Atomic Periodicity as Spectral Structure
- 1Minnesota
Abstract
The periodic system was established from trends in atomic weight and chemical behavior and later explained through electronic structure models, but it has not been derived directly from atomic observables without prior chemical or theoretical knowledge. Here we show that atomic spectra alone encode the full organization of the periodic table. Frequency-domain analysis reveals that elements occupy a bounded spectral space governed by hierarchical scaling between K-edge (π πππ₯ ) and first ionization frequencies. Elements organize into spectral bands (periods) and parallel power law trajectories (groups). Periodic differentiation emerges from bifurcation of spectral modes, and periodic bandwidth (Ξ π ) contracts following Ξ π β π πππ₯ β1.19 (R 2 = 0.9995), establishing a fundamental limit on elemental differentiation. Substituting atomic number for K-edge does not reproduce this organization, indicating that the spectral domain represents the natural scaling coordinate for periodic structure. This two-parameter framework provides an empirical resolution to longstanding classification questions and enables prediction using spectral scaling relations. Leave-one-out cross-validation yields median prediction errors of 1.1% for measured first ionization frequencies and 2.1% for covalent radii, with lanthanide-series prediction errors below 0.3%. Extending these predictions to elements with incomplete data yields new covalent radii for actinium and lawrencium, and ionization frequency for praseodymium. The same two-parameter spectral structure also organizes different types of conductivity and magnetism, from which superconducting behavior is predicted for chromium and silver.
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BibTeX
@misc{abbas2026atomic,
title = {{Atomic Periodicity as Spectral Structure}},
author = {Abdennour Abbas},
howpublished = {ChemRxiv},
year = {2026},
month = may,
doi = {10.26434/chemrxiv.15001341/v3},
url = {https://doi.org/10.26434/chemrxiv.15001341/v3},
note = {CC BY-NC-ND},
}
RIS
TY - UNPB
TI - Atomic Periodicity as Spectral Structure
AU - Abdennour Abbas
PY - 2026
DA - 2026/05/21
PB - ChemRxiv
DO - 10.26434/chemrxiv.15001341/v3
UR - https://doi.org/10.26434/chemrxiv.15001341/v3
AB - The periodic system was established from trends in atomic weight and chemical behavior and later explained through electronic structure models, but it has not been derived directly from atomic observables without prior chemical or theoretical knowledge. Here we show that atomic spectra alone encode the full organization of the periodic table. Frequency-domain analysis reveals that elements occupy a bounded spectral space governed by hierarchical scaling between K-edge (π πππ₯ ) and first ionization frequencies. Elements organize into spectral bands (periods) and parallel power law trajectories (groups). Periodic differentiation emerges from bifurcation of spectral modes, and periodic bandwidth (Ξ π ) contracts following Ξ π β π πππ₯ β1.19 (R 2 = 0.9995), establishing a fundamental limit on elemental differentiation. Substituting atomic number for K-edge does not reproduce this organization, indicating that the spectral domain represents the natural scaling coordinate for periodic structure. This two-parameter framework provides an empirical resolution to longstanding classification questions and enables prediction using spectral scaling relations. Leave-one-out cross-validation yields median prediction errors of 1.1% for measured first ionization frequencies and 2.1% for covalent radii, with lanthanide-series prediction errors below 0.3%. Extending these predictions to elements with incomplete data yields new covalent radii for actinium and lawrencium, and ionization frequency for praseodymium. The same two-parameter spectral structure also organizes different types of conductivity and magnetism, from which superconducting behavior is predicted for chromium and silver.
SN - 2573-2293
ER -