High-Throughput Computational Evaluation of Low Symmetry Pd2L4 Cages to Aid in System Design**

Article abstract of DOI:10.1002/anie.202106721

Unsymmetrical ditopic ligands can self-assemble into reduced-symmetry Pd₂L₄ metallo-cages with anisotropic cavities, with implications for high specificity and affinity guest-binding. Mixtures of cage isomers can form, however, resulting in undesirable system heterogeneity. It is paramount to be able to design components that preferentially form a single isomer. Previous data suggested that computational methods could predict with reasonable accuracy whether unsymmetrical ligands would preferentially self-assemble into single cage isomers under constraints of geometrical mismatch. We successfully apply a collaborative computational and experimental workflow to mitigate costly trial-and-error synthetic approaches. Our rapid computational workflow constructs unsymmetrical ligands and their Pd₂L₄ cage isomers, ranking the likelihood for exclusively forming cis-Pd₂L₄ assemblies. From this narrowed search space, we successfully synthesised four new, low-symmetry, cis-Pd₂L₄ cages.

Full text of DOI:10.1002/anie.202106721

A Journal of the Gesellschaft Deutscher Chemiker
Angewandte
International Edition Chemie
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Accepted Article
Title: High-throughput Computational Evaluation of Low Symmetry
Pd2L4 Cages to Aid in System Design
Authors: Andrew Tarzia, James Lewis, and Kim E Jelfs
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High-throughput Computational Evaluation of Low
Symmetry Pd L Cages to Aid in System Design
2
4
∗
Andrew Tarzia, James E. M. Lewis, Kim E. Jelfs*
July 12, 2021
Abstract
Unsymmetrical ditopic ligands can self-assemble into reduced-symmetry Pd L4
2
metallo-cages with anisotropic cavities, with implications for high specificity and affin-
ity guest-binding. Mixtures of cage isomers can form, however, resulting in undesirable
system heterogeneity. It is paramount to be able to design components that preferen-
tially form a single isomer. Previous data suggested that computational methods could
predict with reasonable accuracy whether unsymmetrical ligands would preferentially
self-assemble into single cage isomers under constraints of geometrical mismatch. We
successfully apply a collaborative computational and experimental workflow to miti-
gate costly trial-and-error synthetic approaches. Our rapid computational workflow
constructs unsymmetrical ligands and their Pd L cage isomers, ranking the likelihood
2
4
for exclusively forming cis-Pd L assemblies. From this narrowed search space, we
2
4
successfully synthesised four new, low-symmetry, cis-Pd L cages.
2
4
∗
Department of Chemistry, Molecular Sciences Research Hub, Imperial College London, White City
Campus, Wood Lane, London, W12 0BZ, UK; james.lewis@imperial.ac.uk, k.jelfs@imperial.ac.uk
1
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Introduction
Nature has evolved spectacular control over self-assembly processes to produce biological ma-
chinery for which high-fidelity of composition and structure is essential for effective function-
ality. The exploitation of non-covalent interactions allows complex architectures, such as en-
zymes, to exhibit high substrate specificity through precise control of binding-site size, shape
and positioning of functional groups. Over the last few decades, chemists have made great
strides in developing approaches to utilise these principles for artificial systems. Metallo-
supramolecular chemistry has become a prevalent method for assembling ever-more-complex
architectures using the predictable coordination geometry of transition metal ions.[1–3]
Since first being reported over twenty years ago,[4] lantern-type Pd L cages,
[5–7]
assem-
2
4
bled from “naked” Pd(II) ions and ditopic ligands (L), have become an extensively studied
class of metal-organic polyhedra (MOPs).[8–12] Wide-ranging applications for these cages
have been investigated, including in drug delivery,[13–15] biomedicine,[16–21] catalysis,[22–25]
and guest encapsulation/recognition.[26–32] To simplify the self-assembly process, most pre-
vious reports have focussed on high-symmetry systems derived from single, symmetrical
ligands. However, it is expected that through the controlled introduction of asymmetry,
cages could be designed with more intricate, anisotropic binding sites with specific shapes
and functionalities.[33]
Pore asymmetry in M L systems has been introduced through the controlled assembly
2
4
of heteroleptic[34–36] and heteronuclear architectures.[37,38] Mixed-ligand [Pd L L ] assem-
a
2 2
b
2
blies have been realised through both steric[39,40] and geometric control.[41,42] Clever and
co-workers have demonstrated the effectiveness of pore asymmetry for improved binding of
bent guests over linear counterparts.[43] Crowley and co-workers recently reported a [PdPtL4]
cage in which the different labilities of the two metal ions allowed selective sequestration of
the Pd(II) ions to open the cage without complete dissociation of the ligands.[44] We[45,46] and
others[47–50] have recently begun to explore an alternative approach that uses unsymmetrical
ligands to access lower symmetry structures.[51] The lack of bilateral symmetry introduced
into the ligand structure means four possible isomers of the resultant dipalladium cage can
form (Figure 1). As with heteroleptic structures, high-fidelity self-sorting into a single isomer
2
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can be achieved using steric and/or geometric constraints. However, the inherent difficulty
in designing such ligands that will reliably self-sort helps explain the paucity of examples in
the literature.
