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We evaluate the f-sum rule on the dynamic structure factor in the imaginary-time domain as a formally exact and simulation-free means of normalizing X-Ray Thomson Scattering (XRTS) spectra. This circumvents error-prone real-time deconvolution of the source function and facilitates calculating the static structure factor from the properly normalized imaginary-time correlation function. We apply our technique to two distinct sets of experimental data, finding that it is effective for both narrow and broad x-ray sources. This approach could be readily adapted to other scattering spectroscopies.

This repository contains all PIMC results related to the publication "Ab initio Density Response and Local Field Factor of Warm Dense Hydrogen". Generally, data formats are identical to figures. Exceptions are 3D ITCF data sets for Figs. 2, 8 and 12: #1 k [a_Bohr^{-1}], #2 tau [Ha^{-1}], #3/#4 F(q,tau)x32 and statistical error and the "ITCF" folders with the raw data for F(q,tau): ITCF: #1 tau [Ha^{-1}]; #2/3: F(q,tau) and statistical error The number after "index" in the file names gives the number of the respective q-vector; see "static_structure_factor_key.dat", columns 1 and 2 for the respective index-to-q mapping, with [q]=a_Bohr{-1}

Hydrogen at extreme temperatures and pressures has significant relevance for cutting-edge technological applications, and its natural occurrence in astrophysical objects further underscores its importance. In this work, we develop a new framework to identify the breaking of bound states due to pressure ionization in bulk hydrogen [1]. Firstly, we show that the dimensionless reduced density gradient (RDG) is a valuable tool for detecting pressure-induced ionization in the medium. Secondly, the generalized RDG is proposed as an effective means for examining the interstitial electronic structure. Finally, our rigorous assessment of a variety of exchange-correlation (XC) functionals in density functional theory calculations for different density regions reveals the crucial role of thermal XC effects in accurately describing density gradients in high-energy density systems. Our exact path integral Monte-Carlo (PIMC) test set generated for this project is freely available online [2]. The insights gained from this research could also have implications for our understanding of astrophysical phenomena, such as white dwarf stars. Furthermore, this study is an addition to our current research on thermal effects in XC functionals, which we are exploring at various complexity levels [3-6]. References: [1] Z. Moldabekov, S. Schwalbe, M. P. Böhme, J. Vorberger, X. Shao, M. Pavanello, F. Graziani, T. Dornheim, Journal of Chemical Theory and Computation (in print) (2023). DOI: 10.1021/acs.jctc.3c00934 ; arXiv:2308.07916. [2] The data is available according to the FAIR principles on the bound state breaking BSB GitLab Repository. 2023; https://gitlab.com/theonov13/bsb [3] Z. Moldabekov, M. Lokamani, J. Vorberger, A. Cangi, and T. Dornheim, The Journal of Physical Chemistry Letters 14 (5), 1326-1333 (2023). [4] Z. Moldabekov, M. Lokamani, J. Vorberger, A. Cangi, T. Dornheim, J. Chem. Phys. 158, 094105 (2023). [5] Z. Moldabekov, T.Dornheim, M. Böhme, J. Vorberger, A. Cangi, J. Chem. Ph

Experiments creating extreme states of matter almost invariably create non-equilibrium states. These are very interesting in their own right but need to be understood even if the ultimate goal is to probe high pressure or high temperature equilibrium properties like the equation of state. Here, we report on the capabilities of the newly developed imaginary time correlation function (ITCF) technique [1] to detect and quantify non-equilibrium in pump-probe experiments fielding time resolved x-ray scattering diagnostics. We find a high sensitivity of the ITCF even to a small fraction of non-equilibrium electrons in the Wigner distribution. The behavior of the ITCF technique is such that modern lasers and detectors should be able to trace the non-equilibrium relaxation from tens of femto-seconds to several 10s of picoseconds without the need for a model.

We present new concepts for the experimental and theoretical study of atomic physics of Be at GBar pressure at the National Ignition Facility.

