Atomic properties of selected biomolecules. Part 1. The interpretation of atomic integration errors
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Bibliographic record
Abstract
Reliable atomic properties can be obtained via the theory of "Atoms in Molecules" (AIM) via integration over a finite volume. These integrations are challenging because of the variety and complexity of the shape of the AIM atoms. In practice the integration of a large number of atoms (100-1000, sampled from many molecules) yields integration errors L(Ω) of varying magnitude. We prove that it is impossible to predict the size of an angular Gauss-Legendre grid (outside the β sphere) that guarantees a pre-set error. Hence it is incorrect to assume that a large grid (~23 000 angular grid points) will automatically yield a low L(Ω) value. The erratic relationship between the integration error and the grid size prompts a statistical interpretation of atomic integration, at a purely practical level. More importantly we have investigated the relationship between L(Ω) and seven atomic properties which include volume, energy, and the magnitudes of five electrostatic multipole moments. The electronic population (N(Ω)) and the volume (v(Ω)) of carbon is linearly correlated with L(Ω), enabling the interpolation or extrapolation of N(Ω) and v(Ω). Other properties of carbon and other atoms (N, O, and S) yield low correlation coefficients but occasionally trends can be observed. For example, we find that some properties are systematically underestimated if L(Ω) is negative. This work has led to an estimate of safe error bars of atomic properties for atoms occurring in biological molecules with reasonably sized integration grids. The most stable properties were found to be the energy and the population. Finally, we have observed that the influence of the grid orientation is less if L(Ω) is small, and that population and energy are the least affected.Key words: electron density, topology, atoms in molecules, atomic properties, amino acids.
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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