2
+
4
x
+ 2 x
(Pd )
a
b
c
d
Figure 1: Schematic representation of the self-assembly of an unsymmetrical ditopic ligand and
palladium(II) into four possible isomers of the homoleptic Pd L cage: (a) “all-up”, (b) “three-
2
4
up-one-down”, (c) cis and (d) trans. Orange and navy colours indicate inequivalent ligand
fragments.
Density functional theory (DFT) calculations have been previously used to rationalise
experimentally observed self-sorting in low symmetry metallo-supramolecular systems by
exploring the relative energies of the potential configurational isomers.[41,43,45,47,48] Indeed,
in recent work, we found that the formation of a single Pd L cage isomer from the self-
2
4
assembly of unsymmetrical ditopic ligands with Pd(II) ions only occurred when there was
−
1
a significant difference in the calculated energies (on the order of at least 5 kJ mol ) of the
possible isomers.[45] As such, we envisaged that a high-throughput computational workflow
could be used to rapidly explore the chemical space of low symmetry MOPs and aid in their
design and minimise trial-and-error experimental efforts.
Computational screening has been successfully applied to aid in the rationalisation and/or
prediction of self-sorting outcomes of porous organic cages using the relative energetics of
possible products.[52–55] Until recently, however, it has not been possible to develop equiv-
alent screening workflows for MOPs because no open-source structure generation software
was available. Some of us previously developed the supramolecular toolkit (stk),[56,57] an
open-source Python framework that handles the structure prediction of supramolecular ar-
chitectures. Here, we highlight the first use of stk to screen candidate MOPs. Young and
3
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co-workers also recently developed the software cgbind, which performs structure prediction
[
58]
of M L cages.
The generalisability of stk, however, makes it ideal for this work, where
2
4
we aim to explore a diverse set of ligand and cage structures.
In this work we present a high-throughput computational workflow that was used to
construct 60 unsymmetrical, ditopic ligands and the four possible Pd L cage isomers for
2
4
each in silico. Using metrics of geometrical stability and relative cage energies, the ligands
were ranked based on their likelihood to form a single Pd L isomer. A selection of five
2
4
ligands with a range of rankings and chemistries were subsequently realised experimentally,
and their self-assembly examined. This computer-aided approach facilitates an experimental
design with a high success rate, leading to several new unsymmetrical cis-Pd L cages being
2
4
prepared. In this manner, the discovery of interesting candidates can be accelerated by
providing a likelihood of success, expediting the synthesis of low symmetry MOPs with
desirable structural properties. Indeed, this work highlights that a computer-aided approach
allows a more efficient exploration of a larger chemical space of potential candidates than a
purely experimental approach.
