Stability of the long-range corrected exchange-correlation functional and the Proca procedural functional in time-dependent density-functional theory
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| Format: | Preprint |
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2025
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| _version_ | 1866917981379887104 |
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| author | Williams, Jared R. Ullrich, Carsten A. |
| author_facet | Williams, Jared R. Ullrich, Carsten A. |
| contents | Excitonic effects in the optical absorption spectra of solids can be described with time-dependent density-functional theory (TDDFT) in the linear-response regime, using a simple class of approximate, long-range corrected (LRC) exchange-correlation functionals. It was recently demonstrated that the LRC approximation can also be employed in real-time TDDFT to describe exciton dynamics. Here, we investigate the numerical stability of the time-dependent LRC approach using a two-dimensional model solid. It is found that the time-dependent Kohn-Sham equation with an LRC vector potential becomes more and more prone to instabilities for increasing exciton binding energies. The origin of these instabilities is traced back to time-averaged violations of the zero-force theorem, which leads to a simple and robust numerical stabilization scheme. This explains and justifies a recently proposed method by Dewhurst et al. [Phys. Rev. B 111, L060302 (2025)] to stabilize the LRC vector potential, known as the Proca procedural functional. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2501_13290 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stability of the long-range corrected exchange-correlation functional and the Proca procedural functional in time-dependent density-functional theory Williams, Jared R. Ullrich, Carsten A. Materials Science Excitonic effects in the optical absorption spectra of solids can be described with time-dependent density-functional theory (TDDFT) in the linear-response regime, using a simple class of approximate, long-range corrected (LRC) exchange-correlation functionals. It was recently demonstrated that the LRC approximation can also be employed in real-time TDDFT to describe exciton dynamics. Here, we investigate the numerical stability of the time-dependent LRC approach using a two-dimensional model solid. It is found that the time-dependent Kohn-Sham equation with an LRC vector potential becomes more and more prone to instabilities for increasing exciton binding energies. The origin of these instabilities is traced back to time-averaged violations of the zero-force theorem, which leads to a simple and robust numerical stabilization scheme. This explains and justifies a recently proposed method by Dewhurst et al. [Phys. Rev. B 111, L060302 (2025)] to stabilize the LRC vector potential, known as the Proca procedural functional. |
| title | Stability of the long-range corrected exchange-correlation functional and the Proca procedural functional in time-dependent density-functional theory |
| topic | Materials Science |
| url | https://arxiv.org/abs/2501.13290 |