Chemical applications of electron localization-delocalization matrices (LDMs) with an emphasis on predicting molecular properties
Bibliographic record
Abstract
A matrix is constructed where the vertices (atoms) are connected by edges (bonds) resulting in a square matrix that is symmetrical.The localization index (unshared electrons) occupies the long diagonal where the delocalization index (shared electrons between two different atoms divided by 2) represent the off-diagonal elements.Such a matrix is called a localization-delocalization matrix or LDM.These matrices have shown promise as a novel Quantitative Structure Activity Relationship (QSAR) method via the Frobenius Distance, a method to compare matrices of similar sizes that returns a Euclidean distance.Some notable results that will be expanded upon are that for a series of 14 para-substituted benzoic acids for pKa prediction (r 2 = 0.986), and a series of 13 polycyclic benzenoid hydrocarbons (PBH) separated by inner and outer rings (r 2 = 0.97).A program (AIMLDM) was developed in Python 3.4.1 to construct these matrices and perform the required calculations.September 12, 2016 i List of Tables 2.1 Frobenius Distance for isoelectronic series . . . . . . . . . . . . . . .2.2 "Scrambled" LDM for acetic acid and resulting eigenvalues . . . . . .2.3 Eigenvalues of LDMs from a series of carboxylic acids . . . . . . . . .3.1 Frobenius distances comparing the subgraph(s) to pK a and max . . .3.2 Frobenius distances from the DMs vs pK a . . . . . . . . . . . . . . .3.3 Frobenius distances from the LDMs vs max . . . . . . . . . . . . . .4.1 RIMs Frobenius distance vs Popular Aromaticity measures . . . . . .4.2 Aromatic ranking agreement of various aromaticity indices with the Frobenius distance dissimilarity to benzene. . . . . . . . . . . . . . .4.3 Pairwise vector angles (in degrees ( )) matrix for the ring in molecules to three decimals . . . . . . . . . . . . . . . . . . . .
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How this classification was reachedexpand
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 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".