Protocol for Identifying Accurate Collective Variables in Enhanced Molecular Dynamics Simulations for the Description of Structural Transformations in Flexible Metal–Organic Frameworks

Abstract

Various kinds of flexibility have been observed in metal–organic frameworks, which may originate from the topology of the material or the presence of flexible ligands. The construction of free energy profiles describing the full dynamical behavior along the phase transition path is challenging since it is not trivial to identify collective variables able to identify all metastable states along the reaction path. In this work, a systematic three-step protocol to uniquely identify the dominant order parameters for structural transformations in flexible metal–organic frameworks and subsequently construct accurate free energy profiles is presented. Methodologically, this protocol is rooted in the time-structure based independent component analysis (tICA), a well-established statistical modeling technique embedded in the Markov state model methodology and often employed to study protein folding, that allows for the identification of the slowest order parameters characterizing the structural transformation. To ensure an unbiased and systematic identification of these order parameters, the tICA decomposition is performed based on information from a prior replica exchange (RE) simulation, as this technique enhances the sampling along all degrees of freedom of the system simultaneously. From this simulation, the tICA procedure extracts the order parameters—often structural parameters—that characterize the slowest transformations in the material. Subsequently, these order parameters are adopted in traditional enhanced sampling methods such as umbrella sampling, thermodynamic integration, and variationally enhanced sampling to construct accurate free energy profiles capturing the flexibility in these nanoporous materials. In this work, the applicability of this tICA-RE protocol is demonstrated by determining the slowest order parameters in both MIL-53(Al) and CAU-13, which exhibit a strongly different type of flexibility. The obtained free energy profiles as a function of this extracted order parameter are furthermore compared to the profiles obtained when adopting less-suited collective variables, indicating the importance of systematically selecting the relevant order parameters to construct accurate free energy profiles for flexible metal–organic frameworks, which is in correspondence with experimental findings. The method succeeds in mapping the full free energy surface in terms of appropriate collective variables for MOFs exhibiting linker flexibility. For CAU-13, we show the decreased stability of the closed pore phase by systematically adding adsorbed xylene molecules in the framework.

Towards modeling spatiotemporal processes in metal–organic frameworks

“…While successful, these simulations also showed how difficult the proper choice of CVs may be for MOFs having an inherent complex behavior with many degrees of freedom. Recently, Demuynck and colleagues used linear dimensionality reduction methods to investigate the phase transformations in zirconium-based MOFs with flexible linkers [97]. Although such methods are promising to unravel complex forms of flexibility, future investigations may have to go beyond linear CV definitions and resort to, for example, kernelized tICA or VAMPnets to systematically construct complex nonlinear CVs [98,99].…”

Large-Scale Molecular Dynamics Simulations Reveal New Insights Into the Phase Transition Mechanisms in MIL-53(Al)

“…Figure 1B shows a series of conceptual free energy curves in terms of a collective variable that is able to uniquely distinguish between all (meta)stable or activated states. For many frameworks the unit cell volume proved to be an appropriate collective variable (Demuynck et al, 2018), however, this may not always be the case. For flexible linkers, more advanced procedures were necessary to find collective variables that allowed to describe the phase transformation.…”

Comparative first principles‐based molecular dynamics study of catalytic mechanism and reaction energetics of water oxidation reaction on 2D‐surface

“…These degrees of freedom are known as CVs 106 . The CVs can be defined by taking into account various measurable such as distance, 107 angles, 108 dihedral angle, 109 and coordination number. For each step, we made an effort to find out two CVs that can define the particular step of the reaction mechanism: CV1 and CV2.…”