Valentina
Santolini
,
Marcin
Miklitz
,
Enrico
Berardo
and
Kim E.
Jelfs
*
Department of Chemistry, Imperial College London, South Kensington, London, SW7 2AZ, UK. E-mail: k.jelfs@imperial.ac.uk; www.twitter.com/JelfsChem; Tel: +44 (0)20759 43438
First published on 16th March 2017
We define a nomenclature for the classification of porous organic cage molecules, enumerating the 20 most probable topologies, 12 of which have been synthetically realised to date. We then discuss the computational challenges encountered when trying to predict the most likely topological outcomes from dynamic covalent chemistry (DCC) reactions of organic building blocks. This allows us to explore the extent to which comparing the internal energies of possible reaction outcomes is successful in predicting the topology for a series of 10 different building block combinations.
For finite molecular hosts, a wide range of different motifs have been realised, including rings, cycles, knots, polyhedra and catenanes.7–9 Here we focus upon molecular cage compounds, defined by IUPAC as polycyclic compounds with the shape of a cage. These have the potential to host other molecules inside their internal cavity, but, unlike macrocycles, also have three dimensional structures with multiple possible entry and exit routes through molecular windows. Organic molecular cages have been of increasing research interest in recent years,9–13 although they have a longer history, including a range of cryptands,14 carcerands,15,16 and capsule-like molecules. Potential applications for these molecular hosts include encapsulation,17 catalysis,18 molecular separations of organic molecules19,20 or gases,21,22 molecular sensing,23,24 molecular reaction vessels, or as porous liquids.25
Whilst framework materials can be related to underlying extended network topologies, the equivalent topologies for molecular materials include, but are not limited to, polyhedra such as Platonic and Archimedean solids, see Fig. 1. Throughout this work, we use the term topology to refer to the underlying connectivity of molecular building blocks (BBs) in the molecular cage, which is unchanged upon any physical deformation. Whilst initially capsule-like topologies (with two end groups such as cavitands connected by multiple ditopic ligands to form a cavity) dominated, in the last decade a broader range of topologies have been synthetically realised. These polyhedra include tetrahedra, cubes, octahedra, square antiprisms and cuboctahedra, although capsules, tetrahedra and cubes are most commonly observed. A molecule with a single topology could adopt multiple different geometrical shapes, dependent upon factors such as the geometry of the component BBs and their conformational flexibility. For example, as shown in Fig. 2, a molecule with an underlying tetrahedral topology could have the approximate geometrical shape of a tetrahedron or an octahedron, or related intermediate shapes, dependent upon the component BBs.
Fig. 2 An example of how two porous organic cages that both have an underlying topology of a tetrahedron adopt different geometric shapes, in one case maintaining a tetrahedron shape26 (right hand side), and in the other adopting an octahedral shape (left hand side).27 The underlying topologies are shown in purple and the geometric shapes in orange. Hydrogen atoms and multiple bonds are omitted for clarity throughout the text. |
The growing interest in the field of organic cage molecules makes it timely to identify the potential topological possibilities for these materials and to establish a uniform classification system for them. As stated by Brunner in 1981, the “synthesis of new structures requires not only chemical skill but also some knowledge of the principal topological possibilities”.28 Hay has recently discussed design principles for metal–organic polygons and polyhedra (MOPs), emphasising that referring to these molecules by their shape can lead to multiple classifications for the same underlying topology, particularly for polyhedra that are face-directed, dependent on how you relate the metals and ligands to the vertices, edges or faces.29 Instead, Hay proposes a nomenclature based upon the number of vertices, edges or faces involved in the MOP and its point group. We agree with this approach, and here lay out an extension of this nomenclature for wholly organic molecules.
We then examine which topologies have been synthetically reported and choose a set of molecules from each topological family described to computationally investigate the underlying factors that influence the observed topological forms. Firstly however, in the following section we discuss the factors that can influence the topology formed for a porous organic cage.
As the majority of organic cages are formed by reversible dynamic covalent chemistry (DCC), the product distribution should be thermodynamically controlled, with those molecules with the lowest free energy being the dominant reaction product. Of course, this depends upon the reaction mixture being able to afford this product, rather than being kinetically trapped into alternative products, which is known to have happened with alkyne metathesis formed cages26 and for 2D imine molecular ladders,36 and may become more common as the number of bond formation reactions in a structure increases. Alternative products could include a range of different size oligomeric products, a polymeric material, alternative molecules with different topologies, or catenated molecules. Whilst reports of catenanes for porous organic cages are so far rare, examples from Hasell et al.37 and Zhang et al.38 suggest that in some cases catenanes can be the thermodynamic product, rather than their monomeric equivalent, as a result of ‘self-templating’ driven by the introduction of intermolecular interactions such as π–π stacking and alkyl–π interactions in the catenated form. In general, it is likely that, dependent on after how much time the product is isolated and characterised, different products might be observed as the mixture evolves. Whilst many organic cage molecules have been isolated in high yield (up to 100%),39 there are reports of systems where a mixture of products has been isolated from a single solution,35 presumably a greater driving force for a single topology being required for isolation of a single product.
