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Simulation and literature data on the electrical and thermal conductivity of iron. The raw simulation data was generated from time-dependent density functional theory calculations. Post-processing was applied to obtain the transport properties (conductivities) as described in the associated journal publication. The literature data was compiled from available publication data as referenced in the associated journal publication.

Higher order correlations influence the physics of the system on many levels. They may be summarized by local field corrections or appear explicitly as non-linear contributions in the density response or in other properties like the stopping power. We present the latest results for nonlinear properties of the electron gas as they have been obtained using real time Green's functions, path integral Monte Carlo, and density functional theory. We show how nonlinear properties can be extracted from simulations with and without external perturbations.

The density values from KS-DFT simulations presented in the paper by Moldabekov et al., J. Phys. Chem. Lett. 2023, 14, 5, 1326–1333

The electronic exchange-correlation (XC) kernel constitutes a fundamental input for the estimation of a gamut of material properties such as the dielectric characteristics, the thermal and electrical conductivity, the construction of effective potentials, or the response to an external perturbation. In practice, no reliable method has been known that allows to compute the kernel of real materials. In this work, we overcome this long-standing limitation by introducing a new, formally exact methodology for the computation of the static XC kernel of arbitrary materials exclusively within the framework of density functional theory (DFT) -- no external input apart from the usual XC-functional is required. As a first practical demonstration of the utility and flexibility of our methodology, we compare our new results with exact quantum Monte Carlo (QMC) data for the archetypical uniform electron gas model at both ambient and warm dense matter conditions. This gives us unprecedented insights into the performance of different XC-functionals, and has important implications for the development of new functionals that are designed for the application at extreme temperatures. In addition, we obtain new DFT results for the XC kernel of warm dense hydrogen as it occurs in fusion applications and astrophysical objects such as planetary interiors. The observed excellent agreement to the recent QMC results by Böhme \emph{et al.}~[Phys.~Rev.~Lett.~\textbf{129}, 066402 (2022)] clearly demonstrates that our framework is capable to even capture nontrivial effects such as XC-induced isotropy breaking in the density response of hydrogen at large wave numbers. Our method can easily be applied using standard DFT codes and will open up new avenues for the computation of the properties of real materials.

This repository contains the DFT simulation results presented in the article "Assessing the accuracy of hybrid exchange-correlation functionals for the density response of warm dense electrons". The minimal dataset that would be necessary to interpret, replicate and build upon the findings reported in the article.

This is the archived datasets used for the publication in the article: Ab initio path integral Monte Carlo simulations of hydrogen snapshots at warm dense matter conditions. The dataset also contains the data-analysis python scripts.

This repository contains the DFT simulation results presented in the article "Ab Initio Static Exchange-Correlation Kernel across Jacob's Ladder without Functional Derivatives"

DFT-MD and HNC data for cryogenic hydrogen and for two-temperature hydrogen

We present novel experimental results of ultra fast heating of Warm Dense Cu diagnosed by means of x-ray absorption and emission spectroscopy carried out at the Draco laser facility at HZDR in 2021. A thin Cu foil was directly heated to few eV temperature by an ultra short laser pulse (40 fs, 2e15 W/cm2) and probed with variable delay in the range 0.2-20 ps by a laser-driven betatron radiation. This betatron radiation, created by a laser wakefield accelerator, is an unique x-ray source with its ultra short duration and broadband spectrum, therefore ideally suited for studies of non-equilibrium dense plasmas while its high brightness allows for single-shot measurement. The sample is studied via the X-ray absorption spectroscopy in the region above the Cu K-edge. This method provides temporally-resolved information about both the ionic structure of the matter and its temperature during the process of ultrafast heating and melting of the material. The measured spectra are understood and analyzed by using Ab initio simulations and the temporal evoution of heatig and melting is compared to PIC simulations to infer the electron to ion energy transer.

DFT data and results for Al and Cu for the DOS, phonon DOS, and Eliashberg function depending on the electron temperature.