We present extensive new \emph{ab initio} path integral Monte Carlo (PIMC) results for a variety of structural properties of warm dense hydrogen and beryllium. To deal with the fermion sign problem -- an exponential computational bottleneck due to the antisymmetry of the electronic thermal density matrix -- we employ the recently proposed [\textit{J.~Chem.~Phys.}~\textbf{157}, 094112 (2022); \textbf{159}, 164113 (2023)] -extrapolation method and find excellent agreement with exact direct PIMC reference data where available. This opens up the intriguing possibility to study a gamut of properties of light elements and potentially material mixtures over a substantial part of the warm dense matter regime, with direct relevance for astrophysics, material science, and inertial confinement fusion research.

Warm dense matter (WDM) is now routinely created and probed in laboratories around the world, providing unprecedented insights into conditions achieved in stellar atmospheres, planetary interiors, and inertial confinement fusion experiments. However, the interpretation of these experiments is often filtered through models with systematic errors that are difficult to quantify. Due to the simultaneous presence of quantum degeneracy and thermal excitation, processes in which free electrons are de-excited into thermally unoccupied bound states transferring momentum and energy to a scattered x-ray photon become viable [1]. Here we show that such free-bound transitions are a particular feature of WDM and vanish in the limits of cold and hot temperatures. The inclusion of these processes into the analysis of recent X-ray Thomson Scattering (XRTS) experiments on WDM at the National Ignition Facility [2] (see the figure below) and the Linac Coherent Light Source [3] significantly improves model fits, indicating that free- bound transitions have been observed without previously being identified. This interpretation is corroborated by agreement with a recently developed model-free thermometry technique [4,5] and presents an important step for precisely characterizing and understanding the complex WDM state of matter.

We have developed an experimental platform for x-ray Thomson scattering (XRTS) at NIF to characterize plasma conditions in ICF indirectly-driven capsule implosions near stagnation [1,2]. This enabled us to investigate up to 30 times compressed ablator materials reaching pressures above 3 Gigabars, at conditions where the distance between the nuclei becomes comparable to the extent of the core shell bound states, which will eventually lead to their pressure ionization. In this talk we will present results from experiments with beryllium shells. We observe reduced elastic scattering for the most extreme conditions [2]. We interpret this reduction as the precursor of pressure ionization of the remaining K-shell electrons, that is, a strongly modified bound state. The beryllium charge state inferred from the data is considerable higher than standard models predict but agrees well with results from DFT simulations [2,3]. Accurate modelling of the K-shell occupation of light elements is imperative for creating predictive capabilities for ICF implosions. Our experiments yield valuable benchmarks for this process and demonstrating a complex pathway of pressure ionization.

We combine ab initio path integral Monte Carlo (PIMC) simulations with fixed ionic configurations, obtained by DFT-MD simulations, in order to solve the electronic problem for hydrogen under warm dense matter conditions. To solve the divergence problem in the Ewald-sum for attractive potentials we employ the pair-approximation. This approach is compared against the much simpler Kelbg pair-potential. We find very favorable convergence behavior towards the latter. Since PIMC does not require any further assumptions regarding exchange and correlations of the many-body system, we then compare electronic densities obtained from our snapshot PIMC calculations with DFT calculations in the metallic regime. Furthermore, we investigate the manifestation of the resulting fermionic sign problem in our snapshot PIMC simulations. This gives us the unique capability to study the properties of warm dense hydrogen from ab initio simulations without any further assumptions, like the functional form of the exchange-correlation effects or fixed fermionic nodes. Thus, snapshot PIMC enables us to obtain the exact density response of warm dense hydrogen. This is extremely valuable to both experiments, like X-Ray Thomson scattering, as well as the development of new XC-functionals.

