One of the greatest strengths of MOFs is their versatility; there are over 90,000 of them, growing by nearly 10% a year, and these structures vary widely in their properties. This means materials exist that can serve a huge range of different functions, but it also poses a challenge: finding the right MOF for the task amongst the thousands of candidates.

We solve this problem using molecular simulations to predict material performance. To do this, we use databases of existing MOF structures and model how molecules interact with the surface charges on each. By varying the conditions, such as the pressure and temperature, and combining the results with what we know about each material we can rapidly build up a picture of what the best candidate materials are and – more generally – what’s important for a material to perform well. To demonstrate the power of this tool, we picked a simple example, the storage of oxygen, and worked to find a material that was optimised for the task.

One of the most important steps here is asking the right question, as this frames what constitutes “best”. Even when considering the simple storage of a single gas, which is more important for the application: volumetric storage capacity, or gravimetric? What temperature/pressure will the gas be stored at, and what is the minimum pressure the system can still deliver gas? For our purposes, we focused mainly on optimising deliverable volumetric capacity (usually the most important quantity) for a system operating between 5 and 140 bar at room temperature. We picked these because they were reasonable conditions for a portable oxygen tank, and because they allowed us to compare with existing literature.

By screening 3,000 of the top materials (Figure 1), we identified a number of relationships between the properties of each MOF and its performance. These relationships extend beyond simple O_{2} storage, and nicely illustrate some of the key considerations for optimising a material for any system.

Figure 1: The deliverable capacity between 140 bar and 5 bar simulated for 3,000 known materials. Capacity is given on a gravimetric (per-weight) basis on the x-axis, and a volumetric basis on the y-axis. Void fraction is denoted by the colour scale, and the largest cavity diameter by the size of each circle.

The simplest properties we can compare between materials are the surface area, the density, the largest cavity diameter (the size of the largest – or only – pore), and the void fraction (the proportion which is hollow). Some of these are easy to relate to the performance we might expect – a higher surface area, for example, gives more surface for the gas to adsorb. Similarly, a less dense material should give a better gravimetric capacity, other things being equal. But by the same token, a less dense material also occupies more space, offering poorer *volumetric* capacity. The key lesson is that material properties are inescapably linked to one another and seeking to optimise for one will force trade-offs. With this in mind, the next question becomes: so which properties matter?

It turns out that the relative importance of a given property is heavily dependent on the conditions you specify. Figure 2 shows, for the top 1% of MOFs at a given pressure, the distribution of values in each of the four properties already mentioned. It is immediately clear that the optimal value in any metric changes depending on the pressure, and furthermore that the values become more constrained at one pressure extreme or another. For instance, the surface areas of the best MOFs have a range of values spanning over 1000 m^{2}/g at 30 bar, yet less than 200 m^{2}/g at 200 bar. Similarly, while the largest cavity diameter must be kept small at lower pressures, as the pressure rises – though it does increase – the precise value becomes less and less important.

Figure 2: Optimal geometric properties for the top 1% of MOF structures. These are shown as box and whisker plots for a) largest cavity diameter, b) void fraction, c) surface area, and d) density, at four increasing pressures. The markers on each box show the minimum, first quartile, median, third quartile, and maximum values.

The trends we uncovered are intuitive: it makes sense, for example, that at higher pressures a greater void fraction will offer more space for the gas to occupy, and that a higher void fraction inescapably forces a trade-off with density. What is perhaps less obvious is what this means for the materials we choose, which can be highly specific to the task they serve: for instance, the best MOF at 30 bar ranked 280^{th} at 140 bar. Considering a more complicated system, such as multi-gas separation, we can see that choosing to run a process under a different set of conditions can dramatically impact its effectiveness – and therefore a material’s suitability.

This is undoubtedly a major source of complexity, and designing any solution where the conditions are not already constrained may need a deal of iteration between the material selection, the process engineering, and the economics. But understanding these structure-property relationships takes a deal of the guesswork out of this iteration, allowing us to intelligently guide each successive round of simulation conditions. In doing so, we can harness this complexity and turn it into an asset, because no other material class offers us so wide a design space as we have with MOFs.

In the end, we took the best material our simulations predicted, and we synthesised it. Its performance matched the simulations to within 0.2%, and it broke the world record, beating the incumbent by 23%. You can learn more about how we did it and what we learned in our paper, which we published in **Nature Communications **in 2018.