Using Nested Contractions and a Hierarchical Tensor Format To Compute Vibrational Spectra of Molecules with Seven Atoms
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Bibliographic record
Abstract
We propose a method for solving the vibrational Schrödinger equation with which one can compute hundreds of energy levels of seven-atom molecules using at most a few gigabytes of memory. It uses nested contractions in conjunction with the reduced-rank block power method (RRBPM) described in J. Chem. Phys. 2014, 140, 174111. Successive basis contractions are organized into a tree, the nodes of which are associated with eigenfunctions of reduced-dimension Hamiltonians. The RRBPM is used recursively to compute eigenfunctions of nodes in bases of products of reduced-dimension eigenfunctions of nodes with fewer coordinates. The corresponding vectors are tensors in what is called CP-format. The final wave functions are therefore represented in a hierarchical CP-format. Computational efficiency and accuracy are significantly improved by representing the Hamiltonian in the same hierarchical format as the wave function. We demonstrate that with this hierarchical RRBPM it is possible to compute energy levels of a 64-D coupled-oscillator model Hamiltonian and also of acetonitrile (CH3CN) and ethylene oxide (C2H4O), for which we use quartic potentials. The most accurate acetonitrile calculation uses 139 MB of memory and takes 3.2 h on a single processor. The most accurate ethylene oxide calculation uses 6.1 GB of memory and takes 14 d on 63 processors. The hierarchical RRBPM shatters the memory barrier that impedes the calculation of vibrational spectra.
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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)
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Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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