M. Waroquier

In this paper, three barostat coupling schemes for pressure control, which are commonly used in molecular dynamics simulations, are critically compared to characterise the rigid MOF-5 and the flexible MIL-53(Al) metal-organic frameworks. We investigate the performance of the three barostats, the Berendsen, the Martyna-Tuckerman-Tobias-Klein (MTTK) and the Langevin coupling methods, in reproducing the cell parameters and the pressure versus volume behaviour in isothermal-isobaric simulations. A thermodynamic integration method is used to construct the free energy profiles as a function of volume at finite temperature. It is observed that the aforementioned static properties are well reproduced with the three barostats. However, for static properties depending nonlinearly on the pressure, the Berendsen barostat might give deviating results as it suppresses pressure fluctuations more drastically. Finally, dynamic properties, which are directly related to the fluctuations of the cell, such as the time to transition from the large-pore to the closed-pore phase, cannot be well reproduced by any of the coupling schemes.

Modeling the flexibility of metal–organic frameworks (MOFs) requires the computation of mechanical properties from first principles, e.g., for screening of materials in a database, for gaining insight into structural transformations, and for force field development. However, this paper shows that computations with periodic density functional theory are challenged by the flexibility of these materials: guidelines from experience with standard solid-state calculations cannot be simply transferred to flexible porous frameworks. Our test case, the MIL-47(V) material, has a large-pore and a narrow-pore shape. The effect of Pulay stress (cf. Pulay forces) leads to drastic errors for a simple structure optimization of the flexible MIL-47(V) material. Pulay stress is an artificial stress that tends to lower the volume and is caused by the finite size of the plane wave basis set. We have investigated the importance of this Pulay stress, of symmetry breaking, and of k-point sampling on (a) the structure optimization and (b) mechanical properties such as elastic constants and bulk modulus, of both the large-pore and narrow-pore structure of MIL-47(V). We found that, in the structure optimization, Pulay effects should be avoided by using a fitting procedure, in which an equation of state E(V) (EOS) is fit to a series of energy versus volume points. Manual symmetry breaking could successfully lower the energy of MIL-47(V) by distorting the vanadium–oxide distances in the vanadyl chains and by rotating the benzene linkers. For the mechanical properties, the curvature of the EOS curve was compared with the Reuss bulk modulus, derived from the elastic tensor in the harmonic approximation. Errors induced by anharmonicity, the eggbox effect, and Pulay effects propagate into the Reuss modulus. The strong coupling of the unit cell axes when the unit cell deforms expresses itself in numerical instability of the Reuss modulus. For a flexible material, it is therefore advisible to resort to the EOS fit procedure.

A full mechanistic investigation is proposed for the industrially important cross-aldol condensation reaction of heptanal with benzaldehyde on the UiO-66 and the amino-functionalized UiO-66-NH2 metal–organic frameworks to form jasminaldehyde. Several experimental studies indicate that the activity for the aldol condensation reaction can be increased by proper functionalization of the material, e.g. by introducing an additional basic amino site and thus creating a bifunctional acid–base catalyst for the aldol condensation. The precise molecular level origin for this behavior is to date unclear. Herein state-of-the-art Density-Functional Theory (DFT) calculations have been performed to unravel the mechanism of the cross- and self-aldol condensations of benzaldehyde and propanal. To this end free energy calculations have been performed on both extended cluster and periodic models. It is found that the mechanism on both catalysts is essentially the same, although a slightly stronger adsorption of the reactants and slightly lower barriers were found on the amino functionalized material, pointing toward higher initial activities. New experiments were performed to confirm these observations. It is indeed found that the initial activity toward cross-aldol condensation on the amino functionalized material is higher, although after about 40 min of reaction both materials become equally active. Our results furthermore point out that the basic amino groups may promote side reactions such as imine formation, which is induced by water. The study as presented can assist to engineer materials at the molecular level toward the desired products.