Systematic exploration of accessible topologies of cage molecules via minimalistic models

Abstract

Cages are macrocyclic structures with an intrinsic internal cavity that support applications in separations, sensing and catalysis. These materials can be synthesised via self-assembly of organic or metal-organic building blocks. Their bottom-up synthesis and the diversity in building block chemistry allows for fine-tuning of their shape and properties towards a target property. However, it is not straightforward to predict the outcome of self-assembly, and, thus, the structures that are practically accessible during synthesis. Indeed, such a prediction becomes more difficult as problems related to the flexibility of the building blocks or increased combinatorics lead to a higher level of complexity and increased computational costs. Molecular models, and their coarse-graining into simplified representations, may be very useful to this end. Here, we develop a minimalistic toy model of cage-like molecules to explore the stable space of different cage topologies based on a few fundamental geometric building block parameters. Our results capture, despite the simplifications of the model, known geometrical design rules in synthetic cage molecules and uncover the role of building block coordination number and flexibility on the stability of cage topologies. This leads to a large-scale and systematic exploration of design principles, generating data that we expect could be analysed through expandable approaches towards the rational design of self-assembled porous architectures.

Fig. 1. Outline of the minimalistic cage model. (a) Input to the model, including defining bond lengths and internal angles in ditopic, tritopic and tetratopic building blocks, and topology graphs. Bead types are provided in the figure and described in Table S2; semicircles represent connections between building blocks. The main parameters of interest are highlighted: the internal ditopic angle (bac) and the two angles defining the tritopic (bnb) and tetratopic (bmb) building blocks. (b) Model construction and optimisation workflow built on stk, OpenMM, resulting in (c) the lowest energy conformer for a given input with a structure and properties. The two structures highlight the visual difference between low and high-energy structures. (d) Schematic of different self-sorting outcomes (unstable, mixed and selective) approximated in this work, where small circles correspond to different topologies, and (e) the mapping of those outcomes to a discrete, accessible topology map based on two general model parameters, A and B. The topology map shows points in phase space as circles, which are coloured by the topologies that are stable in those regions.

Fig. 2. (a) Relationship between ditopic bite-angle and topology preference for square-planar tetratopic building blocks with torsion restrictions. The lowest energy structure for each selected topology is shown; horizontal bars are colour-coordinated to the points in the plot. Green are the a beads, cyan are the m beads, black are the b beads, and grey are the c beads. (b) Comparison of minimal model of Tet⁶Di¹² with target bite angle of 90° with a crystal structure (CCDC: SUPPID). (c) Comparison of minimal model of Tet¹²Di²⁴ with target bite angle of 120° with a crystal structure (CCDC: BIMXIF). The minimal models are minimum energy points in (a) with the same colour as the line at the bottom. In atomistic models, grey are carbon, blue are nitrogen, red are oxygen, cyan are palladium, hydrogens and solvent are not shown for clarity.

Fig. 3. (a) Relationship between target tritopic angle, target ditopic internal angle and energy for Tri⁴Di⁶ topology; the colour map is E_b. White squares show high-energy points. (b) Example low energy structures along the blue line in (b) with varying ditopic and tritopic angles. Green are the a beads, orange are the n beads, black are the b beads, and grey are the c beads. (c) Overlap of a porous organic cage (CCDC code: FOXLAG) and a metal–organic cage (CCDC code: TIXFIP) with two Tri⁴Di⁶ models from our phase space with tritopic angles of 120° and ditopic angles of 125° and 135°, respectively. In atomistic models, grey are carbon, blue are nitrogen, cyan are palladium, hydrogens and solvent are not shown for clarity.

Fig. 4. (a) Percentage of selected topologies (i.e., only one topology is stable for a given building block combination) as a function of the threshold E_b for accessibility for cages formed from ditopic and either tritopic (3C) or tetratopic (4C) building blocks, with and without restricted torsions, described further in Section S3.3. Accessible topology maps for cages formed with torsion restrictions, ditopic building blocks and (b) tritopic or (c) tetratopic building blocks. The colour map for each sub-figure is shown in the corresponding legend.

Fig. 5. (a) Schematic of the preorganisation modified in this work, where the baab torsion (φ; Newmann projection is shown) is either restricted (top; rigid) or not restricted (bottom; flexible). Representations of Tet²Di⁴ structures and the torsion force field term in both cases are shown. (b) The effect of this restriction on the proportion of accessible structures for each topology. The difference in the blue and white bins represents the effect of flexibility.

Fig. 6. Distribution of the deviation from the ideal shapes for (a) Tri⁶Di⁹ (shape measure: TPR-6), (b) Tet⁶Di¹² (shape measure: OC-6), (c) Tri⁸Di¹² (shape measure: CU-8) and (d) Tet⁸Di¹⁶ (shape measure: SAPR-8) with torsion-restrictions for tritopic or tetratopic building blocks. Blue distributions are all cages, and orange is for stable cages. This data is on a log scale due to the high proportion of cages near zero.

Fig. 7. Map of (a) OC-6 shape and (b) CU-8 shape for the tetratopic and tritopic building blocks in the Tet⁶Tri⁸ topology. The colour map shows the deviation from the ideal shapes. Black squares highlight stable cage structures. (c) Low energy structure examples. (d) Approximate pore radius of structures 1–5. Orange are the n beads, cyan are the m beads, and black are the b beads.