Impurity-Preserved Density Matrix Embedding Theory for Local Electronic Excitations

Density matrix embedding theory (DMET), which is usually based on a Schmidt decomposition of Slater determinants by partitioning the full system into impurity and environment in terms of local orthogonal orbitals (LOs), has demonstrated considerable promise in electronic structure studies because it enables the extraction of local properties using a high-level solver within an embedded impurity subsystem with greatly reduced degrees of freedom, thereby achieving a balance between accuracy and computational cost. However, its application to excited states of strongly correlated systems, such as lanthanide complexes, remains challenging because the errors relative to all-electron results can still be significant. Motivated by the success of the previously developed atomic orbitals (AOs) based DMET framework (Ai, Li, and Jiang, Phys. Rev. Lett. 2025, 135, 026502.), termed AO-DMET, which attains improved accuracy by constructing the embedded subspace based on a non-orthogonal decomposition of the Slater determinant in terms of AOs, we propose a new LO-based partitioning scheme that fully preserves the impurity space spanned by corresponding AOs and can achieve accuracy closely matching that of AO-DMET while retaining the orthogonal partition and its associated computational efficiency. The performance of the proposed method is demonstrated through excitation energy calculations for several representative lanthanide complexes. These results establish an efficient and accurate partitioning scheme for describing excited states in strongly correlated systems within the DMET framework.