Applying the Liouville–Lanczos method of time-dependent density-functional theory to warm dense matter

Moldabekov Zhandos A.; Schwalbe Sebastian; Gawne Thomas; Preston Thomas R.; Vorberger Jan; Dornheim Tobias

doi:10.1063/5.0263947

Volume 10 Issue 4

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Moldabekov Zhandos A., Schwalbe Sebastian, Gawne Thomas, Preston Thomas R., Vorberger Jan, Dornheim Tobias. Applying the Liouville–Lanczos method of time-dependent density-functional theory to warm dense matter[J]. Matter and Radiation at Extremes, 2025, 10(4): 047601. doi: 10.1063/5.0263947

Citation:

Moldabekov Zhandos A., Schwalbe Sebastian, Gawne Thomas, Preston Thomas R., Vorberger Jan, Dornheim Tobias. Applying the Liouville–Lanczos method of time-dependent density-functional theory to warm dense matter[J]. Matter and Radiation at Extremes, 2025, 10(4): 047601. doi: 10.1063/5.0263947

Citation:

Moldabekov Zhandos A., Schwalbe Sebastian, Gawne Thomas, Preston Thomas R., Vorberger Jan, Dornheim Tobias. Applying the Liouville–Lanczos method of time-dependent density-functional theory to warm dense matter[J]. Matter and Radiation at Extremes, 2025, 10(4): 047601. doi: 10.1063/5.0263947

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Applying the Liouville–Lanczos method of time-dependent density-functional theory to warm dense matter

doi: 10.1063/5.0263947

1.
Center for Advanced Systems Understanding (CASUS), D-02826 Görlitz, Germany
2.
Helmholtz-Zentrum Dresden-Rossendorf (HZDR), D-01328 Dresden, Germany
3.
European XFEL, D-22869 Schenefeld, Germany

More Information

Corresponding author: a)Author to whom correspondence should be addressed: z.moldabekov@hzdr.de
Received Date: 2025-02-07
Accepted Date: 2025-04-09

Available Online: 2025-11-28

Publish Date: 2025-07-01

Abstract

Abstract

Ab initio modeling of dynamic structure factors (DSF) and related density response properties in the warm dense matter (WDM) regime is a challenging computational task. The DSF, convolved with a probing X-ray beam and instrument function, is measured in X-ray Thomson scattering (XRTS) experiments, which allow the study of electronic structure properties at the microscopic level. Among the various ab initio methods, linear-response time-dependent density-functional theory (LR-TDDFT) is a key framework for simulating the DSF. The standard approach in LR-TDDFT for computing the DSF relies on the orbital representation. A significant drawback of this method is the unfavorable scaling of the number of required empty bands as the wavenumber increases, making LR-TDDFT impractical for modeling XRTS measurements over large energy scales, such as in backward scattering geometry. In this work, we consider and test an alternative approach to LR-TDDFT that employs the Liouville–Lanczos (LL) method for simulating the DSF of WDM. This approach does not require empty states and allows the DSF at large momentum transfer values and over a broad frequency range to be accessed. We compare the results obtained from the LL method with those from the solution of Dyson’s equation using the standard LR-TDDFT within the projector augmented-wave formalism for isochorically heated aluminum and warm dense hydrogen. Additionally, we utilize exact path integral Monte Carlo results for the imaginary-time density-density correlation function (ITCF) of warm dense hydrogen to rigorously benchmark the LL approach. We discuss the application of the LL method for calculating DSFs and ITCFs at different wavenumbers, the effects of pseudopotentials, and the role of Lorentzian smearing. The successful validation of the LL method under WDM conditions makes it a valuable addition to the ab initio simulation landscape, supporting experimental efforts and advancing WDM theory.

Conflict of Interest
The authors have no conflicts to disclose.
Zhandos A. Moldabekov: Conceptualization (lead); Data curation (lead); Formal analysis (lead); Investigation (lead); Methodology (lead); Validation (lead); Visualization (lead); Writing – original draft (lead). Sebastian Schwalbe: Formal analysis (equal); Investigation (equal); Methodology (equal); Writing – original draft (equal). Thomas Gawne: Formal analysis (equal); Investigation (equal); Methodology (equal); Writing – original draft (equal). Thomas R. Preston: Formal analysis (equal); Investigation (equal); Methodology (equal); Writing – original draft (equal). Jan Vorberger: Formal analysis (equal); Investigation (equal); Methodology (equal); Writing – original draft (equal). Tobias Dornheim: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Funding acquisition (lead); Investigation (equal); Methodology (equal); Project administration (equal); Validation (equal); Writing – original draft (equal).
Author Contributions
The data that support the findings of this study are available within the article.

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References(121)

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