We will need to build new materials with specific qualities if we are to meet some of the biggest problems of the 21st century, such as creating clean power or manufacturing high temperature superconductors. Electrons, the subatomic particles that regulate the bonding of atoms to create molecules and are also responsible for the flow of electricity in solids, must be simulated in order to accomplish this in a computer. Accurately modeling the quantum mechanical behavior of electrons remains an ongoing issue after decades of work and numerous notable improvements. We now offer DM21, a neural network with state-of-the-art accuracy on vast sections of chemistry, in a publication (Open Access PDF) published in Science. We are also making our code freely available to the scientific community as a means of hastening its development.

Erwin Schrödinger’s well-known equation for the behavior of quantum mechanical particles was first proposed over a century ago. It is difficult to apply this equation to the electrons in molecules due to the fact that they all oppose each other. This appears to need for keeping tabs on the likelihood of each electron’s location, which is a fairly complicated operation for even a modest number of electrons. In the 1960s, Pierre Hohenberg and Walter Kohn made a breakthrough when they realized that following each electron individually is unnecessary. Instead, it is sufficient to know the chance of any given electron being at each point (i.e., the electron density) in order to precisely calculate all interactions. After demonstrating this, Kohn established Density Functional Theory (DFT) and won the Nobel Prize in Chemistry for his efforts.

Despite the fact that density functional theory (DFT) provides conclusive proof of the existence of a mapping, the precise form of this mapping between electron density and interaction energy (the so-called density functional) has remained unclear for over 50 years, necessitating approximations. DFT is one of the most extensively utilized methods in research despite the fact that it is based on an approximation and is thus the only viable option to investigate the origins of matter’s macroscopic behaviors. Many less-than-precise approximations to the exact functional have been developed by researchers throughout the years. While convenient, these approximations all fall short of the precise functional in one important respect: they fail to represent key mathematical aspects of the functional.

We develop functionals free from key systematic mistakes by encoding the functional as a neural network and including these precise features in the training data, leading to a more accurate representation of a large set of chemical processes.

We focus on fixing two issues that have persisted for a long time in conventional functionals:

The delocalization error: A DFT functional finds the electron configuration that minimizes energy, hence determining the charge density of a molecule. Therefore, the predicted electron density might be off if the functional is flawed. See Fig. 2 for an illustration of how current density functional approximations favor electron concentrations that are unnaturally dispersed across several atoms or molecules rather than being appropriately focused around a single atom or molecule.

Existing functionals have a tendency to unreasonably favor configurations in which a basic symmetry known as spin symmetry is disrupted when modeling the cleavage of chemical bonds. Given the importance of symmetries to the study of physics and chemistry, this artificial symmetry breaking highlights a serious shortcoming in the state of the art in terms of functionals.

Delocalization error may occur in any chemical or physical process that includes the transfer of charge, and spin-symmetry breaking can occur in any process that involves the dissolution of chemical bonds. Despite the centrality of charge transfer and bond breaking in several practical technologies, these issues can result in the qualitative inability of functionals to represent even the simplest molecules, like hydrogen. In order to ask DFT to explain far more complex molecular interactions, such those that may occur in a battery or solar cell, it is necessary to first build functionals that get this fundamental chemistry right.

Figure 2 | Left: According to the standard functional (B3LYP), charge is spread out over two neighboring molecules. Correct: The modeled functional (DM21) accurately identifies the location of charge on a single molecule.

Both of these vexing problems have to do with the behavior of functionals in a system with “fractional electron character.” We showed that the issues of delocalization and spin symmetry-breaking may be addressed by utilizing a neural network to represent the functional and by customizing our training dataset to capture the fractional electron behavior predicted for the precise functional. Moreover, our functional demonstrated remarkable accuracy on general-purpose, large-scale benchmarks, indicating that our data-driven method may capture hitherto elusive facets of the precise functional.

Modern engineering relies heavily on computer simulations, which have been used for years to answer problems like “will this bridge stay up?” questioning “will this rocket reach orbit?” As the search for new materials, drugs, and catalysts moves to the quantum scale, deep learning shows promise as a tool to correctly model matter at this quantum mechanical level.