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| Main Authors: | , |
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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2507.00321 |
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| _version_ | 1866915625139437568 |
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| author | Kumar, Dharamveer Ramabathiran, Amuthan A. |
| author_facet | Kumar, Dharamveer Ramabathiran, Amuthan A. |
| contents | The non-interacting kinetic energy functional, $T_{KS}(ρ)$, plays a fundamental role in Density Functional Theory (DFT), but its explicit form remains unknown for arbitrary $N$-representable densities. Although it can, in principle, be evaluated by solving a constrained optimization problem, the associated adjoint problem is not always well-posed; moreover, even when it is, the corresponding adjoint operator may be singular. To the best of our knowledge, none of the existing approaches in the literature precisely determines the non-interacting kinetic energy functional for a given $N$-representable electron density, $ρ$. In this work, we present a variational framework for computing an extension of $T_{KS}(ρ)$ using an exact trigonometric reparametrization of the density that eliminates the need for an adjoint equation. We present a proof-of-concept numerical validation of the variational principle for the special case of one-dimensional Kohn-Sham systems. Our method, however, is general and provides a systematic foundation for computing $T_{KS}(ρ)$ in higher dimensions too, paving the way for improved kinetic energy functionals in DFT. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_00321 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A direct approach to computing the non-interacting kinetic energy functional Kumar, Dharamveer Ramabathiran, Amuthan A. Chemical Physics Mathematical Physics The non-interacting kinetic energy functional, $T_{KS}(ρ)$, plays a fundamental role in Density Functional Theory (DFT), but its explicit form remains unknown for arbitrary $N$-representable densities. Although it can, in principle, be evaluated by solving a constrained optimization problem, the associated adjoint problem is not always well-posed; moreover, even when it is, the corresponding adjoint operator may be singular. To the best of our knowledge, none of the existing approaches in the literature precisely determines the non-interacting kinetic energy functional for a given $N$-representable electron density, $ρ$. In this work, we present a variational framework for computing an extension of $T_{KS}(ρ)$ using an exact trigonometric reparametrization of the density that eliminates the need for an adjoint equation. We present a proof-of-concept numerical validation of the variational principle for the special case of one-dimensional Kohn-Sham systems. Our method, however, is general and provides a systematic foundation for computing $T_{KS}(ρ)$ in higher dimensions too, paving the way for improved kinetic energy functionals in DFT. |
| title | A direct approach to computing the non-interacting kinetic energy functional |
| topic | Chemical Physics Mathematical Physics |
| url | https://arxiv.org/abs/2507.00321 |