PreprintarXiv licencearXiv
Two-center Dirac equation in a Gaussian basis set
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 H2+ at an internuclear distance R=2.0 a0, 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 H2+ 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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BibTeX
@misc{ferenc2026twocenter,
title = {{Two-center Dirac equation in a Gaussian basis set}},
author = {Dávid Ferenc},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.03217},
eprint = {2610.03217},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.03217},
}
RIS
TY - UNPB
TI - Two-center Dirac equation in a Gaussian basis set
AU - Dávid Ferenc
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2610.03217
UR - https://arxiv.org/abs/2610.03217
AB - 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.
ER -