arXiv subjects

Sebastian Schwalbe

Publications and source records attributed to Sebastian Schwalbe.

At least 37 records · Page 2Linked to original sources

arXiv2025

Fermionic free energies from \textit{ab initio} path integral Monte Carlo simulations of fictitious identical particles

We combine the recent $η-$ensemble path integral Monte Carlo (PIMC) approach to the free energy [T.~Dornheim \textit{et al.}, \textit{Phys.~Rev.~B} \textbf{111}, L041114 (2025)] with a recent fictitious partition function technique based on inserting a continuous variable that interpolates between the bosonic and fermionic limits [Xiong and Xiong, \textit{J.~Chem.~Phys.}~\textbf{157}, 094112 (2022)] to deal with the fermion sign problem. As a practical example, we apply our set-up to the warm dense uniform electron gas over a broad range of densities and temperatures. We obtain accurate results for the exchange--correlation free energy down to half the Fermi temperature, and find excellent agreement with the state-of-the-art parametrization by Groth \textit{et al.}~[\textit{Phys.~Rev.~Lett.}~\textbf{119}, 135001 (2017)]. Our work opens up new avenues for the future study of a host of interacting Fermi-systems, including warm dense matter, ultracold atoms, and electrons in quantum dots.

cond-mat.quant-gas↗

arXiv2025

Strong geometry dependence of the X-ray Thomson Scattering Spectrum in single crystal silicon

We report on results from an experiment at the European XFEL where we measured the x-ray Thomson scattering (XRTS) spectrum of single crystal silicon with ultrahigh resolution. Compared to similar previous experiments, we consider a more complex scattering setup, in which the scattering vector changes orientation through the crystal lattice. In doing so, we are able to observe strong geometric dependencies in the inelastic scattering spectrum of silicon at low scattering angles. Furthermore, the high quality of the experimental data allows us to benchmark state-of-the-art TDDFT calculations, and demonstrate TDDFT's ability to accurately predict these geometric dependencies. Finally, we note that this experimental data was collected at a much faster rate than another recently reported dataset using the same setup, demonstrating that ultrahigh resolution XRTS data can be collected in more general experimental scenarios.

cond-mat.mtrl-sci↗

arXiv2025

eminus -- Pythonic electronic structure theory

In current electronic structure research endeavors such as warm dense matter or machine learning applications, efficient development necessitates non-monolithic software, providing an extendable and flexible interface. The open-source idea offers the advantage of having a source code base that can be reviewed and modified by the community. However, practical implementations can often diverge significantly from their theoretical counterpart. Leveraging the efforts of recent theoretical formulations and the features of Python, we try to mitigate these problems. We present eminus, an education- and development-friendly electronic structure package designed for convenient and customizable workflows, yet built with intelligible and modular implementations.

physics.comp-ph↗

arXiv2024

Chemical potential of the warm dense electron gas from ab initio path integral Monte Carlo simulations

We present extensive new \emph{ab initio} path integral Monte Carlo (PIMC) simulation results for the chemical potential of the warm dense uniform electron gas (UEG), spanning a broad range of densities and temperatures. This is achieved by following two independent routes, i) based on the direct estimation of the free energy [Dornheim \emph{et al.}, arXiv:2407.01044] and ii) using a histogram estimator in PIMC simulations with a varying number of particles. We empirically confirm the expected inverse linear dependence of the exchange--correlation (XC) part of the chemical potential on the simulated number of electrons, which allows for a reliable extrapolation to the thermodynamic limit without the necessity for an additional finite-size correction. We find very good agreement (within $Δμ_\textnormal{xc}\lesssim0.5\%$) with the previous parametrization of the XC-free energy by Groth \emph{et al.}~[\emph{Phys.~Rev.~Lett.}~\textbf{119}, 135001 (2017)], which constitutes an important cross validation of current state-of-the-art UEG equations of state. In addition to being interesting in its own right, our study constitutes the basis for the future PIMC based investigation of the chemical potential of real warm dense matter systems starting with hydrogen.

physics.chem-ph↗

arXiv2024

Ensemble Generalization of the Perdew-Zunger Self-Interaction Correction: a Way Out of Multiple Minima and Symmetry Breaking

