Convergence and computational efficiency enhancements in the iterative solution of the <i>G</i>‐particle‐hole hypervirial equation
Bibliographic record
Abstract
Abstract The G‐particle‐hole hypervirial (GHV) equation has been recently reported (Valdemoro et al., Sixth International Congress of the International Society for Theoretical Chemical Physics Vancouver: Canada, 2008. Alcoba et al., Int J Quantum Chem 2009, 109, 3178; Valdemoro et al., Int J Quantum Chem 2009, 109, 2622). This equation is the newest member of the family of equations which can be obtained by applying a matrix‐contracting mapping (Valdemoro, An R Soc Esp Fís 1983, 79, 106; Valdemoro, Phys Rev A 1985, 31, 2114; Valdemoro, in Density Matrices and Density Functionals, Reidel: Dordrecht, 1987; p 275.) to the matrix representation in the N‐electron space of the Schrödinger, Liouville and hypervirial equations. The procedure that we have applied in order to solve the GHV equation exploits the stationary property of the hypervirials (Hirschfelder, J Chem Phys 1960, 33, 1462; Hirschfelder and Epstein, Phys Rev 1961, 123, 1495) and follows the general lines of Mazziotti's variational approach for solving the anti‐Hermitian contracted Schrödinger equation (ACSE) (Mazziotti, Phys Rev Lett 2006, 97, 143002; Mazziotti, Phys Rev A 2007, 75, 022505; Mazziotti, J Chem Phys 2007, 126, 184101). In this article, we report how the method's convergence has been significantly enhanced and how its computational scaling has been considerably reduced (in both floating‐point operations and storage). The results for a variety of atomic and molecular calculations confirming these methodological improvements are reported here. © 2010 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 | 0.002 | 0.008 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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".