A team of scientists at Freie Universität Berlin has developed

an artificial intelligence (AI) method for calculating the ground

state of the Schrödinger equation in quantum chemistry. The goal

of quantum chemistry is to predict chemical and physical properties

of molecules based solely on the arrangement of their atoms in

space, 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 this is

extremely difficult. Up to now, it has been impossible to find an

exact solution for arbitrary molecules that can be efficiently

computed. But the team at Freie Universität has developed a deep

learning method that can achieve an unprecedented combination of

accuracy and computational efficiency. AI has transformed many

technological and scientific areas, from computer vision to

materials science. “We believe that our approach may

significantly impact the future of quantum chemistry,” says

Professor Frank Noé, who led the team effort. The results were

published in the reputed journalNature Chemistry (DOI: https://doi.org/10.1038/s41557-020-0544-y).

Central to both quantum chemistry and the SchrÃ¶dinger equation

is the wave function â a mathematical object that completely

specifies the behavior of the electrons in a molecule. The wave

function is a high-dimensional entity, and it is therefore

extremely difficult to capture all the nuances that encode how the

individual electrons affect each other. Many methods of quantum

chemistry in fact give up on expressing the wave function

altogether, instead attempting only to determine the energy of a

given molecule. This however requires approximations to be made,

limiting the prediction quality of such methods.

Other methods represent the wave function with the use of an

immense number of simple mathematical building blocks, but such

methods are so complex that they are impossible to put into

practice for more than a mere handful of atoms. âEscaping the

usual trade-off between accuracy and computational cost is the

highest achievement in quantum chemistry,â explains Dr. Jan

Hermann of Freie UniversitÃ¤t Berlin, who designed the key features

of the method in the study. âAs yet, the most popular such

outlier is the extremely cost-effective density functional theory.

We believe that deep âQuantum Monte Carlo,â the approach we are

proposing, could be equally, if not more successful. It offers

unprecedented accuracy at a still acceptable computational

cost.â

The deep neural network designed by Professor NoÃ©âs team is a

new way of representing the wave functions of electrons. âInstead

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,â NoÃ© explains.

âOne peculiar feature of electronic wave functions is their

antisymmetry. When two electrons are exchanged, the wave function

must change its sign. We had to build this property into the neural

network architecture for the approach to work,â adds Hermann.

This feature, known as âPauliâs exclusion principle,â is why

the authors called their method âPauliNet.â

Besides the Pauli exclusion principle, electronic wave functions

also have other fundamental physical properties, and much of the

innovative success of PauliNet is that it integrates these

properties into the deep neural network, rather than letting deep

learning figure them out by just observing the data. âBuilding

the fundamental physics into the AI is essential for its ability to

make meaningful predictions in the field,â says NoÃ©. âThis is

really where scientists can make a substantial contribution to AI,

and exactly what my group is focused on.â

There are still many challenges to overcome before Hermann and

NoÃ©âs method is ready for industrial application. âThis is

still fundamental research,â the authors agree, âbut 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.â

Originally published by

Freie UniversitÃ¤t Berlin

| December 18, 2020

Publication

Jan Hermann, Zeno SchÃ¤tzle, and Frank NoÃ©, Deep neural network

solution of the electronic SchrÃ¶dinger equation. Nature

Chemistry (2020). DOI: https://doi.org/10.1038/s41557-020-0544-y

Contact

Prof. Dr. Frank NoÃ©, Department of Mathematics and Computer

Science, Freie UniversitÃ¤t Berlin, Email: frank.noe@fu-berlin.de, Tel.:

+49 30 838 75354