Representation of electron–nucleus cusps in Slater and Gaussian basis sets
Bibliographic record
Abstract
Prior to spherical averaging, the Coulomb cusp of exact electron densities is described by an equation involving two parameters: the nuclear charge Z and a vector quantifying the cusp anisotropy due to the presence of other nuclei. A similar three-parameter equation describes jump discontinuities of exact kinetic energy densities at nuclear positions. We demonstrate that these same equations, with basis-set-dependent parameters, also describe approximate electron and kinetic energy densities expanded in Slater-type orbitals (STOs) and even cuspless Gaussian-type orbitals (GTOs). Apart from the effective Z values, which are zero for GTOs, the cusp-shape parameters derived from STO and GTO wavefunctions are comparable in magnitude and converge to common complete-basis-set limits. These findings provide a rigorous justification for extending the concepts of effective nuclear charge and density anisotropy vectors to approximate wavefunctions within STO and GTO basis sets. Such extensions are not entailed by the properties of exact solutions to the Schrödinger equation and are not automatically applicable to all basis sets.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.002 | 0.003 |
| 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 | 0.002 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".