Local and linear chemical reactivity response functions at finite temperature in density functional theory
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Bibliographic record
Abstract
We explore the local and nonlocal response functions of the grand canonical potential density functional at nonzero temperature. In analogy to the zero-temperature treatment, local (e.g., the average electron density and the local softness) and nonlocal (e.g., the softness kernel) intrinsic response functions are defined as partial derivatives of the grand canonical potential with respect to its thermodynamic variables (i.e., the chemical potential of the electron reservoir and the external potential generated by the atomic nuclei). To define the local and nonlocal response functions of the electron density (e.g., the Fukui function, the linear density response function, and the dual descriptor), we differentiate with respect to the average electron number and the external potential. The well-known mathematical relationships between the intrinsic response functions and the electron-density responses are generalized to nonzero temperature, and we prove that in the zero-temperature limit, our results recover well-known identities from the density functional theory of chemical reactivity. Specific working equations and numerical results are provided for the 3-state ensemble model.
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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 | 0.001 | 0.000 |
| 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 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
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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