Enhancing the efficiency of time-dependent density functional theory calculations of dynamic response properties
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Abstract
Abstract X-ray Thomson scattering (XRTS) constitutes an essential technique for diagnosing material properties under extreme conditions, such as high pressures and intense laser heating. Time-dependent density functional theory (TDDFT) is one of the most accurate available ab initio methods for modeling XRTS spectra, as well as a host of other dynamic material properties. However, strong thermal excitations, along with the need to account for variations in temperature and density as well as the finite size of the detector significantly increase the computational cost of TDDFT simulations compared to ambient conditions. In this work, we present a broadly applicable method for optimizing and enhancing the efficiency of TDDFT calculations. Our approach is based on a one-to-one mapping between the dynamic structure factor and the imaginary time density–density correlation function, which naturally emerges in Feynman’s path integral formulation of quantum many-body theory. Specifically, we combine rigorous convergence tests in the imaginary time domain with a constraints-based attenuation of narrow-band fluctuations to improve the efficiency of TDDFT modeling without the introduction of any significant bias. As a result, we can report a speed-up by up to an order of magnitude, thus substantially reducing the burden of computational cost required for XRTS analysis.
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OpenAlex topics: Probabilistic and Robust Engineering Design
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References (100+)
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1. Fletcher, L. B. et al. Ultrabright x-ray laser scattering for dynamic warm dense matter physics. Nat. Photonics 9, 274–279 (2015).10.1038/nphoton.2015.41 ↗
2. Descamps, A. et al. An approach for the measurement of the bulk temperature of single crystal diamond using an x-ray free electron laser. Sci. Rep. 10, 14564 (2020).10.1038/s41598-020-71350-x ↗
3. Wollenweber, L. et al. High-resolution inelastic x-ray scattering at the high energy density scientific instrument at the European X-Ray Free-Electron Laser. Rev. Sci. Instrum. 92, 013101 (2021).10.1063/5.0022886 ↗
4. Gawne, T. et al. Ultrahigh resolution x-ray thomson scattering measurements at the european x-ray free electron laser. Phys. Rev. B 109, L241112 (2024).10.1103/PhysRevB.109.L241112 ↗
5. Gawne, T. et al. Strong geometry dependence of the x-ray thomson scattering spectrum in single crystal silicon. Electron. Struct. 7, 025002 (2025).10.1088/2516-1075/adc054 ↗
6. Tschentscher, T. et al. Photon beam transport and scientific instruments at the european xfel. Appl. Sci. 7, https://www.mdpi.com/2076-3417/7/6/592 (2017).10.3390/app7060592 ↗
7. Preston, T. et al. Design and performance characterisation of the hapg von Hámos spectrometer at the high energy density instrument of the European XFEL. J. Instrum. 15, P11033 (2020).10.1088/1748-0221/15/11/P11033 ↗
8. Zastrau, U. et al. The High Energy Density Scientific Instrument at the European XFEL. J. Synchrotron Radiat. 28, 1393–1416 (2021).10.1107/S1600577521007335 ↗
9. Descamps, A. et al. Calibration and characterization of the line-visar diagnostic at the hed-hibef instrument at the European XFEL. Rev. Sci. Instrum. 96, 075206 (2025).10.1063/5.0271027 ↗
10. Ofori-Okai, B. K. et al. A terahertz pump mega-electron-volt ultrafast electron diffraction probe apparatus at the SLAC accelerator structure test area facility. J. Inst. 13, P06014–P06014 (2018).
