An Atoms in Molecules and Electron Localization Function Computational Study on the Molecular Structure of the 6-Tricyclo[3.2.1.0<sup>2,4</sup>]octyl Cation
Bibliographic record
Abstract
The structure of 6-tricyclo[3.2.1.0 2,4 ]octyl cation 1 was optimized at HF, Becke3PW91, Becke3LYP, MP2, and MP2(full) levels with the 6-311G(d,p) basis set. Becke3PW91 and MP2(full) yielded similar values for the geometrical parameters of optimized 1 . When the C4−C6 distance was changed incrementally through the range 1.40−2.32 Å at the Becke3PW91/6-311G(d,p) level, there was no discontinuity in the total energy and the geometrical parameters of the cyclopropyl group underwent marked changes. AIM (the theory of atoms in molecules) and ELF (electron localization function) analyses were carried out to investigate the molecular structure of 1 . No bond path was found between C4 and C6 so 1 is a classical cation without pentacoordinated carbon atoms. Only when the C4−C6 distance was fixed in the range of 1.50−1.62 Å does 1 become a pentacoordinate (nonclassical) species in which C4 is connected to C2, C3, C5, C6, and H13 with bond paths. On the other hand, when the 6-tricyclo[3.2.1.0 2,4 ]octyl cation was substituted with Li and BeH groups at C4 and C5, the optimized equilibrium species exhibted pentacoordinate carbons at C4. Compared with the C1−C2 bond that we take as a normal single bond, the bonds between C4 and C2, C3, C5 are weak, as evidenced by reduced densities ρ ( r ), significantly smaller ∇ 2 ρ ( r ) values, and large ellipticities at the bond critical points (BCPs). The delocalization indices (DIs) the first application of a DI analysis in the study of carbocations for these C−C bonds ranged between 0.733 and 0.860, smaller than unity. The DI between C4 and C6 is 0.634, suggesting that there is a significant degree of homoconjugation between C4 and C6. For polycyclic species such as 1, it appears that a delocalization index of approximately 0.7 and an internuclear distance of 1.6 Å are required for a bond path to materialize between remote carbons. In an ELF analysis we found a small disynaptic basin V(C4,C6) between C4 and C6 that correlated with the existence of a (3, −1) critical point in −∇ 2 ρ ( r ). The properties of ELF disynaptic basins around C4 and a contribution analysis showed a high degree of delocalization at this center.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.006 | 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".