Deepmind Open-Sources DM21: A Deep Learning Model For Quantum Chemistry

Deepmind Open-sources ‘DM21’, a neural network model for mapping electron density to chemical interaction energy, a critical component of quantum mechanical modeling. DM21 outperforms standard models on various benchmarks, and it’s accessible as a PySCF simulation framework addition. 

In a paper published in Science, the model was detailed. The energy density functional component of Density Functional Theory (DFT), which describes the quantum mechanical behavior of molecules, is approximated by DM21 using a neural network. DM21 corrects systemic flaws in prior functional approximations, which failed to treat systems with “fractional electron character” appropriately. The model uses a multilayer perceptron (MLP) architecture with a grid of electron densities. It surpassed four of the “highest performing” current implementations on three benchmark datasets: Bond-breaking Benchmark (BBB), GMTKN55, and QM9.

Deep learning shows promise in precisely simulating matter at the quantum mechanical level, as technology increasingly turns to the quantum scale to investigate concerns concerning materials, medicines, and catalysts, even ones we’ve never seen or even imagined.


Quantum physics’ fundamental concepts to the prediction of chemical characteristics of molecules. DFT simplifies quantum chemistry calculations for scientists, but it requires a functional mapping from electronic probability densities to energy. Although no perfect functional exists, approximation functionals have been employed in domains ranging from solid-state physics to nuclear spectroscopy for many years. 

However, most of the approximations in use run into “pathological errors” in systems with fractional electron properties, such as fractional charge (FC) or fractional spin (FS). Although fractional electrons are a made-up concept, specific real-world systems actually have areas that behave in an FC or FS manner. The team used machine learning to solve the problem since manually developing functionals to handle such scenarios proved impossible. 

Although DFT confirms the existence of mapping, the precise form of this mapping between electron density and interaction energy — the so-called density functional — has remained unknown for more than 50 years and must be estimated.

Two issues with classical functionals that have been there for a long time:

  • The delocalization error is as follows: The functional finds the electron configuration in a DFT computation that minimizes energy and calculates the charge density.
  • Functional faults can cause mistakes in the computed electron density. Instead of accurately concentrated around a single molecule or atom, most present density functional approximations favor electron concentrations that are unreasonably spread out over numerous atoms or molecules.

Many major technological applications rely on charge movement and bond breakage. Yet, the same issues can also result in enormous qualitative failure of functionals to represent the simplest molecules, such as hydrogen.

Because DFT is such an essential technology, it’s critical to create functionals that understand this introductory chemistry before asking them to describe far more complicated molecular interactions, such as those found in a battery or solar cell. 

The researchers used a supervised learning technique to train an MLP neural network. The training dataset included 1161 Kohn-Sham (KS) orbital characteristics sampled on a spatial grid as inputs and “high-accuracy reaction energies” as outputs. A regression loss and a gradient regularization term were incorporated in the training goal, the latter so that the model may be employed in self-consistent field (SCF) computations. 


The scientists tested DM21 against three other benchmarks, including GMTKN55 and QM9, which provide data for chemical tasks that are “quite different” from the training data. DM21 outperformed four other earlier approaches on these benchmarks, setting a new state-of-the-art performance. DM21 outperforms the best hybrid functional and approaches the performance of the far more costly double-hybrid functionals. 

Machine learning in physics and chemistry is a hot topic of research.

Stanford University researchers trained a convolutional neural network (CNN) for use as a DFT functional in 2019 and found that it performed well for “a broad collection of organic compounds.” InfoQ covered Caltech’s use of machine learning to solve Navier-Stokes equations in 2020 and DeepMind’s AlphaFold2 AI for protein structure prediction in 2021.