Crystal Chemical Aspects of Vanadium: Polyhedral Geometries, Characteristic Bond Valences, and Polymerization of (VO<i><sub>n</sub></i>) Polyhedra
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Bibliographic record
Abstract
The distribution of bond lengths in (V 3+ O 6 ) polyhedra shows a maximum between 1.98 and 2.04 Å, and limits of 1.88 and 2.16 Å, respectively. The bond lengths in (V 4+ O n ) and (V 5+ O n ) ( n = 5, 6) polyhedra show distinct populations which allow us to define the following types of bonds: (1a) vanadyl bonds in (V 4+ O n ) polyhedra, shorter than 1.74 Å; (1b) vanadyl bonds in (V 5+ O 5 ) polyhedra, shorter than 1.76 Å; (1c) vanadyl bonds in (V 5+ O 6 ) polyhedra, shorter than 1.74 Å; (2a) equatorial bonds in (V 4+ O n ) polyhedra, in the range 1.90 to 2.12 Å; (2b) equatorial bonds in (V 5+ O 5 ) polyhedra, longer than 1.76 Å; (2c) equatorial bonds in (V 5+ O 6 ) polyhedra with one vanadyl bond, in the range 1.74 to 2.10 Å; (2d) equatorial bonds in (V 5+ O 6 ) polyhedra with two vanadyl bonds, in the range 1.80 to 2.00 Å; (3a) trans bonds in (V 4+ O 6 ) polyhedra, longer than 2.10 Å; (3b) trans bonds in (V 5+ O 6 ) polyhedra with one vanadyl bond, longer than 2.15 Å; (3c) trans bonds in (V 5+ O 6 ) polyhedra with two vanadyl bonds, longer than 2.025 Å. The average equatorial bond length in (V 4+ O n ) and (V 5+ O n ) polyhedra can be used to calculate the mean valence state of V in mixed-valent structures. We define characteristic bond valences for vanadyl, equatorial, and trans bonds in different coordinations and examine which binary linkages are possible and which linkages occur in minerals and synthetic compounds. Here, V 5+ −O−V 5+, V 5+ −O−V 4+, and V 4+ −O−V 4+ linkages between vanadyl− trans and equatorial−equatorial bonds occur often in synthetic compounds, whereas the corresponding V 4+ −O−V 4+ linkages are rare in minerals.
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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) | 0.001 | 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