Combining Density Functional Embedding Theory and DMRG-NEVPT2 to Treat Large Active Spaces: Addressing Electronic Structure Complexity in Single-Atom Alloys

Single-atom alloys (SAAs) are an increasingly popular platform for heterogeneous catalysis because of their distinct electronic structures and ability to break catalytic linear scaling relationships. This popularity has led to a proliferation of computational studies probing SAA reactivity at the density functional theory (DFT) level. However, some phenomena such as photo- and electrocatalysis require use of electronic structure methods beyond DFT; such studies are both rare and fundamentally challenging. Density functional embedding theory (DFET)/embedded correlated wavefunction (ECW) studies of reactions on metal surfaces have been shown to provide a reliable way to correct for DFT-related errors. DFET/ECW studies of chemistry involving SAAs, however, could require active spaces beyond the capabilities of traditional multireference methods when transition-metal dopants give rise to many degenerate states. To overcome this limitation, we combined our DFET/ECW methodology with the density matrix renormalization group (DMRG) complete active space self-consistent field (DMRGSCF) and DMRG N-electron valence state second-order perturbation theory (DMRG-NEVPT2) methods in the PySCF code. Using embedded DMRGSCF and embedded DMRG-NEVPT2, we analyze CO adsorption on Ni-, Rh-, Pd-, and Pt-doped Ag(100) with different active spaces. We show that the active spaces approachable with conventional multireference methods lead to overbinding of CO due to an inability to treat all of the dopant d-orbitals on equal footing. Larger active spaces, which are easily treated by both DMRGSCF and DMRG-NEVPT2, yield much more reasonable adsorption free energies. Our findings suggest that future multireference calculations of these systems should similarly employ active spaces containing all of the dopant d-orbitals along with sp-band orbitals of the host metal near the Fermi level. Emb-DMRG-NEVPT2 is a method that can be broadly applied to study catalytic reactions on metal surfaces when large active spaces are required.