Methane C-H Activation by [Cu2O]2+ and [Cu3O3]2+ in Copper-Exchanged Zeolites: Computational Analysis of Redox Chemistry and X-ray Absorption Spectroscopy

Building on the strengths of a double-hybrid density functional for excitation energies and inverted singlet-triplet energy gaps

It is demonstrated that a double hybrid density functional approximation, ωB88PTPSS, that incorporates equipartition of density functional theory and the non-local correlation, however with a meta-generalized gradient approximation correlation functional, as well as with the range-separated exchange of ωB2PLYP, provides accurate excitation energies for conventional systems, as well as correct prescription of negative singlet-triplet gaps for non-conventional systems with inverted gaps, without any necessity for parametric scaling of the same-spin and opposite-spin non-local correlation energies. Examined over "safe" excitations of the QUESTDB set, ωB88PTPSS performs quite well for open-shell systems, correctly and fairly accurately [relative to equation-of-motion coupled-cluster singles and doubles (EOM-CCSD) reference] predicts negative gaps for 50 systems with inverted singlet-triplet gaps, and is one of the leading performers for intramolecular charge-transfer excitations and achieves near-second-order approximate coupled cluster (CC2) and second-order algebraic diagrammatic construction quality for the Q1 and Q2 subsets. Subsequently, we tested ωB88PTPSS on two sets of real-life examples from recent computational chemistry literature-the low energy bands of chlorophyll a (Chl a) and a set of thermally activated delayed fluorescence (TADF) systems. For Chl a, ωB88PTPSS qualitatively and quantitatively achieves DLPNO-STEOM-CCSD-level performance and provides excellent agreement with experiment. For TADF systems, ωB88PTPSS agrees quite well with spin-component-scaled CC2 (SCS-CC2) excitation energies, as well as experimental values, for the gaps between the S₁ and T₁ excited states.

DFT Analysis of Methane C-H Activation and Over-Oxidation by [Cu2 O]2+ and [Cu2 O2 ]2+ Sites in Zeolite Mordenite: Intra- versus Inter-site Over-Oxidation

Methane over-oxidation by copper-exchanged zeolites prevents realization of high-yield catalytic conversion. However, there has been little description of the mechanism for methane over-oxidation at the copper active sites of these zeolites. Using density functional theory (DFT) computations, we reported that tricopper [Cu₃ O₃ ]²⁺ active sites can over-oxidize methane. However, the role of [Cu₃ O₃ ]²⁺ sites in methane-to-methanol conversion remains under debate. Here, we examine methane over-oxidation by dicopper [Cu₂ O]²⁺ and [Cu₂ O₂ ]²⁺ sites using DFT in zeolite mordenite (MOR). For [Cu₂ O₂ ]²⁺ , we considered the μ-(η² :η² ) peroxo-, and bis(μ-oxo) motifs. These sites were considered in the eight-membered (8MR) ring of MOR. μ-(η² :η² ) peroxo sites are unstable relative to the bis(μ-oxo) motif with a small interconversion barrier. Unlike [Cu₂ O]²⁺ which is active for methane C-H activation, [Cu₂ O₂ ]²⁺ has a very large methane C-H activation barrier in the 8MR. Stabilization of methanol and methyl at unreacted dicopper sites however leads to over-oxidation via sequential hydrogen atom abstraction steps. For methanol, these are initiated by abstraction of the CH₃ group, followed by OH and can proceed near 200 °C. Thus, for [Cu₂ O]²⁺ and [Cu₂ O₂ ]²⁺ species, over-oxidation is an inter-site process. We discuss the implications of these findings for methanol selectivity, especially in comparison to the intra-site process for [Cu₃ O₃ ]²⁺ sites and the role of Brønsted acid sites.

Time-Dependent Long-Range-Corrected Double-Hybrid Density Functionals with Spin-Component and Spin-Opposite Scaling: A Comprehensive Analysis of Singlet-Singlet and Singlet-Triplet Excitation Energies

Following the work on spin-component and spin-opposite scaled (SCS/SOS) global double hybrids for singlet-singlet excitations by Schwabe and Goerigk [ J. Chem. Theory Comput. 2017, 13, 4307-4323] and our own works on new long-range corrected (LC) double hybrids for singlet-singlet and singlet-triplet excitations [ J. Chem. Theory Comput. 2019, 15, 4735-4744 and J. Chem. Phys. 2020, 153, 064106], we present new LC double hybrids with SCS/SOS that demonstrate further improvement over previously published results and methods. We introduce new unscaled and scaled versions of different global and LC double hybrids based on Becke88 or PBE exchange combined with LYP, PBE, or P86 correlation. For singlet-singlet excitations, we cross-validate them on six benchmark sets that cover small to medium-sized chromophores with different excitation types (local-valence, Rydberg, and charge transfer). For singlet-triplet excitations, we perform the cross-validation on three different benchmark sets following the same analysis as in our previous work in 2020. In total, 203 excitations are analyzed. Our results confirm and extend those of Schwabe and Goerigk regarding the superior performance of SCS and SOS variants compared to their unscaled parents by decreasing mean absolute deviations, root-mean-square deviations, or error spans by more than half and bringing absolute mean deviations closer to zero. Our SCS/SOS variants are shown to be highly efficient and robust for the computation of vertical excitation energies, which even outperform specialized double hybrids that also contain an LC in their perturbative part. In particular, our new SCS/SOS-ωPBEPP86 and SCS/SOS-ωB88PP86 functionals are four of the most accurate and robust methods tested in this work, and we fully recommend them for future applications. However, if the relevant SCS and SOS algorithms are not available to the user, we suggest ωPBEPP86 as the best unscaled method in this work.

Heterometallic [Cu–O–M]2+ active sites for methane C–H activation in zeolites: stability, reactivity, formation mechanism and relationship to other active sites

Formation energies and mechanisms, autoreduction and methane C–H reactivities were obtained for [Cu–O–M]²⁺ species (M = Ti–Cu, Zr–Mo and Ru–Ag) in mordenite with DFT. These reveal that [Cu₂O]²⁺ is best suited for MMC.