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Ab initio electronic stopping power of protons in bcc Fe from a hybrid linear-response TDDFT and LDA-Lindhard approach
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DOI：10.1016/j.commatsci.2026.114746.png)
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Abstract
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Electronic stopping in transition metals such as bcc Fe is challenging because a fraction of the d electrons remains localized, and semicore and exchange-correlation effects can influence the response at low projectile velocities. Here, we compute the random electronic stopping power (RESP) of protons in bulk bcc Fe using a velocity-dependent hybrid approach that combines linear-response time-dependent density functional theory (LR-TDDFT) at low and intermediate velocities with a local-density approximation (LDA) based on the Lindhard stopping model at higher velocities. The LR-TDDFT calculations are performed within both the random-phase approximation (RPA) and the adiabatic local-density approximation (ALDA), while the LDA-Lindhard contribution is constructed from the DFT electron density. The crossover velocity is chosen within the overlap window where the two approaches agree, yielding a continuous stopping curve. For Fe, the LDA-Lindhard description captures the high-velocity trend for v >= 2 a.u. and enables an efficient extension of the RESP up to v approximate to 10 a.u.. Exchange-correlation effects, quantified by the ALDA-RPA difference, are sensitive to the valence treatment: including 3s and 3p semicore states broadens the velocity dependence and shifts the maximum of the exchange-correlation correction. The resulting stopping curves are compared with recent real-time TDDFT data, model calculations, and SRIM reference results.
Keywords:
Electronic stopping power
Linear-response TDDFT
bcc iron
Lindhard model
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3.3
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1.3W
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3.6W
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