On the Role of Enthalpic and Entropic Contributions to the Conformational Free Energy Landscape of MIL‐101(Cr) Secondary Building Units

Abstract

The thermo-structural behavior of metal-organic framework (MOF) precursors is responsible for regulating the introduction of defects in MOF structures during synthesis. In this paper, factors affecting the flexibility of MIL-101(Cr) half-secondary building units (half-SBUs) are evaluated in solution using enhanced sampling methods. In particular, entropic and enthalpic contributions to the conformational free energy landscape of isolated MIL-101(Cr) half-SBUs are calculated in water, in the presence and absence of ionic species (Na + and F −), and in N, N-dimethylformamide (DMF). This analysis leads to the observation that the interplay between enthalpy and entropy determines the most probable conformational state for half-SBUs. This observation extends to the most relevant SBU intermediate, in which conformational entropy plays a key role in stabilizing configurations that differ from those found in the MIL-101(Cr) crystal structure. The findings highlight the importance of explicitly considering entropic effects, associated with finite-temperature sampling when estimating the relative stability of different conformers of SBUs.

Identifying Conformational Isomers of Organic Molecules in Solution via Unsupervised Clustering

“…Free energy differences between conformational macrostates i and j of sildenafil in solution were computed from their equilibrium probability Pi and P j as and decomposed into their enthalpic and entropic contributions following the procedure outlined by Gimondi et al 43 , 44 For instance, the difference in free energy between clusters i and j , Δ G i , j , can be expressed as Δ H i , j – T Δ S i , j , where Δ H i , j and Δ S i , j are the enthalpy and entropy differences between states i and j . Hence, the entropic contribution can be obtained by difference as T Δ S i , j = Δ G i , j – Δ H i , j , once the term Δ H i , j is known.…”

“…In models in which explicit solvents are employed, ⟨ E P ⟩ i is typically dominated by the contribution of the solvent molecules, and it is associated with large fluctuations that affect the convergence and accuracy of the Δ U i , j estimate. To improve the statistical accuracy in Δ U i , j , we follow the procedure outlined by Kollias et al 44 and decompose the ensemble average of the potential energy in three components, namely ⟨ E P ⟩ i solute , ⟨ E P ⟩ i solvent , and ⟨ E P ⟩ i solute–solvent . The ⟨ E P ⟩ i solute and ⟨ E P ⟩ i solvent contributions account, respectively, for potential energy terms associated with interactions between atoms that belong exclusively to the solute and to the solvent species.…”

Identifying conformational isomers of organic molecules in solution via unsupervised clustering

“…In models in which explicit solvents are employed, the E P i is typically dominated by the contribution of the solvent molecules, and it is associated with large fluctuations that affect the convergence and accuracy of the ∆U i,j estimate. In order to improve the statistical accuracy in the ∆U i,j , we follow the procedure outlined by Kollias et al 44 and decompose the ensemble average of the potential energy in three components, namely E P that would mask the contribution of conformational transitions to ∆U i,j , and hamper the convergence of the enthalpy and entropy contribution to free energy differences. Despite implementing this strategy the convergence of the enthalpic and entropic contributions require a substantial sampling of the configuration space of the explicitly solvated system.…”

Identifying conformational isomers of organic molecules in solution via unsupervised clustering

“…In order to improve the statistical accuracy in the ∆U i,j , we follow the procedure outlined by Kollias et al 44 and decompose the ensemble average of the potential energy in three components, namely E P solute i , E P solvent i and E P solute−solvent i…”

“…al. 43,44 For instance, the difference in free energy between clusters i and j, ∆G i,j can be expressed as ∆H i,j −T ∆S i,j , where ∆H i,j and ∆S i,j are the enthalpy and entropy differences between states i and j. Hence the entropic contribution can obtained by difference as T ∆S i,j = ∆G i,j − ∆H i,j , once the term ∆H i,j is known.…”