We now consider factors that can influence the topological energy landscape and thus the likely topology and shape of the organic cage molecules formed for a set of BBs.
If the lack of rigidity in MOP assemblies frustrates the simple geometric design of BBs, then this is even more problematic for organic cages that have less strongly directional bonding. In the successful cases of geometric BB design thus far, rigidity of the underlying BBs has assisted in this design simplification. However, rigidity of the precursors is not a requirement for an organic cage assembly and with many functions of these materials, such as the host–guest response behaviour, often relying on dynamic motion of the final assembly, we conclude that it is important not to rule out more flexible BBs as potential cage components. This does however significantly increase the design challenge, and we believe necessitates the application of computational modelling in order to predict the conformations of the resultant assemblies. Of course ‘rigidity’ and ‘flexibility’ are not absolutes; whilst some flexibility and motion of a component is inevitable, excessive flexibility in the linkers is linked to lower product yields9 and increases the likelihood that the end assembly will not be shape persistent.
These criteria, whilst not producing an exhaustive set of possible topologies, result in 20 topologies that are the most plausible organic cage structures and indeed, almost two-thirds have already been synthetically reported. Recently, mathematicians have developed an algorithm for generating maps of ‘stable planar cages’, where they did not restrict themselves to 2-component systems and generated >400000 unique maps.51 The majority of these maps are too complex to be feasible with organic chemistry and thus our limited number of plausible topologies is more practical. However, the topologies we discuss can still be used to describe the underlying connectivity in a multicomponent system and indeed, multiple components may be an attractive design approach for the synthesis of some of the lower symmetry topologies. Several examples of multiple component systems,52–55 including those with orthogonal DCC formation reactions, for example both boronate and imine formation,50,56 have been reported.
For our discussion of organic cage topologies, we introduce a new nomenclature, labelling each structure as:
XmpYn |
We will now discuss each of the topologies within the four families that consist of combinations of different connectivity BBs. The topologies and their features are summarised in Table 1 and experimentally reported topologies in Table 2.
Topology | Edge-directed form | Face-directed form | Solid type | Multiple connections | Point group in high symmetry form | Ring sizes |
---|---|---|---|---|---|---|
Tri 2 Di 3 | 1 triple | D 3h | 43 | |||
Tri 4 Di 6 | Tetrahedron | Platonic | T d | 64 | ||
Tri 42 Di 6 | 2 double | D 2h | 42, 82 | |||
Tri 6 Di 9 | Triangular prism | D 3h | 62, 83 | |||
Tri 8 Di 12 | Cube | Platonic | O h | 86 | ||
Tri 20 Di 30 | Dodecahedron | Platonic | I h | 1012 | ||
Tet 2 Di 4 | 1 quadruple | D 4h | 44 | |||
Tet 33 Di 6 | 3 double | D 3h | 43, 62 | |||
Tet 42 Di 8 | 2 double | C 2v | 42, 64 | |||
Tet 44 Di 8 | 4 double | D 4h | 44, 82 | |||
Tet 55 Di 10 | 5 double | D 5h | 45, 102 | |||
Tet 6 Di 12 | Octahedron | Platonic | O h | 68 | ||
Tet 8 Di 16 | Square antiprism | D 4d | 68, 82 | |||
Tet 16 Di 32 | Cuboctahedron | Archimedean | O h | 68, 86 | ||
Tet 24 Di 48 | Rhombicuboctahedron | Archimedean | O h | 68, 818 | ||
Tri 1 Tri 1 | C 3v | 23 | ||||
Tri 22 Tri 2 | 2 double | D 2h | 22, 42 | |||
Tri 32 Tri 3 | 2 double | C 1 | 22, 44 | |||
Tri 4 Tri 4 | Tetrahedron | Platonic | T d | 46 | ||
Tet 6 Tri 8 | Rhombic-dodecahedron | Catalan | O h | 412 |
Topology | Reported? | CSD reference codes for crystal structures of archetypal examples |
---|---|---|
a This topology has been reported for a single component alkene metathesis reaction.69 b This topology has been reported with a bifunctional ditopic ligand and a cyclisation reaction. | ||
Tri 2 Di 3 | Yes | ZUYPUG,57 AJOHUD,58 SATJAA59 |
Tri 4 Di 6 | Yes | PUDXES,27 TOVWUY,60 EKUKUR61 |
Tri 42 Di 6 | Noa | — |
Tri 6 Di 9 | No | — |
Tri 8 Di 12 | Yes | KATJAS,33 REYMAL,44 ZIRCIO62 |
Tri 20 Di 30 | No | — |
Tet 2 Di 4 | Yes | LUXVAB63 |
Tet 33 Di 6 | Yes | VILCEZ64b |
Tet 42 Di 8 | Yes | No reported crystal structures35 |
Tet 44 Di 8 | Yes | AVAFIN65 |
Tet 55 Di 10 | No | — |
Tet 6 Di 12 | Yes | No reported crystal structures35 |
Tet 8 Di 16 | Yes | No reported crystal structures35 |
Tet 16 Di 32 | No | |
Tet 24 Di 48 | No | |
Tri 1 Tri 1 | Yes | No reported crystal structures66 |
Tri 22 Tri 2 | No | — |
Tri 32 Tri 3 | No | — |
Tri 4 Tri 4 | Yes | VOFROZ67 |
Tet 6 Tri 8 | Yes | QUFYIB, QUFYOH68 |