The Perdew-Zunger (PZ) self-interaction correction (SIC) is an established tool to correct unphysical behavior in density functional approximations. Yet, PZ-SIC is well-known to sometimes break molecular symmetries. An example of this is the benzene molecule, for which PZ-SIC predicts a symmetry-broken electron density and molecular geometry, since the method does not describe the two possible Kekulé structures on an even footing, leading to local minima [Lehtola et al, J. Chem. Theory Comput. 2016, 12, 3195]. PZ-SIC is often implemented with Fermi-Löwdin orbitals (FLOs), yielding the FLO-SIC method, which likewise has issues with symmetry breaking and local minima [Trepte et al, J. Chem. Phys. 2021, 155, 224109]. In this work, we propose a generalization of PZ-SIC - the ensemble PZ-SIC (E-PZ-SIC) method - which shares the asymptotic computational scaling of PZ-SIC (albeit with an additional prefactor). E-PZ-SIC is straightforwardly applicable to various molecules, merely requiring one to average the self-interaction correction over all possible Kekulé structures, in line with chemical intuition. We showcase the implementation of E-PZ-SIC with FLOs, as the resulting E-FLO-SIC method is easy to realize on top of an existing implementation of FLO-SIC. We show that E-FLO-SIC indeed eliminates symmetry breaking, reproducing a symmetric electron density and molecular geometry for benzene. The ensemble approach suggested herein could also be employed within approximate or locally scaled variants of PZ-SIC and their FLO-SIC versions.

physics.chem-ph↗

arXiv2024

Direct free energy calculation from ab initio path integral Monte Carlo simulations of warm dense matter

We carry out highly accurate \emph{ab initio} path integral Monte Carlo (PIMC) simulations to directly estimate the free energy of various warm dense matter systems including the uniform electron gas and hydrogen without any nodal restrictions or other approximations. Since our approach is based on an effective ensemble in a bosonic configuration space, it does not increase the computational complexity beyond the usual fermion sign problem. Its application to inhomogeneous cases such as an electronic system in a fixed external ion potential is straightforward and opens up the enticing possibility to benchmark density functional theory and other existing methods. Finally, it is not limited to warm dense matter, and can be applied to a gamut of other systems such ultracold atoms and electrons in quantum dots.

cond-mat.quant-gas↗

arXiv2024

First principles simulations of dense hydrogen

Accurate knowledge of the properties of hydrogen at high compression is crucial for astrophysics (e.g. planetary and stellar interiors, brown dwarfs, atmosphere of compact stars) and laboratory experiments, including inertial confinement fusion. There exists experimental data for the equation of state, conductivity, and Thomson scattering spectra. However, the analysis of the measurements at extreme pressures and temperatures typically involves additional model assumptions, which makes it difficult to assess the accuracy of the experimental data. rigorously. On the other hand, theory and modeling have produced extensive collections of data. They originate from a very large variety of models and simulations including path integral Monte Carlo (PIMC) simulations, density functional theory (DFT), chemical models, machine-learned models, and combinations thereof. At the same time, each of these methods has fundamental limitations (fermion sign problem in PIMC, approximate exchange-correlation functionals of DFT, inconsistent interaction energy contributions in chemical models, etc.), so for some parameter ranges accurate predictions are difficult. Recently, a number of breakthroughs in first principle PIMC and DFT simulations were achieved which are discussed in this review. Here we use these results to benchmark different simulation methods. We present an update of the hydrogen phase diagram at high pressures, the expected phase transitions, and thermodynamic properties including the equation of state and momentum distribution. Furthermore, we discuss available dynamic results for warm dense hydrogen, including the conductivity, dynamic structure factor, plasmon dispersion, imaginary-time structure, and density response functions. We conclude by outlining strategies to combine different simulations to achieve accurate theoretical predictions.

physics.comp-ph↗

arXiv2024

Ultrahigh Resolution X-ray Thomson Scattering Measurements at the European XFEL

Using a novel ultrahigh resolution ($ΔE \sim 0.1\,$eV) setup to measure electronic features in x-ray Thomson scattering (XRTS) experiments at the European XFEL in Germany, we have studied the collective plasmon excitation in aluminium at ambient conditions, which we can measure very accurately even at low momentum transfers. As a result, we can resolve previously reported discrepancies between ab initio time-dependent density functional theory simulations and experimental observations. The demonstrated capability for high-resolution XRTS measurements will be a game changer for the diagnosis of experiments with matter under extreme densities, temperatures, and pressures, and unlock the full potential of state-of-the-art x-ray free electron laser (XFEL) facilities to study planetary interior conditions, to understand inertial confinement fusion applications, and for material science and discovery.

physics.plasm-ph↗

arXiv2024

Ultrafast Heating Induced Suppression of $d$-band Dominance in the Electronic Excitation Spectrum of Cuprum

