A different Hubbard <i>U</i> value should be used for the metal–oxo cluster node in a metal–organic framework than for its extended phase: A case study of Ce-based materials

Abstract

The Hubbard U for a metal–oxo unit depends on how electrons are screened in its host material. This screening is governed by (i) local screening determined by coordination, oxidation state, and metal–ligand hybridization and (ii) the longer-range dielectric response of the surrounding lattice. Consequently, the common practice of directly transferring U from extended metal oxides to metal–organic frameworks (MOFs) with the same metal–oxo unit risks systematic errors. Here, we take UiO-66(Ce) as a prototypical MOF and determine the node-specific linear-response Hubbard parameter U (ULR) for four commonly employed GGA functionals used to describe the Ce 4f orbitals of the Ce6O8 node. We then benchmark GGA + ULR against experiment and HSE06 for both pristine and the node-reduced UiO-66(Ce). GGA + ULR reproduces the structural and electronic properties, whereas using the U value transferred from CeO2 leads to a deviated description of the redox activity. However, transferring node-specific ULR between MOFs that share the same node and comparable screening environments is physically justified and practically useful for GGA + U calculations of large-cell MOFs. This conditional transferability is validated by applying the ULR derived from UiO-66(Ce) to NU-1000(Ce), successfully reproducing hybrid-functional results across seven proton topologies. The larger ULR obtained for the Ce6O8 node compared to that for CeO2 reflects more ionic Ce–O bonding and distinct redox chemistry of the MOF node. Such deviations are not limited to the present case but are anticipated for metal–oxo units in MOFs more broadly, enabling node chemistries that are different from those of the extended phase.