Results and Discussion
Semi-empirical methods for cage relative energy evaluation
4
+
In previous work it was found that the energy separations of the isomers of [Pd L ] cages
2
4
assembled from unsymmetrical ligands, calculated using DFT methods, correlated well with
experimental observations of single isomer formation.[45] For larger data sets it would be de-
sirable to use efficient, semi-empirical methods for geometry optimisations and energy calcu-
lations to reduce computational cost and increase throughput. Therefore, we tested whether
the xTB family of semi-empirical methods[59] could capture the same relative energy differ-
ences between Pd L cage isomers as DFT methods. The xTB methods are tight-binding
2
4
quantum chemical methods for the geometry optimisation of systems containing elements
up to Z = 86, and represent a robust and significantly cheaper alternative to DFT for
metal-containing species.[60] A comparison of the xTB (specifically GFN2-xTB) and DFT-
4
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calculated energies of previously reported systems was undertaken (structures were taken
directly from the computational workflow described below). DFT energies were obtained
from single-point energy evaluations of xTB geometries using similar methods to those re-
cently applied to related systems[25] (the final selected method uses the PBE0[61] level of
theory using the Ahlrichs basis set def2-SVP,[62,63] Grimme’s D3BJ dispersion correction[64]
and the polarizable continuum model (PCM)[65] implicit solvation representing DMSO; more
details and a comparison to the B97-3c composite method are available in Supporting In-
formation Section S3). The same trends in relative energies were found from both methods
(
Figure 2) and for free energies calculated using GFN2-xTB (Table S2), suggesting that
GFN2-xTB can reasonably represent the relative energetics of the studied cage systems.
Therefore, xTB methods were applied throughout this work for geometry optimisations and
for energy evaluations toward a high-throughput workflow.
N
N
N
N
N
N
N
N
Figure
2:
Comparison
of
GFN2-xTB
(DMSO)
and
DFT
(PBE0/def2-
SVP/D3BJ/CPCM(DMSO)) energy difference between the cis and next most stable isomer of
cages formed in ref. 45 from the ligands 3D1 (crimson), 4D2 (yellow), 5D1 (dark green) and
5
D3 (blue).
5
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Combined experimental and computational workflow
In this work, a joint computational and experimental workflow (Figure 3(a)) was imple-
mented to facilitate the search for new unsymmetrical ligands with sufficient geometrical
constraints to drive the exclusive formation of single Pd L cage isomers. This approach
2
4
started with an initial experimental choice of building blocks. These were combined in silico
to form the candidate ligands and their possible Pd L cage isomers. The cage systems were
2
4
then analysed using computationally cheap structural parameters to assess the likelihood of
successful self-assembly into a single isomer, thus assisting in the synthetic decision-making
process. A focus was placed on using relatively low-cost computational approaches before
any experimental investment to minimise wasted efforts. Such an approach opens up the
ability to search for new unsymmetrical cages with desirable properties, increasing ligand
design efficiency (which is currently based on very few experimental examples).
A major goal of this computational workflow is generalisability, rendering it applicable
to a large chemical space that can be adapted for future iterations of the process. To this
end, stk,[56,57] UFF4MOF (Universal Force Field for MOFs[66,67]) and the xTB family of
semi-empirical methods[59,68] were used for the assembly and geometry optimisation, respec-
tively, of ligand and cage structures. stk assembles building blocks onto topology graphs; this
process includes the placement, alignment and reaction of the building blocks. Before optimi-
sation with xTB, conformer searches were performed on the Pd L systems using a broadly
2
4
applicable force field that can handle common metal complex geometries (UFF4MOF imple-
mented in the General Utility Lattice Program (GULP)[69,70]). Coupling the above methods
affords low-cost structure generation, conformer searching and geometry optimisation (Fig-
ure 3(e)). For each cage, the construction, conformer search and optimisation (at the xTB
level) processes took approximately 2–3 hours on a workstation with an i7-9700K CPU (3.60
GHz), which allows for the evaluation of a ligand and its four isomers overnight on standard
computer hardware.