Several properties of hydrogen in the solid, liquid, and metallic liquid are investigated for different xc functionals

Understanding the electronic transport properties of iron under high temperatures and pressures is essential for constraining geophysical processes. The difficulty of reliably measuring these properties calls for sophisticated theoretical methods that can support diagnostics. We present electrical conductivity results from simulating microscopic Ohm’s law using the real-time formalism of time-dependent density functional theory for conditions ranging from high-pressure solid at ambient temperature to earth-core conditions.

Understanding the electronic transport properties of iron under high temperatures and pressures is essential for constraining geophysical processes. The difficulty of reliably measuring these properties under for sophisticated theoretical methods that can support diagnostics. We present results of the electrical conductivity from simulating microscopic Ohm’s law using time-dependent density functional theory.

Warm dense matter (WDM) is a state of matter with parameters between solids and dense plasmas. WDM is characterized by the relevance of quantum degeneracy, thermal excitations, and strong correlations. Many questions regarding the interplay of these effects in WDM remain open. In this paper, we use an externally perturbed electron gas to investigate how electronic structure and excitations are affected by thermal excitations and density inhomogeneities. The results are reported in our recent articles [1-4]. We present a study of the quality of various exchange-correlation functionals in the KS-DFT method [1,2]. In addition, we show how electronic excitations change due to strong inhomogeneity and thermal effects [3]. Based, on these results, we present a new KS-DFT based methodology for the investigation of the non-linear response of electrons across temperature regimes relevant for WDM [4]. References [1] Z. Moldabekov, T.Dornheim, M. Boehme, J. Vorberger, A. Cangi, The Journal of Chem- ical Physics 155, 124116 (2021). [2] Z. Moldabekov, T.Dornheim, J. Vorberger, A. Cangi, Phys. Rev. B 105, 035134 (2022). [3] Z. Moldabekov, T.Dornheim, A. Cangi, Scientific Reports 12, 1093 (2022) [4] Z.Moldabekov, J. Vorberger, T. Dornheim, Journal of Chemical Theory and Computation, accepted for publication (2022); arXiv:2201.01623.

In this presentation we discuss the results of the analysis of the accuracy of the commonly used exchange-correlation (XC) functionals for warm dense matter simulation [1,2]. The analysis is performed by comparing the path-integral quantum Monte-Carlo (QMC) data with KS-DFT results. The relative deviation of the total density from the reference data is reported for different XC functionals in the case of the inhomogeneous electron gas. Furthermore, a new methodology for the investigation of the non-linear static density response WDM based on KS-DFT method is presented [3]. The results are verified by comparing to the QMC data when thermal temperature is equal to the Fermi temperature. New results for partially and strongly degenerate electrons are presented. Finally, we present the results of the analysis of the electronic local field correction as computed using various XC functionals. By comparing the data to the exact QMC results, we are able to understand the effect of the thermal excitations on XC functional. [1] Z. Moldabekov, T.Dornheim, M. Böhme, J. Vorberger, A. Cangi, The Journal of Chemical Physics 155, 124116 (2021). [2] Z. Moldabekov, T.Dornheim, J. Vorberger, A. Cangi, Phys. Rev. B 105, 035134 (2022). [3] Z.Moldabekov, T. Dornheim, J. Vorberger, Journal of Chemical Theory and Computation (2022).

Understanding the electronic transport properties of iron under high temperatures and pressures is essential for constraining geophysical processes. The difficulty of reliably measuring these properties calls for sophisticated theoretical methods that can support diagnostics. We present results of the electrical conductivity within the pressure and temperature ranges found in Earth's core by simulating microscopic Ohm's law using time-dependent density functional theory.

Time-dependent density functional theory (TDDFT) enables calculating electronic transport properties in the warm dense matter (WDM) and is an alternative to present state-of-the-art approaches. In the real-time formalism of TDDFT (RT-TDDFT), the electrical conductivity is directly computed from the time evolution of the electronic current density and provides direct means to assess the validity of Ohm's law in WDM. Without relying on the methods of diagonalization, the method is computationally fast compared to linear-response TDDFT (LR-TDDFT). We present TDDFT calculations of the electrical conductivity in iron within the pressure and temperature ranges found in Earth's core and discuss the ramifications of using TDDFT for calculating the electrical conductivity in contrast to the Kubo-Greenwood (KG) formalism and dielectric models.

