Nonlinear response theory with relaxation: The first-order hyperpolarizability
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Bibliographic record
Abstract
Based on the Ehrenfest theorem, an equation of motion that takes relaxation into account has been presented in wave-function theory, and the resulting response functions are nondivergent in the off-resonant as well as the resonant regions of optical frequencies. The derivation includes single- and multideterminant reference states. When applied to electric dipole properties, the response functions correspond to the phenomenological sum-over-states expressions of Orr and Ward [Mol. Phys. 20, 513 (1971)] for polarizabilities and hyperpolarizabilities of an isolated system. A universal dispersion formula is derived for the complex second-order response function. Response theory calculations are performed on lithium hydride and para-nitroaniline for off-resonant and resonant frequencies in the electro-optical Kerr effect and second-harmonic generation.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.004 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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 it