Solving Many-Electron Schr\"odinger Equation Using Deep Neural Networks

TL;DR

This paper presents a deep neural network-based approach for solving the many-electron Schrödinger equation, explicitly incorporating the Pauli principle, and demonstrates accurate results for various atomic and molecular systems.

Contribution

Introduces a novel neural network trial wave-function method that explicitly enforces the Pauli principle and scales quadratically with electron number, enabling large-scale quantum system solutions.

Findings

Accurately models ground states of multiple atomic and molecular systems.

Scales quadratically with the number of electrons, suitable for large systems.

Does not rely on prior knowledge like atomic orbitals.

Abstract

We introduce a new family of trial wave-functions based on deep neural networks to solve the many-electron Schr\"odinger 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 Schr\"odinger equation.