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| Formato: | Preprint |
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2026
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| Acceso en línea: | https://arxiv.org/abs/2605.31203 |
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| _version_ | 1866910272047808512 |
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| author | Gaul, Konstantin |
| author_facet | Gaul, Konstantin |
| contents | In the presence of spin-orbit coupling and in geometrically frustrated materials, a noncollinear treatment the magnetization density is essential. However, in density functional theory most exchange--correlation functional approximations were originally developed for locally collinear magnetization. Many practical approaches to noncollinear DFT have emerged over the past decade. However, a first-principles connection between widely used semilocal collinear functionals and their noncollinear generalizations remains lacking. In this work, a locally exact relation between collinear and noncollinear exchange--correlation functionals is derived at the level of gradient expansions within a $u(2)$ matrix representation of the energy functional. Within this framework, collinear semilocal variables naturally acquire distinct dependencies on transverse and longitudinal magnetization gradient components. The widely used Scalmani--Frisch scheme emerges as a first-order approximation. The transformation of collinear functional derivatives to noncollinear space is implemented through numerically robust $SU(2)$ rotations. A consistent description of local magnetic torques is demonstrated for the prototypical spin-frustrated Cr$_3$ cluster. The approach further extends to fully nonlocal functionals and provides a direct route towards numerically stable relativistic response calculations. The influence on magnetic properties in presence of spin-orbit coupling is illustrated through calculations of hyperfine couplings in the high-spin ground states of uranium and the uranium ion. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_31203 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Rigorous extension of semilocal collinear functionals to noncollinear DFT using $SU(2)$ rotations Gaul, Konstantin Chemical Physics Materials Science Computational Physics Quantum Physics In the presence of spin-orbit coupling and in geometrically frustrated materials, a noncollinear treatment the magnetization density is essential. However, in density functional theory most exchange--correlation functional approximations were originally developed for locally collinear magnetization. Many practical approaches to noncollinear DFT have emerged over the past decade. However, a first-principles connection between widely used semilocal collinear functionals and their noncollinear generalizations remains lacking. In this work, a locally exact relation between collinear and noncollinear exchange--correlation functionals is derived at the level of gradient expansions within a $u(2)$ matrix representation of the energy functional. Within this framework, collinear semilocal variables naturally acquire distinct dependencies on transverse and longitudinal magnetization gradient components. The widely used Scalmani--Frisch scheme emerges as a first-order approximation. The transformation of collinear functional derivatives to noncollinear space is implemented through numerically robust $SU(2)$ rotations. A consistent description of local magnetic torques is demonstrated for the prototypical spin-frustrated Cr$_3$ cluster. The approach further extends to fully nonlocal functionals and provides a direct route towards numerically stable relativistic response calculations. The influence on magnetic properties in presence of spin-orbit coupling is illustrated through calculations of hyperfine couplings in the high-spin ground states of uranium and the uranium ion. |
| title | Rigorous extension of semilocal collinear functionals to noncollinear DFT using $SU(2)$ rotations |
| topic | Chemical Physics Materials Science Computational Physics Quantum Physics |
| url | https://arxiv.org/abs/2605.31203 |