In this preliminary work, we propose a hypothesis and initiate a step-by-step, systematic upgrade to the cutting-edge iso-electronium model by further equipping it with order parameters of fractional statistics to encode the topological deformations, spontaneous superfluidic gauge symmetry breaking, correlated helices with long range order, and wavepacket wavefunctions for the toroidal polarizations. For this initial case, we consider the singlet planar coupling of two hydrogen atoms that are interlocked with a Santilli-Shillady strong valence bond to form a molecule with iso-electronium. The enhancement results support our hypothesis and are significant because the order parameters arm the iso-electronium model an extra degree of freedom to work with, which may authorize us to further decode and comprehend the underlying physical mechanisms and features associated with the configuration of the toroidal polarizations. Thus, these outcomes should be subjected to additional rigorous scrutiny and improvement via the scientific method.