Our calculations were performed using a λ value of 0.25, referred to as tPBE0, in analogy with the PBE0 hybrid density functional theory (DFT) functional. DMET and its periodic implementation have been discussed in detail previously. DMET involves a low-level (usually Hartree-Fock) calculation on a whole system followed by a high-level (in our case, CASSCF or NEVPT2) calculation in an unentangled "embedding" subspace consisting of the union of user-specified fragment orbitals and corresponding bath (i.e. entangled environment) orbitals identified using the Schmidt decomposition. The 1-RDM and two-body reduced density matrix (2-RDM) of the whole system consist of the 1-and 2-RDMs, respectively, from the high-level calculation in the embedding subspace combined with those from the low-level calculation in the orthogonal "core" subspace. If (as in this work) only one embedded fragment is considered in each calculation and the low-level wave function (here, restricted open-shell HF or ROHF) is spin-symmetry-adapted and closed-shell in the core subspace, then the expressions for the DMET whole-system 1-and 2-RDMs assume the simple forms: