Fully relativistic self-consistent field under a magnetic field

We present a gauge-invariant implementation of the four-component Dirac-Hartree-Fock method for simulating the electronic structure of heavy element complexes in magnetic fields. The additional cost associated with the magnetic field is shown to be only 10-13% of that at zero field. The Dirac-Hartree-Fock wave function is constructed from gauge-including atomic orbitals. The so-called restricted magnetic balance is used to generate 2-spinor basis functions for the small component. The molecular integrals for the Coulomb and Gaunt interactions are computed using density fitting. Our efficient, parallel implementation allows for simulating the electronic structure of molecules containing more than 100 atoms with a few heavy elements under magnetic fields.