Topological Analysis of the Electron Density Illustrating the Stabilizing Interactions in Some Basic Solid-state Systems
Bibliographic record
Abstract
The solid-state structures of Sodium (Na), Titanium (Ti), Diamond and Graphite, Sodium Chloride (NaCl), Magnesium Oxide (MgO), Cadmium (II) Iodide (CdI<sub>2</sub>) and Zirconium Chloride (ZrCl) have been explored in details using computational electron density methods; the full-potential linearized augmented plane wave (FPLAPW) method plus local orbital (FPLAPW+lo) embodied in the WIEN2k package code. Topological analysis of their DFT-computed electron densities in tandem with Bader’s Atoms in Molecules (AIM) theory reveals a plethora of stabilizing interactions some of which are really strong. Na and Ti metals reveal only metallic bonding, diamond and graphite show covalent bonding between the carbon-atoms. In addition, there exist Van der Waals forces between the carbon-atoms on adjacent planes in the graphene sheets. NaCl and MgO exhibit electrostatic interactions between the metals (Na, Mg) and non-metals (Cl, O) respectively. Furthermore, there exist Van der Waals interactions between Cl and O atoms. CdI<sub>2</sub> and ZrCl both show ionic and Van der Waals forces between the atoms. ZrCl exhibit metallic bonding and NNMs between the Zr-atoms, which are absent in CdI<sub>2</sub> due to longer Cd-Cd bond distances. Analyses of the electron density flatness (f), charge transfer index (c) and molecularity (μ) were computed. It is observed that the different types of interactions increase with complexity of the solid-state structures. Finally, non-nuclear maxima (NNM) were identified for the first time in heteroatomic solid-state systems.
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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 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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".