Representing The World Around Us: Applications of Group Representation Theory to Molecular Orbital (MO) Theory
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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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 | 0.001 |
| 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 | 0.003 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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".