Exterior Complex Scaling Approach for Atoms and Molecules in Strong DC Fields
Bibliographic record
Abstract
We perform a short review of the history of quantum mechanics, with a focus on the historical problems with describing ionization theoretically in the context of quantum mechanics. The essentials of the theory of resonances are presented. The exterior complex scaling method for obtaining resonance parameters within the context of the Schrodinger equation is detailed. We explain how this is implemented for a numerical solution using a finite element method for the scaled variable. Results for the resonance parameters of a one-dimensional hydrogen model in an external direct current (DC) electric field are presented as proof of the independence of the theory from the scaling angle. We apply the theory to the real hydrogen atom in a DC field and present results which agree with literature values. The resonance parameters for singly ionized helium are also presented. Using a model potential energy for the water molecule, we solve for the energy eigenvalues. We then solve for the resonance parameters of the water molecule in a DC field and compare to literature results. Our widths for the valence orbital are shown to agree well with the so-called "coupled-cluster singles and doubles with perturbative triples excitations" method.
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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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.007 | 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".