A numerically exact calculation of vibration-rotation-tunnelling levels of water dimer on a new accurate potential energy surface: achieving sub-cm−1 accuracy from the terahertz to the infrared
Bibliographic record
Abstract
Numerically exact vibrational-rotational-tunnelling (VRT) levels of (H2O)2 and (D2O)2 have been computed in full dimensionality on a new highly accurate two-body potential energy surface (PES). Inter-molecular levels are computed with a basis of products of contracted intramolecular basis functions and inter-molecular functions that are products of three Wigner functions. Intra-molecular levels are computed with a product of contracted intra-molecular basis functions and contracted inter-molecular basis functions. We use a two-body PES that is fitted using the fundamental-invariant neural network (FI-NN) method using 740,000 ab initio points. Energies for points near the bottom of the well are computed without the frozen-core approximation. The PES has a root-mean-square fitting error of only 0.70 cm−1. All the experimental VRT fork origins and tunnelling splittings in the terahertz region (up to 150 cm−1) are in excellent agreement with our calculated levels. The largest error is 0.44 cm−1 for (H2O)2 and 0.85 cm−1 for (D2O)2. The calculated levels also agree very well with the 22, out of a possible 24, observed OD stretch vibration-tunnelling levels of (D2O)2 [J. Chem. Phys. 150, 164307 (2019);160, 114314 (2024)], the largest error being 0.35 cm−1. Coupling, which causes predissociation, makes OH stretch states of (H2O)2 difficult to observe. For the only rotationally resolved experimental OH stretch state, the as[A] “2s” state [J. Chem. Phys 91, 6613 (1989)], near 3738 cm−1, the 3 observed vibrational-tunnelling levels agree with the calculated levels to within 0.35 cm−1.
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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 | 0.000 | 0.001 |
| 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 | 0.001 | 0.001 |
| Open science | 0.001 | 0.000 |
| 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".