A Perturbative Super-CI Approach for Orbital Optimization in Two-Component Relativistic CASSCF

In this work, we developed a new orbital optimization approach, perturbative Super-CI (Super-CIPT), for the two-component complete active space self-consistent field (2C-CASSCF) method. By variationally optimizing spinor orbitals and consistently incorporating spin-orbit coupling (SOC) at the orbital level, the 2C-CASSCF method enables the simultaneous treatment of relativistic effects and static correlation. The Super-CIPT approach demonstrates robust convergence behavior and is applicable to systems with strong SOC. The inclusion of the Gaunt or Breit term via the atomic mean field approximation yields the most accurate results, with errors below 2% for halogen atoms. We systematically assess the performance of 2C-CASSCF on the spin-orbit splittings (SOSs) of selected p-block elements and the ligand-field splittings of complexes. For the SOSs of p-block elements, 2C-CASSCF outperforms conventional one-component (1C) CASSCF. This work establishes 2C-CASSCF with Super-CIPT as a reliable and efficient approach for multireference relativistic quantum chemistry.