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 non-relativistic 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.