Properties of atoms in molecules: Transition probabilities
Bibliographic record
Abstract
The transition probability for electric dipole transitions is a measurable property of a system and is therefore, partitionable into atomic contributions using the physics of a proper open system. The derivation of the dressed property density, whose averaging over an atomic basin yields the atomic contribution to a given oscillator strength, is achieved through the development of perturbation theory for an open system. A dressed density describes the local contribution resulting from the interaction of a single electron at some position r, as determined by the relevant observable, averaged over the motions of all of the remaining particles in the system. In the present work, the transition probability density expressed in terms of the relevant transition density, yields a local measure of the associated oscillator strength resulting from the interaction of the entire molecule with a radiation field. The definition of the atomic contributions to the oscillator strength enables one to determine the extent to which a given electronic or vibrational transition is spatially localized to a given atom or functional group. The concepts introduced in this article are applied to the Rydberg-type transitions observed in the electronic excitation of a nonbonding electron in formaldehyde and ammonia. The atomic partitioning of the molecular density distribution and of the molecular properties by surfaces of zero flux in the gradient vector field of the electron density, the boundary condition defining the physics of a proper open system, is found to apply to the density distributions of the excited, Rydberg states.
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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 | 0.006 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.005 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 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".