The Kernel energy method: Application to graphene and extended aromatics
Bibliographic record
Abstract
Abstract The quantum chemistry of finite aperiodic graphene flakes is a matter of considerable interest because of the anticipated technological importance of such objects. Since real aperiodic graphene flakes will in general be composed of many thousands of carbon atoms, theoretical methods appropriate to such large molecules would need to be used for the ab initio quantum calculation of their properties. The Kernel energy method is discussed here, and it is shown to be accurately applicable to graphenes and analogous extended aromatic molecules. It is necessary to define the kernels of a graphene molecule in a new way because of the extensive aromaticity, which defines its electronic structure. The kernels used in the reconstruction of the full graphene sheet preserve the total number of π‐electrons, Clar sextets, and the approximate overall aromaticity. Sivaramakrishnan et al. [J Phys Chem A, 2005, 109, 1621] define similar “ring conserved isodesmic reactions (RCIR).” The principal innovation of this article is the suggestion that kernels may be mathematically extracted from an extended aromatic molecule such as graphene by a fissioning of aromatic bonds. Hartree Fock (HF) and Møller‐Plesset (MP2) chemical models using a Gaussian basis of 3‐21G orbitals are used to calculate the total energy of a graphene flake. This demonstration calculation is performed on a graphene flake in which dangling bonds are saturated with hydrogens (C78H26) composed of a total of 104 atoms arranged in 27 benzenoid rings. The KEM with both types of chemical model are shown to be accurate to nearly 1 kcal/mol, of a total energy, which is nearly 3000 atomic units, that is, with an absolute error within “chemical accuracy” and a relative error of the order of 5 × 105% of the total energy. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".