Alchemical harmonic approximation based potential for iso-electronic diatomics: Foundational baseline for $Δ$-machine learning
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Bibliographic record
Abstract
We introduce the alchemical harmonic approximation (AHA) of the absolute electronic energy for charge-neutral iso-electronic diatomics at fixed interatomic distance $d_0$. To account for variations in distance, we combine AHA with this Ansatz for the electronic binding potential, $E(d)=(E_{u}-E_s) \left(\frac{E_c-E_s}{E_u-E_s}\right)^{\sqrt{d/d_0}}+E_s$, where $E_u,E_c,E_s$ correspond to the energies of united atom, calibration at $d_0$, and sum of infinitely separated atoms, respectively. Our model covers the entire two-dimensional electronic potential energy surface spanned by distance and difference in nuclear charge from which only one single point (with elements of nuclear charge $Z_1,Z_2$ and distance $d_0$) is drawn to calibrate $E_c$. Using reference data from pbe0/cc-pVDZ, we present numerical evidence for the electronic ground-state of all neutral diatomics with 8, 10, 12, 14 electrons. We assess the validity of our model by comparison to legacy interatomic potentials (Harmonic oscillator, Lennard-Jones, and Morse) within the most relevant range of binding (0.7 - 2.5 A), and find comparable accuracy if restricted to single diatomics, and significantly better predictive power when extrapolating to the entire iso-electronic series. We also investigated $Δ$-learning of the electronic absolute energy using our model as baseline. This baseline model results in a systematic improvement, effectively reducing training data needs for reaching chemical accuracy by up to an order of magnitude from $\sim$1000 to $\sim$100. By contrast, using AHA+Morse as a baseline hardly leads to any improvement, and sometimes even deteriorates the predictive power. Inferring the energy of unseen CO converges to a prediction error of $\sim$0.1 Ha in direct learning, and $\sim$0.04 Ha with our baseline.
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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 | 0.002 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 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 it