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arXiv · 2610.03217

Two-center Dirac equation in a Gaussian basis set

Dávid Ferenc
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Abstract

A method for solving the two-center Dirac equation using a Gaussian-product basis set tailored to the axial symmetry of diatomic systems is presented. For the ground state of H$_2^+$ at an internuclear distance $R=2.0~a_0$, we obtain a relativistic energy with relative precision at the $10^{-18}$ level. The properties of the basis set allow for an analytic Fourier transform of the wave function. As a first application we evaluate, for the first time, the zero-potential contribution to the one-loop self-energy for H$_2^+$ in Feynman and Coulomb gauges. Although this contribution is not separately gauge invariant, its calculation provides a proof of principle for the use of the present framework in prospective QED calculations.

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Dávid Ferenc. 2026-10-02. Two-center Dirac equation in a Gaussian basis set. https://arxiv.org/abs/2610.03217

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