysRevResearch.2.023260. Here, we propose a definition of the ionization based on its effect on the plasma structure as given by the pair distribution function (PDF), and on the concept of effective one-component plasma (eOCP). We also introduce a definition based on the total pressure and on a modelization of the electronic pressure. We show the equivalence of these definitions on two studies of carbon along the 100 eV isotherm and the 10 g/cm^{3} isochor. Simulations along the 100 eV isotherm are obtained with the newly implemented Ext. First principles molecular dynamics (Fpmd) method in Abinit for densities ranging from 1 to 500 g/cm^{3}and along the 10 g/cm^{3} isochor with the recently published Spectral quadrature DFT (Sqdft) simulations, between 8 and 860 eV. The resulting ionizations are compared to the predictions of the average-atom code Qaam which is based on the muffin-tin approximation. A disagreement between the eOCP and the actual PDFs (non-OCP behavior) is interpreted as the onset of bonding in the system.

We performab initiosimulations of beryllium (Be) and magnesium oxide (MgO) at megabar pressures and compare their structural and thermodynamic properties. We make a detailed comparison of our two recently derived phase diagrams of Be (Wuet al2021Phys. Rev.B104014103) and MgO (Soubiran and Militzer 2020Phys. Rev. Lett.125175701) using the thermodynamic integration technique, as they exhibit striking similarities regarding their shape. We explore whether the Lindemann criterion can explain the melting temperatures of these materials through the calculation of the Debye temperature at high pressure. From our free energy calculations, we find that the melting line of both materials is well represented by the Simon-Glazel fitTm(P) =T0(1 +P/a)1/c, whereT0= 1564 K,a= 15.8037 GPa andc= 2.4154 for Be, whileT0= 3010 K,a= 10.5797 GPa andc= 2.8683 for the MgO in the B1. For the B2 phase, we use the valuesa= 26.1163 GPa andc= 2.2426. Both materials exhibit negative Clapeyron slopes on the boundaries between the two solid phases that are strongly affected by anharmonic effects, which also influence the location of the solid-solid-liquid triple point. We find that the quasi-harmonic approximation underestimates the stability range of the low-pressure phases, namely hcp for Be and B1 for MgO. We also compute the phonon dispersion relations at low and high pressure for each of the phases of these materials, and also explore how the phonon density of states is modified by temperature. Finally, we derive secondary shock Hugoniot curves in addition to the principal Hugoniot curve for both materials, and study their offsets in pressure between solid and liquid branches.

The extended first-principles molecular dynamics (Ext. FPMD) model introduced by Shen Zhang et al. has been implemented within the ab initio DFT software package ABINIT and is now publicly available. This model allows performing quantum molecular dynamics simulations (QMD) at high temperatures bypassing the well-known orbitals wall. QMD simulations can be done smoothly in the full range of temperatures from cold condensed matter to hot plasmas (>100 eV) passing by the warm dense matter regime. At high temperature, a minimum of Kohn-Sham orbitals is kept, allowing for deep ionization effects to manifest, such as the Schottky anomaly of the specific heat, in contrast with orbital-free approaches for which this effect is absent. Using the new 9.6 ABINIT version, we present extensive simulations of boron along isochores, from a few Kelvins to thousands of eVs, in the Gigabar regime and construct a table. The Hugoniot curve is found in close agreement with the FPEOS model, for a much lower computational intensity. An ionization analysis, deduced from the pressure or from the structure, emphasizes the crucial contribution of the very deep 1s shell in the maximum compression regime.

The ab initio (ai) Gibbs ensemble (GE) Monte Carlo (MC) method coupled with Kohn-Sham density functional theory is successful in predicting the liquid-vapour equilibrium of insulating systems. Here we show that the aiGEMC method can be used to study also metallic systems, where the excited electronic states play an important role and cannot be neglected. For this we include the electronic free energy in the formulation of the effective energy of the system to be used in the acceptance criteria for the MC moves. The application of this aiGEMC method to sodium yields a good agreement with available experimental data on the liquid-vapour equilibrium densities. We predict a critical point for sodium at 2338 ± 108 K and 0.24 ± 0.03 g cm-3. The liquid structure stemming from aiGEMC simulations is very similar to the one from ab initio molecular dynamics. Since this method can determine phase transition without computing the Gibbs free energy, it may offer a new possibility to study other materials with a reasonable computational cost.