Fig. 4 The tritopic + ditopic topology family. Tritopic vertices are in blue, ditopic linkers in purple. |
The Tri4Di6 topology is formed from a [4 + 6] reaction and is related to a tetrahedron via an edge-directed assembly, with the tritopic BB placed on each of the vertices of the tetrahedron and the ditopic BB along the edges. The topology has four potential access windows and all these have a ring size of 6. Again, this is a very commonly reported topology in the literature, including systems from Cooper and co-workers27 for molecular separations19,20,22 and as porous liquids,25 and from Mastalerz and co-workers for sensing.23
This topology has also been reported for CC1 (Covalent Cage 1), CC2, and CC4 molecules in a triply-interlocked catenated form, which we label c-Tri4Di6.37 A molecule with a Tri4Di6 topology, if shape-persistent, can adopt final shapes ranging anywhere between a tetrahedron at one extreme to an octahedron at the opposite extreme. Reported examples of the Tri4Di6 topology molecules with these shapes are also shown in Fig. 2. For a tetrahedral shape to form, the tritopic BB could adopt a conformation to act as a capping vertex, with (end group)–(centre of mass)–(end group) angles of ∼60°, and the ditopic BB being linear. For an octahedral shape, the tritopic BB could be planar with (end group)–(centre of mass)–(end group) angles of ∼120° and the ditopic BB bent with an angle of ∼60°. With consideration of conformational flexibility in the BBs of organic cages, these geometric requirements are not essential, as compensation in each of the BBs could still achieve a given shape. The transformation of a tetrahedral shape to an octahedral shape occurs through a process of truncation of the tetrahedron's vertices. In Fig. 6, we show this transformation alongside a series of hypothetical porous organic cages of the Tri4Di6 topology, whose changing BBs show one way in which this range of shapes could be accessed. From an initial molecule with both the shape and topology of a tetrahedron, one can cause “flattening” of the corners of the molecule by swapping the starting tritopic BB with a planar tritopic precursor. Then, increasing the size of the planar tritopic BBs can lead to geometric shapes with higher degrees of truncation. Finally, an octahedral geometric shape is obtained by increasing the “bending” of the linear ditopic precursor. The key point is that all these molecules have a tetrahedral topology, despite adopting different geometrical shapes (refer to Fig. 2).
Fig. 5 The tetratopic + ditopic topology family. Tetratopic vertices are in orange, ditopic linkers in purple. |
The Tri42Di6 topology is also formed from a [4 + 6] reaction, but it contains two doubly connected tritopic BBs as well as two singularly connected BBs. The double connections result in two distinct window sizes, two rings of size 4 and two rings of size 8. This topology has not yet been reported for a DCC reaction, however, in 2014 Wang et al. reported the synthesis of this topology via a one-component alkene metathesis reaction.69 The component BB has a C3 symmetry axis and therefore reduced symmetry in the BB need not necessarily be employed to reach this topology if BB flexibility can account for this. This topology should be achievable through two-component DCC reactions.
The Tri6Di9 topology is formed from a [6 + 9] reaction and is related to a triangular prism via an edge-directed assembly and has five potential access windows, two with ring size 6 and three with ring size 8. We do not believe this topology has been synthetically reported, it will require tritopic BBs that have two (end group)–(centre of mass)–(end group) angles of 90° and one of 60°, to form both triangular and square connectivity rings, or BBs that can compensate for the differing angles required. This topology may be more easily achieved with lower symmetry BBs.
The Tri8Di12 topology is formed from a [8 + 12] reaction and is related to a cube via an edge-directed assembly and has 6 potential access windows, all with ring size 8. Multiple examples of this topology have been synthetically reported, although several lack shape-persistence. A catenated form of this topology, c-Tri8Di12 has been reported by Zhang et al.38 This molecule can adopt final geometric shapes ranging from a cube to the opposite extreme of a shape formed from planar tritopic BBs; reported examples of Tri8Di12 topology molecules with these shapes are shown in Fig. 7. For a cubic shape to form, the tritopic BB could adopt a conformation to act as a capping vertex, with (end group)–(centre of mass)–(end group) angles of ∼90°, and the ditopic BB would then be linear. For the vertex-folded shape, the tritopic BB could be more planar with (end group)–(centre of mass)–(end group) angles of ∼120° and the ditopic BB bent.