DFT simulation results for the total density distribution

DFT data concerning the electronic structure and electron-phonon coupling of Co and Fe. NOT the atomistic spin simulations. NO experimental data.

This work presents first insights into the dynamics of free-surface release clouds from dynamically compressed polystyrene and pyrolytic graphite at pressures up to 200 GPa, where they transform into diamond or lonsdaleite, respectively. These ejecta clouds are released into either vacuum or various types of catcher systems, and are monitored with high-speed recordings (frame rates up to 10 MHz). Molecular dynamics simulations are used to give insights to the rate of diamond preservation throughout the free expansion and the catcher impact process, highlighting the challenges of diamond retrieval. Raman spectroscopy data show graphitic signatures on a catcher plate confirming that the shock-compressed PS is transformed. First electron microscopy analyses of solid catcher plates yield an outstanding number of different spherical-like objects in the size range between ten(s) up to hundreds of nanometres, which are one type of two potential diamond candidates identified. The origin of some objects can unambiguously be assigned, while the history of others remains speculative.

Due to its nature as a strongly correlated quantum liquid, ultracold helium is characterized by the nontrivial interplay of different physical effects. Bosonic 4He exhibits superfluidity and Bose-Einstein condensation. Its physical properties have been accurately determined on the basis of ab initio path integral Monte Carlo (PIMC) simulations. In contrast, the corresponding theoretical description of fermionic 3He is severely hampered by the notorious fermion sign problem, and previous PIMC results have been derived by introducing the uncontrolled fixed-node approximation. In this work, we present extensive new PIMC simulations of normal liquid 3He without any nodal constraints. This allows us to to unambiguously quantify the impact of Fermi statistics and to study the effects of temperature on different physical properties like the static structure factor S(q) , the momentum distribution n(q) , and the static density response function χ(q). In addition, the dynamic structure factor S(q, ω) is rigorously reconstructed from imaginary-time PIMC data. From simulations of 3He , we derived the familiar phonon–maxon–roton dispersion function that is well-known for 4He and has been reported previously for two-dimensional 3He films (Nature 483:576–579 (2012)). The comparison of our new results for both S(q) and S(q, ω) with neutron scattering measurements reveals an excellent agreement between theory and experiment.

Talk at Hirschegg workshop "41th International Workshop on High Energy Density Physics with Intense Ion and Laser Beams"

The structure of the fluid carbon phase in the pressure region of the graphite, diamond, and BC8 solid phases is investigated. We find increasing coordination numbers with an increase in density. From zero to 30 GPa, the liquid shows a decrease of packing efficiency with increasing temperature. However, for higher pressures, the coordination number increases with increasing temperature. Up to 1.5 eV and independent of the pressure up to 1500 GPa, a double-peak structure in the ion structure factors exists, indicating persisting covalent bonds. Over the whole pressure range from zero to 3000 GPa, the fluid structure and properties are strongly determined by such covalent bonds.

The numerical modeling of plasmon behavior is crucial for an accurate interpretation of inelastic scattering diagnostics in many experiments. We highlight the utility of linear-response time-dependent density functional theory (LR-TDDFT) as an appropriate first-principles framework for a consistent modeling of plasmon properties. We provide a comprehensive analysis of plasmons from ambient throughout warm dense conditions and assess typical properties such as the dynamical structure factor, the plasmon dispersion, and the plasmon width. We compare them with experimental measurements in aluminum accessible via x-ray Thomson scattering and with other dielectric models such as the Lindhard model, the Mermin approach based on parametrized collision frequencies, and the dielectric function obtained using static local field corrections of the uniform electron gas parametrized from path integral Monte Carlo simulations both at the ground state and at finite temperature. We conclude with the remark that the common practice of extracting and employing plasmon dispersion relations and widths is an insufficient procedure to capture the complicated physics contained in the dynamic structure factor in its full breadth.

