SAP-X2C: Optimally-Simple Two-Component Relativistic Hamiltonian with Size-Intensive Picture Change

We present a simple relativistic exact 2-component (X2C) Hamiltonian that models two-electron picture-change effects using Lehtola’s superposition of atomic potentials (SAP) [S. Lehtola, J. Chem. Theory Comput. 15, 1593–1604 (2019)]. The SAP-X2C approach retains the low cost and technical simplicity of the popular 1-electron X2C (1eX2C) predecessor but is significantly more accurate and has a well-defined thermodynamic limit, making it applicable to extended systems (such as large molecules and periodic crystals). The assessment of the SAP-X2C-based Hartree–Fock total and spinor energies, spin–orbit splittings, equilibrium bond distances, and harmonic vibrational frequencies suggests that SAP-X2C is similar to the more complex atomic mean-field (AMF) X2C counterparts in its ability to approximate the 4-component Dirac–Hartree–Fock reference.