Exploring Intrinsic Bond Properties with the Fukui Matrix from Conceptual Density Matrix Functional Theory
Bibliographic record
Abstract
We extend the traditional conceptual density functional theory (CDFT) to conceptual density matrix functional theory (CDMFT) by replacing the external potential v ( r ) by the one-electron integral h rs in the energy functional. This approach provides a new path for investigating intrinsic bond properties such as bond reactivity. The derivation of the Fukui matrix, i.e., derivative of the density matrix P with respect to the number of electrons N, is elucidated, and the result is illustrated in a case study on H 2 O. The matrix is shown to play a crucial role in quantifying changes of bond strength for electron removal or addition processes via the bond order derivative ( ∂ B ∂ N ) − . Using the Mayer bond order and different atoms-in-molecules partitioning methods, we show that as a first-order response quantity, the bond order derivative agrees well with the finite difference bond order changes. The bond order derivative (bond Fukui function) is a bond reactivity descriptor. We demonstrate this by predicting the regioselectivity of a classical electrophilic addition reaction (the bromination of alkenes) and predicting the initial electron-driven bond cleavage in mass spectrometry. Specifically, the bond order derivative captures all of the major signals from the experimental mass spectra for a series of small molecules with a variety of functional groups.
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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 | 0.001 | 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 | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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 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".