$\Delta$NO and the complexities of electron correlation in simple hydrogen clusters
Bibliographic record
Abstract
The $\Delta$NO two-electron density matrix (2-RDM) and energy expression are derived from a multideterminantal wave function. The approximate $\Delta$NO 2-RDM is combined with an on-top density functional and a double-counting correction to capture electron correlation. A trust-region Newton's method optimization algorithm for the simultaneous optimization of $\Delta$NO orbitals and occupancies is introduced and compared to the previous iterative diagonalization algorithm. The combination of $\Delta$NO and two different on-top density functionals, Colle-Salvetti (CS) and OF, is assessed on small hydrogen clusters and compared to density functional, single-reference coupled cluster, and multireference perturbation theory (MRMP2) methods. The $\Delta$NO-CS and $\Delta$NO-OF methods outperform the single-reference methods, and are comparable to MRMP2. However, there is a distinct qualitative error in the $\Delta$NO potential energy surface for H$_4$ compared to the exact. This discrepancy is explained through analysis of the $\Delta$NO orbitals, occupancies and the two-electron density.
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 | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 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) | 0.001 | 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 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".