11. Hara, T. et al. Two-colour hard x-ray free-electron laser with wide tunability. Nat. Commun. 4, 2919 (2013).10.1038/ncomms3919 ↗
12. Pascarelli, S. et al. Materials under extreme conditions using large x-ray facilities. Nat. Rev. Methods Prim. 3, 82 (2023).10.1038/s43586-023-00264-5 ↗
13. Kraus, D. et al. The structure of liquid carbon elucidated by in situ x-ray diffraction. Nature 642, 351–355 (2025).10.1038/s41586-025-09035-6 ↗
14. White, T. G. et al. Superheating gold beyond the predicted entropy catastrophe threshold. Nature 643, 950–954 (2025).10.1038/s41586-025-09253-y ↗
15. Descamps, A. et al. Evidence for phonon hardening in laser-excited gold using x-ray diffraction at a hard x-ray free electron laser. Sci. Adv. 10, eadh5272 (2024).10.1126/sciadv.adh5272 ↗
16. MacDonald, M. J. et al. Demonstration of a laser-driven, narrow spectral bandwidth x-ray source for collective x-ray scattering experiments. Phys. Plasmas 28, 032708 (2021).10.1063/5.0030958 ↗
17. Moses, E. I., Boyd, R. N., Remington, B. A., Keane, C. J. & Al-Ayat, R. The national ignition facility: Ushering in a new age for high energy density science. Phys. Plasmas 16, 041006 (2009).10.1063/1.3116505 ↗
18. Glenzer, S. H. et al. Observations of plasmons in warm dense matter. Phys. Rev. Lett. 98, 065002 (2007).10.1103/PhysRevLett.98.065002 ↗
19. Döppner, T. et al. Observing the onset of pressure-driven K-shell delocalization. Nature 618, 270–275 (2023).10.1038/s41586-023-05996-8 ↗
20. Glenzer, S. H. & Redmer, R. X-ray thomson scattering in high energy density plasmas. Rev. Mod. Phys. 81, 1625 (2009).10.1103/RevModPhys.81.1625 ↗
21. Dornheim, T. et al. Accurate temperature diagnostics for matter under extreme conditions. Nat. Commun. 13, 7911 (2022).10.1038/s41467-022-35578-7 ↗
22. Bellenbaum, H. M. et al. Toward model-free temperature diagnostics of warm dense matter from multiple scattering angles. Appl. Phys. Lett. 126, 044104 (2025).10.1063/5.0248230 ↗
23. Dornheim, T. et al. Model-free rayleigh weight from x-ray thomson scattering measurements. Phys. Plasmas 32, 052712 (2025).10.1063/5.0238630 ↗
24. Sperling, P. et al. Free-electron x-ray laser measurements of collisional-damped plasmons in isochorically heated warm dense matter. Phys. Rev. Lett. 115, 115001 (2015).10.1103/PhysRevLett.115.115001 ↗
25. Sperling, P. et al. Electrical conductivity calculations in isochorically heated warm dense aluminum. J. Phys. B: At., Mol. Optical Phys. 50, 134002 (2017).10.1088/1361-6455/aa753d ↗
26. Witte, B. B. L. et al. Warm dense matter demonstrating non-drude conductivity from observations of nonlinear plasmon damping. Phys. Rev. Lett. 118, 225001 (2017).10.1103/PhysRevLett.118.225001 ↗
27. Dornheim, T. et al. Unraveling electronic correlations in warm dense quantum plasmas. Nat. Commun. 16, 5103 (2025).10.1038/s41467-025-60278-3 ↗
28. Hentschel, T. W., Kononov, A., Baczewski, A. D. & Hansen, S. B. Statistical inference of collision frequencies from x-ray thomson scattering spectra. Phys. Plasmas 32, 013906 (2025).10.1063/5.0235628 ↗
29. Hentschel, T. W. et al. Improving dynamic collision frequencies: Impacts on dynamic structure factors and stopping powers in warm dense matter. Phys. Plasmas 30, 062703 (2023).10.1063/5.0143738 ↗
