Decoding the self-assembly mechanism of metal-organic frameworks is a crucial step in reducing trial-and-error tests in their synthesis protocols. Atomistic simulations have proven essential in revealing molecular-level features of MOF nucleation, but they still exhibit limitations in the simulation setups due to size constraints (inability of reaching realistic concentrations or exploring non-stoichiometric metal:ligand ratios). In this contribution, we develop a methodology to derive reactive coarse grained force fields based on multiscale coarse graining methods. We apply our novel methodology to the case of the archetypal zeolitic-imidazolate framework ZIF-8. Our coarse grained force field, which we call nb-CG-ZIF-FF, does not contain any explicit connectivity information, but learns the tetrahedral Zn-connectivity from many body correlations within an atomistic benchmark. nb-CG-ZIF-FF quantitatively reproduces the features of bulk, crystalline ZIF-8 as well as the structural evolution of pre-nucleation species in terms of Zn n-fold coordination populations from the atomistic benchmark. While the range of rings that are formed along the synthesis process are well captured by nb-CG-ZIF-FF, the model cannot exactly reproduce ring populations. Our reactive CG force field fitting approach can be applied to any MOF, opening new research avenues in modeling MOF formation, decomposition, defect dynamics and phase transition processes.
even atomistic models fail to reproduce. [51] In this contribution, we employ the MS-CG method (also known as force matching) to develop the first reactive CG force field for a MOF: nb-CG-ZIF-FF (non-bonded coarse grained zeolitic-imidazolate framework force field). nb-CG-ZIF-FF is parametrized to reproduce the net forces experienced by the beads computed from atomistic simulations carried out with nb-ZIF-FF [26]. It is a fully reactive force field composed by three kinds of beads (Zn, ligand and solvent) that interact through pairwise non-bonded interactions. No point charge nor any kind of bonded contribution are explicitly included in the force field. The tetrahedral character of Zn beads is well reproduced without explicitly including any angle-dependent term in the force field to drive it, contrary to what was done in prior works for zeolites, [31,33] suggesting that topology can be learnt by the MS-CG algorithm. nb-CG-ZIF-FF successfully reproduces both crystalline ZIF-8 structure as well as Zn n-fold coordination profiles along the self-assembly process with remarkable accuracy. Furthermore, relevant structural features found in the atomistic model, [28] such as linear chains, rings and the formation of an intermediate amorphous aggregate are all captured by nb-CG-ZIF-FF. All rings that are found in atomistic simulations are also found in the CG case, despite that the relative proportion of ring populations is not reproduced. Our methodology to derive reactive CG force fields for MOFs can be applied to any MOF and even to other porous solids, with a broad impact on the modeling of self-assembly and decomposition processes at experimentally relevant conditions. This article is organized as follows. Section II summarizes the model, simulation conditions and methodological details. Validation of nb-CG-ZIF-FF with respect to crystalline and self-assembling systems is shown in section III, along with a detailed discussion of our findings. Section IV presents our main conclusions and perspectives.
We develop a reactive CG force field using the MS-CG algorithm [38] to study the nucleation part of the ZIF-8 self-assembly. To generate reference all-atom (AA) trajectories that serve as the benchmark for our model, we carry out AA simulations using the non-bonded ZIF force field (nb-ZIF-FF). This force field was developed in our group by Balestra and Semino, [26] employing cationic dummy atom models to capture the anisotropic electronic density surrounding the metal cation. [52] This technique ensures an accurate representation of ZIF-8 topology. nb-ZIF-FF has proven effective in capturing essential properties such as radial distribution function, cell parameters, elastic constant and phase stability in ZIF-8. [26] Additionally, it accurately represents the dynamic reactivity between metal ion centers and organic linkers, including bond formation and breaking. Previous studies have demonstrated the success of nb-ZIF-FF, [26,28,53,54] making it an ideal starting point for the development of a reactive CG force field. Here, we consider two distinct molecular systems to parametrize the CG force field:
(i) Solvated Zn 2+ cations and mIm -anions in dimethyl sulfoxide (DMSO) solvent, for which AA self-assembly trajectories of ZIF-8 formation during the nucleation stage are obtained from previous work in our group by Andarzi and Semino. [28] (ii) Solvent loaded crystalline ZIF-8 framework. To saturate ZIF-8 in DMSO, an empty 2×2×2 supercell of the MOF is constructed to serve as the porous host structure to be filled with DMSO molecules. We employ a hybrid Monte Carlo (MC)-molecular dynamics (MD) simulation approach in LAMMPS, [55] linked to a high-pressure DMSO reservoir (P=10 atm). At the pressure and temperature selected for the reservoir, DMSO is a stable liquid. The simulation protocol consists of AA MD carried out using Nosé-Hover barostat and thermostat [56] with target pressure and temperature of 1 atm and 298 K, respectively, and a 0.01 fs timestep. Grand Canonical Monte Carlo (GCMC) moves, featuring molecular insertion and deletion, are attempted every 500 timesteps. The GCMC moves promote reaching the equilibrium adsorption of DMSO molecules within the ZIF-8 pores while the equations of motion used allowed the framework and the adsorbed solvent molecules to structurally relax along the DMSO pore filling process. The simulation is performed until statistical convergence of the DMSO loading is achieved, ensuring that the solvent density inside the framework reflects realistic thermodynamic equilibrium with the external reservoir (see Fig. 8). The final system contains 115 DMSO molecules (i.e. 14.38 DMSO molecules per ZIF-8 unit cell). To verify that this loading represents true saturation, we perform additional GCMC simulations at reservoir pressures ranging from 10 to 80 atm (see Table II). DMSO loadings remain essentially constant across this pressure range, confirming that the ZIF-8 pores are fully satura
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