非共线张量时域密度泛函理论中的自旋一致性约束
Spin-Consistency Constraints in Noncollinear Tensor TDA
浏览论文内容
中文总结 AI 辅助
研究开壳层体系TDDFT的自旋污染问题，提出从非共线角度审视张量TDDFT方程，借助零激发能定理重铸自旋张量公式内部一致性为约束条件，进而提出无经验参数的核重构方案解决问题，恢复自旋张量结构一致性并消除赝态。
中文摘要 AI 辅助
开壳层体系的时域密度泛函理论（TDDFT），无论自旋守恒还是自旋翻转，长期以来都受自旋污染问题困扰。这是因为基于单个Kohn-Sham行列式构建的单激发空间自旋不完备。采用自旋张量参考态为解决此问题提供了一条优雅且有前景的途径。本文从非共线角度重新审视了Tamm-Dancoff近似（TDA）下的张量TDDFT方程。对于S = 1/2参考态，借助零激发能定理，自旋张量公式的内部一致性可重铸为交换关联核必须满足的一组约束。然而，标准非共线泛函通常无法满足这些约束。为此，我们提出了一种与特定泛函形式无关且无经验参数的核重构方案。该方案强制实施所需约束，恢复全自旋张量结构的内部一致性，并自然实现自旋适配。此外，扩展到其他S值的张量参考态时，该方案消除了所谓的赝态，即激发能严重低估的解。并且，该方案允许在同一统一框架内表达和计算ROKS参考态旨在描述的目标态，这是自旋适配的自旋守恒TDDFT迄今所缺乏的能力。
英文摘要
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.