Hydrogen at extreme temperatures and pressures is ubiquitous throughout our universe and naturally occurs in a variety of astrophysical objects. In addition, it is of key relevance for cutting-edge technological applications, with inertial confinement fusion research being a prime example. In the present work, we present exact \emph{ab initio} path integral Monte Carlo (PIMC) results for the electronic density of warm dense hydrogen along a line of constant degeneracy across a broad range of densities. Using the well-known concept of reduced density gradients, we develop a new framework to identify the breaking of bound states due to pressure ionization in bulk hydrogen. Moreover, we use our PIMC results as a reference to rigorously assess the accuracy of a variety of exchange--correlation (XC) functionals in density functional theory calculations for different density regions. Here a key finding is the importance of thermal XC effects for the accurate description of density gradients in high-energy density systems. Our exact PIMC test set is freely available online and can be used to guide the development of new methodologies for the simulation of warm dense matter and beyond.

All data as needed to generate the figures in the manuscript.

The properties of hydrogen at warm dense matter (WDM) conditions are of high importance for the understanding of astrophysical objects and technological applications such as inertial confinement fusion. In this work, we present extensive new \emph{ab initio} path integral Monte Carlo (PIMC) results for the electronic properties in the Coulomb potential of a fixed ionic configuration. This gives us new insights into the complex interplay between the electronic localization around the protons with their density response to an external harmonic perturbation. We find qualitative agreement between our simulation data and a heuristic model based on the assumption of a local uniform electron gas model, but important trends are not captured by this simplification. In addition to being interesting in their own right, we are convinced that our results will be of high value for future projects, such as the rigorous benchmarking of approximate theories for the simulation of WDM, most notably density functional theory.

Matter at extreme temperatures and pressures -- commonly known as warm dense matter (WDM) in the literature -- is ubiquitous throughout our Universe and occurs in a number of astrophysical objects such as giant planet interiors and brown dwarfs. Moreover, WDM is very important for technological applications such as inertial confinement fusion, and is realized in the laboratory using different techniques. A particularly important property for the understanding of WDM is given by its electronic density response to an external perturbation. Such response properties are routinely probed in x-ray Thomson scattering (XRTS) experiments, and, in addition, are central for the theoretical description of WDM. In this work, we give an overview of a number of recent developments in this field. To this end, we summarize the relevant theoretical background, covering the regime of linear-response theory as well as nonlinear effects, the fully dynamic response and its static, time-independent limit, and the connection between density response properties and imaginary-time correlation functions (ITCF). In addition, we introduce the most important numerical simulation techniques including ab initio path integral Monte Carlo (PIMC) simulations and different thermal density functional theory (DFT) approaches. From a practical perspective, we present a variety of simulation results for different density response properties, covering the archetypal model of the uniform electron gas and realistic WDM systems such as hydrogen. Moreover, we show how the concept of ITCFs can be used to infer the temperature from XRTS measurements of arbitrarily complex systems without the need for any models or approximations. Finally, we outline a strategy for future developments based on the close interplay between simulations and experiments.

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.

The accurate interpretation of experiments with matter at extreme densities and pressures is a notoriously difficult challenge. In a recent work [T.~Dornheim et al., Nature Comm. (in print), arXiv:2206.12805], we have introduced a formally exact methodology that allows extracting the temperature of arbitrarily complex materials without any model assumptions or simulations. Here, we provide a more detailed introduction to this approach and analyze the impact of experimental noise on the extracted temperatures. In particular, we extensively apply our method both to synthetic scattering data and to previous experimental measurements over a broad range of temperatures and wave numbers. We expect that our approach will be of high interest to a gamut of applications, including inertial confinement fusion, laboratory astrophysics, and the compilation of highly accurate equation-of-state databases.

The rigorous diagnostics of experiments with warm dense matter (WDM) is notoriously difficult. A key method is given by X-ray Thomson scattering (XRTS), but the interpretation of XRTS measurements is usually based on theoretical models that entail various approximations. Recently, Dornheim et al. [arXiv:2206.12805] have introduced a new framework for temperature diagnostics of XRTS experiments that is based on imaginary-time correlation functions (ITCF). On the one hand, switching from the frequency- to the imaginary-time domain gives one direct access to a number of physical properties, which facilitates the extraction of the temperature of arbitrarily complex materials without any models or approximations. On the other hand, the bulk of theoretical works in dynamic quantum many-body theory is devoted to the frequency-domain, and, to our knowledge, the manifestation of physics properties within the ITCF remains poorly understood. In the present work, we aim to change this unsatisfactory situation by introducing a simple, semi-analytical model for the imaginary-time dependence of two-body correlations within the framework of imaginary-time path integrals. As a practical example, we compare our new model to extensive ab initio path integral Monte Carlo results for the ITCF of a uniform electron gas, and find excellent agreement over a broad range of wave numbers, densities, and temperatures.

