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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2602.16325 |
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| _version_ | 1866910175371198464 |
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| author | Zhang, Xiaoyu |
| author_facet | Zhang, Xiaoyu |
| contents | Two-component linear-response time-dependent density functional theory (TDDFT) provides a unified framework that encompasses noncollinear excitations in noncollinear reference states, as well as both spin-conserving and spin-flip excitations in collinear reference states. In this work, we present a general formalism for evaluating the expectation value $\langle \hat{S}^2 \rangle$ of electronically excited states obtained within two-component TDDFT. We then derive and analyze specialized forms of the resulting equations for collinear reference determinants, for which the two-component formalism decomposes into conventional spin-conserving and spin-flip TDDFT. The resulting working equations are systematically compared with previously proposed theoretical approaches. On the basis of our analysis, $\langle \hat{S}^2 \rangle$ in the excited states is shown to arise from two distinct sources: (i) $\langle \hat{S}^2 \rangle_0$ in the reference state and (ii) additional $Δ\langle \hat{S}^2 \rangle$ introduced by the excitation process itself. Finally, we evaluate the expectation value $\langle \hat{S}^2 \rangle$ by performing two-component TDDFT calculations based on two-component DFT, unrestricted Kohn-Sham (UKS), and restricted open-shell Kohn-Sham (ROKS) reference states, respectively. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_16325 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Unified Formulation for $\langle \hat{S}^2 \rangle $ in Two-Component TDDFT Zhang, Xiaoyu Chemical Physics Two-component linear-response time-dependent density functional theory (TDDFT) provides a unified framework that encompasses noncollinear excitations in noncollinear reference states, as well as both spin-conserving and spin-flip excitations in collinear reference states. In this work, we present a general formalism for evaluating the expectation value $\langle \hat{S}^2 \rangle$ of electronically excited states obtained within two-component TDDFT. We then derive and analyze specialized forms of the resulting equations for collinear reference determinants, for which the two-component formalism decomposes into conventional spin-conserving and spin-flip TDDFT. The resulting working equations are systematically compared with previously proposed theoretical approaches. On the basis of our analysis, $\langle \hat{S}^2 \rangle$ in the excited states is shown to arise from two distinct sources: (i) $\langle \hat{S}^2 \rangle_0$ in the reference state and (ii) additional $Δ\langle \hat{S}^2 \rangle$ introduced by the excitation process itself. Finally, we evaluate the expectation value $\langle \hat{S}^2 \rangle$ by performing two-component TDDFT calculations based on two-component DFT, unrestricted Kohn-Sham (UKS), and restricted open-shell Kohn-Sham (ROKS) reference states, respectively. |
| title | A Unified Formulation for $\langle \hat{S}^2 \rangle $ in Two-Component TDDFT |
| topic | Chemical Physics |
| url | https://arxiv.org/abs/2602.16325 |