Modern exact two-component Hamiltonians for relativistic quantum chemistry and physics: Two-electron picture-change corrections made simple

Based on atomic mean-field (amf) SCF quantities, we present two simple, yet computationally efficient and numerically accurate matrix approaches to correct scalar-relativistic and spin-orbit two-electron picture-change corrections (PCs) arising within an exact two-component (X2C) Hamiltonian framework.[1] Both approaches, dubbed amfX2C and eamfX2C, allow us to uniquely tailor PCs to mean-field models, viz. Hartree–Fock or Kohn–Sham DFT, in the latter case also avoiding the need of a point-wise calculation of exchange–correlation PCs. We assess the numerical performance of these Hamiltonians on spinor energies of closed-shell and open-shell molecules, achieving a consistent 10^-5 Hartree accuracy compared to reference four-component (4c) data. Excellent agreements with reference data are also observed for molecular properties sensitive to relativistic effects such as EPR or X-ray absorption energies.[2] We believe that our (e)amfX2C Hamiltonians constitute a fundamental milestone towards a universal and reliable relativistic 2c approach for quantum chemistry and physics, maintaining the accuracy of the parent 4c one at a fraction of its computational cost.