6
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(a)
1
2
3
4
. Select ligand building blocks
. Ligand construction
. Cage isomer construction
. Cage ranking
low-cost
computation
5
. Synthesis
time investment
(b)
(e)
j
i
N
k
N
building block alignment
conformer search
i≠k
coordinating groups
(
c)
Br (d)
Br
Br
Br
Br
+ optimisation
N
Br
Br
N
Br
Br
N
1
2
Br
3
6
A
B
D
Br
Br
N
N
N
Br
Br
N
4
5
C
Figure 3: (a) Schematic for the joint experimental and computational workflow showing relative
time frames of each step. (b) Schematic of unsymmetrical cage ligands ijk formed from three
building blocks with the nitrogen coordinating groups highlighted. The library of (c) coordinating
building blocks and (d) core building blocks used to construct the cage ligands in this study.
Purple circles are the connection points between coordinating and core building blocks. (e)
Assembly of a cis-Pd L structure from an unsymmetrical ligand. Firstly, the Pd(II) ions and
2
4
ligands are placed and aligned on the M L topology vertices by stk, generating an expanded
2
4
structure. Geometry optimisation, coupled with a conformer search, was then performed on this
structure to give the optimised geometry.
Automated ligand and cage structure generation
To construct a range of unsymmetrical ditopic cage ligands using stk, the ligand structure was
partitioned into three building blocks (Figure 3(b)): a core (A–D in Figure 3(d)) separating
two inequivalent coordinating building blocks (1–6 in Figure 3(c)). The building blocks
7
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were selected from structures commonly used in metallo-supramolecular systems. In this
initial study, a relatively small selection of building blocks was used, giving a combinatorial
library of 60 unsymmetrical ditopic ligands. With four possible Pd L cage isomers for each
2
4
ligand, a library of 240 cages was generated. Through enumeration of this set of common
building blocks, a set of unconventional unsymmetrical cage ligands were generated and
tested. The step-wise computational assembly and optimisation of ligands and cages (see
Supporting Information Section S2) through stk is automated from the point of input of
the ligand building blocks as text-based SMILES strings (Table S1). Therefore, this work is
straightforward to extend to a larger chemical space using our hierarchical approach.
Ranking ligands by their cage isomer properties
In the final step of the computational workflow, the assembled cages associated with each
ligand were analysed to determine if a single Pd L isomer (targeting the cis isomer) would
2
4
be expected to form to the exclusion of others. Our validation of GFN2-xTB (vide supra) for
providing relative energies of different Pd L structures suggested that a GFN2-xTB energy
2
4
separation of ≈ 6 kJ mol− between the two lowest energy isomers (∆E) appeared to be
sufficient to drive exclusive formation of the lowest energy cage isomer. Of the 60 ligands
in the library, 34 (57 %), including three previously reported examples, had ∆E values of
1
−
1
at least 6 kJ mol , indicating that they might be promising candidates for experimental
synthesis.
While the relative xTB energies provide information about the likely self-sorting be-
haviour of Pd L cage isomers, they do not indicate if the desired Pd L topology will be
2
4
2 4
the favoured product of self-assembly, rather than a larger species. In fact, the prediction
of the preferred topology of palladium cages requires costly computational methods.[71] To
bypass these methods, the assumption was made that if the Pd L cage is geometrically
2
4
stable, then, as the smallest possible Pd L assembly, it is likely to form as the entropically
n
2n
favoured product. As a simple means to probe this, two structural metrics common to every
cage in the library were employed (Figure 4): the maximum sum of the deviation of the
four nitrogen atoms and palladium atom from each calculated average PdN plane (Dmax;
4
0
.0 A indicating no deviation) and the minimum square planar order parameter (qsqp,min;[72]
˚
8
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1
.0 indicating a perfect square planar geometry) of the Pd(II) ions. Both measures quantify
the degree of square-planar-likeness in the most strained palladium ion of the cage. It is
assumed that if the strain in the cage is significant, Pd L formation will be enthalpically
2
4
unfavourable. By applying ∆E (specifically ∆E , which is the relative stability of the
cis
cis cage isomer), Dmax and qsqp,min within the workflow as computationally cheap heuris-
tics, cage ligands with desirable properties can be selected for synthesis from the generated
rankings favouring those that appear most likely to give successful self-assembly outcomes
(
where success is defined as exclusive formation of a single cage isomer). Figure 5 shows the
relationship between the three heuristics used for ranking candidates.
