Atomic Charges Are Measurable Quantum Expectation Values: A Rebuttal of Criticisms of QTAIM Charges
Bibliographic record
Abstract
The charge on an atom in a molecule is defined by the quantum theory of atoms in molecules (QTAIM) as the expectation value of the number operator, a Dirac observable. An atomic charge is measurable and it, together with its change, contributes to numerous measurable properties: to all molecular moments, to molecular polarizability, to intensities of electronic, infrared, and Raman absorption intensities, and to the polarization of a dielectric. The properties resulting from an applied magnetic field parallel those induced by an electric field, with the induced atomic charge being replaced by the atomic current. The phenomena of polarization and magnetization, permanent or induced, have a common physical basis when described in terms of the physics of an open system, all expressions exhibiting a single underlying structure in terms of their atomic contributions. The paper points out that this physics and the appeal the experiment it affords are lost when one employs other definitions of an atomic charge.
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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 | 0.025 | 0.062 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.003 | 0.002 |
| Science and technology studies | 0.004 | 0.069 |
| Scholarly communication | 0.007 | 0.043 |
| Open science | 0.005 | 0.008 |
| Research integrity | 0.008 | 0.025 |
| Insufficient payload (model declined to judge) | 0.005 | 0.002 |
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".