30. Moldabekov, Z., Vorberger, J. & Dornheim, T. From density response to energy functionals and back: An ab initio perspective on matter under extreme conditions. Prog. Part. Nucl. Phys. 140, 104144 (2025).10.1016/j.ppnp.2024.104144 ↗
31. Clark, D. S. et al. Radiation hydrodynamics modeling of the highest compression inertial confinement fusion ignition experiment from the national ignition campaign. Phys. Plasmas 22, 022703 (2015).10.1063/1.4906897 ↗
32. Batani, D. et al. Future for inertial-fusion energy in Europe: a roadmap. High. Power Laser Sci. Eng. 11, e83 (2023).10.1017/hpl.2023.80 ↗
33. Spears, B. K. et al. Predicting fusion ignition at the national ignition facility with physics-informed deep learning. Science 389, 727–731 (2025).10.1126/science.adm8201 ↗
34. Betti, R. A milestone in fusion research is reached. Nat. Rev. Phys. 5, 6–8 (2023).10.1038/s42254-022-00547-y ↗
35. The Indirect Drive ICF Collaboration. Achievement of target gain larger than unity in an inertial fusion experiment. Phys. Rev. Lett. 132, 065102 (2024).10.1103/PhysRevLett.132.065102 ↗
36. Ullrich, C. A. Time-Dependent Density-Functional Theory: Concepts and Applications (Oxford University Press, 2011). https://doi.org/10.1093/acprof:oso/9780199563029.001.0001.10.1093/acprof:oso/9780199563029.001.0001 ↗
37. Byun, Y.-M., Sun, J. & Ullrich, C. A. Time-dependent density-functional theory for periodic solids: assessment of excitonic exchange-correlation kernels. Electron. Struct. 2, 023002 (2020).10.1088/2516-1075/ab7b12 ↗
38. Moldabekov, Z. A., Pavanello, M., Böhme, M. P., Vorberger, J. & Dornheim, T. Linear-response time-dependent density functional theory approach to warm dense matter with adiabatic exchange-correlation kernels. Phys. Rev. Res. 5, 023089 (2023).10.1103/PhysRevResearch.5.023089 ↗
39. Moldabekov, Z. A. et al. Applying the Liouville-Lanczos method of time-dependent density-functional theory to warm dense matter. Matter Radiat. Extremes 10, 047601 (2025).
40. Baczewski, A. D., Shulenburger, L., Desjarlais, M. P., Hansen, S. B. & Magyar, R. J. X-ray thomson scattering in warm dense matter without the Chihara decomposition. Phys. Rev. Lett. 116, 115004 (2016).10.1103/PhysRevLett.116.115004 ↗
41. White, A. J. Dynamical structure factors of warm dense matter from time-dependent orbital-free and mixed-stochastic-deterministic density functional theory. Electron. Struct. 7, 014001 (2025).10.1088/2516-1075/adad24 ↗
42. Dornheim, T. et al. Electronic density response of warm dense matter. Phys. Plasmas 30 (2023).10.1063/5.0138955 ↗
43. MacDonald, A. H., Vosko, S. H. & Coleridge, P. T. Extensions of the tetrahedron method for evaluating spectral properties of solids. J. Phys. C: Solid State Phys 12, 2991 (1979).10.1088/0022-3719/12/15/008 ↗
44. Blanchet, A., Torrent, M. & Clérouin, J. Requirements for very high temperature Kohn-Sham DFT simulations and how to bypass them. Phys. Plasmas 27, 122706 (2020).10.1063/5.0016538 ↗
45. Fiedler, L. et al. Accelerating equilibration in first-principles molecular dynamics with orbital-free density functional theory. Phys. Rev. Res. 4, 043033 (2022).10.1103/PhysRevResearch.4.043033 ↗
46. Moldabekov, Z. A., Vorberger, J., Lokamani, M. & Dornheim, T. Averaging over atom snapshots in linear-response TDDFT of disordered systems: A case study of warm dense hydrogen. J. Chem. Phys. 159, 014107 (2023).10.1063/5.0152126 ↗
