Time-dependent density functional theory based on a noncollinear formulation of the exchange-correlation potential
Bibliographic record
Abstract
In this study we have introduced a formulation of time-dependent density functional theory (TDDFT) based on a noncollinear exchange-correlation potential. This formulation is a generalization of conventional TDDFT. The form of this formulation is exactly the same as that of the conventional TDDFT for the excitation energies of transitions that do not involve spin flips. In addition, this noncollinear TDDFT formulation allows for spin-flip transitions. This feature makes it possible to resolve more fully excited state spin multiplets, while for closed-shell systems, the spin-flip transitions will result in singlet-triplet excitations and this excitation energy calculated from this formulation of TDDFT is exactly the same as that from ordinary TDDFT. This formulation is applied to the dissociation of H(2) in its (1)Sigma(g) (+) ground state and (1)Sigma(u) (+) and (3)Sigma(u) (-) excited states with (3)Sigma(u) (-) (M(s)=+1) as the reference state and the multiplets splitting of some atoms.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.003 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".