Fig. 1. Convergence with respect to the number of Lanczos iterations in LL calculations of the electronic DSF of isochorically heated Al at T = 6 eV. The LL calculation results with 2000 Lanczos iterations (blue curve) are visually nearly indistinguishable from the results with 3000 Lanczos iterations (red curve).

Fig. 2. Comparison of the DSF of isochorically heated Al computed using the LL method and the standard LR-TDDFT at different momentum transfer values for T = 6 eV.

Fig. 3. DSF results for isochorically heated Al at T = 6 eV using LDA and GGA level XC functionals in the LL method employing norm-conserving pseudopotentials and the standard LR-TDDFT within the PAW framework.

Fig. 4. (a) Density distribution in simulation cell (in units of mean density n₀) with N = 14 protons at r_s = 2 and T = 12.58 eV. (b) Illustration of convergence of the DSF calculations of warm dense hydrogen with respect to the number of Lanczos iterations in the LL method. (c) Comparison of DSF results computed using ultrasoft and norm-conserving pseudopotentials in the LL method with standard LR-TDDFT within the PAW framework.

Fig. 5. The same as in Fig. 4(c), but presented over a wider frequency range ω using a logarithmic scale.

Fig. 6. (a) DSF of warm dense hydrogen computed using ten different snapshots of N = 14 protons (red lines) and corresponding averaged result (green line). (b) Shifted ITCF results defined by Eq. (9) from the calculations using the LL method and PIMC. The DSF and ITCF results are compared with the data computed for a UEG model.¹⁰⁷ The LR-TDDFT and PIMC results were computed at r_s = 2, T = 12.58 eV, and q≃1.528Å−1, and using the Lorentzian smearing parameter η = 0.2 eV.

Fig. 7. Simulation results of (a) DSF and (b) shifted ITCF for warm dense hydrogen at r_s = 2 and T = 12.58 eV. The Lorentzian smearing parameter is varied in the range 0.1 eV ≤ η ≤ 0.8 eV. The calculations were performed by averaging over ten different snapshots of 14 protons.

Fig. 8. (a) DSF of warm dense hydrogen computed using ten different snapshots of N = 14 protons (red lines) and corresponding averaged result (green line) at η = 2 eV. (b) Effect of variation of the Lorentzian smearing parameter in the range 0.1 eV ≤ η ≤ 3.0 eV. (c) Shifted ITCF results defined by Eq. (9) from calculations using the LL method (with different η values) and PIMC. The DSF and ITCF results are compared with the data computed using the UEG model.¹⁰⁷ The results are presented for r_s = 2 and T = 12.58 eV.

Fig. 9. Comparison of the DSFs of warm dense hydrogen computed using 14, 32, and 100 particles in the simulation cell at r_s = 2.0 and T = 12.58 eV. The Lorentzian smearing parameter was set to η = 0.3 eV for q≃1.528Å−1 and to η = 3.0 eV for q≃4.584Å−1. The results were computed using the LL approach to LR-TDDFT.

Fig. 10. Simulation results for (a) DSF and (b) shifted ITCF for warm dense hydrogen at q≃0.946Å−1, r_s = 3.23, and T = 4.8 eV, with the Lorentzian smearing parameter set to η = 0.3 eV. The LL method-based LR-TDDFT calculations were performed by averaging over 20 different snapshots of 14 protons. The results are compared with the data computed using the UEG model¹⁰⁷ and with the PIMC results for warm dense hydrogen.⁴⁴

Fig. 11. Simulation results for (a) DSF and (b) shifted ITCF (9) for warm dense hydrogen at q≃2.838Å−1, r_s = 3.23, and T = 4.8 eV, with the Lorentzian smearing parameter set to η = 0.5 eV. The LL method-based LR-TDDFT calculations were performed by averaging over 20 different snapshots of 14 protons. The results are compared with the data computed using the UEG model¹⁰⁷ and with the PIMC results for warm dense hydrogen.⁴⁴

Fig. 12. Comparison of the DSFs of warm dense hydrogen computed using the LL approach to LR-TDDFT with 14 and 32 particles in the simulation cell at r_s = 3.23 and T = 4.8 eV. The Lorentzian smearing parameter was set to η = 0.3 eV for q≃0.946Å−1 and to η = 0.5 eV for q≃2.838Å−1.