🔬 materials science

Reticulating Local Dynamics in Three-Dimensional Covalent Organic Frameworks

By combining synchrotron X-ray pair distribution function analysis with machine learning-accelerated molecular dynamics simulations, this study reveals how varying the geometry and rigidity of building units in three-dimensional covalent organic frameworks tunes local linker dynamics and inter-linker coupling, establishing a design blueprint for controlling guest adsorption and mechanical response.

Original authors: Francesco Tavani, Saber Mirzaei, M. Saeed Mirzaei, Jian Yin, Yen-hsu Lin, Caden Myers, Cheng-Hung Lin, AM Milinda Abeykoon, Simon J. L. Billinge, Omar M. Yaghi

Published 2026-10-20

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CC BY 4.0

Original authors: Francesco Tavani, Saber Mirzaei, M. Saeed Mirzaei, Jian Yin, Yen-hsu Lin, Caden Myers, Cheng-Hung Lin, AM Milinda Abeykoon, Simon J. L. Billinge, Omar M. Yaghi

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine a world built not of bricks and mortar, but of tiny, rigid geometric shapes linked together to form vast, porous scaffolds. These structures, known as covalent organic frameworks, are made entirely of light elements like carbon, nitrogen, and oxygen, stitched together by strong chemical bonds. Scientists have long been able to design these materials to have specific shapes and sizes, making them excellent candidates for capturing gases, filtering water, or acting as catalysts. For years, the focus has been on the static architecture: the size of the holes, the shape of the tunnels, and the overall stability of the framework. However, a material in the real world is never truly still. Just as a building sways slightly in the wind or a bridge flexes under traffic, these molecular frameworks wiggle, tilt, and shift. Understanding how these tiny parts move is crucial because that motion dictates how easily guests, like gas molecules, can enter, travel through, or get trapped inside. Until now, figuring out exactly how these internal parts move has been like trying to see the vibration of a guitar string from a distance; the tools available could tell you the shape of the instrument, but not the subtle, rapid motions of its strings.

A team of researchers has now developed a way to see these hidden movements in three-dimensional covalent organic frameworks. They focused on two specific materials that are almost identical in their construction, sharing one common building block, but differing in the shape and rigidity of the second block used to hold them together. One material was built using a flat, sheet-like molecule that acts as a rigid, twelve-pointed hub. The other was built using a compact, three-dimensional molecule that acts as a six-pointed hub. By swapping just this one component, the researchers created two frameworks with different internal geometries. To observe what happened inside, they combined two powerful techniques. First, they used high-energy X-rays from a massive particle accelerator to measure the distances between every pair of atoms in the material, creating a detailed map of the local structure. Second, they used advanced computer simulations, guided by machine learning, to watch how these atoms moved over time. This combination allowed them to separate the motion of the rigid, fused cores of the molecules from the flapping motion of the dangling rings attached to them.

The researchers found that the rigid cores of the molecules barely moved at all, staying nearly fixed in place like the central pillars of a building. However, the rings hanging off the sides of these cores swung and tilted with significant freedom. In the material with the flat, sheet-like hub, the dangling rings on the two different types of building blocks moved very differently from one another. The rings on the flat hub were somewhat restricted, while the rings on the other block swung widely. This created a mismatch in how the parts moved. But when the researchers swapped the flat hub for the compact, three-dimensional one, the behavior changed in a surprising way. The rings on the new hub swung much more freely, and more importantly, the movement of the two different building blocks became synchronized. Instead of moving independently, the neighboring parts began to coordinate their shifts, moving together in a correlated fashion.

This coordination had a direct effect on the pores, the empty spaces within the framework where molecules would travel. In the first material, the pores were uniform, but the lack of coordination between the moving parts meant the walls of the pores shifted in a somewhat disjointed way. In the second material, the synchronized movement of the building blocks meant that the walls of the pores shifted in unison. Despite this increased motion, the size and shape of the pores remained remarkably stable, not deforming or collapsing under the movement. The study demonstrates that the way a material moves is not just a property of a single molecule, but a result of how that molecule interacts with its neighbors. By choosing a specific partner to link with, scientists can now tune how the entire framework flexes and shifts. This insight provides a new blueprint for designing materials that can be made locally rigid to hold their shape, or locally mobile to adapt to incoming molecules, all without losing the structural integrity needed for practical use.

Technical Summary: Reticulating Local Dynamics in Three-Dimensional Covalent Organic Frameworks

Problem Statement
Covalent organic frameworks (COFs) are crystalline porous materials where the geometry of building units predetermines the global framework topology. While design principles exist for controlling the static structure and functionality of COFs (e.g., for gas capture or catalysis), there is a lack of defined principles relating the choice of building units to the local dynamic properties of the framework. These local motions govern critical functional behaviors such as guest adsorption, diffusion, and mechanical response. Current characterization methods, primarily powder X-ray diffraction (PXRD), are insufficient for probing local structural disorder and dynamics in these light-element systems. Consequently, the ability to rationally design COFs with tunable local dynamics—ranging from local rigidity to modulated pore apertures—remains out of reach.

