Artificial intelligence solves the equation of Schrödinger, a basic question in quantum chemistry,

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In order to solve a fundamental problem in quantum chemistry, scientists at Freie Universität Berlin are developing a deep-learning system.

An artificial intelligence (AI) method has been developed by a team of scientists at Freie Universität Berlin to measure the ground state of the Schrödinger equation in quantum chemistry.

The aim of quantum chemistry is to predict molecules’ chemical and physical properties based solely on the arrangement of their atoms in space, removing the need for laboratory experiments that consume energy and time.

This can be done in theory by resolving the Schrödinger equation, but this is exceedingly difficult in practice.

Until now, for arbitrary molecules, it has not been possible to find an exact solution that can be measured effectively.

But a deep learning approach has been developed by the team at Freie Universität that can achieve an incredible combination of precision and computational efficiency.

Many technical and scientific areas have been changed by AI, from computer vision to materials science. “We believe our approach can have a significant impact on the future of quantum chemistry,” said Professor Frank Noé, who led the work of the team.

The findings were published in Nature Chemistry, a respected journal.

The wave function – a mathematical object which completely specifies the action of electrons in a molecule – is at the heart of both quantum chemistry and the Schrödinger equation.

The wave function is a high-dimensional entity, and all the complexities that encode how individual electrons interact are therefore extremely difficult to capture. In reality, many quantum chemistry methods completely forgo the representation of the wave function and instead try only to determine the energy of a specific molecule.

This, however, allows approximations to be made, restricting the predictive quality of such techniques.

Other methods describe the function of the wave using an unmanageable number of basic mathematical building blocks, but such methods are so complicated that more than a handful of atoms can not be put into operation. The ultimate achievement in quantum chemistry is to avoid the normal trade-off between accuracy and computational expense,”Escaping the usual trade-off between accuracy and computational cost is the ultimate achievement in quantum chemistry,” The most common escape method of this kind so far is the functional theory of extremely low-cost density.

We assume that the deep quantum ‘Monte Carlo’ technique we propose could be just as, if not more, effective.

At still reasonable computing costs, it provides unparalleled precision.

A new way to describe the wave functions of electrons is the deep neural network developed by the team of Professor Noé. “Instead of the standard approach of assembling the wavefunction from relatively simple mathematical components, we designed an artificial neural network capable of learning the complex patterns of how electrons are located around nuclei,” Noé explains. Their antisymmetry is a special feature of electronic wavefunctions.

The wave function must alter the sign when two electrons are exchanged.

“For the approach to work, we had to incorporate this property into the neural network architecture,” adds Hermann.

This property, known as “Pauli’s exclusion principle,” is why the authors called “PauliNet.” as their system.

Electronic wavefunctions have other fundamental physics properties in addition to the exclusion principle of Pauli, and a significant part of the groundbreaking success of PauliNet is that it incorporates these properties into the deep neural network rather than using Deep Learning to find them out by analyzing the data alone. “Integrating fundamental physics into AI is essential to its ability to make meaningful predictions in practice,” Noé says. “That’s really where scientists can make a significant contribution to AI, and exactly what my group is focused on.”

Before Hermann and Noé’s approach is ready for industrial use, there are still many obstacles to address. “It’s still basic research,” the writers agree, “but it’s a new approach to an age-old problem in molecular and materials science, and we’re excited about the possibilities it presents.”

Reference: “Deep-neural-network solution of the electronic Schrödinger equation” by Jan Hermann, Zeno Schätzle and Frank Noé, September 23, 2020, Nature Chemistry.DOI: 10.1038/s41557-020-0544-y

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