Spin-Consistency Constraints in Noncollinear Tensor TDA
Abstract
TDDFT for open-shell systems, whether spin-conserving or spin-flip, has long suffered from spin contamination. This problem arises because the single-excitation space built upon a single Kohn-Sham determinant is not spin-complete. Adopting spin tensor reference states therefore offers an elegant and promising route to resolving this issue. In this work, we revisit the tensor TDDFT equations within the Tamm-Dancoff approximation (TDA) from a noncollinear perspective. We show that, for S = 1/2 reference states, the internal consistency of the spin tensor formulation can, with the aid of the zero-excitation-energy theorem, be recast as a set of constraints that the exchange-correlation kernel must satisfy. Standard noncollinear functionals, however, generally fail to meet these constraints. To address this, we propose a kernel reconstruction scheme that is independent of the specific functional form and free of empirical parameters. This scheme enforces the required constraints, restoring internal consistency in the full spin tensor structure, with spin adaptation following as a natural consequence. Furthermore, when extended to tensor reference states with other values of S, such as S = 1 for the oxygen molecule, the scheme eliminates the so-called artifact states, namely solutions with severely underestimated excitation energies. In addition, the scheme allows the target states that ROKS reference states aim to describe to be expressed and computed, at the TDA level, within the same unified framework as other states, a capability that spin-adapted spin-conserving TDDFT has so far lacked.
Versions
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BibTeX
@misc{qin2026spinconsistency,
title = {{Spin-Consistency Constraints in Noncollinear Tensor TDA}},
author = {Wenxian Qin and Tai Wang and Yue Yu and Yuanyang Liu and Yi Qin Gao and Yunlong Xiao},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2607.19933},
eprint = {2607.19933},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.19933},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Spin-Consistency Constraints in Noncollinear Tensor TDA
AU - Wenxian Qin
AU - Tai Wang
AU - Yue Yu
AU - Yuanyang Liu
AU - Yi Qin Gao
AU - Yunlong Xiao
PY - 2026
DA - 2026/11/02
PB - arXiv
DO - 10.48550/arxiv.2607.19933
UR - https://arxiv.org/abs/2607.19933
AB - TDDFT for open-shell systems, whether spin-conserving or spin-flip, has long suffered from spin contamination. This problem arises because the single-excitation space built upon a single Kohn-Sham determinant is not spin-complete. Adopting spin tensor reference states therefore offers an elegant and promising route to resolving this issue. In this work, we revisit the tensor TDDFT equations within the Tamm-Dancoff approximation (TDA) from a noncollinear perspective. We show that, for S = 1/2 reference states, the internal consistency of the spin tensor formulation can, with the aid of the zero-excitation-energy theorem, be recast as a set of constraints that the exchange-correlation kernel must satisfy. Standard noncollinear functionals, however, generally fail to meet these constraints. To address this, we propose a kernel reconstruction scheme that is independent of the specific functional form and free of empirical parameters. This scheme enforces the required constraints, restoring internal consistency in the full spin tensor structure, with spin adaptation following as a natural consequence. Furthermore, when extended to tensor reference states with other values of S, such as S = 1 for the oxygen molecule, the scheme eliminates the so-called artifact states, namely solutions with severely underestimated excitation energies. In addition, the scheme allows the target states that ROKS reference states aim to describe to be expressed and computed, at the TDA level, within the same unified framework as other states, a capability that spin-adapted spin-conserving TDDFT has so far lacked.
ER -