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The so-called Schrödinger equation is the holy grail of quantum physics.
With the help of this formula, named after the Austrian physicist Erwin Schrödinger (1887 - 1961), it is possible, for example, to calculate where the electron is located in a hydrogen atom.
This does not mean, however, that one could specify an exact position for the particle at any point in time.
An essential difference between quantum physics and classical mechanics à la Newton is that one can basically only specify probabilities for the locations of particles.
The probability distribution resulting from the so-called wave function of the electron can be precisely calculated for the electron of a hydrogen atom using the Schrödinger equation.
Source: WORLD infographic
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For all other atoms with more than one electron, especially for molecules with several atoms and many electrons, the Schrödinger equation can no longer be solved exactly.
In these cases it is a very difficult mathematical problem that can only be solved approximately with great effort.
The fine art is to reconcile the requirement for sufficient accuracy of the result with a reasonable amount of computer calculations.
But even with molecules with only a handful of connected atoms, solving the Schrödinger equation is hardly possible in practice.
Schrödinger received the Nobel Prize in Physics in 1933
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Calculating wave functions and probabilities with the help of the Schrödinger equation is the central task of quantum chemistry, because in this way the properties of molecules can be predicted theoretically - without actually having to manufacture the substances in the laboratory.
Some may still remember those cloud-shaped structures that were drawn between the atoms of a molecule in chemistry lessons.
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These so-called orbitals, which can be shaped very differently, indicate the preferred location of the respective electrons.
And the chemical bonds between the atoms come about via the overlapping electron orbitals.
A more efficient way of finding solutions to the Schrödinger equation would benefit chemists looking for new materials with desirable properties.
The illustration shows spherical s- and dumbbell-shaped p orbitals of an atom
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Researchers at Freie Universität (FU) Berlin have now presented a new method in the journal "Nature Chemistry" that uses artificial intelligence (AI) to find solutions to the Schrödinger equation "with an unprecedented combination of accuracy and speed" .
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The researchers led by Professor Frank Noé have developed a neural network made up of many layers that is capable of so-called "deep learning".
"Instead of the standard principle in which the wave function is assembled from many simple components, we have developed a network that learns the complex movement patterns of electrons around the atomic nucleus," Noé explains the new method. "We think that our approach makes quantum chemistry significant will influence. "
The FU researchers call their AI method for solving the Schrödinger equation "PauliNet".
They are alluding to the physics Nobel Prize winner Wolfgang Pauli (1900 - 1958), to whom the so-called "Pauli exclusion principle" goes back.
Albert Einstein and Wolfgang Pauli working together in 1924
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It says that two electrons in an atom must never be in exactly the same quantum state.
The Berlin scientists taught their neural network this "Pauli ban".
Noé states: "Building basic physical properties into AI is a very important part of making meaningful predictions in the natural sciences with the help of AI."
There are still many challenges before the method developed by him and his colleague Jan Hermann can be used in the chemical industry.
"This is a contribution from basic research," says Frank Noé, but it opens up new possibilities that now have to be explored.