Dipole and quadrupole moments of molecules in crystals: A novel approach based on integration over Hirshfeld surfaces
Bibliographic record
Abstract
Elegant expressions are derived for the computation of dipole and quadrupole moments of molecules using the electrostatic potential and electric field evaluated on an oriented molecular surface. These expressions are implemented for Hirshfeld surfaces, applied to various molecular crystals, and compared with the results from the quantum theory of atoms in molecules. The effect of intermolecular interactions is also explored by examining the differences between electrostatic moments derived from a periodic Hartree-Fock electron density and an electron density resulting from a superposition of noninteracting molecules. The enhancement of the dipole moment for hydrogen bonded molecular crystals is typically 30%-40% and shown to be largely independent of the partitioning scheme. Dipole moments calculated from Hirshfeld surfaces systematically underestimate those from zero-flux surfaces, a result attributed to the translation of the Hirshfeld surface relative to the zero-flux surfaces for these molecules. For acetylene and benzene, the differences between a crystal calculation and the sum of noninteracting molecules are small, and both partitioning schemes yield quadrupole and second moment results in close agreement.
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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 | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
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".