Dynamic Information Compression Model for Atomic Ionization Energies

We propose a novel theoretical framework for atomic ionization energies based on the concept of dynamic information compression efficiency. Traditional quantum mechanical formulas for ionization energy,IE ∝ Z2eff/n2, implicitly assume perfect information compression withan efficiency index κ = 1.0. However, we discover that actual information compression efficiency decreases with increasing electronic complexity. We introduce a dynamic κ index defined as κ = 1.0 − 0.22 ·log(information complexity), leading to the modified formula IE ∝ Z2κeff/n2.This model successfully predicts ionization energies for elements 1-10 with15.3% average error and atomic radii with 14% average error, while revealing the decreasing pattern of information compression efficiency fromhydrogen (κ = 1.0) to neon (κ = 0.82). Notably, closed-shell atoms(helium κ = 0.75, neon κ = 0.82) exhibit significant information compression efficiency loss, reflecting compression difficulties due to electroncloud overlap.Keywords: Information compression, ionization energy, atomic structure, q