The accuracy of Kohn-Sham density functional theory depends strongly on the approximation to the exchange-correlation functional. In this work, we present a new exchange-correlation functional called M11pz (M11 plus rung-3.5 terms with zero Hartree-Fock exchange) that is built on the M11plus functional with the goal of using its rung-3.5 terms without a Hartree-Fock exchange term, especially to improve the accuracy for strongly correlated systems. The M11pz functional is optimized with the same local and rung-3.5 ingredients that are used in M11plus but without any percentage of Hartree-Fock exchange. The performance of M11pz is compared with eight local functionals, and M11pz is found to be in top three when the errors or ranks are averaged over eight grouped and partially overlapping databases: AME418/22, atomic and molecular energies; MGBE172, main-group bond energies; TMBE40, transition-metal bond energies; SR309, single-reference systems; MR54, multireference systems; BH192, barrier heights; NC579, noncovalent interaction energies; and MS20, molecular structures. For calculations of band gaps of solids, M11pz is the second best of the nine tested functionals that have zero Hartree-Fock exchange.
Activating the C-H bonds of alkanes without further oxidation to more thermodynamically stable products, CO and CO2, is a long-sought goal of catalytic chemistry. Inspired by the monocopper active site of methane monooxygenase, we synthesized a Cu-doped ZIF-8 metal-organic framework with 25% Cu and 75% Zn in the nodes and activated it by heating to 200 °C and dosing in a stepwise fashion with O2, methane, and steam. We found that it does oxidize methane to methanol and formaldehyde. The catalysis persists through at least five cycles, and beyond the third cycle, the selectivity improves to the extent that no CO2 can be detected. Experimental characterization and analysis were carried out by PXRD, DRUV-vis, SEM, and XAS (XANES and EXAFS). The reaction is postulated to proceed at open-coordination copper sites generated by defects, and the mechanism of methanol production was explicated by density functional calculations with the revMO6-L exchange-correlation functional. The calculations reveal a catalytic cycle of oxygen-activated CuI involving the conversion of two molecules of CH4 to two molecules of CH3OH by a sequence of hydrogen atom transfer reactions and rebound steps. For most steps in the cycle, the reaction is more favored by singlet species than by triplets.
Quantitative simulations of electronically nonadiabatic molecular processes require both accurate dynamics algorithms and accurate electronic structure information. Direct semiclassical nonadiabatic dynamics is expensive due to the high cost of electronic structure calculations, and hence it is limited to small systems, limited ensemble averaging, ultrafast processes, and/or electronic structure methods that are only semiquantitatively accurate. The cost of dynamics calculations can be made manageable if analytic fits are made to the electronic structure data, and such fits are most conveniently carried out in a diabatic representation because the surfaces are smooth and the couplings between states are smooth scalar functions. Diabatic representations, unlike the adiabatic ones produced by most electronic structure methods, are not unique, and finding suitable diabatic representations often involves time-consuming nonsystematic diabatization steps. The biggest drawback of using diabatic bases is that it can require large amounts of effort to perform a globally consistent diabatization, and one of our goals has been to develop methods to do this efficiently and automatically. In this Feature Article, we introduce the mathematical framework of diabatic representations, and we discuss diabatization methods, including adiabatic-to-diabatic transformations and recent progress toward the goal of automatization.
We calculated the vertical ionization energies (VIE) of 99 species in two ways to examine the accuracy of several long-range-corrected (LC) hybrid meta functionals in comparison with a gradient approximation (GA), global hybrids, and doubly hybrids. In the category of LC functionals, we examined both those with meta ingredients (i.e., that depend on the kinetic energy density) and those without them. The LC-hybrid meta functionals examined are M11, revM11, M11plus, and ωB97M-V. The reference data used to assess accuracy consist of 95 molecules and 4 atoms in the GW100 set. The two methods studied are the ΔSCF method (involving the difference of neutral and cation self-consistent field (SCF) energies) and the ionization energy theorem (involving the orbital energy of the highest occupied molecular orbital, HOMO). We calculated linear correlation coefficients (r2) and mean absolute deviations (MADs) between each approach and the reference VIE value from the CCSD(T)/def2-TZVPP level of theory. We compared the new LC-hybrid meta calculations to calculations with the 10 functionals in a previous VIE study by Brémond et al. and to the calculations with LC-BLYP (LC-Becke, Lee-Yang-Parr), CAM-B3LYP (Coulomb-attenuating-method Becke-3-parameter Lee-Yang-Parr), LC-ωHPBE, and ωB97X-D. The results show that Minnesota LC-hybrid meta functionals have the smallest mean absolute deviation of ionization energy theorem VIEs with the reference data; the LC-ωHPBE functional also does quite well in this test. This is very encouraging and indicates that LC-hybrid meta functionals would be the best starting points for the tuning strategy that has been shown to be a very good procedure for improving time-dependent density functional calculations, and it also helps explain the good success of LC-hybrid meta functionals for molecular excitation energies.
