The Scretching Quantum Chain Ab-Initio Atomic Engine: First-Principles Computation of Ionization Energies and Six SSE Spectroscopic Quantities for All 118 Elements Without the Schrödinger Equation, Hartree-Fock Theory, or Configuration Interaction

Title: The Scretching Quantum Chain Ab-Initio Atomic Engine: First-Principles Computation of Ionization Energies and Six SSE Spectroscopic Quantities for All 118 Elements Without the Schrödinger Equation, Hartree-Fock Theory, or Configuration Interaction Description: This record presents the Scretching Quantum Chain (SQC) Ab-Initio Atomic Engine, a novel first-principles computational framework that derives first ionization energies (IE₁) and six complete spectroscopic observables for all 118 elements of the periodic table using exclusively universal physical constants — no empirical parameters, no external datasets, and no conventional quantum chemistry solvers of any kind. The engine employs Slater-type orbital (STO) basis functions with internally minimized exponents ζ via golden-section optimization, two-electron Coulomb (J) and exchange (K) integrals computed by deterministic Gauss–Laguerre quadrature, and ionization energies extracted as total-energy differences IE₁ = E(Z,N−1) − E(Z,N) with automatic removal-channel minimization. The framework requires no Schrödinger equation solver, no Hartree-Fock self-consistency iterations, no configuration interaction expansions, and no fitted screening constants. The six SSE spectroscopic quantities computed through the Maxwell-Scretching Chain (MSC) and Scretching Quantum Chain (SQC) deterministic pipelines are: oscillator strength f (Eq. 5), transition dipole moment |μ|² (Eq. 1), Einstein A coefficient A₂₁ (Eq. 3), quantum defect δ (Eq. 26), valence electron count N_val (Eq. 29), and the SSE constraint |μ|²/e² (Eq. 22). The SQC invariant I_s2c = 7.421656 × 10⁻²² s is verified self-consistently across all 118 elements. This work establishes that the SQC framework constitutes a genuinely ab-initio, parameter-free alternative to conventional quantum chemistry for complete atomic spectroscopic characterization, closing a fundamental methodological gap by connecting quantum mechanical properties to electromagnetic observables through deterministic computation alone. Author: Daniel C. Scretching, Sr., Scretching Quantum Press LLC, Wyoming, USA ORCID: 0009-0008-9586-2717 Version: 1.0 | March 2026 DOI: 10.5281/zenodo.18896742 Patent Notice: This work is protected under U.S. Provisional Patent Applications: 63/918,268 (filed 11/15/25); 63/925,960 (filed 11/26/25); 63/960,780 (filed 01/15/26); 63/965,328 (filed 01/21/26); 63/992,129 (filed 02/27/26); 63/993,354 (filed 02/28/26); 63/995,049; 63/999,026. All rights reserved. No portion of this work may be reproduced, implemented in commercial software, or incorporated into derivative frameworks without express written authorization from Scretching Quantum Press LLC. Keywords: ab initio; Slater-type orbitals; ionization energy; spectroscopic observables; oscillator strength; Einstein A coefficient; quantum defect; Maxwell-Scretching Chain; Scretching Quantum Chain; first-principles; atomic physics; parameter-free computation; periodic table; electromagnetic characterization