Representing The World Around Us: Applications of Group Representation Theory to Molecular Orbital (MO) Theory
Why this work is in the frame
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Bibliographic record
Abstract
Molecular orbital (MO) theory is a theory at the forefront of modern chemistry, allowing for accurate descriptions of reactivity of molecules by using quantum mechanics to predict the location of electrons within a molecule, and their corresponding energies. The equations which govern their behavior, the Schrodinger equation, are often difficult to solve. Often, we can only approximate a solution using numerical methods. This paper discusses a method which exploits a molecule’s internal symmetry. Specifically, we use Group representation theory to help analyze and break down the molecular symmetry, and then use the analysis to help us find the MO’s. First, we establish key results about irreducible representations and characters. We then establish a correspondence between MO’s and irreducible representations. We then use the results we obtained to perform MO calculations on water (H2O). We then compare the results obtained via our MO theory calculations and Valance Bond Theory (VBT). We conclude by showing these calculations are best used for rough work, being most useful for deciding which atomic orbitals they arose from, and each MO’s energies relative to each other.
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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 | 0.000 | 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 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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 it