Modeling the structural and thermal properties of loaded metal-organic frameworks. An interplay of quantum and anharmonic fluctuations

TL;DR

This work addresses how quantum nuclear effects and anharmonic fluctuations influence the structural and thermal properties of MOFs under gas loading. It develops an accelerated Suzuki-Chin high-order path integral MD framework with a first-principles force field to sample the quantum isothermal-isobaric ensemble efficiently, enabling accurate characterization of MOF-5 with methane across loadings. Key findings show that the MOF framework behaves largely harmonically, while adsorbed methane exhibits strong anharmonicity, with the total heat capacity displaying a non-monotonic temperature dependence driven mainly by host–guest interactions; an empirical scheme is proposed to reproduce these effects at reduced cost. The approach provides a practical path toward high-throughput screening and design of thermally robust MOFs for adsorption-based technologies.

Abstract

Metal-organic frameworks show both fundamental interest and great promise for applications in adsorption-based technologies, such as the separation and storage of gases. The flexibility and complexity of the molecular scaffold poses a considerable challenge to atomistic modeling, especially when also considering the presence of guest molecules. We investigate the role played by quantum and anharmonic fluctuations in the archetypical case of MOF-5, comparing the material at various levels of methane loading. Accurate path integral simulations of such effects are made affordable by the introduction of an accelerated simulation scheme and the use of an optimized force field based on first-principles reference calculations. We find that the level of statistical treatment that is required for predictive modeling depends significantly on the property of interest. The thermal properties of the lattice are generally well described by a quantum harmonic treatment, with the adsorbate behaving in a classical but strongly anharmonic manner. The heat capacity of the loaded framework - which plays an important role in the characterization of the framework and in determining its stability to thermal fluctuations during adsorption/desorption cycles - requires, however, a full quantum and anharmonic treatment, either by path integral methods or by a simple but approximate scheme. We also present molecular-level insight into the nanoscopic interactions contributing to the material's properties and suggest design principles to optimize them

Figures (10)

• Figure 1: The structure of the MOF-5 with a gas loading $x$ of 0, 50, 100, and 150 molecules of methane (left to right) in the conventional unit cell. (8(Zn$_4$O(CO$_2$)$_6$) $\cdot$$x$ CH$_4$) The oxygen, carbon, and zinc atoms are shown in red, silver, and blue respectively. For the sake of aesthetics the hydrogen atoms are not included. The methane molecules are represented by silver tetrahedra.
• Figure 2: Fractional error in the standard (red) and Suzuki-Chin (blue) path integral estimators of the energy (circles) and the heat capacity (triangles) of empty MOF-5 modeled by the corresponding Debye crystal potential, as a function of the number of beads $P$ at 100 K (bottom) and 300 K (top). The values of the energy and the heat capacity were obtained analytically brainthesis.
• Figure 3: Panels (a) and (b) show the lattice parameter $a$ of MOF-5 with $x=0, 50,100,150$ molecules of methane as a function of temperature ($T$), obtained from classical MD and PIMD respectively. Panel (c) shows the linear thermal expansion coefficient ($\alpha$) as a function of $x$. The classical and quantum estimates are respectively shown with dashed and solid lines. Error bars indicate statistical uncertainity.
• Figure 4: The methane distribution in the pores of MOF-5 at different temperatures as obtained from PIMD simulations. Orange spots indicate high probability adsorption sites. Other colors show the distribution of the low probability methane positions in the conventional unit cell and represent the probability representation (from very high (orange), to high (dark blue), to low (white) probability).
• Figure 5: Heat capacity $C_P$ of the empty MOF-5 as a function of temperature $(T)$ computed using classical MD (dashed), PIMD (solid) and the harmonic approximation (dotted). The right pointing arrow shows the Dulong-Petit limit. Different experimental results are shown in black using triangular kloutse2015, square ming2014 and diamond mu2011 markers. Error bars indicate statistical uncertainity.