Fig. 7 The range of geometric shapes possible for Tri8Di12 topology cages, from a vertex-folded shape71 (top), to a cube31 (bottom). |
The final topology that we suggest for this family is a Tri20Di30 molecule from a [20 + 30] reaction and is related to a dodecahedron via an edge-directed assembly and has twelve potential access windows, all with ring size 10. This topology has not been reported for an organic cage molecule, although it has been reported for a MOP.72 It remains an alluring synthetic target, albeit very challenging due to potential issues with the solubility of the intermediates and the need to have a thermodynamic driving force for a dodecahedron over other topologies or an infinite polymeric product. Furthermore, it will be particularly challenging for this large molecule to be shape-persistent. The most obvious way to design this topology is to have an (end group)–(centre of mass)–(end group) angle of ∼108° in the tritopic BB, to match that of a dodecahedron's vertices, and to combine this with a linear ditopic BB. The required angle of ∼108° is close to that of a tetrahedral carbon, thus tri-functionalised methane molecules, such as those used by Olenyuk et al. for the synthesis of the dodecahedral MOP,72 are plausible BBs.
The Tet33Di6 topology is formed from a [3 + 6] reaction, containing three sets of doubly connected tetratopic BBs, so all have the same connectivity environment. The double connections result in two distinct window sizes, three rings of size 4 and two rings of size 6. This topology has been reported using a bifunctional ditopic ligand with a cyclisation reaction.64 The Tet42Di8 topology is formed from a [4 + 8] reaction and contains two double connections, such that each tetratopic BB is part of one double-link and two single-links. The double connections result in two distinct window sizes, two rings of size 4 and four rings of size 6. Although there are no crystal structures reported, Warmuth and co-workers have reported this structure with tetratopic cavitands and ethane diamines in a solvent of tetrahydrofuran and a distorted tetrahedral shape.35
The Tet44Di8 topology is also formed from a [4 + 8] reaction, but in this case there are four double connections, such that each tetratopic BB is doubly connected to its two neighbours. The topology has two distinct window sizes, four windows of ring size 4 and two windows of ring size 8. This structure has been reported by Warmuth and co-workers, again with tetratopic cavitands and ethane diamine, although even in a solvent it forms a folded structure that does not contain an internal void.65 The Tet55Di10 topology is formed from a [5 + 10] reaction that also has all building blocks doubly connected to each of their neighbours, creating two distinct windows, four with ring size 5 and two with ring size 10. This topology has not been experimentally reported and would have a high likelihood of lacking an internal void, as with the Tet44Di8 topology, for this reason we exclude larger topologies with this type of connectivity.
The Tet6Di12 topology is formed from a [6 + 12] reaction and is the first of the (tetratopic + ditopic) family that can be related to a polyhedron. Through an edge-directed assembly it relates to an octahedron, where the tetratopic BBs are placed on the vertices and the ditopic BBs are placed along the edges. The topology has eight windows of ring size 6. Whilst there are no reported crystal structures, this topology has been reported by Warmuth and co-workers, from the same BBs as the Tet42Di8 topology, but using chloroform as a solvent, rather than tetrahydrofuran.35 A molecule with this topology could adopt final shapes ranging from an octahedron to a cube, as shown in Fig. 8. For an octahedral shape to form, the tetratopic BB could adopt a conformation to act as a capping vertex, with (end group)–(centre of mass)–(end group) angles of ∼60°, and the ditopic BB linear. For the cubic shape, the tetratopic BB could be more planar with (end group)–(centre of mass)–(end group) angles of ∼90° and the ditopic BB bent to angles of ∼90° also.
Fig. 8 The range of geometric shapes possible for a Tet6Di12 topology cage,35 from an octahedron (middle) to a cuboctahedron (right). The molecule reported on the left is an example of an octahedral shaped cage. |
The Tet8Di16 topology is formed from a [8 + 16] reaction and can be related to a square antiprism through an edge-directed assembly of tetratopic BBs on vertices and ditopic BBs on edges. The topology has eight windows of ring size 6 and two larger windows of size 8. There are no crystal structures for this topology, however it was reported by Warmuth and co-workers for the same building blocks as the Tet44Di8 and Tet6Di12 topologies, but using a dichloromethane as the solvent.35 Molecular mechanics simulations suggested that their molecule would maintain a square prism shape that is approximately a spherical ring, as shown in Fig. 9.35
Fig. 9 Example of a Tet8Di16 topology cage reported by Warmuth and co-workers (left) with the geometric shape of a square antiprism (right).35 |
The Tet16Di32 topology is formed from a [16 + 32] reaction and can be related to the Archimedean solid of a cuboctahedron through an edge-directed assembly of tetratopic BBs on vertices and ditopic BBs on edges. There are two window sizes, eight of size 6 and six of size 8. There are no synthetic reports of this topology. Finally, there is a Tet24Di48 topology, formed from a [24 + 48] reaction that can be related to another Archimedean solid, the rhombicuboctahedron through edge-directed assembly. There are two window sizes, eight of size 6 and eighteen of size 8. There are also no synthetic reports of this topology, however, Fujita and co-workers have reported the synthesis of a MOP with this topology using square planar Pd2+ as the tetratopic vertex and a dipyridylfuran ligand with an angle of 127° as the edge.34 This structure therefore remains a synthetic design target for an organic cage molecule.
