Density matrix embedding theory (DMET) provides a systematic framework to combine low-level (e.g., Hartree−Fock approximation) and high-level correlated quantum chemistry methods to treat strongly correlated systems. In this work, we propose an efficient quantum embedding approach that combines DMET with the complete active space self-consistent field and subsequent state interaction treatment of spin−orbit coupling (CASSI-SO) and apply it to a theoretical description of single-ion magnets (SIMs). We have developed a novel regularized direct inversion of iterative subspace (R-DIIS) technique that ensures restricted open-shell Hartree−Fock converging to a physically correct ground state, which is found to be crucial for the efficacy of subsequent CASSI-SO calculation. The DMET +CASSI-SO approach can produce reliable zero-field splitting parameters in typical 3d-SIMs with dramatically reduced computational cost compared to its all-electron counterpart. This work therefore demonstrates the great potential of DMET-based multiconfigurational approaches for efficient ab initio study of magneto−structural correlations in complex molecular magnetic systems.

Density matrix embedding theory (DMET) provides a systematic framework to combine low-level (e.g. Hartree-Fock approximation) and high-level correlated quantum chemistry methods to treat strongly correlated systems with remarkable accuracy and efficiency. In this work, we proposed an efficient quantum embedding approach that uses the restricted open-shell Hartree-Fock (ROHF) as the low level solver and combines DMET with the complete active space self-consistent field and subsequent state interaction treatment of spin-orbit coupling (CASSI-SO), and applied it to theoretical description of single-ion magnets (SIMs). We have developed a novel direct inversion of iterative subspace (DIIS) technique that incorporates a regularization term related to the spin polarization entropy, termed as R-DIIS, and ensures ROHF to converge to physically correct ground state, which is found to be crucial for the efficacy of subsequent CASSI-SO calculation. We found that the DMET+CASSI-SO approach can produce reliable zero-field splitting (ZFS) parameters in typical 3d-SIMs with dramatically reduced computational cost compared to its all-electron counterpart. This work therefore demonstrates the great potential of the DMET-based CASSI-SO approach for efficient \textit{ab initio} study of magneto-structural correlations in complex molecular magnetic systems.