Accelerating the calculation of energy levels and wave functions using an efficient preconditioner with the inexact spectral transform method
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
In an earlier paper [J. Chem. Phys. 112, 8765 (2000)] our group introduced a preconditioned inexact spectral transform method for calculating energy levels and wave functions. Although we could calculate high-lying levels with far fewer matrix–vector products than with the filter diagonalization method of Mandelshtam and Taylor, even better performance can be achieved with a better preconditioner. In this paper, we develop an extremely efficient preconditioner consisting of two components: (1) transformation to an optimal separable basis, in which off-diagonal elements of the Hamiltonian matrix are minimized; and (2) removal of all off-diagonal coupling near the energies of interest. The new preconditioner works extremely well; it enables us to calculate high-lying vibrational states of H2O with orders of magnitude fewer matrix–vector products than for all other known methods. The new preconditioner should also accelerate the calculation of other quantities, such as photodissociation cross sections and rate constants.
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.
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 it