Molecular simulations studies of gas adsorption in metal–organic frameworks
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Using computational tools ranging from molecular simulations – including both Monte Carlo and molecular dynamics methods – to quantum mechanical (QM) calculations (primarily at density functional theory (DFT) level), this work focuses on addressing some of the challenges faced in molecular simulations of gas adsorption in metal–organic frameworks (MOFs). This work consists of two themes: one concerns gas adsorption in MOFs with coordinatively unsaturated metal sites (cus’s), and the other one deals with predicting and understanding the breathing behaviour of the flexible MOF MIL-53(Sc). It has been shown experimentally that incorporation of cus’s – also known as “open” metal sites or unsaturated metal centres – into MOFs significantly enhances the uptake of certain gases such as CO2 and CH4. As a result of the considerably enhanced, localized guest-molecule interactions with the cus’s, it, however, remains a challenge to predict correctly adsorption isotherms and/or mechanisms in MOFs with cus’s using grand-canonical Monte Carlo (GCMC) simulations based on generic classical force fields. To address this problem, two multi-scale modelling approaches – which combine GCMC simulations with QM calculations – have been proposed in this work. The first approach is based on the direct implementation of a fluid–framework potential energy surface, calculated by a hybrid DFT/ab initio method, in the GCMC simulations. The second approach involves parameterization of ab initio force fields for GCMC simulations of gas adsorption in MOFs with cus’s. This approach focuses on the generation of accurate ab initio reference data, selection of semiempirical model potentials, and force-field fitting through a multi-objective genetic algorithm approach. The multi-scale simulation strategy not only yields adsorption isotherms in very good agreement with experimental data but also correctly captures adsorption mechanisms, including the adsorption on the cus’s, observed experimentally but absent from GCMC simulations based on generic force fields. The second challenge that this work aims to address concerns the “breathing” phenomenon of MOFs, in which the framework structure adapts its pore opening to accommodate guest molecules, for example. The breathing effect gives rise to some exceptional properties of these MOFs and hence promising applications. However, framework flexibility often poses a challenge for computational studies of such MOFs, because suitable flexible force fields for frameworks are lacking and the effort involved in developing a new one is no less a challenge. Here, an alternative to the force-field-based approach is adopted. Ab initio molecular dynamics (AIMD) simulations – which combine classical molecular dynamics simulations with electronic-structure calculations “on the fly” – have been deployed to study structural changes of the breathing MOF MIL-53(Sc) in response to changes in temperature over the range 100–623 K and adsorption of CO2 at 0–0.9 bar at 196 K. AIMD simulations employing dispersion-corrected DFT accurately simulated the experimentally observed closure of MIL-53(Sc) upon solvent removal and the transition of the empty MOF from the closed-pore phase to the very-narrow-pore phase with increasing temperature. AIMD simulations were also used to mimic the CO2 adsorption of MIL-53(Sc) in silico by allowing the MIL-53(Sc) framework to evolve freely in response to CO2 loadings corresponding to the two steps in the experimental adsorption isotherm. The resulting structures enabled the structure determination of the two CO2-containing intermediate and large-pore phases observed by experimental synchrotron X-ray diffraction studies with increasing CO2 pressure; this would not have been possible for the intermediate structure via conventional methods because of diffraction peak broadening. Furthermore, the strong and anisotropic peak broadening observed for the intermediate structure could be explained in terms of fluctuations of the framework predicted by the AIMD simulations. Fundamental insights from the molecular-level interactions further revealed the origin of the breathing of MIL-53(Sc) upon temperature variation and CO2 adsorption. Both the multi-scale simulation strategy for gas adsorption in MOFs with cus’s and the AIMD study of the stimuli-responsive breathing behaviour of MIL-53(Sc) illustrate the power and promise of combining molecular simulations with quantum mechanical calculations for the prediction and understanding of MOFs.