A team led by scientists from London-based artificial intelligence firm DeepMind has developed the first machine learning model that suggests characteristics of a molecule by predicting the distribution of electrons within it. The approach, described in the December 10 issue of *Science*^{1}, can calculate the properties of certain molecules with more precision than existing techniques.

“Making it as precise as they did is a feat,” says Anatole von Lilienfeld, materials scientist at the University of Vienna.

The article is “solid work,” says Katarzyna Pernal, a computational chemist at Lodz University of Technology in Poland. But she adds that the machine learning model still has a long way to go before it can be of use to computational chemists.

## Predict properties

In principle, the structure of materials and molecules is entirely determined by quantum mechanics, and more precisely by the Schrödinger equation, which governs the behavior of the wave functions of electrons. These are the mathematical gadgets that describe the probability of finding a particular electron at a particular position in space. But because all electrons interact with each other, calculating the structure or molecular orbitals from these first principles is a computer nightmare and can only be done for the simplest molecules, such as benzene, explains James Kirkpatrick, physicist at DeepMind.

To get around this problem, researchers – from pharmacologists to battery engineers – whose work relies on the discovery or development of new molecules have relied for decades on a set of techniques called density functional theory (DFT) to predict the physical properties of molecules. The theory does not attempt to model individual electrons, but rather aims to calculate the overall distribution of the negative electric charge of electrons across the molecule. “DFT looks at the average charge density, so it doesn’t know what individual electrons are,” Kirkpatrick explains. Most of the properties of matter can then be easily calculated from this density.

Since its inception in the 1960s, DFT has become one of the most widely used techniques in the physical sciences: a survey by *Nature*The 2014 press team found that of the top 100 newspapers, 12 were about DFT. Modern databases of material properties, such as the Materials Project, consist to a large extent of DFT calculations.

But the approach has limitations and is known to give erroneous results for certain types of molecules, even some as simple as sodium chloride. And although DFT calculations are much more efficient than those that start from basic quantum theory, they are still cumbersome and often require supercomputers. Thus, during the last decade, theoretical chemists have increasingly started to experiment with machine learning, in particular to study properties such as the chemical reactivity of materials or their capacity to conduct heat.

## ideal problem

The DeepMind team has made possibly the most ambitious attempt to date to deploy AI to calculate electron density, the end result of DFT calculations. “This is sort of the ideal problem for machine learning: you know the answer, but not the formula you want to apply,” says Aron Cohen, a theoretical chemist who has worked on DFT for a long time and is now at DeepMind.

The team trained an artificial neural network using data from 1,161 precise solutions derived from Schrödinger’s equations. To improve accuracy, they also hardwired some of the known physical laws in the network. They then tested the driven system on a set of molecules that are often used as a benchmark for DFT, and the results were impressive, says von Lilienfeld. “It’s the best the community has come up with, and they beat it by a long shot,” he says.

One of the benefits of machine learning, adds von Lilienfeld, is that while it takes a huge amount of computing power to train the models, this process only needs to be done once. Individual predictions can then be made on a regular laptop, dramatically reducing their cost and carbon footprint, compared to the need to perform calculations from scratch every time.

Kirkpatrick and Cohen say DeepMind is releasing its trained system for anyone to use. For now, the model mainly applies to molecules and not to the crystal structures of materials, but future versions could work for materials as well, according to the authors.