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This paper addresses the issue of spin contamination in time-dependent density functional theory (TDDFT) for open-shell systems by introducing spin tensor reference states. By reformulating the tensor TDDFT equations within the Tamm-Dancoff approximation (TDA) and deriving spin-consistency constraints for the exchange-correlation kernel, the authors present a kernel reconstruction scheme that ensures internal consistency in the spin tensor structure. The proposed method not only resolves the artifact states associated with underestimated excitation energies but also integrates the description of target states within a unified framework, enhancing the capabilities of spin-adapted TDDFT.
Spin contamination in TDDFT can be resolved with a kernel reconstruction scheme that ensures internal consistency, eliminating artifact states and enabling a unified treatment of target states.
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.
