Artificial Intelligence solves the Schrödinger Equation, a Basic Problem in Quantum Chemistry

Scientists at the Freie Universität Berlin are developing in-depth study methods to solve fundamental problems in quantum chemistry.

A team of scientists at the Freie Universität Berlin has developed an intelligent method (AI) for calculating the basic state of the Schrödinger equation in quantum chemistry. The purpose of quantum chemistry is to estimate the chemical and physical properties of molecules based solely on the arrangement of atoms in space, avoiding the need for effective and time-consuming laboratory experiments. In principle, this can be achieved by solving the Schrödinger equation, but in practice this is very difficult.

Until now, it has been impossible to find a definite solution for arbitrary molecules that can be calculated efficiently. But the team at Freie Universität has developed a deep learning method that can achieve combinations that have never been better accuracy and computational efficiency. AI has changed many fields of technology and science, from computer vision to material science. “We believe that our approach can significantly affect the future of quantum chemistry,” said Professor Frank Noah, who led the team’s efforts. The results were published in a well-known journal Natural Chemistry,

The center of quantum chemistry and Schrödinger equations is the function of waves – mathematical objects that completely determine the behavior of electrons in a molecule. Wave function is a high-dimensional entity, so it is very difficult to capture all the nuances that encode how each electron affects each other. Many quantum chemical methods in fact give up on expressing the function of all waves, rather than simply trying to determine the proper molecular energy. However, estimates need to be made, limiting the predictive quality of such methods.

Other methods represent wave function by the use of a number of simple mathematical blocks, but such methods are so complex that it is impossible to implement more than a few atoms. “Freeing trade-offs between accuracy and computational cost is one of the highest achievements in quantum chemistry,” explains Dr. Jan Hermann from Freie Universität Berlin, who designed the key features of the method in teaching. “Yet, the most popular of such is the very compact density theory of functionality. We believe that the” Quantum Monte Carlo, “approach we propose, can be the same, if not more successful. accepted. “

The deep neural network designed by Professor Noah’s team is a new way to describe electron wave function. “Instead of the standard approach of arranging wave functions from relatively simple mathematical components, we designed artificial neural networks that can study the intricate patterns of how electrons are located around the nucleus,” explains Noah. “One of the unique features of the electronic wave function is its antimony. When two electrons are exchanged, the wave function must replace the mark. We must build these properties into the neural network architecture to approach the path,” adds Hermann. This feature, known as the “Pauli exclusion principle,” is why the author calls his method “PauliNet.”

In addition to the principle of Pauli exclusion, electronic wave function also has a fundamental physical property, and many of PauliNet’s innovative successes are that it integrates these properties into deep neural networks, rather than letting them study deeply just by observing data. “Building basic physics into AI is crucial to its ability to make meaningful predictions in the field,” said Noah. “This is exactly where scientists can make important contributions to AI, and exactly what my group is focusing on.”

There are still many challenges to overcome before the Hermann and Noah methods are ready for industrial applications. “This is still a basic research,” the authors agree, “but it is a fresh approach to the old problems in molecular science and materials, and we are interested in the possibility of it being opened.”

References: “Internal network solutions of electronic Schrödinger equations” by Jan Hermann, Zeno Schätzle and Frank Noé, September 23, 2020, Natural Chemistry,
DOI: 10.1038 / s41557-020-0544-y

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