The Schrödinger Equation is a crucial formalism at the center of quantum mechanics. It is used to work out how quantum systems are, and how they evolve. It is also very much a challenge to solve precisely for a system made of more than a few particles, with approximations use in most cases.

Computational methods are used to solve the equation for many systems, and a new study published in Nature Chemistry has put forward a new method. The approach, called PauliNet, is a deep neural network that can get the exact solution for the equation for molecules with up to 30 electrons.

This AI is based on the Monte Carlo method, which uses random sampling to deliver numerical results of a mathematical function. This particular version was built with the knowledge of physical laws, including the important Pauli exclusion principle. The algorithm is named after this law.

Solving the equation can provide insights into the formation and behavior of molecules that several of the current methods can’t provide. This has often been too laborious to be worth it, hence why this method could be a game-changer.

"Escaping the usual trade-off between accuracy and computational cost is the highest achievement in quantum chemistry," lead author Dr. Jan Hermann of Freie Universität Berlin, said in a statement. "As yet, the most popular such outlier is the extremely cost-effective density functional theory. We believe that deep 'Quantum Monte Carlo,' the approach we are proposing, could be equally, if not more successful. It offers unprecedented accuracy at a still acceptable computational cost."

PauliNet allows for a solution of the Schrödinger Equation to be found for arbitrary molecules. The versatility and strong physical backbone of the software deliver these results. The equation is a mathematical description of the quantum state known as the wave function, and translating this wave function for many electrons into a computer language was not easy.   

"Instead of the standard approach of composing the wave function from relatively simple mathematical components, we designed an artificial neural network capable of learning the complex patterns of how electrons are located around the nuclei," added Professor Frank Noé, who led the team effort.

There are still many kinks to iron out, but the researchers are excited about the possibilities of this algorithm.

"This is still fundamental research," the authors agree, "but it is a fresh approach to an age-old problem in the molecular and material sciences, and we are excited about the possibilities it opens up."