Hyperfine Coupling Constants of the Mu-<i>t</i>-Butyl Radical in NaY and USY Compared with Similar Data in the Bulk and with Ab Initio Theory
Bibliographic record
Abstract
A first complete μSR study of the T dependences of the (reduced) muon, A μ ′ ( T ), and proton, A p ( T ), β-hyperfine coupling constants (hfcc) of the muoniated t -butyl radical is reported in the faujasitic zeolites NaY and USY, and the results are compared with similar data and with early EPR results in condensed bulk phases. The results are also compared with single-molecule UMP2 and DFT/B3LYP calculations in the bulk and in an NaY zeolite fragment of Si and O atoms with both OH- and H-capping. Muon hfcc are reported for the first time for the Mu-isobutyl radical in the bulk phase and are also compared with theory and with EPR data. The present results for the muon and proton hfcc of Mu- t -butyl in the bulk complement earlier work published elsewhere at higher temperatures but are extended here down to 5 K to facilitate comparisons with in vacuo theory at 0 K. Good fits to the data for both A μ ′ ( T ) and A p ( T ) for Mu- t -butyl are found from the calculated hfcc in both the bulk and in NaY, assuming a Boltzmann-weighted energy dependence given by a simple twofold torsional potential, providing an estimate of the barrier to internal rotation. In contrast to the bulk data, there is no clear discontinuity seen in A μ ′ ( T ) for Mu- t -butyl in NaY or USY at the melting point of isobutene, demonstrating the dominance of single-molecule guest–host interactions in the faujasite supercage. In contrast to the A μ ′ ( T ) dependence in the bulk, there is no discontinuity seen for either of the proton hfcc, A p,CH 3 ( T ) or A p,CH 2 Mu ( T ), at the melting point, which also exhibit similar behavior in NaY, suggesting that its observation in the bulk for only the muon hfcc arises from a specific effect of the intermolecular interactions on the vibrational averaging of the muon hfcc. The measured muon hfcc for Mu- t -butyl in NaY fall below those in the bulk at low temperatures, indicating some transfer of electron spin density to the Na cation, which is confirmed by specific additional level-crossing resonances not observed in USY. The Na nuclear hfcc, A Na ( T ), follow a similar trend with temperature as A μ ′ ( T ), with an estimate of the Na spin density at 0 K that also agrees well with theory.
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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 | 0.000 |
| 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".