Spin-Dependent Terms of the Breit–Pauli Hamiltonian Evaluated with an Explicitly Correlated Gaussian Basis Set for Molecular Computations

This work collects the spin-dependent leading-order relativistic and quantum-electrodynamical corrections for the electronic structure of atoms and molecules within the nonrelativistic quantum electrodynamics framework. We report the computation of perturbative corrections using an explicitly correlated Gaussian basis set, which allows high-precision computations for few-electron systems. In addition to numerical tests for triplet Be, triplet H₂, and triplet H₃ ⁺ states and comparison with no-pair Dirac-Coulomb-Breit Hamiltonian energies, numerical results are reported for electronically excited states of the helium dimer, He₂, for which the present implementation delivers high-precision magnetic coupling curves necessary for a quantitative understanding of the fine structure of its high-resolution rovibronic spectrum.