No 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.

Cation−dipole interactions were previously shown to have a rate-enhancing effect on the cationic ring-opening polymerization (CROP) of 2-oxazolines bearing a side-chain ester functionality. In line with this, a similar rate enhancementvia intermolecular cation−π interactionswas anticipated to occur when π-bonds are introduced into the 2-oxazoline side-chains. Moreover, the incorporation of π-bonds allows for facile postfunctionalization of the resulting poly(2-oxazoline)s with double and triple bonds in the side-chains via various click reactions. Herein, a combined molecular modeling and experimental approach was used to study the CROP reaction rates of 2oxazolines with side-chains having varying degrees of unsaturation and side-chain length. The presence of cation−π interactions and the influence of the degree of unsaturation were initially confirmed by means of regular molecular dynamics simulations on pentameric systems. Furthermore, a combination of enhanced molecular dynamics simulations, static calculations, and a thorough analysis of the noncovalent interactions was performed to unravel to what extent cation−π interactions alter the reaction kinetics. Additionally, the observed trends were confirmed also in the presence of acetonitrile as solvent, in which experimentally the polymerization is performed. Most intriguingly, we found only a limited effect on the intrinsic reaction kinetics of the CROP and a preorganization effect in the reactive complex region. The latter effect was established by the unsaturated side-chains and the cationic center through a complex interplay between cation−π, π−π, π−induced dipole, and cation−dipole interactions. These findings led us to propose a two-step mechanism comprised of an equilibration step and a CROP reaction step. The influence of the degree of unsaturation, through a preorganization effect, on the equilibration step was determined with the following trend for the polymerization rates: n-ButylOx < ButenOx < ButynOx ≥ PentynOx. The trend was experimentally confirmed by determining the polymerization rate constants.