The Rules of the Terms: Hund's Three Sentences and the One Atom They Cannot See

Between 1925 and 1927 Friedrich Hund stated three rules that select the ground term of an atom's configuration — maximum spin, then maximum orbital angular momentum, then the total angular momentum by shell filling — and a century of spectroscopy has run on them. This paper evaluates the rules' warrant at their founding address, converting census attack CC-163 whole. The rules were offered as empirical regularities of the term orderings, with no derivation from the atomic Hamiltonian in the founding papers; the bench therefore audits them as what they are — a selection rule resting on inspection — enumerating every microstate of each declared configuration exactly, reading the rule-selected term off mechanically, and scoring it against the declared observed ground terms across forty atoms. The audit: 39 of 40 rows hit, a rate of 97.500000\%, with the machinery check exact (enumeration and the closed-form extremal reading agree on all 33 configuration cells). The one failure is named and its mechanism is the deficit's own: cerium, where the rules select ^3H_4 and the record's ground term is ^1G_4 — a rival from a different spin sector lying below the selected term, an inversion an ordering that carries no energies cannot see. Census headline, unchanged: NOT SOLVED / PARTIAL · producing-count 0.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-11-06
DOI
https://doi.org/10.5281/zenodo.24026862
Primary Topic
Atomic and Molecular Physics
Type
preprint
Controls
|||
ALL TIME
JAN
FEB
MAR
APR
MAY
JUN
JUL
AUG
SEP
OCT
NOV
preprint

The Rules of the Terms: Hund's Three Sentences and the One Atom They Cannot See

William Alexander Aldred
Zenodo (CERN European Organization for Nuclear Research)
Atomic and Molecular Physics
preprint

The Rules of the Terms: Hund's Three Sentences and the One Atom They Cannot See

William Alexander Aldred
preprint en

Abstract

Between 1925 and 1927 Friedrich Hund stated three rules that select the ground term of an atom's configuration — maximum spin, then maximum orbital angular momentum, then the total angular momentum by shell filling — and a century of spectroscopy has run on them. This paper evaluates the rules' warrant at their founding address, converting census attack CC-163 whole. The rules were offered as empirical regularities of the term orderings, with no derivation from the atomic Hamiltonian in the founding papers; the bench therefore audits them as what they are — a selection rule resting on inspection — enumerating every microstate of each declared configuration exactly, reading the rule-selected term off mechanically, and scoring it against the declared observed ground terms across forty atoms. The audit: 39 of 40 rows hit, a rate of 97.500000\%, with the machinery check exact (enumeration and the closed-form extremal reading agree on all 33 configuration cells). The one failure is named and its mechanism is the deficit's own: cerium, where the rules select ^3H_4 and the record's ground term is ^1G_4 — a rival from a different spin sector lying below the selected term, an inversion an ordering that carries no energies cannot see. Census headline, unchanged: NOT SOLVED / PARTIAL · producing-count 0.

Zenodo (CERN European Organization for Nuclear Research)
Atomic and Molecular Physics
AI Navigator

Ask Laika to Summarize, Analyze, and Connect papers live on the map.

Summarize Papers & Methodologies

Extract key findings, datasets, and comparative methods across publications.

Benchmark Rankings & Visual Analytics

Rank top research institutions, authors, funders, topics, and journals by Field-Weighted Citation Impact (FWCI) and paper volume with instant charts.

Connect Distant Disciplines

Bridge topological clusters on the map to find hidden collaborative intersections.

Laika access coming soon