Fig. 10 The tritopic + tritopic topology family. One of the tritopic precursors is in blue, the other in teal. |
The Tri22Tri2 topology is formed from a [2 + 2] reaction, containing two of each type of tritopic BB, with each BB having one set of double connections and one single connection to the opposite building block. Therefore all BBs have the same connectivity environment and the molecule has two windows of ring size 2 and two of ring size 4. The Tri32Tri3 topology is formed from a [3 + 3] reaction, with two pairs of BBs having double connections and the remainder having single connections. The molecule has two windows of size 2 and four of size 4. There have been no synthetic reports of either the Tri22Tri2 or Tri32Tri3 topology to our knowledge.
The Tri4Tri4 topology is formed from a [4 + 4] reaction and can be related to a tetrahedron through a face-directed assembly, where one of the tritopic BBs is placed on the vertices and another on the faces of the Platonic solid. This type of face-directed assembly has been termed ‘molecular panelling’ when applied to the construction of MOPs.73 All the BBs are singularly linked and there are six windows of ring size 4. This topology has been reported by both Mastalerz and co-workers74 and Cooper and co-workers.67 A molecule with this topology could adopt final shapes ranging from a cube74 to a tetrapod,67 as shown in Fig. 11. For a cubic shape to form, both tritopic BBs could have a similar conformation with (end group)–(centre of mass)–(end group) angles of ∼90°, such that they form the eight corners of the cube between them. For a more tetrapodal shape, one tritopic BB could be planar, with angles of ∼120°, whereas the other could have very narrow angles, acting as the end of each ‘foot’ of the tetrapod.
Fig. 11 The range of shapes possible for the Tri4Tri4 topology cages, from a tetrapod67 (top), to a cube74 (bottom). |
Fig. 12 The Tet6Tri8 topology for the tetratopic + tritopic family. Tetratopic precursors are in orange, tritopic in blue. |
The Tet6Tri8 topology has been reported by Warmuth and co-workers using a tetratopic cavitand and a triphenylamine (although no crystal structure was reported for this experiment)32 and two examples using porphyrin building blocks and triamines by Hong et al. (for which crystal structures are available); the resultant molecules showed selectivity for small gases.68 The range of shapes possible for the Tet6Tri8 topology spans from a rhombic dodecahedron32 through an octahedron to a cube68 as shown in Fig. 13. For a rhombic dodecahedron shape to form, the tritopic and tetratopic BBs should have (end group)–(centre of mass)–(end group) angles of ∼60° and ∼90°, respectively. For a cubic shape to form, the tetratopic BB could be planar, with angles of ∼90° and the tritopic BB acting as a cube corner, with angles of ∼60°.
Fig. 13 The range of geometric shapes possible for a Tet6Tri8 topology cage. Top: The Tet6Tri8 cage32 can assume the shape of a rhombic dodecahedron (middle) when considering both tetratopic and tritopic precursors as vertices of a solid. It has the shape of an octahedron (right) when only the tetratopic vertices are linked together. Bottom: The Tet6Tri8 cage68 can be seen as a rhombic dodecahedron (middle, as before). It assumes the shape of a cube (right) when only the tritopic precursors are linked together. |
In the remainder of this article, we will examine specific case studies for each of the four topology families discussed above. This will allow us to compare the possible reaction outcomes – the alternative topologies that could be formed – and to investigate to what extent computer simulations can assist in predicting the topology from knowledge of the BBs alone.
In cases where the cage molecule is found to be non-shape persistent, with the lowest energy conformations lacking an internal void, we then proceed with our previously developed enhanced sampling technique to “inflate” the molecules and find the open conformations that lie higher on the potential energy landscape.71 This is essential to compare the conformations that the topologies would be adopting in solution when formed. The time requirements of this procedure naturally increase with molecular size, but as an example, the Tet8Di16 molecule described below required multiple simulations of several weeks duration. Once a collection of open conformations was generated, we performed a further refinement with density functional theory (DFT) calculations in order to obtain more reliable relative energies. Each conformation was geometry optimised with the PBE functional,77 and then its energy value was refined further with a single point calculation with the meta-GGA M06-2X functional.78 Following this, relative internal energies were compared for each family of cages. The use of DCC reactions allowed us to assume that the molecule with the lowest relative energy should be the most synthetically accessible. When the comparison of relative energies was not possible due to molecules containing different BBs, formation energies were calculated instead, with the assumption that the molecule with the lowest formation energy is the most likely to form. For full simulation details, please refer to the ESI.†
Firstly, in terms of solvent effects, our previously reported “inflation” procedure71 allows us to look at how a solvent influences the conformations of cage molecules. This approach allows us to reproduce the scaffolding or “templating” effect of the solvent molecules, but does not explicitly model individual solvent interactions. To reproduce explicit solvent interactions, we would firstly have to greatly increase the number of atoms in our simulations due to the necessity of including hundreds of solvent molecules; in previous work we found a single cage molecule to be solvated by ∼80 dichloromethane molecules (400 atoms) even in the solid state solvate structure.33 Secondly, we would then need to sample the conformations of these molecules surrounding the cage molecule to consider the dynamic nature of the solvation. Combined, these simulations are not currently tractable for these systems. An alternative implicit solvation approach, where a dielectric constant is applied to reproduce the dielectric screening a molecule in solution experiences, does not reproduce the scaffolding effect of the solvent, and our preliminary tests have found this to make no significant difference to the relative energies of cage topologies. This issue of solvent effect remains a big challenge in the field and efficient approaches need to be developed for the modelling of such complex systems.
