  Supervised machine learning approaches have been increasingly used in
accelerating electronic structure prediction as surrogates of first-principle
computational methods, such as density functional theory (DFT). While numerous
quantum chemistry datasets focus on chemical properties and atomic forces, the
ability to achieve accurate and efficient prediction of the Hamiltonian matrix
is highly desired, as it is the most important and fundamental physical
quantity that determines the quantum states of physical systems and chemical
properties. In this work, we generate a new Quantum Hamiltonian dataset, named
as QH9, to provide precise Hamiltonian matrices for 999 or 2998 molecular
dynamics trajectories and 130,831 stable molecular geometries, based on the QM9
dataset. By designing benchmark tasks with various molecules, we show that
current machine learning models have the capacity to predict Hamiltonian
matrices for arbitrary molecules. Both the QH9 dataset and the baseline models
are provided to the community through an open-source benchmark, which can be
highly valuable for developing machine learning methods and accelerating
molecular and materials design for scientific and technological applications.
Our benchmark is publicly available at
https://github.com/divelab/AIRS/tree/main/OpenDFT/QHBench.
