A Classical Spiral Model for the Internal Structure of the Water Molecule and Its Microwave Spectrum

The water molecule (H$_2$O), known for its asymmetric structure and strong dipole moment, exhibits prominent rotational features in the microwave spectrum (0.74--125 cm$^{-1}$). This study introduces a classical spiral-shaped small ring model to describe H$_2$O's internal electron dynamics. Electrons are assumed to move along primary orbital paths with superimposed spiral perturbations, driven by electromagnetic interactions with neighboring particles. We derive transverse ($f_3$) and longitudinal ($f_4$) oscillation frequencies, combining them into a composite frequency ($f_{\text{spin}} = \sqrt{f_3^2 + f_4^2}$) that correlates with observed spectral lines. Applied to five orbital types (single-H, O-2s/2p, H-O cross, H-H cross, O-1s), the model accurately reproduces key microwave lines, such as 0.74 cm$^{-1}$ and 22.83 cm$^{-1}$, and extends to 473 cm$^{-1}$ in the far-infrared. Leveraging classical electromagnetism and molecular geometry, this approach validates the utility of classical methods in molecular spectroscopy and sets the stage for future 3D simulations to refine orbital trajectories.