N
N
(
a)
(b)
N
Pd2+
x
n
PdN4
N
Pd2+
N
Pd2+
N
plane
N
N
N
D = x + x + x + x
4
q = 1
0 ≤ q < 1
i
1
2
3
Figure 4: (a) Schematic showing D as the sum of the distance of four nitrogen atoms (one is
i
shown) and the palladium atom from the plane defined by a PdN unit. D
is the maximum Di
4
max
of the two in a Pd L cage. (b) Schematic representation of the square planar order parameter
2
4
[
72]
q .
sqp
−
1
Of the 34 ligands with ∆E values ≥ 6 kJ mol , 12 had lowest energy cage isomers ex-
˚
hibiting very favourable Dmax and qsqp,min values < 0.1 A and > 0.95, respectively. Pleasingly,
[
45]
three had previously been synthesised and shown to exclusively form cis-Pd L isomers.
2
4
Perhaps unsurprisingly, in each of these 12 instances, the cis-Pd L isomer was predicted
2
4
to be the favoured structure, again in agreement with previous work.[45,47,48] Indeed, for
most of the ligands (51 of 60; 85 %), the cis cage isomer was found to be the most stable
(
Figure S4(a)).
9
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Figure 5: The relative stability of the cis cage isomer (∆E ) for each ligand as a function of
cis
qsqp,min of the calculated cis-Pd L structure. Negative values of ∆E indicate that the cis
2
4
cis
isomer is not the most stable. Only structures with qsqp,min > 0.95 are shown here; the full data
set shown in Figure S3(a).
Experimental realisation of new unsymmetrical cages
Five previously unreported ligands were selected for synthesis to investigate their self-
assembly with Pd(II) (Figure 6). These included four ligands from the 12 that adhered
to the chosen parameter thresholds (Table 1), including with naphthalene (5A1) and para-
phenylene (4B1, 4B3, 5B4) core building blocks, with combinations of pyridyl/isoquinolyl
coordinating building blocks. A fifth ligand, 5A3, was also selected that displayed good
˚
structural parameters (Dmax = 0.0 A; q
= 1.0) but a low energy separation (∆Ecis =
sqp,min
−
1
2
.9 kJ mol ) to probe the fidelity of the ∆E value as a quantitative metric in predicting iso-
mer equilibria, given the necessary simplicity of the workflow’s modelling parameters. The
ligands were prepared using standard synthetic techniques, and their identities confirmed by
NMR spectroscopy and mass spectrometry (MS). In each instance, the ligand self-assembly
with Pd(II) was examined by combining the ligand and [Pd(CH CN) ](BF ) in a 2:1 ratio
3
4
4 2
in d -DMSO (followed by standing at room or elevated temperature for a period of time, as
6
necessary to reach equilibrium).
1
0
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(a)
(b)
N
N
N
N
5
A3
5A1
4B1
N
N
N
N
N
N
5B4
4B3
Figure 6: (a) GFN2-xTB optimised structure of the cis isomer of selected cage ligands (hydrogen
atoms omitted; carbon: green, nitrogen: blue, palladium: cyan). Cage ligands are shown next
to each structure with orange and navy colours indicating inequivalent ligand fragments. (b)
[
45]
cis isomer GFN2-xTB(DMSO) stability (∆E ) for all published
cis
and newly selected ligands
(
patterns distinguish their self-assembly outcomes).
