An improved scheme for the calculation of NMR chemical shifts in periodic systems based on gauge including atomic orbitals and density functional theory
Bibliographic record
Abstract
We report here on an improved first principles method that can determine NMR shielding tensors for periodic systems. Our scheme evaluates the shielding tensor as the second derivative of the total electronic energy with respect to a nuclear magnetic moment and an external magnetic field. Both the induced current density J (α) due to the first perturbation from the nuclear magnetic moment as well as the interaction of J (α) with the second perturbation in the form of an external magnetic field are evaluated analytically. Our approach is based on Kohn–Sham density functional theory and gauge-including atomic orbitals. It employs a Bloch basis set made up of Slater-type or numeric atomic orbitals and represents the Kohn–Sham potential fully without the use of effective core potentials. The method is implemented into the periodic program BAND. The new scheme represents an improvement over a previously proposed method in that use can be made of the zero-order Kohn–Sham orbitals from a calculation based on a primitive cell instead of a supercell. Further, J (α) is evaluated analytically rather than by a finite difference approach. The improvements reduce the required computational time by up to two orders of magnitude for three-dimensional systems. Such a reduction is made possible by the fact that we are using atomic centered basis functions. The new implementation is further able to take into account scalar relativistic effects within the zero-order regular approximation. Results from calculations of NMR shielding constants based on the present approach are presented for systems with one-, two-, and three-dimensional periodicity. The reported values are compared to experiment and results from the previously proposed scheme.
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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".