47. Abinit tutorial on real-time time-dependent dft. https://docs.abinit.org/tutorial/rttddft/. Accessed: 2025-08-28.
48. Lentz, M. K., Townsend, J. P. & Cochrane, K. R. DC electrical conductivity of platinum from ab initio simulations. AIP Conf. Proc. 2844, 320003 (2023).10.1063/12.0020403 ↗
49. Desjarlais, M. P., Kress, J. D. & Collins, L. A. Electrical conductivity for warm, dense aluminum plasmas and liquids. Phys. Rev. E. 66, 025401 (2002).10.1103/PhysRevE.66.025401 ↗
50. Dornheim, T. et al. Imaginary-time correlation function thermometry: A new, high-accuracy and model-free temperature analysis technique for x-ray Thomson scattering data. Phys. Plasmas 30 (2023).10.1063/5.0139560 ↗
51. Schörner, M. et al. X-ray thomson scattering spectra from density functional theory molecular dynamics simulations based on a modified chihara formula. Phys. Rev. E. 107, 065207 (2023).10.1103/PhysRevE.107.065207 ↗
52. Shi, N. Y. et al. First-principles analysis of the warm dense plasma jets in double-cone ignition experiments https://arxiv.org/abs/2504.04317 (2025).
53. Schwalbe, S. et al. Static linear density response from x-ray thomson scattering measurements: a case study of warm dense beryllium https://arxiv.org/abs/2504.13611 (2025).
54. Vorberger, J. et al. Revealing non-equilibrium and relaxation in laser heated matter. Phys. Lett. A. 499, 129362 (2024).10.1016/j.physleta.2024.129362 ↗
55. Boninsegni, M. & Ceperley, D. M. Density fluctuations in liquid4He. path integrals and maximum entropy. J. Low. Temp. Phys. 104, 339–357 (1996).10.1007/BF00751861 ↗
56. Dornheim, T., Moldabekov, Z. A. & Vorberger, J. Nonlinear density response from imaginary-time correlation functions: Ab initio path integral monte carlo simulations of the warm dense electron gas. J. Chem. Phys. 155, 054110 (2021).10.1063/5.0058988 ↗
57. Saccani, S., Moroni, S. & Boninsegni, M. Excitation spectrum of a supersolid. Phys. Rev. Lett. 108, 175301 (2012).10.1103/PhysRevLett.108.175301 ↗
58. Dornheim, T., Moldabekov, Z. A., Tolias, P., Böhme, M. & Vorberger, J. Physical insights from imaginary-time density-density correlation functions. Matter Radiat. Extremes 8, 056601 (2023).
59. Dornheim, T. et al. Ab initio density response and local field factor of warm dense hydrogen. Matter Radiat. Extremes 9, 057401 (2024).
60. Chuna, T. M. et al. Second roton feature in the strongly coupled electron liquid. J. Chem. Phys. 163, 034117 (2025).10.1063/5.0281085 ↗
61. Fletcher, L. B. et al. Electron-ion temperature relaxation in warm dense hydrogen observed with picosecond resolved x-ray scattering. Front. Phys. 10 - 2022 https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2022.838524 (2022).10.3389/fphy.2022.838524 ↗
62. Zastrau, U. et al. Resolving ultrafast heating of dense cryogenic hydrogen. Phys. Rev. Lett. 112, 105002 (2014).10.1103/PhysRevLett.112.105002 ↗
63. Hu, S. X., Militzer, B., Goncharov, V. N. & Skupsky, S. Strong coupling and degeneracy effects in inertial confinement fusion implosions. Phys. Rev. Lett. 104, 235003 (2010).10.1103/PhysRevLett.104.235003 ↗
64. Bonitz, M. et al. Toward first principles-based simulations of dense hydrogen. Phys. Plasmas 31, 110501 (2024).10.1063/5.0219405 ↗
65. Moldabekov, Z. A. et al. Excitation signatures of isochorically heated electrons in solids at finite wave number explored from first principles. Phys. Rev. Res. 6, 023219 (2024).10.1103/PhysRevResearch.6.023219 ↗