The combination of isochoric heating of solids by free electron lasers (FEL) and in situ diagnostics by X-ray Thomson scattering (XRTS) allows for measurements of material properties at warm dense matter (WDM) conditions relevant for astrophysics, inertial confinement fusion, and material science. In the case of metals, the FEL beam pumps energy directly into electrons with the lattice structure of ions being nearly unaffected. This leads to a unique transient state that gives rise to a set of interesting physical effects, which can serve as a reliable testing platform for WDM theories. In this work, we present extensive linear-response time-dependent density functional theory (TDDFT) results for the electronic dynamic structure factor of isochorically heated copper with a face-centered cubic lattice. At ambient conditions, the plasmon is heavily damped due to the presence of $d$-band excitations, and its position is independent of the wavenumber. In contrast, the plasmon feature starts to dominate the excitation spectrum and has a Bohm-Gross type plasmon dispersion for temperatures $T \geq 4~{\rm eV}$, where the quasi-free electrons in the interstitial region are in the WDM regime. In addition, we analyze the thermal changes in the $d$-band excitations and outline the possibility to use future XRTS measurements of isochorically heated copper as a controlled testbed for WDM theories.

physics.chem-ph↗

arXiv2024

Excitation signatures of isochorically heated electrons in solids at finite wavenumber explored from first principles

Ultrafast heating of solids with modern X-ray free electron lasers (XFELs) leads to a unique set of conditions that is characterized by the simultaneous presence of heated electrons in a cold ionic lattice. In this work, we analyze the effect of electronic heating on the dynamic structure factor (DSF) in bulk Aluminium (Al) with a face-centered cubic lattice and in silicon (Si) with a crystal diamond structure using first-principles linear-response time-dependent density functional theory simulations. We find a thermally induced red shift of the collective plasmon excitation in both materials. In addition, we show that the heating of the electrons in Al can lead to the formation of a double-plasmon peak due to the extension of the Landau damping region to smaller wavenumbers. Finally, we demonstrate that thermal effects generate a measurable and distinct signature (peak-valley structure) in the DSF of Si at small frequencies. Our simulations indicate that there is a variety of new features in the spectrum of X-ray-driven solids, specifically at finite momentum transfer, which can probed in upcoming X-ray Thomson scattering (XRTS) experiments at various XFEL facilities.

physics.comp-ph↗

arXiv2024

Ab initio Density Response and Local Field Factor of Warm Dense Hydrogen

We present quasi-exact ab initio path integral Monte Carlo (PIMC) results for the partial static density responses and local field factors of hydrogen in the warm dense matter regime, from solid density conditions to the strongly compressed case. The full dynamic treatment of electrons and protons on the same footing allows us to rigorously quantify both electronic and ionic exchange--correlation effects in the system, and to compare with earlier incomplete models such as the archetypal uniform electron gas [Phys. Rev. Lett. 125, 235001 (2020)] or electrons in a fixed ion snapshot potential [Phys. Rev. Lett. 129, 066402 (2022)] that do not take into account the interplay between the two constituents. The full electronic density response is highly sensitive to electronic localization around the ions, and our results constitute unambiguous predictions for upcoming X-ray Thomson scattering (XRTS) experiments with hydrogen jets and fusion plasmas. All PIMC results are made freely available and can directly be used for a gamut of applications, including inertial confinement fusion calculations and the modelling of dense astrophysical objects. Moreover, they constitute invaluable benchmark data for approximate but computationally less demanding approaches such as density functional theory or PIMC within the fixed-node approximation.

physics.plasm-ph↗

arXiv2024

Ab initio path integral Monte Carlo simulations of warm dense two-component systems without fixed nodes: structural properties

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)] $ξ$-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.

physics.comp-ph↗

arXiv2024

Unraveling electronic correlations in warm dense quantum plasmas

The study of matter at extreme densities and temperatures has emerged as a highly active frontier at the interface of plasma physics, material science and quantum chemistry with direct relevance for planetary modeling and inertial confinement fusion. A particular feature of such warm dense matter is the complex interplay of strong Coulomb interactions, quantum effects, and thermal excitations, rendering its rigorous theoretical description a formidable challenge. Here, we report a breakthrough in path integral Monte Carlo simulations that allows us to unravel this intricate interplay for light elements without nodal restrictions. This new capability gives us access to electronic correlations previously unattainable. As an example, we apply our method to strongly compressed beryllium to describe x-ray Thomson scattering (XRTS) data obtained at the National Ignition Facility. We find excellent agreement between simulation and experiment. Our analysis shows an unprecedented level of consistency for independent observations without the need for any empirical input parameters.

