Density Matrix Embedding Pair-Density Functional Theory for Molecules

We combine density matrix embedding theory (DMET) with multiconfiguration pair-density functional theory (MC-PDFT) to explore finite systems exhibiting localized strong electron correlation effects. This methodology, termed density matrix embedded pair-density functional theory (DME-PDFT), provides a substantial cost reduction compared to traditional non-embedded MC-PDFT. Additionally, we compare it with second order n-electron valence state perturbation theory within DMET (NEVPT2-DMET). We have validated these methods by computing the bond dissociation in methyl diazine and spin-splitting energy gap in the \ce{[Fe(H_2O)_6]^{2+}} complex, showing that DME-PDFT splitting energies converge faster compared to NEVPT2-DMET to the corresponding non-embedding limits. We finally compare embedding schemes with truncation schemes for transition metal extended complexes, \ce{Fe[N(H)Ar$^*$]_2} and \ce{[NiC_{90}N_{20}H_{120}]^{2+}}, and show that embedding schemes are superior when the transition metal is not fully coordinated.