A 4D Electrostatic Model for Fast Computational Chemistry: Using Explicit Electron Internal Structure.

Electrons have internal structure, you cannot have spin without internal structure, you

cannot have chemistry without spin, computing with out an explicit model for spin has

made chemists’ lives hard.

We present a deterministic framework for computational chemistry that replaces the

probabilistic wave function with a classical electromagnetic model of the electron possessing

internal temporal structure. By recognizing the electron as a half-photon electromagnetic

field configuration oscillating between two temporal poles separated by δ0 = λC /2 ≈1.21

pm, we resolve the classical radiation catastrophe and recover atomic stability without quan-

tum axioms. The electron’s energy resides entirely in the half-photon field oscillation at

frequency ω0 = mec2/ℏ, not in electrostatic self-energy of the temporal poles. Angular mo-

mentum conservation (L= ℏ) makes the electron stiff against stretching but compressible

under strong nuclear fields, with compression energy E(δ) = ℏc/δ increasing hyperbolically

as δ < δ0. This temporal structure naturally regularizes the nuclear Coulomb potential,

predicting the hydrogen ground state to 0.18% accuracy. The exchange interaction emerges

as magnetic phase-locking between antiparallel electron pairs, calibrated from Cooper pair

coherence lengths in superconductors. This mechanism reproduces the lithium ionization

energy (0.8% error) and derives nitrogen’s sp3 geometry from magnetic dipole packing con-

straints. The Pauli exclusion principle arises from two physical mechanisms: (1) compressed

electrons cannot phase-lock with uncompressed electrons due to frequency mismatch, and

(2) half-photon analytic paths resist spatial overlap. The model offers O(N2) computational

scaling for molecular systems, presenting a classical alternative to density functional theory.