Artificial intelligence solves Schrödinger’s equation, a fundamental problem in quantum chemistry

A team of scientists from Freie Universität Berlin have developed an artificial intelligence (AI) method to calculate the ground state of the Schrödinger equation in quantum chemistry. The goal of quantum chemistry is to predict the chemical and physical properties of molecules based solely on the arrangement of their atoms in space, thus avoiding the need for resource-intensive and time-consuming laboratory experiments. In principle, this can be achieved by solving the Schrödinger equation, but in practice it is extremely difficult.

Until now, it was impossible to find an exact solution for arbitrary molecules that can be calculated efficiently. But the Freie Universität team has developed a deep learning method that can achieve an unprecedented combination of precision and computational efficiency. AI has transformed many fields of technology and science, from computer vision to materials science. “We believe our approach can have a significant impact on the future of quantum chemistry,” says Professor Frank Noé, who led the team effort. The results were published in the reputable journal Chemistry of nature.

The wave function is at the heart of quantum chemistry and the Schrödinger equation – a mathematical object that completely specifies the behavior of electrons in a molecule. The wave function is a large-dimensional entity, and therefore it is extremely difficult to capture all of the nuances that code how individual electrons influence each other. Many methods of quantum chemistry in fact forgo completely expressing the wave function, instead trying to determine only the energy of a given molecule. However, this requires approximations, limiting the quality of prediction of such methods.

Other methods represent the wave function with the use of an immense number of simple mathematical building blocks, but these methods are so complex that they are impossible to practice for more than just a handful of atoms. “Escaping the usual compromise between precision and computational cost is the greatest achievement in quantum chemistry,” explains Dr Jan Hermann of Freie Universität Berlin, who devised the main features of the method in the study. “The most popular outlier to date is the extremely profitable density functional theory. We believe that the deep “Quantum Monte Carlo” approach we are proposing could be just as, if not more effective. It offers unprecedented precision at a still acceptable computational cost. “

The deep neural network designed by Professor Noé’s team is a new way of representing the wave functions of electrons. “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 electrons localization around nuclei,” Noah explains. “A particular characteristic of electronic wave functions is their antisymmetry. When two electrons are exchanged, the wave function must change sign. We had to integrate this property into the architecture of the neural network for the approach to work, ”adds Hermann. This feature, known as the “Pauli Exclusion Principle”, explains why the authors called their method “PauliNet”.

Apart from the Pauli exclusion principle, electronic wave functions also have other fundamental physical properties, and much of PauliNet’s innovative success is that it integrates these properties into the deep neural network, rather than leaving deep learning understand them by simply observing the data. “The integration of fundamental physics into AI is essential for its ability to make meaningful predictions in the field,” says Noah. “This is really where scientists can make a substantial contribution to AI, and that’s exactly what my group is focusing on.”

There are still many challenges to overcome before the Hermann and Noah method is ready for industrial application. “It’s still basic research,” agree the authors, “but it’s a new take on an age-old problem in molecular and material sciences, and we’re excited about the possibilities it opens up.

Reference: “Deep Neural Network Solution of the Schrödinger Electronic Equation” by Jan Hermann, Zeno Schätzle and Frank Noé, September 23, 2020, Chemistry of nature.
DOI: 10.1038 / s41557-020-0544-y