Artificial intelligence solves the Schrödinger equation

Jan Hermann, Zeno Schätzle and Frank Noé, researchers at the Freie Universität Berlin, have made an important advance by applying deep learning to quantum chemistry: the electronic Schrödinger equation can only be solved analytically for the hydrogen atom, but their neural network, PauliNet, obtains nearly exact numerical solutions for molecules with up to 30 electrons. Quantum chemistry aims to predict chemical and physical properties from the arrangement of a molecule's atoms in space, without consuming huge amounts of computing resources.

The research team's method in Berlin produced nearly exact numerical solutions of the equation for molecules with up to 30 electrons, something earlier methods could only do at an enormous computational cost. These results open up new opportunities in chemical science.

The wave function is a representation of the behavior of the electrons in a molecule, it depends on a large number of variables, which makes it difficult to specify this function and, in turn, leads to inaccurate results, limiting the fundamental predictions of chemical methods. Both the Schrödinger equation and quantum chemistry depend on the wave function.

Hermann, Schätzle and Noé decided to develop a deep learning method, which makes it possible to obtain nearly exact solutions of the equation at a moderate computational cost. The team's neural network can represent the wave functions of electrons. Instead of a standard approach built from simple mathematical components, they opted for a network that learns the more complex patterns of how electrons are arranged around nuclei.

Since then, neural-network wave functions have grown into a field of their own within quantum chemistry, and these methods now also compute excited states and several molecular geometries at once. Hermann and Noé reviewed this progress with other researchers in “Ab initio quantum chemistry with neural-network wavefunctions”, published in Nature Reviews Chemistry in 2023.

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