−
1
For the three ligands with calculated energy differences in excess of 6.0 kJ mol (5B4,
1
5
A1 and 4B1), quantitative conversion to a single species was observed by H NMR (Fig-
ure 7(a)–(c), respectively) and diffusion-ordered spectroscopy (DOSY). Calculated solvody-
ꢀ
ꢀ
ꢀ
namic radii (R ) from the latter (10.2 A, 8.4 A and 9.7 A, respectively) indicated formation
S
of assemblies of similar size to the calculated Pd L cage structures. Additionally, isotopic
2
4
patterns consistent with MOPs of these formulas were found by MS. Through-space interac-
tions between the inequivalent coordinating moieties of the ligands were observed by NOESY
1
which, alongside the symmetry of the H NMR spectra, dictated that either the cis or trans
isomers had been formed. Disappointingly, despite multiple attempts, no single crystals suit-
able for study by X-ray diffraction were obtained. Based on the calculated structures and
1
1
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extrapolating from previous work,[45] however, we are confident that the structures obtained
were the anticipated cis-Pd L cages.
2
4
(
a)
b)
(
(c)
(
d)
e)
(
1
0.5
10.0
9.5
9.0
δ (ppm)
8.5
8.0
7.5
(f)
-
-
-
-
-
8
10
10
10
10
10
9
10
11
12
1
0.0
9.5
9.0
δ (ppm)
8.5
8.0
(g)
b
N
a
n
a
o
N
n
o
b
9.4
9
.6
.8
9
10.0
10.2
10.0
9.5
9.0
8.5
8.0
δ (ppm)
1
Figure 7: Partial H NMR spectra (500 MHz, d -DMSO, 298 K) of equilibrated mixtures of 1:2
6
[
Pd(CH CN) ](BF ) and a) 5B4, b) 5A1, c) 4B1, d) 4B3, and e) 5A3. f) DOSY, and g)
3 4 4 2
NOESY (500 MHz, d -DMSO, 298 K) spectra of [Pd (5A3) ](BF ) .
6
2
4
4 4
In the case of 4B3 a major product formed but, even after prolonged heating, multiple
1
species could still be observed by H NMR (Figure 7(d)). Although it could not be de-
termined absolutely, using similar reasoning to that outlined above, it was concluded that
the cis-Pd L cage was the major species present in solution. It was clear that, under the
2
4
conditions examined, the difference in energy between this major species and other potential
products was not sufficient to drive the exclusive formation of a single assembly.
Intriguingly, despite there being less than 3.6 kJ mol 1 difference in energy between the
−
1
2
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4
+
calculated structures of the cis, trans and “three-up-one-down” isomers of [Pd (5A3) ] , a
2
4
single species was found to form upon the self-assembly of 5A3 with Pd(II) (Figure 7(e)).
ꢀ
1
Once again, DOSY (Figure 7(f); R = 10.4 A), MS, the symmetry of the H NMR spectrum
S
and cross-peaks observed by NOESY (Figure 7(g)) led to the conclusion that either the
cis or trans assembly had formed. Disappointingly, without single-crystal X-ray diffraction,
4
+
whether the cis or trans isomer of the [Pd (5A3) ] assembly had formed could not be
2
4
determined with absolute certainty with the spectroscopic data available.
From the five ligands examined experimentally, the calculated cis-Pd L structures of
2
4
three (5B4, 5A1 and 4B1) adhered strictly to our estimated parameter values necessary
for quantitative self-assembly of these assemblies. In each instance, exclusive formation
of a single Pd L isomer was observed and concluded to be the anticipated cis-Pd L by
2
4
2 4
spectroscopic and computational data. For two of the ligands (4B3 and 5A3), the xTB
values of ∆E fell at or below the predicted threshold. Interestingly, the ligand associated
with the lower value of ∆E (5A3) successfully self-assembled into a single Pd L cage isomer,
2
4
whilst the other formed an isomeric mixture. It can be concluded that smaller values of ∆E
make predictions of self-assembly outcomes more precarious. This is likely due to effects
not taken into consideration within the current computational workflow, such as template
effects from anions and/or solvent molecules. Such computationally expensive factors were
purposefully omitted to streamline the process and increase throughput. Higher values of
∆
E, however, appear to be associated with increased experimental success rates and highlight
the efficacy of the workflow for indicating systems with the greatest chance of forming single
isomers of the desired cage topology.
