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We present a three-dimensional Ising model where lines of equal spins are frozen in such that they form an ordered framework structure. The frame spins impose an external field on the rest of the spins (active spins). We demonstrate that this porous Ising model can be seen as a minimal model for condensation transitions of gas molecules in metal-organic frameworks. Using Monte Carlo simulation techniques, we compare the phase behavior of a porous Ising model with that of a particle-based model for the condensation of methane (CH$_4$) in the isoreticular metal-organic framework IRMOF-16. For both models, we find a line of first-order phase transitions that end in a critical point. We show that the critical behavior in both cases belongs to the 3D Ising universality class, in contrast to other phase transitions in confinement such as capillary condensation.
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Metal-Organic Frameworks (MOFs) have gained much interest due to their intrinsic tunable nature. In this work, we study how linker functionalization modifies the electronic structure of the host MOF, more specifically the MIL-47(V)-R (R=-F, -Cl, -Br, -OH, -CH$_3$, -CF$_3$, and -OCH$_3$). It is shown that the presence of a functional group leads to a splitting of the $pi$-orbital on the linker. Moreover, the upward shift of the split-off $pi$-band correlates well with the electron withdrawing/donating nature of the functional groups. For halide functional groups the presence of lone-pair back donation is corroborated by calculated Hirshfeld-I charges. In case of the ferromagnetic configuration of the host MIL-47(V$^{mathrm{+IV}}$) material a half-metal to insulator transition is noted for the -Br, -OCH$_3$, and -OH functional groups, while for the anti-ferromagnetic configuration only the hydroxy-group results in an effective reduction of the band gap.
We develop a proper nonempirical spin-density formalism for the van der Waals density functional (vdW-DF) method. We show that this generalization, termed svdW-DF, is firmly rooted in the single-particle nature of exchange and we test it on a range of spin systems. We investigate in detail the role of spin in the nonlocal-correlation driven adsorption of H$_2$ and CO$_2$ in the linear magnets Mn-MOF74, Fe-MOF74, Co-MOF74, and Ni-MOF74. In all cases, we find that spin plays a significant role during the adsorption process despite the general weakness of the molecular-magnetic responses. The case of CO$_2$ adsorption in Ni-MOF74 is particularly interesting, as the inclusion of spin effects results in an increased attraction, opposite to what the diamagnetic nature of CO$_2$ would suggest. We explain this counter-intuitive result, tracking the behavior to a coincidental hybridization of the O $p$ states with the Ni $d$ states in the down-spin channel. More generally, by providing insight on nonlocal correlation in concert with spin effects, our nonempirical svdW-DF method opens the door for a deeper understanding of weak nonlocal magnetic interactions.
The metal-organic framework (MOF) MFU-4l containing Co(II) centers and Cl- ligands has recently shown promising redox activity. Aiming for further improved MOF catalysts for oxidation processes employing molecular oxygen we present a density-functional theory (DFT) based computational screening approach to identify promising metal center and ligand combinations within the MFU-4l structural family. Using the O2 binding energy as a descriptor for the redox property, we show that relative energetic trends in this descriptor can reliably be obtained at the hybrid functional DFT level and using small cluster (scorpionate-type complex) models. Within this efficient computational protocol we screen a range of metal center / ligand combinations and identify several candidate systems that offer more exothermic O2 binding than the original Co/Cl-based MFU-4l framework.
The ability of metal-organic frameworks (MOFs) to gelate under specific synthetic conditions opens up new opportunities in the preparation and shaping of hierarchically porous MOF monoliths, which could be directly implemented for catalytic and adsorptive applications. In this work, we present the first examples of xero- or aerogel monoliths consisting solely of nanoparticles of several prototypical Zr4+-based MOFs: UiO-66-X (X = H, NH2, NO2, (OH)2), UiO-67, MOF-801, MOF-808 and NU-1000. High reactant and water concentrations during synthesis were observed to induce the formation of gels, which were converted to monolithic materials by drying in air or supercritical CO2. Electron microscopy, combined with N2 physisorption experiments, was used to show that an irregular nanoparticle packing leads to pure MOF monoliths with hierarchical pore systems, featuring both intraparticle micropores and interparticle mesopores. Finally, UiO-66 gels were shaped into monolithic spheres of 600 micrometer diameter using an oil-drop method, creating promising candidates for packed-bed catalytic or adsorptive applications, where hierarchical pore systems can greatly mitigate mass transfer limitations.
Cooperative adsorption of gases by porous frameworks permits more efficient uptake and removal than does the more usual non-cooperative (Langmuir-type) adsorption. Cooperativity, signaled by a step-like isotherm, is usually attributed to a phase transition of the framework. However, the class of metal-organic frameworks mmen-M$_2$(dobpdc) exhibit cooperative adsorption of CO2 but show no evidence of a phase transition. Here we show how cooperativity emerges in these frameworks in the absence of a phase transition. We use a combination of quantum and statistical mechanics to show that cooperativity results from a sharp but finite increase, with pressure, of the mean length of chains of CO2 molecules that polymerize within the framework. Our study provides microscopic understanding of the emergent features of cooperative binding, including the position, slope and height of the isotherm step, and indicates how to optimize gas storage and separation in these materials.
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