A Classical Spiral Orbit Model for Molecular Spectra and Electron Spin: Applications to H$_2$

This study introduces a classical spiral orbit model that unifies molecular spectra and electron spin for H$_2$ (bond length \(\SI{7.4e-11}{\meter}\)), offering a deterministic alternative to quantum mechanics' intrinsic assumptions. Electron motion is modeled as a helical trajectory driven by electromagnetic forces, yielding four characteristic frequencies—\( f_1 = \SI{6.76e17}{\hertz} \), \( f_2 = \SI{1.35e18}{\hertz} \), \( f_3 = \SI{2.23e12}{\hertz} \), \( f_4 = \SI{5.03e10}{\hertz} \)—spanning ultraviolet to microwave spectra. Spin emerges from the primary orbit (\( v = \SI{5e7}{\meter\per\second} \), \( r = \SI{1.15e-12}{\meter} \)), precisely matching \(\mu_B = \SI{9.27e-24}{\ampere\meter\squared}\) and \(\frac{\hbar}{2}\). Validation against H$_2$ data confirms rotational lines (\( f_{\text{spin}} \approx \SI{2.23e12}{\hertz} \)) and suggests ultraviolet bands arise from coupled sub-momenta. This framework reinterprets quantum phenomena through classical dynamics, with potential to extend across molecular systems and reshape microscopic physics.