Analysis computes the electric field and energy in hydrogen molecules using the Fermi-Dirac function, suggesting influences on charge density.
Abstract The electric field is addressed for the charge density based on the Fermi-Dirac function in the presence of two protons at points A and B at low temperature. The Poisson equation is solved for the electrostatic potential φ with two asymptotic boundary conditions: φ ~ 1/rA as rA → 0 for a point A, and φ ~ 1/rB as rB → 0 for a point B. The energy of the field is computed relying on the value of the chemical potential for electrons as defined by the Fermi-Dirac function itself.
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В. К. Кочнев (2025) studied this question.