1
3
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Table 1: Calculated properties of the cis isomer of the selected ligands. Energy separations (∆E)
are the difference in energy from the cis isomer to the next most stable isomer at both levels of
˚
theory. Dmax is in A.
−
1
cis isomer
∆E [kJ mol ]
ligand qsqp,min Dmax xTB
DFT
71.0
24.6
21.1
16.0
7.0
experimental outcome
5B4
5A1
4B1
4B3
5A3
0.973 0.023 18.5
0.985 0.003 15.0
0.982 0.020 7.0
0.988 0.030 5.8
0.996 0.005 2.9
cis-Pd L4
2
cis-Pd L4
2
cis-Pd L4
2
isomeric mixture
cis-Pd L4
2
For the five synthesised ligands, we compared the xTB-calculated energy separations of
their isomers with DFT single point calculations and found that the relative energy rela-
tionships were similar (Supporting Information Section S5). The relative stabilities of the
cis isomers do change among these candidates. This suggests that ranking the ability of
each ligand to self-sort using xTB, whilst qualitatively equivalent to DFT, is not quantita-
−
1
tive. Additionally, the value of the relative energy threshold changes from ≈ 6 kJ mol to
−
1
≈
10 kJ mol for the methods applied here based on the energy separation of 5D3. These
[
59]
energy differences are well within DFT error for such complex systems and GFN2-xTB
is not parameterised to produce energies accurately. However, this validation supports that
the suggestions made by the computational rankings would be equivalent if more costly DFT
methods were used.
Low-cost exploration of cage property space
Although five high-ranking candidates were selected for synthesis, models of many potential
assemblies were generated in the computational workflow. This allows for an exploration
of these calculated systems to search for those with desirable structural properties. The
controlled introduction of anisotropy is of particular interest to the development of cages
with advanced functionality.[33] For these Pd L systems, a simple definition of anisotropy
2
4
1
4
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would be the displacement of the Pd(II) centres from alignment perpendicular to the PdN4
planes (∆ , shown inset in Figure 8(a)). For Pd L systems assembled from symmetrical
Pd
2 4
˚
ligands, ∆Pd should be 0 A. To this end, an analysis of ∆ values compared to Pd· · ·Pd
Pd
distance (Figure 8(a)) and pore size[73] (Figure 8(b)) was undertaken; example structures
with increasing anisotropy are shown in Figure 8(c).
(a)
(b)
N
Pd2+ N
ΔPd
6C1
6C1
4
A2
N
Pd2+ N
4A2
A2
5
A2
5
3
C2
3C2
5
D2
5D2
3B1
3
B1
(c)
3B1 5D2
3C2
5A2
anisotropy
4A2
6C1
Figure 8: Cage anisotropy (∆ ) as a function of (a) Pd· · ·Pd distance (∆ schematic inset)
Pd
Pd
and (b) pore diameter (only cages with qsqp,min > 0.9 shown). (c) Example cages with increasing
anisotropy; none of these examples were synthesised and are not necessarily thermodynamically
favourable structures.
[
45]
The combined family of cis-Pd L cages previously reported
and realised in this work
2
4
are represented within this analysis. A diverse anisotropy-property space is demonstrated
˚
˚
with ∆Pd values ranging from 1.2 to 7.2 A and Pd···Pd distances between 9.3 and 11.3 A. The
successfully synthesised cages also show interesting, non-linear, relationships between their
size (Pd···Pd) and calculated pore diameter (using a spherical probe), which we expect to be
a crucial property to control for the application of reduced-symmetry cages. The calculated
cis-Pd L structures from ligands 4A2 and 6C1, for example, are of interest as they represent
2
4
high-anisotropy assemblies with large and small pore diameters, respectively. Indeed, cis-
1
5
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4
+
[
Pd (6C1) ] possesses two effectively isolated binding pockets within the cavity, in contrast
2 4
4
+
to the large, single pore of cis-[Pd (4A2) ] (Figure 8(c)).
