Rigorous extension of semilocal collinear functionals to noncollinear DFT using $SU(2)$ rotations

• URL: http://arxiv.org/abs/2605.31203v1
• Date: Fri, 29 May 2026 12:09:02 GMT
• Title: Rigorous extension of semilocal collinear functionals to noncollinear DFT using $SU(2)$ rotations
• Abstract summary: In density functional theory, most exchange--correlation functional approximations were originally developed for locally collinear magnetization.<n>A first-principles connection between widely used semilocal collinear functionals and their noncollinear generalizations remains lacking.<n>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.
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• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: 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.

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