66. Moldabekov, Z. et al. Ultrafast heating-induced suppression of d-band dominance in the electronic excitation spectrum of cuprum. ACS Omega 9, 25239–25250 (2024).10.1021/acsomega.4c02920 ↗
67. Dornheim, T. et al. Extraction of the frequency moments of spectral densities from imaginary-time correlation function data. Phys. Rev. B. 107, 155148 (2023).10.1103/PhysRevB.107.155148 ↗
68. Dornheim, T., Vorberger, J., Moldabekov, Z. & Böhme, M. Analysing the dynamic structure of warm dense matter in the imaginary-time domain: theoretical models and simulations. Philos. Trans. R. Soc. A. 381, 20220217 (2023).10.1098/rsta.2022.0217 ↗
69. Mo, C. et al. First-principles method for x-ray thomson scattering including both elastic and inelastic features in warm dense matter. Phys. Rev. B. 102, 195127 (2020).10.1103/PhysRevB.102.195127 ↗
70. Gregori, G., Glenzer, S. H., Rozmus, W., Lee, R. W. & Landen, O. L. Theoretical model of x-ray scattering as a dense matter probe. Phys. Rev. E. 67, 026412 (2003).10.1103/PhysRevE.67.026412 ↗
71. Bellenbaum, H. M. et al. Estimating ionization states and continuum lowering from ab initio path integral Monte Carlo simulations for warm dense hydrogen. Phys. Rev. Res. 7, 033016 (2025).10.1103/9d7r-1xbm ↗
72. Moldabekov, Z. A. et al. Ab initio density functional theory approach to warm dense hydrogen: from density response to electronic correlations. Matter Radiat. Extremes 1, 025401 (2026).10.1063/5.0297301 ↗
73. Melton, C. A. et al. Transport coefficients of warm dense matter from Kohn-Sham density functional theory. Phys. Plasmas 31, 043903 (2024).10.1063/5.0198005 ↗
74. Timrov, I., Vast, N., Gebauer, R. & Baroni, S. turboEELS-A code for the simulation of the electron energy loss and inelastic X-ray scattering spectra using the Liouville-Lanczos approach to time-dependent density-functional perturbation theory. Comput. Phys. Commun. 196, 460–469 (2015).10.1016/j.cpc.2015.05.021 ↗
75. Acharya, D., Rani, A., Agarwal, S. & Singh, V. Application of adaptive Savitzky-Golay filter for eeg signal processing. Perspect. Sci. 8, 677–679 (2016).10.1016/j.pisc.2016.06.056 ↗
76. Schmid, M., Rath, D. & Diebold, U. Why and how Savitzky-Golay filters should be replaced. ACS Meas. Sci. Au. 2, 185–196 (2022).10.1021/acsmeasuresciau.1c00054 ↗
77. Savitzky, A. & Golay, M. J. E. Smoothing and differentiation of data by simplified least squares procedures. Anal. Chem. 36, 1627–1639 (1964).10.1021/ac60214a047 ↗
78. HURVICH, C. M. & TSAI, C.-L. Regression and time series model selection in small samples. Biometrika 76, 297–307 (1989).10.1093/biomet/76.2.297 ↗
79. Moldabekov, Z. & Schwalbe, S. Constraints-Based_Filter_TDDFT. https://gitlab.com/moldab50/Constraints-Based_Filter_TDDFT.git (2025). GitLab repository.
80. Tolias, P., Vorberger, J. & Dornheim, T. Exact series expansion for even frequency moments of the dynamic structure factor https://arxiv.org/abs/2506.10410 (2025).10.1063/5.0284989 ↗
81. Jarrell, M. & Gubernatis, J. Bayesian inference and the analytic continuation of imaginary-time quantum monte carlo data. Phys. Rep. 269, 133–195 (1996).10.1016/0370-1573(95)00074-7 ↗
82. Goulko, O., Mishchenko, A. S., Pollet, L., Prokof’ev, N. & Svistunov, B. Numerical analytic continuation: Answers to well-posed questions. Phys. Rev. B. 95, 014102 (2017).10.1103/PhysRevB.95.014102 ↗