2
4
Conclusion
The synthesis and investigation of unsymmetrical Pd L assemblies with asymmetric pores,
2
4
with potential utility in high specificity and affinity guest binding properties, is a growing
field. The design of such systems to ensure high-fidelity self-assembly, however, remains non-
trivial. Here we have shown that a simple and low-cost computational workflow can be used
to inform decisions in experimental work, resulting in a “high hit-rate” synthesis of targeted
unsymmetrical cis-Pd L cages. The open-source and generalisable computational procedure
2
4
provided efficient, and sufficiently accurate, predictions of cage structures starting from a
combinatorially constructed library of 60 unsymmetrical ligands. Using a computational
ranking scheme based on a small number of cheap and calculable metrics (parameterised
based on limited existing experimental results), we have realised four previously unreported
low-symmetry, cis-Pd L cages, greatly expanding the existing repertoire of these systems
2
4
and validating our workflow. Additionally, this work is a platform for further exploring the
chemical space of unsymmetrical Pd L assemblies. In this manner, the synthetic chemist
2
4
can choose ligands and/or cages with desirable properties with confidence in the reliability
of their self-assembly profile.
It was shown that a hierarchical and combinatorial computational screening approach,
facilitated by open-source software, allowed the construction of large precursor and cage
libraries for high-throughput screening. While focussed initially on a limited number of
common building blocks, expanding the initial precursor library is trivial because the only
required inputs to the automated workflow are SMILES strings. Additionally, the use of
common building blocks did not limit the generation of unconventional and novel unsym-
metrical cage ligands in this work. The applied computational workflow can be generalised
to future problems to explore a much larger chemical space of metal-organic cages and other
materials classes.
Finally, our experimental efforts led to one ligand out of five for which self-assembly with
1
6
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Pd(II) did not produce a single species. In agreement with the metrics employed, however, a
single cage isomer did appear to be predominate. This highlights that the heuristics applied
do not capture all of the necessary information to ensure absolute fidelity of self-sorting, and
we suggest that the role of ligand flexibility and explicit solvent/counter-ion templation could
be significant. However, given the simplicity and high-throughput nature of this approach,
it is remarkably effective for informing experimental decisions. As experimental data in this
field is still limited, additional information obtained from this and future studies will help
recognise metrics of importance to incorporate into the workflow, leading to a refinement
of the process. Ultimately this will lead to improved certainty in future synthetic decisions
using a joint computational and experimental discovery workflow.
Code Availability
All code used in this work is available at https://github.com/andrewtarzia/unsymm_
match.
Data Availability
All structure data and ligand ranking is available at https://github.com/andrewtarzia/
citable_data/tree/master/tarzia_lewis_2021.
Acknowledgements
KEJ thanks the Royal Society for a University Research Fellowship and a Royal Society En-
hancement Award 2018, and the ERC through Agreement Number 758370 (ERC-StG-PE5-
CoMMaD). JEML is grateful for an Imperial College Research Fellowship. This work used
the ARCHER2 UK National Supercomputing Service (https://www.archer2.ac.uk) via the
UK’s HEC Materials Chemistry Consortium, which is funded by the EPSRC (EP/L000202,
EP/R029431, EP/T022213). Dr Lukas Turcani is thanked for assistance with stk and stko
development. Dr Alejandro Santana-Bonilla is thanked for assistance with DFT calculations.
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7
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Dr Nike Dattani and Andrew Rosen are thanked for online discussions. Professor Matthew
J. Fuchter is thanked for useful discussions and access to equipment and resources.
Conflicts of Interests
The authors declare no conflicts of interests.
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ligand assembly
cage assembly + ranking
ligand design
i
j
k
N
N
i != k
synthesis
computation experiment
2 4
computer-aided system design of anisotropic M L cages
Towards the development of sophisticated metal-organic hosts, low-symmetry
metallo-supramolecular cages assembled from unsymmetrical ligands are of emerging
interest. Designing systems to avoid forming isomeric mixtures, however, is challenging.
We report the use of a rapid computational workflow to predict self-assembly outcomes,
informing experimental decisions and optimising synthetic realisation of low-symmetry,
cis-Pd L cages.
2
4
2
4
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