Ideally we would go beyond the relative internal energies from DFT calculations and compare free energies. This would include a consideration of the translational, rotational and vibrational entropy of the systems, which should tend to disfavour the formation of larger assemblies over smaller ones. Practically, this would require a frequency analysis for each molecular conformation, and this is computationally intractable on a routine basis even for the smaller cage systems. Indeed, in our previous work we had to resort to considering only fragments of a comparably small molecular cage for calculations of the free energy correction to guest binding energies to be tractable.79
Whilst not the focus of our work, one can also consider the use of simulations to predict preferential catenane formation over monomeric forms of the topologies discussed. Catenanes could be expected to form as thermodynamic products if a combination of solvent interactions, steric compatibility of the BBs involved in the reaction, and the formation of stabilising interactions between the two monomeric units act as a thermodynamic driving force. The obvious starting point for simulations is to calculate the binding energy of a catenane pair by comparing the total energy to that of two gas phase monomers. An unfavourable binding energy, for example resulting from steric clashes of the molecules in a catenated form, would suggest that the monomeric form would be preferred. However, favourable binding energies would need to be considered with caution, as these would indicate stabilisation of the catenane relative only to isolated gas phase monomers, without consideration of stabilisation of those monomers by either solvent interactions or intermolecular interactions gained via crystal packing. Thus, arguably, for a series of systems, binding energies might be best used to qualitatively rank a series of monomers in terms of the likelihood of catenane preference over monomeric forms. We further note that for some systems there would be significant, and even potentially prohibitive, sampling requirements when looking for low energy catenated forms. These would arise from the requirement to consider both different mechanical interlocking arrangements and also configurational sampling for each interlocked form. Finally, reliable binding energies across a series of different systems are likely to require DFT calculations, rather than computationally cheaper forcefield calculations.
Fig. 16 The relative energies of the lowest energy conformations of the CC3-based tritopic + ditopic topologies, as calculated by M06-2X. |
Synthetically realised? | Energy relative to Tri4Di6 per [2 + 3] unit (kJ mol−1) | Shape persistent? | Void diameter (Å) | |
---|---|---|---|---|
Tri 2 Di 3 | No | 52 | Yes | 1.3 |
Tri 4 Di 6 | Yes | 0 | Yes | 5.5 |
Tri 42 Di 6 | No | 39 | Yes | 3.1 |
Tri 6 Di 9 | No | 14 | No | 5.2 |
Tri 8 Di 12 | No | 5 | No | 7.4 |
The Tri4Di6 molecule lies lowest in energy and is the synthetically realised topology, which can therefore be rationalised on the energy of the gas phase conformations alone. This is followed by the higher energy metastable inflated conformers of Tri8Di12 (5 kJ mol−1 per [2 + 3] unit) and Tri6Di9 (14 kJ mol−1 per [2 + 3] unit). An alternative topology is available with a [4 + 6] reaction, in which precursors are assembled into a doubly-bonded ring to give Tri42Di6, however this is considerably higher in energy (39 kJ mol−1 per [2 + 3] unit). The Tri2Di3, in which the precursors are assembled into a capsule, is the topology with the highest energy, 52 kJ mol−1 per [2 + 3] unit higher, unsurprisingly the geometry is characterised by a high degree of strain. To compare not only the topological prediction, but also the structure prediction, we overlaid our predicted structure of the Tri4Di6CC3 molecule to that of the single crystal X-ray diffraction structure.27 We found a Root Mean Square Deviation (RMSD) value of 0.107 Å, showing that the conformation is well reproduced, as shown in Fig. S1-A.†
Fig. 18 The relative energies of the lowest energy conformations of the CC5 and CC8-based ditopic + tritopic topologies, as calculated by M06-2X. |
Synthetically realised? | Energy relative to Tri8Di12 per [2 + 3] unit (kJ mol−1) | Shape persistent? | Void diameter (Å) | |
---|---|---|---|---|
CC5 Tri 2 Di 3 | No | 87 | — | 0.4 |
CC5 Tri 4 Di 6 | Yes | −1 | Yes | 7.3 |
CC5 Tri 8 Di 12 | No | 0 | No | 10.1 |
CC8 Tri 2 Di 3 | No | 67 | — | 1.6 |
CC8 Tri 4 Di 6 | No | 25 | Yes | 6.5 |
CC8 Tri 8 Di 12 | Yes | 0 | No | 9.2 |
For both cage families, the Tri2Di3 molecule, with only two carbon atoms bridging the tritopic BBs, is strained and consequently high in energy compared to the other topological possibilities in all cases (by >40 kJ mol−1). It is not surprising therefore that this topology is not experimentally observed. For the CC8 molecule, the lowest energy conformation has the large Tri8Di12 topology, with an approximately octahedral symmetry. This corresponds to the experimental reports of this molecule formed with the diaminocyclohexene group.33 As we previously reported,71 the computed open conformation for CC8 is a good match to the single crystal X-ray diffraction structure of the solvate (with an RMSD value of 1.672 Å, see Fig. S2-A†), which improves slightly when minimising the single crystal structure (with the RMSD value moving to 0.629 Å, see Fig. S2-B†), suggesting some influence of the solvent molecules in opening the vertices slightly outwards.