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

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.

We combine ab initio path integral Monte Carlo (PIMC) simulations with fixed ionic configurations, obtained by DFT-MD simulations, in order to solve the electronic problem for hydrogen under warm dense matter conditions. To solve the divergence problem in the Ewald-sum for attractive potentials we employ the pair-approximation. This approach is compared against the much simpler Kelbg pair-potential. We find very favorable convergence behavior towards the latter. Since PIMC does not require any further assumptions regarding exchange and correlations of the many-body system, we then compare electronic densities obtained from our snapshot PIMC calculations with DFT calculations in the metallic regime. Furthermore, we investigate the manifestation of the resulting fermionic sign problem in our snapshot PIMC simulations. This gives us the unique capability to study the properties of warm dense hydrogen from ab initio simulations without any further assumptions, like the functional form of the exchange-correlation effects or fixed fermionic nodes. Thus, snapshot PIMC enables us to obtain the exact density response of warm dense hydrogen. This is extremely valuable to both experiments, like X-Ray Thomson scattering, as well as the development of new XC-functionals.

Automated test generators, such as search-based software testing (SBST) techniques are primarily guided by coverage information. As a result, they are very effective at achieving high code coverage. However, is high code coverage alone sufficient to detect bugs effectively In this paper, we propose a new SBST technique, predictive many objective sorting algorithm (PreMOSA), which augments coverage information with defect prediction information to decide where to increase the test coverage in the class under test (CUT). Through an experimental evaluation using 420 labelled bugs on the Defects4J benchmark and using theoretical defect predictors, we demonstrate the improved effectiveness and efficiency of PreMOSA in detecting bugs when using any acceptable defect predictor, i.e., a defect predictor with recall and precision 75%, compared to the state-of-the-art dynamic many objective sorting algorithm (DynaMOSA). PreMOSA detects up to 8.3% more labelled bugs on average than DynaMOSA when given a time budget of 2 minutes for test generation per CUT.

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).

The properties of hydrogen under extreme conditions are important for many applications, including inertial confinement fusion and astrophysical models. A key quantity is given by the electronic density response to an external perturbation, which is probed in X-ray Thomson scattering (XRTS) experiments -- the state of the art diagnostics from which system parameters like the free electron density , the electronic temperature , and the charge state can be inferred. In this work, we present highly accurate path integral Monte Carlo (PIMC) results for the electronic density response of hydrogen. We obtain the exchange-correlation (XC) kernel , which is of central relevance for many applications, such as time-dependent density functional theory (TD-DFT). This gives us a first unbiased look into the electronic density response of hydrogen in the warm-dense matter regime, thereby opening up a gamut of avenues for future research.

The experimental investigation of matter under extreme densities and temperatures as they occur for example in astrophysical objects and nuclear fusion applications constitutes one of the most active frontiers at the interface of material science, plasma physics, and engineering. The central obstacle is given by the rigorous interpretation of the experimental results, as even the diagnosis of basic parameters like the temperature T is rendered highly difficult by the extreme conditions. In this work, we present a simple, approximation-free method to extract the temperature of arbitrarily complex materials from scattering experiments, without the need for any simulations or an explicit deconvolution. This new paradigm can be readily implemented at modern facilities and corresponding experiments will have a profound impact on our understanding of warm dense matter and beyond, and open up a gamut of appealing possibilities in the context of thermonuclear fusion, laboratory astrophysics, and related disciplines.

This repository contains the PIMC raw data for the static electronic density response of warm dense hydrogen. Units etc are the same as in the figures in the main text / supplemental material.