This work introduces a group-theoretical framework for modeling the electronic structures of individual atoms, with a particular focus on hypothetical and superheavy elements (Z > 140). Unlike conventional quantum chemical approaches, this method treats atomic orbitals as elements of a mathematical group and incorporates irreducible representations to encode orbital symmetries directly into the atomic energy functional. The framework allows systematic prediction of stable electron configurations, magnetic properties, chemical reactivity, and optical transitions for unknown superheavy elements. High-angular-momentum orbitals (g and h shells) are found to dominate magnetic and chemical behavior, while closed-shell orbitals remain largely inert. The approach is fully theoretical, and no experimental validation has yet been performed. This repository provides the full manuscript, including derivations, algorithms for energy minimization, and illustrative examples for hypothetical superheavy elements.
Ren Matsuoka (Mon,) studied this question.