A team of researchers from the Freie Universität, in Berlin, has managed to develop a method based on Artificial Intelligence to solve 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, which avoids having to do costly and lengthy, resource-consuming laboratory experiments.
In theory, this would only be possible by solving the Schrödinger equation, something that is extremely difficult in practice.
Until now, in effect, it had been impossible to find an exact solution of the equation to apply to the study and development of molecules, since the necessary calculations are so complicated that it is often impractical to tackle them.
But researchers at the Freie Universität have approached the problem from a totally different point of view, developing a method of deep learning “Deep learning” that has been shown to achieve an unprecedented combination of computational precision and efficiency. “We believe that our approach,” says Frank Noé, studio director. may have a significant impact on the future of quantum chemistry». The results of the work have just been published in « Nature Chemistry».
The elusive wave function
Both quantum chemistry and the Schrödinger equation, formulated in 1925 by the Austrian physicist Erwin Schrödinger, are based on a fundamental parameter called a “wave function”, a mathematical object that specifies how the electrons behave within a molecule.
The wave function, however, depends on a large number of variables, so it is extremely difficult to capture each and every nuance that determines how exactly each individual electron interacts with all the others in the molecule. In fact, many methods for studying quantum chemistry completely dispense with the wave function and instead settle for determining the total amount of energy in a given molecule. Which results in inaccurate results and approximations that limit the predictability of these methods.
Other techniques, on the other hand, represent the complexities of the wave function using an immense number of simple mathematical “bricks,” but such methods are so complex that they are impossible to implement for more than a mere handful of atoms.
“Escaping the usual balance between precision and computational cost – explains Jan Hermann, co-author of the research – is the greatest achievement of quantum chemistry. We believe that the method Quantum Monte Carlo, the approach we propose, could be as successful, if not more so, as the more popular methods, because it offers unprecedented precision at a computational cost that is still acceptable.
A new approach
The deep neural network designed by Noah’s team it is, in fact, a way of representing the wave functions of electrons. “Instead of the standard approach of composing the wave function from relatively simple mathematical components,” the researcher explains, “we designed an artificial neural network capable of learning the complex patterns of how electrons are located around nuclei.”
“A peculiar characteristic of electronic wave functions,” Hermann adds, “is their antisymmetry. When two electrons are exchanged, the wave function must change sign. We had to build this property into the neural network architecture for the approach to work. This feature, known as «Pauli exclusion principle“Is why the scientists named their method” PauliNet. “
In addition to the Pauli exclusion principle, electronic wave functions also have other fundamental physical properties, and much of the innovative success of PauliNet is that integrates these properties into the deep neural network. “Incorporating fundamental physics into AI is essential to its ability to make meaningful predictions,” says Noah. This is really where scientists can make a substantial contribution to AI, and that’s exactly what my group is focusing on. ‘
Of course still many challenges remain to be overcome before the Hermann and Noah method is ready for industrial application. “This is still fundamental research,” the authors write, “but it is a new approach to an old problem in the molecular and materials sciences, and we are excited about the possibilities it opens up.”