Earth's lowermost mantle displays complex geological phenomena that likely result from its heterogeneous physical interaction with the core. Geophysical models of core-mantle interaction rely on the thermal and electrical conductivities of appropriate geomaterials which, however, have never been probed at representative pressure and temperature (P-T) conditions. Here we report on the opacity of single crystalline bridgmanite and ferropericlase and link it to their radiative and electrical conductivities. Our results show that light absorption in the visible spectral range is enhanced upon heating in both minerals but the rate of change in opacity with temperature is a factor of six higher in ferropericlase. As a result, bridgmanite in the lowermost mantle is moderately transparent while ferropericlase is highly opaque. Our measurements support previous indirect estimates of low (< 1 W/m/K) and largely temperature-independent radiative conductivity in the lowermost mantle. This implies that the radiative mechanism has not contributed significantly to cooling the Earth's core throughout the geologic time. Opaque ferropericlase is electrically conducting and mediates strong core-mantle electromagnetic coupling, explaining the intradecadal oscillations in the length of day, low secular geomagnetic variations in Central Pacific, and the preferred paths of geomagnetic pole reversals. (C) 2021 Elsevier B.V. All rights reserved.

We put together a first-principles equation of state (FPEOS) database for matter at extreme conditions by combining results from path integral Monte Carlo and density functional molecular dynamics simulations of the elements H, He, B, C, N, O, Ne, Na, Mg, Al, and Si as well as the compounds LiF, B_{4}C, BN, CH_{4}, CH_{2}, C_{2}H_{3}, CH, C_{2}H, MgO, and MgSiO_{3}. For all these materials, we provide the pressure and internal energy over a density-temperature range from ∼0.5 to 50 g cm^{-3} and from ∼10^{4} to 10^{9} K, which are based on ∼5000 different first-principles simulations. We compute isobars, adiabats, and shock Hugoniot curves in the regime of L- and K-shell ionization. Invoking the linear mixing approximation, we study the properties of mixtures at high density and temperature. We derive the Hugoniot curves for water and alumina as well as for carbon-oxygen, helium-neon, and CH-silicon mixtures. We predict the maximal shock compression ratios of H_{2}O, H_{2}O_{2}, Al_{2}O_{3}, CO, and CO_{2} to be 4.61, 4.64, 4.64, 4.89, and 4.83, respectively. Finally we use the FPEOS database to determine the points of maximum shock compression for all available binary mixtures. We identify mixtures that reach higher shock compression ratios than their end members. We discuss trends common to all mixtures in pressure-temperature and particle-shock velocity spaces. In the Supplemental Material, we provide all FPEOS tables as well as computer codes for interpolation, Hugoniot calculations, and plots of various thermodynamic functions.

We present the story of full three‐dimensional ab initio simulation techniques of dense plasmas based on the Kohn–Sham realization of the density functional theory, starting from early attempts using the Car–Parrinello method to the most recent approaches based on density matrix. We recall the decisive role played by two experiments, one on the Nova laser and the other at a much smaller scale, with pulsed electrical discharges. We emphasize that the essential roles of the Physics of Non‐Ideal Plasmas (PNP) and Strongly Coupled Coulomb Systems (SCCS) conference series were most results, and simulation tools were presented and discussed under the benevolent presence of Vladimir Fortov.

We have developed a Python-based open-source package to analyze the results stemming from ab initio molecular-dynamics simulations of fluids. The package is best suited for applications on natural systems, like silicate and oxide melts, water-based fluids, and various supercritical fluids. The package is a collection of Python scripts that include two major libraries dealing with file formats and with crystallography. All the scripts are run at the command line. We propose a simplified format to store the atomic trajectories and relevant thermodynamic information of the simulations, which is saved in UMD files, standing for Universal Molecular Dynamics. The UMD package allows the computation of a series of structural, transport and thermodynamic properties. Starting with the pair-distribution function it defines bond lengths, builds an interatomic connectivity matrix, and eventually determines the chemical speciation. Determining the lifetime of the chemical species allows running a full statistical analysis. Then dedicated scripts compute the mean-square displacements for the atoms as well as for the chemical species. The implemented self-correlation analysis of the atomic velocities yields the diffusion coefficients and the vibrational spectrum. The same analysis applied on the stresses yields the viscosity. The package is available via the GitHub website and via its own dedicated page of the ERC IMPACT project as open-access package.