physics.plasm-ph↗

arXiv2023

Ab initio path integral Monte Carlo simulations of the uniform electron gas on large length scales

The accurate description of non-ideal quantum many-body systems is of prime importance for a host of applications within physics, quantum chemistry, material science, and related disciplines. At finite temperatures, the gold standard is given by \textit{ab initio} path integral Monte Carlo (PIMC) simulations, which do not require any empirical input, but exhibit an exponential increase in the required compute time for fermionic systems with increasing the system size $N$. Very recently, it has been suggested to compute fermionic properties without this bottleneck based on PIMC simulations of fictitious identical particles. In the present work, we use this technique to carry out very large ($N\leq1000$) PIMC simulations of the warm dense electron gas and demonstrate that it is capable of providing a highly accurate description of investigated properties, i.e., the static structure factor, the static density response function, and local field correction, over the entire range of length scales.

physics.chem-ph↗

arXiv2023

Bound state breaking and the importance of thermal exchange-correlation effects in warm dense hydrogen

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.

physics.chem-ph↗

arXiv2023

Bond formation insights into the Diels-Alder reaction: A bond perception and self-interaction perspective

The behavior of electrons during bond formation and breaking cannot commonly be accessed from experiments. Thus, bond perception is often based on chemical intuition or rule-based algorithms. Utilizing computational chemistry methods, we present intrinsic bond descriptors for the Diels-Alder reaction, allowing for an automatic bond perception. We show that these bond descriptors are available from localized orbitals and self-interaction correction calculations, e.g., from Fermi-orbital descriptors. The proposed descriptors allow a sparse, simple, and educational inspection of the Diels-Alder reaction from an electronic perspective. We demonstrate that bond descriptors deliver a simple visual representation of the concerted bond formation and bond breaking, which agrees with Lewis' theory of bonding.

physics.chem-ph↗

arXiv2022

How good are recent density functionals for ground and excited states of one-electron systems?

Sun et al. [J. Chem. Phys. 144, 191101 (2016)] suggested that common density functional approximations (DFAs) should exhibit large energy errors for excited states as a necessary consequence of orbital nodality. Motivated by self-interaction corrected density functional calculations on many-electron systems, we continue their study with the exactly solvable $1s$, $2p$, and $3d$ states of 36 hydrogenic one-electron ions (H-Kr$^{35+}$) and demonstrate with self-consistent calculations that state-of-the-art DFAs indeed exhibit large errors for the $2p$ and $3d$ excited states. We consider 56 functionals at the local density approximation (LDA), generalized gradient approximation (GGA) as well as meta-GGA levels, also including several hybrid functionals like the recently proposed machine-learned DM21 local hybrid functional. The best non-hybrid functional for the $1s$ ground state is revTPSS. The $2p$ and $3d$ excited states are more difficult for DFAs as Sun et al. predicted, and LDA functionals turn out to yield the most systematic accuracy for these states amongst non-hybrid functionals. The best performance for the three states overall is observed with the BHandH global hybrid GGA functional, which contains 50% Hartree-Fock exchange and 50% LDA exchange. The performance of DM21 is found to be inconsistent, yielding good accuracy for some states and systems and poor accuracy for others. Based on these results, we recommend including a variety of one-electron cations in future training of machine-learned density functionals.

physics.comp-ph↗

arXiv2022

Effect of molecular and electronic geometries on the electronic density in FLO-SIC

Recently, Trepte et al. [J. Chem. Phys., vol. 155, 2021] pointed out the importance of analyzing dipole moments in the Fermi-Löwdin orbital (FLO) self-interaction correction (SIC) for cyclic, planar molecules. In this manuscript, the effect of the molecular and electronic geometries on dipole moments and polarizabilities is discussed for non-cyclic molecules. Computed values are presented for water, formaldehyde, and nitromethane. Continuing the work of Schwalbe et al. [J. Chem. Phys. vol. 153, (2020)], we reconfirm that systematic numerical parameter studies are essential to obtain consistent results in density functional theory (DFT) and SIC. In agreement with Trepte et al. [J. Chem. Phys., vol. 155, 2021], DFT agrees well with experiment for dipole moments, while SIC slightly overestimates them. A Linnett double-quartet electronic geometry is found to be energetically preferred for nitromethane.

physics.chem-ph↗