For the CC5 molecule, there was a very different result to the CC8 molecule; now there is no clear preference between the Tri4Di6 and Tri8Di12 molecules, with a relative energy difference of only 1 kJ mol−1 per [2 + 3] unit. This molecule has in fact been synthetically realised only as a Tri4Di6 topology, which had a BET SA of 1333 m2 g−1.81 An overlay of the computed and single crystal X-ray diffraction structure of the solvate (see Fig. S3†) finds a good match, with an RMSD of 0.706 Å. Again, this match improves when the solvate conformation is geometry optimised (RMSD of 0.449 Å), which contracts the molecule, suggesting a scaffolding effect of the solvent that is lost in the calculations when the conformation is completely energy minimised after our artificial inflation procedure. In this case therefore, the calculations would not have been able to successfully distinguish between whether a Tri4Di6 or Tri8Di12 topology was formed, although it was clearly a different scenario to the CC8 topological energy landscape. We attribute this to our not being able to consider all solvent effects in our simulations (as evidenced by the overlays). Further, as discussed in the Computational challenges section, if the entropic contribution to the free energies was able to be considered, this can be expected to destabilise the larger Tri8Di12 topology relative to the Tri4Di6.
Fig. 20 The relative energies of the lowest energy conformations of the CC11-based tritopic + tritopic topologies, as calculated by M06-2X. |
Synthetically realised? | Energy relative to Tri4Tri4 per [1 + 1] unit (kJ mol−1) | Shape persistent? | Void diameter (Å) | |
---|---|---|---|---|
Tri 1 Tri 1 | No | 376 | — | 1.2 |
Tri 2 Tri 2 | No | 123 | — | 0.4 |
Tri 4 Tri 4 | Yes | 0 | Yes | 3.2 |
Fig. 22 The relative energies of the lowest energy conformations of the Warmuth tetratopic + tritopic topologies, as calculated by M06-2X. The error bar on point Tet8Di16 shows the range of energies covered by conformations with differing degrees of inflation (see Table S1 and Fig. S4†), with more open conformers displaying higher energies. |
Synthetically realised? | Energy relative to Tet4Di8 per [1 + 2] unit (kJ mol−1) | Relative formation energy per bond formed (kJ mol−1) | Shape persistent? | Void diameter (Å) | |
---|---|---|---|---|---|
Tet 2 Di 4 -A | No | 27 | 8 | Yes | 5.8 |
Tet 2 Di 4 -B | Yes | — | 6 | Yes | 5.1 |
Tet 2 Di 4 -C | Yes | — | 0 | Yes | 4.6 |
Tet 3 Di 6 | No | 17 | — | Yes | 3.1 |
Tet 42 Di 8 | Yes | 0 | — | Yes | 6.3 |
Tet 6 Di 12 | Yes | 1 | — | No | 12.3 |
Tet 8 Di 16 | Yes | Range from −21 to 17 | — | No | 8.4–10.4 |
The cage with the lowest energy was a partially collapsed conformer of Tet8Di16. The cage was not found to be shape persistent after high temperature MD, and the inflating procedure provided us with a very large number of higher energy metastable conformers, some of which were partially open, like the lowest energy one reported, and others containing a larger pore size (as shown in Fig. S4†). As no crystal structure was available and it was not possible to be certain whether a single conformation represented the open structure, we plot the range of energies found for conformations with varying pore sizes in Fig. 22 and show the conformation with the widest pore diameter (10.4 Å) in Fig. 21. This more open conformation is located 38 kJ mol−1 above the less inflated lower energy conformer, which has a smaller pore diameter of 8.4 Å. The degree of strain of the structure increases with the degree of inflation.
Experimentally, the formation of Tet8Di16 was obtained using CH2Cl2 as a solvent. We carried out a structural analysis on the resulting cage, in order to understand whether it was possible to relate the solvent used during the synthesis to the final topology. Tet8Di16 has 10 windows, with diameters that range from 4–6 Å for the 8 triangular windows and from 6–9 Å for the 2 square windows, depending on the degree of inflation (see Table S1†). About 22 and 21 kJ mol−1 above the lowest energy conformer of Tet8Di16 are Tet6Di12 and Tet42Di8, that were respectively found experimentally in THF and chloroform. We analysed their windows’ diameters (an average of 5.2 Å for the 8 triangular windows of the octahedral Tet6Di12, and an average of 5.6 Å for the 4 biggest windows of Tet42Di8), but we were not able to find any geometric correlation between the solvent used for the synthesis and the cage topologies. We leave this particular aspect to further studies.
