Researchers from Freie Universität Berlin have developed an artificial intelligence method for calculating the ground state of the Schrödinger equation. This Schrödinger equation is one of the fundamental problems in quantum chemistry. The goal of quantum chemistry is to predict the chemical and physical properties of molecules based entirely on the arrangement of their atoms in space.
Being able to do so would eliminate the need for resource-intensive and time-consuming laboratory experiments. In principle, solving the Schrödinger equation would allow the prediction of properties of molecules based on the arrangement of their atoms in space. However, solving the equation is extremely difficult. Researchers say that it’s been impossible to find an exact solution for arbitrary molecules that can be efficiently computed until now.
The researchers developed a deep learning method to achieve a combination of accuracy and computational efficiency that’s unprecedented. One researcher on the project says that the team believes their approach could significantly impact the future of quantum chemistry. One of the central tenets of the Schrödinger equation and quantum chemistry, in general, is the wave function. We function as a mathematical object that completely specifies the behavior of electrons of a molecule.
The challenge is that wave function is a high dimensional construct, and it is extremely difficult to capture all the nuances that encode individual electrons and how they may affect each other. The deep neural network that the researchers developed is a new way of representing the wave functions of electrons. The team says instead of the standard approach of composing the wave function from relatively simple mathematical components, the artificial neural network can learn the complex patterns of how electrons are located around a nuclei.
The team notes that a peculiar feature of electronic wave functions is high asymmetry. When two electrons are exchanged, wave functions have to change their sign. The team had to build the property into the neural network architecture for their approach to work. That features are known as Pauli’s exclusion principle and is why the neural network was dubbed “PauliNet.” Research into the neural network is ongoing.