Alchemical diastereomers from antisymmetric alchemical perturbations
Bibliographic record
Abstract
The energy difference between two iso-electronic systems can be approximated by the first order Hellmann-Feynman derivative with respect to the linear alchemical coupling parameter, evaluated using the electron density of the corresponding averaged Hamiltonian. This approximation is exact up to third order because even-order contributions cancel out. This finding holds for any iso-electronic compound pair (dubbed "alchemical diastereomers"), regardless of differences in configuration, composition, or energy, and consequently, relative energy estimates for all possible iso-electronic alchemical diastereomer pairs require only O(1) self-consistent field cycles for any given averaging reference Hamiltonian. We discuss the relation to the Verlet algorithm, alchemical harmonic approximation (AHA) [Krug et al., J. Chem. Phys. 162, 044101 (2025)], relative properties such as forces, ionization potential or electron affinities, and Levy's formula for relative energies among iso-electronic systems that uses the averaged electron density of the two systems [Levy, J. Chem. Phys. 70, 1573 (1979)]. Density functional theory based estimates accurately reflect trends in the charge-neutral iso-electronic diatomic molecule series with 14 protons (N2, CO, BF, BeNe, LiNa, HeMg, HAl), with systematically increasing errors. Using alchemical Hellmann-Feynman derivatives for toluene, we demonstrate the concept's broader applicability by estimating relative energies for all 36 possible alchemical diastereomer pairs from vertical iso-electronic charge-neutral antisymmetric BN doping of toluene's aromatic ring, with mean absolute errors of a few milli-Hartrees.
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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 | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.004 | 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".