The hypothetical topologies we generated, Tet33Di6 and Tet2Di4, are more strained and thus higher in energy, explaining the fact that they have not been experimentally observed. They are located respectively 17 and 27 kJ mol−1 higher than Tet42Di8. We then investigated the effect of changing the ditopic BB's geometry on the topological landscape. The study carried out by Warmuth and co-workers suggested that it was not possible to synthesise a cage with the shape of a Tet2Di4 capsule when using ethylene-1,2-diamine, which is rationalisable by the fact that it lies 27 kJ mol−1 higher in energy per [1 + 2] unit than the observed Tet42Di8 topology.35 However, they did find that the Tet2Di4 capsule could be formed by using different ditopic BBs, benzenes amino-functionalised in the meta or para position. We therefore generated two capsules in a [2 + 4] ratio, Tet2Di4-B and Tet2Di4-C, using m-phenylenediamine (10) and the chiral precursor p-xylylenediamine (11) respectively. As these molecules contain different BBs, we cannot directly compare their relative energies per formula unit, and therefore instead compare the relative formation energies of the three capsular Tet2Di4 molecules (see Table 6). In agreement with experimental results, both cages B and C are lower in energy than A, in particular Tet2Di4-C is 6 kJ mol−1 per imine bond lower than Tet2Di4-B, and Tet2Di4-C is 8 kJ mol−1 lower than Tet2Di4-A. This is because kinked or twisted diamines allow the two cavitands to align in a more stable and less hindered conformation than when using BB 9. The latter should adopt a very strained gauche conformation to permit the cavitands to align in the coplanar conformation required to reduce the strain.
Synthetically realised? | Relative formation energy per bond formed (kJ mol−1) | Shape persistent? | Void diameter (Å) | |
---|---|---|---|---|
Tet 2 Tri 4 | Yes | 3 | Yes | 9.9 |
Tet 6 Tri 8 -A | Yes | 4 | Yes | 17.8 |
Tet 6 Tri 8 -B | No | 3 | Yes | 12.2 |
Tet 6 Tri 8 -C | No | 0 | Yes | 15.5 |
Considering the possible interest in a porous molecule of this cavity volume, the effect of the size of the triamine BB was investigated and two similar molecules with the Tet6Tri8 topology were generated. Cavitand 8 was mixed with 1,3,5-triaminobenzene (13) to give Tet6Tri8-B and with 4,4′,4-triaminotriphenylamine (14) to obtain Tet6Tri8-C. Both molecules were found to be shape persistent and therefore the formation energies per bond were calculated and compared to that of Tet6Tri8-A (see Table 7). Tet6Tri8-B was found to have a formation energy ∼1 kJ mol−1 lower than Tet6Tri8-A, thus is potentially equally likely to form. Tet6Tri8-C shows a less strained geometry; we attribute this to the central nitrogen atom on each tritopic BB allowing rotational freedom, bringing the formation energy 4 kJ mol−1 per imine bond lower than Tet6Tri8-A. This suggests that Tet6Tri8-C could be a particularly promising synthetic target. Both molecules are porous, showing respectively a shape persistent pore diameter of 12.2 Å and 15.5 Å.
We have tested to what extent calculations focusing on relative internal energies can assist in the prediction of topological outcomes for a given DCC reaction that should afford the thermodynamic product. This approach was successful in the majority of the BB combinations we examined, including for CC3, CC5, CC11, the (tetratopic + ditopic) family from Warmuth and the (tetratopic + tritopic) family from Warmuth. However, for the case of the emergent behaviour in the CC5 and CC8 systems, whilst we can correctly identify that the cyclohexane BB leads to a Tri8Di12 topology, for the cyclopentane BB, we could not distinguish between the relative energies of Tri4Di6 and Tri8Di12, thus not correctly identifying the experimental outcome of a Tri4Di6 topology. We believe that this result is likely due to a combination of the influence of the solvent in disturbing the energy landscape and an entropic contribution disfavouring the larger topology, which we were not able to directly include in our simulations. For the Warmuth (tetratopic + ditopic) family, where the topology is known to be influenced by solvent choice, we were not able to find any obvious geometric correlation between the structures and the successful solvent, thus this remains the subject of future research.
We highlight the design opportunity behind using simulations to consider the thermodynamic viability of a given target, which, together with chemical intuition, can provide new developments for this emerging field. The natural evolution of this project would be to explore the topological outcome for a much wider library of precursors with different topicity, length, angles, and rigidity, with the goal being to rationalise which criteria would favour the formation of promising porous organic cages. However, we have shown here computational challenges with modelling a relatively small set of organic precursors, suggesting that the brute force screening of large libraries is not currently computationally feasible. Instead, we would suggest it is better to focus on answering specific questions with smaller library subsets, such as: how does variation in the BB geometry influence topological outcome? Which BBs provide the most promising route to a desired topology? Which BB features are most critical to shape persistence in a desired topology?
Footnote |
† Electronic supplementary information (ESI) available: Additional computational details, results, figures and structure files. See DOI: 10.1039/C7NR00703E |
This journal is © The Royal Society of Chemistry 2017 |