The development of highly selective and active catalysts to catalyze an industrially important semihydrogenation reaction remains an open challenge. Here, we report the design of a bimetallic Pd/Cu(111) catalyst with Pd rafts confined in a Cu nanosheet, which exhibits desirable catalytic performance for acetylene semihydrogenation to ethylene with the selectivity of >90%. Theory calculations show that Pd atoms replacing neighboring Cu atoms in Cu(111) can improve the catalytic activity by reducing the energy barrier of the semihydrogenation reaction, as compared to unsubstituted Cu(111), and can improve the selectivity by weakening the adsorption of C2H4, as compared to a Pd(111) surface. The presence of Pd rafts confined in Cu nanosheets effectively turns on Cu nanosheets for semihydrogenation of acetylene with high activity and selectivity under mild reaction conditions. This work offers a well-defined nanostructured Pd/Cu(111) model catalyst that bridges the pressure and materials' gap between surface-science catalysis and practical catalysis.
Acetylene , Copper , Catalysis , Membrane Microdomains , Palladium
A desirable feature of metal-organic frameworks (MOFs) is their well-defined structural periodicity and the presence of well-defined catalyst grafting sites (e.g., reactive -OH and -OH2 groups) that can support single-site heterogeneous catalysts. However, one should not overlook the potential role of residual organic moieties, specifically formate ions that can occupy the catalyst anchoring sites during MOF synthesis. Here we show how these residual formate species in a Zr-based MOF, NU-1000, critically alter the structure, redox capability, and catalytic activity of postsynthetically incorporated Cu(II) ions. Single-crystal X-ray diffraction measurements established that there are two structurally distinct types of Cu(II) ions in NU-1000: one type with residual formate and one without. In NU-1000 with formate, Cu(II) solely binds to the node via the formate-unoccupied, bridging µ3-OH, whereas in the formate-free case, it displaces protons from two node hydroxo ligands and resides close to the terminal -OH2. Under an inert atmosphere, node-bound formate facilitates the unanticipated reduction of isolated Cu(II) to nanoparticulate Cu(0)-a behavior which is essentially absent in the formate-free analogue because no other sacrificial reductant is present. When the two MOFs were tested as benzyl alcohol oxidation catalysts, we observed that residual formate boosts the catalytic turnover frequency. Density functional calculations showed that node-bound formate acts as a sacrificial two-electron donor and assists in reducing Cu(II) to Cu(0) by a nonradical pathway. The negative Gibbs free energy of reaction (ΔG) and enthalpy of reaction (ΔH) indicate that the reduction is thermodynamically favorable. The work presented here highlights how the often-neglected residual formate prevalent in nearly all zirconium-based MOFs can significantly modulate the properties of supported catalysts.
Multi-configuration pair-density functional theory (MC-PDFT) has previously been applied successfully to carry out ground-state and excited-state calculations. However, because they include no interaction between electronic states, MC-PDFT calculations in which each state's PDFT energy is calculated separately can give an unphysical double crossing of potential energy surfaces (PESs) in a region near a conical intersection. We have recently proposed state-interaction pair-density functional theory (SI-PDFT) to treat nearly degenerate states by creating a set of intermediate states with state interaction; although this method is successful, it is inconvenient because two SCF calculations and two sets of orbitals are required and because it puts the ground state on an unequal footing with the excited states. Here we propose two new methods, called extended-multi-state-PDFT (XMS-PDFT) and variational-multi-state-PDFT (VMS-PDFT), that generate the intermediate states in a balanced way with a single set of orbitals. The former uses the intermediate states proposed by Granovsky for extended multi-configuration quasi-degenerate perturbation theory (XMC-QDPT); the latter obtains the intermediate states by maximizing the sum of the MC-PDFT energies for the intermediate states. We also propose a Fourier series expansion to make the variational optimizations of the VMS-PDFT method convenient, and we implement this method (FMS-PDFT) both for conventional configuration-interaction solvers and for density-matrix-renormalization-group solvers. The new methods are tested for eight systems, exhibiting avoided crossings among two to six states. The FMS-PDFT method is successful for all cases for which it has been tested (all cases in this paper except O3 for which it was not tested), and XMS-PDFT is successful for all eight cases except the mixed-valence case. Since both XMS-PDFT and VMS-PDFT are less expensive than XMS-CASPT2, they will allow well-correlated calculations on much larger systems for which perturbation theory is unaffordable.
Direct nonadiabatic dynamics is used to study processes involving multiple electronic states from small molecules to materials. Compared with dynamics with fitted analytical potential energy surfaces, direct dynamics is more user-friendly in that it obtains all needed energies, gradients, and nonadiabatic couplings (NACs) by electronic structure calculations. However, the NAC that is usually used does not conserve angular momentum or the center of mass in widely used mixed quantum-classical nonadiabatic dynamics algorithms, in particular, trajectory surface hopping, semiclassical Ehrenfest, and coherent switching with decay of mixing. We show that by using a projection operator to remove the translational and rotational components of the originally computed NAC, one can restore the conservation.
