Solving many-electron Schrödinger equation using deep neural networks

We introduce a new family of trial wave-functions based on deep neural networks to solve the many-electron Schrödinger equation. The Pauli exclusion principle is dealt with explicitly to ensure that the trial wave-functions are physical. The optimal trial wave-function is obtained through variational Monte Carlo and the computational cost scales quadratically with the number of electrons. The algorithm does not make use of any prior knowledge such as atomic orbitals. Yet it is able to represent accurately the ground-states of the tested systems, including He, H2, Be, B, LiH, and a chain of 10 hydrogen atoms. This opens up new possibilities for solving large-scale many-electron Schrödinger equation. •The algorithm makes no use of prior knowledge such as atomic orbitals.•The algorithm learns from scratch the shell structure of the electrons.•The complexity of evaluating the wavefunction is quadratic with the number of electrons involved.