The theoretical understanding of plasmon behavior is crucial for an accurate interpretation of inelastic scattering diagnostics in many experiments. We highlight the utility of linear-response time-dependent density functional theory (LR-TDDFT) as a first-principles framework for consistently modeling plasmon properties. We provide a comprehensive analysis of plasmons in aluminum from ambient to warm dense matter conditions and assess typical properties such as the dynamical structure factor, the plasmon dispersion, and the plasmon lifetime. We compare our results with scattering measurements and with other TDDFT results as well as models such as the random phase approximation, the Mermin approach, and the dielectric function obtained using static local field corrections of the uniform electron gas parametrized from path-integral Monte Carlo simulations. We conclude that results for the plasmon dispersion and lifetime are inconsistent between experiment and theories and that the common practice of extracting and studying plasmon dispersion relations is an insufficient procedure to capture the complicated physics contained in the dynamic structure factor in its full breadth.

Average atom (AA) models allow one to efficiently compute electronic and optical properties of materials over a wide range of conditions and are thus often employed to interpret experimental data. However, at high pressure, predictions from AA models have been shown to disagree with results from many-body {\it ab initio} computer simulations. Here we reconcile these deviations by developing an innovative type of AA model, \Avion, that computes the electronic eigenstates with novel boundary conditions within the ion sphere. Bound and free states are thus derived consistently. We drop the common AA assumption that the free-particle spectrum starts at the potential threshold, which we found to be incompatible with {\it ab initio} calculations. We perform {\it ab initio} simulations of crystalline and liquid carbon and aluminum over a wide range of densities and show that the computed band structure is in very good agreement with predictions from \Avion.

Experimental diagnostics as well as theoretical modeling of warm dense matter (WDM) heavily rely on linear response theory. However, Dornheim et. al. [Phys. Rev. Lett.125, 085001 (2020)] showed that assuming the linear regime may not always be justified in experiments studying WDM. In addition, the intentional driving of non-linear effects should make new insight into many-particle effects possible. We use ab initio Path-Integral Monte-Carlo (PIMC) to obtain exact results for a harmonically perturbed homogeneous electron gas. A thorough analysis for different perturbation amplitudes is carried out. The corresponding density response reveals resonances at the higher harmonics of the perturbation wave vector. Analyzing the induced density response as a function of the perturbation amplitude shows the importance of the cubic response at the first harmonic and of the quadratic response at the second harmonic.

We present structure measurements of biaxially orientated polyethylene terephthalate (PET, (C10H8O4)n , also called mylar) shock-compressed to (155+/-20) GPa and (6000+/-1000) K using in situ X-ray diffraction. Comparing to density functional theory molecular dynamics simulations, we find a highly correlated liquid that exhibits a temperature signficantly lower than predicted by some equation-of-state tables, which underlines the influence of complex chemical interactions in this regime. Indeed, at the inferred temperature and pressure, formation of nanodiamonds may be expected as recently observed in polystyrene at similar conditions. While some hints of diamond formation from PET are visible in the diffraction data, the strong liquid correlations prevent a conclusive statement as to whether diamonds are formed inside the sample volume.

Iron is one of the most plentiful components on the planet earth and plays a crucial role in our lives. The analysis of iron at high pressures and temperatures is of great geophysical importance because iron makes up the majority of the Earth’s liquid outer core and solid inner core. The technical utility of iron is due to the large phase space of iron-based alloys, which is the source of a wide range of steel microstructures that can be produced with minor compositional changes and proper thermal treatment. The iron phase structure at the extreme conditions under the inner core conditions of the earth is still not conclusive especially in the vicinity of temperature around 6000 K and pressures nearing 300 GPa. Time-dependent density functional theory (TDDFT) enables calculating electronic transport properties in warm dense matter (WDM) and is an alternative to present state-of-the-art approaches. In TDDFT, the electrical conductivity is computed from the time evolution of the electronic current density and provides direct means to assess the validity of Ohm’s law in WDM. We present TDDFT calculations of the electrical conductivity for iron within the pressure and temperature range found in Earth’s core. We discuss the ramifications of using TDDFT for calculating the electrical conductivity in contrast to the Kubo-Greenwood formalism and dielectric models.