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# How to create designer materials

Finding ways to improve a material, let alone creating a brand new one, is experimentally challenging and requires time, money and resources.
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To understand and improve the materials we use in the world around us, and even to design brand new materials, sometimes with properties we’ve never seen before, we need to understand matter at the most fundamental level – the level of quantum physics. To understand a material’s properties, we need to know how its electrons behave, because it’s the electrons which govern the atomic structure and the chemical bonds which hold the material together. But electrons are quantum particles, so this means solving the Schrodinger equation to determine their wavefunction. The wavefunction tells you everything about the electrons, but it depends on all of the possible positions of all the electrons.
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If you only have one electron, this isn’t too bad – you might even be able to solve the equation directly, but in general we have to solve it numerically using a computer. The computer calculates the wavefunction at particular points in space – for example, a 10 x 10 x10 grid of points over a small region, so 1000 points in total. Let’s add a second electron, though. Now the wavefunction depends on the positions of both electrons, so we can’t just calculate the 1000 data points of electron 1’s position any more – we need all the combinations of the positions of the two electrons, which means 1000 x 1000 = a million data points.
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If we add a third electron, the wavefunction depends on all three positions, so we have 1000 x 1000 x 1000 – a billion data points. In fact, every electron we add needs us to compute and store a thousand times more data. Even if each data point only needs 1 byte of information, we would exhaust the whole of the world’s data storage by the time we got to 7 electrons – that’s just one atom of nitrogen. So how can we possibly model a real material with quantum mechanics? In 1964 there was a breakthrough in quantum theory, we call density functional theory, or DFT, which proved that we only need the probability density of the electrons – not the full wavefunction.
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The probability density tells you how many electrons you expect to find at each point in space, so it doesn’t depend on the positions of every individual electron, just the position in space – 1000 data points, in our earlier example. If I add another electron to my system, then the probability density changes – but it still only depends on the position in space, so you still only have 1000 data points. The data changes when you add an electron, but the amount of data stays the same. Remember that system of 7 electrons, that single atom of nitrogen, which needed the whole of the world’s data storage?
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With DFT, we can routinely simulate dozens of atoms on a laptop, and hundreds, even thousands of atoms on a supercomputer. DFT modelling software has become so important that it’s used by thousands of companies across the globe to develop and improve materials and chemicals for pretty much every use you can imagine, including solar cells, batteries, catalysts, medicines everything from stain-resistant tap coatings to rocket fuel.

Finding ways to improve a material, let alone creating a brand new one, is experimentally challenging and requires time, money and resources. This effort is only worthwhile if the final material has desirable properties.

## The need for quantum mechanics

Therefore we need to be able to predict the properties of materials before they are made, in order to focus the effort where it will be most useful. For many properties, such as electrical conductivity, optical absorption, or chemical bonding, this means predicting the behaviour of the material’s electrons – and this requires quantum mechanics.

The behaviour of an electron is described by an equation called the Schrödinger equation – named after the famous physicist.

## Density functional theory

If we try to solve the Schrödinger equation numerically, this requires enormous computational resources to model even a small number of electrons. Density functional theory (DFT) provides a practical way forward here. In DFT, we only need to know the electron density – the probability of finding electrons in a particular place. This means that there is no need to compute data for every individual electron, requiring much less computing power and still leading to very accurate computer simulations of materials.

The success and widespread use of DFT is not only due to the theory itself, but also the development of fast, reliable, user-friendly simulation software. CASTEP software combines advances in theoretical quantum physics with cutting-edge research software engineering. It is enabling scientists in universities and businesses alike to design materials at the atomic scale, ushering in a new golden age for advanced materials research.