Bridging the Homogeneous-Heterogeneous Divide: Modeling Spin for Reactivity in Single Atom Catalysis

Abstract

Single atom catalysts (SACs) are emergent catalytic materials that have the promise of merging the scalability of heterogeneous catalysts with the high activity and atom economy of homogeneous catalysts. Computational, first-principles modeling can provide essential insight into SAC mechanism and active site configuration, where the sub-nm-scale environment can challenge even the highest-resolution experimental spectroscopic techniques. Nevertheless, the very properties that make SACs attractive in catalysis, such as localized d electrons of the isolated transition metal center, make them challenging to study with conventional computational modeling using density functional theory (DFT). For example, Fe/N-doped graphitic SACs have exhibited spin-state dependent reactivity that remains poorly understood. However, spin-state ordering in DFT is very sensitive to the nature of the functional approximation chosen. In this work, we develop accurate benchmarks from correlated wavefunction theory (WFT) for relevant octahedral complexes. We use those benchmarks to evaluate optimal DFT functional choice for predicting spin state ordering in small octahedral complexes as well as models of pyridinic and pyrrolic nitrogen environments expected in larger SACs. Using these guidelines, we determine Fe/N-doped graphene SAC model properties and reactivity as well as their sensitivities to DFT functional choice. Finally, we conclude with broad recommendations for computational modeling of open-shell transition metal single-atom catalysts.

Impact of Approximate DFT Density Delocalization Error on Potential Energy Surfaces in Transition Metal Chemistry

“…Only singlets were calculated in a restricted formalism. As in prior work 22,24,29,54 , exchange sensitivities of relevant geometric and energetic properties, p, were computed as linear approximations:…”

“…The valence (i.e., d or f) electrons of open shell transition metal complexes are particularly sensitive to DE imbalances, leading to strongly xc-dependent predictions of spin-state [19][20][21][22][23][24] or magnetic ordering [25][26][27] and thus electronic properties. Although effort has been made to overcome some of these limitations through "higher rung" density functionals [28][29][30][31][32][33] , semi-local generalized gradient approximation (GGA) DFT remains widely used in transition metal chemistry for its simplicity and low computational cost.…”

“…(right) The sensitivity of spin-state energetics with respect to HF exchange (i.e., ∂ΔE H/I-L /∂a HF , in kcal/mol . HFX) for the systems studied on the left following the same color scheme (I-L in black and H-L in gray).To assess the effect of HF exchange on spin-state ordering across these transition metal dioxides, we compare the approximate, linearized exchange sensitivity22,24,29,54 (see Sec. 2) of the HS/IS to LS adiabatic energy difference (i.e., ΔE H-L or ΔE I-L , Supporting Information Table…”

Impact of Approximate DFT Density Delocalization Error on Potential Energy Surfaces in Transition Metal Chemistry

“…To assess the effect of HF exchange on spin-state ordering across these transition metal dioxides, we compare the approximate, linearized exchange sensitivity 22,24,29,54 (see Sec. 2) of the HS/IS to LS adiabatic energy difference (i.e., ΔE H-L or ΔE I-L , Supporting Information Table S9).…”

Making machine learning a useful tool in the accelerated discovery of transition metal complexes

“…Unlike in closed-shell organic chemistry, a gold standard wavefunction theory (WFT) method remains elusive here [64][65][66] due to the unique challenges of spatially close orbitals that are also close in energy. 57,67 As a result, WFT predictions of transition metal complex properties are, like their DFT counterparts, highly sensitive both to method choice 64,65 and to adjustable parameters 59,68,69 within each method. With few exceptions, 70,71 these methodological choices are conventionally viewed as only robustly made by the expert researcher after careful hand tuning and thus inherently at odds with high-throughput discovery.…”