Methodology
To address this gap, the authors combined synchrotron X-ray pair distribution function (PDF) analysis with molecular dynamics (MD) simulations accelerated by machine learning interatomic potentials (MLIPs).

Experimental: Synchrotron X-ray total scattering data were collected at 290 K for two specific 3D imine-linked COFs. The resulting PDFs provided a real-space map of interatomic distances spanning local to long-range order.
Computational: MD simulations were performed using the Universal Model for Atoms (UMA), a transferable MLIP trained on diverse quantum-mechanical datasets. This approach allowed for simulations at length and time scales beyond ab initio methods while maintaining near-DFT accuracy for both covalent bonding and non-covalent contacts.
Validation: The MD trajectories were validated against the experimental PDFs. Ensemble-averaged theoretical PDFs were computed from 100 snapshots per trajectory to ensure agreement with experimental peak positions and intensities.
Analysis: Once validated, the MD trajectories were analyzed to resolve the amplitude, time scale, and spatial extent of linker motions. Key metrics included second-order orientational correlation functions ( $C_2(t)$ ) for reorientation, distributions of equilibrium tilt angles, and cross-correlation matrices of linker center-of-mass displacements to assess translational coupling.

System Design
The study focused on two 3D COFs constructed from a common 4-connected, square-planar linker, 4,4',4'',4'''-(pyrene-1,3,6,8-tetrayl)tetraaniline (PyTTA), which features a rigid, planar fused pyrene core. The variable component was the second building unit:

COF-412: PyTTA reticulated with a 12-connected nanographene linker, hexakis[3,5-bis(p-formylphenyl)-4,6-dimethoxyphenyl]hexabenzocoronene (HBC-LA12). This unit possesses a rigid, planar hexabenzocoronene core, resulting in a $(3,4,6)$ -connected cez topology.
COF-564: PyTTA reticulated with a 6-connected triptycene linker, 2,3,6,7,14,15-hexakis(4-formylphenyl)triptycene (Trip-CHO). This unit features a compact, 3D trigonal prismatic core, resulting in a $(4,6)$ -connected stp topology.

By holding PyTTA constant and varying the rigidity and geometry of its partner, the authors isolated the influence of the second building unit on framework dynamics.

Key Results

Local Structure Resolution: The combined PDF-MD approach successfully resolved the local structure, distinguishing between the fused aromatic cores and the pendant aryl rings. The MD simulations accurately reproduced experimental PDF features, including intramolecular bond distances and inter-linker correlations up to 12 Å.
Dynamics of COF-412:
- Reorientation: The fused aromatic cores (pyrene and hexabenzocoronene) exhibited minimal reorientation ( $C_2(t) \approx 1$ ), indicating they are rigid and undergo only limited libration (median tilt $\sim 6\text{--}9^\circ$ ). In contrast, the pendant aryl rings underwent large-amplitude reorientation (median tilt $\sim 18\text{--}38^\circ$ ).
- Translation: Linkers translated largely independently. The cross-correlation matrix showed weak coupling between linkers, with the exception of the two nanographene units facing a shared pore, which exhibited anticorrelated motion.
- Pore Metrics: Despite significant local mobility of the pendant rings, the pore volume distribution remained narrow, indicating that local motions did not significantly alter the pore metrics.
Dynamics of COF-564:
- Effect of Substitution: Replacing the nanographene with the triptycene unit altered the dynamics of both linkers. The PyTTA linker showed a slight increase in core libration and a decrease in pendant ring tilt.
- Enhanced Mobility: The pendant rings of the Trip-CHO linker exhibited significantly larger tilt amplitudes ( $30.1^\circ$ ) compared to the nanographene arms in COF-412 ( $18.0^\circ$ ), a difference of $12.1^\circ$ .
- Translational Coupling: Unlike COF-412, COF-564 displayed significant translational coupling between neighboring linkers. The cross-correlation matrix revealed that triptycene units bounding a common pore moved in opposition, while units on the same side moved in concert. This coupling was absent in the nanographene-based framework.
- Pore Diversity: The substitution introduced three distinct pore sizes (approx. 19, 9.7, and 4.8 $\times 10^3$ Å $^3$ ), all maintaining narrow volume distributions.

Significance and Claims
The paper claims to provide a blueprint for understanding and designing the local dynamical properties of COFs. The authors establish two primary design principles:

Separation of Stiffness and Mobility: Rigidity and mobility occupy distinct, predictable positions within the framework. The fused aromatic cores provide structural rigidity, while motion is localized to the pendant rings and the joints between building units. This allows for the selection of linkers to control dynamics without compromising pore metrics.
Context-Dependent Dynamics: The dynamic signature of a building unit is not intrinsic but is a property of the reticulated pair. A linker carries only part of its dynamic signature from one COF to another; its behavior is modulated by the geometry and rigidity of its partner (e.g., a broad aromatic sheet vs. a compact 3D node).

The authors conclude that this combined experimental-theoretical approach enables the screening of building unit combinations to tailor intra- and inter-linker dynamics for specific functions, such as modulating pore apertures or facilitating guest diffusion, before synthesis.

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