83. Giuliani, G. & Vignale, G. Quantum Theory of the Electron Liquid. (Cambridge University Press, Cambridge, 2008).
84. Alexandrov, A. F., Bogdankevich, L. S. & Rukhadze, A. A. Principles of Plasma Electrodynamics, vol. 9 of Springer Series in Electronics and Photonics (Springer Berlin Heidelberg, 1984).10.1007/978-3-642-69247-5 ↗
85. Preston, T. R. et al. Measurements of the momentum-dependence of plasmonic excitations in matter around 1 mbar using an x-ray free electron laser. Appl. Phys. Lett. 114, 014101 (2019).10.1063/1.5070140 ↗
86. Panholzer, M., Gatti, M. & Reining, L. Nonlocal and nonadiabatic effects in the charge-density response of solids: A time-dependent density-functional approach. Phys. Rev. Lett. 120, 166402 (2018).10.1103/PhysRevLett.120.166402 ↗
87. Kononov, A., Hentschel, T. W., Hansen, S. B. & Baczewski, A. D. Trajectory sampling and finite-size effects in first-principles stopping power calculations. npj Computational Mater 9, 205 (2023).10.1038/s41524-023-01157-7 ↗
88. Gawne, T. et al. Orientational effects in the low pair continuum of aluminium. Contrib. Plasma Phys. e70127, https://doi.org/10.1002/ctpp.70127 (2026).10.1002/ctpp.70127 ↗
89. Baczewski, A. D., Hentschel, T., Kononov, A. & Hansen, S. B. Predictions of bound-bound transition signatures in x-ray thomson scattering https://arxiv.org/abs/2109.09576 (2021).
90. Chapman, D. A. et al. Simulating x-ray Thomson scattering signals from high-density, millimetre-scale plasmas at the national ignition facility. Phys. Plasmas 21, 082709 (2014).10.1063/1.4893146 ↗
91. Kasim, M. F., Galligan, T. P., Topp-Mugglestone, J., Gregori, G. & Vinko, S. M. Inverse problem instabilities in large-scale modeling of matter in extreme conditions. Phys. Plasmas 26, 112706 (2019).10.1063/1.5125979 ↗
92. Ding, Y. H., White, A. J., Hu, S. X., Certik, O. & Collins, L. A. Ab initio studies on the stopping power of warm dense matter with time-dependent orbital-free density functional theory. Phys. Rev. Lett. 121, 145001 (2018).10.1103/PhysRevLett.121.145001 ↗
93. White, A. J. & Collins, L. A. Fast and universal Kohn-Sham density functional theory algorithm for warm dense matter to hot dense plasma. Phys. Rev. Lett. 125, 055002 (2020).10.1103/PhysRevLett.125.055002 ↗
94. Nicoul, M., Shymanovich, U., Tarasevitch, A., von der Linde, D. & Sokolowski-Tinten, K. Picosecond acoustic response of a laser-heated gold-film studied with time-resolved x-ray diffraction. Appl. Phys. Lett. 98, 191902 (2011).10.1063/1.3584864 ↗
95. White, T. G. et al. Electron-phonon equilibration in laser-heated gold films. Phys. Rev. B. 90, 014305 (2014).10.1103/PhysRevB.90.014305 ↗
96. Ramakrishna, K. & Vorberger, J. Ab initio dielectric response function of diamond and other relevant high pressure phases of carbon. J. Phys.: Condens. Matter 32, 095401 (2019).
97. Hamann, P., Dornheim, T., Vorberger, J., Moldabekov, Z. A. & Bonitz, M. Dynamic properties of the warm dense electron gas based on abinitio path integral monte carlo simulations. Phys. Rev. B. 102, 125150 (2020).10.1103/PhysRevB.102.125150 ↗
98. Calderín, L., Karasiev, V. & Trickey, S. Kubo-Greenwood electrical conductivity formulation and implementation for projector augmented wave datasets. Comput. Phys. Commun. 221, 118–142 (2017).10.1016/j.cpc.2017.08.008 ↗
99. Hadad, R. E., Roy, A., Rabani, E., Redmer, R. & Baer, R. Stochastic density functional theory combined with Langevin dynamics for warm dense matter. Phys. Rev. E. 109, 065304 (2024).10.1103/PhysRevE.109.065304 ↗
100. Ullrich, C. Time-Dependent Density-Functional Theory: Concepts and Applications. Oxford Graduate Texts (OUP Oxford, 2012). https://books.google.de/books?id=hCNNsC4sEtkC.